1
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Carlucci LA, Johnson KC, Thomas WE. FimH-mannose noncovalent bonds survive minutes to hours under force. Biophys J 2024; 123:3038-3050. [PMID: 38961621 PMCID: PMC11427783 DOI: 10.1016/j.bpj.2024.07.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Revised: 05/10/2024] [Accepted: 07/01/2024] [Indexed: 07/05/2024] Open
Abstract
The adhesin FimH is expressed by commensal Escherichia coli and is implicated in urinary tract infections, where it mediates adhesion to mannosylated glycoproteins on urinary and intestinal epithelial cells in the presence of a high-shear fluid environment. The FimH-mannose bond exhibits catch behavior in which bond lifetime increases with force, because tensile force induces a transition in FimH from a compact native to an elongated activated conformation with a higher affinity to mannose. However, the lifetime of the activated state of FimH has not been measured under force. Here we apply multiplexed magnetic tweezers to apply a preload force to activate FimH bonds with yeast mannan, then we measure the lifetime of these activated bonds under a wide range of forces above and below the preload force. A higher fraction of FimH-mannan bonds were activated above than below a critical preload force, confirming the FimH catch bond behavior. Once activated, FimH detached from mannose with multi-state kinetics, suggesting the existence of two bound states with a 20-fold difference in dissociation rates. The average lifetime of activated FimH-mannose bonds was 1000 to 10,000 s at forces of 30-70 pN. Structural explanations of the two bound states and the high force resistance provide insights into structural mechanisms for long-lived, force-resistant biomolecular interactions.
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Affiliation(s)
- Laura A Carlucci
- Department of Bioengineering, University of Washington, Seattle, Washington
| | - Keith C Johnson
- Department of Bioengineering, University of Washington, Seattle, Washington
| | - Wendy E Thomas
- Department of Bioengineering, University of Washington, Seattle, Washington.
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2
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van Galen M, Bok A, Peshkovsky T, van der Gucht J, Albada B, Sprakel J. De novo DNA-based catch bonds. Nat Chem 2024:10.1038/s41557-024-01571-4. [PMID: 38914727 DOI: 10.1038/s41557-024-01571-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2023] [Accepted: 06/06/2024] [Indexed: 06/26/2024]
Abstract
All primary chemical interactions weaken under mechanical stress, which imposes fundamental mechanical limits on the materials constructed from them. Biological materials combine plasticity with strength, for which nature has evolved a unique solution-catch bonds, supramolecular interactions that strengthen under tension. Biological catch bonds use force-gated conformational switches to convert weak bonds into strong ones. So far, catch bonds remain exclusive to nature, leaving their potential as mechanoadaptive elements in synthetic systems untapped. Here we report the design and realization of artificial catch bonds. Starting from a minimal set of thermodynamic design requirements, we created a molecular motif capable of catch bonding. It consists of a DNA duplex featuring a cryptic domain that unfolds under tension to strengthen the interaction. We show that these catch bonds recreate force-enhanced rolling adhesion, a hallmark feature of biological catch bonds in bacteria and leukocytes. This Article introduces catch bonds into the synthetic domain, and could lead to the creation of artificial catch-bonded materials.
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Affiliation(s)
- Martijn van Galen
- Laboratory of Biochemistry, Wageningen University & Research, Wageningen, Netherlands
- Physical Chemistry and Soft Matter, Wageningen University & Research, Wageningen, Netherlands
| | - Annemarie Bok
- Laboratory of Biochemistry, Wageningen University & Research, Wageningen, Netherlands
| | - Taieesa Peshkovsky
- Physical Chemistry and Soft Matter, Wageningen University & Research, Wageningen, Netherlands
| | - Jasper van der Gucht
- Physical Chemistry and Soft Matter, Wageningen University & Research, Wageningen, Netherlands
| | - Bauke Albada
- Laboratory of Organic Chemistry, Wageningen University & Research, Wageningen, Netherlands.
| | - Joris Sprakel
- Laboratory of Biochemistry, Wageningen University & Research, Wageningen, Netherlands.
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3
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Rahmati N, Keshavarz Motamed P, Maftoon N. Numerical study of ultra-large von Willebrand factor multimers in coagulopathy. Biomech Model Mechanobiol 2024; 23:737-756. [PMID: 38217745 DOI: 10.1007/s10237-023-01803-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Accepted: 11/30/2023] [Indexed: 01/15/2024]
Abstract
An excessive von Willebrand factor (VWF) secretion, coupled with a moderate to severe deficiency of ADAMTS13 activity, serves as a linking mechanism between inflammation to thrombosis. The former facilitates platelet adhesion to the vessel wall and the latter is required to cleave VWF multimers. As a result, the ultra-large VWF (UL-VWF) multimers released by Weibel-Palade bodies remain uncleaved. In this study, using a computational model based on first principles, we quantitatively show how the uncleaved UL-VWF multimers interact with the blood cells to initiate microthrombosis. We observed that platelets first adhere to unfolded and stretched uncleaved UL-VWF multimers anchored to the microvessel wall. By the end of this initial adhesion phase, the UL-VWF multimers and platelets make a mesh-like trap in which the red blood cells increasingly accumulate to initiate a gradually growing microthrombosis. Although high-shear rate and blood flow velocity are required to activate platelets and unfold the UL-VWFs, during the initial adhesion phase, the blood velocity drastically drops after thrombosis, and as a result, the wall shear stress is elevated near UL-VWF roots, and the pressure drops up to 6 times of the healthy condition. As the time passes, these trends progressively continue until the microthrombosis fully develops and the effective size of the microthrombosis and these flow quantities remain almost constant. Our findings quantitatively demonstrate the potential role of UL-VWF in coagulopathy.
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Affiliation(s)
- Nahid Rahmati
- Department of Systems Design Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
- Centre for Bioengineering and Biotechnology, University of Waterloo, Waterloo, ON, Canada
| | - Pouyan Keshavarz Motamed
- Department of Systems Design Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
- Centre for Bioengineering and Biotechnology, University of Waterloo, Waterloo, ON, Canada
| | - Nima Maftoon
- Department of Systems Design Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada.
- Centre for Bioengineering and Biotechnology, University of Waterloo, Waterloo, ON, Canada.
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4
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Rahmati N, Maftoon N. Computational analysis of cancer cell adhesion in curved vessels affected by wall shear stress for prediction of metastatic spreading. Front Bioeng Biotechnol 2024; 12:1393413. [PMID: 38860135 PMCID: PMC11163055 DOI: 10.3389/fbioe.2024.1393413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/29/2024] [Accepted: 04/19/2024] [Indexed: 06/12/2024] Open
Abstract
Introduction: The dynamics of circulating tumor cells (CTCs) within blood vessels play a pivotal role in predicting metastatic spreading of cancer within the body. However, the limited understanding and method to quantitatively investigate the influence of vascular architecture on CTC dynamics hinders our ability to predict metastatic process effectively. To address this limitation, the present study was conducted to investigate the influence of blood vessel tortuosity on the behaviour of CTCs, focusing specifically on establishing methods and examining the role of shear stress in CTC-vessel wall interactions and its subsequent impact on metastasis. Methods: We computationally simulated CTC behaviour under various shear stress conditions induced by vessel tortuosity. Our computational model, based on the lattice Boltzmann method (LBM) and a coarse-grained spectrin-link membrane model, efficiently simulates blood plasma dynamics and CTC deformability. The model incorporates fluid-structure interactions and receptor-ligand interactions crucial for CTC adhesion using the immersed boundary method (IBM). Results: Our findings reveal that uniform shear stress in straight vessels leads to predictable CTC-vessel interactions, whereas in curved vessels, asymmetrical flow patterns and altered shear stress create distinct adhesion dynamics, potentially influencing CTC extravasation. Quantitative analysis shows a 25% decrease in the wall shear stress in low-shear regions and a 58.5% increase in the high-shear region. We observed high-shear regions in curved vessels to be potential sites for increased CTC adhesion and extravasation, facilitated by elevated endothelial expression of adhesion molecules. This phenomenon correlates with the increased number of adhesion bonds, which rises to approximately 40 in high-shear regions, compared to around 12 for straight vessels and approximately 5-6 in low-shear regions. The findings also indicate an optimal cellular stiffness necessary for successful CTC extravasation in curved vessels. Discussion: By the quantitative assessment of the risk of CTC extravasation as a function of vessel tortuosity, our study offers a novel tool for the prediction of metastasis risk to support the development of personalized therapeutic interventions based on individual vascular characteristics and tumor cell properties.
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Affiliation(s)
- Nahid Rahmati
- Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada
- Centre for Bioengineering and Biotechnology, University of Waterloo, Waterloo, ON, Canada
| | - Nima Maftoon
- Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada
- Centre for Bioengineering and Biotechnology, University of Waterloo, Waterloo, ON, Canada
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5
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Wang S, Ma S, Li H, Dao M, Li X, Karniadakis GE. Two-component macrophage model for active phagocytosis with pseudopod formation. Biophys J 2024; 123:1069-1084. [PMID: 38532625 PMCID: PMC11079866 DOI: 10.1016/j.bpj.2024.03.026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Revised: 11/20/2023] [Accepted: 03/21/2024] [Indexed: 03/28/2024] Open
Abstract
Macrophage phagocytosis is critical for the immune response, homeostasis regulation, and tissue repair. This intricate process involves complex changes in cell morphology, cytoskeletal reorganization, and various receptor-ligand interactions controlled by mechanical constraints. However, there is a lack of comprehensive theoretical and computational models that investigate the mechanical process of phagocytosis in the context of cytoskeletal rearrangement. To address this issue, we propose a novel coarse-grained mesoscopic model that integrates a fluid-like cell membrane and a cytoskeletal network to study the dynamic phagocytosis process. The growth of actin filaments results in the formation of long and thin pseudopods, and the initial cytoskeleton can be disassembled upon target entry and reconstructed after phagocytosis. Through dynamic changes in the cytoskeleton, our macrophage model achieves active phagocytosis by forming a phagocytic cup utilizing pseudopods in two distinct ways. We have developed a new algorithm for modifying membrane area to prevent membrane rupture and ensure sufficient surface area during phagocytosis. In addition, the bending modulus, shear stiffness, and cortical tension of the macrophage model are investigated through computation of the axial force for the tubular structure and micropipette aspiration. With this model, we simulate active phagocytosis at the cytoskeletal level and investigate the mechanical process during the dynamic interplay between macrophage and target particles.
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Affiliation(s)
- Shuo Wang
- Department of Engineering Mechanics and Center for X-Mechanics, Zhejiang University, Hangzhou, Zhejiang, China
| | - Shuhao Ma
- Department of Engineering Mechanics and Center for X-Mechanics, Zhejiang University, Hangzhou, Zhejiang, China
| | - He Li
- School of Chemical, Materials and Biomedical Engineering, University of Georgia, Athens, Georgia
| | - Ming Dao
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
| | - Xuejin Li
- Department of Engineering Mechanics and Center for X-Mechanics, Zhejiang University, Hangzhou, Zhejiang, China.
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6
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Tuna R, Yi W, Crespo Cruz E, Romero JP, Ren Y, Guan J, Li Y, Deng Y, Bluestein D, Liu ZL, Sheriff J. Platelet Biorheology and Mechanobiology in Thrombosis and Hemostasis: Perspectives from Multiscale Computation. Int J Mol Sci 2024; 25:4800. [PMID: 38732019 PMCID: PMC11083691 DOI: 10.3390/ijms25094800] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2024] [Revised: 04/19/2024] [Accepted: 04/24/2024] [Indexed: 05/13/2024] Open
Abstract
Thrombosis is the pathological clot formation under abnormal hemodynamic conditions, which can result in vascular obstruction, causing ischemic strokes and myocardial infarction. Thrombus growth under moderate to low shear (<1000 s-1) relies on platelet activation and coagulation. Thrombosis at elevated high shear rates (>10,000 s-1) is predominantly driven by unactivated platelet binding and aggregating mediated by von Willebrand factor (VWF), while platelet activation and coagulation are secondary in supporting and reinforcing the thrombus. Given the molecular and cellular level information it can access, multiscale computational modeling informed by biology can provide new pathophysiological mechanisms that are otherwise not accessible experimentally, holding promise for novel first-principle-based therapeutics. In this review, we summarize the key aspects of platelet biorheology and mechanobiology, focusing on the molecular and cellular scale events and how they build up to thrombosis through platelet adhesion and aggregation in the presence or absence of platelet activation. In particular, we highlight recent advancements in multiscale modeling of platelet biorheology and mechanobiology and how they can lead to the better prediction and quantification of thrombus formation, exemplifying the exciting paradigm of digital medicine.
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Affiliation(s)
- Rukiye Tuna
- Department of Chemical & Biomedical Engineering, FAMU-FSU College of Engineering, Tallahassee, FL 32310, USA; (R.T.); (E.C.C.); (Z.L.L.)
| | - Wenjuan Yi
- Department of Chemical & Biomedical Engineering, FAMU-FSU College of Engineering, Tallahassee, FL 32310, USA; (R.T.); (E.C.C.); (Z.L.L.)
| | - Esmeralda Crespo Cruz
- Department of Chemical & Biomedical Engineering, FAMU-FSU College of Engineering, Tallahassee, FL 32310, USA; (R.T.); (E.C.C.); (Z.L.L.)
| | - JP Romero
- Department of Chemical & Biomedical Engineering, FAMU-FSU College of Engineering, Tallahassee, FL 32310, USA; (R.T.); (E.C.C.); (Z.L.L.)
| | - Yi Ren
- Department of Biomedical Sciences, College of Medicine, Florida State University, Tallahassee, FL 32304, USA
| | - Jingjiao Guan
- Department of Chemical & Biomedical Engineering, FAMU-FSU College of Engineering, Tallahassee, FL 32310, USA; (R.T.); (E.C.C.); (Z.L.L.)
- Institute for Successful Longevity, Florida State University, Tallahassee, FL 32304, USA
| | - Yan Li
- Department of Chemical & Biomedical Engineering, FAMU-FSU College of Engineering, Tallahassee, FL 32310, USA; (R.T.); (E.C.C.); (Z.L.L.)
- Institute for Successful Longevity, Florida State University, Tallahassee, FL 32304, USA
| | - Yuefan Deng
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA
| | - Danny Bluestein
- Department of Biomedical Engineering, Stony Brook University, Stony Brook, NY 11794, USA;
| | - Zixiang Leonardo Liu
- Department of Chemical & Biomedical Engineering, FAMU-FSU College of Engineering, Tallahassee, FL 32310, USA; (R.T.); (E.C.C.); (Z.L.L.)
- Institute for Successful Longevity, Florida State University, Tallahassee, FL 32304, USA
| | - Jawaad Sheriff
- Department of Biomedical Engineering, Stony Brook University, Stony Brook, NY 11794, USA;
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7
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Du Y, Cheng D, Yang Z, Liu Y, Zhao Q, Sun M, Li H, Zhao X. A Simulation of the Mechanical Testing of the Cell Membrane and Cytoskeleton. MICROMACHINES 2024; 15:431. [PMID: 38675243 PMCID: PMC11052030 DOI: 10.3390/mi15040431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2024] [Revised: 03/16/2024] [Accepted: 03/18/2024] [Indexed: 04/28/2024]
Abstract
Cell models play a crucial role in analyzing the mechanical response of cells and quantifying cellular damage incurred during micromanipulation. While traditional models can capture the overall mechanical behavior of cells, they often lack the ability to discern among distinct cellular components. Consequently, by employing dissipative particle dynamics, this study constructed a triangular network-like representation of the cell membrane along with cross-linked cytoskeletal chains. The mechanical properties of both the membrane and cytoskeleton were then analyzed through a series of simulated mechanical tests, validated against real-world experiments. The investigation utilized particle-tracking rheology to monitor changes in the mean square displacements of membrane particles over time, facilitating the analysis of the membrane's storage and loss moduli. Additionally, the cytoskeletal network's storage and loss moduli were examined via a double-plate oscillatory shear experiment. The simulation results revealed that both the membrane and cytoskeleton exhibit viscoelastic behavior, as evidenced by the power-law dependency of their storage and loss moduli on frequency. Furthermore, indentation and microinjection simulations were conducted to examine the overall mechanical properties of cells. In the indentation experiments, an increase in the shear modulus of the membrane's WLCs correlated with a higher Young's modulus for the entire cell. Regarding the microinjection experiment, augmenting the microinjection speed resulted in reduced deformation of the cell at the point of membrane rupture and a lower percentage of high strain.
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Affiliation(s)
- Yue Du
- The School of Computer and Information Science, Qinghai University of Science and Technology, Xining 810016, China;
- The Department of Computer Technology and Application, Qinghai University, Xining 810016, China
| | - Dai Cheng
- Institute of Robotics and Automatic Information System, The Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin 300350, China; (D.C.); (Z.Y.); (Y.L.); (Q.Z.); (M.S.)
| | - Zhanli Yang
- Institute of Robotics and Automatic Information System, The Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin 300350, China; (D.C.); (Z.Y.); (Y.L.); (Q.Z.); (M.S.)
| | - Yaowei Liu
- Institute of Robotics and Automatic Information System, The Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin 300350, China; (D.C.); (Z.Y.); (Y.L.); (Q.Z.); (M.S.)
- Institute of Intelligence Technology and Robotic Systems, Shenzhen Research Institute of Nankai University, Shenzhen 518083, China
| | - Qili Zhao
- Institute of Robotics and Automatic Information System, The Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin 300350, China; (D.C.); (Z.Y.); (Y.L.); (Q.Z.); (M.S.)
- Institute of Intelligence Technology and Robotic Systems, Shenzhen Research Institute of Nankai University, Shenzhen 518083, China
| | - Mingzhu Sun
- Institute of Robotics and Automatic Information System, The Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin 300350, China; (D.C.); (Z.Y.); (Y.L.); (Q.Z.); (M.S.)
- Institute of Intelligence Technology and Robotic Systems, Shenzhen Research Institute of Nankai University, Shenzhen 518083, China
| | - Haifeng Li
- The School of Computer and Information Science, Qinghai University of Science and Technology, Xining 810016, China;
- The Department of Computer Technology and Application, Qinghai University, Xining 810016, China
| | - Xin Zhao
- Institute of Robotics and Automatic Information System, The Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin 300350, China; (D.C.); (Z.Y.); (Y.L.); (Q.Z.); (M.S.)
- Institute of Intelligence Technology and Robotic Systems, Shenzhen Research Institute of Nankai University, Shenzhen 518083, China
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8
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Laha S, Dhar D, Adak M, Bandopadhyay A, Das S, Chatterjee J, Chakraborty S. Electric field-mediated adhesive dynamics of cells inside bio-functionalised microchannels offers important cues for active control of cell-substrate adhesion. SOFT MATTER 2024; 20:2610-2623. [PMID: 38426537 DOI: 10.1039/d4sm00083h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/02/2024]
Abstract
Adhesive dynamics of cells plays a critical role in determining different biophysical processes orchestrating health and disease in living systems. While the rolling of cells on functionalised substrates having similarity with biophysical pathways appears to be extensively discussed in the literature, the effect of an external stimulus in the form of an electric field on the same remains underemphasized. Here, we bring out the interplay of fluid shear and electric field on the rolling dynamics of adhesive cells in biofunctionalised micro-confinements. Our experimental results portray that an electric field, even restricted to low strengths within the physiologically relevant regimes, can significantly influence the cell adhesion dynamics. We quantify the electric field-mediated adhesive dynamics of the cells in terms of two key parameters, namely, the voltage-altered rolling velocity and the frequency of adhesion. The effect of the directionality of the electric field with respect to the flow direction is also analysed by studying cellular migration with electrical effects acting both along and against the flow. Our experiment, on one hand, demonstrates the importance of collagen functionalisation in the adhesive dynamics of cells through micro channels, while on the other hand, it reveals how the presence of an axial electric field can lead to significant alteration in the kinetic rate of bond breakage, thereby modifying the degree of cell-substrate adhesion and quantifying in terms of the adhesion frequency of the cells. Proceeding further forward, we offer a simple theoretical explanation towards deriving the kinetics of cellular bonding in the presence of an electric field, which corroborates favourably with our experimental outcome. These findings are likely to offer fundamental insights into the possibilities of local control of cellular adhesion via electric field mediated interactions, bearing critical implications in a wide variety of medical conditions ranging from wound healing to cancer metastasis.
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Affiliation(s)
- Sampad Laha
- Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, India.
| | - Dhruba Dhar
- School of Medical Science and Technology, Indian Institute of Technology, Kharagpur, India
| | - Mainak Adak
- National Institute of Technology, Tiruchirappalli, India
| | - Aditya Bandopadhyay
- Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, India.
| | - Soumen Das
- School of Medical Science and Technology, Indian Institute of Technology, Kharagpur, India
| | - Jyotirmoy Chatterjee
- School of Medical Science and Technology, Indian Institute of Technology, Kharagpur, India
| | - Suman Chakraborty
- Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, India.
- School of Medical Science and Technology, Indian Institute of Technology, Kharagpur, India
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9
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Chrit FE, Li P, Sulchek T, Alexeev A. Adhesion-based high-throughput label-free cell sorting using ridged microfluidic channels. SOFT MATTER 2024; 20:1913-1921. [PMID: 38323349 DOI: 10.1039/d3sm01117h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2024]
Abstract
Numerous applications in medical diagnostics, cell engineering therapy, and biotechnology require the identification and sorting of cells that express desired molecular surface markers. We developed a microfluidic method for high-throughput and label-free sorting of biological cells by their affinity of molecular surface markers to target ligands. Our approach consists of a microfluidic channel decorated with periodic skewed ridges and coated with adhesive molecules. The periodic ridges form gaps with the opposing channel wall that are smaller than the cell diameter, thereby ensuring cell contact with the adhesive surfaces. Using three-dimensional computer simulations, we examine trajectories of adhesive cells in the ridged microchannels. The simulations reveal that cell trajectories are sensitive to the cell adhesion strength. Thus, the differential cell trajectories can be leveraged for adhesion-based cell separation. We probe the effect of cell elasticity on the adhesion-based sorting and show that cell elasticity can be utilized to enhance the resolution of the sorting. Furthermore, we investigate how the microchannel ridge angle can be tuned to achieve an efficient adhesion-based sorting of cells with different compliance.
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Affiliation(s)
- Fatima Ezahra Chrit
- George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
| | - Peiru Li
- George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
| | - Todd Sulchek
- George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
| | - Alexander Alexeev
- George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
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10
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Liu S, Chen S, Xiao L, Zhang K, Qi Y, Li H, Cheng Y, Hu Z, Lin C. Unraveling the motion and deformation characteristics of red blood cells in a deterministic lateral displacement device. Comput Biol Med 2024; 168:107712. [PMID: 38006825 DOI: 10.1016/j.compbiomed.2023.107712] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2023] [Revised: 10/16/2023] [Accepted: 11/15/2023] [Indexed: 11/27/2023]
Abstract
Deterministic Lateral Displacement (DLD) device has gained widespread recognition and trusted for filtering blood cells. However, there remains a crucial need to explore the complex interplay between deformable cells and flow within the DLD device to improve its design. This paper presents an approach utilizing a mesoscopic cell-level numerical model based on dissipative particle dynamics to effectively capture this complex phenomenon. To establish the model's credibility, a series of numerical simulations were conducted and the numerical results were validated with nominal experimental data from the literature. These include single cell stretching experiment, comparisons of the morphological characteristics of cells in DLD, and comparison the specific row-shift fraction of DLD required to initiate the zigzag mode. Additionally, we investigate the effect of cell rigidity, which serves as an indicator of cell health, on average flow velocity, trajectory, and asphericity. Moreover, we extend the existing theory of predicting zigzag mode for solid spherical particles to encompass the behavior of red blood cells. To achieve this, we introduce a new concept of effective diameter and demonstrate its applicability in providing highly accurate predictions across a wide range of conditions.
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Affiliation(s)
- Shuai Liu
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China
| | - Shuo Chen
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China.
| | - Lanlan Xiao
- School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China
| | - Kaixuan Zhang
- School of Medicine, Nankai University, Tianjin, 300071, China
| | - Yuan Qi
- Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai, 200433, China
| | - Hao Li
- Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai, 200433, China
| | - Yuan Cheng
- Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai, 200433, China
| | - Zixin Hu
- Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai, 200433, China; Fudan Zhangjiang Institute, Shanghai, 201203, China; Shanghai Pudong Hospital, Shanghai, 201399, China
| | - Chensen Lin
- Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai, 200433, China; Fudan Zhangjiang Institute, Shanghai, 201203, China; Shanghai Pudong Hospital, Shanghai, 201399, China.
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11
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Li G, Qiang Y, Li H, Li X, Buffet PA, Dao M, Karniadakis GE. A combined computational and experimental investigation of the filtration function of splenic macrophages in sickle cell disease. PLoS Comput Biol 2023; 19:e1011223. [PMID: 38091361 PMCID: PMC10752522 DOI: 10.1371/journal.pcbi.1011223] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Revised: 12/27/2023] [Accepted: 11/03/2023] [Indexed: 12/26/2023] Open
Abstract
Being the largest lymphatic organ in the body, the spleen also constantly controls the quality of red blood cells (RBCs) in circulation through its two major filtration components, namely interendothelial slits (IES) and red pulp macrophages. In contrast to the extensive studies in understanding the filtration function of IES, fewer works investigate how the splenic macrophages retain the aged and diseased RBCs, i.e., RBCs in sickle cell disease (SCD). Herein, we perform a computational study informed by companion experiments to quantify the dynamics of RBCs captured and retained by the macrophages. We first calibrate the parameters in the computational model based on microfluidic experimental measurements for sickle RBCs under normoxia and hypoxia, as those parameters are not available in the literature. Next, we quantify the impact of key factors expected to dictate the RBC retention by the macrophages in the spleen, namely, blood flow conditions, RBC aggregation, hematocrit, RBC morphology, and oxygen levels. Our simulation results show that hypoxic conditions could enhance the adhesion between the sickle RBCs and macrophages. This, in turn, increases the retention of RBCs by as much as four-fold, which could be a possible cause of RBC congestion in the spleen of patients with SCD. Our study on the impact of RBC aggregation illustrates a 'clustering effect', where multiple RBCs in one aggregate can make contact and adhere to the macrophages, leading to a higher retention rate than that resulting from RBC-macrophage pair interactions. Our simulations of sickle RBCs flowing past macrophages for a range of blood flow velocities indicate that the increased blood velocity could quickly attenuate the function of the red pulp macrophages on detaining aged or diseased RBCs, thereby providing a possible rationale for the slow blood flow in the open circulation of the spleen. Furthermore, we quantify the impact of RBC morphology on their tendency to be retained by the macrophages. We find that the sickle and granular-shaped RBCs are more likely to be filtered by macrophages in the spleen. This finding is consistent with the observation of low percentages of these two forms of sickle RBCs in the blood smear of SCD patients. Taken together, our experimental and simulation results aid in our quantitative understanding of the function of splenic macrophages in retaining the diseased RBCs and provide an opportunity to combine such knowledge with the current knowledge of the interaction between IES and traversing RBCs to apprehend the complete filtration function of the spleen in SCD.
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Affiliation(s)
- Guansheng Li
- Division of Applied Mathematics, Brown University, Providence, Rhode Island, United States of America
| | - Yuhao Qiang
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - He Li
- School of Chemical, Materials and Biomedical Engineering, University of Georgia, Athens, Georgia, United States of America
| | - Xuejin Li
- Department of Engineering Mechanics and Center for X-Mechanics, Zhejiang University, Hangzhou, Zhejiang, China
| | - Pierre A. Buffet
- Université Paris Cité and Université des Antilles, Inserm, Biologie Intégrée du Globule Rouge, Paris, France
| | - Ming Dao
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - George Em Karniadakis
- Division of Applied Mathematics, Brown University, Providence, Rhode Island, United States of America
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12
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Belyaev AV, Fedotova IV. Molecular mechanisms of catch bonds and their implications for platelet hemostasis. Biophys Rev 2023; 15:1233-1256. [PMID: 37974999 PMCID: PMC10643804 DOI: 10.1007/s12551-023-01144-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 09/07/2023] [Indexed: 11/19/2023] Open
Abstract
Adhesive molecular bonds between blood cells are essential for thrombosis and hemostasis as they provide means for platelet adhesion, aggregation, and signaling in flowing blood. According to the nowadays conventional definition, a "catch" bond is a type of non-covalent bio-molecular bridge, whose dissociation lifetime counter-intuitively increases with applied tensile force. Following recent experimental findings, such receptor-ligand protein bonds are vital to the blood cells involved in the prevention of bleeding (hemostatic response) and infection (immunity). In this review, we examine the up-to-date experimental discoveries and theoretical insights about catch bonds between the blood cells, their biomechanical principles at the molecular level, and their role in platelet thrombosis and hemostasis.
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Affiliation(s)
- Aleksey V. Belyaev
- Faculty of Physics, M.V.Lomonosov Moscow State University, 1, Leninskiye Gory, build.2, Moscow, 119991 Russia
| | - Irina V. Fedotova
- Faculty of Physics, M.V.Lomonosov Moscow State University, 1, Leninskiye Gory, build.2, Moscow, 119991 Russia
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13
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Li G, Qiang Y, Li H, Li X, Dao M, Karniadakis GE. In silico and in vitro study of the adhesion dynamics of erythrophagocytosis in sickle cell disease. Biophys J 2023; 122:2590-2604. [PMID: 37231647 PMCID: PMC10323029 DOI: 10.1016/j.bpj.2023.05.022] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Revised: 04/12/2023] [Accepted: 05/18/2023] [Indexed: 05/27/2023] Open
Abstract
Erythrophagocytosis occurring in the spleen is a critical process for removing senescent and diseased red blood cells (RBCs) from the microcirculation. Although some progress has been made in understanding how the biological signaling pathways mediate the phagocytic processes, the role of the biophysical interaction between RBCs and macrophages, particularly under pathological conditions such as sickle cell disease, has not been adequately studied. Here, we combine computational simulations with microfluidic experiments to quantify RBC-macrophage adhesion dynamics under flow conditions comparable to those in the red pulp of the spleen. We also investigate the RBC-macrophage interaction under normoxic and hypoxic conditions. First, we calibrate key model parameters in the adhesion model using microfluidic experiments for normal and sickle RBCs under normoxia and hypoxia. We then study the adhesion dynamics between the RBC and the macrophage. Our simulation illustrates three typical adhesion states, each characterized by a distinct dynamic motion of the RBCs, namely firm adhesion, flipping adhesion, and no adhesion (either due to no contact with macrophages or detachment from the macrophages). We also track the number of bonds formed when RBCs and macrophages are in contact, as well as the contact area between the two interacting cells, providing mechanistic explanations for the three adhesion states observed in the simulations and microfluidic experiments. Furthermore, we quantify, for the first time to our knowledge, the adhesive forces between RBCs (normal and sickle) and macrophages under different oxygenated conditions. Our results show that the adhesive forces between normal cells and macrophages under normoxia are in the range of 33-58 pN and 53-92 pN for sickle cells under normoxia and 155-170 pN for sickle cells under hypoxia. Taken together, our microfluidic and simulation results improve our understanding of the biophysical interaction between RBCs and macrophages in sickle cell disease and provide a solid foundation for investigating the filtration function of the splenic macrophages under physiological and pathological conditions.
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Affiliation(s)
- Guansheng Li
- Division of Applied Mathematics, Brown University, Providence, Rhode Island
| | - Yuhao Qiang
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
| | - He Li
- School of Chemical, Materials and Biomedical Engineering, University of Georgia, Athens, Georgia.
| | - Xuejin Li
- Department of Engineering Mechanics and Center for X-Mechanics, Zhejiang University, Hangzhou, China
| | - Ming Dao
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts.
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14
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Li G, Qiang Y, Li H, Li X, Buffet PA, Dao M, Karniadakis GE. A combined computational and experimental investigation of the filtration function of splenic macrophages in sickle cell disease. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.05.31.543007. [PMID: 37398427 PMCID: PMC10312537 DOI: 10.1101/2023.05.31.543007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/04/2023]
Abstract
Being the largest lymphatic organ in the body, the spleen also constantly controls the quality of red blood cells (RBCs) in circulation through its two major filtration components, namely interendothelial slits (IES) and red pulp macrophages. In contrast to the extensive studies in understanding the filtration function of IES, there are relatively fewer works on investigating how the splenic macrophages retain the aged and diseased RBCs, i.e., RBCs in sickle cell disease (SCD). Herein, we perform a computational study informed by companion experiments to quantify the dynamics of RBCs captured and retained by the macrophages. We first calibrate the parameters in the computational model based on microfluidic experimental measurements for sickle RBCs under normoxia and hypoxia, as those parameters are not available in the literature. Next, we quantify the impact of a set of key factors that are expected to dictate the RBC retention by the macrophages in the spleen, namely, blood flow conditions, RBC aggregation, hematocrit, RBC morphology, and oxygen levels. Our simulation results show that hypoxic conditions could enhance the adhesion between the sickle RBCs and macrophages. This, in turn, increases the retention of RBCs by as much as five-fold, which could be a possible cause of RBC congestion in the spleen of patients with SCD. Our study on the impact of RBC aggregation illustrates a 'clustering effect', where multiple RBCs in one aggregate can make contact and adhere to the macrophages, leading to a higher retention rate than that resulting from RBC-macrophage pair interactions. Our simulations of sickle RBCs flowing past macrophages for a range of blood flow velocities indicate that the increased blood velocity could quickly attenuate the function of the red pulp macrophages on detaining aged or diseased RBCs, thereby providing a possible rationale for the slow blood flow in the open circulation of the spleen. Furthermore, we quantify the impact of RBC morphology on their tendency to be retained by the macrophages. We find that the sickle and granular-shaped RBCs are more likely to be filtered by macrophages in the spleen. This finding is consistent with the observation of low percentages of these two forms of sickle RBCs in the blood smear of SCD patients. Taken together, our experimental and simulation results aid in our quantitative understanding of the function of splenic macrophages in retaining the diseased RBCs and provide an opportunity to combine such knowledge with the current knowledge of the interaction between IES and traversing RBCs to apprehend the complete filtration function of the spleen in SCD.
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Affiliation(s)
- Guansheng Li
- Division of Applied Mathematics, Brown University, Providence, Rhode Island, 02906
| | - Yuhao Qiang
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139
| | - He Li
- School of Chemical, Materials and Biomedical Engineering, University of Georgia, Athens, Georgia, 30602
| | - Xuejin Li
- Department of Engineering Mechanics and Center for X-Mechanics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Pierre A. Buffet
- Université Paris Cité and Université des Antilles, Inserm, Biologie Intégrée du Globule Rouge, 75015, Paris, France
- Laboratoire d′Excellence du Globule Rouge, 75015, Paris, France
| | - Ming Dao
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139
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15
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Zhang Z, Zhu J, Liu Y, Shao J, Xie S. Effects of cell deformability and adhesion strength on dynamic cell seeding: Cell-scale investigation via mesoscopic modeling. J Biomech 2023; 153:111589. [PMID: 37137273 DOI: 10.1016/j.jbiomech.2023.111589] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Revised: 03/26/2023] [Accepted: 04/11/2023] [Indexed: 05/05/2023]
Abstract
The flow of cell suspension through a porous scaffold is a common process in dynamic cell seeding, which determines the initial distribution of cells for constructing tissue-engineered grafts. Physical insights into the transport and adhesion behaviors of cells in this process are of great significance to the precise control of cell density and its distribution in the scaffold. Revealing of dynamic mechanisms underlying these cell behaviors through experiments is still difficult. The numerical approach therefore plays an important role in such studies. However, existing studies have mostly focused on external factors (e.g., flow conditions and scaffold architecture) but ignored the intrinsic biomechanical properties of cells as well as their associated effects. The present work utilized a well-established mesoscopic model to simulate the dynamic cell seeding within a porous scaffold, based on which a thorough investigation of the effects of cell deformability and cell-scaffold adhesion strength on the seeding process was carried out. The results show that the increase in either the stiffness or the bond strength of cells would augment the firm-adhesion rate and thus enhance seeding efficiency. In comparison to cell deformability, bond strength seems to play a more dominant role. Especially in the cases with weak bond strength, remarkable losses of seeding efficiency and distribution uniformity are observed. Noteworthily, it is found that both the firm-adhesion rate and the seeding efficiency are quantiatively related to the adhesion strength which is measured as the detachment force, suggesting a straightforward way to estimate the seeding outcome.
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Affiliation(s)
- Ziying Zhang
- College of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, PR China
| | - Junwei Zhu
- College of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, PR China
| | - Yangyang Liu
- Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
| | - Jiaru Shao
- College of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, PR China.
| | - Shuangyi Xie
- College of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, PR China
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16
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Okuda S, Hiraiwa T. Long-term adherent cell dynamics emerging from energetic and frictional interactions at the interface. Phys Rev E 2023; 107:034406. [PMID: 37073061 DOI: 10.1103/physreve.107.034406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2022] [Accepted: 02/21/2023] [Indexed: 04/20/2023]
Abstract
Cell adhesion plays an important role in a wide range of biological situations, including embryonic development, cancer invasion, and wound healing. Although several computational models describing adhesion dynamics have been proposed, models applicable to long-term, large-length-scale cell dynamics are lacking. In this study we investigated possible states of long-term adherent cell dynamics in three-dimensional space by constructing a continuum model of interfacial interactions between adhesive surfaces. In this model a pseudointerface is supposed between each pair of triangular elements that discretize cell surfaces. By introducing a distance between each pair of elements, the physical properties of the interface are given by interfacial energy and friction. The proposed model was implemented into the model of a nonconservative fluid cell membrane where the cell membrane dynamically flows with turnover. Using the implemented model, numerical simulations of adherent cell dynamics on a substrate under flow were performed. The simulations not only reproduced the previously reported dynamics of adherent cells, such as detachment, rolling, and fixation on the substrate, but also discovered other dynamic states, including cell slipping and membrane flow patterns, corresponding to behaviors that occur on much longer timescales than the dissociation of adhesion molecules. These results illustrate the variety of long-term adherent cell dynamics, which are more diverse than the short-term ones. The proposed model can be extended to arbitrarily shaped membranes, thus being useful for the mechanical analysis of a wide range of long-term cell dynamics where adhesion is essential.
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Affiliation(s)
- Satoru Okuda
- Nano Life Science Institute, Kakuma-machi, Kanazawa 920-1192, Japan
| | - Tetsuya Hiraiwa
- Mechanobiology Institute, National University of Singapore, 5A Engineering Drive 117411, Singapore
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17
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Xiao L, Chu J, Lin C, Zhang K, Chen S, Yang L. Simulation of a tumor cell flowing through a symmetric bifurcated microvessel. Biomech Model Mechanobiol 2023; 22:297-308. [PMID: 36287312 DOI: 10.1007/s10237-022-01649-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Accepted: 10/08/2022] [Indexed: 11/24/2022]
Abstract
Microvessel bifurcations serve as the major sites of tumor cell adhesion and further extravasation. In this study, the movement, deformation, and adhesion of a circulating tumor cell flowing in a symmetric microvessel with diverging and converging bifurcations were simulated by dissipative particle dynamics combined with a spring-based network model. Effects of the initial position of the CTC, externally-applied acceleration and the presence of RBCs on the motion of the CTC were investigated. The results demonstrated that the CTC released at the centerline of the parent vessel would attach to the vessel wall when arriving at the apex of diverging bifurcation and slide into the daughter branch determined by its centroid deflection and finally form firm adhesion at relatively lower flow rates. As the external acceleration increases, the increasing shear force enlarges the contact area for the adherent CTC on the one hand and reduces the residence time on the other hand. With the presence of RBCs in the bloodstream, the collision between the adherent tumor cell at the diverging bifurcation and flowing RBCs promotes the firm adhesion of CTC at lower flow rates.
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Affiliation(s)
- Lanlan Xiao
- School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, China
| | - Jie Chu
- School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, China
| | - Chensen Lin
- Artificial Intelligence Innovation and Incubation Institute, Fudan University, Shanghai, China.
| | - Kaixuan Zhang
- School of Medicine, Nankai University, Tianjin, China
| | - Shuo Chen
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China
| | - Liu Yang
- Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong, China
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18
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Li L, Wang S, Han K, Qi X, Ma S, Li L, Yin J, Li D, Li X, Qian J. Quantifying Shear-induced Margination and Adhesion of Platelets in Microvascular Blood Flow. J Mol Biol 2023; 435:167824. [PMID: 36108775 DOI: 10.1016/j.jmb.2022.167824] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Revised: 09/04/2022] [Accepted: 09/06/2022] [Indexed: 02/04/2023]
Abstract
Platelet margination and adhesion are two critical and closely related steps in thrombus formation. Using dissipative particle dynamics (DPD) method that seamlessly models blood cells, blood plasma, and vessel walls with functionalized surfaces, we quantify the shear-induced margination and adhesion of platelets in microvascular blood flow. The results show that the occurrence of shear-induced RBC-platelet collisions has a remarkable influence on the degree of platelet margination. We characterize the lateral motion of individual platelets by a mean square displacement analysis of platelet trajectories, and find that the wall-induced lift force and the shear-induced displacement in wall-bounded flow cause the variation in near-wall platelet distribution. We then investigate the platelet adhesive dynamics under different flow conditions, by conducting DPD simulations of blood flow in a microtube with fibrinogen-coated wall surfaces. We find that the platelet adhesion is enhanced with the increase of fibrinogen concentration level but decreased with the increase of shear rate. These results are consistent with available experimental results. In addition, we demonstrate that the adherent platelets have a negative impact on the margination dynamics of the circulating platelets, which is mainly due to the climbing effect induced by the adherent ones. Taken together, these findings provide useful insights into the platelet margination and adhesion dynamics, which may facilitate the understanding of the predominant processes governing the initial stage of thrombus formation.
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Affiliation(s)
- Lujuan Li
- State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, China; Department of Engineering Mechanics, Zhejiang University, Hangzhou, China
| | - Shuo Wang
- State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, China; Department of Engineering Mechanics, Zhejiang University, Hangzhou, China
| | - Keqin Han
- State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, China; Department of Engineering Mechanics, Zhejiang University, Hangzhou, China
| | - Xiaojing Qi
- State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, China; Department of Engineering Mechanics, Zhejiang University, Hangzhou, China
| | - Shuhao Ma
- State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, China; Department of Engineering Mechanics, Zhejiang University, Hangzhou, China
| | - Li Li
- Department of Endocrinology and Metabolism, Ningbo First Hospital, Ningbo, China
| | - Jun Yin
- State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, China; School of Mechanical Engineering, Zhejiang University, Hangzhou, China
| | - Dechang Li
- State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, China; Department of Engineering Mechanics, Zhejiang University, Hangzhou, China.
| | - Xuejin Li
- State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, China; Department of Engineering Mechanics, Zhejiang University, Hangzhou, China; The Second Affiliated Hospital of Zhejiang University School of Medicine, Hangzhou, China.
| | - Jin Qian
- State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, China; Department of Engineering Mechanics, Zhejiang University, Hangzhou, China.
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19
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Jerri HA, Torres-Díaz I, Zhang L, Impellizzeri N, Benczédi D, Bevan MA. Surface Morphology-Enhanced Delivery of Bioinspired Eco-Friendly Microcapsules. ACS APPLIED MATERIALS & INTERFACES 2022; 14:41499-41507. [PMID: 36041180 DOI: 10.1021/acsami.2c08305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We report the development of novel mineralized protein microcapsules to address critical challenges in the environmental impact and performance of consumer, pharmaceutical, agrochemical, cosmetic, and paint products. We designed environment-friendly capsules composed of proteins and biominerals as an alternative to solid microplastic particles or core-shell capsules made of nonbiodegradable synthetic polymeric resins. We synthesized mineralized capsule surface morphologies to mimic the features of natural pollens, which dramatically improved the deposition of high value-added fragrance chemicals on target substrates in realistic application conditions. A mechanistic model accurately captures the observed enhanced deposition behavior and shows how surface features generate an adhesive torque that resists shear detachment. Mineralized protein capsule performance is shown to depend both on material selection that determines van der Waals attraction and on capsule-substrate energy landscapes as parameterized by a geometric taxonomy for surface morphologies. These findings have broad implications for engineering multifunctional environmentally friendly delivery systems.
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Affiliation(s)
- Huda A Jerri
- R&D Division, Firmenich Inc., Plainsboro, New Jersey 08536, United States
| | - Isaac Torres-Díaz
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Lechuan Zhang
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | | | - Daniel Benczédi
- Corporate Research Division, Firmenich SA., 1242 Satigny, Switzerland
| | - Michael A Bevan
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
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20
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Puleri DF, Martin AX, Randles A. Distributed Acceleration of Adhesive Dynamics Simulations. PROCEEDINGS OF 2022 29TH EUROPEAN MPI USERS' GROUP MEETING (EUROMPI/USA'2022) : SEPTEMBER 26-28, 2022, CHATTANOOGA, TN. EUROPEAN MPI USERS' GROUP MEETING (29TH : 2022 : CHATTANOOGA, TENN.) 2022; 2022:37-45. [PMID: 38204519 PMCID: PMC10777536 DOI: 10.1145/3555819.3555832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
Cell adhesion plays a critical role in processes ranging from leukocyte migration to cancer cell transport during metastasis. Adhesive cell interactions can occur over large distances in microvessel networks with cells traveling over distances much greater than the length scale of their own diameter. Therefore, biologically relevant investigations necessitate efficient modeling of large field-of-view domains, but current models are limited by simulating such geometries at the sub-micron scale required to model adhesive interactions which greatly increases the computational requirements for even small domain sizes. In this study we introduce a hybrid scheme reliant on both on-node and distributed parallelism to accelerate a fully deformable adhesive dynamics cell model. This scheme leads to performant system usage of modern supercomputers which use a many-core per-node architecture. On-node acceleration is augmented by a combination of spatial data structures and algorithmic changes to lessen the need for atomic operations. This deformable adhesive cell model accelerated with hybrid parallelization allows us to bridge the gap between high-resolution cell models which can capture the sub-micron adhesive interactions between the cell and its microenvironment, and large-scale fluid-structure interaction (FSI) models which can track cells over considerable distances. By integrating the sub-micron simulation environment into a distributed FSI simulation we enable the study of previously unfeasible research questions involving numerous adhesive cells in microvessel networks such as cancer cell transport through the microcirculation.
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Affiliation(s)
- Daniel F Puleri
- Department of Biomedical Engineering, Duke University, Durham, NC, USA
| | | | - Amanda Randles
- Department of Biomedical Engineering, Duke University, Durham, NC, USA
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21
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Puleri DF, Randles A. The role of adhesive receptor patterns on cell transport in complex microvessels. Biomech Model Mechanobiol 2022; 21:1079-1098. [PMID: 35507242 PMCID: PMC10777541 DOI: 10.1007/s10237-022-01575-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Accepted: 02/26/2022] [Indexed: 01/13/2023]
Abstract
Cell transport is governed by the interaction of fluid dynamic forces and biochemical factors such as adhesion receptor expression and concentration. Although the effect of endothelial receptor density is well understood, it is not clear how the spacing and local spatial distribution of receptors affect cell adhesion in three-dimensional microvessels. To elucidate the effect of vessel shape on cell trajectory and the arrangement of endothelial receptors on cell adhesion, we employed a three-dimensional deformable cell model that incorporates microscale interactions between the cell and the endothelium. Computational cellular adhesion models are systematically altered to assess the influence of receptor spacing. We demonstrate that the patterns of receptors on the vessel walls are a key factor guiding cell movement. In straight microvessels, we show a relationship between cell velocity and the spatial distribution of adhesive endothelial receptors, with larger receptor patches producing lower translational velocities. The joint effect of the complex vessel topology seen in microvessel shapes such as curved and bifurcated vessels when compared to straight tubes is explored with results which showed the spatial distribution of receptors affecting cell trajectory. Our findings here represent demonstration of the previously undescribed relationship between receptor pattern and geometry that guides cellular movement in complex microenvironments.
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Affiliation(s)
- Daniel F Puleri
- Department of Biomedical Engineering, Duke University, Durham, NC, 27708, USA
| | - Amanda Randles
- Department of Biomedical Engineering, Duke University, Durham, NC, 27708, USA.
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22
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Multiphysics and multiscale modeling of microthrombosis in COVID-19. PLoS Comput Biol 2022; 18:e1009892. [PMID: 35255089 PMCID: PMC8901059 DOI: 10.1371/journal.pcbi.1009892] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2021] [Accepted: 02/02/2022] [Indexed: 12/21/2022] Open
Abstract
Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. Because of the infectious nature of SARS-CoV-2, patients’ fresh blood samples are limited to access for in vitro experimental investigations. Herein, we employ a novel multiscale and multiphysics computational framework to perform predictive modeling of the pathological thrombus formation in the microvasculature using data from patients with COVID-19. This framework seamlessly integrates the key components in the process of blood clotting, including hemodynamics, transport of coagulation factors and coagulation kinetics, blood cell mechanics and adhesive dynamics, and thus allows us to quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19. Our simulation results show that among the coagulation factors considered, antithrombin and factor V play more prominent roles in promoting thrombosis. Our simulations also suggest that recruitment of WBCs to the endothelial cells exacerbates thrombogenesis and contributes to the blockage of the blood flow. Additionally, we show that the recent identification of flowing blood cell clusters could be a result of detachment of WBCs from thrombogenic sites, which may serve as a nidus for new clot formation. These findings point to potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19. Altogether, our computational framework provides a powerful tool for quantitative understanding of the mechanism of pathological thrombus formation and offers insights into new therapeutic approaches for treating COVID-19 associated thrombosis. Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. We employ a novel multiphysics and multiscale computational framework to investigate the underlying mechanism of the pathological formation of microthrombi and circulating cell clusters in COVID-19. We quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19, through which we identify the potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19.
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23
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Numerical simulation and experimental validation of bacterial detachment using a spherical produce model in an industrial-scale flume washer. Food Control 2021. [DOI: 10.1016/j.foodcont.2021.108300] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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24
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Nguyen VL, Obara H. Investigation of vessel occlusion during cell seeding process. Biomech Model Mechanobiol 2021; 20:2437-2450. [PMID: 34480225 DOI: 10.1007/s10237-021-01517-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2021] [Accepted: 08/25/2021] [Indexed: 11/26/2022]
Abstract
The seeding of cells into an organ is an important step in cell therapy because the final functional properties of the organ are related to the initial cell distribution throughout the organ. However, vessel occlusion is a serious problem that prevents uniform distribution of the cells in the entire organ. Understanding the mechanism of vessel occlusion can help optimize the seeding process. In this study, the vessel occlusion phenomenon under perfusion conditions during cell seeding was investigated. First, we applied a microfluidic system that enabled the observation of the occlusion events during injection. Second, we applied a multiphase numerical model that can describe the cell-cell interactions and cell-fluid interactions to investigate the vessel occlusion phenomenon during the seeding process. In particular, the effects of cell concentration and flow rate were investigated. The results indicate the importance of cell-cell interactions and cell-vessel interactions for the occurrence of vessel occlusion. In addition, it is found that the probability of occurrence of vessel occlusion increases with the increase in cell concentration and decrease in flow rate. The simulation model can help determine the optimum parameters to enhance cell seeding efficiency.
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Affiliation(s)
- Van Lap Nguyen
- Department of Mechanical Systems Engineering, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo, 192-0397, Japan.
- Faculty of Mechanical Engineering, Thuyloi University, 175 Tay Son, Dong Da, Hanoi, Vietnam.
| | - Hiromichi Obara
- Department of Mechanical Systems Engineering, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo, 192-0397, Japan
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25
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Anvari S, Osei E, Maftoon N. Interactions of platelets with circulating tumor cells contribute to cancer metastasis. Sci Rep 2021; 11:15477. [PMID: 34326373 PMCID: PMC8322323 DOI: 10.1038/s41598-021-94735-y] [Citation(s) in RCA: 38] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2021] [Accepted: 07/09/2021] [Indexed: 02/07/2023] Open
Abstract
Recent studies have suggested that platelets have a crucial role in enhancing the survival of circulating tumor cells in the bloodstream and aggravating cancer metastasis. The main function of platelets is to bind to the sites of the damaged vessels to stop bleeding. However, in cancer patients, activated platelets adhere to circulating tumor cells and exacerbate metastatic spreading. Several hypotheses have been proposed about the platelet-cancer cell interactions, but the underlying mechanisms of these interactions are not completely understood yet. In this work, we quantitatively investigated the interactions between circulating tumor cells, red blood cells, platelets, plasma flow and microvessel walls via computational modelling at the cellular scale. Our highly detailed computational model allowed us to understand and quantitatively explain the role of platelets in deformation, adhesion and survival of tumor cells in their active arrest to the endothelium.
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Affiliation(s)
- Sina Anvari
- Department of Systems Design Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
- Centre for Bioengineering and Biotechnology, University of Waterloo, Waterloo, ON, Canada
| | - Ernest Osei
- Department of Systems Design Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
- Department of Medical Physics, Grand River Regional Cancer Centre, Kitchener, ON, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, Canada
- Department of Clinical Studies, Ontario Veterinary College, University of Guelph, Guelph, ON, Canada
| | - Nima Maftoon
- Department of Systems Design Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada.
- Centre for Bioengineering and Biotechnology, University of Waterloo, Waterloo, ON, Canada.
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26
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Durán-Laforet V, Peña-Martínez C, García-Culebras A, Alzamora L, Moro MA, Lizasoain I. Pathophysiological and pharmacological relevance of TLR4 in peripheral immune cells after stroke. Pharmacol Ther 2021; 228:107933. [PMID: 34174279 DOI: 10.1016/j.pharmthera.2021.107933] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2021] [Revised: 06/12/2021] [Accepted: 06/16/2021] [Indexed: 02/07/2023]
Abstract
Stroke is a very common disease being the leading cause of death and disability worldwide. The immune response subsequent to an ischemic stroke is a crucial factor in its physiopathology and outcome. This response is not limited to the injury site. In fact, the immune response to the ischemic process mobilizes mainly circulating cells which upon activation will be recruited to the injury site. When a stroke occurs, molecules that are usually retained inside the cell bodies are released into the extracellular space by uncontrolled cell death. These molecules can bind to the Toll-like receptor 4 (TLR4) in circulating immune cells which are then activated, eliciting, although not exclusively, the inflammatory response to the stroke. In this review, we present an up-to-date summary of the role of the different peripheral immune cells in stroke as well as the role of TLR4 in the function of each cell type in ischemia. Also, we summarize the different antagonists developed against TLR4 and their potential as a pharmacological tool for stroke treatment.
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Affiliation(s)
- V Durán-Laforet
- Unidad de Investigación Neurovascular, Departamento de Farmacología y Toxicología, Facultad de Medicina, Instituto Universitario de Investigación en Neuroquímica, Universidad Complutense de Madrid, Instituto de Investigación Hospital, 12 de Octubre (imas12), Madrid, Spain.
| | - C Peña-Martínez
- Unidad de Investigación Neurovascular, Departamento de Farmacología y Toxicología, Facultad de Medicina, Instituto Universitario de Investigación en Neuroquímica, Universidad Complutense de Madrid, Instituto de Investigación Hospital, 12 de Octubre (imas12), Madrid, Spain
| | - A García-Culebras
- Neurovascular Pathophysiology Group, Centro Nacional de Investigaciones Cardiovasculares Carlos III (CNIC), Madrid, Spain
| | - L Alzamora
- Unidad de Investigación Neurovascular, Departamento de Farmacología y Toxicología, Facultad de Medicina, Instituto Universitario de Investigación en Neuroquímica, Universidad Complutense de Madrid, Instituto de Investigación Hospital, 12 de Octubre (imas12), Madrid, Spain
| | - M A Moro
- Neurovascular Pathophysiology Group, Centro Nacional de Investigaciones Cardiovasculares Carlos III (CNIC), Madrid, Spain
| | - I Lizasoain
- Unidad de Investigación Neurovascular, Departamento de Farmacología y Toxicología, Facultad de Medicina, Instituto Universitario de Investigación en Neuroquímica, Universidad Complutense de Madrid, Instituto de Investigación Hospital, 12 de Octubre (imas12), Madrid, Spain.
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27
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Porter CL, Diamond SL, Sinno T, Crocker JC. Shear-driven rolling of DNA-adhesive microspheres. Biophys J 2021; 120:2102-2111. [PMID: 33838138 PMCID: PMC8390808 DOI: 10.1016/j.bpj.2021.03.038] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2020] [Revised: 02/14/2021] [Accepted: 03/12/2021] [Indexed: 11/24/2022] Open
Abstract
Many biologically important cell binding processes, such as the rolling of leukocytes in the vasculature, are multivalent, being mediated by large numbers of weak binding ligands. Quantitative agreement between experiments and models of rolling has been elusive and often limited by the poor understanding of the binding and unbinding kinetics of the ligands involved. Here, we present a cell-free experimental model for such rolling, consisting of polymer microspheres whose adhesion to a glass surface is mediated by ligands with well-understood force-dependent binding free energy-short complementary DNA strands. We observe robust rolling activity for certain values of the shear rate and the grafted DNA strands' binding free energy and force sensitivity. The simulation framework developed to model leukocyte rolling, adhesive dynamics, quantitatively captures the mean rolling velocity and lateral diffusivity of the experimental particles using known values of the experimental parameters. Moreover, our model captures the velocity variations seen within the trajectories of single particles. Particle-to-particle variations can be attributed to small, plausible differences in particle characteristics. Overall, our findings confirm that state-of-the-art adhesive dynamics simulations are able to capture the complex physics of particle rolling, boding well for their extension to modeling more complex systems of rolling cells.
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Affiliation(s)
- Christopher L Porter
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania
| | - Scott L Diamond
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania
| | - Talid Sinno
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania
| | - John C Crocker
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania.
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28
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Ye H, Shen Z, Li Y. Adhesive rolling of nanoparticles in a lateral flow inspired from diagnostics of COVID-19. EXTREME MECHANICS LETTERS 2021; 44:101239. [PMID: 33644275 PMCID: PMC7897962 DOI: 10.1016/j.eml.2021.101239] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/05/2020] [Revised: 02/01/2021] [Accepted: 02/17/2021] [Indexed: 06/12/2023]
Abstract
Due to the lack of therapeutics and vaccines, diagnostics of COVID-19 emerges as one of the primary tools for controlling the spread of SARS-COV-2. Here we aim to develop a theoretical model to study the detection process of SARS-COV-2 in lateral flow device (LFD), which can achieve rapid antigen diagnostic tests. The LFD is modeled as the adhesion of a spherical nanoparticle (NP) coated with ligands on the surface, mimicking the SARS-COV-2, on an infinite substrate distributed with receptors under a simple shear flow. The adhesive behaviors of NPs in the LFD are governed by the ligand-receptor binding (LRB) and local hydrodynamics. Through energy balance analysis, three types of motion are predicted: (i) firm-adhesion (FA); (ii) adhesive-rolling (AR); and (iii) free-rolling (FR), which correspond to LRB-dominated, LRB-hydrodynamics-competed, and hydrodynamics-dominated regimes, respectively. The transitions of FA-to-AR and AR-to-FR are found to be triggered by overcoming LRB barrier and saturation of LRB torque, respectively. Most importantly, in the AR regime, the smaller NPs can move faster than their larger counterparts, induced by the LRB effect that depends on the radius R of NPs. In addition, a scaling law is found in the AR regime that v ∝ γ ˙ R α (rolling velocity v and shear rate γ ˙ ), with an approximate scaling factor α ∼ - 0 . 2 ± 0 . 05 identified through fitting both theoretical and numerical results. The scaling factor emerges from the energy-based stochastic LRB model, and is confirmed to be universal by examining selections of different LRB model parameters. This size-dependent rolling behavior under the control of flow strength may provide the theoretical guidance for designing efficient LFD in detecting infectious disease.
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Affiliation(s)
- Huilin Ye
- Department of Mechanical Engineering and Polymer Program, Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA
| | - Zhiqiang Shen
- Department of Mechanical Engineering and Polymer Program, Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA
| | - Ying Li
- Department of Mechanical Engineering and Polymer Program, Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA
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29
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Puleri DF, Balogh P, Randles A. Computational models of cancer cell transport through the microcirculation. Biomech Model Mechanobiol 2021; 20:1209-1230. [PMID: 33765196 DOI: 10.1007/s10237-021-01452-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Accepted: 03/08/2021] [Indexed: 02/07/2023]
Abstract
The transport of cancerous cells through the microcirculation during metastatic spread encompasses several interdependent steps that are not fully understood. Computational models which resolve the cellular-scale dynamics of complex microcirculatory flows offer considerable potential to yield needed insights into the spread of cancer as a result of the level of detail that can be captured. In recent years, in silico methods have been developed that can accurately and efficiently model the circulatory flows of cancer and other biological cells. These computational methods are capable of resolving detailed fluid flow fields which transport cells through tortuous physiological geometries, as well as the deformation and interactions between cells, cell-to-endothelium interactions, and tumor cell aggregates, all of which play important roles in metastatic spread. Such models can provide a powerful complement to experimental works, and a promising approach to recapitulating the endogenous setting while maintaining control over parameters such as shear rate, cell deformability, and the strength of adhesive binding to better understand tumor cell transport. In this review, we present an overview of computational models that have been developed for modeling cancer cells in the microcirculation, including insights they have provided into cell transport phenomena.
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Affiliation(s)
- Daniel F Puleri
- Department of Biomedical Engineering, Duke University, Durham, NC, 27708, USA
| | - Peter Balogh
- Department of Biomedical Engineering, Duke University, Durham, NC, 27708, USA
| | - Amanda Randles
- Department of Biomedical Engineering, Duke University, Durham, NC, 27708, USA.
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30
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Liu ZL, Ku DN, Aidun CK. Mechanobiology of shear-induced platelet aggregation leading to occlusive arterial thrombosis: A multiscale in silico analysis. J Biomech 2021; 120:110349. [PMID: 33711601 DOI: 10.1016/j.jbiomech.2021.110349] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 02/22/2021] [Indexed: 12/13/2022]
Abstract
Occlusive thrombosis in arteries causes heart attacks and strokes. The rapid growth of thrombus at elevated shear rates (~10,000 1/s) relies on shear-induced platelet aggregation (SIPA) thought to come about from the entanglement of von Willebrand factor (VWF) molecules. The mechanism for SIPA is not yet understood in terms of cell- and molecule-level dynamics in fast flowing bloodstreams. Towards this end, we develop a multiscale computational model to recreate SIPA in silico, where the suspension dynamics and interactions of individual platelets and VWF multimers are resolved directly. The platelet-VWF interaction via GP1b-A1 bonds is prescribed with intrinsic binding rates theoretically derived and informed by single-molecule measurements. The model is validated against existing microfluidic SIPA experiments, showing good agreement with the in vitro observations in terms of the morphology, traveling distance and capture time of the platelet aggregates. Particularly, the capture of aggregates can occur in a few milliseconds, comparable to the platelet transit time through pathologic arterial stenotic sections and much shorter than the time for shear-induced platelet activation. The multiscale SIPA simulator provides a cross-scale tool for exploring the biophysical mechanisms of SIPA in silico that are difficult to access with single-molecule measurements or micro-/macro-fluidic assays only.
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Affiliation(s)
- Zixiang L Liu
- George W. Woodruff School of Mechanical Engineering, and Parker H. Petit Institute for Bioengineering and Biosciences, Georgia Institute of Technology, GE 30332, United States.
| | - David N Ku
- George W. Woodruff School of Mechanical Engineering, and Parker H. Petit Institute for Bioengineering and Biosciences, Georgia Institute of Technology, GE 30332, United States.
| | - Cyrus K Aidun
- George W. Woodruff School of Mechanical Engineering, and Parker H. Petit Institute for Bioengineering and Biosciences, Georgia Institute of Technology, GE 30332, United States.
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31
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Wang S, Ye T, Li G, Zhang X, Shi H. Margination and adhesion dynamics of tumor cells in a real microvascular network. PLoS Comput Biol 2021; 17:e1008746. [PMID: 33606686 PMCID: PMC7928530 DOI: 10.1371/journal.pcbi.1008746] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Revised: 03/03/2021] [Accepted: 01/27/2021] [Indexed: 01/09/2023] Open
Abstract
In tumor metastasis, the margination and adhesion of tumor cells are two critical and closely related steps, which may determine the destination where the tumor cells extravasate to. We performed a direct three-dimensional simulation on the behaviors of the tumor cells in a real microvascular network, by a hybrid method of the smoothed dissipative particle dynamics and immersed boundary method (SDPD-IBM). The tumor cells are found to adhere at the microvascular bifurcations more frequently, and there is a positive correlation between the adhesion of the tumor cells and the wall-directed force from the surrounding red blood cells (RBCs). The larger the wall-directed force is, the closer the tumor cells are marginated towards the wall, and the higher the probability of adhesion behavior happen is. A relatively low or high hematocrit can help to prevent the adhesion of tumor cells, and similarly, increasing the shear rate of blood flow can serve the same purpose. These results suggest that the tumor cells may be more likely to extravasate at the microvascular bifurcations if the blood flow is slow and the hematocrit is moderate.
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Affiliation(s)
- Sitong Wang
- Department of Computational Mathematics, School of Mathematics, Jilin University, Changchun, China
| | - Ting Ye
- Department of Computational Mathematics, School of Mathematics, Jilin University, Changchun, China
- * E-mail:
| | - Guansheng Li
- Department of Computational Mathematics, School of Mathematics, Jilin University, Changchun, China
| | - Xuejiao Zhang
- Department of Computational Mathematics, School of Mathematics, Jilin University, Changchun, China
| | - Huixin Shi
- Department of Computational Mathematics, School of Mathematics, Jilin University, Changchun, China
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32
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Xiao L, Song X, Chen S. Motion of a tumour cell under the blood flow at low Reynolds number in a curved microvessel. MOLECULAR SIMULATION 2020. [DOI: 10.1080/08927022.2020.1856377] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Affiliation(s)
- L.L. Xiao
- School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, People’s Republic of China
| | - X.J. Song
- School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, People’s Republic of China
| | - S. Chen
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, People’s Republic of China
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33
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Cui J, Liu Y, Xiao L, Chen S, Fu BM. Numerical study on the adhesion of a circulating tumor cell in a curved microvessel. Biomech Model Mechanobiol 2020; 20:243-254. [PMID: 32809129 DOI: 10.1007/s10237-020-01380-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2020] [Accepted: 08/10/2020] [Indexed: 12/17/2022]
Abstract
The adhesion of a circulating tumor cell (CTC) in a three-dimensional curved microvessel was numerically investigated. Simulations were first performed to characterize the differences in the dynamics and adhesion of a CTC in the straight and curved vessels. After that, a parametric study was performed to investigate the effects of the applied driven force density f (or the flow Reynolds number Re) and the CTC membrane bending modulus Kb on the CTC adhesion. Our simulation results show that the CTC prefers to adhere to the curved vessel as more bonds are formed around the transition region of the curved part due to the increased cell-wall contact by the centrifugal force. The parametric study also indicates that when the flow driven force f (or Re) increases or when the CTC becomes softer (Kb decreases), the bond formation probability increases and the bonds will be formed at more sites of a curved vessel. The increased f (or Re) brings a larger centrifugal force, while the decreased Kb generates more contact areas at the cell-wall interface, both of which are beneficial to the bond formation. In the curved vessel, it is found that the site where bonds are formed the most (hotspot) varies with the applied f and the Kb. For our vessel geometry, when f is small, the hotspot tends to be within the first bend of the vessel, while as f increases or Kb decreases, the hotspot may shift to the second bend of the vessel.
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Affiliation(s)
- Jingyu Cui
- Research Centre for Fluid-Structure Interactions, Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China
| | - Yang Liu
- Research Centre for Fluid-Structure Interactions, Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China.
| | - Lanlan Xiao
- School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, China
| | - Shuo Chen
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China
| | - Bingmei M Fu
- Department of Biomedical Engineering, The City College of the City University of New York, New York, USA
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34
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Campbell EJ, Bagchi P. A computational study of amoeboid motility in 3D: the role of extracellular matrix geometry, cell deformability, and cell-matrix adhesion. Biomech Model Mechanobiol 2020; 20:167-191. [PMID: 32772275 DOI: 10.1007/s10237-020-01376-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Accepted: 08/01/2020] [Indexed: 12/24/2022]
Abstract
Amoeboid cells often migrate using pseudopods, which are membrane protrusions that grow, bifurcate, and retract dynamically, resulting in a net cell displacement. Many cells within the human body, such as immune cells, epithelial cells, and even metastatic cancer cells, can migrate using the amoeboid phenotype. Amoeboid motility is a complex and multiscale process, where cell deformation, biochemistry, and cytosolic and extracellular fluid motions are coupled. Furthermore, the extracellular matrix (ECM) provides a confined, complex, and heterogeneous environment for the cells to navigate through. Amoeboid cells can migrate without significantly remodeling the ECM using weak or no adhesion, instead utilizing their deformability and the microstructure of the ECM to gain enough traction. While a large volume of work exists on cell motility on 2D substrates, amoeboid motility is 3D in nature. Despite recent progress in modeling cellular motility in 3D, there is a lack of systematic evaluations of the role of ECM microstructure, cell deformability, and adhesion on 3D motility. To fill this knowledge gap, here we present a multiscale, multiphysics modeling study of amoeboid motility through 3D-idealized ECM. The model is a coupled fluid‒structure and coarse-grain biochemistry interaction model that accounts for large deformation of cells, pseudopod dynamics, cytoplasmic and extracellular fluid motion, stochastic dynamics of cell-ECM adhesion, and microstructural (pore-scale) geometric details of the ECM. The key finding of the study is that cell deformation and matrix porosity strongly influence amoeboid motility, while weak adhesion and microscale structural details of the ECM have secondary but subtle effects.
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Affiliation(s)
- Eric J Campbell
- Mechanical and Aerospace Engineering Department, Rutgers, The State University of New Jersey, Piscataway, NJ, 08854, USA
| | - Prosenjit Bagchi
- Mechanical and Aerospace Engineering Department, Rutgers, The State University of New Jersey, Piscataway, NJ, 08854, USA.
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35
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Bacon K, Lavoie A, Rao BM, Daniele M, Menegatti S. Past, Present, and Future of Affinity-based Cell Separation Technologies. Acta Biomater 2020; 112:29-51. [PMID: 32442784 PMCID: PMC10364325 DOI: 10.1016/j.actbio.2020.05.004] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Revised: 04/29/2020] [Accepted: 05/05/2020] [Indexed: 02/06/2023]
Abstract
Progress in cell purification technology is critical to increase the availability of viable cells for therapeutic, diagnostic, and research applications. A variety of techniques are now available for cell separation, ranging from non-affinity methods such as density gradient centrifugation, dielectrophoresis, and filtration, to affinity methods such as chromatography, two-phase partitioning, and magnetic-/fluorescence-assisted cell sorting. For clinical and analytical procedures that require highly purified cells, the choice of cell purification method is crucial, since every method offers a different balance between yield, purity, and bioactivity of the cell product. For most applications, the requisite purity is only achievable through affinity methods, owing to the high target specificity that they grant. In this review, we discuss past and current methods for developing cell-targeting affinity ligands and their application in cell purification, along with the benefits and challenges associated with different purification formats. We further present new technologies, like stimuli-responsive ligands and parallelized microfluidic devices, towards improving the viability and throughput of cell products for tissue engineering and regenerative medicine. Our comparative analysis provides guidance in the multifarious landscape of cell separation techniques and highlights new technologies that are poised to play a key role in the future of cell purification in clinical settings and the biotech industry. STATEMENT OF SIGNIFICANCE: Technologies for cell purification have served science, medicine, and industrial biotechnology and biomanufacturing for decades. This review presents a comprehensive survey of this field by highlighting the scope and relevance of all known methods for cell isolation, old and new alike. The first section covers the main classes of target cells and compares traditional non-affinity and affinity-based purification techniques, focusing on established ligands and chromatographic formats. The second section presents an excursus of affinity-based pseudo-chromatographic and non-chromatographic technologies, especially focusing on magnetic-activated cell sorting (MACS) and fluorescence-activated cell sorting (FACS). Finally, the third section presents an overview of new technologies and emerging trends, highlighting how the progress in chemical, material, and microfluidic sciences has opened new exciting avenues towards high-throughput and high-purity cell isolation processes. This review is designed to guide scientists and engineers in their choice of suitable cell purification techniques for research or bioprocessing needs.
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Affiliation(s)
- Kaitlyn Bacon
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC 27695-7905, USA
| | - Ashton Lavoie
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC 27695-7905, USA
| | - Balaji M Rao
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC 27695-7905, USA; Biomanufacturing Training and Education Center (BTEC), North Carolina State University, Raleigh, NC 27695-7928, USA
| | - Michael Daniele
- Joint Department of Biomedical Engineering, North Carolina State University - University of North Carolina Chapel Hill, North Carolina, United States
| | - Stefano Menegatti
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC 27695-7905, USA; Biomanufacturing Training and Education Center (BTEC), North Carolina State University, Raleigh, NC 27695-7928, USA.
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36
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Fang Y, Gong H, Yang R, Lai KWC, Quan M. An Active Biomechanical Model of Cell Adhesion Actuated by Intracellular Tensioning-Taxis. Biophys J 2020; 118:2656-2669. [PMID: 32380000 PMCID: PMC7264853 DOI: 10.1016/j.bpj.2020.04.016] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2019] [Revised: 02/10/2020] [Accepted: 04/16/2020] [Indexed: 11/23/2022] Open
Abstract
Cell adhesion to the extracellular matrix (ECM) is highly active and plays a crucial role in various physiological functions. The active response of cells to physicochemical cues has been universally discovered in multiple microenvironments. However, the mechanisms to rule these active behaviors of cells are still poorly understood. Here, we establish an active model to probe the biomechanical mechanisms governing cell adhesion. The framework of cells is modeled as a tensional integrity that is maintained by cytoskeletons and extracellular matrices. Active movement of the cell model is self-driven by its intrinsic tendency to intracellular tensioning, defined as tensioning-taxis in this study. Tensioning-taxis is quantified as driving potential to actuate cell adhesion, and the traction forces are solved by our proposed numerical method of local free energy adaptation. The modeling results account for the active adhesion of cells with dynamic protruding of leading edge and power-law development of mechanical properties. Furthermore, the morphogenesis of cells evolves actively depending on actin filaments alignments by a predicted mechanism of scaling and directing traction forces. The proposed model provides a quantitative way to investigate the active mechanisms of cell adhesion and holds the potential to guide studies of more complex adhesion and motion of cells coupled with multiple external cues.
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Affiliation(s)
- Yuqiang Fang
- School of Mechanical and Aerospace Engineering, Jilin University, Changchun, China.
| | - He Gong
- School of Mechanical and Aerospace Engineering, Jilin University, Changchun, China
| | - Ruiguo Yang
- Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska
| | - King W C Lai
- Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Hong Kong, China
| | - Meiling Quan
- Department of Orthopedics, Daejeon St. Mary's Hospital, College of Medicine, The Catholic University of Korea, Daejeon, Republic of Korea.
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37
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Khorram A, Vahidi B, Ahmadian B. Computational analysis of adhesion between a cancer cell and a white blood cell in a bifurcated microvessel. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2020; 186:105195. [PMID: 31734471 DOI: 10.1016/j.cmpb.2019.105195] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2019] [Revised: 11/03/2019] [Accepted: 11/07/2019] [Indexed: 06/10/2023]
Abstract
BACKGROUND AND OBJECTIVE Cancer is one of the diseases caused by irregular and uncontrolled growth of cells and their propagation into various parts of the body. The motion and adhesion of cancer cells in a blood vessel is a critical step in tumor progression that depends on some vascular parameters such as vessel branching. In this study, effect of microvessel branching on the bonds between a cancer cell and a white blood has been investigated as compared to an analogous problem in a straight vessel. METHODS The analysis is performed using finite elements and fluid-structure interaction methods. Moreover, the equations for adhesion of the cancer cell to white blood cell are coded in MATLAB for calculating forces between them and the code is coupled directly and simultaneously with the COMSOL software. For fluid-structure interaction analysis, it is assumed that the properties of the blood and the cells are homogeneous and the fluid is incompressible and Newtonian. Cancer cell is modeled as a rigid body and white blood cell is assumed as linear elastic. RESULTS The results show that although the geometry of the vessel does not affect on the separation distance of cancer cell considerably, but at the area near a bifurcation, high fluctuations in cancer cell velocity is occurred due to increasing in number of bond formation between the cancer cell and the white blood cell. Accordingly, it can be predicted that higher concentration of adhered particles occurs near the bifurcations. Moreover, shear stress at the point of contact of the cancer cell and the white blood cell in the branched vessel is greater than that in the straight path. In addition to, the probability of breaking of the bond between the cancer cell and the white blood cell increases in the branched vessel. CONCLUSIONS Through consideration in the adhesion charts of this study along with observations from medical interventions such as drug delivery to cancer patients, considerable developments on the treatment or prevention of cancer metastasis may be achieved.
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Affiliation(s)
- Asghar Khorram
- Division of Biomedical Engineering, Department of Life Science Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran
| | - Bahman Vahidi
- Division of Biomedical Engineering, Department of Life Science Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran.
| | - Bahram Ahmadian
- Division of Biomedical Engineering, Department of Life Science Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran
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38
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Noori MS, Bodle SJ, Showalter CA, Streator ES, Drozek DS, Burdick MM, Goetz DJ. Sticking to the Problem: Engineering Adhesion in Molecular Endoscopic Imaging. Cell Mol Bioeng 2020; 13:113-124. [PMID: 32175025 DOI: 10.1007/s12195-020-00609-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2019] [Accepted: 01/03/2020] [Indexed: 12/24/2022] Open
Abstract
Cancers of the digestive tract cause nearly one quarter of the cancer deaths worldwide, and nearly half of these are due to cancers of the esophagus and colon. Early detection of cancer significantly increases the rate of survival, and thus it is critical that cancer within these organs is detected early. In this regard, endoscopy is routinely used to screen for transforming/cancerous (i.e. dysplastic to fully cancerous) tissue. Numerous studies have revealed that the biochemistry of the luminal surface of such tissue within the colon and esophagus becomes altered throughout disease progression. Molecular endoscopic imaging (MEI), an emerging technology, seeks to exploit these changes for the early detection of cancer. The general approach for MEI is as follows: the luminal surface of an organ is exposed to molecular ligands, or particulate probes bearing a ligand, cognate to biochemistry unique to pre-cancerous/cancerous tissue. After a wash, the tissue is imaged to determine the presence of the probes. Detection of the probes post-washing suggests pathologic tissue. In the current review we provide a succinct, but extensive, review of ligands and target moieties that could be, or are currently being investigated, as possible cognate chemistries for MEI. This is followed by a review of the biophysics that determines, in large part, the success of a particular MEI design. The work draws an analogy between MEI and the well-advanced field of cell adhesion and provides a road map for engineering MEI to achieve assays that yield highly selective recognition of transforming/cancerous tissue in situ.
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Affiliation(s)
- Mahboubeh S Noori
- Department of Chemical and Biomolecular Engineering, Ohio University, Athens, OH 45701 USA
| | - Sarah J Bodle
- Department of Chemical and Biomolecular Engineering, Ohio University, Athens, OH 45701 USA.,Biomedical Engineering Program, Ohio University, Athens, OH 45701 USA
| | - Christian A Showalter
- Department of Biological Sciences, Ohio University, Athens, OH 45701 USA.,Molecular and Cellular Biology Program, Ohio University, Athens, OH 45701 USA
| | - Evan S Streator
- Department of Chemical and Biomolecular Engineering, Ohio University, Athens, OH 45701 USA
| | - David S Drozek
- Department of Specialty Medicine, Ohio University, Athens, OH 45701 USA
| | - Monica M Burdick
- Department of Chemical and Biomolecular Engineering, Ohio University, Athens, OH 45701 USA.,Biomedical Engineering Program, Ohio University, Athens, OH 45701 USA.,Molecular and Cellular Biology Program, Ohio University, Athens, OH 45701 USA.,Edison Biotechnology Institute, Ohio University, Athens, OH 45701 USA
| | - Douglas J Goetz
- Department of Chemical and Biomolecular Engineering, Ohio University, Athens, OH 45701 USA.,Biomedical Engineering Program, Ohio University, Athens, OH 45701 USA
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39
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Calamak S, Ermis M, Sun H, Islam S, Sikora M, Nguyen M, Hasirci V, Steinmetz LM, Demirci U. A Circulating Bioreactor Reprograms Cancer Cells Toward a More Mesenchymal Niche. ACTA ACUST UNITED AC 2020; 4:e1900139. [PMID: 32293132 DOI: 10.1002/adbi.201900139] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2019] [Revised: 10/15/2019] [Indexed: 11/08/2022]
Abstract
Cancer is a complex and heterogeneous disease, and cancer cells dynamically interact with the mechanical microenvironment such as hydrostatic pressure, fluid shear, and interstitial flow. These factors play an essential role in cell fate and circulating tumor cell heterogeneity, and can influence the cellular phenotype. In this study, a peristaltic continuous flow reactor is designed and applied to HCT-116 colorectal carcinoma cells to mimic the fluid dynamics of circulation. With this intervention, a CD44/CD24-cell subpopulation emerges, and 100 genes are significantly regulated. The expression of cells at 4 h in the flow reactor is very similar to TGF-ß treatment, which is an inducer of epithelial-mesenchymal transition. ATF3 and SERPINE1 are significantly upregulated in these groups, suggesting that the mesenchymal transition is induced through this signaling pathway. This flow reactor model is satisfactory on its own to reprogram colorectal cancer cells toward a more mesenchymal niche mimicking circulation of the blood.
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Affiliation(s)
- Semih Calamak
- Bio-Acoustic-MEMS in Medicine (BAMM) Laboratory, Canary Center at Stanford for Cancer Early Detection, Department of Radiology, Stanford University School of Medicine, Palo Alto, CA, 94304, USA.,Department of Basic Pharmaceutical Sciences, Faculty of Pharmacy, Hacettepe University, Ankara, 06100, Turkey
| | - Menekse Ermis
- Bio-Acoustic-MEMS in Medicine (BAMM) Laboratory, Canary Center at Stanford for Cancer Early Detection, Department of Radiology, Stanford University School of Medicine, Palo Alto, CA, 94304, USA.,BIOMATEN, Middle East Technical University (METU) Center of Excellence in Biomaterials and Tissue Engineering, Ankara, 06800, Turkey
| | - Han Sun
- Department of Genetics and Stanford Genome Technology Center, School of Medicine Stanford University, Palo Alto, CA, 94305, USA
| | - Saiful Islam
- Department of Genetics and Stanford Genome Technology Center, School of Medicine Stanford University, Palo Alto, CA, 94305, USA
| | - Michael Sikora
- Department of Genetics and Stanford Genome Technology Center, School of Medicine Stanford University, Palo Alto, CA, 94305, USA
| | - Michelle Nguyen
- Department of Genetics and Stanford Genome Technology Center, School of Medicine Stanford University, Palo Alto, CA, 94305, USA
| | - Vasif Hasirci
- BIOMATEN, Middle East Technical University (METU) Center of Excellence in Biomaterials and Tissue Engineering, Ankara, 06800, Turkey.,Department of Medical Engineering, School of Engineering, Acıbadem University, Istanbul, 34752, Turkey
| | - Lars M Steinmetz
- Department of Genetics and Stanford Genome Technology Center, School of Medicine Stanford University, Palo Alto, CA, 94305, USA.,European Molecular Biology Laboratory, Genome Biology Unit, 69117, Heidelberg, Germany
| | - Utkan Demirci
- Bio-Acoustic-MEMS in Medicine (BAMM) Laboratory, Canary Center at Stanford for Cancer Early Detection, Department of Radiology, Stanford University School of Medicine, Palo Alto, CA, 94304, USA.,Electrical Engineering Department by Courtesy, Stanford University, Stanford, CA, 94305, USA
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40
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A 3D computational model of perfusion seeding for investigating cell transport and adhesion within a porous scaffold. Biomech Model Mechanobiol 2020; 19:1461-1475. [PMID: 31900653 DOI: 10.1007/s10237-019-01281-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2019] [Accepted: 12/17/2019] [Indexed: 10/25/2022]
Abstract
The process of cell seeding within a porous scaffold is an essential first step in the development of tissue-engineered bone grafts. Understanding the underlying mechanisms of cell distribution and adhesion is fundamental for the design and optimization of the seeding process. To that end, we present a numerical model to investigate the perfusion cell seeding process that incorporates cell mechanics, cell-fluid interaction, and cell-scaffold adhesion. The individual cells are modeled as deformable spherical capsules capable of adhering to the scaffold surface as well as to other cells with probabilistic bond formation and rupture. The mechanical deformation of the cell is calibrated with the stretching of mice mesenchymal stem cells induced by optical tweezers, while the predicted adhesive forces are consistent with the experimental data reported in the literature. A sub-domain is numerically reconstructed as the region of interest (ROI) which is representative of an actual scaffold. Through the simulations, the perfusion seeding kinetics within the ROI involving detailed transport and adhesion of cells over time is analyzed. The effects of the perfusion pressure and initial cell concentration on the seeding kinetics are studied in terms of adhesion rates, cell cluster formation, seeding uniformity, and efficiency, as well as scaffold permeability. The results highlight the importance of cell-fluid interaction and adhesion dynamics in modeling the dynamic seeding process. This bottom-up model provides a way to bridge detailed behaviors of individual cells to the seeding outcomes at the macroscopic scale, allowing for finding the best configuration to enhance cell seeding.
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41
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Ye T, Shi H, Phan-Thien N, Lim CT. The key events of thrombus formation: platelet adhesion and aggregation. Biomech Model Mechanobiol 2019; 19:943-955. [PMID: 31754949 DOI: 10.1007/s10237-019-01262-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2019] [Accepted: 11/11/2019] [Indexed: 01/20/2023]
Abstract
Thrombus formation is a complex, dynamic and multistep process, involving biochemical reactions, mechanical stimulation, hemodynamics, and so on. In this study, we concentrate on its two crucial steps: (i) platelets adhered to a vessel wall, or simply platelet adhesion, and (ii) platelets clumping and arrested to the adherent platelets, named platelet aggregation. We report the first direct simulation of three modes of platelet adhesion, detachment, rolling adhesion and firm adhesion, as well as the formation, disintegration, arrestment and consolidation of platelet plugs. The results show that the bond dissociation in the detachment mode is mainly attributed to a high probability of rupturing bonds, such that any existing bond can be quickly ruptured and all bonds would be completely broken. In the rolling adhesion, however, it is mainly attributed to the strong traction from the shear flow or erythrocytes, causing that the bonds are ruptured at the trailing edge of the platelet. The erythrocytes play an important role in platelet activities, such as the formation, disintegration, arrestment and consolidation of platelet plugs. They exert an aggregate force on platelets, a repulsion at a near distance but an attraction at a far distance to the platelets. This aggregate force can promote platelets to form a plug and/or bring along a part of a platelet plug causing its disintegration. It also greatly influences the arrestment and consolidation of platelet plugs, together with the adhesive force from the thrombus.
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Affiliation(s)
- Ting Ye
- School of Mathematics, Jilin University, Qianjin Ave. 2699, Changchun, 130012, China.
| | - Huixin Shi
- School of Mathematics, Jilin University, Qianjin Ave. 2699, Changchun, 130012, China
| | - Nhan Phan-Thien
- Department of Mechanical Engineering, National University of Singapore, Singapore, 117576, Singapore
| | - Chwee Teck Lim
- Department of Mechanical Engineering, National University of Singapore, Singapore, 117576, Singapore
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42
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Paddillaya N, Mishra A, Kondaiah P, Pullarkat P, Menon GI, Gundiah N. Biophysics of Cell-Substrate Interactions Under Shear. Front Cell Dev Biol 2019; 7:251. [PMID: 31781558 PMCID: PMC6857480 DOI: 10.3389/fcell.2019.00251] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Accepted: 10/10/2019] [Indexed: 12/31/2022] Open
Abstract
Cells adhere to substrates through mechanosensitive focal adhesion complexes. Measurements that probe how cells detach from substrates when they experience an applied force connect molecular-scale aspects of cell adhesion with the biophysical properties of adherent cells. Such forces can be applied through shear devices that flow fluid in a controlled manner across cells. The signaling pathways associated with focal adhesions, in particular those that involve integrins and receptor tyrosine kinases, are complex, receiving mechano-chemical feedback from the sensing of substrate stiffness as well as of external forces. This article reviews the signaling processes involved in mechanosensing and mechanotransduction during cell-substrate interactions, describing the role such signaling plays in cancer metastasis. We examine some recent progress in quantifying the strength of these interactions, describing a novel fluid shear device that allows for the visualization of the cell and its sub-cellular structures under a shear flow. We also summarize related results from a biophysical model for cellular de-adhesion induced by applied forces. Quantifying cell-substrate adhesions under shear should aid in the development of mechano-diagnostic techniques for diseases in which cell-adhesion is mis-regulated, such as cancers.
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Affiliation(s)
- Neha Paddillaya
- Centre for Biosystems Science and Engineering, Indian Institute of Science, Bangalore, India
| | - Ashish Mishra
- Soft Condensed Matter Group, Raman Research Institute, Bangalore, India
| | - Paturu Kondaiah
- Department of Molecular Reproduction, Development and Genetics, Indian Institute of Science, Bangalore, India
| | - Pramod Pullarkat
- Soft Condensed Matter Group, Raman Research Institute, Bangalore, India
| | - Gautam I Menon
- The Institute of Mathematical Sciences, Chennai, India.,Homi Bhabha National Institute, Mumbai, India.,Department of Physics, Ashoka University, Sonepat, India
| | - Namrata Gundiah
- Centre for Biosystems Science and Engineering, Indian Institute of Science, Bangalore, India.,Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India
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43
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Zhang Z, Du J, Wei Z, Chen Z, Shu C, Wang Z, Li M. Numerical investigation of adhesion dynamics of a deformable cell pair on an adhesive substrate in shear flow. Phys Rev E 2019; 100:033111. [PMID: 31640031 DOI: 10.1103/physreve.100.033111] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2019] [Indexed: 12/13/2022]
Abstract
Adhesion dynamics of cells is of great value to biological systems and adhesion-based biomedical applications. Although adhesion of a single cell or capsule has been widely studied, physical insights into the adhesion dynamics of aggregates containing two or more cells remain elusive. In this paper, we numerically investigate the dynamic adhesion of a deformable cell pair to a flat substrate under shear flow. Specifically, the immersed boundary-lattice Boltzmann method is utilized as the flow solver, and the stochastic receptor-ligand kinetics model is implemented to recover cell-substrate and cell-cell adhesive interactions. Special attention is paid to the roles of the cell deformability and adhesion strengths in cellular motion. Four distinct adhesion states, namely, rolling, tumbling, firm adhesion, and detachment, are identified and presented in phase diagrams as a function of the adhesion strengths for cell pairs with different deformabilities. The simulation results suggest that both the cell-cell and cell-substrate adhesion strengths act as the resistance to the rolling motion, and dominate the transition among various adhesion states. The cell deformability not only enhances the resistance effect, but also contributes to detachment or fast tumbling of the cell pair. These findings enrich the understanding of adhesion dynamics of cell aggregates, which could shed light on complex adhesion processes and provide instructions in developing adhesion-based applications.
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Affiliation(s)
- Ziying Zhang
- School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China.,Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
| | - Jun Du
- School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
| | - Zhengying Wei
- School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
| | - Zhen Chen
- Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
| | - Chang Shu
- Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
| | - Zhen Wang
- Department of Orthopaedic Oncology, Xi-Jing Hospital, Air Force Military Medical University, Xi'an 710032, People's Republic of China
| | - Minghui Li
- Department of Orthopaedic Oncology, Xi-Jing Hospital, Air Force Military Medical University, Xi'an 710032, People's Republic of China
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44
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Parr A, Anderson NR, Hammer DA. A simulation of the random and directed motion of dendritic cells in chemokine fields. PLoS Comput Biol 2019; 15:e1007295. [PMID: 31589599 PMCID: PMC6797211 DOI: 10.1371/journal.pcbi.1007295] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2019] [Revised: 10/17/2019] [Accepted: 07/30/2019] [Indexed: 11/18/2022] Open
Abstract
Dendritic cells (DCs) are the most effective professional antigen-presenting cell. They ferry antigen from the extremities to T cells and are essential for the initiation of an adaptive immune response. Despite interest in how DCs respond to chemical stimuli, there have been few attempts to model DC migration. In this paper, we simulate the motility of DCs by modeling the generation of forces by filopodia and a force balance on the cell. The direction of fliopodial extension is coupled to differential occupancy of cognate chemokine receptors across the cell. Our model simulates chemokinesis and chemotaxis in a variety of chemical and mechanical environments. Simulated DCs undergoing chemokinesis were measured to have a speed of 5.1 ± 0.07 μm·min-1 and a persistence time of 3.2 ± 0.46 min, consistent with experiment. Cells undergoing chemotaxis exhibited a stronger chemotactic response when exposed to lower average chemokine concentrations, also consistent with experiment. We predicted that when placed in two opposing gradients, cells will cluster in a line, which we call the "line of equistimulation;" this clustering has also been observed. We calculated the effect of varying gradient steepness on the line of equistimulation, with steeper gradients resulting in tighter clustering. Moreover, gradients are found to be most potent when cells are in a gradient of chemokine whose mean concentration is close to the binding of the Kd to the receptor, and least potent when the mean concentration is 0.1Kd. Comparing our simulations to experiment, we can give a quantitative measure of the strength of certain chemokines relative to others. Assigning the signal of CCL19 binding CCR7 a baseline strength of 1, we found CCL21 binding CCR7 had a strength of 0.28, and CXCL12 binding CXCR4 had a strength of 0.30. These differences emerge despite both chemokines having virtually the same Kd, suggesting a mechanism of signal amplification in DCs requiring further study.
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Affiliation(s)
- Avery Parr
- Harriton High School, Rosemont, Pennsylvania, United States of America
- Department of Chemical and Biological Engineering, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
| | - Nicholas R. Anderson
- Department of Chemical and Biological Engineering, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
| | - Daniel A. Hammer
- Department of Chemical and Biological Engineering, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
- Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
- * E-mail:
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45
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Bai F, Sun R. A Theoretical Analysis of Receptor-Mediated Endocytosis of Nanoparticles in Wall Shear Flow. ACTA ACUST UNITED AC 2019. [DOI: 10.1142/s1793048019500048] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This study theoretically investigates receptor–ligand-mediated endocytosis of nanoparticles (NPs) in wall shear flow. The endocytosis is modeled as a birth–death process and relationships between coefficients in the model and the wall shear rate have been derived to deal with the effects of the shear flow. Model predictions show that flow-induced alteration in bond formation rates does not affect the endocytosis significantly, and the suppression of hydrodynamic load on endocytosis is eminent only when diameters of NPs are large (around 700[Formula: see text]nm) and the shear rate is sufficiently high. In the latter case, it is shown that the hydrodynamic load suppresses the initial attachment of NPs to cells more than the following internalization. The model also predicts that shear-promoted expression of certain ligands can lead to observable increase in the number of endocytozed NPs in typical flow-chamber experiments, and the promotion can also cause selective endocytosis of NPs by cells at high shear rate regions if the ligand surface density on NPs or the original expression of receptors on cells in the absence of flow is low.
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Affiliation(s)
- Fan Bai
- Department of Engineering Mechanics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, P. R. China
| | - Ren Sun
- Department of Engineering Mechanics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, P. R. China
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46
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A stochastic model for cell adhesion to the vascular wall. J Math Biol 2019; 79:1665-1697. [PMID: 31485777 DOI: 10.1007/s00285-019-01407-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2019] [Revised: 06/05/2019] [Indexed: 10/26/2022]
Abstract
Cell dynamics in the vicinity of the vascular wall involves several factors of mechanical or biochemical origins. It is driven by the competition between the drag force of the blood flow and the resistive force generated by the bonds created between the circulating cell and the endothelial wall. Here, we propose a minimal mathematical model for the adhesive interaction between a circulating cell and the blood vessel wall in shear flow when the cell shape is neglected. The bond dynamics in cell adhesion is modeled as a nonlinear Markovian Jump process that takes into account the growth of adhesion complexes. Performing scaling limits in the spirit of Joffe and Metivier (Adv Appl Probab 18(1):20, 1986), Ethier and Kurtz (Markov processes: characterization and convergence, Wiley, New York, 2009), we obtain deterministic and stochastic continuous models, whose analysis allow to identify a threshold shear velocity associated with the transition from cell rolling and firm adhesion. We also give an estimation of the mean stopping time of the cell resulting from this dynamics. We believe these results can have strong implications for the understanding of major biological phenomena such as cell immunity and metastatic development.
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47
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Unraveling the Vascular Fate of Deformable Circulating Tumor Cells Via a Hierarchical Computational Model. Cell Mol Bioeng 2019. [DOI: 10.1007/s12195-019-00587-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
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48
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Noori MS, Streator ES, Carlson GE, Drozek DS, Burdick MM, Goetz DJ. An adhesion based approach for the detection of esophageal cancer. Integr Biol (Camb) 2019; 10:747-757. [PMID: 30398503 DOI: 10.1039/c8ib00132d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Esophageal cancer has a 5 year survival rate of ∼20%. This dismal prognosis is due, in part, to the fact that esophageal cancer often presents at a late stage. Thus, there is a critical need for assays that enable the early detection of cancerous tissue within the esophagus. The luminal surface of the esophagus expresses signature molecule(s) at sites of transformation providing an avenue for the development of in situ assays that detect neoplastic growth within the esophagus. An attractive approach, receiving increased attention, is the endoscopic administration of particles conjugated with ligands to signature molecules present on transforming tissue. Detection of the particles within the esophagus, post-washing, would indicate the presence of the signature molecule and thus transforming tissue. In this work, we utilized cancerous and normal esophageal cells to provide in vitro proof of principle for this approach utilizing ligand-conjugated microspheres and demonstrate the need, and provide the framework for, engineering this technology. Specifically, the study (i) reveals selective increased expression of signature molecules on cancerous esophageal cells relative to normal cells; (ii) demonstrates selective binding of ligand-conjugated microspheres to cancerous esophageal cells relative to normal cells; (iii) demonstrates that the selective recognition of cancerous, relative to normal esophageal cells, is highly dependent on the biophysical design of the assay; and (iv) advocates utilizing the knowledge from the field of cell adhesion as a guide for the effective development of ligand-conjugated particle-based schemes that seek to detect esophageal oncogenesis in situ.
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Affiliation(s)
- Mahboubeh S Noori
- Department of Chemical and Biomolecular Engineering, Ohio University, Athens, Ohio 45701, USA.
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49
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Dasanna AK, Fedosov DA, Gompper G, Schwarz US. State diagram for wall adhesion of red blood cells in shear flow: from crawling to flipping. SOFT MATTER 2019; 15:5511-5520. [PMID: 31241632 DOI: 10.1039/c9sm00677j] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Red blood cells in shear flow show a variety of different shapes due to the complex interplay between hydrodynamics and membrane elasticity. Malaria-infected red blood cells become generally adhesive and less deformable. Adhesion to a substrate leads to a reduction in shape variability and to a flipping motion of the non-spherical shapes during the mid-stage of infection. Here, we present a complete state diagram for wall adhesion of red blood cells in shear flow obtained by simulations, using a particle-based mesoscale hydrodynamics approach, multiparticle collision dynamics. We find that cell flipping at a substrate is replaced by crawling beyond a critical shear rate, which increases with both membrane stiffness and viscosity contrast between the cytosol and suspending medium. This change in cell dynamics resembles the transition between tumbling and tank-treading for red blood cells in free shear flow. In the context of malaria infections, the flipping-crawling transition would strongly increase the adhesive interactions with the vascular endothelium, but might be suppressed by the combined effect of increased elasticity and viscosity contrast.
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Affiliation(s)
- Anil K Dasanna
- BioQuant and Institute of Theoretical Physics, Heidelberg University, Heidelberg, Germany. and Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Dmitry A Fedosov
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Ulrich S Schwarz
- BioQuant and Institute of Theoretical Physics, Heidelberg University, Heidelberg, Germany.
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Irons L, Owen MR, O'Dea RD, Brook BS. Effect of Loading History on Airway Smooth Muscle Cell-Matrix Adhesions. Biophys J 2019; 114:2679-2690. [PMID: 29874617 DOI: 10.1016/j.bpj.2018.04.026] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2017] [Revised: 04/05/2018] [Accepted: 04/16/2018] [Indexed: 01/06/2023] Open
Abstract
Integrin-mediated adhesions between airway smooth muscle (ASM) cells and the extracellular matrix (ECM) regulate how contractile forces generated within the cell are transmitted to its external environment. Environmental cues are known to influence the formation, size, and survival of cell-matrix adhesions, but it is not yet known how they are affected by dynamic fluctuations associated with tidal breathing in the intact airway. Here, we develop two closely related theoretical models to study adhesion dynamics in response to oscillatory loading of the ECM, representing the dynamic environment of ASM cells in vivo. Using a discrete stochastic-elastic model, we simulate individual integrin binding and rupture events and observe two stable regimes in which either bond formation or bond rupture dominate, depending on the amplitude of the oscillatory loading. These regimes have either a high or low fraction of persistent adhesions, which could affect the level of strain transmission between contracted ASM cells and the airway tissue. For intermediate loading, we observe a region of bistability and hysteresis due to shared loading between existing bonds; the level of adhesion depends on the loading history. These findings are replicated in a related continuum model, which we use to investigate the effect of perturbations mimicking deep inspirations (DIs). Because of the bistability, a DI applied to the high adhesion state could either induce a permanent switch to a lower adhesion state or allow a return of the system to the high adhesion state. Transitions between states are further influenced by the frequency of oscillations, cytoskeletal or ECM stiffnesses, and binding affinities, which modify the magnitudes of the stable adhesion states as well as the region of bistability. These findings could explain (in part) the transient bronchodilatory effect of a DI observed in asthmatics compared to a more sustained effect in normal subjects.
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Affiliation(s)
- Linda Irons
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom.
| | - Markus R Owen
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
| | - Reuben D O'Dea
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
| | - Bindi S Brook
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
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