1
|
Motahari F, Carlsson AE. Thermodynamically consistent treatment of the growth of a biopolymer in the presence of a smooth obstacle interaction potential. Phys Rev E 2020; 100:042409. [PMID: 31770877 DOI: 10.1103/physreve.100.042409] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2018] [Indexed: 01/05/2023]
Abstract
We investigate the effect of filament-obstacle interactions on the force-velocity relation of growing biopolymers, via calculations explicitly treating obstacle diffusion and stochastic addition and subtraction of subunits. We first show that the instantaneous subunit on- and off-rates satisfy a rigorous thermodynamic relationship determined by the filament-obstacle interaction potential, which has been violated by several calculations in the literature. The instantaneous rates depend not only on the average force on the obstacle but also on the shape of the potential on the nanometer length scale. Basing obstacle-induced reduction of the on-rate entirely on the force, as previous work has often done, is thermodynamically inconsistent and can overestimate the stall force, sometimes by more than a factor of two. We perform simulations and analytic calculations of the force-velocity relation satisfying the thermodynamic relationship. The force-velocity relation can deviate strongly from the Brownian-Ratchet predictions. For shallow potential wells of depth ∼5k_{B}T, which might correspond to transient filament-membrane attachments, the velocity drops more rapidly than predicted by the Brownian-Ratchet model, in some cases by as much as a factor of 50 at an opposing force of only 1 pN. On the other hand, the zero-force velocity is much less affected than would be expected from naive use of the Boltzmann factor. Furthermore, the growth velocity has a surprisingly strong dependence on the obstacle diffusion coefficient even when the dimensionless diffusion coefficient is large. For deep potential wells, as might result from strong filament-membrane links, both the on- and off-rates are reduced significantly, slowing polymerization. Such potentials can sustain pulling forces while polymerizing but only if the attractive well is relatively flat over a region comparable to or greater than the monomer size. For double-well potentials, which have such a flat region, the slowing of polymerization by external pushing force is almost linear up to the stall force in some parameter ranges.
Collapse
Affiliation(s)
- F Motahari
- Department of Physics and Center for Engineering Mechanobiology, Washington University, St. Louis, Missouri 63130, USA
| | - A E Carlsson
- Department of Physics and Center for Engineering Mechanobiology, Washington University, St. Louis, Missouri 63130, USA
| |
Collapse
|
2
|
Datta P, Barui A, Wu Y, Ozbolat V, Moncal KK, Ozbolat IT. Essential steps in bioprinting: From pre- to post-bioprinting. Biotechnol Adv 2018; 36:1481-1504. [PMID: 29909085 DOI: 10.1016/j.biotechadv.2018.06.003] [Citation(s) in RCA: 68] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2018] [Revised: 05/15/2018] [Accepted: 06/10/2018] [Indexed: 12/17/2022]
Abstract
An increasing demand for directed assembly of biomaterials has inspired the development of bioprinting, which facilitates the assembling of both cellular and acellular inks into well-arranged three-dimensional (3D) structures for tissue fabrication. Although great advances have been achieved in the recent decade, there still exist issues to be addressed. Herein, a review has been systematically performed to discuss the considerations in the entire procedure of bioprinting. Though bioprinting is advancing at a rapid pace, it is seen that the whole process of obtaining tissue constructs from this technique involves multiple-stages, cutting across various technology domains. These stages can be divided into three broad categories: pre-bioprinting, bioprinting and post-bioprinting. Each stage can influence others and has a bearing on the performance of fabricated constructs. For example, in pre-bioprinting, tissue biopsy and cell expansion techniques are essential to ensure a large number of cells are available for mass organ production. Similarly, medical imaging is needed to provide high resolution designs, which can be faithfully bioprinted. In the bioprinting stage, compatibility of biomaterials is needed to be matched with solidification kinetics to ensure constructs with high cell viability and fidelity are obtained. On the other hand, there is a need to develop bioprinters, which have high degrees of freedom of movement, perform without failure concerns for several hours and are compact, and affordable. Finally, maturation of bioprinted cells are governed by conditions provided during the post-bioprinting process. This review, for the first time, puts all the bioprinting stages in perspective of the whole process of bioprinting, and analyzes their current state-of-the art. It is concluded that bioprinting community will recognize the relative importance and optimize the parameter of each stage to obtain the desired outcomes.
Collapse
Affiliation(s)
- Pallab Datta
- Centre for Healthcare Science and Technology, Indian Institute of Engineering Science and Technology Shibpur, Howrah 711103, West Bengal, India
| | - Ananya Barui
- Centre for Healthcare Science and Technology, Indian Institute of Engineering Science and Technology Shibpur, Howrah 711103, West Bengal, India
| | - Yang Wu
- Engineering Science and Mechanics Department, Penn State University, University Park, PA 16802, USA; The Huck Institutes of the Life Sciences, Penn State University, University Park, PA 16802, USA
| | - Veli Ozbolat
- Engineering Science and Mechanics Department, Penn State University, University Park, PA 16802, USA; The Huck Institutes of the Life Sciences, Penn State University, University Park, PA 16802, USA; Ceyhan Engineering Faculty, Cukurova University, Adana 01950, Turkey
| | - Kazim K Moncal
- Engineering Science and Mechanics Department, Penn State University, University Park, PA 16802, USA; The Huck Institutes of the Life Sciences, Penn State University, University Park, PA 16802, USA
| | - Ibrahim T Ozbolat
- Engineering Science and Mechanics Department, Penn State University, University Park, PA 16802, USA; The Huck Institutes of the Life Sciences, Penn State University, University Park, PA 16802, USA; Biomedical Engineering Department, Penn State University, University Park, PA 16802, USA; Materials Research Institute, Penn State University, University Park, PA 16802, USA.
| |
Collapse
|
3
|
Rajagopal V, Holmes WR, Lee PVS. Computational modeling of single-cell mechanics and cytoskeletal mechanobiology. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2018; 10:e1407. [PMID: 29195023 PMCID: PMC5836888 DOI: 10.1002/wsbm.1407] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Revised: 08/19/2017] [Accepted: 09/07/2017] [Indexed: 01/10/2023]
Abstract
Cellular cytoskeletal mechanics plays a major role in many aspects of human health from organ development to wound healing, tissue homeostasis and cancer metastasis. We summarize the state-of-the-art techniques for mathematically modeling cellular stiffness and mechanics and the cytoskeletal components and factors that regulate them. We highlight key experiments that have assisted model parameterization and compare the advantages of different models that have been used to recapitulate these experiments. An overview of feed-forward mechanisms from signaling to cytoskeleton remodeling is provided, followed by a discussion of the rapidly growing niche of encapsulating feedback mechanisms from cytoskeletal and cell mechanics to signaling. We discuss broad areas of advancement that could accelerate research and understanding of cellular mechanobiology. A precise understanding of the molecular mechanisms that affect cell and tissue mechanics and function will underpin innovations in medical device technologies of the future. WIREs Syst Biol Med 2018, 10:e1407. doi: 10.1002/wsbm.1407 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.
Collapse
Affiliation(s)
- Vijay Rajagopal
- Cell Structure and Mechanobiology Group, Department of Biomedical EngineeringUniversity of MelbourneMelbourneAustralia
| | - William R. Holmes
- Department of Physics and AstronomyVanderbilt UniversityNashvilleTNUSA
| | - Peter Vee Sin Lee
- Cell and Tissue Biomechanics Laboratory, Department of Biomedical EngineeringUniversity of MelbourneMelbourneAustralia
| |
Collapse
|
4
|
Nijenhuis N, Zhao X, Carisey A, Ballestrem C, Derby B. Combining AFM and acoustic probes to reveal changes in the elastic stiffness tensor of living cells. Biophys J 2015; 107:1502-12. [PMID: 25296302 DOI: 10.1016/j.bpj.2014.07.073] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2013] [Revised: 07/22/2014] [Accepted: 07/30/2014] [Indexed: 12/20/2022] Open
Abstract
Knowledge of how the elastic stiffness of a cell affects its communication with its environment is of fundamental importance for the understanding of tissue integrity in health and disease. For stiffness measurements, it has been customary to quote a single parameter quantity, e.g., Young's modulus, rather than the minimum of two terms of the stiffness tensor required by elasticity theory. In this study, we use two independent methods (acoustic microscopy and atomic force microscopy nanoindentation) to characterize the elastic properties of a cell and thus determine two independent elastic constants. This allows us to explore in detail how the mechanical properties of cells change in response to signaling pathways that are known to regulate the cell's cytoskeleton. In particular, we demonstrate that altering the tensioning of actin filaments in NIH3T3 cells has a strong influence on the cell's shear modulus but leaves its bulk modulus unchanged. In contrast, altering the polymerization state of actin filaments influences bulk and shear modulus in a similar manner. In addition, we can use the data to directly determine the Poisson ratio of a cell and show that in all cases studied, it is less than, but very close to, 0.5 in value.
Collapse
Affiliation(s)
- Nadja Nijenhuis
- School of Materials, Faculty of Engineering and Physical Sciences, Faculty of Life Sciences, University of Manchester, Manchester, United Kingdom; Wellcome Trust Centre for Cell-Matrix Research, Faculty of Life Sciences, University of Manchester, Manchester, United Kingdom
| | - Xuegen Zhao
- School of Materials, Faculty of Engineering and Physical Sciences, Faculty of Life Sciences, University of Manchester, Manchester, United Kingdom
| | - Alex Carisey
- Wellcome Trust Centre for Cell-Matrix Research, Faculty of Life Sciences, University of Manchester, Manchester, United Kingdom
| | - Christoph Ballestrem
- Wellcome Trust Centre for Cell-Matrix Research, Faculty of Life Sciences, University of Manchester, Manchester, United Kingdom
| | - Brian Derby
- School of Materials, Faculty of Engineering and Physical Sciences, Faculty of Life Sciences, University of Manchester, Manchester, United Kingdom.
| |
Collapse
|
5
|
Kim JS, Lee CH, Su BY, Coulombe PA. Mathematical modeling of the impact of actin and keratin filaments on keratinocyte cell spreading. Biophys J 2013. [PMID: 23199911 DOI: 10.1016/j.bpj.2012.09.016] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
Keratin intermediate filaments (IFs) form cross-linked arrays to fulfill their structural support function in epithelial cells and tissues subjected to external stress. How the cross-linking of keratin IFs impacts the morphology and differentiation of keratinocytes in the epidermis and related surface epithelia remains an open question. Experimental measurements have established that keratinocyte spreading area is inversely correlated to the extent of keratin IF bundling in two-dimensional culture. In an effort to quantitatively explain this relationship, we developed a mathematical model in which isotropic cell spreading is considered as a first approximation. Relevant physical properties such as actin protrusion, adhesion events, and the corresponding response of lamellum formation at the cell periphery are included in this model. Through optimization with experimental data that relate time-dependent changes in keratinocyte surface area during spreading, our simulation results confirm the notion that the organization and mechanical properties of cross-linked keratin filaments affect cell spreading; in addition, our results provide details of the kinetics of this effect. These in silico findings provide further support for the notion that differentiation-related changes in the density and intracellular organization of keratin IFs affect tissue architecture in epidermis and related stratified epithelia.
Collapse
Affiliation(s)
- Jin Seob Kim
- Department of Biochemistry and Molecular Biology, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, Maryland, USA.
| | | | | | | |
Collapse
|
6
|
Abstract
Two theoretical models dominate current understanding of actin-based propulsion: microscopic polymerization ratchet model predicts that growing and writhing actin filaments generate forces and movements, while macroscopic elastic propulsion model suggests that deformation and stress of growing actin gel are responsible for the propulsion. We examine both experimentally and computationally the 2D movement of ellipsoidal beads propelled by actin tails and show that neither of the two models can explain the observed bistability of the orientation of the beads. To explain the data, we develop a 2D hybrid mesoscopic model by reconciling these two models such that individual actin filaments undergoing nucleation, elongation, attachment, detachment and capping are embedded into the boundary of a node-spring viscoelastic network representing the macroscopic actin gel. Stochastic simulations of this ‘in silico’ actin network show that the combined effects of the macroscopic elastic deformation and microscopic ratchets can explain the observed bistable orientation of the actin-propelled ellipsoidal beads. To test the theory further, we analyze observed distribution of the curvatures of the trajectories and show that the hybrid model's predictions fit the data. Finally, we demonstrate that the model can explain both concave-up and concave-down force-velocity relations for growing actin networks depending on the characteristic time scale and network recoil. To summarize, we propose that both microscopic polymerization ratchets and macroscopic stresses of the deformable actin network are responsible for the force and movement generation. There are two major ideas about how actin networks generate force against an obstacle: one is that the force comes directly from the elongation and bending of individual actin filaments against the surface of the obstacle; the other is that a growing actin gel can build up stress around the obstacle to squeeze it forward. Neither of the two models can explain why actin-propelled ellipsoidal beads move with equal bias toward long- and short-axes. We propose a hybrid model by combining those two ideas so that individual actin filaments are embedded into the boundary of a deformable actin gel. Simulations of this model show that the combined effects of pushing from individual filaments and squeezing from the actin network explain the observed bi-orientation of ellipsoidal beads as well as the curvature of trajectories of spherical beads and the force-velocity relation of actin networks.
Collapse
Affiliation(s)
| | - Alex Mogilner
- Department of Neurobiology, Physiology and Behavior and Department of Mathematics, University of California, Davis, Davis, California United States of America
- * E-mail:
| |
Collapse
|
7
|
Computational and Modeling Strategies for Cell Motility. COMPUTATIONAL MODELING OF BIOLOGICAL SYSTEMS 2012. [DOI: 10.1007/978-1-4614-2146-7_11] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
|
8
|
Rubinstein B, Fournier MF, Jacobson K, Verkhovsky AB, Mogilner A. Actin-myosin viscoelastic flow in the keratocyte lamellipod. Biophys J 2009; 97:1853-63. [PMID: 19804715 DOI: 10.1016/j.bpj.2009.07.020] [Citation(s) in RCA: 104] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2009] [Revised: 06/25/2009] [Accepted: 07/13/2009] [Indexed: 01/23/2023] Open
Abstract
The lamellipod, the locomotory region of migratory cells, is shaped by the balance of protrusion and contraction. The latter is the result of myosin-generated centripetal flow of the viscoelastic actin network. Recently, quantitative flow data was obtained, yet there is no detailed theory explaining the flow in a realistic geometry. We introduce models of viscoelastic actin mechanics and myosin transport and solve the model equations numerically for the flat, fan-shaped lamellipodial domain of keratocytes. The solutions demonstrate that in the rapidly crawling cell, myosin concentrates at the rear boundary and pulls the actin network inward, so the centripetal actin flow is very slow at the front, and faster at the rear and at the sides. The computed flow and respective traction forces compare well with the experimental data. We also calculate the graded protrusion at the cell boundary necessary to maintain the cell shape and make a number of other testable predictions. We discuss model implications for the cell shape, speed, and bi-stability.
Collapse
Affiliation(s)
- Boris Rubinstein
- Stowers Institute for Medical Research, Kansas City, Missouri, USA
| | | | | | | | | |
Collapse
|