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Malope N, Momoniat E, Herbst RS. The Stochastic Nature Exhibited by Proteins inside the Cell Membrane during Cell-to-Cell Communication. BIOLOGY 2023; 12:1102. [PMID: 37626988 PMCID: PMC10452553 DOI: 10.3390/biology12081102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Revised: 07/23/2023] [Accepted: 07/27/2023] [Indexed: 08/27/2023]
Abstract
The movement of proteins through the cell membrane is essential for cell-to-cell communication, which is a process that allows the body's immune system to identify any foreign cells, such as cells from another organism and pathogens; this movement is also essential for protein-to-protein interactions and protein-to-membrane interactions which play a significant role in drug discovery. This paper presents the stochastic nature exhibited by proteins during cell-to-cell communication. We study the movement of proteins through the cell membrane under the influence of an external force F and drag force with drag coefficient γ. We derive the stochastic diffusion equation, which governs the motion of the proteins; we start by describing the random motion exhibited by the proteins in terms of probability using a one-dimensional lattice model; this occurs when proteins move inside the cell membrane and bind with other proteins inside the cell membrane. We then introduce an external force and a drag coefficient into a Brownian motion description of the movement of proteins when they move outside the cell membrane and bind with proteins from other cells; this phenomenon occurs during cell communication when one cell releases messenger proteins to relay information to other cells. This, in turn, allows us to obtain the stochastic diffusion equation by applying Ito^'s Lemma.
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Affiliation(s)
| | | | - Rhameez Sheldon Herbst
- Department of Pure and Applied Mathematics, University of Johannesburg, Johannesburg 2006, South Africa
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2
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Chai YJ, Cheng CY, Liao YH, Lin CH, Hsieh CL. Heterogeneous nanoscopic lipid diffusion in the live cell membrane and its dependency on cholesterol. Biophys J 2022; 121:3146-3161. [PMID: 35841144 PMCID: PMC9463655 DOI: 10.1016/j.bpj.2022.07.008] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2021] [Revised: 03/08/2022] [Accepted: 07/06/2022] [Indexed: 11/02/2022] Open
Abstract
Cholesterol plays a unique role in the regulation of membrane organization and dynamics by modulating the membrane phase transition at the nanoscale. Unfortunately, due to their small sizes and dynamic nature, the effects of cholesterol-mediated membrane nanodomains on membrane dynamics remain elusive. Here, using ultrahigh-speed single-molecule tracking with advanced optical microscope techniques, we investigate the diffusive motion of single phospholipids in the live cell plasma membrane at the nanoscale and its dependency on the cholesterol concentration. We find that both saturated and unsaturated phospholipids undergo anomalous subdiffusion on the length scale of 10-100 nm. The diffusion characteristics exhibit considerable variations in space and in time, indicating that the nanoscopic lipid diffusion is highly heterogeneous. Importantly, through the statistical analysis, apparent dual-mobility subdiffusion is observed from the mixed diffusion behaviors. The measured subdiffusion agrees well with the hop diffusion model that represents a diffuser moving in a compartmentalized membrane created by the cytoskeleton meshwork. Cholesterol depletion diminishes the lipid mobility with an apparently smaller compartment size and a stronger confinement strength. Similar results are measured with temperature reduction, suggesting that the more heterogeneous and restricted diffusion is connected to the nanoscopic membrane phase transition. Our conclusion supports the model that cholesterol depletion induces the formation of gel-phase, solid-like membrane nanodomains. These nanodomains undergo restricted diffusion and act as diffusion obstacles to the membrane molecules that are excluded from the nanodomains. This work provides the experimental evidence that the nanoscopic lipid diffusion in the cell plasma membrane is heterogeneous and sensitive to the cholesterol concentration and temperature, shedding new light on the regulation mechanisms of nanoscopic membrane dynamics.
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Affiliation(s)
- Yu-Jo Chai
- Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, Taipei, Taiwan
| | - Ching-Ya Cheng
- Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, Taipei, Taiwan
| | - Yi-Hung Liao
- Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, Taipei, Taiwan
| | - Chih-Hsiang Lin
- Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, Taipei, Taiwan
| | - Chia-Lung Hsieh
- Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, Taipei, Taiwan.
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3
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Zarshenas M, Gervilla V, Sangiovanni DG, Sarakinos K. Room-temperature diffusion of metal clusters on graphene. Phys Chem Chem Phys 2021; 23:13087-13094. [PMID: 34059869 DOI: 10.1039/d1cp00522g] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We study the diffusion dynamics, the diffusion mechanisms, and the adsorption energetics of Ag, Au, Cu, and Pd dimers, as well as of Ag trimers on single-layer graphene (SLG) by means of ab initio molecular dynamics (AIMD) simulations and density-functional theory (DFT) calculations. The simulations show that Ag, Cu, and Au clusters exhibit a super-diffusive pattern characterized by long jumps, which can be explained by the flat potential energy landscape (PEL) (corrugation of a few tens of meV) encountered by those clusters on SLG. Pd dimers, instead, diffuse in a pattern that is reminiscent of conventional random walk, which is consistent with a significantly rougher PEL of the order of 100 meV. Moreover, our data show that all clusters exhibit diffusion mechanisms that include both concerted translation and rotation. The overall results of the present study provide key insights for modeling the growth of metal layers and nanostructures on graphene and other van der Waals materials, which is a prerequisite for the directed growth of multifunctional metal contacts in a broad range of enabling devices.
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Affiliation(s)
- Mohammad Zarshenas
- Nanoscale Engineering Division, Department of Physics, Chemistry and Biology, Linköping University, SE-58183, Linköping, Sweden.
| | - Victor Gervilla
- Nanoscale Engineering Division, Department of Physics, Chemistry and Biology, Linköping University, SE-58183, Linköping, Sweden.
| | - Davide G Sangiovanni
- Theoretical Physics Division, Department of Physics, Chemistry and Biology, Linköping University, SE-58183, Linköping, Sweden
| | - Kostas Sarakinos
- Nanoscale Engineering Division, Department of Physics, Chemistry and Biology, Linköping University, SE-58183, Linköping, Sweden.
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4
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Parameter estimation in fluorescence recovery after photobleaching: quantitative analysis of protein binding reactions and diffusion. J Math Biol 2021; 83:1. [PMID: 34129100 PMCID: PMC8205911 DOI: 10.1007/s00285-021-01616-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2019] [Revised: 09/15/2020] [Accepted: 10/27/2020] [Indexed: 02/07/2023]
Abstract
Fluorescence recovery after photobleaching (FRAP) is a common experimental method for investigating rates of molecular redistribution in biological systems. Many mathematical models of FRAP have been developed, the purpose of which is usually the estimation of certain biological parameters such as the diffusivity and chemical reaction rates of a protein, this being accomplished by fitting the model to experimental data. In this article, we consider a two species reaction–diffusion FRAP model. Using asymptotic analysis, we derive new FRAP recovery curve approximation formulae, and formally re-derive existing ones. On the basis of these formulae, invoking the concept of Fisher information, we predict, in terms of biological and experimental parameters, sufficient conditions to ensure that the values all model parameters can be estimated from data. We verify our predictions with extensive computational simulations. We also use computational methods to investigate cases in which some or all biological parameters are theoretically inestimable. In these cases, we propose methods which can be used to extract the maximum possible amount of information from the FRAP data.
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5
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Debets VE, Janssen LMC, Šarić A. Characterising the diffusion of biological nanoparticles on fluid and cross-linked membranes. SOFT MATTER 2020; 16:10628-10639. [PMID: 33084724 DOI: 10.1039/d0sm00712a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Tracing the motion of macromolecules, viruses, and nanoparticles adsorbed onto cell membranes is currently the most direct way of probing the complex dynamic interactions behind vital biological processes, including cell signalling, trafficking, and viral infection. The resulting trajectories are usually consistent with some type of anomalous diffusion, but the molecular origins behind the observed anomalous behaviour are usually not obvious. Here we use coarse-grained molecular dynamics simulations to help identify the physical mechanisms that can give rise to experimentally observed trajectories of nanoscopic objects moving on biological membranes. We find that diffusion on membranes of high fluidities typically results in normal diffusion of the adsorbed nanoparticle, irrespective of the concentration of receptors, receptor clustering, or multivalent interactions between the particle and membrane receptors. Gel-like membranes on the other hand result in anomalous diffusion of the particle, which becomes more pronounced at higher receptor concentrations. This anomalous diffusion is characterised by local particle trapping in the regions of high receptor concentrations and fast hopping between such regions. The normal diffusion is recovered in the limit where the gel membrane is saturated with receptors. We conclude that hindered receptor diffusivity can be a common reason behind the observed anomalous diffusion of viruses, vesicles, and nanoparticles adsorbed on cell and model membranes. Our results enable direct comparison with experiments and offer a new route for interpreting motility experiments on cell membranes.
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Affiliation(s)
- V E Debets
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands.
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6
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Gesper A, Wennmalm S, Hagemann P, Eriksson SG, Happel P, Parmryd I. Variations in Plasma Membrane Topography Can Explain Heterogenous Diffusion Coefficients Obtained by Fluorescence Correlation Spectroscopy. Front Cell Dev Biol 2020; 8:767. [PMID: 32903922 PMCID: PMC7443568 DOI: 10.3389/fcell.2020.00767] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Accepted: 07/21/2020] [Indexed: 01/18/2023] Open
Abstract
Fluorescence correlation spectroscopy (FCS) is frequently used to study diffusion in cell membranes, primarily the plasma membrane. The diffusion coefficients reported in the plasma membrane of the same cell type and even within single cells typically display a large spread. We have investigated whether this spread can be explained by variations in membrane topography throughout the cell surface, that changes the amount of membrane in the FCS focal volume at different locations. Using FCS, we found that diffusion of the membrane dye DiI in the apical plasma membrane was consistently faster above the nucleus than above the cytoplasm. Using live cell scanning ion conductance microscopy (SICM) to obtain a topography map of the cell surface, we demonstrate that cell surface roughness is unevenly distributed with the plasma membrane above the nucleus being the smoothest, suggesting that the difference in diffusion observed in FCS is related to membrane topography. FCS modeled on simulated diffusion in cell surfaces obtained by SICM was consistent with the FCS data from live cells and demonstrated that topography variations can cause the appearance of anomalous diffusion in FCS measurements. Furthermore, we found that variations in the amount of the membrane marker DiD, a proxy for the membrane, but not the transmembrane protein TCRζ or the lipid-anchored protein Lck, in the FCS focal volume were related to variations in diffusion times at different positions in the plasma membrane. This relationship was seen at different positions both at the apical cell and basal cell sides. We conclude that it is crucial to consider variations in topography in the interpretation of FCS results from membranes.
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Affiliation(s)
| | - Stefan Wennmalm
- SciLifeLab, Royal Institute of Technology, Stockholm, Sweden
| | | | | | | | - Ingela Parmryd
- Institute of Biomedicine, University of Gothenburg, Gothenburg, Sweden
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7
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Qin X, Liu L, Lee SK, Alsina A, Liu T, Wu C, Park H, Yu C, Kim H, Chu J, Triller A, Tang BZ, Hyeon C, Park CY, Park H. Increased Confinement and Polydispersity of STIM1 and Orai1 after Ca 2+ Store Depletion. Biophys J 2019; 118:70-84. [PMID: 31818466 DOI: 10.1016/j.bpj.2019.11.019] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2019] [Revised: 11/14/2019] [Accepted: 11/18/2019] [Indexed: 12/18/2022] Open
Abstract
STIM1 (a Ca2+ sensor in the endoplasmic reticulum (ER) membrane) and Orai1 (a pore-forming subunit of the Ca2+-release-activated calcium channel in the plasma membrane) diffuse in the ER membrane and plasma membrane, respectively. Upon depletion of Ca2+ stores in the ER, STIM1 translocates to the ER-plasma membrane junction and binds Orai1 to trigger store-operated Ca2+ entry. However, the motion of STIM1 and Orai1 during this process and its roles to Ca2+ entry is poorly understood. Here, we report real-time tracking of single STIM1 and Orai1 particles in the ER membrane and plasma membrane in living cells before and after Ca2+ store depletion. We found that the motion of single STIM1 and Orai1 particles exhibits anomalous diffusion both before and after store depletion, and their mobility-measured by the radius of gyration of the trajectories, mean-square displacement, and generalized diffusion coefficient-decreases drastically after store depletion. We also found that the measured displacement distribution is non-Gaussian, and the non-Gaussian parameter drastically increases after store depletion. Detailed analyses and simulations revealed that single STIM1 and Orai1 particles are confined in the compartmentalized membrane both before and after store depletion, and the changes in the motion after store depletion are explained by increased confinement and polydispersity of STIM1-Orai1 complexes formed at the ER-plasma membrane junctions. Further simulations showed that this increase in the confinement and polydispersity after store depletion localizes a rapid increase of Ca2+ influx, which can facilitate the rapid activation of local Ca2+ signaling pathways and the efficient replenishing of Ca2+ store in the ER in store-operated Ca2+ entry.
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Affiliation(s)
- Xianan Qin
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Lei Liu
- School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Korea
| | - Sang Kwon Lee
- Department of Biological Sciences, School of Life Sciences, Ulsan National Institute of Science and Technology, Ulsan, Korea
| | - Adolfo Alsina
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong; Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
| | - Teng Liu
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | | | - Hojeong Park
- Division of Biomedical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | | | - Hajin Kim
- Department of Biomedical Engineering and Department of Physics, Ulsan National Institute of Science and Technology, Ulsan, Korea
| | - Jun Chu
- Research Lab for Biomedical Optics and Molecular Imaging, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
| | - Antoine Triller
- Biologie Cellulaire de la Synapse N&P, IBENS, Institut de Biologie de L'ENS, Ecole Normale Supérieure, Paris, France
| | - Ben Zhong Tang
- Division of Biomedical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong; Department of Chemistry, Kowloon, Hong Kong, China, Kowloon, Hong Kong, China
| | - Changbong Hyeon
- School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Korea.
| | - Chan Young Park
- Department of Biological Sciences, School of Life Sciences, Ulsan National Institute of Science and Technology, Ulsan, Korea.
| | - Hyokeun Park
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong; Division of Life Science; State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China.
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8
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Chew WX, Kaizu K, Watabe M, Muniandy SV, Takahashi K, Arjunan SNV. Surface reaction-diffusion kinetics on lattice at the microscopic scale. Phys Rev E 2019; 99:042411. [PMID: 31108654 DOI: 10.1103/physreve.99.042411] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2018] [Indexed: 01/06/2023]
Abstract
Microscopic models of reaction-diffusion processes on the cell membrane can link local spatiotemporal effects to macroscopic self-organized patterns often observed on the membrane. Simulation schemes based on the microscopic lattice method (MLM) can model these processes at the microscopic scale by tracking individual molecules, represented as hard spheres, on fine lattice voxels. Although MLM is simple to implement and is generally less computationally demanding than off-lattice approaches, its accuracy and consistency in modeling surface reactions have not been fully verified. Using the Spatiocyte scheme, we study the accuracy of MLM in diffusion-influenced surface reactions. We derive the lattice-based bimolecular association rates for two-dimensional (2D) surface-surface reaction and one-dimensional (1D) volume-surface adsorption according to the Smoluchowski-Collins-Kimball model and random walk theory. We match the time-dependent rates on lattice with off-lattice counterparts to obtain the correct expressions for MLM parameters in terms of physical constants. The expressions indicate that the voxel size needs to be at least 0.6% larger than the molecule to accurately simulate surface reactions on triangular lattice. On square lattice, the minimum voxel size should be even larger, at 5%. We also demonstrate the ability of MLM-based schemes such as Spatiocyte to simulate a reaction-diffusion model that involves all dimensions: three-dimensional (3D) diffusion in the cytoplasm, 2D diffusion on the cell membrane, and 1D cytoplasm-membrane adsorption. With the model, we examine the contribution of the 2D reaction pathway to the overall reaction rate at different reactant diffusivity, reactivity, and concentrations.
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Affiliation(s)
- Wei-Xiang Chew
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan.,Department of Physics, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia
| | - Kazunari Kaizu
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan
| | - Masaki Watabe
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan
| | - Sithi V Muniandy
- Department of Physics, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia
| | - Koichi Takahashi
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan
| | - Satya N V Arjunan
- Laboratory for Biologically Inspired Computing, RIKEN Center for Biosystems Dynamics Research, Suita, Osaka, Japan
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9
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Johnston ST, Crampin EJ. Corrected pair correlation functions for environments with obstacles. Phys Rev E 2019; 99:032124. [PMID: 30999485 DOI: 10.1103/physreve.99.032124] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2018] [Indexed: 01/30/2023]
Abstract
Environments with immobile obstacles or void regions that inhibit and alter the motion of individuals within that environment are ubiquitous. Correlation in the location of individuals within such environments arises as a combination of the mechanisms governing individual behavior and the heterogeneous structure of the environment. Measures of spatial structure and correlation have been successfully implemented to elucidate the roles of the mechanisms underpinning the behavior of individuals. In particular, the pair correlation function has been used across biology, ecology, and physics to obtain quantitative insight into a variety of processes. However, naively applying standard pair correlation functions in the presence of obstacles may fail to detect correlation, or suggest false correlations, due to a reliance on a distance metric that does not account for obstacles. To overcome this problem, here we present an analytic expression for calculating a corrected pair correlation function for lattice-based domains containing obstacles. We demonstrate that this obstacle pair correlation function is necessary for isolating the correlation associated with the behavior of individuals, rather than the structure of the environment. Using simulations that mimic cell migration and proliferation we demonstrate that the obstacle pair correlation function recovers the short-range correlation known to be present in this process, independent of the heterogeneous structure of the environment. Further, we show that the analytic calculation of the obstacle pair correlation function derived here is significantly faster to implement than the corresponding numerical approach.
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Affiliation(s)
- Stuart T Johnston
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Parkville, Victoria 3010, Australia.,ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Melbourne School of Engineering, University of Melbourne, Parkville, Victoria 3010, Australia
| | - Edmund J Crampin
- Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, University of Melbourne, Parkville, Victoria 3010, Australia.,ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Melbourne School of Engineering, University of Melbourne, Parkville, Victoria 3010, Australia.,School of Medicine, Faculty of Medicine Dentistry and Health Sciences, University of Melbourne, Parkville, Victoria 3010, Australia
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10
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Adler J, Sintorn IM, Strand R, Parmryd I. Conventional analysis of movement on non-flat surfaces like the plasma membrane makes Brownian motion appear anomalous. Commun Biol 2019; 2:12. [PMID: 30652124 PMCID: PMC6325064 DOI: 10.1038/s42003-018-0240-2] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2018] [Accepted: 11/26/2018] [Indexed: 01/09/2023] Open
Abstract
Cells are neither flat nor smooth, which has serious implications for prevailing plasma membrane models and cellular processes like cell signalling, adhesion and molecular clustering. Using probability distributions from diffusion simulations, we demonstrate that 2D and 3D Euclidean distance measurements substantially underestimate diffusion on non-flat surfaces. Intuitively, the shortest within surface distance (SWSD), the geodesic distance, should reduce this problem. The SWSD is accurate for foldable surfaces but, although it outperforms 2D and 3D Euclidean measurements, it still underestimates movement on deformed surfaces. We demonstrate that the reason behind the underestimation is that topographical features themselves can produce both super- and subdiffusion, i.e. the appearance of anomalous diffusion. Differentiating between topography-induced and genuine anomalous diffusion requires characterising the surface by simulating Brownian motion on high-resolution cell surface images and a comparison with the experimental data.
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Affiliation(s)
- Jeremy Adler
- Science for Life Laboratory, Medical Cell Biology, Uppsala University, Uppsala University, Box 571, 751 21 Uppsala, Sweden
| | - Ida-Maria Sintorn
- Department of Information Technology, Uppsala University, Box 331, 751 05 Uppsala, Sweden
| | - Robin Strand
- Department of Information Technology, Uppsala University, Box 331, 751 05 Uppsala, Sweden
| | - Ingela Parmryd
- Science for Life Laboratory, Medical Cell Biology, Uppsala University, Uppsala University, Box 571, 751 21 Uppsala, Sweden
- Institute of Biomedicine, The Sahlgrenska Academy, University of Gothenburg, 405 30 Gothenburg, Sweden
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11
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Smith S, Cianci C, Grima R. Macromolecular crowding directs the motion of small molecules inside cells. J R Soc Interface 2018; 14:rsif.2017.0047. [PMID: 28615492 PMCID: PMC5493789 DOI: 10.1098/rsif.2017.0047] [Citation(s) in RCA: 40] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2017] [Accepted: 05/18/2017] [Indexed: 11/12/2022] Open
Abstract
It is now well established that cell interiors are significantly crowded by macromolecules, which impede diffusion and enhance binding rates. However, it is not fully appreciated that levels of crowding are heterogeneous, and can vary substantially between subcellular regions. In this article, starting from a microscopic model, we derive coupled nonlinear partial differential equations for the concentrations of two populations of large and small spherical particles with steric volume exclusion. By performing an expansion in the ratio of the particle sizes, we find that the diffusion of a small particle in the presence of large particles obeys an advection–diffusion equation, with a reduced diffusion coefficient and a velocity directed towards less crowded regions. The interplay between advection and diffusion leads to behaviour that differs significantly from Brownian diffusion. We show that biologically plausible distributions of macromolecules can lead to highly non-Gaussian probability densities for the small particle position, including asymmetrical and multimodal densities. We confirm all our results using hard-sphere Brownian dynamics simulations.
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Affiliation(s)
- Stephen Smith
- School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JR, UK
| | - Claudia Cianci
- School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JR, UK
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JR, UK
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12
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Gupta R. Self-crowding of AMPA receptors in the excitatory postsynaptic density can effectuate anomalous receptor sub-diffusion. PLoS Comput Biol 2018; 14:e1005984. [PMID: 29444074 PMCID: PMC5812565 DOI: 10.1371/journal.pcbi.1005984] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2017] [Accepted: 01/15/2018] [Indexed: 12/03/2022] Open
Abstract
AMPA receptors (AMPARs) and their associations with auxiliary transmembrane proteins are bulky structures with large steric-exclusion volumes. Hence, self-crowding of AMPARs, depending on the local density, may affect their lateral diffusion in the postsynaptic membrane as well as in the highly crowded postsynaptic density (PSD) at excitatory synapses. Earlier theoretical studies considered only the roles of transmembrane obstacles and the AMPAR-binding submembranous scaffold proteins in shaping receptor diffusion within PSD. Using lattice model of diffusion, the present study investigates the additional impacts of self-crowding on the anomalousity and effective diffusion coefficient (Deff) of AMPAR diffusion. A recursive algorithm for avoiding false self-blocking during diffusion simulation is also proposed. The findings suggest that high density of AMPARs in the obstacle-free membrane itself engenders strongly anomalous diffusion and severe decline in Deff. Adding transmembrane obstacles to the membrane accentuates the anomalousity arising from self-crowding due to the reduced free diffusion space. Contrarily, enhanced AMPAR-scaffold binding, either through increase in binding strength or scaffold density or both, ameliorates the anomalousity resulting from self-crowding. However, binding has differential impacts on Deff depending on the receptor density. Increase in binding causes consistent decrease in Deff for low and moderate receptor density. For high density, binding increases Deff as long as it reduces anomalousity associated with intense self-crowding. Given a sufficiently strong binding condition when diffusion acquires normal behavior, further increase in binding causes decrease in Deff. Supporting earlier experimental observations are mentioned and implications of present findings to the experimental observations on AMPAR diffusion are also drawn. The transmembrane AMPA receptors (AMPARs) prominently exhibit lateral diffusion in the postsynaptic membrane at excitatory synapses. Steric obstructions to AMPAR diffusion due to the crowd of other relatively static transmembrane proteins and binding of AMPARs to the submembranous scaffold proteins in the specialized region of postsynaptic density (PSD) are well known to retard receptor diffusion, which causes receptor trapping and accumulation within PSD. However, AMPARs are significantly bulky structures and may also obstruct their own diffusion paths in the presence of their high density. It is shown here that intense self-crowding of AMPARs may lead to highly obstructed and confined receptor diffusion even in the obstacle-free medium, and the presence of other obstacles further aggravates this effect. AMPAR-scaffold binding reduces confined diffusion arising from self-crowding and strong binding engenders normal diffusion even at high receptor density. However, it overall causes reduction in the effective diffusion coefficient of the receptor diffusion.
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Affiliation(s)
- Rahul Gupta
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, India
- * E-mail:
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13
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Azimzade Y, Mashaghi A. Search efficiency of biased migration towards stationary or moving targets in heterogeneously structured environments. Phys Rev E 2018; 96:062415. [PMID: 29347391 DOI: 10.1103/physreve.96.062415] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Indexed: 01/27/2023]
Abstract
Efficient search acts as a strong selective force in biological systems ranging from cellular populations to predator-prey systems. The search processes commonly involve finding a stationary or mobile target within a heterogeneously structured environment where obstacles limit migration. An open generic question is whether random or directionally biased motions or a combination of both provide an optimal search efficiency and how that depends on the motility and density of targets and obstacles. To address this question, we develop a simple model that involves a random walker searching for its targets in a heterogeneous medium of bond percolation square lattice and used mean first passage time (〈T〉) as an indication of average search time. Our analysis reveals a dual effect of directional bias on the minimum value of 〈T〉. For a homogeneous medium, directionality always decreases 〈T〉 and a pure directional migration (a ballistic motion) serves as the optimized strategy, while for a heterogeneous environment, we find that the optimized strategy involves a combination of directed and random migrations. The relative contribution of these modes is determined by the density of obstacles and motility of targets. Existence of randomness and motility of targets add to the efficiency of search. Our study reveals generic and simple rules that govern search efficiency. Our findings might find application in a number of areas including immunology, cell biology, ecology, and robotics.
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Affiliation(s)
- Youness Azimzade
- Department of Physics, University of Tehran, Tehran 14395-547, Iran.,Leiden Academic Centre for Drug Research, Faculty of Mathematics and Natural Sciences, Leiden University, Leiden 2300 RA, The Netherlands
| | - Alireza Mashaghi
- Leiden Academic Centre for Drug Research, Faculty of Mathematics and Natural Sciences, Leiden University, Leiden 2300 RA, The Netherlands
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14
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Stefferson MW, Norris SL, Vernerey FJ, Betterton MD, Hough LE. Effects of soft interactions and bound mobility on diffusion in crowded environments: a model of sticky and slippery obstacles. Phys Biol 2017; 14:045008. [PMID: 28597848 DOI: 10.1088/1478-3975/aa7869] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Crowded environments modify the diffusion of macromolecules, generally slowing their movement and inducing transient anomalous subdiffusion. The presence of obstacles also modifies the kinetics and equilibrium behavior of tracers. While previous theoretical studies of particle diffusion have typically assumed either impenetrable obstacles or binding interactions that immobilize the particle, in many cellular contexts bound particles remain mobile. Examples include membrane proteins or lipids with some entry and diffusion within lipid domains and proteins that can enter into membraneless organelles or compartments such as the nucleolus. Using a lattice model, we studied the diffusive movement of tracer particles which bind to soft obstacles, allowing tracers and obstacles to occupy the same lattice site. For sticky obstacles, bound tracer particles are immobile, while for slippery obstacles, bound tracers can hop without penalty to adjacent obstacles. In both models, binding significantly alters tracer motion. The type and degree of motion while bound is a key determinant of the tracer mobility: slippery obstacles can allow nearly unhindered diffusion, even at high obstacle filling fraction. To mimic compartmentalization in a cell, we examined how obstacle size and a range of bound diffusion coefficients affect tracer dynamics. The behavior of the model is similar in two and three spatial dimensions. Our work has implications for protein movement and interactions within cells.
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Affiliation(s)
- Michael W Stefferson
- Department of Physics, University of Colorado, Boulder, United States of America
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15
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Zhokh A, Strizhak P. Non-Fickian diffusion of methanol in mesoporous media: Geometrical restrictions or adsorption-induced? J Chem Phys 2017; 146:124704. [PMID: 28388159 DOI: 10.1063/1.4978944] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The methanol mass transfer in the mesoporous silica and alumina/zeolite H-ZSM-5 grains has been studied. We demonstrate that the methanol diffusion is characterized as a time-fractional for both solids. Methanol transport occurs in the super-diffusive regime, which is faster comparing to the Fickian diffusion. We show that the fractional exponents defining the regime of transport are different for each porous grain. The difference between the values of the fractional exponents is associated with a difference in the energetic strength of the active sites of the surface of the media of different chemical nature as well as the geometrical restrictions of the porous media. Increasing by six-fold, the pore diameter leads to a 1.1 fold increase of the fractional exponent. Decreasing by three-fold, the methanol desorption energy results into the same increasing the fractional exponent. Our findings support that mainly the adsorption process, which is defined by the energetic disorder of the corresponding surface active sites, is likely to be the driving force of the abnormality of the mass transfer in the porous media. Therefore, the fractional exponent is a fundamental characteristic which is individual for each combination of the porous solid and diffusing species.
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Affiliation(s)
- Alexey Zhokh
- L.V. Pisarzhevsky Institute of Physical Chemistry, National Academy of Sciences of Ukraine, Prospect Nauki, 31, Kiev 03028, Ukraine
| | - Peter Strizhak
- L.V. Pisarzhevsky Institute of Physical Chemistry, National Academy of Sciences of Ukraine, Prospect Nauki, 31, Kiev 03028, Ukraine
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16
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Nandigrami P, Grove B, Konya A, Selinger RLB. Gradient-driven diffusion and pattern formation in crowded mixtures. Phys Rev E 2017; 95:022107. [PMID: 28297895 DOI: 10.1103/physreve.95.022107] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2016] [Indexed: 11/07/2022]
Abstract
Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion affects microstructure, which in turn affects diffusivity; a key question is how this complex coupling controls both transport and pattern formation. To examine these mechanisms, we study a two-dimensional multicomponent lattice gas model, where "tracer" molecules diffuse between a source and a sink separated by a solution of sticky "crowder" molecules that cluster to form dynamically evolving obstacles. In the high-temperature limit, crowders and tracers are miscible, and transport may be predicted analytically. At intermediate temperatures, crowders phase separate into clusters that drift toward the tracer sink. As a result, steady-state tracer diffusivity depends nonmonotonically on both temperature and crowder density, and we observe a variety of complex microstructures. In the low-temperature limit, crowders rapidly aggregate to form obstacles that are kinetically arrested; if crowder density is near the percolation threshold, resulting tracer diffusivity shows scaling behavior with the same scaling exponent as the random resistor network model. Though highly idealized, this simple model reveals fundamental mechanisms governing coupled gradient-driven diffusion, phase separation, and microstructural evolution in crowded mixtures.
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Affiliation(s)
| | - Brandy Grove
- Department of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, Ohio 44106, USA
| | - Andrew Konya
- Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA
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17
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Li L, Xu GK, Song F. Impact of lipid rafts on the T-cell-receptor and peptide-major-histocompatibility-complex interactions under different measurement conditions. Phys Rev E 2017; 95:012403. [PMID: 28208397 DOI: 10.1103/physreve.95.012403] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2016] [Indexed: 01/02/2023]
Abstract
The interactions between T-cell receptor (TCR) and peptide-major-histocompatibility complex (pMHC), which enable T-cell development and initiate adaptive immune responses, have been intensively studied. However, a central issue of how lipid rafts affect the TCR-pMHC interactions remains unclear. Here, by using a statistical-mechanical membrane model, we show that the binding affinity of TCR and pMHC anchored on two apposing cell membranes is significantly enhanced because of the lipid raft-induced signaling protein aggregation. This finding may provide an alternative insight into the mechanism of T-cell activation triggered by very low densities of pMHC. In the case of cell-substrate adhesion, our results indicate that the loss of lateral mobility of the proteins on the solid substrate leads to the inhibitory effect of lipid rafts on TCR-pMHC interactions. Our findings help to understand why different experimental methods for measuring the impact of lipid rafts on the receptor-ligand interactions have led to contradictory conclusions.
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Affiliation(s)
- Long Li
- State Key Laboratory of Nonlinear Mechanics (LNM) and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Guang-Kui Xu
- International Center for Applied Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Fan Song
- State Key Laboratory of Nonlinear Mechanics (LNM) and Beijing Key Laboratory of Engineered Construction and Mechanobiology, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China.,School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China
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18
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Lenzi EK, Ribeiro HV, Tateishi AA, Zola RS, Evangelista LR. Anomalous diffusion and transport in heterogeneous systems separated by a membrane. Proc Math Phys Eng Sci 2016; 472:20160502. [PMID: 27956877 DOI: 10.1098/rspa.2016.0502] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Diffusion of particles in a heterogeneous system separated by a semipermeable membrane is investigated. The particle dynamics is governed by fractional diffusion equations in the bulk and by kinetic equations on the membrane, which characterizes an interface between two different media. The kinetic equations are solved by incorporating memory effects to account for anomalous diffusion and, consequently, non-Debye relaxations. A rich variety of behaviours for the particle distribution at the interface and in the bulk may be found, depending on the choice of characteristic times in the boundary conditions and on the fractional index of the modelling equations.
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Affiliation(s)
- E K Lenzi
- Departamento de Física , Universidade Estadual de Ponta Grossa , Ponta Grossa, Paraná 87030-900, Brazil
| | - H V Ribeiro
- Departamento de Física , Universidade Estadual de Maringá , Maringá, Paraná 87020-900, Brazil
| | - A A Tateishi
- Departamento de Física , Universidade Tecnológica Federal do Paraná , Pato Branco, Paraná 85503-390, Brazil
| | - R S Zola
- Departamento de Física, Universidade Estadual de Maringá, Maringá, Paraná 87020-900, Brazil; Departamento de Física, Universidade Tecnológica Federal do Paraná, Apucarana, Paraná 86812-460, Brazil
| | - L R Evangelista
- Departamento de Física , Universidade Estadual de Maringá , Maringá, Paraná 87020-900, Brazil
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19
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Ellery AJ, Baker RE, Simpson MJ. An analytical method for disentangling the roles of adhesion and crowding for random walk models on a crowded lattice. Phys Biol 2016; 13:05LT02. [PMID: 27597573 DOI: 10.1088/1478-3975/13/5/05lt02] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Migration of cells and molecules in vivo is affected by interactions with obstacles. These interactions can include crowding effects, as well as adhesion/repulsion between the motile cell/molecule and the obstacles. Here we present an analytical framework that can be used to separately quantify the roles of crowding and adhesion/repulsion using a lattice-based random walk model. Our method leads to an exact calculation of the long time Fickian diffusivity, and avoids the need for computationally expensive stochastic simulations.
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Affiliation(s)
- Adam J Ellery
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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20
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Poger D, Caron B, Mark AE. Validating lipid force fields against experimental data: Progress, challenges and perspectives. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2016; 1858:1556-65. [DOI: 10.1016/j.bbamem.2016.01.029] [Citation(s) in RCA: 51] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2015] [Revised: 01/07/2016] [Accepted: 01/27/2016] [Indexed: 01/16/2023]
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Abstract
SUMMARYIt is estimated that allergies afflict up to 40% of the world's population. A primary mediator for allergies is the aggregation of antigens and IgE antibodies bound to cell-surface receptors, FcεRI. Antibody/antigen aggregate formation causes stimulation of mast cells and basophils, initiating cellular degranulation and releasing immune mediators which produce an allergic or anaphylactic response. Understanding the shape and structure of these aggregates can provide critical insights into the allergic response. We have previously developed methods to geometrically model, simulate and analyze antibody aggregation inspired by rigid body robotic motion simulations. Our technique handles the large size and number of molecules involved in aggregation, providing an advantage over traditional simulations such as molecular dynamics (MD) and coarse-grained energetic models. In this paper, we study the impact of model resolution on simulations of geometric structures using both our previously developed Monte Carlo simulation and a novel application of rule-based modeling. These methods complement each other, the former providing explicit geometric detail and the latter providing a generic representation where multiple resolutions can be captured. Our exploration is focused on two antigens, a man-made antigen with three binding sites, DF3, and a common shrimp allergen (antigen), Pen a 1. We find that impact of resolution is minimal for DF3, a small globular antigen, but has a larger impact on Pen a 1, a rod-shaped molecule. The volume reduction caused by the loss in resolution allows more binding site accessibility, which can be quantified using a rule-based model with implicit geometric input. Clustering analysis of our simulation shows good correlation when compared with available experimental results. Moreover, collisions in all-atom reconstructions are negligible, at around 0.2% at 90% reduction.
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22
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Ellery AJ, Baker RE, Simpson MJ. Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice. J Chem Phys 2016; 144:171104. [DOI: 10.1063/1.4948782] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Adam J. Ellery
- School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia
| | - Ruth E. Baker
- Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, United Kingdom
| | - Matthew J. Simpson
- School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia
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23
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Li H, Zhang Y, Ha V, Lykotrafitis G. Modeling of band-3 protein diffusion in the normal and defective red blood cell membrane. SOFT MATTER 2016; 12:3643-3653. [PMID: 26977476 DOI: 10.1039/c4sm02201g] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We employ a two-component red blood cell (RBC) membrane model to simulate lateral diffusion of band-3 proteins in the normal RBC and in the RBC with defective membrane proteins. The defects reduce the connectivity between the lipid bilayer and the membrane skeleton (vertical connectivity), or the connectivity of the membrane skeleton itself (horizontal connectivity), and are associated with the blood disorders of hereditary spherocytosis (HS) and hereditary elliptocytosis (HE) respectively. Initially, we demonstrate that the cytoskeleton limits band-3 lateral mobility by measuring the band-3 macroscopic diffusion coefficients in the normal RBC membrane and in a lipid bilayer without the cytoskeleton. Then, we study band-3 diffusion in the defective RBC membrane and quantify the relation between band-3 diffusion coefficients and percentage of protein defects in HE RBCs. In addition, we illustrate that at low spectrin network connectivity (horizontal connectivity) band-3 subdiffusion can be approximated as anomalous diffusion, while at high horizontal connectivity band-3 diffusion is characterized as confined diffusion. Our simulations show that the band-3 anomalous diffusion exponent depends on the percentage of protein defects in the membrane cytoskeleton. We also confirm that the introduction of attraction between the lipid bilayer and the spectrin network reduces band-3 diffusion, but we show that this reduction is lower than predicted by the percolation theory. Furthermore, we predict that the attractive force between the spectrin filament and the lipid bilayer is at least 20 times smaller than the binding forces at band-3 and glycophorin C, the two major membrane binding sites. Finally, we explore diffusion of band-3 particles in the RBC membrane with defects related to vertical connectivity. We demonstrate that in this case band-3 diffusion can be approximated as confined diffusion for all attraction levels between the spectrin network and the lipid bilayer. By comparing the diffusion coefficients measured in horizontal vs. vertical defects, we conclude that band-3 mobility is primarily controlled by the horizontal connectivity.
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Affiliation(s)
- He Li
- Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
| | - Yihao Zhang
- Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road, Unit 3139, Storrs, CT 06269-3139, USA.
| | - Vi Ha
- Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road, Unit 3139, Storrs, CT 06269-3139, USA.
| | - George Lykotrafitis
- Department of Mechanical Engineering, University of Connecticut, 191 Auditorium Road, Unit 3139, Storrs, CT 06269-3139, USA. and Department of Biomedical Engineering, University of Connecticut, Storrs, CT 06269, USA
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24
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Santos G, Díaz M, Torres NV. Lipid Raft Size and Lipid Mobility in Non-raft Domains Increase during Aging and Are Exacerbated in APP/PS1 Mice Model of Alzheimer's Disease. Predictions from an Agent-Based Mathematical Model. Front Physiol 2016; 7:90. [PMID: 27014089 PMCID: PMC4791387 DOI: 10.3389/fphys.2016.00090] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2015] [Accepted: 02/25/2016] [Indexed: 12/13/2022] Open
Abstract
A connection between lipid rafts and Alzheimer's disease has been studied during the last decades. Mathematical modeling approaches have recently been used to correlate the effects of lipid composition changes in the physicochemical properties of raft-like membranes. Here we propose an agent based model to assess the effect of lipid changes in lipid rafts on the evolution and progression of Alzheimer's disease using lipid profile data obtained in an established model of familial Alzheimer's disease. We have observed that lipid raft size and lipid mobility in non-raft domains are two main factors that increase during age and are accelerated in the transgenic Alzheimer's disease mouse model. The consequences of these changes are discussed in the context of neurotoxic amyloid β production. Our agent based model predicts that increasing sterols (mainly cholesterol) and long-chain polyunsaturated fatty acids (LCPUFA) (mainly DHA, docosahexaenoic acid) proportions in the membrane composition might delay the onset and progression of the disease.
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Affiliation(s)
- Guido Santos
- Systems Biology and Mathematical Modelling Group, Departamento de Bioquímica, Microbiología, Biología Celular y Genética, Instituto de Tecnologías Biomédicas, CIBICAN, Universidad de La Laguna San Cristóbal de La Laguna, Spain
| | - Mario Díaz
- Laboratorio de Fisiología y Biofísica de Membranas, Departamento de Biología Animal y Edafología y Geología, Facultad de Ciencias, Unidad Asociada de Investigación ULL-CSIC, Universidad de La Laguna San Cristóbal de La Laguna, Spain
| | - Néstor V Torres
- Systems Biology and Mathematical Modelling Group, Departamento de Bioquímica, Microbiología, Biología Celular y Genética, Instituto de Tecnologías Biomédicas, CIBICAN, Universidad de La Laguna San Cristóbal de La Laguna, Spain
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25
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Xiao F, Hrabe J, Hrabetova S. Anomalous extracellular diffusion in rat cerebellum. Biophys J 2016; 108:2384-95. [PMID: 25954895 DOI: 10.1016/j.bpj.2015.02.034] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2014] [Revised: 02/05/2015] [Accepted: 02/25/2015] [Indexed: 12/31/2022] Open
Abstract
Extracellular space (ECS) is a major channel transporting biologically active molecules and drugs in the brain. Diffusion-mediated transport of these substances is hindered by the ECS structure but the microscopic basis of this hindrance is not fully understood. One hypothesis proposes that the hindrance originates in large part from the presence of dead-space (DS) microdomains that can transiently retain diffusing molecules. Because previous theoretical and modeling work reported an initial period of anomalous diffusion in similar environments, we expected that brain regions densely populated by DS microdomains would exhibit anomalous extracellular diffusion. Specifically, we targeted granular layers (GL) of rat and turtle cerebella that are populated with large and geometrically complex glomeruli. The integrative optical imaging (IOI) method was employed to evaluate diffusion of fluorophore-labeled dextran (MW 3000) in GL, and the IOI data analysis was adapted to quantify the anomalous diffusion exponent dw from the IOI records. Diffusion was significantly anomalous in rat GL, where dw reached 4.8. In the geometrically simpler turtle GL, dw was elevated but not robustly anomalous (dw = 2.6). The experimental work was complemented by numerical Monte Carlo simulations of anomalous ECS diffusion in several three-dimensional tissue models containing glomeruli-like structures. It demonstrated that both the duration of transiently anomalous diffusion and the anomalous exponent depend on the size of model glomeruli and the degree of their wrapping. In conclusion, we have found anomalous extracellular diffusion in the GL of rat cerebellum. This finding lends support to the DS microdomain hypothesis. Transiently anomalous diffusion also has a profound effect on the spatiotemporal distribution of molecules released into the ECS, especially at diffusion distances on the order of a few cell diameters, speeding up short-range diffusion-mediated signals in less permeable structures.
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Affiliation(s)
- Fanrong Xiao
- Department of Cell Biology, State University of New York, Downstate Medical Center, Brooklyn, New York
| | - Jan Hrabe
- Department of Cell Biology, State University of New York, Downstate Medical Center, Brooklyn, New York; Medical Physics Laboratory, Nathan S. Kline Institute, Orangeburg, New York
| | - Sabina Hrabetova
- Department of Cell Biology, State University of New York, Downstate Medical Center, Brooklyn, New York; The Robert F. Furchgott Center for Neural and Behavioral Science, State University of New York Downstate Medical Center, Brooklyn, New York.
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26
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Seeliger C, Le Novère N. Enabling surface dependent diffusion in spatial simulations using Smoldyn. BMC Res Notes 2015; 8:752. [PMID: 26647064 PMCID: PMC4673859 DOI: 10.1186/s13104-015-1723-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2015] [Accepted: 11/19/2015] [Indexed: 11/30/2022] Open
Abstract
Background Spatial computer simulations are becoming more feasible and relevant for studies of signaling pathways due to technical advances in experimental techniques yielding better high resolution data. However, many common single particle simulation
environments used in computational systems biology lack the functionality to easily implement spatially heterogeneous membrane environments. Results We introduce an extension to
the single particle simulator Smoldyn that allows modeling of surface-dependent diffusion, without unnecessarily increasing molecular states or numbers, hence avoiding explosion of molecule and reaction definitions. Conclusions We demonstrate the usefulness of this approach studying AMPA receptor diffusion at the postsynaptic density and its spatial trapping without introducing hypothetical scaffold elements or membrane barriers. Electronic supplementary material The online version of this article (doi:10.1186/s13104-015-1723-6) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Christine Seeliger
- European Bioinformatics Institute, Wellcome Trust Genome Campus, Cambridge, CB10 1SD, UK.
| | - Nicolas Le Novère
- European Bioinformatics Institute, Wellcome Trust Genome Campus, Cambridge, CB10 1SD, UK. .,The Babraham Institute, Babraham Research Campus, Babraham, CB22 3AT, UK.
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27
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Poger D, Mark AE. Effect of Ring Size in ω-Alicyclic Fatty Acids on the Structural and Dynamical Properties Associated with Fluidity in Lipid Bilayers. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:11574-11582. [PMID: 26444798 DOI: 10.1021/acs.langmuir.5b02635] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Fatty acids containing a terminal cyclic group such as cyclohexyl and cycloheptyl are commonly found in prokaryotic membranes, especially in those of thermo-acidophilic bacteria. These so-called ω-alicyclic fatty acids have been proposed to stabilize the membranes of bacteria by reducing the fluidity in membranes and increasing lipid packing and lipid chain order. In this article, molecular dynamics simulations are used to examine the effect of 3- to 7-membered cycloalkyl saturated and unsaturated (cyclopent-2-enyl and phenyl) rings in ω-alicyclic fatty acyl chains on the structure (lipid packing, lipid chain order, and fraction of gauche defects in the chains) and dynamics (lateral lipid diffusion) of a model lipid bilayer. It was found that ω-alicyclic chains in which the ring was saturated reduced lipid condensation and lowered chain order which would be associated with enhanced fluidity. However, this effect was limited. The lateral diffusion of the lipids diminished as the ring size increased. In particular, ω-cyclohexyl and ω-cycloheptyl acyl tails led to a decrease in lipid diffusion. In contrast, ω-alicyclic acyl chains that contain an unsaturated ring promoted membrane fluidity both in terms of changes in membrane structure and lipid diffusion. This may indicate that saturated and unsaturated terminal rings in ω-alicyclic fatty acids fulfill alternative functions within membranes. Overall, the simulations suggest that ω-alicyclic fatty acids in which the terminal ring is saturated might protect the membrane of thermo-acidophilic bacteria from high-temperature and low-pH conditions through a "dynamical barrier" that would limit lipid diffusion and transmembrane diffusion of undesired ions and molecules.
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Affiliation(s)
- David Poger
- School of Chemistry and Molecular Biosciences, The University of Queensland , Brisbane QLD 4072, Australia
| | - Alan E Mark
- School of Chemistry and Molecular Biosciences, The University of Queensland , Brisbane QLD 4072, Australia
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28
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Hasnain S, Bandyopadhyay P. An analytical correlated random walk model and its application to understand subdiffusion in crowded environment. J Chem Phys 2015; 143:114104. [PMID: 26395684 DOI: 10.1063/1.4930275] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Subdiffusion in crowded environment such as movement of macromolecule in a living cell has often been observed experimentally. The primary reason for subdiffusion is volume exclusion by the crowder molecules. However, other effects such as hydrodynamic interaction may also play an important role. Although there are a large number of computer simulation studies on understanding molecular crowding, there is a lack of theoretical models that can be connected to both experiment and simulation. In the current work, we have formulated a one-dimensional correlated random walk model by connecting this to the motion in a crowded environment. We have found the exact solution of the probability distribution function of the model by solving it analytically. The parameters of our model can be obtained either from simulation or experiment. It has been shown that this analytical model captures some of the general features of diffusion in crowded environment as given in the previous literature and its prediction for transient subdiffusion closely matches the observations of a previous study of computer simulation of Escherichia coli cytoplasm. It is likely that this model will open up more development of theoretical models in this area.
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Affiliation(s)
- Sabeeha Hasnain
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Pradipta Bandyopadhyay
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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29
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Veya L, Piguet J, Vogel H. Single Molecule Imaging Deciphers the Relation between Mobility and Signaling of a Prototypical G Protein-coupled Receptor in Living Cells. J Biol Chem 2015; 290:27723-35. [PMID: 26363070 DOI: 10.1074/jbc.m115.666677] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2015] [Indexed: 01/10/2023] Open
Abstract
Lateral diffusion enables efficient interactions between membrane proteins, leading to signal transmission across the plasma membrane. An open question is how the spatiotemporal distribution of cell surface receptors influences the transmembrane signaling network. Here we addressed this issue by studying the mobility of a prototypical G protein-coupled receptor, the neurokinin-1 receptor, during its different phases of cellular signaling. Attaching a single quantum dot to individual neurokinin-1 receptors enabled us to follow with high spatial and temporal resolution over long time regimes the fate of individual receptors at the plasma membrane. Single receptor trajectories revealed a very heterogeneous mobility distribution pattern with diffusion constants ranging from 0.0005 to 0.1 μm(2)/s comprising receptors freely diffusing and others confined in 100-600-nm-sized membrane domains as well as immobile receptors. A two-dimensional representation of mobility and confinement resolved two major, broadly distributed receptor populations, one showing high mobility and low lateral restriction and the other showing low mobility and high restriction. We found that about 40% of the receptors in the basal state are already confined in membrane domains and are associated with clathrin. After stimulation with an agonist, an additional 30% of receptors became further confined. Using inhibitors of clathrin-mediated endocytosis, we found that the fraction of confined receptors at the basal state depends on the quantity of membrane-associated clathrin and is correlated to a significant decrease of the canonical pathway activity of the receptors. This shows that the high plasticity of receptor mobility is of central importance for receptor homeostasis and fine regulation of receptor activity.
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Affiliation(s)
- Luc Veya
- From the Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Joachim Piguet
- From the Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Horst Vogel
- From the Institute of Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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30
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Gmachowski L. Fractal model of anomalous diffusion. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2015; 44:613-21. [PMID: 26129728 PMCID: PMC4628625 DOI: 10.1007/s00249-015-1054-5] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/15/2015] [Revised: 04/24/2015] [Accepted: 06/09/2015] [Indexed: 12/17/2022]
Abstract
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.
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Affiliation(s)
- Lech Gmachowski
- Institute of Chemistry, Warsaw University of Technology, 09-400, Plock, Poland.
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Blumenthal D, Goldstien L, Edidin M, Gheber LA. Universal Approach to FRAP Analysis of Arbitrary Bleaching Patterns. Sci Rep 2015; 5:11655. [PMID: 26108191 PMCID: PMC4479983 DOI: 10.1038/srep11655] [Citation(s) in RCA: 58] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2014] [Accepted: 05/07/2015] [Indexed: 11/23/2022] Open
Abstract
The original approach to calculating diffusion coefficients of a fluorescent probe from Fluorescence Recovery After Photobleaching (FRAP) measurements assumes bleaching with a circular laser beam of a Gaussian intensity profile. This method was used without imaging the bleached cell. An empirical equation for calculating diffusion coefficients from a rectangular bleaching geometry, created in a confocal image, was later published, however a single method allowing the calculation of diffusion coefficients for arbitrary geometry does not exist. Our simulation approach allows computation of diffusion coefficients regardless of bleaching geometry used in the FRAP experiment. It accepts a multiple-frame TIFF file, representing the experiment as input, and simulates the (pure) diffusion of the fluorescent probes (2D random walk) starting with the first post-bleach frame of the actual data. It then fits the simulated data to the real data and extracts the diffusion coefficient. We validate our approach using a well characterized diffusing molecule (DiIC18) against well-established analytical procedures. We show that the algorithm is able to calculate the absolute value of diffusion coefficients for arbitrary bleaching geometries, including exaggeratedly large ones. It is provided freely as an ImageJ plugin, and should facilitate quantitative FRAP measurements for users equipped with standard fluorescence microscopy setups.
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Affiliation(s)
- Daniel Blumenthal
- The Avram and Stella Goldstein-Goren Department of Biotechnology Engineering, Ben Gurion University of the Negev, Beer-Sheva, ISRAEL
| | - Leo Goldstien
- The Avram and Stella Goldstein-Goren Department of Biotechnology Engineering, Ben Gurion University of the Negev, Beer-Sheva, ISRAEL
| | - Michael Edidin
- Department of Biology, Johns Hopkins University, Baltimore, MD, USA
| | - Levi A. Gheber
- The Avram and Stella Goldstein-Goren Department of Biotechnology Engineering, Ben Gurion University of the Negev, Beer-Sheva, ISRAEL
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Leake MC. Analytical tools for single-molecule fluorescence imaging in cellulo. Phys Chem Chem Phys 2015; 16:12635-47. [PMID: 24626744 DOI: 10.1039/c4cp00219a] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
Recent technological advances in cutting-edge ultrasensitive fluorescence microscopy have allowed single-molecule imaging experiments in living cells across all three domains of life to become commonplace. Single-molecule live-cell data is typically obtained in a low signal-to-noise ratio (SNR) regime sometimes only marginally in excess of 1, in which a combination of detector shot noise, sub-optimal probe photophysics, native cell autofluorescence and intrinsically underlying stochasticity of molecules result in highly noisy datasets for which underlying true molecular behaviour is non-trivial to discern. The ability to elucidate real molecular phenomena is essential in relating experimental single-molecule observations to both the biological system under study as well as offering insight into the fine details of the physical and chemical environments of the living cell. To confront this problem of faithful signal extraction and analysis in a noise-dominated regime, the 'needle in a haystack' challenge, such experiments benefit enormously from a suite of objective, automated, high-throughput analysis tools that can home in on the underlying 'molecular signature' and generate meaningful statistics across a large population of individual cells and molecules. Here, I discuss the development and application of several analytical methods applied to real case studies, including objective methods of segmenting cellular images from light microscopy data, tools to robustly localize and track single fluorescently-labelled molecules, algorithms to objectively interpret molecular mobility, analysis protocols to reliably estimate molecular stoichiometry and turnover, and methods to objectively render distributions of molecular parameters.
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Affiliation(s)
- M C Leake
- Biological Physical Sciences Institute (BPSI), Departments of Physics and Biology, University of York, York, YO10 5DD, UK.
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Kepten E, Weron A, Sikora G, Burnecki K, Garini Y. Guidelines for the fitting of anomalous diffusion mean square displacement graphs from single particle tracking experiments. PLoS One 2015; 10:e0117722. [PMID: 25680069 PMCID: PMC4334513 DOI: 10.1371/journal.pone.0117722] [Citation(s) in RCA: 76] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2014] [Accepted: 12/30/2014] [Indexed: 12/15/2022] Open
Abstract
Single particle tracking is an essential tool in the study of complex systems and biophysics and it is commonly analyzed by the time-averaged mean square displacement (MSD) of the diffusive trajectories. However, past work has shown that MSDs are susceptible to significant errors and biases, preventing the comparison and assessment of experimental studies. Here, we attempt to extract practical guidelines for the estimation of anomalous time averaged MSDs through the simulation of multiple scenarios with fractional Brownian motion as a representative of a large class of fractional ergodic processes. We extract the precision and accuracy of the fitted MSD for various anomalous exponents and measurement errors with respect to measurement length and maximum time lags. Based on the calculated precision maps, we present guidelines to improve accuracy in single particle studies. Importantly, we find that in some experimental conditions, the time averaged MSD should not be used as an estimator.
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Affiliation(s)
- Eldad Kepten
- Physics Department & Institute of Nanotechnology, Bar Ilan University, Ramat Gan, Israel
| | - Aleksander Weron
- Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wroclaw, Poland
| | - Grzegorz Sikora
- Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wroclaw, Poland
| | - Krzysztof Burnecki
- Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wroclaw, Poland
| | - Yuval Garini
- Physics Department & Institute of Nanotechnology, Bar Ilan University, Ramat Gan, Israel
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Kalay Z, Fujiwara TK, Otaka A, Kusumi A. Lateral diffusion in a discrete fluid membrane with immobile particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022724. [PMID: 25353525 DOI: 10.1103/physreve.89.022724] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2013] [Indexed: 06/04/2023]
Abstract
Due to the coupling between the plasma membrane and the actin cytoskeleton, membrane molecules such as receptor proteins can become immobilized by binding to cytoskeletal structures. We investigate the effect of immobile membrane molecules on the diffusion of mobile ones by modeling the membrane as a two-dimensional (2D) fluid composed of hard particles and performing event-driven molecular dynamics simulations at a particle density where the system is in an isotropic liquid state. We show that the diffusion coefficient sharply decreases with increasing immobile fraction, dropping by a factor of ∼ 3 as the fraction of immobile particles increases from 0 to 0.1, in a system-size dependent manner. By combining our results with earlier calculations, we estimate that a factor-of-∼ 20 reduction in diffusion coefficients in live cell membranes, a puzzling finding in cell biology, can be accounted for when less than ∼ 22% of the particles in our model system is immobilized. Furthermore, we investigate the effects of confinement induced by a correlated distribution of immobile particles by calculating the distribution of the time it takes for particles to escape from a corral. In the regime where the particles can always escape from the corral, it is found that the escape times follow an exponential distribution, and the mean escape time grows exponentially with the density of obstacles at the corral boundary, increasing by a factor of 3-5 when immobile particles cover 50% of the boundary, and is approximately proportional to the area of the corral. We believe that our findings will be useful in interpreting (1) single molecule observations of membrane molecules and (2) results of particle based simulations that explore the effect of fluid dynamics on molecular transport in a 2D fluid.
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Affiliation(s)
- Ziya Kalay
- Institute for Integrated Cell-Material Sciences (WPI-iCeMS), Kyoto University, Kyoto 606-8501, Japan
| | - Takahiro K Fujiwara
- Institute for Integrated Cell-Material Sciences (WPI-iCeMS), Kyoto University, Kyoto 606-8501, Japan
| | - Akihisa Otaka
- Institute for Integrated Cell-Material Sciences (WPI-iCeMS), Kyoto University, Kyoto 606-8501, Japan and Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 615-8540, Japan
| | - Akihiro Kusumi
- Institute for Integrated Cell-Material Sciences (WPI-iCeMS), Kyoto University, Kyoto 606-8501, Japan and Institute for Frontier Medical Sciences, Kyoto University, Kyoto 606-8507, Japan
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35
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Marinov TM, Santamaria F. Computational modeling of diffusion in the cerebellum. PROGRESS IN MOLECULAR BIOLOGY AND TRANSLATIONAL SCIENCE 2014; 123:169-89. [PMID: 24560145 DOI: 10.1016/b978-0-12-397897-4.00007-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Diffusion is a major transport mechanism in living organisms. In the cerebellum, diffusion is responsible for the propagation of molecular signaling involved in synaptic plasticity and metabolism, both intracellularly and extracellularly. In this chapter, we present an overview of the cerebellar structure and function. We then discuss the types of diffusion processes present in the cerebellum and their biological importance. We particularly emphasize the differences between extracellular and intracellular diffusion and the presence of tortuosity and anomalous diffusion in different parts of the cerebellar cortex. We provide a mathematical introduction to diffusion and a conceptual overview of various computational modeling techniques. We discuss their scope and their limit of application. Although our focus is the cerebellum, we have aimed at presenting the biological and mathematical foundations as general as possible to be applicable to any other area in biology in which diffusion is of importance.
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Affiliation(s)
- Toma M Marinov
- UTSA Neurosciences Institute, University of Texas at San Antonio, San Antonio, Texas, USA
| | - Fidel Santamaria
- UTSA Neurosciences Institute, University of Texas at San Antonio, San Antonio, Texas, USA
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36
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Angstmann CN, Donnelly IC, Henry BI, Langlands TAM. Continuous-time random walks on networks with vertex- and time-dependent forcing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022811. [PMID: 24032887 DOI: 10.1103/physreve.88.022811] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2013] [Indexed: 06/02/2023]
Abstract
We have investigated the transport of particles moving as random walks on the vertices of a network, subject to vertex- and time-dependent forcing. We have derived the generalized master equations for this transport using continuous time random walks, characterized by jump and waiting time densities, as the underlying stochastic process. The forcing is incorporated through a vertex- and time-dependent bias in the jump densities governing the random walking particles. As a particular case, we consider particle forcing proportional to the concentration of particles on adjacent vertices, analogous to self-chemotactic attraction in a spatial continuum. Our algebraic and numerical studies of this system reveal an interesting pair-aggregation pattern formation in which the steady state is composed of a high concentration of particles on a small number of isolated pairs of adjacent vertices. The steady states do not exhibit this pair aggregation if the transport is random on the vertices, i.e., without forcing. The manifestation of pair aggregation on a transport network may thus be a signature of self-chemotactic-like forcing.
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Affiliation(s)
- C N Angstmann
- School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia
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37
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Bruna M, Chapman SJ. Diffusion of Finite-Size Particles in Confined Geometries. Bull Math Biol 2013; 76:947-82. [DOI: 10.1007/s11538-013-9847-0] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2012] [Accepted: 04/22/2013] [Indexed: 10/26/2022]
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Haack F, Burrage K, Redmer R, Uhrmacher AM. Studying the role of lipid rafts on protein receptor bindings with cellular automata. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2013; 10:760-770. [PMID: 24091408 DOI: 10.1109/tcbb.2013.40] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
It is widely accepted that lipid rafts promote receptor clustering and thereby facilitate signaling transduction. The role of lipid rafts in inducing and promoting receptor accumulation within the cell membrane has been explored by several computational and experimental studies. However, it remains unclear whether lipid rafts influence the recruitment and binding of proteins from the cytosol as well. To provide an answer to this question a spatial membrane model has been developed based on cellular automata. Our results indicate that lipid rafts indeed influence protein receptor bindings. In particular processes with slow dissociation and binding kinetics are promoted by lipid rafts, whereas fast binding processes are slightly hampered. However, the impact depends on a variety of parameters, such as the size and mobility of the lipid rafts, the induced slow down of receptors within rafts, and also the dissociation and binding kinetics of the cytosolic proteins. Thus, for any individual signaling pathway the influence of lipid rafts on protein binding might be different. To facilitate analyzing this influence given a specific pathway, our approach has been generalized into LiRaM, a modeling and simulation tool for lipid rafts models.
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39
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Höfling F, Franosch T. Anomalous transport in the crowded world of biological cells. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2013; 76:046602. [PMID: 23481518 DOI: 10.1088/0034-4885/76/4/046602] [Citation(s) in RCA: 589] [Impact Index Per Article: 53.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.
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Affiliation(s)
- Felix Höfling
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, and Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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40
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Hannestad JK, Brune R, Czolkos I, Jesorka A, El-Sagheer AH, Brown T, Albinsson B, Orwar O. Kinetics of diffusion-mediated DNA hybridization in lipid monolayer films determined by single-molecule fluorescence spectroscopy. ACS NANO 2013; 7:308-315. [PMID: 23215045 DOI: 10.1021/nn304010p] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We use single-molecule fluorescence microscopy to monitor individual hybridization reactions between membrane-anchored DNA strands, occurring in nanofluidic lipid monolayer films deposited on Teflon AF substrates. The DNA molecules are labeled with different fluorescent dyes, which make it possible to simultaneously monitor the movements of two different molecular species, thus enabling tracking of both reactants and products. We employ lattice diffusion simulations to determine reaction probabilities upon interaction. The observed hybridization rate of the 40-mer DNA was more than 2-fold higher than that of the 20-mer DNA. Since the lateral diffusion coefficient of the two different constructs is nearly identical, the effective molecule radius determines the overall kinetics. This implies that when two DNA molecules approach each other, hydrogen bonding takes place distal from the place where the DNA is anchored to the surface. Strand closure then propagates bidirectionally through a zipper-like mechanism, eventually bringing the lipid anchors together. Comparison with hybridization rates for corresponding DNA sequences in solution reveals that hybridization rates are lower for the lipid-anchored strands and that the dependence on strand length is stronger.
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Affiliation(s)
- Jonas K Hannestad
- Department of Chemical and Biological Engineering, Chalmers University of Technology, 412 96, Göteborg, Sweden
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41
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Marquez-Lago TT, Leier A, Burrage K. Anomalous diffusion and multifractional Brownian motion: simulating molecular crowding and physical obstacles in systems biology. IET Syst Biol 2013; 6:134-42. [PMID: 23039694 DOI: 10.1049/iet-syb.2011.0049] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
There have been many recent studies from both experimental and simulation perspectives in order to understand the effects of spatial crowding in molecular biology. These effects manifest themselves in protein organisation on the plasma membrane, on chemical signalling within the cell and in gene regulation. Simulations are usually done with lattice- or meshless-based random walks but insights can also be gained through the computation of the underlying probability density functions of these stochastic processes. Until recently much of the focus had been on continuous time random walks, but some very recent work has suggested that fractional Brownian motion may be a good descriptor of spatial crowding effects in some cases. The study compares both fractional Brownian motion and continuous time random walks and highlights how well they can represent different types of spatial crowding and physical obstacles. Simulated spatial data, mimicking experimental data, was first generated by using the package Smoldyn. We then attempted to characterise this data through continuous time anomalously diffusing random walks and multifractional Brownian motion (MFBM) by obtaining MFBM paths that match the statistical properties of our sample data. Although diffusion around immovable obstacles can be reasonably characterised by a single Hurst exponent, we find that diffusion in a crowded environment seems to exhibit multifractional properties in the form of a different short- and long-time behaviour.
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Robson A, Burrage K, Leake MC. Inferring diffusion in single live cells at the single-molecule level. Philos Trans R Soc Lond B Biol Sci 2012; 368:20120029. [PMID: 23267182 DOI: 10.1098/rstb.2012.0029] [Citation(s) in RCA: 61] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The movement of molecules inside living cells is a fundamental feature of biological processes. The ability to both observe and analyse the details of molecular diffusion in vivo at the single-molecule and single-cell level can add significant insight into understanding molecular architectures of diffusing molecules and the nanoscale environment in which the molecules diffuse. The tool of choice for monitoring dynamic molecular localization in live cells is fluorescence microscopy, especially so combining total internal reflection fluorescence with the use of fluorescent protein (FP) reporters in offering exceptional imaging contrast for dynamic processes in the cell membrane under relatively physiological conditions compared with competing single-molecule techniques. There exist several different complex modes of diffusion, and discriminating these from each other is challenging at the molecular level owing to underlying stochastic behaviour. Analysis is traditionally performed using mean square displacements of tracked particles; however, this generally requires more data points than is typical for single FP tracks owing to photophysical instability. Presented here is a novel approach allowing robust Bayesian ranking of diffusion processes to discriminate multiple complex modes probabilistically. It is a computational approach that biologists can use to understand single-molecule features in live cells.
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Affiliation(s)
- Alex Robson
- Clarendon Laboratory, Department of Physics, Oxford University, Parks Road, Oxford OX1 3PU, UK
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43
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Bruna M, Chapman SJ. Diffusion of multiple species with excluded-volume effects. J Chem Phys 2012. [DOI: 10.1063/1.4767058] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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44
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Kusumi A, Fujiwara TK, Chadda R, Xie M, Tsunoyama TA, Kalay Z, Kasai RS, Suzuki KGN. Dynamic organizing principles of the plasma membrane that regulate signal transduction: commemorating the fortieth anniversary of Singer and Nicolson's fluid-mosaic model. Annu Rev Cell Dev Biol 2012; 28:215-50. [PMID: 22905956 DOI: 10.1146/annurev-cellbio-100809-151736] [Citation(s) in RCA: 284] [Impact Index Per Article: 23.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The recent rapid accumulation of knowledge on the dynamics and structure of the plasma membrane has prompted major modifications of the textbook fluid-mosaic model. However, because the new data have been obtained in a variety of research contexts using various biological paradigms, the impact of the critical conceptual modifications on biomedical research and development has been limited. In this review, we try to synthesize our current biological, chemical, and physical knowledge about the plasma membrane to provide new fundamental organizing principles of this structure that underlie every molecular mechanism that realizes its functions. Special attention is paid to signal transduction function and the dynamic aspect of the organizing principles. We propose that the cooperative action of the hierarchical three-tiered mesoscale (2-300 nm) domains--actin-membrane-skeleton induced compartments (40-300 nm), raft domains (2-20 nm), and dynamic protein complex domains (3-10 nm)--is critical for membrane function and distinguishes the plasma membrane from a classical Singer-Nicolson-type model.
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Affiliation(s)
- Akihiro Kusumi
- Institute for Integrated Cell-Material Sciences, Kyoto University, Kyoto 606-8507, Japan.
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45
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Espinoza FA, Wester MJ, Oliver JM, Wilson BS, Andrews NL, Lidke DS, Steinberg SL. Insights into cell membrane microdomain organization from live cell single particle tracking of the IgE high affinity receptor FcϵRI of mast cells. Bull Math Biol 2012; 74:1857-911. [PMID: 22733211 DOI: 10.1007/s11538-012-9738-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2011] [Accepted: 05/21/2012] [Indexed: 10/28/2022]
Abstract
Current models propose that the plasma membrane of animal cells is composed of heterogeneous and dynamic microdomains known variously as cytoskeletal corrals, lipid rafts and protein islands. Much of the experimental evidence for these membrane compartments is indirect. Recently, live cell single particle tracking studies using quantum dot-labeled IgE bound to its high affinity receptor FcϵRI, provided direct evidence for the confinement of receptors within micrometer-scale cytoskeletal corrals. In this study, we show that an innovative time-series analysis of single particle tracking data for the high affinity IgE receptor, FcϵRI, on mast cells provides substantial quantitative information about the submicrometer organization of the membrane. The analysis focuses on the probability distribution function of the lengths of the jumps in the positions of the quantum dots labeling individual IgE FcϵRI complexes between frames in movies of their motion. Our results demonstrate the presence, within the micrometer-scale cytoskeletal corrals, of smaller subdomains that provide an additional level of receptor confinement. There is no characteristic size for these subdomains; their size varies smoothly from a few tens of nanometers to a over a hundred nanometers. In QD-IGE labeled unstimulated cells, jumps of less than 70 nm predominate over longer jumps. Addition of multivalent antigen to crosslink the QD-IgE-FcϵRI complexes causes a rapid slowing of receptor motion followed by a long tail of mostly jumps less than 70 nm. The reduced receptor mobility likely reflects both the membrane heterogeneity revealed by the confined motion of the monomeric receptor complexes and the antigen-induced cross linking of these complexes into dimers and higher oligomers. In both cases, the probability distribution of the jump lengths is well fit, from 10 nm to over 100 nm, by a novel power law. The fit for short jumps suggests that the motion of the quantum dots can be modeled as diffusion in a fractal space of dimension less than two.
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Affiliation(s)
- Flor A Espinoza
- Department of Mathematics and Statistics, University of New Mexico, Albuquerque, 87131-1141, USA.
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46
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Soula HA, Coulon A, Beslon G. Membrane microdomains emergence through non-homogeneous diffusion. BMC BIOPHYSICS 2012; 5:6. [PMID: 22546236 PMCID: PMC3528627 DOI: 10.1186/2046-1682-5-6] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2011] [Accepted: 02/29/2012] [Indexed: 11/16/2022]
Abstract
Background In the classical view, cell membrane proteins undergo isotropic random motion, that is a 2D Brownian diffusion that should result in an homogeneous distribution of concentration. It is, however, far from the reality: Membrane proteins can assemble into so-called microdomains (sometimes called lipid rafts) which also display a specific lipid composition. We propose a simple mechanism that is able to explain the colocalization of protein and lipid rafts. Results Using very simple mathematical models and particle simulations, we show that a variation of membrane viscosity directly leads to variation of the local concentration of diffusive particles. Since specific lipid phases in the membrane can account for diffusion variation, we show that, in such a situation, the freely diffusing proteins (or any other component) still undergo a Brownian motion but concentrate in areas of lower diffusion. The amount of this so-called overconcentration at equilibrium issimply related to the ratio of diffusion coefficients between zones of high and low diffusion. Expanding the model to include particle interaction, we show that inhomogeneous diffusion can impact particles clusterization as well. The clusters of particles were more numerous and appear for a lower value of interaction strength in the zones of low diffusion compared to zones of high diffusion. Conclusion Provided we assume stable viscosity heterogeneity in the membrane, our model propose a simple mechanism to explain particle concentration heterogeneity. It has also a non-trivial impact on density of particles when interaction is added. This could potentially have an impact on membrane chemical reactions and oligomerization.
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Affiliation(s)
- Hédi A Soula
- Université de Lyon Inserm UMR1060, F-69621, Villeurbanne Cédex, France.
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47
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Skaug MJ, Faller R, Longo ML. Correlating anomalous diffusion with lipid bilayer membrane structure using single molecule tracking and atomic force microscopy. J Chem Phys 2012; 134:215101. [PMID: 21663377 DOI: 10.1063/1.3596377] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
Anomalous diffusion has been observed abundantly in the plasma membrane of biological cells, but the underlying mechanisms are still unclear. In general, it has not been possible to directly image the obstacles to diffusion in membranes, which are thought to be skeleton bound proteins, protein aggregates, and lipid domains, so the dynamics of diffusing particles is used to deduce the obstacle characteristics. We present a supported lipid bilayer system in which we characterized the anomalous diffusion of lipid molecules using single molecule tracking, while at the same time imaging the obstacles to diffusion with atomic force microscopy. To explain our experimental results, we performed lattice Monte Carlo simulations of tracer diffusion in the presence of the experimentally determined obstacle configurations. We correlate the observed anomalous diffusion with obstacle area fraction, fractal dimension, and correlation length. To accurately measure an anomalous diffusion exponent, we derived an expression to account for the time-averaging inherent to all single molecule tracking experiments. We show that the length of the single molecule trajectories is critical to the determination of the anomalous diffusion exponent. We further discuss our results in the context of confinement models and the generating stochastic process.
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Affiliation(s)
- Michael J Skaug
- Department of Chemical Engineering and Materials Science, University of California Davis, Davis, California 95616, USA
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Kusumi A, Fujiwara TK, Morone N, Yoshida KJ, Chadda R, Xie M, Kasai RS, Suzuki KGN. Membrane mechanisms for signal transduction: the coupling of the meso-scale raft domains to membrane-skeleton-induced compartments and dynamic protein complexes. Semin Cell Dev Biol 2012; 23:126-44. [PMID: 22309841 DOI: 10.1016/j.semcdb.2012.01.018] [Citation(s) in RCA: 106] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2012] [Accepted: 01/24/2012] [Indexed: 01/09/2023]
Abstract
Virtually all biological membranes on earth share the basic structure of a two-dimensional liquid. Such universality and peculiarity are comparable to those of the double helical structure of DNA, strongly suggesting the possibility that the fundamental mechanisms for the various functions of the plasma membrane could essentially be understood by a set of simple organizing principles, developed during the course of evolution. As an initial effort toward the development of such understanding, in this review, we present the concept of the cooperative action of the hierarchical three-tiered meso-scale (2-300 nm) domains in the plasma membrane: (1) actin membrane-skeleton-induced compartments (40-300 nm), (2) raft domains (2-20 nm), and (3) dynamic protein complex domains (3-10nm). Special attention is paid to the concept of meso-scale domains, where both thermal fluctuations and weak cooperativity play critical roles, and the coupling of the raft domains to the membrane-skeleton-induced compartments as well as dynamic protein complexes. The three-tiered meso-domain architecture of the plasma membrane provides an excellent perspective for understanding the membrane mechanisms of signal transduction.
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Affiliation(s)
- Akihiro Kusumi
- Institute for Integrated Cell-Material Sciences (iCeMS), Kyoto University, Kyoto 606-8507, Japan.
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Tateishi AA, Lenzi EK, da Silva LR, Ribeiro HV, Picoli S, Mendes RS. Different diffusive regimes, generalized Langevin and diffusion equations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:011147. [PMID: 22400552 DOI: 10.1103/physreve.85.011147] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2011] [Revised: 10/28/2011] [Indexed: 05/31/2023]
Abstract
We investigate a generalized Langevin equation (GLE) in the presence of an additive noise characterized by the mixture of the usual white noise and an arbitrary one. This scenario lead us to a wide class of diffusive processes, in particular the ones whose noise correlation functions are governed by power laws, exponentials, and Mittag-Leffler functions. The results show the presence of different diffusive regimes related to the spreading of the system. In addition, we obtain a fractional diffusionlike equation from the GLE, confirming the results for long time.
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Affiliation(s)
- A A Tateishi
- Departamento de Física, Universidade Estadual de Maringá Avenida Colombo, 5790-87020-900 Maringá-PR, Brazil
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50
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Kusumi A, Suzuki KGN, Kasai RS, Ritchie K, Fujiwara TK. Hierarchical mesoscale domain organization of the plasma membrane. Trends Biochem Sci 2011; 36:604-15. [PMID: 21917465 DOI: 10.1016/j.tibs.2011.08.001] [Citation(s) in RCA: 243] [Impact Index Per Article: 18.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2011] [Revised: 08/06/2011] [Accepted: 08/08/2011] [Indexed: 11/27/2022]
Abstract
Based on recent single-molecule imaging results in the living cell plasma membrane, we propose a hierarchical architecture of three-tiered mesoscale (2-300nm) domains to represent the fundamental functional organization of the plasma membrane: (i) membrane compartments of 40-300nm in diameter due to the partitioning of the entire plasma membrane by the actin-based membrane skeleton 'fence' and transmembrane protein 'pickets' anchored to the fence; (ii) raft domains (2-20nm); and (iii) dimers/oligomers and greater complexes of membrane-associated proteins (3-10nm). The basic molecular interactions required for the signal transduction function of the plasma membrane can be fundamentally understood and conveniently summarized as the cooperative actions of these mesoscale domains, where thermal fluctuations/movements of molecules and weak cooperativity play crucial roles.
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Affiliation(s)
- Akihiro Kusumi
- Institute for Integrated Cell-Material Sciences (iCeMS), Kyoto University, Kyoto 606-8507, Japan.
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