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Waigh TA, Korabel N. Heterogeneous anomalous transport in cellular and molecular biology. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:126601. [PMID: 37863075 DOI: 10.1088/1361-6633/ad058f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Accepted: 10/20/2023] [Indexed: 10/22/2023]
Abstract
It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.
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Affiliation(s)
- Thomas Andrew Waigh
- Biological Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| | - Nickolay Korabel
- Department of Mathematics, The University of Manchester, Manchester M13 9PL, United Kingdom
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Sakamoto K, Akimoto T, Muramatsu M, Sansom MSP, Metzler R, Yamamoto E. Heterogeneous biological membranes regulate protein partitioning via fluctuating diffusivity. PNAS NEXUS 2023; 2:pgad258. [PMID: 37593200 PMCID: PMC10427746 DOI: 10.1093/pnasnexus/pgad258] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/06/2023] [Revised: 06/22/2023] [Accepted: 07/27/2023] [Indexed: 08/19/2023]
Abstract
Cell membranes phase separate into ordered L o and disordered L d domains depending on their compositions. This membrane compartmentalization is heterogeneous and regulates the localization of specific proteins related to cell signaling and trafficking. However, it is unclear how the heterogeneity of the membranes affects the diffusion and localization of proteins in L o and L d domains. Here, using Langevin dynamics simulations coupled with the phase-field (LDPF) method, we investigate several tens of milliseconds-scale diffusion and localization of proteins in heterogeneous biological membrane models showing phase separation into L o and L d domains. The diffusivity of proteins exhibits temporal fluctuations depending on the field composition. Increases in molecular concentrations and domain preference of the molecule induce subdiffusive behavior due to molecular collisions by crowding and confinement effects, respectively. Moreover, we quantitatively demonstrate that the protein partitioning into the L o domain is determined by the difference in molecular diffusivity between domains, molecular preference of domain, and molecular concentration. These results pave the way for understanding how biological reactions caused by molecular partitioning may be controlled in heterogeneous media. Moreover, the methodology proposed here is applicable not only to biological membrane systems but also to the study of diffusion and localization phenomena of molecules in various heterogeneous systems.
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Affiliation(s)
- Ken Sakamoto
- Department of System Design Engineering, Keio University, Yokohama, Kanagawa 223-8522, Japan
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Mayu Muramatsu
- Department of Mechanical Engineering, Keio University, Yokohama, Kanagawa 223-8522, Japan
| | - Mark S P Sansom
- Department of Biochemistry, University of Oxford, South Parks Road, Oxford OX1 3QU, UK
| | - Ralf Metzler
- Institute of Physics & Astronomy, University of Potsdam, Potsdam-Golm 14476, Germany
- Asia Pacific Centre for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Eiji Yamamoto
- Department of System Design Engineering, Keio University, Yokohama, Kanagawa 223-8522, Japan
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Fedotov S, Han D, Zubarev AY, Johnston M, Allan VJ. Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200317. [PMID: 34275365 DOI: 10.1098/rsta.2020.0317] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 01/21/2021] [Indexed: 06/13/2023]
Abstract
In this paper, we formulate the space-dependent variable-order fractional master equation to model clustering of particles, organelles, inside living cells. We find its solution in the long-time limit describing non-uniform distribution due to a space-dependent fractional exponent. In the continuous space limit, the solution of this fractional master equation is found to be exactly the same as the space-dependent variable-order fractional diffusion equation. In addition, we show that the clustering of lysosomes, an essential organelle for healthy functioning of mammalian cells, exhibit space-dependent fractional exponents. Furthermore, we demonstrate that the non-uniform distribution of lysosomes in living cells is accurately described by the asymptotic solution of the space-dependent variable-order fractional master equation. Finally, Monte Carlo simulations of the fractional master equation validate our analytical solution. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.
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Affiliation(s)
- Sergei Fedotov
- Department of Mathematics, University of Manchester, M13 9PL, Manchester, UK
| | - Daniel Han
- Department of Mathematics, University of Manchester, M13 9PL, Manchester, UK
- Faculty of Biology, Medicine and Health, School of Biological Sciences, University of Manchester, M13 9PL, Manchester, UK
| | | | - Mark Johnston
- Faculty of Biology, Medicine and Health, School of Biological Sciences, University of Manchester, M13 9PL, Manchester, UK
| | - Victoria J Allan
- Faculty of Biology, Medicine and Health, School of Biological Sciences, University of Manchester, M13 9PL, Manchester, UK
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Goiko M, de Bruyn JR, Heit B. Membrane Diffusion Occurs by Continuous-Time Random Walk Sustained by Vesicular Trafficking. Biophys J 2019; 114:2887-2899. [PMID: 29925025 DOI: 10.1016/j.bpj.2018.04.024] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2018] [Revised: 03/06/2018] [Accepted: 04/16/2018] [Indexed: 10/28/2022] Open
Abstract
Diffusion in cellular membranes is regulated by processes that occur over a range of spatial and temporal scales. These processes include membrane fluidity, interprotein and interlipid interactions, interactions with membrane microdomains, interactions with the underlying cytoskeleton, and cellular processes that result in net membrane movement. The complex, non-Brownian diffusion that results from these processes has been difficult to characterize, and moreover, the impact of factors such as membrane recycling on membrane diffusion remains largely unexplored. We have used a careful statistical analysis of single-particle tracking data of the single-pass plasma membrane protein CD93 to show that the diffusion of this protein is well described by a continuous-time random walk in parallel with an aging process mediated by membrane corrals. The overall result is an evolution in the diffusion of CD93: proteins initially diffuse freely on the cell surface but over time become increasingly trapped within diffusion-limiting membrane corrals. Stable populations of freely diffusing and corralled CD93 are maintained by an endocytic/exocytic process in which corralled CD93 is selectively endocytosed, whereas freely diffusing CD93 is replenished by exocytosis of newly synthesized and recycled CD93. This trafficking not only maintained CD93 diffusivity but also maintained the heterogeneous distribution of CD93 in the plasma membrane. These results provide insight into the nature of the biological and biophysical processes that can lead to significantly non-Brownian diffusion of membrane proteins and demonstrate that ongoing membrane recycling is critical to maintaining steady-state diffusion and distribution of proteins in the plasma membrane.
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Affiliation(s)
- Maria Goiko
- Department of Microbiology and Immunology, The University of Western Ontario, London, Ontario, Canada; Department of Physics and Astronomy, The University of Western Ontario, London, Ontario, Canada
| | - John R de Bruyn
- Department of Physics and Astronomy, The University of Western Ontario, London, Ontario, Canada
| | - Bryan Heit
- Department of Microbiology and Immunology, The University of Western Ontario, London, Ontario, Canada; Centre for Human Immunology, The University of Western Ontario, London, Ontario, Canada.
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Abstract
Bulk-level measurements of dynamics have suggested that phase-separated, protein-nucleic acid rich droplets can be viewed as simple liquids. In this report, we show that histone proteins spontaneously phase separate into liquid-like droplets in the presence of DNA. Using super-resolution fluorescence microscopy, we find that molecular transport in these droplets is non-Fickian (subdiffusive) at nanoscopic length scales. This observation cannot be explained by charge-charge interactions. Instead, our results strongly suggest that cation-π interactions drive the non-Fickian behavior. Given the ubiquity of cationic and aromatic moieties in protein-nucleic acid rich liquid-like phases observed in cells, we anticipate that non-Fickian diffusion is a general transport mechanism in such phases.
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Affiliation(s)
- Anisha Shakya
- Center for Soft and Living Matter, Institute for Basic Science, Ulsan 44919, Republic of Korea
| | - John T. King
- Center for Soft and Living Matter, Institute for Basic Science, Ulsan 44919, Republic of Korea
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Muñoz-Gil G, Charalambous C, García-March MA, Garcia-Parajo MF, Manzo C, Lewenstein M, Celi A. Transient subdiffusion from an Ising environment. Phys Rev E 2018; 96:052140. [PMID: 29347809 DOI: 10.1103/physreve.96.052140] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2017] [Indexed: 11/07/2022]
Abstract
We introduce a model in which a particle performs a continuous-time random walk (CTRW) coupled to an environment with Ising dynamics. The particle shows locally varying diffusivity determined by the geometrical properties of the underlying Ising environment, that is, the diffusivity depends on the size of the connected area of spins pointing in the same direction. The model shows anomalous diffusion when the Ising environment is at critical temperature. We show that any finite scale introduced by a temperature different from the critical one, or a finite size of the environment, cause subdiffusion only during a transient time. The characteristic time, at which the system returns to normal diffusion after the subdiffusive plateau depends on the limiting scale and on how close the temperature is to criticality. The system also displays apparent ergodicity breaking at intermediate time, while ergodicity breaking at longer time occurs only under the idealized infinite environment at the critical temperature.
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Affiliation(s)
- G Muñoz-Gil
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - C Charalambous
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - M A García-March
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - M F Garcia-Parajo
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.,ICREA-Pg. Lluís Companys 23, 08010 Barcelona, Spain
| | - C Manzo
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.,Universitat de Vic-Universitat Central de Catalunya (UVic-UCC), C. de la Laura, 13, 08500 Vic, Spain
| | - M Lewenstein
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.,ICREA-Pg. Lluís Companys 23, 08010 Barcelona, Spain
| | - A Celi
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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