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Law E, Li Y, Kahraman O, Haselwandter CA. Stochastic self-assembly of reaction-diffusion patterns in synaptic membranes. Phys Rev E 2021; 104:014403. [PMID: 34412234 DOI: 10.1103/physreve.104.014403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Accepted: 06/14/2021] [Indexed: 11/07/2022]
Abstract
Synaptic receptor and scaffold molecules self-assemble into membrane protein domains, which play an important role in signal transmission across chemical synapses. Experiment and theory have shown that the formation of receptor-scaffold domains of the characteristic size observed in nerve cells can be understood from the receptor and scaffold reaction and diffusion processes suggested by experiments. We employ here kinetic Monte Carlo (KMC) simulations to explore the self-assembly of synaptic receptor-scaffold domains in a stochastic lattice model of receptor and scaffold reaction-diffusion dynamics. For reaction and diffusion rates within the ranges of values suggested by experiments we find, in agreement with previous mean-field calculations, self-assembly of receptor-scaffold domains of a size similar to that observed in experiments. Comparisons between the results of our KMC simulations and mean-field solutions suggest that the intrinsic noise associated with receptor and scaffold reaction and diffusion processes accelerates the self-assembly of receptor-scaffold domains, and confers increased robustness to domain formation. In agreement with experimental observations, our KMC simulations yield a prevalence of scaffolds over receptors in receptor-scaffold domains. Our KMC simulations show that receptor and scaffold reaction-diffusion dynamics can inherently give rise to plasticity in the overall properties of receptor-scaffold domains, which may be utilized by nerve cells to regulate the receptor number at chemical synapses.
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Affiliation(s)
- Everest Law
- Department of Physics and Astronomy and Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, USA
| | - Yiwei Li
- Department of Physics and Astronomy and Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, USA
| | - Osman Kahraman
- Department of Physics and Astronomy and Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, USA
| | - Christoph A Haselwandter
- Department of Physics and Astronomy and Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, USA
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Demirkan I, Unlu MB, Bilen B. Determining sodium diffusion through acoustic impedance measurements using 80 MHz Scanning Acoustic Microscopy: Agarose phantom verification. ULTRASONICS 2019; 94:10-19. [PMID: 30606650 DOI: 10.1016/j.ultras.2018.12.013] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2018] [Revised: 12/22/2018] [Accepted: 12/22/2018] [Indexed: 06/09/2023]
Abstract
The purpose of this study is to explore the feasibility of time-dependent acoustic impedance measurement by Scanning Acoustic Microscopy (SAM) for analyzing the sodium diffusion. The purpose is motivated by the fact that sodium monitoring is challenging and still in the area of exploratory analysis despite its biological importance. To our knowledge, this is the first study in which sodium diffusion has been investigated by time-dependent acoustic impedance measurements provided by SAM. We first tested the idea in an agarose phantom as a proof-of-concept. Accordingly, we designed the agarose phantom which initially contains a well of sodium chloride (NaCl) solution moving radially into the phantom. By using NaCl diffusion in the phantom, we obtained two-dimensional (2D) acoustic impedance (Z) maps over time through SAM operating with 80 MHz ultrasonic transducer having a lateral resolution of 20 μm. A linear correlation between the changes in the concentration profile of the phantom and its acoustic impedance was introduced. Analysis of experimental data proved that spatially changing acoustic impedance could be ascribed to the diffusion process and produced a diffusion coefficient in the order of 10-5 cm2/s which matches well with the literature. Our results showed that SAM could monitor the time-dependent alterations in acoustic impedance resulting from the diffusion of sodium inside the agarose phantom. With this study, SAM shows a promise as a monitoring tool not only to obtain static images but also to perform dynamic investigations of sodium ions with the advantages of providing images in micrometer resolution with a scanning time no longer than 2 min for an image area of 4.8 mm × 4.8 mm.
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Affiliation(s)
- Irem Demirkan
- Bogazici University, Department of Physics, Istanbul 34342, Turkey.
| | - Mehmet Burcin Unlu
- Bogazici University, Department of Physics, Istanbul 34342, Turkey; Global Station for Quantum Medical Science and Engineering, Global Institution for Collaborative Research and Education (GI-CoRE), Hokkaido University, Sapporo 060-8648, Japan; Department of Radiation Oncology, Stanford University School of Medicine, Stanford, CA, USA
| | - Bukem Bilen
- Bogazici University, Department of Physics, Istanbul 34342, Turkey
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Multiscale Modeling of Diffusion in a Crowded Environment. Bull Math Biol 2017; 79:2672-2695. [PMID: 28924915 DOI: 10.1007/s11538-017-0346-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2016] [Accepted: 09/06/2017] [Indexed: 10/18/2022]
Abstract
We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump rates in this mesoscopic model from local first exit times, which account for the microscopic positions of the crowding molecules, while the diffusing molecules jump on a coarser Cartesian grid. We then extract a macroscopic description from the resulting jump rates, where the excluded volume effect is modeled by a diffusion equation with space-dependent diffusion coefficient. The crowding molecules can be of arbitrary shape and size, and numerical experiments demonstrate that those factors together with the size of the diffusing molecule play a crucial role on the magnitude of the decrease in diffusive motion. When correcting the reaction rates for the altered diffusion we can show that molecular crowding either enhances or inhibits chemical reactions depending on local fluctuations of the obstacle density.
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Li Y, Kahraman O, Haselwandter CA. Distribution of randomly diffusing particles in inhomogeneous media. Phys Rev E 2017; 96:032139. [PMID: 29347048 DOI: 10.1103/physreve.96.032139] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2017] [Indexed: 06/07/2023]
Abstract
Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct particle hopping rates. Starting from the master equations (MEs) governing diffusion in inhomogeneous media we derive here, for arbitrary spatial dimensions, the deterministic lattice equations (DLEs) specifying the average particle number at each lattice site for randomly diffusing particles in inhomogeneous media. We consider the case of free (Fickian) diffusion with no steric constraints on the maximum particle number per lattice site as well as the case of diffusion under steric constraints imposing a maximum particle concentration. We find, for both transient and asymptotic regimes, excellent agreement between the DLEs and kinetic Monte Carlo simulations of the MEs. The DLEs provide a computationally efficient method for predicting the (average) distribution of randomly diffusing particles in inhomogeneous media, with the number of DLEs associated with a given system being independent of the number of particles in the system. From the DLEs we obtain general analytic expressions for the steady-state particle distributions for free diffusion and, in special cases, diffusion under steric constraints in inhomogeneous media. We find that, in the steady state of the system, the average fraction of particles in a given domain is independent of most system properties, such as the arrangement and shape of domains, and only depends on the number of lattice sites in each domain, the particle hopping rates, the number of distinct particle species in the system, and the total number of particles of each particle species in the system. Our results provide general insights into the role of spatially inhomogeneous particle hopping rates in setting the particle distributions in inhomogeneous media.
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Affiliation(s)
- Yiwei Li
- Department of Physics & Astronomy and Molecular and Computational Biology Program, Department of Biological Sciences, University of Southern California, Los Angeles, California 90089, USA
| | - Osman Kahraman
- Department of Physics & Astronomy and Molecular and Computational Biology Program, Department of Biological Sciences, University of Southern California, Los Angeles, California 90089, USA
| | - Christoph A Haselwandter
- Department of Physics & Astronomy and Molecular and Computational Biology Program, Department of Biological Sciences, University of Southern California, Los Angeles, California 90089, USA
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Li Y, Kahraman O, Haselwandter CA. Stochastic lattice model of synaptic membrane protein domains. Phys Rev E 2017; 95:052406. [PMID: 28618626 DOI: 10.1103/physreve.95.052406] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2017] [Indexed: 11/07/2022]
Abstract
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.
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Affiliation(s)
- Yiwei Li
- Department of Physics & Astronomy and Molecular and Computational Biology Program, Department of Biological Sciences, University of Southern California, Los Angeles, California 90089, USA
| | - Osman Kahraman
- Department of Physics & Astronomy and Molecular and Computational Biology Program, Department of Biological Sciences, University of Southern California, Los Angeles, California 90089, USA
| | - Christoph A Haselwandter
- Department of Physics & Astronomy and Molecular and Computational Biology Program, Department of Biological Sciences, University of Southern California, Los Angeles, California 90089, USA
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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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Kondrat S, Zimmermann O, Wiechert W, Lieres EV. The effect of composition on diffusion of macromolecules in a crowded environment. Phys Biol 2015; 12:046003. [DOI: 10.1088/1478-3975/12/4/046003] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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