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  1. Watabe M, Arjunan SNV, Chew WX, Kaizu K, Takahashi K
    Phys Rev E, 2019 Jul;100(1-1):010402.
    PMID: 31499827 DOI: 10.1103/PhysRevE.100.010402
    We propose a computational method to quantitatively evaluate the systematic uncertainties that arise from undetectable sources in biological measurements using live-cell imaging techniques. We then demonstrate this method in measuring the biological cooperativity of molecular binding networks, in particular, ligand molecules binding to cell-surface receptor proteins. Our results show how the nonstatistical uncertainties lead to invalid identifications of the measured cooperativity. Through this computational scheme, the biological interpretation can be more objectively evaluated and understood under a specific experimental configuration of interest.
  2. Tay BA
    Phys Rev E, 2021 Apr;103(4-1):042124.
    PMID: 34005972 DOI: 10.1103/PhysRevE.103.042124
    We consider the reduced dynamics of a molecular chain weakly coupled to a phonon bath. With a small and constant inhomogeneity in the coupling, the excitation relaxation rates are obtained in closed form. They are dominated by transitions between exciton modes lying next to each other in the energy spectrum. The rates are quadratic in the number of sites in a long chain. Consequently, the evolution of site occupation numbers exhibits longer coherence lifetime for short chains only. When external source and sink are added, the rate equations of exciton occupation numbers are similar to those obtained earlier by Fröhlich to explain energy storage and energy transfer in biological systems. There is a clear separation of timescale into a faster one pertaining to internal influence of the chain and phonon bath, and a slower one determined by external influence, such as the pumping rate of the source, the absorption rate of the sink, and the rate of radiation loss. The energy transfer efficiency at steady state depends strongly on these external parameters and is robust against a change in the internal parameters, such as temperature and inhomogeneity. Excitations are predicted to concentrate to the lowest energy mode when the source power is sufficiently high. In the site basis, this implies that when sustained by a high power source, a sink positioned at the center of the chain is more efficient in trapping energy than a sink placed at its end. Analytic expressions of energy transfer efficiency are obtained in the high power and low-power source limit. Parameters of a photosynthetic system are used as examples to illustrate the results.
  3. Belousov R, Cohen EG, Rondoni L
    Phys Rev E, 2016 Sep;94(3-1):032127.
    PMID: 27739763
    In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an external force. To do this, we extend the Langevin equation to include a bias, which is introduced by an external force and alters the Gaussian structure of the system's fluctuations. In addition, by solving this extended equation, we provide a physical interpretation for the statistical properties of the fluctuations in these systems. Connections of the extended Langevin equation with the theory of active Brownian motion are discussed as well.
  4. Chew WX, Kaizu K, Watabe M, Muniandy SV, Takahashi K, Arjunan SNV
    Phys Rev E, 2019 Apr;99(4-1):042411.
    PMID: 31108654 DOI: 10.1103/PhysRevE.99.042411
    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.
  5. Watabe M, Arjunan SNV, Chew WX, Kaizu K, Takahashi K
    Phys Rev E, 2019 Dec;100(6-1):062407.
    PMID: 31962468 DOI: 10.1103/PhysRevE.100.062407
    While cooperativity in ligand-induced receptor dimerization has been linked with receptor-receptor couplings via minimal representations of physical observables, effects arising from higher-order oligomer, e.g., trimer and tetramer, formations of unobserved receptors have received less attention. Here we propose a dimerization model of ligand-induced receptors in multivalent form representing physical observables under basis vectors of various aggregated receptor states. Our simulations of multivalent models not only reject Wofsy-Goldstein parameter conditions for cooperativity, but show that higher-order oligomer formations can shift cooperativity from positive to negative.
  6. Belousov R, Cohen EGD, Rondoni L
    Phys Rev E, 2017 Aug;96(2-1):022125.
    PMID: 28950465 DOI: 10.1103/PhysRevE.96.022125
    The present paper is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the related deterministic parameters of the Langevin equation for a Couette flow in a microscopic molecular dynamics model of a simple fluid. In this paper we find all the remaining constants of the stochastic dynamics, which then is simulated numerically and compared directly with the original physical system. By using these data, we study in detail the accuracy and precision of a second-order Langevin model for nonequilibrium physical systems theoretically and computationally. We find an intriguing relation between an applied external force and cumulants of the resulting flow fluctuations. This is characterized by a linear dependence of an athermal cumulant ratio, an apposite quantity introduced here. In addition, we discuss how the order of a given Langevin dynamics can be raised systematically by introducing colored noise.
  7. Chibbaro S, Dematteis G, Josserand C, Rondoni L
    Phys Rev E, 2017 Aug;96(2-1):021101.
    PMID: 28950466 DOI: 10.1103/PhysRevE.96.021101
    The Sagdeev-Zaslavski (SZ) equation for wave turbulence is analytically derived, both in terms of a generating function and of a multipoint probability density function (PDF), for weakly interacting waves with initial random phases. When the initial amplitudes are also random, a one-point PDF equation is derived. Such analytical calculations remarkably agree with results obtained in totally different fashions. Numerical investigations of the two-dimensional nonlinear Schrödinger equation (NLSE) and of a vibrating plate prove the following: (i) Generic Hamiltonian four-wave systems rapidly attain a random distribution of phases independently of the slower dynamics of the amplitudes, vindicating the hypothesis of initially random phases. (ii) Relaxation of the Fourier amplitudes to the predicted stationary distribution (exponential) happens on a faster time scale than relaxation of the spectrum (Rayleigh-Jeans distribution). (iii) The PDF equation correctly describes dynamics under different forcings: The NLSE has an exponential PDF corresponding to a quasi-Gaussian solution, as the vibrating plates, that also shows some intermittency at very strong forcings.
  8. Ng KC, Sheu TWH
    Phys Rev E, 2017 Oct;96(4-1):043302.
    PMID: 29347538 DOI: 10.1103/PhysRevE.96.043302
    It has been observed previously that the physical behaviors of Schmidt number (Sc) and Prandtl number (Pr) of an energy-conserving dissipative particle dynamics (eDPD) fluid can be reproduced by the temperature-dependent weight function appearing in the dissipative force term. In this paper, we proposed a simple and systematic method to develop the temperature-dependent weight function in order to better reproduce the physical fluid properties. The method was then used to study a variety of phase-change problems involving solidification. The concept of the "mushy" eDPD particle was introduced in order to better capture the temperature profile in the vicinity of the solid-liquid interface, particularly for the case involving high thermal conductivity ratio. Meanwhile, a way to implement the constant temperature boundary condition at the wall was presented. The numerical solutions of one- and two-dimensional solidification problems were then compared with the analytical solutions and/or experimental results and the agreements were promising.
  9. Abdullaev FK, Hadi MSA, Umarov B, Taib LA, Salerno M
    Phys Rev E, 2023 Apr;107(4-1):044218.
    PMID: 37198780 DOI: 10.1103/PhysRevE.107.044218
    We demonstrate the existence of compactons matter waves in binary mixtures of Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) subjected to equal contributions of intraspecies Rashba and Dresselhaus spin-orbit coupling (SOC) under periodic time modulations of the intraspecies scattering length. We show that these modulations lead to a rescaling of the SOC parameters that involves the density imbalance of the two components. This gives rise to density dependent SOC parameters that strongly influence the existence and the stability of compacton matter waves. The stability of SOC-compactons is investigated both by linear stability analysis and by time integrations of the coupled Gross-Pitaevskii equations. We find that SOC restricts the parameter ranges for stable stationary SOC-compacton existence but, on the other side, it gives a more stringent signature of their occurrence. In particular, SOC-compactons should appear when the intraspecies interactions and the number of atoms in the two components are perfectly balanced (or close to being balanced for the metastable case). The possibility to use SOC-compactons as a tool for indirect measurements of the number of atoms and/or the intraspecies interactions is also suggested.
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