arXiv subjects

Madoka Nakayama

Publications and source records attributed to Madoka Nakayama.

7 recordsLinked to original sources

arXiv2026

Necessary and sufficient condition for hysteresis in the mathematical model of the cell type regulation of \textit{Bacillus subtilis}

The key to a robust life system is to ensure that each cell population is maintained in an appropriate state. In this work, a mathematical model was used to investigate the control of the switching between the migrating and non-migrating states of the Bacillus subtilis cell population. In this case, the motile cells and matrix producers were the predominant cell types in the migrating cell population and non-migrating state, respectively, and could be suitably controlled according to the environmental conditions and cell density information. A minimal smooth model consisting of four ordinary differential equations was used as the mathematical model to control the B. subtilis cell types. Furthermore, the necessary and sufficient conditions for the hysteresis, which pertains to the change in the pheromone concentration, were clarified. In general, the hysteretic control of the cell state enables stable switching between the migrating and growth states of the B. subtilis cell population, thereby facilitating the biofilm life cycle. The results of corresponding culture experiments were examined, and the obtained corollaries were used to develop a model to input environmental conditions, especially, the external pH. On this basis, the environmental conditions were incorporated in a simulation model for the cell type control. In combination with a mathematical model of the cell population dynamics, a prediction model for colony growth involving multiple cell states, including concentric circular colonies of B. subtilis, could be established.

q-bio.CB↗

arXiv2026

Turing patterns on non-fluctuating surfaces under mechanical stresses

This paper presents a numerical study of Turing patterns (TPs) governed by reaction diffusion equations for the activator $u$ and the inhibitor $v$ on two- and three-dimensional lattices without vertex fluctuations. In this framework, $u$ and $v$ are fixed at discrete spatial locations, as pigment cells on zebrafish skin or shell patterns. Mechanical effects are incorporated through the Finsler geometry modeling formulation, which introduces an internal degree of freedom, $\vecτ$, representing the direction of mechanical stress. A tensile-stress formula based on the Gaussian bond potential is shown to be well defined on non-fluctuating lattices, enabling the entropy associated with stress relaxation to be evaluated in a manner analogous to that on fluctuating surfaces. The results indicate that biological TPs respond to external mechanical forces in much the same way as TPs on fluctuating membranes. Simulation codes are provided in the Supplementary Material.

nlin.PS↗

arXiv2023

Langevin and Navier-Stokes Simulation of Three-Dimensional Protoplasmic Streaming

In this paper, we report the numerical results obtained using the Langevin Navier-Stokes (LNS) simulation of the velocity distribution of three-dimensional (3D) protoplasmic streaming in plant cells, such as those of {\it Nitella flexilis}. The LNS simulations are performed on 3D cylinders discretized by regular cubes in which fluid velocities are activated by boundary velocities parallel and nonparallel to the longitudinal direction and a random Brownian force with strength $D$. We find that, for a finite $D$, the velocity distribution $h(V), V\!=\!|\vec{V}|$, has two different peaks at a small non-zero $V$ and a finite $V$, and the distribution $h(V_z)$ for $|V_z|$ along the longitudinal direction also has a peak at finite $V_z$. These results are in good agreement with the reported velocity distributions observed using laser Doppler velocimetry. Moreover, we study the effects of the Brownian force on biological material mixing and find that mixing along the $\vec{V}$ direction enhanced by the nonparallel circular motion is further improved by the Brownian force in the experimentally relevant region of $D$. In addition, the experimentally relevant $D$ is found to be consistent with the expectation from the fluctuation dissipation relation between the random stress and viscosity in the LNS equation of Landau and Lifschitz for incompressible fluids.

physics.flu-dyn↗

arXiv2023

Numerical study of anisotropic diffusion in Turing patterns based on Finsler geometry modeling

We numerically study the anisotropic Turing patterns (TPs) of an activator-inhibitor system, focusing on anisotropic diffusion by using the Finsler geometry (FG) modeling technique. In the FG modeling prescription, the diffusion coefficients are dynamically generated to be direction dependent owing to an internal degree of freedom (IDOF) and its interaction with the activator and inhibitor under the presence of thermal fluctuations. In this sense, FG modeling contrasts sharply with the standard numerical technique, where direction-dependent diffusion coefficients are assumed in the reaction-diffusion (RD) equations of Turing. To find the solution of the RD equations, we use a hybrid numerical technique as a combination of the metropolis Monte Carlo method for IDOF updates and discrete RD equations for steady-state configurations of activator-inhibitor variables. We find that the newly introduced IDOF and its interaction are one possible origin of spontaneously emergent anisotropic patterns on living organisms such as zebra and fishes. Moreover, the IDOF makes TPs controllable by external conditions if the IDOF is identified with lipids on cells or cell mobility.

nlin.PS↗

arXiv2022

Langevin Navier-Stokes simulation of protoplasmic streaming by 2D MAC method

We study protoplasmic streaming in plant cells such as chara brauni by simplifying the flow field to a two-dimensional Couette flow with Brownian random motion inside parallel plates. Protoplasmic streaming is receiving a lot of attention in many areas, such as agriculture-technology and biotechnology. The plant size depends on the velocity of streaming and the driving force originating in molecular motors. Therefore, it is interesting to study detailed information on the velocity of streaming. Recently, experimentally observed peaks in the velocity distribution have been simulated by a 2D Langevin Navier-Stokes (LNS) equation for vortex and flow function. However, to simulate actual 3D flows, we have to use the NS equation for velocity, which, in the case of 2D flows, is not always equivalent to that for vorticity and stream function. In this paper, we report that a 2D LNS equation for velocity and pressure successfully simulates protoplasmic streaming by comparing the results with the experimental data and those obtained by 2D LNS simulations for vortex and flow function. Moreover, a dimensional analysis clarifies the dependence of numerical results on the strength $D$ of Brownian random force and physical parameters such as kinematic viscosity and cell size. We find from this analysis how the peak position in normalized velocity distribution moves depending on these parameters.

physics.flu-dyn↗

arXiv2020

Stochastic Fluid Dynamics Simulations of the Velocity Distribution in Protoplasmic Streaming

Protoplasmic streaming in plant cells is directly visible in the cases of \textit{Chara corallina} and \textit{Nitella flexilis}, and this streaming is understood to play a role in the transport of biological materials. For this reason, related studies have focused on molecular transportation from a fluid mechanics viewpoint. However, the experimentally observed distribution of the velocity along the flow direction $x$, which exhibits two peaks at $V_x\!=\!0$ and at a finite $V_x(\not=\!0)$, remains to be studied. In this paper, we numerically study whether this behavior of the flow field can be simulated by a 2D stochastic Navier-Stokes (NS) equation for Couette flow, in which random Brownian force is assumed. We present the first numerical evidence that these peaks are reproduced by the stochastic NS equation, which implies that the Brownian motion of the fluid particles plays an essential role in the emergence of these peaks in the velocity distribution. We also find that the position of the peak at $V_x(\not=\!0)$ moves with the variation in the strength $D$ of the random Brownian force, which also changes depending on physical parameters such as the kinematic viscosity, boundary velocity and diameter of the plant cells.

cond-mat.stat-mech↗

arXiv2013

Pattern formation in a diffusion-ODE model with hysteresis

Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations (diffusion-ODE models), which differ from the usual reaction-diffusion systems. One of the mechanisms of pattern formation in such systems is based on the existence of multiple steady states and hysteresis in the ODE subsystem. Diffusion tries to average different states and is the cause of spatio-temporal patterns. In this paper we provide a systematic description of stationary solutions of such systems, having the form of transition or boundary layers. The solutions are discontinuous in the case of non-diffusing variables whose quasi-stationary dynamics exhibit hysteresis. The considered model is motivated by biological applications and elucidates a possible mechanism of formation of patterns with sharp transitions.

math.AP↗