Biology subjects

Sukekawa, T.

Publications and source records attributed to Sukekawa, T..

2 recordsLinked to original sources

bioRxiv2026

Pattern dynamics on mass-conserved reaction-diffusion compartment model

Mass-conserved reaction-diffusion systems are used as mathematical models for various phenomena such as cell polarity. Numerical simulations of this system present transient dynamics in which multiple stripe patterns converge to spatially monotonic patterns. Previous studies indicated that the transient dynamics are driven by a mass conservation law and by variations in the amount of substance contained in each pattern, which we refer to as "pattern flux". However, it is challenging to mathematically investigate these pattern dynamics. In this study, we introduce a reaction-diffusion compartment model to investigate the pattern dynamics in view of the conservation law and the pattern flux. This model is defined on multiple intervals (compartments), and diffusive couplings are imposed on each boundary of the compartments. Corresponding to the transient dynamics in the original system, we consider the dynamics around stripe patterns in the compartment model. We derive ordinary differential equations describing the pattern dynamics of the compartment model and analyze the existence and stability of equilibria for the reduced ODE with respect to the boundary parameters. For a specific parameter setting, we obtained results consistent with previous studies. Moreover, we present that the stripe patterns in the compartment model are potentially stabilized by changing the parameter, which is not observed in the original system. We expect that the methodology developed in this paper is extendable to various directions, such as membrane-induced pattern control.

biophysics↗

bioRxiv2025

Imaging Data-based Model Description Combining OptimalTransport and Phase-field Model

The geometrical properties of a cell are not merely passive consequences of cellular function but actively regulate key biological processes during development, morphogenesis, and disease. Although modern live-imaging techniques now allow detailed monitoring of cell morphology, incorporating such complex geometrical information into mathematical models has remained a major challenge. Conventional modeling approaches often rely on artificial cell shape assumptions or purely in silico constructions, and discrete imaging data remain fundamentally mismatched with continuous biochemical models based on differential equations. As a result, current models struggle to accurately reproduce biochemical dynamics within realistic, dynamically changing cell geometries. To overcome these limitations, we establish a novel mathematical framework, Imaging Data-based Model Description (IDMD), which integrates Optimal Transport (OT) theory with phase-field (PF) modeling to bridge imaging data and mathematical models. Using live-imaging data from in vitro cultured cells and the one-cell C. elegans embryo, we demonstrate the versatility of our framework. By directly incorporating real cell geometry into mathematical modeling, our framework provides a powerful new avenue for investigating how geometrical constraints regulate biochemical pattern formation and cell-fate decisions. More broadly, this study highlights a promising direction for integrating modern data science techniques with mathematical modeling, opening new conceptual and methodological possibilities for understanding geometry-driven biological processes in development and disease.

biophysics↗