細胞運動の新しい数理モデル(A new mathematical model of cellular movement)

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2022-05-16 ペンシルベニア州立大学(PennState)

細胞が運動する際にどのように形を変えるかを記述する数理モデルによると、その運動は主に “ミオシン” と呼ばれる骨格タンパク質の収縮によって駆動されていることが示唆された。ペンシルベニア州立大学で開発された新しいモデルは、細胞の動きが重要な役割を果たす様々な生物学的プロセスの理解を深めるのに役立ち、また、生物学的プロセスを模倣する人工システムの開発にも役立つ可能性があるとのことです。

<関連情報>

収縮駆動型細胞運動の漸近的安定 Asymptotic stability of contraction-driven cell motion

C. Alex Safsten, Volodmyr Rybalko, and Leonid Berlyand
Physical Review E  Published 14 February 2022
DOI:https://doi.org/10.1103/PhysRevE.105.024403

Abstract

We study the onset of motion of a living cell (e.g., a keratocyte) driven by myosin contraction with focus on a transition from unstable radial stationary states to stable asymmetric moving states. We introduce a two- dimensional free-boundary model that generalizes a previous one-dimensional model [P. Recho, T. Putelat, and L. Truskinovsky, Phys. Rev. Lett. 111, 108102 (2013)] by combining a Keller-Segel model, a Hele-Shaw boundary condition, and the Young-Laplace law with a regularizing term which precludes blowup or collapse by ensuring that membrane-cortex interaction is sufficiently strong. We find a family of asymmetric traveling solutions bifurcating from stationary solutions. Our main result is nonlinear asymptotic stability of traveling solutions that model observable steady cell motion. We derive an explicit asymptotic formula for the stability-determining eigenvalue via asymptotic expansions in small speed. This formula greatly simplifies computation of this eigenvalue and shows that stability is determined by the change in total myosin mass when stationary solutions bifurcate to traveling solutions. Our spectral analysis reveals the physical mechanisms of stability.

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