Nakamura Kento, Kobayashi Tetsuya J
RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.
The University of Tokyo, Institute of Industrial Science, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505 Japan.
Phys Rev E. 2024 Dec;110(6-1):064407. doi: 10.1103/PhysRevE.110.064407.
Eukaryotic cells perform chemotaxis by determining the direction of chemical gradients based on stochastic sensing of concentrations at the cell surface. To examine the efficiency of this process, previous studies have investigated the limit of estimation accuracy for gradients. However, most studies have treated a circular cell shape, and the few considering elongated shapes assume the elongated direction as fixed. This leaves the question of how adaptive regulation of cell shape affects the estimation limit. Dynamics of cell shape during gradient sensing is biologically ubiquitous and can influence the estimation by altering the way the concentration is measured, and cells may strategically regulate their shape to improve estimation accuracy. To address this gap, we investigate the estimation limits in dynamic situations where elongated cells change their orientation adaptively depending on the sensed signal. We approach this problem by analyzing the stationary solution of the Bayesian nonlinear filtering equation. By applying diffusion approximation to the ligand-receptor binding process and the Laplace method for the posterior expectation under a high signal-to-noise ratio regime, we obtain an analytical expression for the estimation limit. This expression indicates that estimation accuracy can be improved by aligning the elongated direction perpendicular to the estimated direction, which is also confirmed by numerical simulations. Our analysis provides a basis for clarifying the interplay between estimation and control in gradient sensing and sheds light on how cells optimize their shape to enhance chemotactic efficiency.
真核细胞通过基于细胞表面浓度的随机感知来确定化学梯度的方向来进行趋化作用。为了检验这一过程的效率，先前的研究已经探究了梯度估计精度的极限。然而，大多数研究都处理的是圆形细胞形状，而少数考虑细长形状的研究则假定细长方向是固定的。这就留下了一个问题，即细胞形状的适应性调节如何影响估计极限。在梯度感知过程中细胞形状的动态变化在生物学上是普遍存在的，并且可以通过改变浓度测量方式来影响估计，细胞可能会策略性地调节其形状以提高估计精度。为了填补这一空白，我们研究了动态情况下的估计极限，即细长细胞根据感知到的信号自适应地改变其方向。我们通过分析贝叶斯非线性滤波方程的稳态解来解决这个问题。通过对配体 - 受体结合过程应用扩散近似以及在高信噪比条件下对后验期望应用拉普拉斯方法，我们得到了估计极限的解析表达式。该表达式表明，通过将细长方向与估计方向垂直对齐可以提高估计精度，这也通过数值模拟得到了证实。我们的分析为阐明梯度感知中估计与控制之间的相互作用提供了基础，并揭示了细胞如何优化其形状以提高趋化效率。
