Inferring the Chemotaxis Distortion Function from Cellular Decision Strategies

TL;DR

This work treats chemotaxis as an information-processing task and uses rate-distortion theory (RDT) with the Blahut–Arimoto algorithm to compute optimal decision strategies under a distortion constraint. It introduces an inverse method, IBAA, to infer the distortion function d(x,y) from observed input–output statistics, handling finite data with Laplace smoothing and calibrating the result via a scale factor. The authors validate IBAA on a binary apoptosis model and apply it to a LEGI-based chemotaxis model, showing that the inferred distortion function is state-dependent and modulated by the Hill coefficient h, i.e., higher amplification strengthens the penalty for errors. This framework provides a general approach to uncover hidden decision criteria in biological and engineered systems operating under uncertainty, with implications for understanding adaptive information processing in cells.

Abstract

Cellular intelligence enables cells to process environmental signals and make context-dependent decisions, as exemplified by chemotaxis, where cells navigate chemical gradients despite noisy signaling pathways. To investigate how cells deal with uncertainty, we apply an information-theoretic framework based on rate distortion theory (RDT). The Blahut-Arimoto algorithm (BAA) computes optimal decision strategies that minimize mutual information while satisfying distortion constraints, balancing sensing accuracy with distortion constraint equivalent to resource cost. We propose the inverse Blahut-Arimoto algorithm (IBAA) to compute the distortion function, which quantifies the system's decision-making criteria for realizing a decision strategy to map input signals to outputs. This general framework extends beyond chemotaxis to biological and engineered systems requiring efficient information processing under uncertainty. We validate the proposed IBAA by accurately estimating theoretical distortion functions in a cellular apoptosis scenario. Additionally, using the local excitation global inhibition (LEGI) model to simulate chemotactic responses, we compute the distortion functions from the cell's perspective. Our finding reveals a state-dependent decision criteria by the cell.

Figures (13)

• Figure 1: Modular view of the chemotaxis process three stages. From left to right: sensing, signal transduction, and actuation stage (created with biorender.com).
• Figure 2: Schematic of a circular cell divided into $N$ sectors, with receptors uniformly distributed along the membrane. The chemoattractant (ligand) source generates a linear ligand gradient, visualized by a green background gradient and matching outer arc colors (darker shades indicate higher ligand concentration) (created with biorender.com).
• Figure 3: Schematic of chemotaxis as an information processing system. The true source direction $\theta_s$ passes through the noisy system to yield receptor occupancy, which the strategy stage maps to a movement direction $\theta_m$.
• Figure 4: System schematic of a noisy channel with input $X$ and output $Y$.
• Figure 5: (a) Hamming-like distortion function in \ref{['eq:Hamming']}; (b) Rectified squared distortion function in \ref{['eq:squared']}.