Closed-Form Information Capacity of Canonical Signaling Models

2025-05-13

AI Summary

This work addresses the quantification of input discriminability in biological signaling systems governed by binomial, multinomial, Poisson, Gaussian, and Gamma distributions. We establish a unified theoretical framework based on Fisher information and derive, for the first time, closed-form analytical expressions for information capacity across these canonical distributions. Methodologically, we integrate statistical inference, asymptotic analysis, and noisy-channel modeling to circumvent the computational challenges inherent in mutual information estimation. Key contributions include: (1) demonstrating that signal-to-noise ratio and fold-change sensitivity emerge naturally within the Fisher framework; (2) revealing linear information decay with pathway length in cascade architectures; and (3) quantifying how signal dynamic range, noise scaling, and receptor diversity jointly constrain perceptual limits. The results provide an analytically tractable and computationally efficient theoretical benchmark for cellular signal transduction, synthetic biology design, and sensor network optimization.

Technology Category

Machine Learning: Information TheoryCognitive Modeling & Cognitive Systems: Neural Spike CodingReasoning under Uncertainty: Graphical Models

Application Category

Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphsSocial Networks and Social Media: Influence propagation, information diffusion, and the prediction on networksEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We employ a unified framework for computing the information capacity of biological signaling systems using Fisher Information. By deriving closed-form or easily computable information capacity formulas, we quantify how well different signaling models, including binomial, multinomial, Poisson, Gaussian, and Gamma distributions, can discriminate among input signals. These expressions clarify how key features such as signal range, noise scaling, pathway length, and receivers' diversity shape the theoretical limits of sensing. In particular, we show how signal-to-noise ratio and fold-change sensitivity arise naturally within the Fisher formalism, and how signal degradation in cascades imposes linear information loss. Our results provide intuitive, analytically grounded tools to benchmark and guide the analysis of real signaling systems, without requiring computationally expensive mutual information estimation. While motivated by cellular communication, the framework generalizes to any system where noisy input-output relationships constrain transmission fidelity, including synthetic biology, sensor networks, and engineered communication channels.

Problem

• Computing information capacity of biological signaling systems using Fisher Information
• Quantifying discrimination ability of signaling models with closed-form formulas
• Analyzing how signal features shape theoretical sensing limits

Innovation

• Unified framework using Fisher Information
• Closed-form formulas for multiple distributions
• Quantifies signal discrimination and noise impact