# Multi-dimensional biochemical information processing of dynamical patterns

## TL;DR

This paper investigates how biochemical systems decode multi-dimensional dynamical patterns of signaling molecules, optimizing information transfer under noise constraints and proposing biochemical implementations of the decoding networks.

## Contribution

It models and optimizes linear response decoders for biochemical signaling, revealing how noise influences the effectiveness of multi-pattern information extraction and proposing biochemical network implementations.

## Key findings

- Decoders with different response functions extract more information at low noise levels.
- High noise levels reduce the advantage of using multiple distinct decoders.
- Biochemical implementations of decoders can be achieved through cascade-type networks.

## Abstract

Cells receive signaling molecules by receptors and relay information via sensory networks so that they can respond properly depending on the type of signal. Recent studies have shown that cells can extract multi-dimensional information from dynamical concentration patterns of signaling molecules. We herein study how biochemical systems can process multi-dimensional information embedded in dynamical patterns. We model the decoding networks by linear response functions, and optimize the functions with the calculus of variations to maximize the mutual information between patterns and output. We find that, when the noise intensity is lower, decoders with different linear response functions, i.e., distinct decoders, can extract much information. However, when the noise intensity is higher, distinct decoders do not provide the maximum amount of information. This indicates that, when transmitting information by dynamical patterns, embedding information in multiple patterns is not optimal when the noise intensity is very large. Furthermore, we explore the biochemical implementations of these decoders using control theory and demonstrate that these decoders can be implemented biochemically through the modification of cascade-type networks, which are prevalent in actual signaling pathways.