# An Information-Theoretic Approach to Cellular Decision-Making Strategies: How Rate Distortion Theory Provides an Optimal Method for Describing Binary Cellular Decision-Making Systems

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## Date

2014

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## Authors

Mangum, Joshua, B.

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## Abstract

Rate distortion theory, a branch of information theory, was originally developed to help improve the efficiency of data transmission in telecommunications. It's currently being used as a major modeling method to provide a quantitative description for analyzing biological signaling pathways. Rate distortion theory provides a way to compute probability functions that describe how cells should respond given various stimuli or environmental changes, independent of the mechanism responsible for these decisions. In this thesis, mathematical models describing binary cell decisions will be studied and analyzed within the framework of rate distortion theory. / / In this project we discuss the history, terminology, mathematical structure, and major aspects of rate distortion theory. These aspects of the theory will then provide the foundation for how can be applied in a biological context. The principle elements of these models depict cellular decision-making strategies as conditional probabilities, where environmental stimuli such as temperature fluctuations or concentration gradients are considered to be the input. The decisions made in response to these changing stimuli are the output of the algorithm. A rate distortion function defines the average amount of "incorrect" decisions given a stimulus, and a rate distortion curve quantifies stochastically, the fate of the given cell, given the stimulation. A Blahut Arimoto algorithm is used to compute the rate distortion curve that provides the optimal decision-making pathways. / / According to Perkins and Swain, (Perkins and Swain, 2009) cellular decision-making has the following main features: a cell must (1) estimate the state of its environment by sensing stimuli; (2) make a decision informed by the consequences of the alternatives; and (3) perform these functions in a way that maximizes the fitness of the population. The consistency of these axioms and the effort to investigate, explain, and interpret observable characteristics of cellular functions such as hysteresis, irreversibility, and random strategies will be discussed. This theory provides a method for explaining why cells partake in self-destructive behavior such as apoptosis in order to benefit the population of the cells. /