Variability in mRNA Translation: A Random Matrix Theory Approach

TL;DR

This paper introduces a novel theoretical framework using random matrix theory to analyze how stochastic variability in translation rates affects protein production, revealing a universality principle that stabilizes overall protein output.

Contribution

It develops a new approach modeling translation rates as random variables and applies random matrix theory to explain protein production stability amidst cellular noise.

Findings

Average protein production depends only on the distribution of translation rates.

The framework explains stabilization of protein synthesis despite stochastic variability.

Universality principle applies to cellular translation processes.

Abstract

The rate of mRNA translation depends on the initiation, elongation, and termination rates of ribosomes along the mRNA. These rates depend on many "local" factors like the abundance of free ribosomes and tRNA molecules in the vicinity of the mRNA molecule. All these factors are stochastic and their experimental measurements are also noisy. An important question is how protein production in the cell is affected by this considerable variability. We develop a new theoretical framework for addressing this question by modeling the rates as identically and independently distributed random variables and using tools from random matrix theory to analyze the steady-state production rate. The analysis reveals a principle of universality: the average protein production rate depends only on the of the set of possible values that the random variable may attain. This explains how total protein production can be stabilized despite the overwhelming stochasticticity underlying cellular processes.