Translation is a fundamental cellular process in gene expression. During translation, complex micro-molecules called ribosomes sequentially scan the genetic information encoded in the mRNA molecule and transform it into a chain of amino-acids that is further processed to yield a functional protein. The speed of 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 cognate tRNA molecules in the vicinity of the mRNA . Consequently, copies of the same mRNA moleculelocated at different parts of the cell may be translated in different rates. An important question is how total protein production in the cell is regulated,despite this considerable variability. We develop a  theoretical framework for addressing this question that is based on: (1) considering a computational model for the flow of ribosomes along the mRNA, called the ribosome flow model, but with rates that are random variables ; and (2) analyzing the model steady-state behaviour using tools from random matrix theory . Our results show that if all the rates are modeled as i. i.d. random variables bounded from below by a value B then as the length of the mRNA increases the total protein production converges, with probability one, to a value that depends only on B. This reveals a principle of universality: total protein production is insensitive to many of the details underlying the distribution of the random variables .
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 .
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Translation is a fundamental cellular process in gene expression. During translation, complex micro-molecules called ribosomes sequentially scan the genetic information encoded in the mRNA molecule and transform it into a chain of amino-acids that is further processed to yield a functional protein. The speed of
The rate of mRNA
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``local''
"local"
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cognate
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. Consequently, copies of the same mRNA moleculelocated at different parts of the cell may be translated in different rates.
molecule. All these factors are stochastic and their experimental measurements are also noisy.
D
total
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regulated,despite
affected by
A
new
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that is based on: (1) considering a computational model for the flow of ribosomes along the mRNA, called the ribosome flow model, but with rates that are random variables ; and (2) analyzing the model steady-state behaviour
by modeling the rates as identically and independently distributed random variables and
R
. Our results show that if all the rates are modeled as i. i.d. random variables bounded from below by a value B then as the length of the mRNA increases the total protein production converges, with probability one, to a value that
to analyze the steady-state production rate. The analysis reveals a principle of universality: the average protein production rate
R
B. This reveals a principle of universality:
the of the set of possible values that the random variable may attain. This explains how
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is insensitive to many of the details underlying the distribution of the random variables
can be stabilized despite the overwhelming stochasticticity underlying cellular processes