Stochastic noise in translation

Translation lies at the heart of every living organism, it is the process synthesizing the proteins, a main component in the cells. Earlier studies have considered protein synthesis as mainly initiation limited, modeling it as a first-order reaction with respect to free ribosomes and mRNA. In such studies, the noise is therefore coming from initiation phase only. We have previously studied a continuous deterministic model for translation, taking into account the ribosome elongation and a possible behavior similar to a “traffic jam” of ribosomes on the mRNA chain. This modeling allowed us to observe that there was a trade-off between ribosome density (fraction of an mRNA chain bound by ribosomes) and protein synthesis rate, with the optimal value in a region of elongation- and initiation-limited synthesis rate. In the present study we implemented an exact stochastic model for translation, based on a modified Gillespie’s algorithm with additional Monte-Carlo steps to follow individual stochastic behavior of all molecules. Based on this, we investigated the relation of initiation noise to the noise in protein synthesis. Additionally we examine if there is also a trade-off between optimal synthesis rate and noise. The study is performed for different ribosome densities and various mRNA lengths.

Vassily Hatzimanikatis, Julien Racle, Adam Stefaniuk

2011

Deciphering translation - a genome-wide analysis of translation in Escherichia coli

Vassily Hatzimanikatis, Julien Racle

Protein synthesis is one of the central elements in every living cell. For this process, mRNAs coding for genes are simultaneously competing for the same translation machinery (ribosomes and amino acids). But the ultimate determinants of cellular functions are the proteins, a good understanding of this process is therefore of crucial importance. For this purpose, we developed a genome-wide, mechanistic, mathematical model of translation, taking into account individual codon kinetics. It is used to quantify the rate limiting steps of translation and gain insight into the mechanism of regulation of expression between different proteins. We observe for each gene in a first low-occupancy phase a nearly linear increase in protein synthesis rate with amount of bound ribosomes to the mRNA, followed by a plateau of maximum synthesis rate. A further increase in the ribosomal coverage of the mRNA leads to a decrease in protein production rate, and might act as sinks for system resources like ribosomes. Native E. coli gene sequences are also compared to randomly obtained synonymous sequences, coding the same protein, and it is found some genes of higher significance for the cell have been better optimized for protein synthesis rate than other.

2010

Noise analysis of genome-scale protein synthesis using a discrete computational model of translation

Vassily Hatzimanikatis, Julien Racle, Adam Stefaniuk

Noise in genetic networks has been the subject of extensive experimental and computational studies. However, very few of these studies have considered noise properties using mechanistic models that account for the discrete movement of ribosomes and RNA polymerases along their corresponding templates (mRNA and DNA). The large size of these systems, which scales with the number of genes, mRNA copies, codons per mRNA, and ribosomes, is responsible for some of the challenges. Additionally, one should be able to describe the dynamics of ribosome exchange between the free ribosome pool and those bound to mRNAs, as well as how mRNA species compete for ribosomes. We developed an efficient algorithm for stochastic simulations that addresses these issues and used it to study the contribution and trade-offs of noise to translation properties (rates, time delays, rate-limiting steps). The algorithm scales linearly with the number of mRNA copies, which allowed us to study the importance of genome-scale competition between mRNAs for the same ribosomes. We determined that noise is minimized under conditions maximizing the specific synthesis rate. Moreover, sensitivity analysis of the stochastic system revealed the importance of the elongation rate in the resultant noise, whereas the translation initiation rate constant was more closely related to the average protein synthesis rate. We observed significant differences between our results and the noise properties of the most commonly used translation models. Overall, our studies demonstrate that the use of full mechanistic models is essential for the study of noise in translation and transcription.

Amer Inst Physics2015