scholarly journals Fitness costs of noise in biochemical reaction networks and the evolutionary limits of cellular robustness

2016 ◽  
Author(s):  
J. David Van Dyken
Keyword(s):  
Gene Expression ◽  
Cell Size ◽  
Cell Function ◽  
Noise Control ◽  
Average Rate ◽  
Transcriptional Noise ◽  
Gene Expression Noise ◽  
Expression Noise ◽  
Regulatory Complexity ◽  
Gene Regulatory

ABSTRACTGene expression is inherently noisy, but little is known about whether noise affects cell function or, if so, how and by how much. Here I present a theoretical framework to quantify the fitness costs of gene expression noise and identify the evolutionary and synthetic targets of noise control. I find that gene expression noise reduces fitness by slowing the average rate of nutrient uptake and protein synthesis. This is a direct consequence of the hyperbolic (Michaelis-Menten) kinetics of most biological reactions, which I show cause “hyperbolic filtering”, a process that diminishes both the average rate and noise propagation of stochastic reactions. Interestingly, I find that transcriptional noise directly slows growth by slowing the average translation rate. Perhaps surprisingly, this is the largest fitness cost of transcriptional noise since translation strongly filters mRNA noise, making protein noise largely independent of transcriptional noise, consistent with empirical data. Translation, not transcription, then, is the primary target of protein noise control. Paradoxically, selection for protein-noise control favors increased ribosome-mRNA binding affinity, even though this increases translational bursting. However, I find that the efficacy of selection to suppress noise decays faster than linearly with increasing cell size. This predicts a stark, cell-size-mediated taxonomic divide in selection pressures for noise control: small unicellular species, including most prokaryotes, face fairly strong selection to suppress gene expression noise, whereas larger unicells, including most eukaryotes, experience extremely weak selection. I suggest that this taxonomic discrepancy in selection efficacy contributed to the evolution of greater gene-regulatory complexity in eukaryotes.ARTICLE SUMMARYGene expression is a probabilistic process, resulting in random variation in mRNA and protein abundance among cells called “noise”. Understanding how noise affects cell function is a major problem in biology. Here I present theory demonstrating that gene expression noise slows the average rate of cell division. Furthermore, by modeling stochastic gene expression with non-linearity, I identify novel mechanisms of cellular robustness. However, I find that the cost of noise, and therefore the strength of selection favoring robustness, decays faster than linearly with increasing cell size. This may help explain the vast differences in gene-regulatory complexity between prokaryotes and eukaryotes.

scholarly journals Coordination of gene expression noise with cell size: analytical results for agent-based models of growing cell populations

2021 ◽  
Vol 18 (178) ◽  
pp. 20210274
Author(s):  
Philipp Thomas ◽  
Vahid Shahrezaei
Keyword(s):  
Gene Expression ◽  
Master Equation ◽  
Cell Size ◽  
Chemical Master Equation ◽  
Gillespie Algorithm ◽  
Agent Based Models ◽  
Extrinsic Noise ◽  
Gene Expression Noise ◽  
Agent Based ◽  
Expression Noise

The chemical master equation and the Gillespie algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise. We find that the solution of the chemical master equation—including static extrinsic noise—exactly agrees with the agent-based formulation when the network under study exhibits stochastic concentration homeostasis , a novel condition that generalizes concentration homeostasis in deterministic systems to higher order moments and distributions. We illustrate stochastic concentration homeostasis for a range of common gene expression networks. When this condition is not met, we demonstrate by extending the linear noise approximation to agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the chemical master equation. Surprisingly, the total noise of the agent-based approach can still be well approximated by extrinsic noise models.

scholarly journals Noise propagation shapes condition-dependent gene expression noise in Escherichia coli

2019 ◽  
Author(s):  
Arantxa Urchueguía ◽  
Luca Galbusera ◽  
Gwendoline Bellement ◽  
Thomas Julou ◽  
Erik van Nimwegen
Keyword(s):  
Gene Expression ◽  
Growth Conditions ◽  
Transcriptional Noise ◽  
Noise Propagation ◽  
Gene Expression Noise ◽  
E Coli ◽  
Expression Noise ◽  
Rate Dependent ◽  
Genome Wide ◽  
Principal Axes

AbstractAlthough it is well appreciated that gene expression is inherently noisy and that transcriptional noise is encoded in a promoter’s sequence, little is known about the variation in transcriptional noise across growth conditions. Using flow cytometry we here quantify transcriptional noise in E. coli genome-wide across 8 growth conditions, and find that noise and gene regulation are intimately coupled. Apart from a growth-rate dependent lower bound on noise, we find that individual promoters show highly condition-dependent noise and that condition-dependent expression noise is shaped by noise propagation from regulators to their targets. A simple model of noise propagation identifies TFs that most contribute to both condition-specific and condition-independent noise propagation. The overall correlation structure of sequence and expression properties of E. coli genes uncovers that genes are organized along two principal axes, with the first axis sorting genes by their mean expression and evolutionary rate of their coding regions, and the second axis sorting genes by their expression noise, the number of regulatory inputs in their promoter, and their expression plasticity.

scholarly journals Division rate, cell size and proteome allocation: impact on gene expression noise and implications for the dynamics of genetic circuits

2017 ◽  
Author(s):  
François Bertaux ◽  
Samuel Marguerat ◽  
Vahid Shahrezaei
Keyword(s):  
Gene Expression ◽  
Cell Division ◽  
Cell Size ◽  
Global Changes ◽  
Noise Levels ◽  
Division Rate ◽  
Gene Expression Noise ◽  
Expression Noise ◽  
Cell Division Rate ◽  
Degradation Rates

AbstractThe cell division rate, size, and gene expression programmes change in response to external conditions. These global changes impact on average concentrations of biomolecule and their variability or noise. Gene expression is inherently stochastic, and noise levels of individual proteins depend on synthesis and degradation rates as well as on cell-cycle dynamics. We have modelled stochastic gene expression inside growing and dividing cells to study the effect of division rates on noise in mRNA and protein expression. We use assumptions and parameters relevant to Escherichia coli, for which abundant quantitative data are available. We find that coupling of transcription, but not translation rates to the rate of cell division can result in protein concentration and noise homeostasis across conditions. Interestingly, we find that the increased cell size at fast division rates, observed in E. coli d other unicellular organisms, buffers noise levels even for proteins with decreased expression at faster growth. We then investigate the functional importance of these regulations using gene regulatory networks that exhibit bi-stability and oscillations. We find that network topology affects robustness to changes in division rate in complex and unexpected ways. In particular, a simple model of persistence, based on global physiological feedback, predicts increased proportion of persistors cells at slow division rates. Altogether, our study reveals how cell size regulation in response to cell division rate could help controlling gene expression noise. It also highlights that understanding of circuits’ robustness across growth conditions is key for the effective design of synthetic biological systems.

scholarly journals A System for Gene Expression Noise Control in Yeast

2018 ◽  
Vol 7 (11) ◽  
pp. 2618-2626 ◽  
Author(s):  
Max Mundt ◽  
Alexander Anders ◽  
Seán M. Murray ◽  
Victor Sourjik
Keyword(s):  
Gene Expression ◽  
Noise Control ◽  
Gene Expression Noise ◽  
Expression Noise

scholarly journals Division rate, cell size and proteome allocation: impact on gene expression noise and implications for the dynamics of genetic circuits

2018 ◽  
Vol 5 (3) ◽  
pp. 172234 ◽  
Author(s):  
François Bertaux ◽  
Samuel Marguerat ◽  
Vahid Shahrezaei
Keyword(s):  
Gene Expression ◽  
Cell Division ◽  
Cell Size ◽  
Global Changes ◽  
Noise Levels ◽  
Division Rate ◽  
Gene Expression Noise ◽  
Expression Noise ◽  
Cell Division Rate ◽  
Degradation Rates

The cell division rate, size and gene expression programmes change in response to external conditions. These global changes impact on average concentrations of biomolecule and their variability or noise. Gene expression is inherently stochastic, and noise levels of individual proteins depend on synthesis and degradation rates as well as on cell-cycle dynamics. We have modelled stochastic gene expression inside growing and dividing cells to study the effect of division rates on noise in mRNA and protein expression. We use assumptions and parameters relevant to Escherichia coli , for which abundant quantitative data are available. We find that coupling of transcription, but not translation rates to the rate of cell division can result in protein concentration and noise homeostasis across conditions. Interestingly, we find that the increased cell size at fast division rates, observed in E. coli and other unicellular organisms, buffers noise levels even for proteins with decreased expression at faster growth. We then investigate the functional importance of these regulations using gene regulatory networks that exhibit bi-stability and oscillations. We find that network topology affects robustness to changes in division rate in complex and unexpected ways. In particular, a simple model of persistence, based on global physiological feedback, predicts increased proportion of persister cells at slow division rates. Altogether, our study reveals how cell size regulation in response to cell division rate could help controlling gene expression noise. It also highlights that understanding circuits' robustness across growth conditions is key for the effective design of synthetic biological systems.

scholarly journals A system for gene expression noise control in yeast

2018 ◽  
Author(s):  
Max Mundt ◽  
Alexander Anders ◽  
Seán Murray ◽  
Victor Sourjik
Keyword(s):  
Gene Expression ◽  
Noise Control ◽  
Stochastic Variation ◽  
Gene Expression Noise ◽  
Protein Levels ◽  
Expression Noise ◽  
Degradation Rates ◽  
Output Noise ◽  
Complex Regulatory Network ◽  
Synthesis And Degradation

AbstractGene expression noise arises from stochastic variation in the synthesis and degradation of mRNA and protein molecules and creates differences in protein numbers across populations of genetically identical cells. Such variability can lead to imprecision and reduced performance of both native and synthetic networks. In principle, gene expression noise can be controlled through the rates of transcription, translation and degradation, such that different combinations of those rates lead to the same protein concentrations but at different noise levels. Here, we present a “noise tuner” which allows orthogonal control over the transcription and the mRNA degradation rates by two different inducer molecules. Combining experiments with theoretical analysis, we show that in this system the noise is largely determined by the transcription rate whereas mean expression can be independently adjusted by mRNA stability. This noise tuner enables twofold changes in gene expression noise over a fivefold range of mean protein levels. We demonstrated the efficacy of the noise tuner in a complex regulatory network by varying gene expression noise in the mating pathway of Saccharomyces cerevisiae, which allowed us to control the output noise and the mutual information transduced through the pathway. The noise tuner thus represents an effective tool of gene expression noise control, both to interrogate noise sensitivity of natural networks and enhance performance of synthetic circuits.

scholarly journals Coordination of gene expression noise with cell size: extrinsic noise versus agent-based models of growing cell populations

2020 ◽  
Author(s):  
Philipp Thomas ◽  
Vahid Shahrezaei
Keyword(s):  
Gene Expression ◽  
Master Equation ◽  
Cell Size ◽  
Chemical Master Equation ◽  
Simulation Algorithm ◽  
Agent Based Models ◽  
Extrinsic Noise ◽  
Gene Expression Noise ◽  
Agent Based ◽  
Expression Noise

The chemical master equation and the stochastic simulation algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled for through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise in a growing population. We find that the solution of the chemical master equation – including static extrinsic noise – exactly agrees with the one of the agent-based formulation when a simple condition on the network’s topology is met. We illustrate this result for a range of common gene expression networks. When these conditions are not met, we demonstrate using analytical solutions of the agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the effective master equation. Surprisingly, the latter distorts total noise in gene regulatory networks by at most 8% independently of network parameters. Our results highlight the accuracy of extrinsic noise modelling within the chemical master equation framework.

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