Rules for biological regulation based on error minimization

The control of gene expression involves complex mechanisms that show large variation in design. For example, genes can be turned on either by the binding of an activator (positive control) or the unbinding of a repressor (negative control). What determines the choice of mode of control for each gene? This study proposes rules for gene regulation based on the assumption that free regulatory sites are exposed to nonspecific binding errors, whereas sites bound to their cognate regulators are protected from errors. Hence, the selected mechanisms keep the sites bound to their designated regulators for most of the time, thus minimizing fitness-reducing errors. This offers an explanation of the empirically demonstrated Savageau demand rule: Genes that are needed often in the natural environment tend to be regulated by activators, and rarely needed genes tend to be regulated by repressors; in both cases, sites are bound for most of the time, and errors are minimized. The fitness advantage of error minimization appears to be readily selectable. The present approach can also generate rules for multi-regulator systems. The error-minimization framework raises several experimentally testable hypotheses. It may also apply to other biological regulation systems, such as those involving protein-protein interactions.Comment: biological physics, complex networks, systems biology, transcriptional regulation http://www.weizmann.ac.il/complex/tlusty/papers/PNAS2006.pdf http://www.pnas.org/content/103/11/3999.ful

Nonlinear Protein Degradation and the Function of Genetic Circuits

The functions of most genetic circuits require sufficient degrees of cooperativity in the circuit components. While mechanisms of cooperativity have been studied most extensively in the context of transcriptional initiation control, cooperativity from other processes involved in the operation of the circuits can also play important roles. In this study, we examine a simple kinetic source of cooperativity stemming from the nonlinear degradation of multimeric proteins. Ample experimental evidence suggests that protein subunits can degrade less rapidly when associated in multimeric complexes, an effect we refer to as cooperative stability. For dimeric transcription factors, this effect leads to a concentration-dependence in the degradation rate because monomers, which are predominant at low concentrations, will be more rapidly degraded. Thus cooperative stability can effectively widen the accessible range of protein levels in vivo. Through theoretical analysis of two exemplary genetic circuits in bacteria, we show that such an increased range is important for the robust operation of genetic circuits as well as their evolvability. Our calculations demonstrate that a few-fold difference between the degradation rate of monomers and dimers can already enhance the function of these circuits substantially. These results suggest that cooperative stability needs to be considered explicitly and characterized quantitatively in any systematic experimental or theoretical study of gene circuits.Comment: 42 pages, 10 figure

Regulatory control and the costs and benefits of biochemical noise

Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions.Comment: Revised manuscript;35 pages, 4 figures, REVTeX4; to appear in PLoS Computational Biolog

The role of input noise in transcriptional regulation

Even under constant external conditions, the expression levels of genes fluctuate. Much emphasis has been placed on the components of this noise that are due to randomness in transcription and translation; here we analyze the role of noise associated with the inputs to transcriptional regulation, the random arrival and binding of transcription factors to their target sites along the genome. This noise sets a fundamental physical limit to the reliability of genetic control, and has clear signatures, but we show that these are easily obscured by experimental limitations and even by conventional methods for plotting the variance vs. mean expression level. We argue that simple, global models of noise dominated by transcription and translation are inconsistent with the embedding of gene expression in a network of regulatory interactions. Analysis of recent experiments on transcriptional control in the early Drosophila embryo shows that these results are quantitatively consistent with the predicted signatures of input noise, and we discuss the experiments needed to test the importance of input noise more generally.Comment: 11 pages, 5 figures minor correction

Transcriptional Infidelity Promotes Heritable Phenotypic Change in a Bistable Gene Network

Bistable epigenetic switches are fundamental for cell fate determination in unicellular and multicellular organisms. Regulatory proteins associated with bistable switches are often present in low numbers and subject to molecular noise. It is becoming clear that noise in gene expression can influence cell fate. Although the origins and consequences of noise have been studied, the stochastic and transient nature of RNA errors during transcription has not been considered in the origin or modeling of noise nor has the capacity for such transient errors in information transfer to generate heritable phenotypic change been discussed. We used a classic bistable memory module to monitor and capture transient RNA errors: the lac operon of Escherichia coli comprises an autocatalytic positive feedback loop producing a heritable all-or-none epigenetic switch that is sensitive to molecular noise. Using single-cell analysis, we show that the frequency of epigenetic switching from one expression state to the other is increased when the fidelity of RNA transcription is decreased due to error-prone RNA polymerases or to the absence of auxiliary RNA fidelity factors GreA and GreB (functional analogues of eukaryotic TFIIS). Therefore, transcription infidelity contributes to molecular noise and can effect heritable phenotypic change in genetically identical cells in the same environment. Whereas DNA errors allow genetic space to be explored, RNA errors may allow epigenetic or expression space to be sampled. Thus, RNA infidelity should also be considered in the heritable origin of altered or aberrant cell behaviour

From segment to somite: segmentation to epithelialization analyzed within quantitative frameworks

One of the most visually striking patterns in the early developing embryo is somite segmentation. Somites form as repeated, periodic structures in pairs along nearly the entire caudal vertebrate axis. The morphological process involves short- and long-range signals that drive cell rearrangements and cell shaping to create discrete, epithelialized segments. Key to developing novel strategies to prevent somite birth defects that involve axial bone and skeletal muscle development is understanding how the molecular choreography is coordinated across multiple spatial scales and in a repeating temporal manner. Mathematical models have emerged as useful tools to integrate spatiotemporal data and simulate model mechanisms to provide unique insights into somite pattern formation. In this short review, we present two quantitative frameworks that address the morphogenesis from segment to somite and discuss recent data of segmentation and epithelialization

Deterministic and stochastic descriptions of gene expression dynamics

A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or implicitly etc. Here we consider simple systems of unregulated (constitutive) gene expression and compare different mathematical descriptions systematically to obtain insight into the errors that are introduced by various common approximations such as describing cell growth and division by an effective protein degradation term. In particular, we show that the population average of protein content of a cell exhibits a subtle dependence on the dynamics of growth and division, the specific model for volume growth and the age structure of the population. Nevertheless, the error made by models with implicit cell growth and division is quite small. Furthermore, we compare various models that are partially stochastic to investigate the impact of different sources of (intrinsic) noise. This comparison indicates that different sources of noise (protein synthesis, partitioning in cell division) contribute comparable amounts of noise if protein synthesis is not or only weakly bursty. If protein synthesis is very bursty, the burstiness is the dominant noise source, independent of other details of the model. Finally, we discuss two sources of extrinsic noise: cell-to-cell variations in protein content due to cells being at different stages in the division cycles, which we show to be small (for the protein concentration and, surprisingly, also for the protein copy number per cell) and fluctuations in the growth rate, which can have a significant impact.Comment: 23 pages, 5 figures; Journal of Statistical physics (2012

A Genome-Wide Analysis of Promoter-Mediated Phenotypic Noise in Escherichia coli

Gene expression is subject to random perturbations that lead to fluctuations in the rate of protein production. As a consequence, for any given protein, genetically identical organisms living in a constant environment will contain different amounts of that particular protein, resulting in different phenotypes. This phenomenon is known as “phenotypic noise.” In bacterial systems, previous studies have shown that, for specific genes, both transcriptional and translational processes affect phenotypic noise. Here, we focus on how the promoter regions of genes affect noise and ask whether levels of promoter-mediated noise are correlated with genes' functional attributes, using data for over 60% of all promoters in Escherichia coli. We find that essential genes and genes with a high degree of evolutionary conservation have promoters that confer low levels of noise. We also find that the level of noise cannot be attributed to the evolutionary time that different genes have spent in the genome of E. coli. In contrast to previous results in eukaryotes, we find no association between promoter-mediated noise and gene expression plasticity. These results are consistent with the hypothesis that, in bacteria, natural selection can act to reduce gene expression noise and that some of this noise is controlled through the sequence of the promoter region alon

Phenotypic Variation and Bistable Switching in Bacteria

Microbial research generally focuses on clonal populations. However, bacterial cells with identical genotypes frequently display different phenotypes under identical conditions. This microbial cell individuality is receiving increasing attention in the literature because of its impact on cellular differentiation, survival under selective conditions, and the interaction of pathogens with their hosts. It is becoming clear that stochasticity in gene expression in conjunction with the architecture of the gene network that underlies the cellular processes can generate phenotypic variation. An important regulatory mechanism is the so-called positive feedback, in which a system reinforces its own response, for instance by stimulating the production of an activator. Bistability is an interesting and relevant phenomenon, in which two distinct subpopulations of cells showing discrete levels of gene expression coexist in a single culture. In this chapter, we address techniques and approaches used to establish phenotypic variation, and relate three well-characterized examples of bistability to the molecular mechanisms that govern these processes, with a focus on positive feedback.

Effect of promoter architecture on the cell-to-cell variability in gene expression

According to recent experimental evidence, the architecture of a promoter, defined as the number, strength and regulatory role of the operators that control the promoter, plays a major role in determining the level of cell-to-cell variability in gene expression. These quantitative experiments call for a corresponding modeling effort that addresses the question of how changes in promoter architecture affect noise in gene expression in a systematic rather than case-by-case fashion. In this article, we make such a systematic investigation, based on a simple microscopic model of gene regulation that incorporates stochastic effects. In particular, we show how operator strength and operator multiplicity affect this variability. We examine different modes of transcription factor binding to complex promoters (cooperative, independent, simultaneous) and how each of these affects the level of variability in transcription product from cell-to-cell. We propose that direct comparison between in vivo single-cell experiments and theoretical predictions for the moments of the probability distribution of mRNA number per cell can discriminate between different kinetic models of gene regulation.Comment: 35 pages, 6 figures, Submitte