Analysis of Stochastic Strategies in Bacterial Competence: A Master Equation Approach

Competence is a transiently differentiated state that certain bacterial cells reach when faced with a stressful environment. Entrance into competence can be attributed to the excitability of the dynamics governing the genetic circuit that regulates this cellular behavior. Like many biological behaviors, entrance into competence is a stochastic event. In this case cellular noise is responsible for driving the cell from a vegetative state into competence and back. In this work we present a novel numerical method for the analysis of stochastic biochemical events and use it to study the excitable dynamics responsible for competence in Bacillus subtilis. Starting with a Finite State Projection (FSP) solution of the chemical master equation (CME), we develop efficient numerical tools for accurately computing competence probability. Additionally, we propose a new approach for the sensitivity analysis of stochastic events and utilize it to elucidate the robustness properties of the competence regulatory genetic circuit. We also propose and implement a numerical method to calculate the expected time it takes a cell to return from competence. Although this study is focused on an example of cell-differentiation in Bacillus subtilis, our approach can be applied to a wide range of stochastic phenomena in biological systems

Optimal Strategy for Competence Differentiation in Bacteria

A phylogenetically diverse subset of bacterial species are naturally competent for transformation by DNA. Transformation entails recombination of genes between different lineages, representing a form of bacterial sex that increases standing genetic variation. We first assess whether homologous recombination by transformation is favored by evolution. Using stochastic population genetic computer simulations in which beneficial and deleterious mutations occur at many loci throughout the whole genome, we find that transformation can increase both the rate of adaptive evolution and the equilibrium level of fitness. Secondly, motivated by experimental observations of Bacillus subtilis, we assume that competence additionally entails a weak persister phenotype, i.e., the rates of birth and death are reduced for these cells. Consequently, persisters evolve more slowly than non-persisters. We show via simulation that strains which stochastically switch into and out of the competent phenotype are evolutionarily favored over strains that express only a single phenotype. Our model's simplicity enables us to derive and numerically solve a system of finite- deterministic equations that describe the evolutionary dynamics. The observed tradeoff between the benefit of recombination and the cost of persistence may explain the previously mysterious observation that only a fractional subpopulation of B. subtilis cells express competence. More generally, this work demonstrates that population genetic forces can give rise to phenotypic diversity even in an unchanging and homogeneous environment

Disentangling Direct from Indirect Co-Evolution of Residues in Protein Alignments

Predicting protein structure from primary sequence is one of the ultimate challenges in computational biology. Given the large amount of available sequence data, the analysis of co-evolution, i.e., statistical dependency, between columns in multiple alignments of protein domain sequences remains one of the most promising avenues for predicting residues that are contacting in the structure. A key impediment to this approach is that strong statistical dependencies are also observed for many residue pairs that are distal in the structure. Using a comprehensive analysis of protein domains with available three-dimensional structures we show that co-evolving contacts very commonly form chains that percolate through the protein structure, inducing indirect statistical dependencies between many distal pairs of residues. We characterize the distributions of length and spatial distance traveled by these co-evolving contact chains and show that they explain a large fraction of observed statistical dependencies between structurally distal pairs. We adapt a recently developed Bayesian network model into a rigorous procedure for disentangling direct from indirect statistical dependencies, and we demonstrate that this method not only successfully accomplishes this task, but also allows contacts with weak statistical dependency to be detected. To illustrate how additional information can be incorporated into our method, we incorporate a phylogenetic correction, and we develop an informative prior that takes into account that the probability for a pair of residues to contact depends strongly on their primary-sequence distance and the amount of conservation that the corresponding columns in the multiple alignment exhibit. We show that our model including these extensions dramatically improves the accuracy of contact prediction from multiple sequence alignments

Variability in gene expression underlies incomplete penetrance

The phenotypic differences between individual organisms can often be ascribed to underlying genetic and environmental variation. However, even genetically identical organisms in homogeneous environments vary, indicating that randomness in developmental processes such as gene expression may also generate diversity. To examine the consequences of gene expression variability in multicellular organisms, we studied intestinal specification in the nematode Caenorhabditis elegans in which wild-type cell fate is invariant and controlled by a small transcriptional network. Mutations in elements of this network can have indeterminate effects: some mutant embryos fail to develop intestinal cells, whereas others produce intestinal precursors. By counting transcripts of the genes in this network in individual embryos, we show that the expression of an otherwise redundant gene becomes highly variable in the mutants and that this variation is subjected to a threshold, producing an ON/OFF expression pattern of the master regulatory gene of intestinal differentiation. Our results demonstrate that mutations in developmental networks can expose otherwise buffered stochastic variability in gene expression, leading to pronounced phenotypic variation.National Institutes of Health (U.S.). Pioneer AwardMathematical Sciences Postdoctoral Research Fellowships (DMS-0603392)National Institutes of Health (U.S.). Ruth L. Kirschstein National Research Service Award (5F32GM080966

Equation-Free Analysis of Two-Component System Signalling Model Reveals the Emergence of Co-Existing Phenotypes in the Absence of Multistationarity

Phenotypic differences of genetically identical cells under the same environmental conditions have been attributed to the inherent stochasticity of biochemical processes. Various mechanisms have been suggested, including the existence of alternative steady states in regulatory networks that are reached by means of stochastic fluctuations, long transient excursions from a stable state to an unstable excited state, and the switching on and off of a reaction network according to the availability of a constituent chemical species. Here we analyse a detailed stochastic kinetic model of two-component system signalling in bacteria, and show that alternative phenotypes emerge in the absence of these features. We perform a bifurcation analysis of deterministic reaction rate equations derived from the model, and find that they cannot reproduce the whole range of qualitative responses to external signals demonstrated by direct stochastic simulations. In particular, the mixed mode, where stochastic switching and a graded response are seen simultaneously, is absent. However, probabilistic and equation-free analyses of the stochastic model that calculate stationary states for the mean of an ensemble of stochastic trajectories reveal that slow transcription of either response regulator or histidine kinase leads to the coexistence of an approximate basal solution and a graded response that combine to produce the mixed mode, thus establishing its essential stochastic nature. The same techniques also show that stochasticity results in the observation of an all-or-none bistable response over a much wider range of external signals than would be expected on deterministic grounds. Thus we demonstrate the application of numerical equation-free methods to a detailed biochemical reaction network model, and show that it can provide new insight into the role of stochasticity in the emergence of phenotypic diversity

Dynamic Allostery in the Methionine Repressor Revealed by Force Distribution Analysis

Many fundamental cellular processes such as gene expression are tightly regulated by protein allostery. Allosteric signal propagation from the regulatory to the active site requires long-range communication, the molecular mechanism of which remains a matter of debate. A classical example for long-range allostery is the activation of the methionine repressor MetJ, a transcription factor. Binding of its co-repressor SAM increases its affinity for DNA several-fold, but has no visible conformational effect on its DNA binding interface. Our molecular dynamics simulations indicate correlated domain motions within MetJ, and quenching of these dynamics upon SAM binding entropically favors DNA binding. From monitoring conformational fluctuations alone, it is not obvious how the presence of SAM is communicated through the largely rigid core of MetJ and how SAM thereby is able to regulate MetJ dynamics. We here directly monitored the propagation of internal forces through the MetJ structure, instead of relying on conformational changes as conventionally done. Our force distribution analysis successfully revealed the molecular network for strain propagation, which connects collective domain motions through the protein core. Parts of the network are directly affected by SAM binding, giving rise to the observed quenching of fluctuations. Our results are in good agreement with experimental data. The force distribution analysis suggests itself as a valuable tool to gain insight into the molecular function of a whole class of allosteric proteins

On the spontaneous stochastic dynamics of a single gene: complexity of the molecular interplay at the promoter

International audienceBACKGROUND: Gene promoters can be in various epigenetic states and undergo interactions with many molecules in a highly transient, probabilistic and combinatorial way, resulting in a complex global dynamics as observed experimentally. However, models of stochastic gene expression commonly consider promoter activity as a two-state on/off system. We consider here a model of single-gene stochastic expression that can represent arbitrary prokaryotic or eukaryotic promoters, based on the combinatorial interplay between molecules and epigenetic factors, including energy-dependent remodeling and enzymatic activities. RESULTS: We show that, considering the mere molecular interplay at the promoter, a single-gene can demonstrate an elaborate spontaneous stochastic activity (eg. multi-periodic multi-relaxation dynamics), similar to what is known to occur at the gene-network level. Characterizing this generic model with indicators of dynamic and steady-state properties (including power spectra and distributions), we reveal the potential activity of any promoter and its influence on gene expression. In particular, we can reproduce, based on biologically relevant mechanisms, the strongly periodic patterns of promoter occupancy by transcription factors (TF) and chromatin remodeling as observed experimentally on eukaryotic promoters. Moreover, we link several of its characteristics to properties of the underlying biochemical system. The model can also be used to identify behaviors of interest (eg. stochasticity induced by high TF concentration) on minimal systems and to test their relevance in larger and more realistic systems. We finally show that TF concentrations can regulate many aspects of the stochastic activity with a considerable flexibility and complexity. CONCLUSIONS: This tight promoter-mediated control of stochasticity may constitute a powerful asset for the cell. Remarkably, a strongly periodic activity that demonstrates a complex TF concentration-dependent control is obtained when molecular interactions have typical characteristics observed on eukaryotic promoters (high mobility, functional redundancy, many alternate states/pathways). We also show that this regime results in a direct and indirect energetic cost. Finally, this model can constitute a framework for unifying various experimental approaches. Collectively, our results show that a gene - the basic building block of complex regulatory networks - can itself demonstrate a significantly complex behavior

Long-Range Intra-Protein Communication Can Be Transmitted by Correlated Side-Chain Fluctuations Alone

Allosteric regulation is a key component of cellular communication, but the way in which information is passed from one site to another within a folded protein is not often clear. While backbone motions have long been considered essential for long-range information conveyance, side-chain motions have rarely been considered. In this work, we demonstrate their potential utility using Monte Carlo sampling of side-chain torsional angles on a fixed backbone to quantify correlations amongst side-chain inter-rotameric motions. Results indicate that long-range correlations of side-chain fluctuations can arise independently from several different types of interactions: steric repulsions, implicit solvent interactions, or hydrogen bonding and salt-bridge interactions. These robust correlations persist across the entire protein (up to 60 Å in the case of calmodulin) and can propagate long-range changes in side-chain variability in response to single residue perturbations

Noise regulation by quorum sensing in low mRNA copy number systems

<p>Abstract</p> <p>Background</p> <p>Cells must face the ubiquitous presence of noise at the level of signaling molecules. The latter constitutes a major challenge for the regulation of cellular functions including communication processes. In the context of prokaryotic communication, the so-called quorum sensing (QS) mechanism relies on small diffusive molecules that are produced and detected by cells. This poses the intriguing question of how bacteria cope with the fluctuations for setting up a reliable information exchange.</p> <p>Results</p> <p>We present a stochastic model of gene expression that accounts for the main biochemical processes that describe the QS mechanism close to its activation threshold. Within that framework we study, both numerically and analytically, the role that diffusion plays in the regulation of the dynamics and the fluctuations of signaling molecules. In addition, we unveil the contribution of different sources of noise, intrinsic and transcriptional, in the QS mechanism.</p> <p>Conclusions</p> <p>The interplay between noisy sources and the communication process produces a repertoire of dynamics that depends on the diffusion rate. Importantly, the total noise shows a non-monotonic behavior as a function of the diffusion rate. QS systems seems to avoid values of the diffusion that maximize the total noise. These results point towards the direction that bacteria have adapted their communication mechanisms in order to improve the signal-to-noise ratio.</p