Biological role of noise encoded in a genetic network motif

A logic-incorporated gene regulatory network deciphers principles in cell fate decisions

Organisms utilize gene regulatory networks (GRN) to make fate decisions, but the regulatory mechanisms of transcription factors (TF) in GRNs are exceedingly intricate. A longstanding question in this field is how these tangled interactions synergistically contribute to decision-making procedures. To comprehensively understand the role of regulatory logic in cell fate decisions, we constructed a logic-incorporated GRN model and examined its behavior under two distinct driving forces (noise-driven and signal-driven). Under the noise-driven mode, we distilled the relationship among fate bias, regulatory logic, and noise profile. Under the signal-driven mode, we bridged regulatory logic and progression-accuracy trade-off, and uncovered distinctive trajectories of reprogramming influenced by logic motifs. In differentiation, we characterized a special logic-dependent priming stage by the solution landscape. Finally, we applied our findings to decipher three biological instances: hematopoiesis, embryogenesis, and trans-differentiation. Orthogonal to the classical analysis of expression profile, we harnessed noise patterns to construct the GRN corresponding to fate transition. Our work presents a generalizable framework for top-down fate-decision studies and a practical approach to the taxonomy of cell fate decisions.

The interplay between metabolic stochasticity and cAMP-CRP regulation in single E. coli cells

The inherent stochasticity of metabolism raises a critical question for understanding homeostasis: are cellular processes regulated in response to internal fluctuations? Here, we show that, in E. coli cells under constant external conditions, catabolic enzyme expression continuously responds to metabolic fluctuations. The underlying regulatory feedback is enabled by the cyclic AMP (cAMP) and cAMP receptor protein (CRP) system, which controls catabolic enzyme expression based on metabolite concentrations. Using single-cell microscopy, genetic constructs in which this feedback is disabled, and mathematical modeling, we show how fluctuations circulate through the metabolic and genetic network at sub-cell-cycle timescales. Modeling identifies four noise propagation modes, including one specific to CRP regulation. Together, these modes correctly predict noise circulation at perturbed cAMP levels. The cAMP-CRP system may thus have evolved to control internal metabolic fluctuations in addition to external growth conditions. We conjecture that second messengers may more broadly function to achieve cellular homeostasis.

Understanding noise in cell signalling in the prospect of drug-targets

The introduction of noise to signals can alter central regulatory switches of cellular processes leading to diseases. Noise is inherently present in the cellular signalling system and plays a decisive role in the input-output (I/O) relation. The current study aims to understand the noise tolerance of motif structures in the cell signalling processes. The vulnerability of a node to noise could be a significant factor in causing signalling error and need to be controlled. We developed stochastic differential equation (SDE) based mathematical models for different network motifs with two nodes and studied the association between motif structure and signal-noise relation. A two-dimensional parameter space analysis on motif sensitivity with noise and input signal variation was performed to classify and rank the motifs. Identifying sensitive motifs and their high druggability infers their significance in screening potential drug-target candidates. Finally, we proposed a theoretical framework to identify nodes from a network as potential drug targets. We applied this mathematical formalism to three cancer networks to identify drug-targets and validated them with existing databases.

Effect of dedifferentiation on noise propagation in cellular hierarchy

Many fast renewing tissues have a hierarchical structure. Tissue-specific stem cells are at the root of this cellular hierarchy, which give rive to a whole range of specialized cells via cellular differentiation. However, increasing evidence shows that the hierarchical structure can be broken due to cellular dedifferentiation in which cells at differentiated stages can revert to the stem cell stage. Dedifferentiation has significant impacts on many aspects of hierarchical tissues. Here we investigate the effect of dedifferentiation on noise propagation by developing a stochastic model composed of different cell types. The moment equations are derived, via which we systematically investigate how the noise in the cell number is changed by dedifferentiation. Our results suggest that dedifferentiation have different effects on the noises in the numbers of stem cells and nonstem cells. Specifically, the noise in the number of stem cells is significantly reduced by increasing dedifferentiation probability. Due to the dual effect of dedifferentiation on nonstem cells, however, more complex changes could happen to the noise in the number of nonstem cells by increasing dedifferentiation probability. Furthermore, it is found that even though dedifferentiation could turn part of the noise propagation process into a noise-amplifying step, it is very unlikely to turn the entire process into a noise-amplifying cascade.

Extrinsic noise of the target gene governs abundance pattern of feed-forward loop motifs

Feed-forward loop (FFL) is found to be a recurrent structure in bacterial and yeast gene transcription regulatory networks. In a generic FFL, transcription factor (TF) S regulates production of another TF X while both of these TFs regulate production of final gene-product Y. Depending upon the regulatory programs (activation or repression), FFLs are grouped into two broad classes: coherent (C) and incoherent (I), each class containing four distinct types (C1-C4 and I1-I4). These FFL types are experimentally observed to occur with varied frequencies, C1 and I1 being the abundant ones. Here we present a stochastic framework singling out the absolute value of the normalized covariance of X and Y to be the determining factor behind the abundance of FFLs while considering differential promoter activities of X and Y. Our theoretical construct employs two possible signal integration mechanisms (additive and multiplicative) to synthesize Y while steady-state population level of S remains fixed or becomes tunable reflecting two possible environmental signaling scenarios. Our model categorically points out that abundant FFLs exhibit higher amount of the designated metric which has a biophysical connotation of extrinsic noise for the target gene Y. Our predictions emanating from an overarching analytical expression utilizing biologically plausible parametric conditions are substantiated by stochastic simulation.

Role of integrated noise in pathway-specific signal propagation in feed-forward loops

Cells impose optimal noise control mechanism in diverse situations to cope with distinct environmental cues. Sometimes, it is desirable for the cell to utilize fluctuations for noise-driven processes. In other cases, noise can be harmful to the cell to show optimal fitness. It is, therefore, important to unravel the noise propagation mechanism inside the cell. Such noise controlling mechanism is accomplished by using gene transcription regulatory networks. One such gene regulatory network is feed-forward loop, having three regulatory nodes S, X and Y. Here, we consider the most abundant type 1 of coherent and incoherent feed-forward loops with both OR and AND logic functions, forming four different architectures. In OR logic function, the functions representing S and X act additively for the regulation of Y, while in AND logic function, the same functions (S and X) act multiplicatively for the regulation of Y. Measurement of susceptibility of the signal at output Y is done using elasticity of each regulation in FFLs. Using susceptibility, we demonstrate the nature of pathway integration by which one-step and two-step pathways get overlapped. The integration type is competitive for motifs having OR gate, while it is noncompetitive for the same with AND gate. The pathway integration property explains the output noise behavior of the motifs properly but cannot infer about the mechanism by which the upstream noise propagates to output. To account this, the total output noise is decomposed, which results in integrated noise as an additional noise source along with pathway-specific noise components. The integrated noise is found to appear as a consequence of integration between the pathways and has different functional characteristics explaining noise amplification and noise attenuation property of coherent and incoherent feed-forward loops, respectively. The noise decomposition also quantifies the contribution of different noise sources toward total noise. Finally, the noise propagation is being tuned as a function of input signal noise and its time scale of fluctuations, which shows considerable intrinsic noise strength and relatively slow relaxation time scale causes a higher degree of noise propagation in FFLs.

Functional roles of microbial cell-to-cell heterogeneity and emerging technologies for analysis and control

Clonal cell populations often display significant cell-to-cell phenotypic heterogeneity, even when maintained under constant external conditions. This variability can result from the inherently stochastic nature of transcription and translation processes, which leads to varying numbers of transcripts and proteins per cell. Here, we showcase studies that reveal links between stochastic cellular events and biological functions in isogenic microbial populations. Then, we highlight emerging tools from engineering, computation, and synthetic and molecular biology that enable precise measurement, control, and analysis of gene expression noise in microorganisms. The capabilities offered by this sophisticated toolbox will shape future directions in the field and generate insight into the behavior of living systems at the single-cell level.

Noise-driven cell differentiation and the emergence of spatiotemporal patterns

The emergence of phenotypic diversity in a population of cells and their arrangement in space and time is one of the most fascinating features of living systems. In fact, understanding multicellularity is unthinkable without explaining the proximate and the ultimate causes of cell differentiation in time and space. Simpler forms of cell differentiation can be found in unicellular organisms, such as bacterial biofilm, where reversible cell differentiation results in phenotypically diverse populations. In this manuscript, we attempt to start with the simple case of reversible nongenetic phenotypic to construct a model of differentiation and pattern formation. Our model, which we refer to as noise-driven differentiation (NDD) model, is an attempt to consider the prevalence of noise in biological systems, alongside what is known about genetic switches and signaling, to create a simple model which generates spatiotemporal patterns from bottom-up. Our simulations indicate that the presence of noise in cells can lead to reversible differentiation and the addition of signaling can create spatiotemporal pattern.

Sensitivities of Regulation Intensities in Feed-Forward Loops with Multistability

Gene regulatory networks depict the interactions among genes, proteins, and other components of the cell. These interactions are stochastic when large differences in reaction rates and small copy number of molecules are involved. Discrete Chemical Master Equation (dCME) provides a general framework for understanding the stochastic nature of these networks. Here we used the Accurate Chemical Master Equation method to directly compute the exact steady state probability landscape of the feed-forward loop motif (FFL). FFL is one of the most abundant gene regulatory networks motifs where the regulation is carried out from the top nodes to the bottom ones. We examine the behavior of stochastic FFLs under different conditions of various regulation intensities. Under the conditions with slow promoter binding, we show how FFL can exhibit different multistabilities in their landscapes. We also study the sensitivities of regulations of FFLs and introduce a new definition of stochastic sensitivity to characterize how FFLs respond in their probability distributions at the steady state to perturbations of system parameters. We show how change in gene expression under FFL regulations are sensitive to system parameters, including the state of multistability in FFLs.

Identifying functions and prognostic biomarkers of network motifs marked by diverse chromatin states in human cell lines

Epigenetic modifications play critical roles in modulating gene expression, yet their roles in regulatory networks in human cell lines remain poorly characterized. We integrated multiomics data to construct directed regulatory networks with nodes and edges labeled with chromatin states in human cell lines. We observed extensive association of diverse chromatin states and network motifs. The gene expression analysis showed that diverse chromatin states of coherent type-1 feedforward loop (C1-FFL) and incoherent type-1 feedforward loops (I1-FFL) contributed to the dynamic expression patterns of targets. Notably, diverse chromatin state compositions could help C1- or I1-FFL to control a large number of distinct biological functions in human cell lines, such as four different types of chromatin state compositions cooperating with K562-associated C1-FFLs controlling “regulation of cytokinesis,” “G1/S transition of mitotic cell cycle,” “DNA recombination,” and “telomere maintenance,” respectively. Remarkably, we identified six chromatin state-marked C1-FFL instances (HCFC1-NFYA-ABL1, THAP1-USF1-BRCA2, ZNF263-USF1-UBA52, MYC-ATF1-UBA52, ELK1-EGR1-CCT4, and YY1-EGR1-INO80C) could act as prognostic biomarkers of acute myelogenous leukemia though influencing cancer-related biological functions, such as cell proliferation, telomere maintenance, and DNA recombination. Our results will provide novel insight for better understanding of chromatin state-mediated gene regulation and facilitate the identification of novel diagnostic and therapeutic biomarkers of human cancers.

Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise

In transcriptional regulatory networks (TRNs), a canonical 3-node feed-forward loop (FFL) is hypothesized to evolve to filter out short spurious signals. We test this adaptive hypothesis against a novel null evolutionary model. Our mutational model captures the intrinsically high prevalence of weak affinity transcription factor binding sites. We also capture stochasticity and delays in gene expression that distort external signals and intrinsically generate noise. Functional FFLs evolve readily under selection for the hypothesized function but not in negative controls. Interestingly, a 4-node “diamond” motif also emerges as a short spurious signal filter. The diamond uses expression dynamics rather than path length to provide fast and slow pathways. When there is no idealized external spurious signal to filter out, but only internally generated noise, only the diamond and not the FFL evolves. While our results support the adaptive hypothesis, we also show that non-adaptive factors, including the intrinsic expression dynamics, matter.

Feed‐forward loops (FFLs) can filter out noise, but whether their overrepresentation in GRNs reflects adaptive evolution for this function is debated. Here, the authors develop a null model of regulatory evolution and find that FFLs evolve readily under selection for the noise filtering function.

The Reaction of Dimerization by Itself Reduces the Noise Intensity of the Protein Monomer

Because of the small particle number of intracellular species participating in genetic circuits, stochastic fluctuations are inevitable. This intracellular noise is detrimental to precise regulation. To maintain the proper function of a cell, some natural motifs attenuate the noise at the protein level. In many biological systems, the protein monomer is used as a regulator, but the protein dimer also exists. In the present study, we demonstrated that the dimerization reaction reduces the noise intensity of the protein monomer. Compared with two common noise-buffering motifs, the incoherent feedforward loop (FFL) and negative feedback control, the coefficient of variation (COV) in the case of dimerization was 25% less. Furthermore, we examined a system with direct interaction between proteins and other ligands. Both the incoherent FFL and negative feedback control failed to buffer the noise, but the dimerization was effective. Remarkably, the formation of only one protein dimer was sufficient to cause a 7.5% reduction in the COV.

Maximum Caliber Can Build and Infer Models of Oscillation in a Three-Gene Feedback Network

Single-cell protein expression time trajectories provide rich temporal data quantifying cellular variability and its role in dictating fitness. However, theoretical models to analyze and fully extract information from these measurements remain limited for three reasons: (i) gene expression profiles are noisy, rendering models of averages inapplicable, (ii) experiments typically measure only a few protein species while leaving other molecular actors-necessary to build traditional bottom-up models-unnoticed, and (iii) measured data are in fluorescence, not particle number. We recently addressed these challenges in an alternate top-down approach using the principle of Maximum Caliber (MaxCal) to model genetic switches with one and two protein species. In the present work we address scalability and broader applicability of MaxCal by extending to a three-gene (A, B, C) feedback network that exhibits oscillation, commonly known as the repressilator. We test MaxCal's inferential power by using synthetic data of noisy protein number time traces-serving as a proxy for experimental data-generated from a known underlying model. We notice that the minimal MaxCal model-accounting for production, degradation, and only one type of symmetric coupling between all three species-reasonably infers several underlying features of the circuit such as the effective production rate, degradation rate, frequency of oscillation, and protein number distribution. Next, we build models of higher complexity including different levels of coupling between A, B, and C and rigorously assess their relative performance. While the minimal model (with four parameters) performs remarkably well, we note that the most complex model (with six parameters) allowing all possible forms of crosstalk between A, B, and C slightly improves prediction of rates, but avoids ad hoc assumption of all the other models. It is also the model of choice based on Bayesian information criteria. We further analyzed time trajectories in arbitrary fluorescence (using synthetic trajectories) to mimic realistic data. We conclude that even with a three-protein system including both fluorescence noise and intrinsic gene expression fluctuations, MaxCal can faithfully infer underlying details of the network, opening future directions to model other network motifs with many species.

Role of noise and parametric variation in the dynamics of gene regulatory circuits

Stochasticity in gene expression impacts the dynamics and functions of gene regulatory circuits. Intrinsic noises, including those that are caused by low copy number of molecules and transcriptional bursting, are usually studied by stochastic simulations. However, the role of extrinsic factors, such as cell-to-cell variability and heterogeneity in the microenvironment, is still elusive. To evaluate the effects of both the intrinsic and extrinsic noises, we develop a method, named sRACIPE, by integrating stochastic analysis with random circuit perturbation (RACIPE) method. RACIPE uniquely generates and analyzes an ensemble of models with random kinetic parameters. Previously, we have shown that the gene expression from random models form robust and functionally related clusters. In sRACIPE we further develop two stochastic simulation schemes, aiming to reduce the computational cost without sacrificing the convergence of statistics. One scheme uses constant noise to capture the basins of attraction, and the other one uses simulated annealing to detect the stability of states. By testing the methods on several synthetic gene regulatory circuits and an epithelial-mesenchymal transition network in squamous cell carcinoma, we demonstrate that sRACIPE can interpret the experimental observations from single-cell gene expression data. We observe that parametric variation (the spread of parameters around a median value) increases the spread of the gene expression clusters, whereas high noise merges the states. Our approach quantifies the robustness of a gene circuit in the presence of noise and sheds light on a new mechanism of noise-induced hybrid states. We have implemented sRACIPE as an R package.

Mathematical modeling identifies Lck as a potential mediator for PD-1 induced inhibition of early TCR signaling

Programmed cell death-1 (PD-1) is an inhibitory immune checkpoint receptor that negatively regulates the functioning of T cell. Although the direct targets of PD-1 were not identified, its inhibitory action on the TCR signaling pathway was known much earlier. Recent experiments suggest that the PD-1 inhibits the TCR and CD28 signaling pathways at a very early stage ─ at the level of phosphorylation of the cytoplasmic domain of TCR and CD28 receptors. Here, we develop a mathematical model to investigate the influence of inhibitory effect of PD-1 on the activation of early TCR and CD28 signaling molecules. Proposed model recaptures several quantitative experimental observations of PD-1 mediated inhibition. Model simulations show that PD-1 imposes a net inhibitory effect on the Lck kinase. Further, the inhibitory effect of PD-1 on the activation of TCR signaling molecules such as Zap70 and SLP76 is significantly enhanced by the PD-1 mediated inhibition of Lck. These results suggest a critical role for Lck as a mediator for PD-1 induced inhibition of TCR signaling network. Multi parametric sensitivity analysis explores the effect of parameter uncertainty on model simulations.

The Insight into Protein-Ligand Interactions, a Novel Way of Buffering Protein Noise in Gene Expression

Random fluctuations are often considered detrimental in the context of gene regulation. Studies aimed at discovering the noise-buffering strategies are important. In this study, we demonstrated a novel design of attenuating noise at protein-level. The protein-ligand interaction dramatically reduced noise so that the coefficient of variation (COV) became roughly 1/3. Remarkably, in comparison to the other two noise-buffering methods, the negative feedback control and the incoherent feedforward loop, the COV of the target protein in the case of protein-ligand interaction appeared to be less than 1/2 of that of the other two methods. The high correlation of the target protein and the ligand grants the present method great ability to buffer noise. Further, it buffers noise at the stage after translation so it is also capable of attenuating the noise inherited from the process of translation.

Detection of network motifs using three-way ANOVA

Motivation

Gene regulatory networks (GRN) can be determined via various experimental techniques, and also by computational methods, which infer networks from gene expression data. However, these techniques treat interactions separately such that interdependencies of interactions forming meaningful subnetworks are typically not considered.

Methods

For the investigation of network properties and for the classification of different (sub-)networks based on gene expression data, we consider biological network motifs consisting of three genes and up to three interactions, e.g. the cascade chain (CSC), feed-forward loop (FFL), and dense-overlapping regulon (DOR). We examine several conventional methods for the inference of network motifs, which typically consider each interaction individually. In addition, we propose a new method based on three-way ANOVA (ANalysis Of VAriance) (3WA) that analyzes entire subnetworks at once. To demonstrate the advantages of such a more holistic perspective, we compare the ability of 3WA and other methods to detect and categorize network motifs on large real and artificial datasets.

Results

We find that conventional methods perform much better on artificial data (AUC up to 80%), than on real E. coli expression datasets (AUC 50% corresponding to random guessing). To explain this observation, we examine several important properties that differ between datasets and analyze predicted motifs in detail. We find that in case of real networks our new 3WA method outperforms (AUC 70% in E. coli) previous methods by exploiting the interdependencies in the full motif structure. Because of important differences between current artificial datasets and real measurements, the construction and testing of motif detection methods should focus on real data.

Perspective: Engineering noise in biological systems towards predictive stochastic design

Significant progress has been made towards engineering both single-cell and multi-cellular systems through a combination of synthetic and systems biology, nanobiotechnology, pharmaceutical science, and computational approaches. However, our ability to engineer systems that begin to approach the complexity of natural pathways is severely limited by important challenges, e.g. due to noise, or the fluctuations in gene expression and molecular species at multiple scales (e.g. both intra- and inter-cellular fluctuations). This barrier to engineering requires that biological noise be recognized as a design element with fundamentals that can be actively controlled. Here we highlight studies of an emerging discipline that collectively strives to engineer noise towards predictive stochastic design using interdisciplinary approaches at multiple-scales in diverse living systems.

Organization of feed-forward loop motifs reveals architectural principles in natural and engineered networks

Network motifs are significantly overrepresented subgraphs that have been proposed as building blocks for natural and engineered networks. Detailed functional analysis has been performed for many types of motif in isolation, but less is known about how motifs work together to perform complex tasks. To address this issue, we measure the aggregation of network motifs via methods that extract precisely how these structures are connected. Applying this approach to a broad spectrum of networked systems and focusing on the widespread feed-forward loop motif, we uncover striking differences in motif organization. The types of connection are often highly constrained, differ between domains, and clearly capture architectural principles. We show how this information can be used to effectively predict functionally important nodes in the metabolic network of Escherichia coli. Our findings have implications for understanding how networked systems are constructed from motif parts and elucidate constraints that guide their evolution.

Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise

This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable Lévy fluctuations. By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that via examining the mean first exit time (MFET) and the first escape probability (FEP), the asymmetric fluctuations, interacting with nonlinearity in the system, lead to peculiar likelihood for transcription. This includes, in the additive noise case, realizing higher likelihood of transcription for larger positive skewness (i.e., asymmetry) index β, causing a stochastic bifurcation at the non-Gaussianity index value α = 1 (i.e., it is a separating point or line for the likelihood for transcription), and achieving a turning point at the threshold value β≈-0.5 (i.e., beyond which the likelihood for transcription suddenly reversed for α values). The stochastic bifurcation and turning point phenomena do not occur in the symmetric noise case (β = 0). While in the multiplicative noise case, non-Gaussianity index value α = 1 is a separating point or line for both the MFET and the FEP. We also investigate the noise enhanced stability phenomenon. Additionally, we are able to specify the regions in the whole parameter space for the asymmetric noise, in which we attain desired likelihood for transcription. We have conducted a series of numerical experiments in "regulating" the likelihood of gene transcription by tuning asymmetric stable Lévy noise indexes. This work offers insights for possible ways of achieving gene regulation in experimental research.

Building Predictive Models of Genetic Circuits Using the Principle of Maximum Caliber

Learning the underlying details of a gene network is a major challenge in cellular and synthetic biology. We address this challenge by building a chemical kinetic model that utilizes information encoded in the stochastic protein expression trajectories typically measured in experiments. The applicability of the proposed method is demonstrated in an auto-activating genetic circuit, a common motif in natural and synthetic gene networks. Our approach is based on the principle of maximum caliber (MaxCal)-a dynamical analog of the principle of maximum entropy-and builds a minimal model using only three constraints: 1) protein synthesis, 2) protein degradation, and 3) positive feedback. The MaxCal-generated model (described with four parameters) was benchmarked against synthetic data generated using a Gillespie algorithm on a known reaction network (with seven parameters). MaxCal accurately predicts underlying rate parameters of protein synthesis and degradation as well as experimental observables such as protein number and dwell-time distributions. Furthermore, MaxCal yields an effective feedback parameter that can be useful for circuit design. We also extend our methodology and demonstrate how to analyze trajectories that are not in protein numbers but in arbitrary fluorescence units, a more typical condition in experiments. This "top-down" methodology based on minimal information-in contrast to traditional "bottom-up" approaches that require ad hoc knowledge of circuit details-provides a powerful tool to accurately infer underlying details of feedback circuits that are not otherwise visible in experiments and to help guide circuit design.

Noise Decomposition Principle in a Coherent Feed-Forward Transcriptional Regulatory Loop

Coherent feed-forward loops exist extensively in realistic biological regulatory systems, and are common signaling motifs. Here, we study the characteristics and the propagation mechanism of the output noise in a coherent feed-forward transcriptional regulatory loop that can be divided into a main road and branch. Using the linear noise approximation, we derive analytical formulae for the total noise of the full loop, the noise of the branch, and the noise of the main road, which are verified by the Gillespie algorithm. Importantly, we find that (i) compared with the branch motif or the main road motif, the full motif can effectively attenuate the output noise level; (ii) there is a transition point of system state such that the noise of the main road is dominated when the underlying system is below this point, whereas the noise of the branch is dominated when the system is beyond the point. The entire analysis reveals the mechanism of how the noise is generated and propagated in a simple yet representative signaling module.

MIST1 and PTF1 Collaborate in Feed-Forward Regulatory Loops That Maintain the Pancreatic Acinar Phenotype in Adult Mice

Much remains unknown regarding the regulatory networks formed by transcription factors in mature, differentiated mammalian cells in vivo, despite many studies of individual DNA-binding transcription factors. We report a constellation of feed-forward loops formed by the pancreatic transcription factors MIST1 and PTF1 that govern the differentiated phenotype of the adult pancreatic acinar cell. PTF1 is an atypical basic helix-loop-helix transcription factor complex of pancreatic acinar cells and is critical to acinar cell fate specification and differentiation. MIST1, also a basic helix-loop-helix transcription factor, enhances the formation and maintenance of the specialized phenotype of professional secretory cells. The MIST1 and PTF1 collaboration controls a wide range of specialized cellular processes, including secretory protein synthesis and processing, exocytosis, and homeostasis of the endoplasmic reticulum. PTF1 drives Mist1 transcription, and MIST1 and PTF1 bind and drive the transcription of over 100 downstream acinar genes. PTF1 binds two canonical bipartite sites within a 0.7-kb transcriptional enhancer upstream of Mist1 that are essential for the activity of the enhancer in vivo MIST1 and PTF1 coregulate target genes synergistically or additively, depending on the target transcriptional enhancer. The frequent close binding proximity of PTF1 and MIST1 in pancreatic acinar cell chromatin implies extensive collaboration although the collaboration is not dependent on a stable physical interaction.

Noise Expands the Response Range of the Bacillus subtilis Competence Circuit

Gene regulatory circuits must contend with intrinsic noise that arises due to finite numbers of proteins. While some circuits act to reduce this noise, others appear to exploit it. A striking example is the competence circuit in Bacillus subtilis, which exhibits much larger noise in the duration of its competence events than a synthetically constructed analog that performs the same function. Here, using stochastic modeling and fluorescence microscopy, we show that this larger noise allows cells to exit terminal phenotypic states, which expands the range of stress levels to which cells are responsive and leads to phenotypic heterogeneity at the population level. This is an important example of how noise confers a functional benefit in a genetic decision-making circuit.

Fluctuations, or “noise”, in the response of a system is usually thought to be harmful. However, it is becoming increasingly clear that in single-celled organisms, noise can sometimes help cells survive. This is because noise can enhance the diversity of responses within a cell population. In this study, we identify a novel benefit of noise in the competence response of a population of Bacillus subtilis bacteria, where competence is the ability of bacteria to take in DNA from their environment when under stress. We use computational modeling and experiments to show that noise increases the range of stress levels for which these bacteria exhibit a highly dynamic response, meaning that they are neither unresponsive, nor permanently in the competent state. Since a dynamic response is thought to be optimal for survival, this study suggests that noise is exploited to increase the fitness of the bacterial population.

Post-transcriptional regulation tends to attenuate the mRNA noise and to increase the mRNA gain

Post-transcriptional regulation is ubiquitous in prokaryotic and eukaryotic cells, but how it impacts gene expression remains to be fully explored. Here, we analyze a simple gene model in which we assume that mRNAs are produced in a constitutive manner but are regulated post-transcriptionally by a decapping enzyme that switches between the active state and the inactive state. We derive the analytical mRNA distribution governed by a chemical master equation, which can be well used to analyze the mechanism of how post-transcription regulation influences the mRNA expression level including the mRNA noise. We demonstrate that the mean mRNA level in the stochastic case is always higher than that in the deterministic case due to the stochastic effect of the enzyme, but the size of the increased part depends mainly on the switching rates between two enzyme states. More interesting is that we find that in contrast to transcriptional regulation, post-transcriptional regulation tends to attenuate noise in mRNA. Our results provide insight into the role of post-transcriptional regulation in controlling the transcriptional noise.

Role of relaxation time scale in noisy signal transduction

Intra-cellular fluctuations, mainly triggered by gene expression, are an inevitable phenomenon observed in living cells. It influences generation of phenotypic diversity in genetically identical cells. Such variation of cellular components is beneficial in some contexts but detrimental in others. To quantify the fluctuations in a gene product, we undertake an analytical scheme for studying few naturally abundant linear as well as branched chain network motifs. We solve the Langevin equations associated with each motif under the purview of linear noise approximation and derive the expressions for Fano factor and mutual information in close analytical form. Both quantifiable expressions exclusively depend on the relaxation time (decay rate constant) and steady state population of the network components. We investigate the effect of relaxation time constraints on Fano factor and mutual information to indentify a time scale domain where a network can recognize the fluctuations associated with the input signal more reliably. We also show how input population affects both quantities. We extend our calculation to long chain linear motif and show that with increasing chain length, the Fano factor value increases but the mutual information processing capability decreases. In this type of motif, the intermediate components act as a noise filter that tune up input fluctuations and maintain optimum fluctuations in the output. For branched chain motifs, both quantities vary within a large scale due to their network architecture and facilitate survival of living system in diverse environmental conditions.

The physics of bacterial decision making

The choice that bacteria make between sporulation and competence when subjected to stress provides a prototypical example of collective cell fate determination that is stochastic on the individual cell level, yet predictable (deterministic) on the population level. This collective decision is performed by an elaborated gene network. Considerable effort has been devoted to simplify its complexity by taking physics approaches to untangle the basic functional modules that are integrated to form the complete network: (1) A stochastic switch whose transition probability is controlled by two order parameters-population density and internal/external stress. (2) An adaptable timer whose clock rate is normalized by the same two previous order parameters. (3) Sensing units which measure population density and external stress. (4) A communication module that exchanges information about the cells' internal stress levels. (5) An oscillating gate of the stochastic switch which is regulated by the timer. The unique circuit architecture of the gate allows special dynamics and noise management features. The gate opens a window of opportunity in time for competence transitions, during which the circuit generates oscillations that are translated into a chain of short intervals with high transition probability. In addition, the unique architecture of the gate allows filtering of external noise and robustness against variations in circuit parameters and internal noise. We illustrate that a physics approach can be very valuable in investigating the decision process and in identifying its general principles. We also show that both cell-cell variability and noise have important functional roles in the collectively controlled individual decisions.

Temporal dynamics and transcriptional control using single-cell gene expression analysis

Background

Changes in environmental conditions lead to expression variation that manifest at the level of gene regulatory networks. Despite a strong understanding of the role noise plays in synthetic biological systems, it remains unclear how propagation of expression heterogeneity in an endogenous regulatory network is distributed and utilized by cells transitioning through a key developmental event.

Results

Here we investigate the temporal dynamics of a single-cell transcriptional network of 45 transcription factors in THP-1 human myeloid monocytic leukemia cells undergoing differentiation to macrophages. We systematically measure temporal regulation of expression and variation by profiling 120 single cells at eight distinct time points, and infer highly controlled regulatory modules through which signaling operates with stochastic effects. This reveals dynamic and specific rewiring as a cellular strategy for differentiation. The integration of both positive and negative co-expression networks further identifies the proto-oncogene MYB as a network hinge to modulate both the pro- and anti-differentiation pathways.

Conclusions

Compared to averaged cell populations, temporal single-cell expression profiling provides a much more powerful technique to probe for mechanistic insights underlying cellular differentiation. We believe that our approach will form the basis of novel strategies to study the regulation of transcription at a single-cell level.

Construction of an effective landscape for multistate genetic switches

Multistate genetic switches play a crucial role during embryonic development and tumorigenesis. An archetypical example is the three-way switch regulating epithelial-hybrid-mesenchymal transitions. We devise a special WKB-based approach to investigate white Gaussian and shot noise effects on three-way switches, and construct an effective landscape in good quantitative agreement with stochastic simulations. This approach allows efficient analytical or numerical calculation of the landscape contours, the optimal path, and the state relative stability for general multicomponent multistate switches.

Modeling stochastic noise in gene regulatory systems

The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady-states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems.

Noise in biology

Noise permeates biology on all levels, from the most basic molecular, sub-cellular processes to the dynamics of tissues, organs, organisms and populations. The functional roles of noise in biological processes can vary greatly. Along with standard, entropy-increasing effects of producing random mutations, diversifying phenotypes in isogenic populations, limiting information capacity of signaling relays, it occasionally plays more surprising constructive roles by accelerating the pace of evolution, providing selective advantage in dynamic environments, enhancing intracellular transport of biomolecules and increasing information capacity of signaling pathways. This short review covers the recent progress in understanding mechanisms and effects of fluctuations in biological systems of different scales and the basic approaches to their mathematical modeling.

Determinants of expression variability

The amount of tissue-specific expression variability (EV) across individuals is an essential characteristic of a gene and believed to have evolved, in part, under functional constraints. However, the determinants and functional implications of EV are only beginning to be investigated. Our analyses based on multiple expression profiles in 41 primary human tissues show that a gene’s EV is significantly correlated with a number of features pertaining to the genomic, epigenomic, regulatory, polymorphic, functional, structural and network characteristics of the gene. We found that (i) EV of a gene is encoded, in part, by its genomic context and is further influenced by the epigenome; (ii) strong promoters induce less variable expression; (iii) less variable gene loci evolve under purifying selection against copy number polymorphisms; (iv) genes that encode inherently disordered or highly interacting proteins exhibit lower variability; and (v) genes with less variable expression are enriched for house-keeping functions, while genes with highly variable expression tend to function in development and extra-cellular response and are associated with human diseases. Thus, our analysis reveals a number of potential mediators as well as functional and evolutionary correlates of EV, and provides new insights into the inherent variability in eukaryotic gene expression.

Turning oscillations into opportunities: lessons from a bacterial decision gate

Sporulation vs. competence provides a prototypic example of collective cell fate determination. The decision is performed by the action of three modules: 1) A stochastic competence switch whose transition probability is regulated by population density, population stress and cell stress. 2) A sporulation timer whose clock rate is regulated by cell stress and population stress. 3) A decision gate that is coupled to the timer via a special repressilator-like loop. We show that the distinct circuit architecture of this gate leads to special dynamics and noise management characteristics: The gate opens a time-window of opportunity for competence transitions during which it generates oscillations that are turned into a chain of transition opportunities – each oscillation opens a short interval with high transition probability. The special architecture of the gate also leads to filtering of external noise and robustness against internal noise and variations in the circuit parameters.

Probing cell-free gene expression noise in femtoliter volumes

Cell-free systems offer a simplified and flexible context that enables important biological reactions while removing complicating factors such as fitness, division, and mutation that are associated with living cells. However, cell-free expression in unconfined spaces is missing important elements of expression in living cells. In particular, the small volume of living cells can give rise to significant stochastic effects, which are negligible in bulk cell-free reactions. Here, we confine cell-free gene expression reactions to cell-relevant 20 fL volumes (between the volumes of Escherichia coli and Saccharomyces cerevisiae ), in polydimethylsiloxane (PDMS) containers. We demonstrate that expression efficiency varies widely among different containers, likely due to non-Poisson distribution of expression machinery at the observed scale. Previously, this phenomenon has been observed only in liposomes. In addition, we analyze gene expression noise. This analysis is facilitated by our use of cell-free systems, which allow the mapping of the measured noise properties to intrinsic noise models. In contrast, previous live cell noise analysis efforts have been complicated by multiple noise sources. Noise analysis reveals signatures of translational bursting, while noise dynamics suggest that overall cell-free expression is limited by a diminishing translation rate. In addition to offering a unique approach to understanding noise in gene circuits, our work contributes to a deeper understanding of the biophysical properties of cell-free expression systems, thus aiding efforts to harness cell-free systems for synthetic biology applications.

Topology of molecular interaction networks

Molecular interactions are often represented as network models which have become the common language of many areas of biology. Graphs serve as convenient mathematical representations of network models and have themselves become objects of study. Their topology has been intensively researched over the last decade after evidence was found that they share underlying design principles with many other types of networks.Initial studies suggested that molecular interaction network topology is related to biological function and evolution. However, further whole-network analyses did not lead to a unified view on what this relation may look like, with conclusions highly dependent on the type of molecular interactions considered and the metrics used to study them. It is unclear whether global network topology drives function, as suggested by some researchers, or whether it is simply a byproduct of evolution or even an artefact of representing complex molecular interaction networks as graphs.Nevertheless, network biology has progressed significantly over the last years. We review the literature, focusing on two major developments. First, realizing that molecular interaction networks can be naturally decomposed into subsystems (such as modules and pathways), topology is increasingly studied locally rather than globally. Second, there is a move from a descriptive approach to a predictive one: rather than correlating biological network topology to generic properties such as robustness, it is used to predict specific functions or phenotypes.Taken together, this change in focus from globally descriptive to locally predictive points to new avenues of research. In particular, multi-scale approaches are developments promising to drive the study of molecular interaction networks further.

Synthetic biological networks

Despite their obvious relationship and overlap, the field of physics is blessed with many insightful laws, while such laws are sadly absent in biology. Here we aim to discuss how the rise of a more recent field known as synthetic biology may allow us to more directly test hypotheses regarding the possible design principles of natural biological networks and systems. In particular, this review focuses on synthetic gene regulatory networks engineered to perform specific functions or exhibit particular dynamic behaviors. Advances in synthetic biology may set the stage to uncover the relationship of potential biological principles to those developed in physics.

Effects of bursty protein production on the noisy oscillatory properties of downstream pathways

Experiments show that proteins are translated in sharp bursts; similar bursty phenomena have been observed for protein import into compartments. Here we investigate the effect of burstiness in protein expression and import on the stochastic properties of downstream pathways. We consider two identical pathways with equal mean input rates, except in one pathway proteins are input one at a time and in the other proteins are input in bursts. Deterministically the dynamics of these two pathways are indistinguishable. However the stochastic behavior falls in three categories: (i) both pathways display or do not display noise-induced oscillations; (ii) the non-bursty input pathway displays noise-induced oscillations whereas the bursty one does not; (iii) the reverse of (ii). We derive necessary conditions for these three cases to classify systems involving autocatalysis, trimerization and genetic feedback loops. Our results suggest that single cell rhythms can be controlled by regulation of burstiness in protein production.

Stochastic effects as a force to increase the complexity of signaling networks

Cellular signaling networks are complex and appear to include many nonfunctional elements. Recently, it was suggested that nonfunctional interactions of proteins cause signaling noise, which, perhaps, shapes the signal transduction mechanism. However, the conditions under which molecular noise influences cellular information processing remain unclear. Here, we explore a large number of simple biological models of varying network sizes to understand the architectural conditions under which the interactions of signaling proteins can exhibit specific stochastic effects—called deviant effects—in which the average behavior of a biological system is substantially altered in the presence of molecular noise. We find that a small fraction of these networks does exhibit deviant effects and shares a common architectural feature whereas most of the networks show only insignificant levels of deviations. Interestingly, addition of seemingly unimportant interactions into protein networks gives rise to deviant effects.

Modeling gene expression in time and space

Cell populations rarely exhibit gene-expression profiles that are homogeneous in time and space. In the temporal domain, dynamical behaviors such as oscillations and pulses of protein production pervade cell biology, underlying phenomena as diverse as circadian rhythmicity, cell cycle control, stress and damage responses, and stem-cell pluripotency. In multicellular populations, spatial heterogeneities are crucial for decision making and development, among many other functions. Cells need to exquisitely coordinate this temporal and spatial variation to survive. Although the spatiotemporal character of gene expression is challenging to quantify experimentally at the level of individual cells, it is beneficial from the modeling viewpoint, because it provides strong constraints that can be probed by theoretically analyzing mathematical models of candidate gene and protein circuits. Here, we review recent examples of temporal dynamics and spatial patterning in gene expression to show how modeling such phenomenology can help us unravel the molecular mechanisms of cellular function.

Quartz-Seq: a highly reproducible and sensitive single-cell RNA sequencing method, reveals non-genetic gene-expression heterogeneity

Development of a highly reproducible and sensitive single-cell RNA sequencing (RNA-seq) method would facilitate the understanding of the biological roles and underlying mechanisms of non-genetic cellular heterogeneity. In this study, we report a novel single-cell RNA-seq method called Quartz-Seq that has a simpler protocol and higher reproducibility and sensitivity than existing methods. We show that single-cell Quartz-Seq can quantitatively detect various kinds of non-genetic cellular heterogeneity, and can detect different cell types and different cell-cycle phases of a single cell type. Moreover, this method can comprehensively reveal gene-expression heterogeneity between single cells of the same cell type in the same cell-cycle phase.

The utility of paradoxical components in biological circuits

A recurring theme in biological circuits is the existence of components that are antagonistically bifunctional, in the sense that they simultaneously have two opposing effects on the same target or biological process. Examples include bifunctional enzymes that carry out two opposing reactions such as phosphorylating and dephosphorylating the same target, regulators that activate and also repress a gene in circuits called incoherent feedforward loops, and cytokines that signal immune cells to both proliferate and die. Such components are termed "paradoxical", and in this review we discuss how they can provide useful features to cell circuits that are otherwise difficult to achieve. In particular, we summarize how paradoxical components can provide robustness, generate temporal pulses, and provide fold-change detection, in which circuits respond to relative rather than absolute changes in signals.

The role of single-cell analyses in understanding cell lineage commitment

The study of cell lineage commitment is critical for improving our understanding of tissue development and regeneration, and for realizing stem cell-based therapies and engineered tissue replacements. Recently, the discovery of an unanticipated degree of variability in fundamental biological processes, including divergent responses of genetically identical cells to various stimuli, has provided mechanistic insight into cellular decision making and the collective behavior of cell populations. Therefore, the study of lineage commitment with single-cell resolution could provide greater knowledge of cellular differentiation mechanisms and the influence of noise on cellular processes. This will require the adoption of new technologies for single-cell analysis as traditional methods typically measure average values of bulk population behavior. This review discusses the recent developments in methods for analyzing the behavior of individual cells, and how these approaches are leading to a deeper understanding and better control of cellular decision making.

Hierarchical dynamics of a transcription factors network in E. coli

In the present work we study the transcription-factor regulatory network that controls the synthesis of flagella in E. coli. Our objective is to address how the transcription-factor dynamics (in terms of their promoter activities and associated rates) correlate with their positions in the hierarchical organization of this regulatory network. Our results suggest that global-regulator promoters express at higher rates than those of local regulators, particularly when the bacterial populations are actively growing. Furthermore, promoter activity decreases together with the rate of cellular division. And finally, local-regulator promoters reach their maximal activity later than global-regulator promoters do. In summary, our results suggest a strong correlation between promoter activities and their hierarchical organization in this particular regulatory network.

Teasing apart translational and transcriptional components of stochastic variations in eukaryotic gene expression

The intrinsic stochasticity of gene expression leads to cell-to-cell variations, noise, in protein abundance. Several processes, including transcription, translation, and degradation of mRNA and proteins, can contribute to these variations. Recent single cell analyses of gene expression in yeast have uncovered a general trend where expression noise scales with protein abundance. This trend is consistent with a stochastic model of gene expression where mRNA copy number follows the random birth and death process. However, some deviations from this basic trend have also been observed, prompting questions about the contribution of gene-specific features to such deviations. For example, recent studies have pointed to the TATA box as a sequence feature that can influence expression noise by facilitating expression bursts. Transcription-originated noise can be potentially further amplified in translation. Therefore, we asked the question of to what extent sequence features known or postulated to accompany translation efficiency can also be associated with increase in noise strength and, on average, how such increase compares to the amplification associated with the TATA box. Untangling different components of expression noise is highly nontrivial, as they may be gene or gene-module specific. In particular, focusing on codon usage as one of the sequence features associated with efficient translation, we found that ribosomal genes display a different relationship between expression noise and codon usage as compared to other genes. Within nonribosomal genes we found that sequence high codon usage is correlated with increased noise relative to the average noise of proteins with the same abundance. Interestingly, by projecting the data on a theoretical model of gene expression, we found that the amplification of noise strength associated with codon usage is comparable to that of the TATA box, suggesting that the effect of translation on noise in eukaryotic gene expression might be more prominent than previously appreciated.

The stochastic nature of gene expression leads to cell-to-cell differences in protein level referred to as noise. Expression noise can be disadvantageous, by affecting the precision of biological functions, but it may also be advantageous by enabling heterogeneous stress-response programs to environmental changes. Therefore various genes and gene groups might display various levels of expression noise. Importantly, gene expression is a multi-step process and the stochasticity of its individual steps, including transcription and translation, contributes to the resulting variability. Recent single cell analyses of gene expression in yeast have confirmed the theoretically predicted general trend where expression noise scales with protein abundance. However, some deviations from this basic trend have also been observed, prompting questions about the contribution of gene-specific features to such deviations. Accounting for noise heterogeneity in different gene groups, we revealed a clear relationship between noise and translation-related genomic features, specifically codon usage and 5′ UTR secondary structure. Our results suggest that the effect of translation on these deviations might be more prominent than previously appreciated, and provide important clues towards understanding expression stochasticity in yeast.

Artefacts in statistical analyses of network motifs: general framework and application to metabolic networks

Few-node subgraphs are the smallest collective units in a network that can be investigated. They are beyond the scale of individual nodes but more local than, for example, communities. When statistically over- or under-represented, they are called network motifs. Network motifs have been interpreted as building blocks that shape the dynamic behaviour of networks. It is this promise of potentially explaining emergent properties of complex systems with relatively simple structures that led to an interest in network motifs in an ever-growing number of studies and across disciplines. Here, we discuss artefacts in the analysis of network motifs arising from discrepancies between the network under investigation and the pool of random graphs serving as a null model. Our aim was to provide a clear and accessible catalogue of such incongruities and their effect on the motif signature. As a case study, we explore the metabolic network of Escherichia coli and show that only by excluding ever more artefacts from the motif signature a strong and plausible correlation with the essentiality profile of metabolic reactions emerges.

Feed-forward loops and diamond motifs lead to tunable transmission of information in the frequency domain

Using a Gaussian model, we study the transmission of time-varying biochemical signals through feed-forward motifs and diamond motifs. To this end, we compute the frequency dependence of the gain, the noise, as well as their ratio, the gain-to-noise ratio, which measures how reliably a network transmits signals at different frequencies. We find that both coherent and incoherent feed-forward motifs can either act as low-pass or high-pass filters for information: The frequency dependence of the gain-to-noise ratio increases or decreases with increasing frequency, respectively. Our analysis of diamond motifs reveals that cooperative activation of the output component can increase the gain-to-noise ratio. This means that from the perspective of information transmission, it can be beneficial to split the input signal in two and recombine the two propagated signals at the output. Cooperative activation can be implemented via the formation of homo- or heteromultimers that then bind and activate the output component or via the binding of individual molecules of the intermediate species to the output component.

Modeling suggests that gene circuit architecture controls phenotypic variability in a bacterial persistence network

BACKGROUND

Bacterial persistence is a non-inherited bet-hedging mechanism where a subpopulation of cells enters a dormant state, allowing those cells to survive environmental stress such as treatment with antibiotics. Persister cells are not mutants; they are formed by natural stochastic variation in gene expression. Understanding how regulatory architecture influences the level of phenotypic variability can help us explain how the frequency of persistence events can be tuned.

RESULTS

We present a model of the regulatory network controlling the HipBA toxin-antitoxin system from Escherichia coli. Using a biologically realistic model we first determine that the persistence phenotype is not the result of bistability within the network. Next, we develop a stochastic model and show that cells can enter persistence due to random fluctuations in transcription, translation, degradation, and complex formation. We then examine alternative gene circuit architectures for controlling hipBA expression and show that networks with more noise (more persisters) and less noise (fewer persisters) are straightforward to achieve. Thus, we propose that the gene circuit architecture can be used to tune the frequency of persistence, a trait that can be selected for by evolution.

CONCLUSIONS

We develop deterministic and stochastic models describing how the regulation of toxin and antitoxin expression influences phenotypic variation within a population. Persistence events are the result of stochastic fluctuations in toxin levels that cross a threshold, and their frequency is controlled by the regulatory topology governing gene expression.