Bistability versus bimodal distributions in gene regulatory processes from population balance

Dimerization induces bimodality in protein number distributions

We examined gene expression with DNA switching between two states, active and inactive. Subpopulations emerge from mechanisms that do not arise from trivial transcriptional heterogeneity. Although the RNA demonstrates a unimodal distribution, dimerization intriguingly causes protein bimodality. No control loop or deterministic bistability are present. In such a situation, increasing the degradation rate of the protein does not lead to bimodality. The bimodality is achieved through the interplay between the protein monomer and the formation of protein dimer. We applied Stochastic Simulation Algorithm (SSA) and found that cells spontaneously change states at the protein level. While sweeping parameters, decreasing the rate constant of dimerization severely impairs the bimodality. We also examined the influence of DNA switching. To have bimodality, the system requires a proper ratio of DNA in the active state to the inactive state. In addition to bimodality of the monomer, tetramerization also causes the bimodality of the dimer.

Beyond the chemical master equation: Stochastic chemical kinetics coupled with auxiliary processes

The chemical master equation and its continuum approximations are indispensable tools in the modeling of chemical reaction networks. These are routinely used to capture complex nonlinear phenomena such as multimodality as well as transient events such as first-passage times, that accurately characterise a plethora of biological and chemical processes. However, some mechanisms, such as heterogeneous cellular growth or phenotypic selection at the population level, cannot be represented by the master equation and thus have been tackled separately. In this work, we propose a unifying framework that augments the chemical master equation to capture such auxiliary dynamics, and we develop and analyse a numerical solver that accurately simulates the system dynamics. We showcase these contributions by casting a diverse array of examples from the literature within this framework and applying the solver to both match and extend previous studies. Analytical calculations performed for each example validate our numerical results and benchmark the solver implementation.

Populations of genetically identical cells tend to exhibit remarkable variability. This seemingly counter-intuitive observation has broad and fascinating implications, and has thus been a focal point of biological modeling. Many important processes act on this cellular heterogeneity at the population level, leading to an intricate coupling between the single-cell and the population-level dynamics. For example, selection pressures or growth rates may depend crucially on the expression of a particular gene (or gene family). Classical single-cell modeling approaches, such as the chemical master equation, can accurately describe the mechanisms driving cellular noise, however, they cannot encapsulate how the aforementioned auxiliary processes affect the population composition. In this work, we propose a unifying framework that extends the classical chemical master equation to faithfully capture the single-cell variability alongside the population-level evolution. We develop, analyse, and showcase an open-source numerical tool to simulate the dynamics of such populations in time. The tool is designed for straightforward use by a non-technical audience: a high-level description of the underlying chemical and population-level processes suffices to simulate complex system dynamics. Simultaneously, we retain high customisability of the underlying mathematical representation for the more advanced user. Ultimately, the unifying framework and the associated computational tool open new horizons in the study of how fundamental microscopic dynamics give rise to complex macroscopic phenomena.

Exposure to One Antibiotic Leads to Acquisition of Resistance to Another Antibiotic via Quorum Sensing Mechanisms

The vancomycin-resistant Enterococci (VRE) have progressively become a severe medical problem. Although clinics have started to reduce vancomycin prescription, vancomycin resistance has not been contained. We found that the transfer of vancomycin resistance in Enterococcus faecalis increased more than 30-fold upon treatment by streptomycin. Notably, treatment with an antibiotic caused the bacteria to become resistant to another. The response was even stronger in the well-studied plasmid pCF10 and the number of transconjugants increased about 100,000-fold. We tested four different antibiotics, and all of them induced conjugal response. Through a mathematical model based on gene regulation, we found a plausible explanation. Via quorum sensing, the change of the cell density triggers the conjugation. Moreover, we searched for generality and found a similar strategy in Bacillus subtilis. The outcome of the present study suggests that even common antibiotics must not be overused.

Trajectory-based energy landscapes of gene regulatory networks

Multistability and natural biological variability can result in significant heterogeneity within a cell population, leading to challenges in understanding and modulating cell behavior. Energy landscapes can offer qualitatively intuitive visualizations of cell phenotype and facilitate a more quantitative understanding of cellular dynamics, but current methods for landscape generation are mathematically involved and often require specific system properties (e.g., ergodicity or independent gene/protein probability distributions) that do not always hold. Here, we present a simple kinetic Monte Carlo-based method for landscape generation from a system of ordinary differential equations using only simulation trajectories initialized throughout the phase space of interest. The resulting landscape produces three quantitative features relevant to understanding cell behavior: stability (reflected by the depth or potential of landscape valleys), velocity (representing average directional movement on the landscape), and variance in velocity (indicative of landscape positions with heterogeneous movements). We applied this method to a genetic toggle switch, a core decision-making network in binary cellular responses, to elucidate effects of biologically relevant intrinsic and extrinsic cues. Intrinsic noise, such as stochasticity in transcription-translation and differences in cell cycle position, manifests through changes in valley width and position, reflecting increased population heterogeneity and more probabilistic cell fate transitions. The landscapes also capture the effect of an external inducer, revealing a quantitative correlation between the rate of cell fate transition and the energy barrier above a threshold inducer concentration determined by the permissivity of the valley. Further, in tracking dynamically changing landscapes under time-varying external cues, we unexpectedly found that an oscillatory inducer input can modulate cell fate heterogeneity and lead to periodic cell fate transitions entrained to the input frequency, depending on the intrinsic degradation rate of the switch. The landscape generation approach outlined herein is generalizable to other network topologies and may provide new quantitative insights into their dynamics.

Modeling the intracellular dynamics of the dengue viral infection and the innate immune response

The interplay between the dengue virus and the innate immune response is not fully understood. Here, we use deterministic and stochastic approaches to investigate the dynamics of the interaction between the interferon-mediated innate immune response and the dengue virus. We aim to develop a quantitative representation of these complex interactions and predict their system-level dynamics. Our simulation results predict bimodal and bistable dynamics that represent viral clearance and virus-producing states. Under normal conditions, we determined that the viral infection outcome is modulated by the innate immune response and the positive-strand viral RNA concentration. Additionally, we tested system perturbations by external stimulation, such as the direct induction of the innate immune response by interferon, and a therapeutic intervention consisting of the direct application of mRNA encoding for several interferon-stimulated genes. Our simulation results suggest optimal regimes for the studied intervention approaches.

Theoretical study of the impact of adaptation on cell-fate heterogeneity and fractional killing

Fractional killing illustrates the cell propensity to display a heterogeneous fate response over a wide range of stimuli. The interplay between the nonlinear and stochastic dynamics of biochemical networks plays a fundamental role in shaping this probabilistic response and in reconciling requirements for heterogeneity and controllability of cell-fate decisions. The stress-induced fate choice between life and death depends on an early adaptation response which may contribute to fractional killing by amplifying small differences between cells. To test this hypothesis, we consider a stochastic modeling framework suited for comprehensive sensitivity analysis of dose response curve through the computation of a fractionality index. Combining bifurcation analysis and Langevin simulation, we show that adaptation dynamics enhances noise-induced cell-fate heterogeneity by shifting from a saddle-node to a saddle-collision transition scenario. The generality of this result is further assessed by a computational analysis of a detailed regulatory network model of apoptosis initiation and by a theoretical analysis of stochastic bifurcation mechanisms. Overall, the present study identifies a cooperative interplay between stochastic, adaptation and decision intracellular processes that could promote cell-fate heterogeneity in many contexts.

Stochastic reaction networks in dynamic compartment populations

Many biochemical processes in living systems take place in compartmentalized environments, where individual compartments can interact with each other and undergo dynamic remodeling. Studying such processes through mathematical models poses formidable challenges because the underlying dynamics involve a large number of states, which evolve stochastically with time. Here we propose a mathematical framework to study stochastic biochemical networks in compartmentalized environments. We develop a generic population model, which tracks individual compartments and their molecular composition. We then show how the time evolution of this system can be studied effectively through a small number of differential equations, which track the statistics of the population. Our approach is versatile and renders an important class of biological systems computationally accessible.

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress toward addressing this problem in the context of specific biological systems, but a general and sufficiently effective approach remains lacking. In this work, we propose a mathematical framework based on counting processes that allows us to study dynamic compartment populations with arbitrary interactions and internal biochemistry. We derive an efficient description of the dynamics in terms of differential equations which capture the statistics of the population. We demonstrate the relevance of our approach by analyzing models inspired by different biological processes, including subcellular compartmentalization and tissue homeostasis.

An analog to digital converter controls bistable transfer competence development of a widespread bacterial integrative and conjugative element

Conjugative transfer of the integrative and conjugative element ICEclc in Pseudomonas requires development of a transfer competence state in stationary phase, which arises only in 3–5% of individual cells. The mechanisms controlling this bistable switch between non-active and transfer competent cells have long remained enigmatic. Using a variety of genetic tools and epistasis experiments in P. putida, we uncovered an ‘upstream’ cascade of three consecutive transcription factor-nodes, which controls transfer competence initiation. One of the uncovered transcription factors (named BisR) is representative for a new regulator family. Initiation activates a feedback loop, controlled by a second hitherto unrecognized heteromeric transcription factor named BisDC. Stochastic modelling and experimental data demonstrated the feedback loop to act as a scalable converter of unimodal (population-wide or ‘analog’) input to bistable (subpopulation-specific or ‘digital’) output. The feedback loop further enables prolonged production of BisDC, which ensures expression of the ‘downstream’ functions mediating ICE transfer competence in activated cells. Phylogenetic analyses showed that the ICEclc regulatory constellation with BisR and BisDC is widespread among Gamma- and Beta-proteobacteria, including various pathogenic strains, highlighting its evolutionary conservation and prime importance to control the behaviour of this wide family of conjugative elements.

Mobile DNA elements are pieces of genetic material that can jump from one bacterium to another, and even across species. They are often useful to their host, for example carrying genes that allow bacteria to resist antibiotics.

One example of bacterial mobile DNA is the ICEclc element. Usually, ICEclc sits passively within the bacterium’s own DNA, but in a small number of cells, it takes over, hijacking its host to multiply and to get transferred to other bacteria. Cells that can pass on the elements cannot divide, and so this ability is ultimately harmful to individual bacteria. Carrying ICEclc can therefore be positive for a bacterium but passing it on is not in the cell’s best interest. On the other hand, mobile DNAs like ICEclc have evolved to be disseminated as efficiently as possible. To shed more light on this tense relationship, Carraro et al. set out to identify the molecular mechanisms ICEclc deploys to control its host.

Experiments using mutant bacteria revealed that for ICEclc to successfully take over the cell, a number of proteins needed to be produced in the correct order. In particular, a protein called BisDC triggers a mechanism to make more of itself, creating a self-reinforcing ‘feedback loop’.

Mathematical simulations of the feedback loop showed that it could result in two potential outcomes for the cell. In most of the ‘virtual cells’, ICEclc ultimately remained passive; however, in a few, ICEclc managed to take over its hosts. In this case, the feedback loop ensured that there was always enough BisDC to maintain ICEclc’s control over the cell. Further analyses suggested that this feedback mechanism is also common in many other mobile DNA elements, including some that help bacteria to resist drugs.

These results are an important contribution to understand how mobile DNAs manipulate their bacterial host in order to propagate and disperse. In the future, this knowledge could help develop new strategies to combat the spread of antibiotic resistance.

Single-Cell Analysis Reveals that the Enterococcal Sex Pheromone Response Results in Expression of Full-Length Conjugation Operon Transcripts in All Induced Cells

For high-frequency transfer of pCF10 between E. faecalis cells, induced expression of the pCF10 genes encoding conjugative machinery from the prgQ operon is required. This process is initiated by the cCF10 (C) inducer peptide produced by potential recipient cells. The expression timing of prgB, an "early" gene just downstream of the inducible promoter, has been studied extensively in single cells. However, several previous studies suggest that only 1 to 10% of donors induced for early prgQ gene expression actually transfer plasmids to recipients, even at a very high recipient population density. One possible explanation for this is that only a minority of pheromone-induced donors actually transcribe the entire prgQ operon. Such cells would not be able to functionally conjugate but might play another role in the group behavior of donors. Here, we sought to (i) simultaneously assess the presence of RNAs produced from the proximal (early induced transcripts [early Q]) and distal (late Q) portions of the prgQ operon in individual cells, (ii) investigate the prevalence of heterogeneity in induced transcript length, and (iii) evaluate the temporality of induced transcript expression. Using fluorescent in situ hybridization chain reaction (HCR) transcript labeling and single-cell microscopic analysis, we observed that most cells expressing early transcripts (Q_L, prgB, and prgA) also expressed late transcripts (prgJ, pcfC, and pcfG). These data support the conclusion that, after induction is initiated, transcription likely extends through the end of the conjugation machinery operon for most, if not all, induced cells.IMPORTANCE In Enterococcus faecalis, conjugative plasmids like pCF10 often carry antibiotic resistance genes. With antibiotic treatment, bacteria benefit from plasmid carriage; however, without antibiotic treatment, plasmid gene expression may have a fitness cost. Transfer of pCF10 is mediated by cell-to-cell signaling, which activates the expression of conjugation genes and leads to efficient plasmid transfer. Yet, not all donor cells in induced populations transfer the plasmid. We examined whether induced cells might not be able to functionally conjugate due to premature induced transcript termination. Single-cell analysis showed that most induced cells do, in fact, express all of the genes required for conjugation, suggesting that premature transcription termination within the prgQ operon does not account for failure of induced donor cell gene transfer.

Interaction variability shapes succession of synthetic microbial ecosystems

Cellular interactions are a major driver for the assembly and functioning of microbial communities. Their strengths are shown to be highly variable in nature; however, it is unclear how such variations regulate community behaviors. Here we construct synthetic Lactococcus lactis consortia and mathematical models to elucidate the role of interaction variability in ecosystem succession and to further determine if casting variability into modeling empowers bottom-up predictions. For a consortium of bacteriocin-mediated cooperation and competition, we find increasing the variations of cooperation, from either altered labor partition or random sampling, drives the community into distinct structures. When the cooperation and competition are additionally modulated by pH, ecosystem succession becomes jointly controlled by the variations of both interactions and yields more diversified dynamics. Mathematical models incorporating variability successfully capture all of these experimental observations. Our study demonstrates interaction variability as a key regulator of community dynamics, providing insights into bottom-up predictions of microbial ecosystems.

Cellular interactions are a major driver of microbial communities and shown highly variable in strength. Here the authors construct synthetic consortia and mathematical models to elucidate the role of interaction variability in driving ecosystem succession.

Controlling cell-to-cell variability with synthetic gene circuits

Cell-to-cell variability originating, for example, from the intrinsic stochasticity of gene expression, presents challenges for designing synthetic gene circuits that perform robustly. Conversely, synthetic biology approaches are instrumental in uncovering mechanisms underlying variability in natural systems. With a focus on reducing noise in individual genes, the field has established a broad synthetic toolset. This includes noise control by engineering of transcription and translation mechanisms either individually, or in combination to achieve independent regulation of mean expression and its variability. Synthetic feedback circuits use these components to establish more robust operation in closed-loop, either by drawing on, but also by extending traditional engineering concepts. In this perspective, we argue that major conceptual advances will require new theory of control adapted to biology, extensions from single genes to networks, more systematic considerations of origins of variability other than intrinsic noise, and an exploration of how noise shaping, instead of noise reduction, could establish new synthetic functions or help understanding natural functions.

Population dynamics of driven autocatalytic reactive mixtures

Motivated by the effect of electroautocatalysis (explicit concentration dependence) on the stability of electrochemically driven phase-separating single particles, we apply the Fokker-Planck equation to describe the population dynamics of a general ensemble of chemically reactive particles. For phase-separating ensembles, we show that mosaic instability (from a homogeneous initial state to a multimodal probability distribution) may be suppressed or enhanced by autoinhibitory or autocatalytic reactions, respectively. In some cases, autocatalysis may induce two distinct populations in thermodynamically stable single-phase ensembles. Asymmetric reaction kinetics also results in qualitatively different population dynamics upon reversing the reaction direction. In the limit of negligible fluctuations, we use the method of characteristics and linearization to study the evolution of the concentration variance as well as the condition for mosaic instability, in good agreement with the full numerical solution. Applications include Li-ion batteries characterized by in situ x-ray diffraction.

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.

A Simple and Flexible Computational Framework for Inferring Sources of Heterogeneity from Single-Cell Dynamics

Single-cell time-lapse data provide the means for disentangling sources of cell-to-cell and intra-cellular variability, a key step for understanding heterogeneity in cell populations. However, single-cell analysis with dynamic models is a challenging open problem: current inference methods address only single-gene expression or neglect parameter correlations. We report on a simple, flexible, and scalable method for estimating cell-specific and population-average parameters of non-linear mixed-effects models of cellular networks, demonstrating its accuracy with a published model and dataset. We also propose sensitivity analysis for identifying which biological sub-processes quantitatively and dynamically contribute to cell-to-cell variability. Our application to endocytosis in yeast demonstrates that dynamic models of realistic size can be developed for the analysis of single-cell data and that shifting the focus from single reactions or parameters to nuanced and time-dependent contributions of sub-processes helps biological interpretation. Generality and simplicity of the approach will facilitate customized extensions for analyzing single-cell dynamics.

Estimation methods for heterogeneous cell population models in systems biology

Heterogeneity among individual cells is a characteristic and relevant feature of living systems. A range of experimental techniques to investigate this heterogeneity is available, and multiple modelling frameworks have been developed to describe and simulate the dynamics of heterogeneous populations. Measurement data are used to adjust computational models, which results in parameter and state estimation problems. Methods to solve these estimation problems need to take the specific properties of data and models into account. The aim of this review is to give an overview on the state of the art in estimation methods for heterogeneous cell population data and models. The focus is on models based on the population balance equation, but stochastic and individual-based models are also discussed. It starts with a brief discussion of common experimental approaches and types of measurement data that can be obtained in this context. The second part describes computational modelling frameworks for heterogeneous populations and the types of estimation problems occurring for these models. The third part starts with a discussion of observability and identifiability properties, after which the computational methods to solve the various estimation problems are described.

Impact of Zygosity on Bimodal Phenotype Distributions

Allele number, or zygosity, is a clear determinant of gene expression in diploid cells. However, the relationship between the number of copies of a gene and its expression can be hard to anticipate, especially when the gene in question is embedded in a regulatory circuit that contains feedback. Here, we study this question making use of the natural genetic variability of human populations, which allows us to compare the expression profiles of a receptor protein in natural killer cells among donors infected with human cytomegalovirus with one or two copies of the allele. Crucially, the distribution of gene expression in many of the donors is bimodal, which indicates the presence of a positive feedback loop somewhere in the regulatory environment of the gene. Three separate gene-circuit models differing in the location of the positive feedback loop with respect to the gene can all reproduce the homozygous data. However, when the resulting fitted models are applied to the hemizygous donors, one model (the one with the positive feedback located at the level of gene transcription) is superior in describing the experimentally observed gene-expression profile. In that way, our work shows that zygosity can help us relate the structure and function of gene regulatory networks.

Stochasticity in the enterococcal sex pheromone response revealed by quantitative analysis of transcription in single cells

In Enterococcus faecalis, sex pheromone-mediated transfer of antibiotic resistance plasmids can occur under unfavorable conditions, for example, when inducing pheromone concentrations are low and inhibiting pheromone concentrations are high. To better understand this paradox, we adapted fluorescence in situ hybridization chain reaction (HCR) methodology for simultaneous quantification of multiple E. faecalis transcripts at the single cell level. We present direct evidence for variability in the minimum period, maximum response level, and duration of response of individual cells to a specific inducing condition. Tracking of induction patterns of single cells temporally using a fluorescent reporter supported HCR findings. It also revealed subpopulations of rapid responders, even under low inducing pheromone concentrations where the overall response of the entire population was slow. The strong, rapid induction of small numbers of cells in cultures exposed to low pheromone concentrations is in agreement with predictions of a stochastic model of the enterococcal pheromone response. The previously documented complex regulatory circuitry controlling the pheromone response likely contributes to stochastic variation in this system. In addition to increasing our basic understanding of the biology of a horizontal gene transfer system regulated by cell-cell signaling, demonstration of the stochastic nature of the pheromone response also impacts any future efforts to develop therapeutic agents targeting the system. Quantitative single cell analysis using HCR also has great potential to elucidate important bacterial regulatory mechanisms not previously amenable to study at the single cell level, and to accelerate the pace of functional genomic studies.

Inhibitors Alter the Stochasticity of Regulatory Proteins to Force Cells to Switch to the Other State in the Bistable System

The cellular behaviors under the control of genetic circuits are subject to stochastic fluctuations, or noise. The stochasticity in gene regulation, far from a nuisance, has been gradually appreciated for its unusual function in cellular activities. In this work, with Chemical Master Equation (CME), we discovered that the addition of inhibitors altered the stochasticity of regulatory proteins. For a bistable system of a mutually inhibitory network, such a change of noise led to the migration of cells in the bimodal distribution. We proposed that the consumption of regulatory protein caused by the addition of inhibitor is not the only reason for pushing cells to the specific state; the change of the intracellular stochasticity is also the main cause for the redistribution. For the level of the inhibitor capable of driving 99% of cells, if there is no consumption of regulatory protein, 88% of cells were guided to the specific state. It implied that cells were pushed, by the inhibitor, to the specific state due to the change of stochasticity.

Driving Cells to the Desired State in a Bimodal Distribution through Manipulation of Internal Noise with Biologically Practicable Approaches

The stochastic nature of gene regulatory networks described by Chemical Master Equation (CME) leads to the distribution of proteins. A deterministic bistability is usually reflected as a bimodal distribution in stochastic simulations. Within a certain range of the parameter space, a bistable system exhibits two stable steady states, one at the low end and the other at the high end. Consequently, it appears to have a bimodal distribution with one sub-population (mode) around the low end and the other around the high end. In most cases, only one mode is favorable, and guiding cells to the desired state is valuable. Traditionally, the population was redistributed simply by adjusting the concentration of the inducer or the stimulator. However, this method has limitations; for example, the addition of stimulator cannot drive cells to the desired state in a common bistable system studied in this work. In fact, it pushes cells only to the undesired state. In addition, it causes a position shift of the modes, and this shift could be as large as the value of the mode itself. Such a side effect might damage coordination, and this problem can be avoided by applying a new method presented in this work. We illustrated how to manipulate the intensity of internal noise by using biologically practicable methods and utilized it to prompt the population to the desired mode. As we kept the deterministic behavior untouched, the aforementioned drawback was overcome. Remarkably, more than 96% of cells has been driven to the desired state. This method is genetically applicable to biological systems exhibiting a bimodal distribution resulting from bistability. Moreover, the reaction network studied in this work can easily be extended and applied to many other systems.

A Comparison of Deterministic and Stochastic Modeling Approaches for Biochemical Reaction Systems: On Fixed Points, Means, and Modes

In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still expected to provide relevant indications on the underlying dynamics.

Bidirectional interconversion of stem and non-stem cancer cell populations: A reassessment of theoretical models for tumor heterogeneity

Resolving the origin of intratumor heterogeneity has proven to be one of the central challenges in cancer research during recent years. Two theoretical models explaining the emergence of intratumor heterogeneity have come to dominate cancer biology literature: the clonal evolution model and the hierarchical/cancer stem cell model. Recently, a plastic model that combines elements of both the clonal and the hierarchical model has gained traction. Basically, this model proposes that cancer stem cells engage in bidirectional interconversion with non-stem cells, thereby providing the missing link between the 2 conventional models. Confirming bidirectional interconversion as a hallmark of cancer is a crucial step in understanding tumor heterogeneity and has important therapeutic implications. In this review, current methodologies and theoretical and empirical evidence regarding bidirectional interconversion will be discussed.

Cis-Antisense Transcription Gives Rise to Tunable Genetic Switch Behavior: A Mathematical Modeling Approach

Antisense transcription has been extensively recognized as a regulatory mechanism for gene expression across all kingdoms of life. Despite the broad importance and extensive experimental determination of cis-antisense transcription, relatively little is known about its role in controlling cellular switching responses. Growing evidence suggests the presence of non-coding cis-antisense RNAs that regulate gene expression via antisense interaction. Recent studies also indicate the role of transcriptional interference in regulating expression of neighboring genes due to traffic of RNA polymerases from adjacent promoter regions. Previous models investigate these mechanisms independently, however, little is understood about how cells utilize coupling of these mechanisms in advantageous ways that could also be used to design novel synthetic genetic devices. Here, we present a mathematical modeling framework for antisense transcription that combines the effects of both transcriptional interference and cis-antisense regulation. We demonstrate the tunability of transcriptional interference through various parameters, and that coupling of transcriptional interference with cis-antisense RNA interaction gives rise to hypersensitive switches in expression of both antisense genes. When implementing additional positive and negative feed-back loops from proteins encoded by these genes, the system response acquires a bistable behavior. Our model shows that combining these multiple-levels of regulation allows fine-tuning of system parameters to give rise to a highly tunable output, ranging from a simple-first order response to biologically complex higher-order response such as tunable bistable switch. We identify important parameters affecting the cellular switch response in order to provide the design principles for tunable gene expression using antisense transcription. This presents an important insight into functional role of antisense transcription and its importance towards design of synthetic biological switches.

CONSTRICTOR: constraint modification provides insight into design of biochemical networks

Advances in computational methods that allow for exploration of the combinatorial mutation space are needed to realize the potential of synthetic biology based strain engineering efforts. Here, we present Constrictor, a computational framework that uses flux balance analysis (FBA) to analyze inhibitory effects of genetic mutations on the performance of biochemical networks. Constrictor identifies engineering interventions by classifying the reactions in the metabolic model depending on the extent to which their flux must be decreased to achieve the overproduction target. The optimal inhibition of various reaction pathways is determined by restricting the flux through targeted reactions below the steady state levels of a baseline strain. Constrictor generates unique in silico strains, each representing an “expression state”, or a combination of gene expression levels required to achieve the overproduction target. The Constrictor framework is demonstrated by studying overproduction of ethylene in Escherichia coli network models iAF1260 and iJO1366 through the addition of the heterologous ethylene-forming enzyme from Pseudomonas syringae. Targeting individual reactions as well as combinations of reactions reveals in silico mutants that are predicted to have as high as 25% greater theoretical ethylene yields than the baseline strain during simulated exponential growth. Altering the degree of restriction reveals a large distribution of ethylene yields, while analysis of the expression states that return lower yields provides insight into system bottlenecks. Finally, we demonstrate the ability of Constrictor to scan networks and provide targets for a range of possible products. Constrictor is an adaptable technique that can be used to generate and analyze disparate populations of in silico mutants, select gene expression levels and provide non-intuitive strategies for metabolic engineering.

Applications of flow cytometry to characterize bacterial physiological responses

Although reports of flow cytometry (FCM) applied to bacterial analysis are increasing, studies of FCM related to human cells still vastly outnumber other reports. However, current advances in FCM combined with a new generation of cellular reporter probes have made this technique suitable for analyzing physiological responses in bacteria. We review how FCM has been applied to characterize distinct physiological conditions in bacteria including responses to antibiotics and other cytotoxic chemicals and physical factors, pathogen-host interactions, cell differentiation during biofilm formation, and the mechanisms governing development pathways such as sporulation. Since FCM is suitable for performing studies at the single-cell level, we describe how this powerful technique has yielded invaluable information about the heterogeneous distribution of differently and even specialized responding cells and how it may help to provide insights about how cell interaction takes place in complex structures, such as those that prevail in bacterial biofilms.

Population Balance Modeling: Current Status and Future Prospects

Population balance modeling is undergoing phenomenal growth in its applications, and this growth is accompanied by multifarious reviews. This review aims to fortify the model's fundamental base, as well as point to a variety of new applications, including modeling of crystal morphology, cell growth and differentiation, gene regulatory processes, and transfer of drug resistance. This is accomplished by presenting the many faces of population balance equations that arise in the foregoing applications.

Revitalizing personalized medicine: respecting biomolecular complexities beyond gene expression

Despite recent advancements in "omic" technologies, personalized medicine has not realized its fullest potential due to isolated and incomplete application of gene expression tools. In many instances, pharmacogenomics is being interchangeably used for personalized medicine, when actually it is one of the many facets of personalized medicine. Herein, we highlight key issues that are hampering the advancement of personalized medicine and highlight emerging predictive tools that can serve as a decision support mechanism for physicians to personalize treatments.

Role of intracellular stochasticity in biofilm growth. Insights from population balance modeling

There is increasing recognition that stochasticity involved in gene regulatory processes may help cells enhance the signal or synchronize expression for a group of genes. Thus the validity of the traditional deterministic approach to modeling the foregoing processes cannot be without exception. In this study, we identify a frequently encountered situation, i.e., the biofilm, which has in the past been persistently investigated with intracellular deterministic models in the literature. We show in this paper circumstances in which use of the intracellular deterministic model appears distinctly inappropriate. In Enterococcus faecalis, the horizontal gene transfer of plasmid spreads drug resistance. The induction of conjugation in planktonic and biofilm circumstances is examined here with stochastic as well as deterministic models. The stochastic model is formulated with the Chemical Master Equation (CME) for planktonic cells and Reaction-Diffusion Master Equation (RDME) for biofilm. The results show that although the deterministic model works well for the perfectly-mixed planktonic circumstance, it fails to predict the averaged behavior in the biofilm, a behavior that has come to be known as stochastic focusing. A notable finding from this work is that the interception of antagonistic feedback loops to signaling, accentuates stochastic focusing. Moreover, interestingly, increasing particle number of a control variable could lead to an even larger deviation. Intracellular stochasticity plays an important role in biofilm and we surmise by implications from the model, that cell populations may use it to minimize the influence from environmental fluctuation.

Cooperative binding of transcription factors promotes bimodal gene expression response

In the present work we extend and analyze the scope of our recently proposed stochastic model for transcriptional regulation, which considers an arbitrarily complex cis-regulatory system using only elementary reactions. Previously, we determined the role of cooperativity on the intrinsic fluctuations of gene expression for activating transcriptional switches, by means of master equation formalism and computer simulation. This model allowed us to distinguish between two cooperative binding mechanisms and, even though the mean expression levels were not affected differently by the acting mechanism, we showed that the associated fluctuations were different. In the present generalized model we include other regulatory functions in addition to those associated to an activator switch. Namely, we introduce repressive regulatory functions and two theoretical mechanisms that account for the biphasic response that some cis-regulatory systems show to the transcription factor concentration. We have also extended our previous master equation formalism in order to include protein production by stochastic translation of mRNA. Furthermore, we examine the graded/binary scenarios in the context of the interaction energy between transcription factors. In this sense, this is the first report to show that the cooperative binding of transcription factors to DNA promotes the "all-or-none" phenomenon observed in eukaryotic systems. In addition, we confirm that gene expression fluctuation levels associated with one of two cooperative binding mechanism never exceed the fluctuation levels of the other.

Computational modeling and analysis of insulin induced eukaryotic translation initiation

Insulin, the primary hormone regulating the level of glucose in the bloodstream, modulates a variety of cellular and enzymatic processes in normal and diseased cells. Insulin signals are processed by a complex network of biochemical interactions which ultimately induce gene expression programs or other processes such as translation initiation. Surprisingly, despite the wealth of literature on insulin signaling, the relative importance of the components linking insulin with translation initiation remains unclear. We addressed this question by developing and interrogating a family of mathematical models of insulin induced translation initiation. The insulin network was modeled using mass-action kinetics within an ordinary differential equation (ODE) framework. A family of model parameters was estimated, starting from an initial best fit parameter set, using 24 experimental data sets taken from literature. The residual between model simulations and each of the experimental constraints were simultaneously minimized using multiobjective optimization. Interrogation of the model population, using sensitivity and robustness analysis, identified an insulin-dependent switch that controlled translation initiation. Our analysis suggested that without insulin, a balance between the pro-initiation activity of the GTP-binding protein Rheb and anti-initiation activity of PTEN controlled basal initiation. On the other hand, in the presence of insulin a combination of PI3K and Rheb activity controlled inducible initiation, where PI3K was only critical in the presence of insulin. Other well known regulatory mechanisms governing insulin action, for example IRS-1 negative feedback, modulated the relative importance of PI3K and Rheb but did not fundamentally change the signal flow.