Simulation of prokaryotic genetic circuits

Stabilization of the human cytomegalovirus UL136p33 reactivation determinant overcomes the requirement for UL135 for replication in hematopoietic cells

Human cytomegalovirus (HCMV) is a beta herpesvirus that persists indefinitely in the human host through a latent infection. The polycistronic UL133-UL138 gene locus of HCMV encodes genes regulating latency and reactivation. While UL138 is pro-latency, restricting virus replication in CD34+ hematopoietic progenitor cells (HPCs), UL135 overcomes this restriction and is required for reactivation. By contrast, UL136 is expressed with later kinetics and encodes multiple proteins with differential roles in latency and reactivation. Like UL135, the largest UL136 isoform, UL136p33, is required for reactivation from latency in HPCs; viruses failing to express either protein are unresponsive to reactivation stimuli. Furthermore, UL136p33 is unstable, and its instability is important for the establishment of latency, and sufficient accumulation of UL136p33 is a checkpoint for reactivation. We hypothesized that stabilizing UL136p33 might overcome the requirement of UL135 for replication. We generated recombinant viruses lacking UL135 that expressed a stabilized variant of UL136p33. Stabilizing UL136p33 did not impact the replication of the UL135 mutant virus in fibroblasts. However, in the context of infection in HPCs, stabilization of UL136p33 strikingly compensated for the loss of UL135, resulting in increased replication in CD34+ HPCs and in humanized NOD-scid IL2Rγcnull (huNSG) mice. This finding suggests that while UL135 is essential for replication in HPCs, it functions largely at steps preceding the accumulation of UL136p33, and that stabilized expression of UL136p33 largely overcomes the requirement for UL135. Taken together, our genetic evidence indicates an epistatic relationship between UL136p33 and UL135, whereby UL135 may initiate events early in reactivation that drive the accumulation of UL136p33 to a threshold required for productive reactivation. IMPORTANCE Human cytomegalovirus (HCMV) is one of nine human herpesviruses and a significant human pathogen. While HCMV establishes a lifelong latent infection that is typically asymptomatic in healthy individuals, its reactivation from latency can have devastating consequences in the immunocompromised. Defining viral genes important in the establishment of or reactivation from latency is important to defining the molecular basis of latent and replicative states and in controlling infection and CMV disease. Here we define a genetic relationship between two viral genes in controlling virus reactivation from latency using primary human hematopoietic progenitor cells and humanized mouse models.

UL135 and UL136 Epistasis Controls Reactivation of Human Cytomegalovirus

Human cytomegalovirus (HCMV) is beta herpesvirus that persists indefinitely in the human host through a protracted, latent infection. The polycistronic UL133-UL138 gene locus of HCMV encodes genes regulating latency and reactivation. While UL138 is pro-latency, restricting virus replication in CD34+ hematopoietic progenitor cells (HPCs), UL135 overcomes this restriction for reactivation. By contrast, UL136 is expressed with later kinetics and encodes multiple protein isoforms with differential roles in latency and reactivation. Like UL135, the largest UL136 isoform, UL136p33, is required for reactivation from latency in hematopoietic cells. Furthermore, UL136p33 is unstable, and its instability is important for the establishment of latency and sufficient accumulation of UL136p33 is a checkpoint for reactivation. We hypothesized that stabilizing UL136p33 might overcome the requirement of UL135 for reactivation. To test this, we generated recombinant viruses lacking UL135 that expressed a stabilized variant of UL136p33. Stabilizing UL136p33 did not impact replication of the UL135-mutant virus in fibroblasts. However, in the context of infection in hematopoietic cells, stabilization of UL136p33 strikingly compensated for the loss of UL135, resulting in increased replication in CD34+ HPCs and in humanized NOD- scid IL2Rγ _c ^null (NSG) mice. This finding suggests that while UL135 is essential for reactivation, it functions at steps preceding the accumulation of UL136p33 and that stabilized expression of UL136p33 largely overcomes the requirement for UL135 in reactivation. Taken together, our genetic evidence indicates an epistatic relationship between UL136p33 and UL135 whereby UL135 may initiate events early in reactivation that will result in the accumulation of UL136p33 to a threshold required for productive reactivation.

SIGNIFICANCE

Human cytomegalovirus (HCMV) is one of nine human herpesviruses and a significant human pathogen. While HCMV establishes a life-long latent infection that is typically asymptomatic in healthy individuals, its reactivation from latency can have devastating consequences in the immune compromised. Defining virus-host and virus-virus interactions important for HCMV latency, reactivation and replication is critical to defining the molecular basis of latent and replicative states and in controlling infection and CMV disease. Here we define a genetic relationship between two viral genes in controlling virus reactivation from latency using primary human hematopoietic progenitor cell and humanized mouse models.

A Half Century Defining the Logic of Cellular Life

Over more than fifty years, I have studied how the logic that controls and integrates cell function is built into the dynamic architecture of living cells. I worked with a succession of exceptionally talented students and postdocs, and we discovered that the bacterial cell is controlled by an integrated genetic circuit in which transcriptional and translational controls are interwoven with the three-dimensional deployment of key regulatory and morphological proteins. Caulobacter's interconnected genetic regulatory network includes logic that regulates sets of genes expressed at specific times in the cell cycle and mechanisms that synchronize the advancement of the core cyclical circuit with chromosome replication and cytokinesis. Here, I have traced my journey from New York City art student to Stanford developmental biologist.

Costless metabolic secretions as drivers of interspecies interactions in microbial ecosystems

Metabolic exchange mediates interactions among microbes, helping explain diversity in microbial communities. As these interactions often involve a fitness cost, it is unclear how stable cooperation can emerge. Here we use genome-scale metabolic models to investigate whether the release of “costless” metabolites (i.e. those that cause no fitness cost to the producer), can be a prominent driver of intermicrobial interactions. By performing over 2 million pairwise growth simulations of 24 species in a combinatorial assortment of environments, we identify a large space of metabolites that can be secreted without cost, thus generating ample cross-feeding opportunities. In addition to providing an atlas of putative interactions, we show that anoxic conditions can promote mutualisms by providing more opportunities for exchange of costless metabolites, resulting in an overrepresentation of stable ecological network motifs. These results may help identify interaction patterns in natural communities and inform the design of synthetic microbial consortia.

In considering cross-feeding among microbes within communities, it is typically assumed that metabolic secretions are costly to produce. However, Pacheco et al. use metabolic models to show that ‘costless’ secretions could be common in some environments and important for structuring interactions among microbes.

TGF-β and IL-6 family signalling crosstalk: an integrated model

Mathematical models for TGF-β and IL-6 signalling have been linked, providing a platform for analyzing the crosstalk between the systems. An integrated IL-6:TGF-β model was developed via a reduced set of reaction equations which incorporate both feedback loops and appropriate time-delays for transcription and translation processes. The model simulates stable, robust and realistic responses to both ligands. Pulsatile (multiple pulses) inputs for both TGF-β and IL-6 have been simulated to investigate the effects of each ligand on the sensitivity, equilibrium and dynamic responses of the integrated signalling system. In our simulations the crosstalk between constant IL-6 and TGF-β signalling via SMAD7 does not appear to be sufficient to render the cells resistant to TGF-β inhibition. However, the simulations predict that pulsatile IL-6 stimulation would increase SMAD7 levels substantially and consequentially, lead to resistance to TGF-β. The model also allows the prediction of the integrated signalling pathway responses to the mutation of key components, e.g. Gp130 ^F/F.

On the role of topology in regulating transcriptional cascades

Topology of interactions in a transcriptional cascade determines the behavior of its signal-response profile and the activation states of genes.

Genetic circuit design automation

Computation can be performed in living cells by DNA-encoded circuits that process sensory information and control biological functions. Their construction is time-intensive, requiring manual part assembly and balancing of regulator expression. We describe a design environment, Cello, in which a user writes Verilog code that is automatically transformed into a DNA sequence. Algorithms build a circuit diagram, assign and connect gates, and simulate performance. Reliable circuit design requires the insulation of gates from genetic context, so that they function identically when used in different circuits. We used Cello to design 60 circuits forEscherichia coli(880,000 base pairs of DNA), for which each DNA sequence was built as predicted by the software with no additional tuning. Of these, 45 circuits performed correctly in every output state (up to 10 regulators and 55 parts), and across all circuits 92% of the output states functioned as predicted. Design automation simplifies the incorporation of genetic circuits into biotechnology projects that require decision-making, control, sensing, or spatial organization.

Parameter estimation methods for gene circuit modeling from time-series mRNA data: a comparative study

Parameter estimation is a challenging computational problem in the reverse engineering of biological systems. Because advances in biotechnology have facilitated wide availability of time-series gene expression data, systematic parameter estimation of gene circuit models from such time-series mRNA data has become an important method for quantitatively dissecting the regulation of gene expression. By focusing on the modeling of gene circuits, we examine here the performance of three types of state-of-the-art parameter estimation methods: population-based methods, online methods and model-decomposition-based methods. Our results show that certain population-based methods are able to generate high-quality parameter solutions. The performance of these methods, however, is heavily dependent on the size of the parameter search space, and their computational requirements substantially increase as the size of the search space increases. In comparison, online methods and model decomposition-based methods are computationally faster alternatives and are less dependent on the size of the search space. Among other things, our results show that a hybrid approach that augments computationally fast methods with local search as a subsequent refinement procedure can substantially increase the quality of their parameter estimates to the level on par with the best solution obtained from the population-based methods while maintaining high computational speed. These suggest that such hybrid methods can be a promising alternative to the more commonly used population-based methods for parameter estimation of gene circuit models when limited prior knowledge about the underlying regulatory mechanisms makes the size of the parameter search space vastly large.

Computing the functional proteome: recent progress and future prospects for genome-scale models

Constraint-based models enable the computation of feasible, optimal, and realized biological phenotypes from reaction network reconstructions and constraints on their operation. To date, stoichiometric reconstructions have largely focused on metabolism, resulting in genome-scale metabolic models (M-Models). Recent expansions in network content to encompass proteome synthesis have resulted in models of metabolism and protein expression (ME-Models). ME-Models advance the predictions possible with constraint-based models from network flux states to the spatially resolved molecular composition of a cell. Specifically, ME-Models enable the prediction of transcriptome and proteome allocation and limitations, and basal expression states and regulatory needs. Continued expansion in reconstruction content and constraints will result in an increasingly refined representation of cellular composition and behavior.

Evolution of communication protocols using an artificial regulatory network

I describe the Utrecht Machine (UM), a discrete artificial regulatory network designed for studying how evolution discovers biochemical computation mechanisms. The corresponding binary genome format is compatible with gene deletion, duplication, and recombination. In the simulation presented here, an agent consisting of two UMs, a sender and a receiver, must encode, transmit, and decode a binary word over time using the narrow communication channel between them. This communication problem has chicken-and-egg structure in that a sending mechanism is useless without a corresponding receiving mechanism. An in-depth case study reveals that a coincidence creates a minimal partial solution, from which a sequence of partial sending and receiving mechanisms evolve. Gene duplications contribute by enlarging the regulatory network. Analysis of 60,000 sample runs under a variety of parameter settings confirms that crossover accelerates evolution, that stronger selection tends to find clumsier solutions and finds them more slowly, and that there is implicit selection for robust mechanisms and genomes at the codon level. Typical solutions associate each input bit with an activation speed and combine them almost additively. The parents of breakthrough organisms sometimes have lower fitness scores than others in the population, indicating that populations can cross valleys in the fitness landscape via outlying members. The simulation exhibits back mutations and population-level memory effects not accounted for in traditional population genetics models. All together, these phenomena suggest that new evolutionary models are needed that incorporate regulatory network structure.

Coarse-grained analysis of stochastically simulated cell populations with a positive feedback genetic network architecture

Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and efficient study of their long-time behaviour over a wide range of parameter values, the performance of solely direct temporal simulations requires significantly high computational time. In addition, when the dynamics of the cell populations exhibit non-trivial bistable behaviour, such an analysis becomes a prohibitive task, since a large ensemble of initial states need to be tested for the quest of possibly co-existing steady state solutions. In this work, we study cell populations which carry the lac operon network exhibiting solution multiplicity over a wide range of extracellular conditions (inducer concentration). By adopting ideas from the so-called "equation-free" methodology, we perform systems-level analysis, which includes numerical tasks such as the computation of coarse steady state solutions, coarse bifurcation analysis, as well as coarse stability analysis. Dynamically stable and unstable macroscopic (population level) steady state solutions are computed by means of bifurcation analysis utilising short bursts of fine-scale simulations, and the range of bistability is determined for different sizes of cell populations. The results are compared with the deterministic cell population balance model, which is valid for large populations, and we demonstrate the increased effect of stochasticity in small size populations with asymmetric partitioning mechanisms.

Evolving kinetics of gene expression in stochastic environments

Recent studies have shown that the in vivo dynamics of RNA numbers in bacteria is regulated, to a great extent, by the kinetics of rate limiting steps in transcription. Strong evidence suggests that the kinetics of these steps is sequence dependent. We investigate the selective advantages of rate limiting steps of differing kinetics. For that, we model the kinetics of expression of a gene responsible for promoting cell division at the expense of resources in the environment in individual cells of a population. We model mutations that affect the kinetics of the rate limiting steps and selective pressure in various environmental conditions. Depletion of resources leads to cell death. We find that small changes in the evolutionary constraints can favor widely different noise levels in RNA and protein numbers. Increasing the cost in nutrients for division favors noisier expression. The results provide a better understanding of why different genes differ in the kinetics of production of RNA and proteins.

Evolution of biological interaction networks: from models to real data

We are beginning to uncover common mechanisms leading to the evolution of biological networks. The driving force behind these advances is the increasing availability of comparative data in several species.

Multiscale stochastic modelling of gene expression

Stochastic phenomena in gene regulatory networks can be modelled by the chemical master equation for gene products such as mRNA and proteins. If some of these elements are present in significantly higher amounts than the rest, or if some of the reactions between these elements are substantially faster than others, it is often possible to reduce the master equation to a simpler problem using asymptotic methods. We present examples of such a procedure and analyse the relationship between the reduced models and the original.

Deterministic and stochastic population-level simulations of an artificial lac operon genetic network

BACKGROUND

The lac operon genetic switch is considered as a paradigm of genetic regulation. This system has a positive feedback loop due to the LacY permease boosting its own production by the facilitated transport of inducer into the cell and the subsequent de-repression of the lac operon genes. Previously, we have investigated the effect of stochasticity in an artificial lac operon network at the single cell level by comparing corresponding deterministic and stochastic kinetic models.

RESULTS

This work focuses on the dynamics of cell populations by incorporating the above kinetic scheme into two Monte Carlo (MC) simulation frameworks. The first MC framework assumes stochastic reaction occurrence, accounts for stochastic DNA duplication, division and partitioning and tracks all daughter cells to obtain the statistics of the entire cell population. In order to better understand how stochastic effects shape cell population distributions, we develop a second framework that assumes deterministic reaction dynamics. By comparing the predictions of the two frameworks, we conclude that stochasticity can create or destroy bimodality, and may enhance phenotypic heterogeneity.

CONCLUSIONS

Our results show how various sources of stochasticity act in synergy with the positive feedback architecture, thereby shaping the behavior at the cell population level. Further, the insights obtained from the present study allow us to construct simpler and less computationally intensive models that can closely approximate the dynamics of heterogeneous cell populations.

Look before you leap: a confidence-based method for selecting species criticality while avoiding negative populations in τ-leaping

The stochastic simulation algorithm was introduced by Gillespie and in a different form by Kurtz. There have been many attempts at accelerating the algorithm without deviating from the behavior of the simulated system. The crux of the explicit τ-leaping procedure is the use of Poisson random variables to approximate the number of occurrences of each type of reaction event during a carefully selected time period, τ. This method is acceptable providing the leap condition, that no propensity function changes "significantly" during any time-step, is met. Using this method there is a possibility that species numbers can, artificially, become negative. Several recent papers have demonstrated methods that avoid this situation. One such method classifies, as critical, those reactions in danger of sending species populations negative. At most, one of these critical reactions is allowed to occur in the next time-step. We argue that the criticality of a reactant species and its dependent reaction channels should be related to the probability of the species number becoming negative. This way only reactions that, if fired, produce a high probability of driving a reactant population negative are labeled critical. The number of firings of more reaction channels can be approximated using Poisson random variables thus speeding up the simulation while maintaining the accuracy. In implementing this revised method of criticality selection we make use of the probability distribution from which the random variable describing the change in species number is drawn. We give several numerical examples to demonstrate the effectiveness of our new method.

The stochastic quasi-steady-state assumption: reducing the model but not the noise

Highly reactive species at small copy numbers play an important role in many biological reaction networks. We have described previously how these species can be removed from reaction networks using stochastic quasi-steady-state singular perturbation analysis (sQSPA). In this paper we apply sQSPA to three published biological models: the pap operon regulation, a biochemical oscillator, and an intracellular viral infection. These examples demonstrate three different potential benefits of sQSPA. First, rare state probabilities can be accurately estimated from simulation. Second, the method typically results in fewer and better scaled parameters that can be more readily estimated from experiments. Finally, the simulation time can be significantly reduced without sacrificing the accuracy of the solution.

Codon usage variability determines the correlation between proteome and transcriptome fold changes

Background

The availability of high throughput experimental methods has made possible to observe the relationships between proteome and transcirptome. The protein abundances show a positive but weak correlation with the concentrations of their cognate mRNAs. This weak correlation implies that there are other crucial effects involved in the regulation of protein translation, different from the sole availability of mRNA. It is well known that ribosome and tRNA concentrations are sources of variation in protein levels. Thus, by using integrated analysis of omics data, genomic information, transcriptome and proteome, we aim to unravel important variables affecting translation.

Results

We identified how much of the variability in the correlation between protein and mRNA concentrations can be attributed to the gene codon frequencies. We propose the hypothesis that the influence of codon frequency is due to the competition of cognate and near-cognate tRNA binding; which in turn is a function of the tRNA concentrations. Transcriptome and proteome data were combined in two analytical steps; first, we used Self-Organizing Maps (SOM) to identify similarities among genes, based on their codon frequencies, grouping them into different clusters; and second, we calculated the variance in the protein mRNA correlation in the sampled genes from each cluster. This procedure is justified within a mathematical framework.

Conclusions

With the proposed method we observed that in all the six studied cases most of the variability in the relation protein-transcript could be explained by the variation in codon composition.

Transcription by the numbers redux: experiments and calculations that surprise

The study of transcription has witnessed an explosion of quantitative effort both experimentally and theoretically. In this article we highlight some of the exciting recent experimental efforts in the study of transcription with an eye to the demands that such experiments put on theoretical models of transcription. From a modeling perspective, we focus on two broad classes of models: the so-called thermodynamic models that use statistical mechanics to reckon the level of gene expression as probabilities of promoter occupancy, and rate-equation treatments that focus on the temporal evolution of the activity of a given promoter and that make it possible to compute the distributions of messenger RNA and proteins. We consider several appealing case studies to illustrate how quantitative models have been used to dissect transcriptional regulation.

A mathematical and computational approach for integrating the major sources of cell population heterogeneity

Several approaches have been used in the past to model heterogeneity in bacterial cell populations, with each approach focusing on different source(s) of heterogeneity. However, a holistic approach that integrates all the major sources into a comprehensive framework applicable to cell populations is still lacking. In this work we present the mathematical formulation of a cell population master equation (CPME) that describes cell population dynamics and takes into account the major sources of heterogeneity, namely stochasticity in reaction, DNA-duplication, and division, as well as the random partitioning of species contents into the two daughter cells. The formulation also takes into account cell growth and respects the discrete nature of the molecular contents and cell numbers. We further develop a Monte Carlo algorithm for the simulation of the stochastic processes considered here. To benchmark our new framework, we first use it to quantify the effect of each source of heterogeneity on the intrinsic and the extrinsic phenotypic variability for the well-known two-promoter system used experimentally by Elowitz et al. (2002). We finally apply our framework to a more complicated system and demonstrate how the interplay between noisy gene expression and growth inhibition due to protein accumulation at the single cell level can result in complex behavior at the cell population level. The generality of our framework makes it suitable for studying a vast array of artificial and natural genetic networks. Using our Monte Carlo algorithm, cell population distributions can be predicted for the genetic architecture of interest, thereby quantifying the effect of stochasticity in intracellular reactions or the variability in the rate of physiological processes such as growth and division. Such in silico experiments can give insight into the behavior of cell populations and reveal the major sources contributing to cell population heterogeneity.

Set-base dynamical parameter estimation and model invalidation for biochemical reaction networks

BACKGROUND

Mathematical modeling and analysis have become, for the study of biological and cellular processes, an important complement to experimental research. However, the structural and quantitative knowledge available for such processes is frequently limited, and measurements are often subject to inherent and possibly large uncertainties. This results in competing model hypotheses, whose kinetic parameters may not be experimentally determinable. Discriminating among these alternatives and estimating their kinetic parameters is crucial to improve the understanding of the considered process, and to benefit from the analytical tools at hand.

RESULTS

In this work we present a set-based framework that allows to discriminate between competing model hypotheses and to provide guaranteed outer estimates on the model parameters that are consistent with the (possibly sparse and uncertain) experimental measurements. This is obtained by means of exact proofs of model invalidity that exploit the polynomial/rational structure of biochemical reaction networks, and by making use of an efficient strategy to balance solution accuracy and computational effort.

CONCLUSIONS

The practicability of our approach is illustrated with two case studies. The first study shows that our approach allows to conclusively rule out wrong model hypotheses. The second study focuses on parameter estimation, and shows that the proposed method allows to evaluate the global influence of measurement sparsity, uncertainty, and prior knowledge on the parameter estimates. This can help in designing further experiments leading to improved parameter estimates.

Robustness under functional constraint: the genetic network for temporal expression in Drosophila neurogenesis

Precise temporal coordination of gene expression is crucial for many developmental processes. One central question in developmental biology is how such coordinated expression patterns are robustly controlled. During embryonic development of the Drosophila central nervous system, neural stem cells called neuroblasts express a group of genes in a definite order, which leads to the diversity of cell types. We produced all possible regulatory networks of these genes and examined their expression dynamics numerically. From the analysis, we identified requisite regulations and predicted an unknown factor to reproduce known expression profiles caused by loss-of-function or overexpression of the genes in vivo, as well as in the wild type. Following this, we evaluated the stability of the actual Drosophila network for sequential expression. This network shows the highest robustness against parameter variations and gene expression fluctuations among the possible networks that reproduce the expression profiles. We propose a regulatory module composed of three types of regulations that is responsible for precise sequential expression. This study suggests that the Drosophila network for sequential expression has evolved to generate the robust temporal expression for neuronal specification.

Cell fate specification is of key importance in the development of multicellular organisms. To specify various cell fates correctly, genetic networks precisely coordinate spatial and temporal gene expression patterns during various developmental stages. One central question in developmental biology is to elucidate the relationship between the pattern formation and the network architecture. During embryonic development of the Drosophila central nervous system, the neural stem cells express a group of genes in a definite order, which is responsible for the diversity of neural cells. To elucidate the underlying mechanism of the process, we analyzed the structure and dynamics of the genetic network for the temporal changes occurring in the Drosophila neural stem cells. Searching all the possible regulatory networks of these genes using a computer program, we detected the requisite regulations that reproduce observed gene expression profiles. By comparing the stability of the dynamics among the functional networks, we uncovered the robust nature of the actual Drosophila network against environmental and intrinsic fluctuations. These results indicate that the genetic network for sequential expression has evolved to be robust under functional constraints. Our study proposes regulatory modules that are responsible for the precise sequential expressions, which might exist in genetic networks for other temporal patterning processes.

Numerical modelling of microRNA-mediated mRNA decay identifies novel mechanism of microRNA controlled mRNA downregulation

Post-transcriptional control of mRNA by micro-RNAs (miRNAs) represents an important mechanism of gene regulation. miRNAs act by binding to the 3' untranslated region (3'UTR) of an mRNA, affecting the stability and translation of the target mRNA. Here, we present a numerical model of miRNA-mediated mRNA downregulation and its application to analysis of temporal microarray data of HepG2 cells transfected with miRNA-124a. Using the model our analysis revealed a novel mechanism of mRNA accumulation control by miRNA, predicting that specific mRNAs are controlled in a digital, switch-like manner. Specifically, the contribution of miRNAs to mRNA degradation is switched from maximum to zero in a very short period of time. Such behaviour suggests a model of control in which mRNA is at a certain moment protected from binding of miRNA and further accumulates with a basal rate. Genes associated with this process were identified and parameters of the model for all miRNA-124a affected mRNAs were computed.

Genetic algorithms and their application to in silico evolution of genetic regulatory networks

A genetic algorithm (GA) is a procedure that mimics processes occurring in Darwinian evolution to solve computational problems. A GA introduces variation through "mutation" and "recombination" in a "population" of possible solutions to a problem, encoded as strings of characters in "genomes," and allows this population to evolve, using selection procedures that favor the gradual enrichment of the gene pool with the genomes of the "fitter" individuals. GAs are particularly suitable for optimization problems in which an effective system design or set of parameter values is sought.In nature, genetic regulatory networks (GRNs) form the basic control layer in the regulation of gene expression levels. GRNs are composed of regulatory interactions between genes and their gene products, and are, inter alia, at the basis of the development of single fertilized cells into fully grown organisms. This paper describes how GAs may be applied to find functional regulatory schemes and parameter values for models that capture the fundamental GRN characteristics. The central ideas behind evolutionary computation and GRN modeling, and the considerations in GA design and use are discussed, and illustrated with an extended example. In this example, a GRN-like controller is sought for a developmental system based on Lewis Wolpert's French flag model for positional specification, in which cells in a growing embryo secrete and detect morphogens to attain a specific spatial pattern of cellular differentiation.

Delayed stochastic model of transcription at the single nucleotide level

We present a delayed stochastic model of transcription at the single nucleotide level. The model accounts for the promoter open complex formation and includes alternative pathways to elongation, namely pausing, arrest, misincorporation and editing, pyrophosphorolysis, and premature termination. We confront the dynamics of this detailed model with a single-step multi-delayed stochastic model and with measurements of expression of a repressed gene at the single molecule level. At low expression rates both models match the experiments but, at higher rates the two models differ significantly, with consequences to cell-to-cell phenotypic variability. The alternative pathway reactions, due to, for example, causing polymerases to collide more often on the template, are the cause for the difference in dynamical behaviors. Next, we confront the model with measurements of the transcriptional dynamics at the single RNA level of an induced gene and show that RNA production, besides its bursting dynamics, also exhibits pulses (2 or more RNAs produced in intervals smaller than the smallest interval between initiations). The distribution of occurrences and amplitudes of pulses match the experimental measurements. This pulsing and the noise at the elongation stage are shown to play a role in the dynamics of a genetic switch.

Comparison of deterministic and stochastic models of the lac operon genetic network

The lac operon has been a paradigm for genetic regulation with positive feedback, and several modeling studies have described its dynamics at various levels of detail. However, it has not yet been analyzed how stochasticity can enrich the system's behavior, creating effects that are not observed in the deterministic case. To address this problem we use a comparative approach. We develop a reaction network for the dynamics of the lac operon genetic switch and derive corresponding deterministic and stochastic models that incorporate biological details. We then analyze the effects of key biomolecular mechanisms, such as promoter strength and binding affinities, on the behavior of the models. No assumptions or approximations are made when building the models other than those utilized in the reaction network. Thus, we are able to carry out a meaningful comparison between the predictions of the two models to demonstrate genuine effects of stochasticity. Such a comparison reveals that in the presence of stochasticity, certain biomolecular mechanisms can profoundly influence the region where the system exhibits bistability, a key characteristic of the lac operon dynamics. For these cases, the temporal asymptotic behavior of the deterministic model remains unchanged, indicating a role of stochasticity in modulating the behavior of the system.

Regulation by transcription factors in bacteria: beyond description

Transcription is an essential step in gene expression and its understanding has been one of the major interests in molecular and cellular biology. By precisely tuning gene expression, transcriptional regulation determines the molecular machinery for developmental plasticity, homeostasis and adaptation. In this review, we transmit the main ideas or concepts behind regulation by transcription factors and give just enough examples to sustain these main ideas, thus avoiding a classical ennumeration of facts. We review recent concepts and developments: cis elements and trans regulatory factors, chromosome organization and structure, transcriptional regulatory networks (TRNs) and transcriptomics. We also summarize new important discoveries that will probably affect the direction of research in gene regulation: epigenetics and stochasticity in transcriptional regulation, synthetic circuits and plasticity and evolution of TRNs. Many of the new discoveries in gene regulation are not extensively tested with wetlab approaches. Consequently, we review this broad area in Inference of TRNs and Dynamical Models of TRNs. Finally, we have stepped backwards to trace the origins of these modern concepts, synthesizing their history in a timeline schema.

Evolving synaptic plasticity with an evolutionary cellular development model

Since synaptic plasticity is regarded as a potential mechanism for memory formation and learning, there is growing interest in the study of its underlying mechanisms. Recently several evolutionary models of cellular development have been presented, but none have been shown to be able to evolve a range of biological synaptic plasticity regimes. In this paper we present a biologically plausible evolutionary cellular development model and test its ability to evolve different biological synaptic plasticity regimes. The core of the model is a genomic and proteomic regulation network which controls cells and their neurites in a 2D environment. The model has previously been shown to successfully evolve behaving organisms, enable gene related phenomena, and produce biological neural mechanisms such as temporal representations. Several experiments are described in which the model evolves different synaptic plasticity regimes using a direct fitness function. Other experiments examine the ability of the model to evolve simple plasticity regimes in a task -based fitness function environment. These results suggest that such evolutionary cellular development models have the potential to be used as a research tool for investigating the evolutionary aspects of synaptic plasticity and at the same time can serve as the basis for novel artificial computational systems.

Cooperativity, sensitivity, and noise in biochemical signaling

Cooperative interactions in the binding of multiple signaling molecules is a common mechanism for enhancing the sensitivity of biological signaling systems. It is widely assumed this increase in sensitivity of the mean response implies the ability to detect smaller signals. Extending the classic work of Berg and Purcell [Biophys. J. 20, 193 (1977)] on the physical limits of chemoreception, we show that the random arrival of diffusing signaling molecules at receptor sites constitutes a noise source that is not reduced by cooperativity. Cooperativity makes reaching this limit easier, but cannot reduce the limit itself.

Positive feedback in cellular control systems

Feedback loops have been identified in a variety of regulatory systems and organisms. While feedback loops of the same type (negative or positive) tend to have properties in common, they can play distinctively diverse roles in different regulatory systems, where they can affect virulence in a pathogenic bacterium, maturation patterns of vertebrate oocytes and transitions through cell cycle phases in eukaryotic cells. This review focuses on the properties and functions of positive feedback in biological systems, including bistability, hysteresis and activation surges.

Inevitable evolutionary temporal elements in neural processing: a study based on evolutionary simulations

Recent studies have suggested that some neural computational mechanisms are based on the fine temporal structure of spiking activity. However, less effort has been devoted to investigating the evolutionary aspects of such mechanisms. In this paper we explore the issue of temporal neural computation from an evolutionary point of view, using a genetic simulation of the evolutionary development of neural systems. We evolve neural systems in an environment with selective pressure based on mate finding, and examine the temporal aspects of the evolved systems. In repeating evolutionary sessions, there was a significant increase during evolution in the mutual information between the evolved agent's temporal neural representation and the external environment. In ten different simulated evolutionary sessions, there was an increased effect of time -related neural ablations on the agents' fitness. These results suggest that in some fitness landscapes the emergence of temporal elements in neural computation is almost inevitable. Future research using similar evolutionary simulations may shed new light on various biological mechanisms.

Mathematical modeling and synthetic biology

Synthetic biology is an engineering discipline that builds on our mechanistic understanding of molecular biology to program microbes to carry out new functions. Such predictable manipulation of a cell requires modeling and experimental techniques to work together. The modeling component of synthetic biology allows one to design biological circuits and analyze its expected behavior. The experimental component merges models with real systems by providing quantitative data and sets of available biological 'parts' that can be used to construct circuits. Sufficient progress has been made in the combined use of modeling and experimental methods, which reinforces the idea of being able to use engineered microbes as a technological platform.

Coordination logic of the sensing machinery in the transcriptional regulatory network of Escherichia coli

The active and inactive state of transcription factors in growing cells is usually directed by allosteric physicochemical signals or metabolites, which are in turn either produced in the cell or obtained from the environment by the activity of the products of effector genes. To understand the regulatory dynamics and to improve our knowledge about how transcription factors (TFs) respond to endogenous and exogenous signals in the bacterial model, Escherichia coli, we previously proposed to classify TFs into external, internal and hybrid sensing classes depending on the source of their allosteric or equivalent metabolite. Here we analyze how a cell uses its topological structures in the context of sensing machinery and show that, while feed forward loops (FFLs) tightly integrate internal and external sensing TFs connecting TFs from different layers of the hierarchical transcriptional regulatory network (TRN), bifan motifs frequently connect TFs belonging to the same sensing class and could act as a bridge between TFs originating from the same level in the hierarchy. We observe that modules identified in the regulatory network of E. coli are heterogeneous in sensing context with a clear combination of internal and external sensing categories depending on the physiological role played by the module. We also note that propensity of two-component response regulators increases at promoters, as the number of TFs regulating a target operon increases. Finally we show that evolutionary families of TFs do not show a tendency to preserve their sensing abilities. Our results provide a detailed panorama of the topological structures of E. coli TRN and the way TFs they compose off, sense their surroundings by coordinating responses.

Investigation of metabolic objectives in cultured hepatocytes

Using optimization based methods to predict fluxes in metabolic flux balance models has been a successful approach for some microorganisms, enabling construction of in silico models and even inference of some regulatory motifs. However, this success has not been translated to mammalian cells. The lack of knowledge about metabolic objectives in mammalian cells is a major obstacle that prevents utilization of various metabolic engineering tools and methods for tissue engineering and biomedical purposes. In this work, we investigate and identify possible metabolic objectives for hepatocytes cultured in vitro. To achieve this goal, we present a special data-mining procedure for identifying metabolic objective functions in mammalian cells. This multi-level optimization based algorithm enables identifying the major fluxes in the metabolic objective from MFA data in the absence of information about critical active constraints of the system. Further, once the objective is determined, active flux constraints can also be identified and analyzed. This information can be potentially used in a predictive manner to improve cell culture results or clinical metabolic outcomes. As a result of the application of this method, it was found that in vitro cultured hepatocytes maximize oxygen uptake, coupling of urea and TCA cycles, and synthesis of serine and urea. Selection of these fluxes as the metabolic objective enables accurate prediction of the flux distribution in the system given a limited amount of flux data; thus presenting a workable in silico model for cultured hepatocytes. It is observed that an overall homeostasis picture is also emergent in the findings.

Putative cold acclimation pathways in Arabidopsis thaliana identified by a combined analysis of mRNA co-expression patterns, promoter motifs and transcription factors

Background

With the advent of microarray technology, it has become feasible to identify virtually all genes in an organism that are induced by developmental or environmental changes. However, relying solely on gene expression data may be of limited value if the aim is to infer the underlying genetic networks. Development of computational methods to combine microarray data with other information sources is therefore necessary. Here we describe one such method.

Results

By means of our method, previously published Arabidopsis microarray data from cold acclimated plants at six different time points, promoter motif sequence data extracted from ~24,000 Arabidopsis promoters and known transcription factor binding sites were combined to construct a putative genetic regulatory interaction network. The inferred network includes both previously characterised and hitherto un-described regulatory interactions between transcription factor (TF) genes and genes that encode other TFs or other proteins. Part of the obtained transcription factor regulatory network is presented here. More detailed information is available in the additional files.

Conclusion

The rule-based method described here can be used to infer genetic networks by combining data from microarrays, promoter sequences and known promoter binding sites. This method should in principle be applicable to any biological system. We tested the method on the cold acclimation process in Arabidopsis and could identify a more complex putative genetic regulatory network than previously described. However, it should be noted that information on specific binding sites for individual TFs were in most cases not available. Thus, gene targets for the entire TF gene families were predicted. In addition, the networks were built solely by a bioinformatics approach and experimental verifications will be necessary for their final validation. On the other hand, since our method highlights putative novel interactions, more directed experiments could now be performed.

PARE: a tool for comparing protein abundance and mRNA expression data

BACKGROUND

Techniques for measuring protein abundance are rapidly advancing and we are now in a situation where we anticipate many protein abundance data sets will be available in the near future. Since proteins are translated from mRNAs, their expression is expected to be related to their abundance, to some degree.

RESULTS

We have developed a web tool, called PARE (Protein Abundance and mRNA Expression; http://proteomics.gersteinlab.org), to correlate these two quantities. In addition to globally comparing the quantities of protein and mRNA, PARE allows users to select subsets of proteins for focused study (based on functional categories and complexes). Furthermore, it highlights correlation outliers, which are potentially worth further examination.

CONCLUSION

We anticipate PARE will facilitate comparative studies on mRNA and protein abundance by the proteomics community.

Indeterminacy of reverse engineering of Gene Regulatory Networks: the curse of gene elasticity

BACKGROUND

Gene Regulatory Networks (GRNs) have become a major focus of interest in recent years. A number of reverse engineering approaches have been developed to help uncover the regulatory networks giving rise to the observed gene expression profiles. However, this is an overspecified problem due to the fact that more than one genotype (network wiring) can give rise to the same phenotype. We refer to this phenomenon as "gene elasticity." In this work, we study the effect of this particular problem on the pure, data-driven inference of gene regulatory networks.

METHODOLOGY

We simulated a four-gene network in order to produce "data" (protein levels) that we use in lieu of real experimental data. We then optimized the network connections between the four genes with a view to obtain the original network that gave rise to the data. We did this for two different cases: one in which only the network connections were optimized and the other in which both the network connections as well as the kinetic parameters (given as reaction probabilities in our case) were estimated. We observed that multiple genotypes gave rise to very similar protein levels. Statistical experimentation indicates that it is impossible to differentiate between the different networks on the basis of both equilibrium as well as dynamic data.

CONCLUSIONS

We show explicitly that reverse engineering of GRNs from pure expression data is an indeterminate problem. Our results suggest the unsuitability of an inferential, purely data-driven approach for the reverse engineering transcriptional networks in the case of gene regulatory networks displaying a certain level of complexity.

Examining emergence of functional gene clustering in a simulated evolution

Recent research suggests that rather than being random, gene order may be coupled with gene functionality. These findings may be explained by mechanisms that require physical proximity such as co-expression and co-regulation. Alternatively, they may be due to evolutionary-dynamics forces, as expressed in genetic drift or linkage disequilibrium. This paper proposes a biologically plausible model for evolutionary development. Using the model, which includes natural selection and the development of gene networks and cellular organisms, the co-evolution of recombination rate and gene functionality is examined. The results presented here are compatible with previous biological findings showing that functionally related genes are clustered. These results imply that evolutionary pressure in a complex environment is sufficient for the emergence of gene order that is coupled with functionality. They shed further light on the mechanisms that may cause such gene clusters.

Studying genetic regulatory networks at the molecular level: Delayed reaction stochastic models

Current advances in molecular biology enable us to access the rapidly increasing body of genetic information. It is still challenging to model gene systems at the molecular level. Here, we propose two types of reaction kinetic models for constructing genetic networks. Time delays involved in transcription and translation are explicitly considered to explore the effects of delays, which may be significant in genetic networks featured with feedback loops. One type of model is based on delayed effective reactions, each reaction modeling a biochemical process like transcription without involving intermediate reactions. The other is based on delayed virtual reactions, each reaction being converted from a mathematical function to model a biochemical function like gene inhibition. The latter stochastic models are derived from the corresponding mean-field models. The former ones are composed of single gene expression modules. We thus design a model of gene expression. This model is verified by our simulations using a delayed stochastic simulation algorithm, which accurately reproduces the stochastic kinetics in a recent experimental study. Various simplified versions of the model are given and evaluated. We then use the two methods to study the genetic toggle switch and the repressilator. We define the "on" and "off" states of genes and extract a binary code from the stochastic time series. The binary code can be described by the corresponding Boolean network models in certain conditions. We discuss these conditions, suggesting a method to connect Boolean models, mean-field models, and stochastic chemical models.