Coherent activation of a synthetic mammalian gene network

A quantitative analysis of naturally-occurring regulatory networks, especially those present in mammalian cells, is difficult due to their high complexity. Much simpler gene networks can be engineered in model organisms and analyzed as isolated regulatory modules. Recently, several synthetic networks have been constructed in mammalian systems. However, most of these engineered mammalian networks have been characterized using steady-state population level measurements. Here, we use an integrated experimental-computational approach to analyze the dynamical response of a synthetic positive feedback network in individual mammalian cells. We observe a switch-like activation of the network with variable delay times in individual cells. In agreement with a stochastic model of the network, we find that increasing the strength of the positive feedback results in a decrease in the mean delay time and a more coherent activation of individual cells. Our results are important for gaining insight into biological processes which rely on positive feedback regulation.     

Identification of genetic networks

In this report, we propose the use of structural equations as a tool for identifying and modeling genetic networks and genetic algorithms for searching the most likely genetic networks that best fit the data. After genetic networks are identified, it is fundamental to identify those networks influencing cell phenotypes. To accomplish this task we extend the concept of differential expression of the genes, widely used in gene expression data analysis, to genetic networks. We propose a definition for the differential expression of a genetic network and use the generalized T2 statistic to measure the ability of genetic networks to distinguish different phenotypes. However, describing the differential expression of genetic networks is not enough for understanding biological systems because differences in the expression of genetic networks do not directly reflect regulatory strength between gene activities. Therefore, in this report we also introduce the concept of differentially regulated genetic networks, which has the potential to assess changes of gene regulation in response to perturbation in the environment and may provide new insights into the mechanism of diseases and biological processes. We propose five novel statistics to measure the differences in regulation of genetic networks. To illustrate the concepts and methods for reconstruction of genetic networks and identification of association of genetic networks with function, we applied the proposed models and algorithms to three data sets.     

Transient dynamics of reduced-order models of genetic regulatory networks

In systems biology, a number of detailed genetic regulatory networks models have been proposed that are capable of modeling the fine-scale dynamics of gene expression. However, limitations on the type and sampling frequency of experimental data often prevent the parameter estimation of the detailed models. Furthermore, the high computational complexity involved in the simulation of a detailed model restricts its use. In such a scenario, reduced-order models capturing the coarse-scale behavior of the network are frequently applied. In this paper, we analyze the dynamics of a reduced-order Markov Chain model approximating a detailed Stochastic Master Equation model. Utilizing a reduction mapping that maintains the aggregated steady-state probability distribution of stochastic master equation models, we provide bounds on the deviation of the Markov Chain transient distribution from the transient aggregated distributions of the stochastic master equation model.     

Stochastic Modeling of Gene Regulation by Noncoding Small RNAs in the Strong Interaction Limit

Noncoding small RNAs (sRNAs) are known to play a key role in regulating diverse cellular processes, and their dysregulation is linked to various diseases such as cancer. Such diseases are also marked by phenotypic heterogeneity, which is often driven by the intrinsic stochasticity of gene expression. Correspondingly, there is significant interest in developing quantitative models focusing on the interplay between stochastic gene expression and regulation by sRNAs. We consider the canonical model of regulation of stochastic gene expression by sRNAs, wherein interaction between constitutively expressed sRNAs and mRNAs leads to stoichiometric mutual degradation. The exact solution of this model is analytically intractable given the nonlinear interaction term between sRNAs and mRNAs, and theoretical approaches typically invoke the mean-field approximation. However, mean-field results are inaccurate in the limit of strong interactions and low abundances; thus, alternative theoretical approaches are needed. In this work, we obtain analytical results for the canonical model of regulation of stochastic gene expression by sRNAs in the strong interaction limit. We derive analytical results for the steady-state generating function of the joint distribution of mRNAs and sRNAs in the limit of strong interactions and use the results derived to obtain analytical expressions characterizing the corresponding protein steady-state distribution. The results obtained can serve as building blocks for the analysis of genetic circuits involving sRNAs and provide new insights into the role of sRNAs in regulating stochastic gene expression in the limit of strong interactions.     

Noise-Driven Causal Inference in Biomolecular Networks

Single-cell RNA and protein concentrations dynamically fluctuate because of stochastic ("noisy") regulation. Consequently, biological signaling and genetic networks not only translate stimuli with functional response but also random fluctuations. Intuitively, this feature manifests as the accumulation of fluctuations from the network source to the target. Taking advantage of the fact that noise propagates directionally, we developed a method for causation prediction that does not require time-lagged observations and therefore can be applied to data generated by destructive assays such as immunohistochemistry. Our method for causation prediction, "Inference of Network Directionality Using Covariance Elements (INDUCE)," exploits the theoretical relationship between a change in the strength of a causal interaction and the associated changes in the single cell measured entries of the covariance matrix of protein concentrations. We validated our method for causation prediction in two experimental systems where causation is well established: in an E. coli synthetic gene network, and in MEK to ERK signaling in mammalian cells. We report the first analysis of covariance elements documenting noise propagation from a kinase to a phosphorylated substrate in an endogenous mammalian signaling network.     

Stochastic modeling of gene positive autoregulation networks involving signal molecules

Positive autoregulation in gene regulation networks has been shown in the past to exhibit stochastic behavior, including stochastic bistability, in which an initially uniform cell population develops into two distinct subpopulations. However, positive autoregulation is often mediated by signal molecules, which have not been considered in prior stochastic analysis of these networks. Here we propose both a full model of such a network that includes a signal molecule, and a simplified model in which the signal molecules have been eliminated through the use of two simplifications. The simplified model is amenable to direct mathematical analysis that shows that stochastic bistability is possible. We use stochastic Petri networks for simulating both types of models. The simulation results show that 1), the stochastic behavior of the two models is similar; and 2), that the analytical steady-state distribution of the simplified model matches well the transient results at times equal to that of a cell generation. A discussion of the simplifications we used in the context of the results indicates the importance of the signal molecule number as a factor determining the presence of bistability. This is further supported from a deterministic steady-state analysis of the full model that is shown to be a useful indicator of potential stochastic bistability. We use the regulation of SdiA in Escherichia coli as an example, due to the importance of this protein and of the signal molecule, a bacterial autoinducer, that is involved. However, the use of kinetic parameter values representing typical cellular activities make the conclusions applicable to other signal-mediated positive autoregulation networks as well.     

Modeling stochastic noise in gene regulatory systems

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

Stochastic S-system modeling of gene regulatory network

Microarray gene expression data can provide insights into biological processes at a system-wide level and is commonly used for reverse engineering gene regulatory networks (GRN). Due to the amalgamation of noise from different sources, microarray expression profiles become inherently noisy leading to significant impact on the GRN reconstruction process. Microarray replicates (both biological and technical), generated to increase the reliability of data obtained under noisy conditions, have limited influence in enhancing the accuracy of reconstruction . Therefore, instead of the conventional GRN modeling approaches which are deterministic, stochastic techniques are becoming increasingly necessary for inferring GRN from noisy microarray data. In this paper, we propose a new stochastic GRN model by investigating incorporation of various standard noise measurements in the deterministic S-system model. Experimental evaluations performed for varying sizes of synthetic network, representing different stochastic processes, demonstrate the effect of noise on the accuracy of genetic network modeling and the significance of stochastic modeling for GRN reconstruction . The proposed stochastic model is subsequently applied to infer the regulations among genes in two real life networks: (1) the well-studied IRMA network, a real-life in-vivo synthetic network constructed within the Saccharomycescerevisiae yeast, and (2) the SOS DNA repair network in Escherichiacoli.     

A Genetic Strategy for Stochastic Gene Activation with Regulated Sparseness (STARS)

It remains a challenge to establish a straightforward genetic approach for controlling the probability of gene activation or knockout at a desired level. Here, we developed a method termed STARS: stochastic gene activation with genetically regulated sparseness. The stochastic expression was achieved by two cross-linked, mutually-exclusive Cre-mediated recombinations. The stochastic level was further controlled by regulating Cre/lox reaction kinetics through varying the intrachromosomal distance between the lox sites mediating one of the recombinations. In mammalian cell lines stably transfected with a single copy of different STARS transgenes, the activation/knockout of reporter genes was specifically controlled to occur in from 5% to 50% of the cell population. STARS can potentially provide a convenient way for genetic labeling as well as gene expression/knockout in a population of cells with a desired sparseness level.     

Programs of Gene Expression During the Laying Down of Memory Formation as Revealed by DNA Microarrays

Many experiments in the past have demonstrated the requirement of de novo gene expression during memory formation. In contrast to the initial reductionistic view that genes relevant to learning and memory would be easily found and would provide a simple key to understand this brain function, it is becoming apparent that the genetic contribution to memory is complex. Previous approaches have been focused on individual genes or genetic pathways and failed to address the massively parallel nature of genome activities and collective behavior of the genes that ultimately control the molecular mechanisms underlying brain function. In view of the broad variety of genes and the cross talk of genetic pathways involved in this regulation, only gene expression profiles may reflect the complete behavior of regulatory pathways. In this review we illustrate how DNA microarray-based gene expression profiling may help to dissect and analyze the complex mechanisms involved in gene regulation during the acquisition and storage of memory in the mammalian brain.     

The Structure of a Gene Co-Expression Network Reveals Biological Functions Underlying eQTLs

What are the commonalities between genes, whose expression level is partially controlled by eQTL, especially with regard to biological functions? Moreover, how are these genes related to a phenotype of interest? These issues are particularly difficult to address when the genome annotation is incomplete, as is the case for mammalian species. Moreover, the direct link between gene expression and a phenotype of interest may be weak, and thus difficult to handle. In this framework, the use of a co-expression network has proven useful: it is a robust approach for modeling a complex system of genetic regulations, and to infer knowledge for yet unknown genes. In this article, a case study was conducted with a mammalian species. It showed that the use of a co-expression network based on partial correlation, combined with a relevant clustering of nodes, leads to an enrichment of biological functions of around 83%. Moreover, the use of a spatial statistics approach allowed us to superimpose additional information related to a phenotype; this lead to highlighting specific genes or gene clusters that are related to the network structure and the phenotype. Three main results are worth noting: first, key genes were highlighted as a potential focus for forthcoming biological experiments; second, a set of biological functions, which support a list of genes under partial eQTL control, was set up by an overview of the global structure of the gene expression network; third, pH was found correlated with gene clusters, and then with related biological functions, as a result of a spatial analysis of the network topology.     

Optimization of a stochastically simulated gene network model via simulated annealing

By rearranging naturally occurring genetic components, gene networks can be created that display novel functions. When designing these networks, the kinetic parameters describing DNA/protein binding are of great importance, as these parameters strongly influence the behavior of the resulting gene network. This article presents an optimization method based on simulated annealing to locate combinations of kinetic parameters that produce a desired behavior in a genetic network. Since gene expression is an inherently stochastic process, the simulation component of simulated annealing optimization is conducted using an accurate multiscale simulation algorithm to calculate an ensemble of network trajectories at each iteration of the simulated annealing algorithm. Using the three-gene repressilator of Elowitz and Leibler as an example, we show that gene network optimizations can be conducted using a mechanistically realistic model integrated stochastically. The repressilator is optimized to give oscillations of an arbitrary specified period. These optimized designs may then provide a starting-point for the selection of genetic components needed to realize an in vivo system.     

Roles of microRNAs in mammalian reproduction: from the commitment of germ cells to peri‐implantation embryos

MicroRNAs (miRNAs) are active regulators of numerous biological and physiological processes including most of the events of mammalian reproduction. Understanding the biological functions of miRNAs in the context of mammalian reproduction will allow a better and comparative understanding of fertility and sterility in male and female mammals. Herein, we summarize recent progress in miRNA‐mediated regulation of mammalian reproduction and highlight the significance of miRNAs in different aspects of mammalian reproduction including the biogenesis of germ cells, the functionality of reproductive organs, and the development of early embryos. Furthermore, we focus on the gene expression regulatory feedback loops involving hormones and miRNA expression to increase our understanding of germ cell commitment and the functioning of reproductive organs. Finally, we discuss the influence of miRNAs on male and female reproductive failure, and provide perspectives for future studies on this topic.     

Integration of Steady-State and Temporal Gene Expression Data for the Inference of Gene Regulatory Networks

We develop a new regression algorithm, cMIKANA, for inference of gene regulatory networks from combinations of steady-state and time-series gene expression data. Using simulated gene expression datasets to assess the accuracy of reconstructing gene regulatory networks, we show that steady-state and time-series data sets can successfully be combined to identify gene regulatory interactions using the new algorithm. Inferring gene networks from combined data sets was found to be advantageous when using noisy measurements collected with either lower sampling rates or a limited number of experimental replicates. We illustrate our method by applying it to a microarray gene expression dataset from human umbilical vein endothelial cells (HUVECs) which combines time series data from treatment with growth factor TNF and steady state data from siRNA knockdown treatments. Our results suggest that the combination of steady-state and time-series datasets may provide better prediction of RNA-to-RNA interactions, and may also reveal biological features that cannot be identified from dynamic or steady state information alone. Finally, we consider the experimental design of genomics experiments for gene regulatory network inference and show that network inference can be improved by incorporating steady-state measurements with time-series data.     

Digital signal processing reveals circadian baseline oscillation in majority of mammalian genes

In mammals, circadian periodicity has been described for gene expression in the hypothalamus and multiple peripheral tissues. It is accepted that 10%–15% of all genes oscillate in a daily rhythm, regulated by an intrinsic molecular clock. Statistical analyses of periodicity are limited by the small size of datasets and high levels of stochastic noise. Here, we propose a new approach applying digital signal processing algorithms separately to each group of genes oscillating in the same phase. Combined with the statistical tests for periodicity, this method identifies circadian baseline oscillation in almost 100% of all expressed genes. Consequently, circadian oscillation in gene expression should be evaluated in any study related to biological pathways. Changes in gene expression caused by mutations or regulation of environmental factors (such as photic stimuli or feeding) should be considered in the context of changes in the amplitude and phase of genetic oscillations.     

Gene regulatory network modeling via global optimization of high-order dynamic Bayesian network

ABSTRACT: BACKGROUND: Dynamic Bayesian network (DBN) is among the mainstream approaches for modeling various biological networks, including the gene regulatory network (GRN). Most current methods for learning DBN employ either local search such as hill-climbing, or a meta stochastic global optimization framework such as genetic algorithm or simulated annealing, which are only able to locate sub-optimal solutions. Further, current DBN applications have essentially been limited to small sized networks. RESULTS: To overcome the above difficulties, we introduce here a deterministic global optimization based DBN approach for reverse engineering genetic networks from time course gene expression data. For such DBN models that consist only of inter time slice arcs, we show that there exists a polynomial time algorithm for learning the globally optimal network structure. The proposed approach, named GlobalMIT+, employs the recently proposed information theoretic scoring metric named mutual information test (MIT). GlobalMIT+ is able to learn high-order time delayed genetic interactions, which are common to most biological systems. Evaluation of the approach using both synthetic and real data sets, including a 733 cyanobacterial gene expression data set, shows significantly improved performance over other techniques. CONCLUSIONS: Our studies demonstrate that deterministic global optimization approaches can infer large scale genetic networks.     

Heat shock response in CHO mammalian cells is controlled by a nonlinear stochastic process

In many biological systems, the interactions that describe the coupling between different units in a genetic network are nonlinear and stochastic. We study the interplay between stochasticity and nonlinearity using the responses of Chinese hamster ovary (CHO) mammalian cells to different temperature shocks. The experimental data show that the mean value response of a cell population can be described by a mathematical expression (empirical law) which is valid for a large range of heat shock conditions. A nonlinear stochastic theoretical model was developed that explains the empirical law for the mean response. Moreover, the theoretical model predicts a specific biological probability distribution of responses for a cell population. The prediction was experimentally confirmed by measurements at the single-cell level. The computational approach can be used to study other nonlinear stochastic biological phenomena.