Stochastic modeling for the expression of a gene regulated by competing transcription factors

It is widely accepted that gene expression regulation is a stochastic event. The common approach for its computer simulation requires detailed information on the interactions of individual molecules, which is often not available for the analyses of biological experiments. As an alternative approach, we employed a more intuitive model to simulate the experimental result, the Markov-chain model, in which a gene is regulated by activators and repressors, which bind the same site in a mutually exclusive manner. Our stochastic simulation in the presence of both activators and repressors predicted a Hill-coefficient of the dose-response curve closer to the experimentally observed value than the calculated value based on the simple additive effects of activators alone and repressors alone. The simulation also reproduced the heterogeneity of gene expression levels among individual cells observed by Fluorescence Activated Cell Sorting analysis. Therefore, our approach may help to apply stochastic simulations to broader experimental data.     

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.     

Stochastic gene expression in fluctuating environments

Stochastic mechanisms can cause a group of isogenic bacteria, each subject to identical environmental conditions, to nevertheless exhibit diverse patterns of gene expression. The resulting phenotypic subpopulations will typically have distinct growth rates. This behavior has been observed in several contexts, including sugar metabolism and pili phase variation. Under fixed environmental conditions, the net growth rate of the population is maximized when all cells are of the fastest growing phenotype, so it is unclear what fitness advantage is conferred by population heterogeneity. However, unlike ideal laboratory conditions, natural environments tend to fluctuate, either periodically or randomly. Here we use a stochastic population model to show that, during growth in such fluctuating environments, a dynamically heterogenous bacterial population can sometimes achieve a higher net growth rate than a homogenous one. By using stochastic mechanisms to sample several distinct phenotypes, the bacteria are able to anticipate and take advantage of sudden changes in their environment. However, this heterogeneity is beneficial only if the bacterial response rate is sufficiently low. Our results could be useful in the design of artificial evolution experiments and in the optimization of fermentation processes.     

Stochastic gene expression in switching environments

Organisms are known to adapt to regularly varying environments. However, in most cases, the fluctuations of the environment are irregular and stochastic, alternating between favorable and unfavorable regimes, so that cells must cope with an uncertain future. A possible response is population diversification. We assume here that the cell population is divided into two groups, corresponding to two phenotypes, having distinct growth rates, and that cells can switch randomly their phenotypes. In static environments, the net growth rate is maximized when the population is homogeneously composed of cells having the largest growth rate. In random environments, growth rates fluctuate and observations reveal that sometimes heterogeneous populations have a larger net growth rate than homogeneous ones, a fact illustrated recently through Monte-Carlo simulations based on a birth and migration process in a random environment. We study this process mathematically by focusing on the proportion f(t) of cells having the largest growth rate at time t, and give explicitly the related steady state distribution π. We also prove the convergence of empirical averages along trajectories to the first moment , and provide efficient numerical methods for computing .      

Stochastic modeling of T cell receptor gamma gene rearrangement

The mechanisms controlling the recombination process of the gamma genes that encode the gamma chain of the antigen receptor of the gammadelta T lymphocytes are unclear. Based on experimental data on the recombination status of the two major TCR gamma genes expressed in V(gamma)4+ and V(gamma)1+ thymocytes, we tested the plausibility of three possible rearrangement mechanisms: (1) a time window mechanism according to which the two chromosomes are accessible to the recombination machinery during a defined period of time; (2) a feedback mechanism in which recombination stops shortly after the first in-frame rearrangement event anywhere in both chromosomes; and (3) a feedback mechanism with asynchronous chromosome accessibility, in which there is a first period when only one chromosome is accessible for recombination, followed by a second period when both chromosomes are accessible; shortly after the first in-frame rearrangement event, during any of these two periods, recombination will definitely stop. We model the time window mechanism using a pure probabilistic approach and the two feedback mechanisms using a continuous-time Markov chain formalism. We used maximum likelihood methodology to infer the goodness-of-fit of the models showing evidence for the last model, which best fits the data. Further analysis of this model suggests an evolutionary tradeoff between allelic and isotypic exclusion and the probability that a precursor differentiates into a mature gammadelta T lymphocyte.     

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.     

Stochastic gene expression stabilization as a new therapeutic strategy for cancer

Current differentiation therapies for cancer may not be effective because it might not be enough to only use molecules targeting chromatin remodelers. It may also be necessary to stabilize the re-expressed genes to convert malignant cells into benign ones.     

Stochastic models for inferring genetic regulation from microarray gene expression data

Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information.     

Bayesian modeling of differential gene expression

We present a Bayesian hierarchical model for detecting differentially expressing genes that includes simultaneous estimation of array effects, and show how to use the output for choosing lists of genes for further investigation. We give empirical evidence that expression-level dependent array effects are needed, and explore different nonlinear functions as part of our model-based approach to normalization. The model includes gene-specific variances but imposes some necessary shrinkage through a hierarchical structure. Model criticism via posterior predictive checks is discussed. Modeling the array effects (normalization) simultaneously with differential expression gives fewer false positive results. To choose a list of genes, we propose to combine various criteria (for instance, fold change and overall expression) into a single indicator variable for each gene. The posterior distribution of these variables is used to pick the list of genes, thereby taking into account uncertainty in parameter estimates. In an application to mouse knockout data, Gene Ontology annotations over- and underrepresented among the genes on the chosen list are consistent with biological expectations.     

Stochastic gene expression: bacterial elites in chemotaxis

Even in the absence of genetic or environmental differences, cells differ from each other in their molecular make‐up. The consequences of these phenotypic differences are often not well understood. New work by Waite et al ( 2016 ) directly links variation in the molecular composition of individual bacterial cells to their population‐level performance.     

Stochastic decision modeling for sustainable pavement designs

Purpose

In the USA, several studies have been conducted to analyze the energy consumption and atmospheric emissions of Warm-mix Asphalt (WMA) pavements. However, the direct and indirect environmental, economic, and social impacts, termed as Triple-Bottom-Line (TBL), were not addressed sufficiently. Hence, the aim of this study is to develop TBL-oriented sustainability assessment model to evaluate the environmental and socio-economic impacts of pavements constructed with different types of WMA mixtures and compare them to a conventional Hot-mix Asphalt (HMA). The types of WMA technologies investigated in this research include Asphamin® WMA, Evotherm? WMA, and Sasobit® WMA.

Methods

To achieve this goal, supply and use tables published by the U.S. Bureau of Economic Analysis were merged with 16 macro-level sustainability metrics. A hybrid TBL-LCA model was built to evaluate the life-cycle sustainability performance of using WMA technologies in construction of asphalt pavements. The impacts on the sustainability were calculated in terms of socio-economic (import, income, gross operating surplus, government tax, work-related injuries, and employment) and environmental (water withdrawal, energy use, carbon footprint, hazardous waste generation, toxic releases into air, and land use). A stochastic compromise programming model was then developed for finding the optimal allocation of different pavement types for the U.S. highways.

Results and discussion

WMAs did not perform better in terms of environmental impacts compared to HMA. Asphamin® WMA was found to have the highest environmental and socio-economic impacts compared to other pavement types. Material extractions and processing phase had the highest contribution to all environmental impact indicators that shows the importance of cleaner production strategies for pavement materials. Based on stochastic compromised programming results, in a balanced weighting situation, Sasobit® WMA had the highest percentage of allocation (61 %); while only socio-economic aspects matter, Asphamin® WMA had the largest share (57 %) among the asphalt pavements. The optimization results also supported the significance of an increased WMA use in the U.S. highways.

Conclusions

This research complemented previous LCA studies by evaluating pavements not only from environmental emissions and energy consumption standpoint, but also from socio-economic perspectives. Multi-objective optimization results also provided important insights for decision makers when finding the optimum allocation of pavement alternatives based on different environmental and socio-economic priorities. Consequently, this study aimed to increase awareness of the inherent benefits of economic input–output analysis and multi-criteria decision making through application to emerging sustainable pavement practices.     

Stochastic context-free grammars for tRNA modeling.

Stochastic context-free grammars (SCFGs) are applied to the problems of folding, aligning and modeling families of tRNA sequences. SCFGs capture the sequences' common primary and secondary structure and generalize the hidden Markov models (HMMs) used in related work on protein and DNA. Results show that after having been trained on as few as 20 tRNA sequences from only two tRNA subfamilies (mitochondrial and cytoplasmic), the model can discern general tRNA from similar-length RNA sequences of other kinds, can find secondary structure of new tRNA sequences, and can produce multiple alignments of large sets of tRNA sequences. Our results suggest potential improvements in the alignments of the D- and T-domains in some mitochondrial tRNAs that cannot be fit into the canonical secondary structure.     

A computer program for modeling the kinetics of gene expression

Enzyme induction may be modeled on the basis of four, quantifiable processes that control the rates at which specific gene products accumulate and decay. These processes include synthesis of functional mRNA, translation and degradation of mRNA, and degradation of the protein product. We present a simple computer program that permits mathematical simulation of gene expression on the basis of experimentally determined rates of synthesis and degradation. The program was implemented as a spreadsheet using Microsoft Excel for Macintosh and MS-DOS operating systems and also was adapted for HyperCard on the Macintosh. It contains a formula to account for growth of tissue or cell populations. The program predicts amounts of individual mRNAs and proteins (or enzyme activities) in cells as a function of time after a stimulus alters their rates of synthesis or degradation.     

Stochastic Boolean networks: An efficient approach to modeling gene regulatory networks

ABSTRACT: BACKGROUND: Various computational models have been of interest due to their use in the modelling of gene regulatory networks (GRNs). As a logical model, probabilistic Boolean networks (PBNs) consider molecular and genetic noise, so the study of PBNs provides significant insights into the understanding of the dynamics of GRNs. This will ultimately lead to advances in developing therapeutic methods that intervene in the process of disease development and progression. The applications of PBNs, however, are hindered by the complexities involved in the computation of the state transition matrix and the steady-state distribution of a PBN. For a PBN with n genes and N Boolean networks, the complexity to compute the state transition matrix is O(nN22n) or O(nN2n) for a sparse matrix. RESULTS: This paper presents a novel implementation of PBNs based on the notions of stochastic logic and stochastic computation. This stochastic implementation of a PBN is referred to as a stochastic Boolean network (SBN). An SBN provides an accurate and efficient simulation of a PBN without and with random gene perturbation. The state transition matrix is computed in an SBN with a complexity of O(nL2n), where L is a factor related to the stochastic sequence length. Since the minimum sequence length required for obtaining an evaluation accuracy approximately increases in a polynomial order with the number of genes, n, and the number of Boolean networks, N, usually increases exponentially with n, L is typically smaller than N, especially in a network with a large number of genes. Hence, the computational complexity of an SBN is primarily limited by the number of genes, but not directly by the total possible number of Boolean networks. Furthermore, a time-frame expanded SBN enables an efficient analysis of the steady-state distribution of a PBN. These findings are supported by the simulation results of a simplified p53 network, several randomly generated networks and a network inferred from a T cell immune response dataset. An SBN can also implement the function of an asynchronous PBN and is potentially useful in a hybrid approach in combination with a continuous or single-molecule level stochastic model. CONCLUSIONS: Stochastic Boolean networks (SBNs) are proposed as an efficient approach to modelling gene regulatory networks (GRNs). The SBN approach is able to recover biologically-proven regulatory behaviours, such as the oscillatory dynamics of the p53-Mdm2 network and the dynamic attractors in a T cell immune response network. The proposed approach can further predict the network dynamics when the genes are under perturbation, thus providing biologically meaningful insights for a better understanding of the dynamics of GRNs. The algorithms and methods described in this paper have been implemented in Matlab packages, which are attached as Additional files.