Modeling a hox gene network in silico using a stochastic simulation algorithm

Computational Systems Biology in Cancer: Modeling Methods and Applications

In recent years it has become clear that carcinogenesis is a complex process, both at the molecular and cellular levels. Understanding the origins, growth and spread of cancer, therefore requires an integrated or system-wide approach. Computational systems biology is an emerging sub-discipline in systems biology that utilizes the wealth of data from genomic, proteomic and metabolomic studies to build computer simulations of intra and intercellular processes. Several useful descriptive and predictive models of the origin, growth and spread of cancers have been developed in an effort to better understand the disease and potential therapeutic approaches. In this review we describe and assess the practical and theoretical underpinnings of commonly-used modeling approaches, including ordinary and partial differential equations, petri nets, cellular automata, agent based models and hybrid systems. A number of computer-based formalisms have been implemented to improve the accessibility of the various approaches to researchers whose primary interest lies outside of model development. We discuss several of these and describe how they have led to novel insights into tumor genesis, growth, apoptosis, vascularization and therapy.

ANALYSIS OF NONLINEAR RELATIONS BETWEEN EXPRESSION PROFILES BY THE PRINCIPAL CURVES OF ORIENTED-POINTS APPROACH

DNA microarray technology enables high-throughput gene expression analysis and allows researchers to test the activity of thousands of genes at one time in multiple cellular conditions. This approach is based on principal curves of oriented points (PCOP) analysis and minimum spanning trees to analyze temporal and nontemporal series data to relate the genes. PCOP is a very suitable method, non–hypothesis-driven, for nonlinear relationship recognition between multivariable sets of data. Initially, a gene-relations tree is generated from the correlation between each pair of genes, calculated by PCOP analysis. Next, the researcher can introduce the query genes to be studied into the zoom-in operation, and the system selects the genes which connect the previously provided ones, beyond the activation pathways, using the minimum spanning tree. Thus, this zoom-in operation generates the nonlinear pattern of the intraset expression behavior for the new gene set. This inner expression pattern relates the query and selected genes to study their mutual interdependence in detail. This detailed information is especially useful in the biomedical environment, where such information is not possible to obtain by applying the current analytical methods.

TEMPERATURE EFFECTS ON THE STOCHASTIC GATING OF THE IP3R CALCIUM RELEASE CHANNEL: A NUMERICAL SIMULATION STUDY

The importance of the kinetic study of endoplasmatic calcium ion channels in different intracellular processes is known today. Although there are few experimental reports on the temperature dependency of IP3R channel functions, we did not find any detailed theoretical study on this subject. For this purpose, we used a modified Gillespie algorithm to investigate the effect of temperature on the conditions affecting the open state of a single subunit of the De Young-Keizer (DYK) model. Population of the states was considered as the subject of fluctuation. Key features of the channel, such as bell-shaped dependency of open probability to the Calcium concentrations were modeled at different temperatures, too. The range of temperature variation was selected by regarding the experimental data on IP3R channel.

By increasing the temperature, we had the very slow time domains (t: 10-1 s ) and the much slower time domains (t: 100 s ) in addition to other time domains, which could be seen as new time categories in InsP3R studies, and so the results were reported in these time domains, as well.

We found out that increase in temperature declined the open probability in some concentrations of Ca 2+ and/or IP3. Also, by introducing the intensity graphs, broadening of the range of fluctuations and lowering of the order of frequency of fluctuations for the population of each state were observed due to the temperature increments.

The temperature effects on the activation and inactivation states of the channel were studied in the framework of the reaction paths. We did not find similar paths at different time domains; several paths observed which were totally different all together. These time-dependent reaction paths are also depending on the Ca 2+ and/or the IP3 concentrations. So, one can predict the most probable reaction paths at different concentrations and temperatures and also determine which kind of the path it is; a path for closing the channel or a path to open it.

Finally, the temperature effects on the calcium inhibited states were studied. We found out that calcium ion inhibitions were shifted to lower calcium concentration by increasing the temperature. The results suggests that inhibiting role of calcium is not only [ Ca 2+] and/or [IP3] dependent, but also temperature dependent.

Inferring Drosophila gap gene regulatory network: a parameter sensitivity and perturbation analysis

BACKGROUND

Inverse modelling of gene regulatory networks (GRNs) capable of simulating continuous spatio-temporal biological processes requires accurate data and a good description of the system. If quantitative relations between genes cannot be extracted from direct measurements, an efficient method to estimate the unknown parameters is mandatory. A model that has been proposed to simulate spatio-temporal gene expression patterns is the connectionist model. This method describes the quantitative dynamics of a regulatory network in space. The model parameters are estimated by means of model-fitting algorithms. The gene interactions are identified without making any prior assumptions concerning the network connectivity. As a result, the inverse modelling might lead to multiple circuits showing the same quantitative behaviour and it is not possible to identify one optimal circuit. Consequently, it is important to address the quality of the circuits in terms of model robustness.

RESULTS

Here we investigate the sensitivity and robustness of circuits obtained from reverse engineering a model capable of simulating measured gene expression patterns. As a case study we use the early gap gene segmentation mechanism in Drosophila melanogaster. We consider the limitations of the connectionist model used to describe GRN Inferred from spatio-temporal gene expression. We address the problem of circuit discrimination, where the selection criterion within the optimization technique is based of the least square minimization on the error between data and simulated results.

CONCLUSION

Parameter sensitivity analysis allows one to discriminate between circuits having significant parameter and qualitative differences but exhibiting the same quantitative pattern. Furthermore, we show that using a stochastic model derived from a deterministic solution, one can introduce fluctuations within the model to analyze the circuits' robustness. Ultimately, we show that there is a close relation between circuit sensitivity and robustness to fluctuation, and that circuit robustness is rather modular than global. The current study shows that reverse engineering of GRNs should not only focus on estimating parameters by minimizing the difference between observation and simulation but also on other model properties. Our study suggests that multi-objective optimization based on robustness and sensitivity analysis has to be considered.

Kinetic modeling of biological systems

The dynamics of how the constituent components of a natural system interact defines the spatio-temporal response of the system to stimuli. Modeling the kinetics of the processes that represent a biophysical system has long been pursued with the aim of improving our understanding of the studied system. Due to the unique properties of biological systems, in addition to the usual difficulties faced in modeling the dynamics of physical or chemical systems, biological simulations encounter difficulties that result from intrinsic multi-scale and stochastic nature of the biological processes.This chapter discusses the implications for simulation of models involving interacting species with very low copy numbers, which often occur in biological systems and give rise to significant relative fluctuations. The conditions necessitating the use of stochastic kinetic simulation methods and the mathematical foundations of the stochastic simulation algorithms are presented. How the well-organized structural hierarchies often seen in biological systems can lead to multi-scale problems and the possible ways to address the encountered computational difficulties are discussed. We present the details of the existing kinetic simulation methods and discuss their strengths and shortcomings. A list of the publicly available kinetic simulation tools and our reflections for future prospects are also provided.

Stochastic Simulations of the Cytochrome P450 Catalytic Cycle

Cytochrome P450 enzymes involve a complex reaction cycle which has been described, for the first time, by a stochastic simulation of the system in the present work. A series of models are developed for a basic catalytic cycle, employing a set of microscopic rate constants for the oxidation of p-alkoxyacylanilides catalyzed by the cytochrome P450 1A2. By analyzing the effects of low concentrations of enzyme and substrate on the system, and the dependence of the system on several rate constants, it is discovered that the system evolves along relatively stable patterns from its initial state, as indicated from different runs of simulations. Strong fluctuations appear at the entrance and exit of the pathway, with very weak fluctuations in the middle sections of the cycle. Although noises are apparent when the reactant populations are very low, basically, the fundamental feature of the P450 cycle based on a microscopic view is that it is deterministic in nature. Meanwhile, the mathematical models we developed are qualitatively validated by a comparison with those experimental results of the P450 cycle. The findings of this work will be helpful for a further deeper understanding of the catalytic mechanism of cytochrome P450 enzymes.

A kinetic Monte Carlo simulation study of inositol 1,4,5-trisphosphate receptor (IP3R) calcium release channel

Most of the previously theoretical studies about the stochastic nature of the IP3R calcium release channel gating use the chemical master equation (CME) approach. Because of the limitations of this approach we have used a stochastic simulation algorithm (SSA) presented by Gillespie. A single subunit of De Young-Keizer (DYK) model was simulated using Gillespie algorithm. The model has been considered in its complete form with eight states. We investigate the conditions which affect the open state of the model. Calcium concentrations were the subject of fluctuation in the previous works while in this study the population of the states is the subject of stochastic fluctuations. We found out that decreasing open probability is a function of Ca(2+) concentration in fast time domain, while in slow time domain it is a function of IP3 concentration. Studying the population of each state shows a time dependent reaction pattern in fast and medium time domains (10(-4) and 10(-3)s). In this pattern the state of X(010) has a determinative role in selecting the open state path. Also, intensity and frequency of fluctuations and Ca(2+) inhibitions have been studied. The results indicate that Gillespie algorithm can be a better choice for studying such systems, without using any approximation or elimination while having acceptable accuracy. In comparison with the chemical master equation, Gillespie algorithm is also provides a wide area for studying biological systems from other points of view.

Expression profiling of the mouse early embryo: reflections and perspectives

The laboratory mouse model plays important roles in our understanding of early mammalian development and provides an invaluable model for human early embryos, which are difficult to study for ethical and technical reasons. A comprehensive collection of cDNA clones, their sequences, and complete genome sequence information, which have been accumulated over the past two decades, reveal even further the value of the mouse models. Here, the progress in global gene expression profiling in early mouse embryos and, to some extent, stem cells is reviewed and future directions and challenges are discussed. The discussions include the restatement of global gene expression profiles as a snapshot of cellular status, and subsequent distinction between the differentiation state and physiological state of the cells. The discussions then extend to the biological problems that can be addressed only through global expression profiling, including a bird's-eye view of global gene expression changes, molecular index for developmental potency, cell lineage trajectory, microarray-guided cell manipulation, and the possibility of delineating gene regulatory cascades and networks.

DEMSIM: a discrete event based mechanistic simulation platform for gene expression and regulation dynamics

In this paper, a discrete event based mechanistic simulation platform DEMSIM is developed for testing and validating putative regulatory interactions. The proposed framework models the main processes in gene expression, which are transcription, translation and decay processes, as stand-alone modules while superimposing the regulatory circuitry to obtain an accurate time evolution of the system. The stochasticity inherent to gene expression and regulation processes is captured using Monte Carlo based sampling. The proposed framework is applied to the extensively studied lac operon system, the SOS response system and the araBAD operon system of Escherichia coli. The results for the lac gene system demonstrate the simulation framework's ability to capture the dynamics of gene regulation, whereas the results for the SOS response system indicate that the framework is able to make accurate predictions about system behavior in response to perturbations. Finally, simulation studies for the araBAD system suggest that the developed framework is able to distinguish between different plausible regulatory mechanisms postulated to explain observed gene expression profiles. Overall, the obtained results highlight the effectiveness of DEMSIM at describing the underlying biological processes involved in gene regulation for querying alternative regulatory hypotheses.

In silico simulation of biological network dynamics

Realistic simulation of biological networks requires stochastic simulation approaches because of the small numbers of molecules per cell. The high computational cost of stochastic simulation on conventional microprocessor-based computers arises from the intrinsic disparity between the sequential steps executed by a microprocessor program and the highly parallel nature of information flow within biochemical networks. This disparity is reduced with the Field Programmable Gate Array (FPGA)-based approach presented here. The parallel architecture of FPGAs, which can simulate the basic reaction steps of biological networks, attains simulation rates at least an order of magnitude greater than currently available microprocessors.

The Engineering of Gene Regulatory Networks

The rapid accumulation of genetic information and advancement of experimental techniques have opened a new frontier in biomedical engineering. With the availability of well-characterized components from natural gene networks, the stage has been set for the engineering of artificial gene regulatory networks with sophisticated computational and functional capabilities. In these efforts, the ability to construct, analyze, and interpret qualitative and quantitative models is becoming increasingly important. In this review, we consider the current state of gene network engineering from a combined experimental and modeling perspective. We discuss how networks with increased complexity are being constructed from simple modular components and how quantitative deterministic and stochastic modeling of these modules may provide the foundation for accurate in silico representations of gene regulatory network function in vivo.

Auto/cross-regulation of Hoxb3 expression in posterior hindbrain and spinal cord

The complex and dynamic pattern of Hoxb3 expression in the developing hindbrain and the associated neural crest of mouse embryos is controlled by three separate cis-regulatory elements: element I (region A), element IIIa, and the r5 enhancer (element IVa). We have examined the cis-regulatory element IIIa by transgenic and mutational analysis to determine the upstream trans-acting factors and mechanisms that are involved in controlling the expression of the mouse Hoxb3 gene in the anterior spinal cord and hindbrain up to the r5/r6 boundary, as well as the associated neural crest which migrate to the third and posterior branchial arches and to the gut. By deletion analysis, we have identified the sequence requirements within a 482-bp element III482. Two Hox binding sites are identified in element III482 and we have shown that in vitro both Hoxb3 and Hoxb4 proteins can interact with these Hox binding sites, suggesting that auto/cross-regulation is required for establishing the expression of Hoxb3 in the neural tube domain. Interestingly, we have identified a novel GCCAGGC sequence motif within element III482, which is also required to direct gene expression to a subset of the expression domains except for rhombomere 6 and the associated neural crest migrating to the third and posterior branchial arches. Element III482 can direct a higher level of reporter gene expression in r6, which led us to investigate whether kreisler is involved in regulating Hoxb3 expression in r6 through this element. However, our transgenic and mutational analysis has demonstrated that, although kreisler binding sites are present, they are not required for the establishment or maintenance of reporter gene expression in r6. Our results have provided evidence that the expression of Hoxb3 in the neural tube up to the r5/r6 boundary is auto/cross-regulated by Hox genes and expression of Hoxb3 in r6 does not require kreisler.

Control, exploitation and tolerance of intracellular noise

Noise has many roles in biological function, including generation of errors in DNA replication leading to mutation and evolution, noise-driven divergence of cell fates, noise-induced amplification of signals, and maintenance of the quantitative individuality of cells. Yet there is order to the behaviour and development of cells. They operate within strict parameters and in many cases this behaviour seems robust, implying that noise is largely filtered by the system. How can we explain the use, rejection and sensitivity to noise that is found in biological systems? An exploration of the sources and consequences of noise calls for the use of stochastic models.