CellLine, a stochastic cell lineage simulator

Summary: We present CellLine, a simulator of the dynamics ofgene regulatory networks (GRN) in the cells of a lineage. Fromuser-defined reactions and initial substance quantities, itgenerates cell lineages, i.e. genealogic pedigrees of cellsrelated through mitotic division. Each cell's dynamics is drivenby a delayed stochastic simulation algorithm (delayed SSA),allowing multiple time delayed reactions. The cells of the lineage can be individually subject to ‘perturbations’,such as gene deletion, duplication and mutation. External interventions,such as adding or removing a substance at a given moment, canbe specified. Cell differentiation lineages, where differentiationis stochastically driven or externally induced, can be modeledas well. Finally, CellLine can generate and simulate the dynamicsof multiple copies of any given cell of the lineage. As examples of CellLine use, we simulate the following systems:cell lineages containing a model of the P53-Mdm2 feedback loop,a differentiation lineage where each cell contains a 4 generepressilator (a bistable circuit), a model of the differentiationof the cells of the retinal mosaic required for color visionin Drosophila melanogaster, where the differentiation pathwaydepends on one substance's concentration that is controlledby a stochastic process, and a 9 gene GRN to illustrate theadvantage of using CellLine rather than simulating multipleindependent cells, in cases where the cells of the lineage aredynamically correlated. Availability: The CellLine program, instructions and examplesare available at http://www.cs.tut.fi/~sanchesr/CellLine/CellLine.html Contact: andre.sanchesribeiro{at}tut.fi Associate Editor: Limsoon Wong     

Robust stability of stochastic delayed genetic regulatory networks

Gene regulation is an intrinsically noisy process, which is subject to intracellular and extracellular noise perturbations and environment fluctuations. In this paper, we consider the robust stability analysis problem of genetic regulatory networks with time-varying delays and stochastic perturbation. Different from other papers, the genetic regulate system considers not only stochastic perturbation but also parameter disturbances, it is in close proximity to the real gene regulation process than determinate model. Based on the Lyapunov functional theory, sufficient conditions are given to ensure the stability of the genetic regulatory networks. All the stability conditions are given in terms of LMIs which are easy to be verified. Illustrative examples are presented to show the effectiveness of the obtained results.     

Dizzy: stochastic simulation of large-scale genetic regulatory networks

We describe Dizzy, a software tool for stochastically and deterministically modeling the spatially homogeneous kinetics of integrated large-scale genetic, metabolic, and signaling networks. Notable features include a modular simulation framework, reusable modeling elements, complex kinetic rate laws, multi-step reaction processes, steady-state noise estimation, and spatial compartmentalization.     

Robust filtering for stochastic genetic regulatory networks with time-varying delay

This paper addresses the robust filtering problem for a class of linear genetic regulatory networks (GRNs) with stochastic disturbances, parameter uncertainties and time delays. The parameter uncertainties are assumed to reside in a polytopic region, the stochastic disturbance is state-dependent described by a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. We aim to estimate the true concentrations of mRNA and protein by designing a linear filter such that, for all admissible time delays, stochastic disturbances as well as polytopic uncertainties, the augmented state estimation dynamics is exponentially mean square stable with an expected decay rate. A delay-dependent linear matrix inequality (LMI) approach is first developed to derive sufficient conditions that guarantee the exponential stability of the augmented dynamics, and then the filter gains are parameterized in terms of the solution to a set of LMIs. Note that LMIs can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.     

GenomeMixer: a complex genetic cross simulator

GenomeMixer is a cross-platform application that simulates meiotic recombination events for large and complex multigenerational genetic crosses among sexually reproducing diploid species and outputs simulated progeny to several standard mapping programs. AVAILABILITY: Documentation, C++ source, and binaries for Mac OS X and x86 Linux are freely available at http://www.nervenet.org/genome_mixer/. GenomeMixer can be compiled on any system with support for the Trolltech Qt toolkit, including Windows.     

A method for estimating stochastic noise in large genetic regulatory networks

MOTIVATION: Genetic regulatory networks are often affected by stochastic noise, due to the low number of molecules taking part in certain reactions. The networks can be simulated using stochastic techniques that model each reaction as a stochastic event. As models become increasingly large and sophisticated, however, the solution time can become excessive; particularly if one wishes to determine the effect on noise of changes to a series of parameters, or the model structure. Methods are therefore required to rapidly estimate stochastic noise. RESULTS: This paper presents an algorithm, based on error growth techniques from non-linear dynamics, to rapidly estimate the noise characteristics of genetic networks of arbitrary size. The method can also be used to determine analytical solutions for simple sub-systems. It is demonstrated on a number of cases, including a prototype model of the galactose regulatory pathway in yeast. AVAILABILITY: A software tool which incorporates the algorithm is available for use as part of the stochastic simulation package Dizzy. It is available for download at http://labs.systemsbiology.net/bolouri/software/Dizzy/ CONTACT: dorrell@systemsbiology.org SUPPLEMENTARY INFORMATION: A conceptual model of the regulatory part of the galactose utilization pathway in yeast, used as an example in the paper, is available at http://labs.systemsbiology.net/bolouri/models/galconcept.dizzy     

On construction of stochastic genetic networks based on gene expression sequences

Reconstruction of genetic regulatory networks from time series data of gene expression patterns is an important research topic in bioinformatics. Probabilistic Boolean Networks (PBNs) have been proposed as an effective model for gene regulatory networks. PBNs are able to cope with uncertainty, corporate rule-based dependencies between genes and discover the sensitivity of genes in their interactions with other genes. However, PBNs are unlikely to use directly in practice because of huge amount of computational cost for obtaining predictors and their corresponding probabilities. In this paper, we propose a multivariate Markov model for approximating PBNs and describing the dynamics of a genetic network for gene expression sequences. The main contribution of the new model is to preserve the strength of PBNs and reduce the complexity of the networks. The number of parameters of our proposed model is O(n2) where n is the number of genes involved. We also develop efficient estimation methods for solving the model parameters. Numerical examples on synthetic data sets and practical yeast data sequences are given to demonstrate the effectiveness of the proposed model.     

Mean square exponential and robust stability of stochastic discrete-time genetic regulatory networks with uncertainties

This paper aims to analyze global robust exponential stability in the mean square sense of stochastic discrete-time genetic regulatory networks with stochastic delays and parameter uncertainties. Comparing to the previous research works, time-varying delays are assumed to be stochastic whose variation ranges and probability distributions of the time-varying delays are explored. Based on the stochastic analysis approach and some analysis techniques, several sufficient criteria for the global robust exponential stability in the mean square sense of the networks are derived. Moreover, two numerical examples are presented to show the effectiveness of the obtained results.     

Cyto-Sim: a formal language model and stochastic simulator of membrane-enclosed biochemical processes

MOTIVATION: Compartments and membranes are the basis of cell topology and more than 30% of the human genome codes for membrane proteins. While it is possible to represent compartments and membrane proteins in a nominal way with many mathematical formalisms used in systems biology, few, if any, explicitly model the topology of the membranes themselves. Discrete stochastic simulation potentially offers the most accurate representation of cell dynamics. Since the details of every molecular interaction in a pathway are often not known, the relationship between chemical species in not necessarily best described at the lowest level, i.e. by mass action. Simulation is a form of computer-aided analysis, relying on human interpretation to derive meaning. To improve efficiency and gain meaning in an automatic way, it is necessary to have a formalism based on a model which has decidable properties. RESULTS: We present Cyto-Sim, a stochastic simulator of membrane-enclosed hierarchies of biochemical processes, where the membranes comprise an inner, outer and integral layer. The underlying model is based on formal language theory and has been shown to have decidable properties (Cavaliere and Sedwards, 2006), allowing formal analysis in addition to simulation. The simulator provides variable levels of abstraction via arbitrary chemical kinetics which link to ordinary differential equations. In addition to its compact native syntax, Cyto-Sim currently supports models described as Petri nets, can import all versions of SBML and can export SBML and MATLAB m-files. AVAILABILITY: Cyto-Sim is available free, either as an applet or a stand-alone Java program via the web page (http://www.cosbi.eu/Rpty_Soft_CytoSim.php). Other versions can be made available upon request.     

EvoluZion: a computer simulator for teaching genetic and evolutionary concepts

EvoluZion is a forward-in-time genetic simulator developed in Java and designed to perform real time simulations on the evolutionary history of virtual organisms. These model organisms harbour a set of 13 genes that codify an equal number of phenotypic features. These genes change randomly during replication, and mutant genes can have null, positive or negative effects on the organisms’ fitness, allowing to model effects of both selection pressures and drift on gene evolution. There are two versions of this program: version 1.6.x_haploid; focused on macroevolutionary events and depicting prokaryote-like organisms, and version 2.3.x_diploid that simulate diploid, sexually reproducing organisms, and it is more adequate to teach micro-evolution as well as key genetic concepts such as Mendel’s laws, epistasis, genetic linkage, genetic mapping among others. Different data sets can be collected periodically during running in order to perform further analyses. In addition, the complete genealogy of extant as well as extinct organisms can be recorded. EvoluZion is well suited for teaching evolutionary biology concepts to students of all levels in a pedagogic way. This is mainly due to three main program features: (i) its intuitive and simple graphical interface (ii) a visualisation similar to videogames (iii) flexible integration of a wide range of biological phenomena into a single simulation.     

Evolving modular genetic regulatory networks with a recursive,top-down approach

Being able to design genetic regulatory networks (GRNs) to achieve a desired cellular function is one of the main goals of synthetic biology. However, determining minimal GRNs that produce desired time-series behaviors is non-trivial. In this paper, we propose a ‘top-down’ approach to evolving small GRNs and then use these to recursively boot-strap the identification of larger, more complex, modular GRNs. We start with relatively dense GRNs and then use differential evolution (DE) to evolve interaction coefficients. When the target dynamical behavior is found embedded in a dense GRN, we narrow the focus of the search and begin aggressively pruning out excess interactions at the end of each generation. We first show that the method can quickly rediscover known small GRNs for a toggle switch and an oscillatory circuit. Next we include these GRNs as non-evolvable subnetworks in the subsequent evolution of more complex, modular GRNs. Successful solutions found in canonical DE where we truncated small interactions to zero, with or without an interaction penalty term, invariably contained many excess interactions. In contrast, by incorporating aggressive pruning and the penalty term, the DE was able to find minimal or nearly minimal GRNs in all test problems.     

solQTL: a tool for QTL analysis,visualization and linking to genomes at SGN database

Background  

A common approach to understanding the genetic basis of complex traits is through identification of associated quantitative trait loci (QTL). Fine mapping QTLs requires several generations of backcrosses and analysis of large populations, which is time-consuming and costly effort. Furthermore, as entire genomes are being sequenced and an increasing amount of genetic and expression data are being generated, a challenge remains: linking phenotypic variation to the underlying genomic variation. To identify candidate genes and understand the molecular basis underlying the phenotypic variation of traits, bioinformatic approaches are needed to exploit information such as genetic map, expression and whole genome sequence data of organisms in biological databases.     

Spreading dynamics on complex networks: a general stochastic approach

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.     

A stochastic simulator of a blood product donation environment with demand spikes and supply shocks

The availability of an adequate blood supply is a critical public health need. An influenza epidemic or another crisis affecting population mobility could create a critical donor shortage, which could profoundly impact blood availability. We developed a simulation model for the blood supply environment in the United States to assess the likely impact on blood availability of factors such as an epidemic. We developed a simulator of a multi-state model with transitions among states. Weekly numbers of blood units donated and needed were generated by negative binomial stochastic processes. The simulator allows exploration of the blood system under certain conditions of supply and demand rates, and can be used for planning purposes to prepare for sudden changes in the public's health. The simulator incorporates three donor groups (first-time, sporadic, and regular), immigration and emigration, deferral period, and adjustment factors for recruitment. We illustrate possible uses of the simulator by specifying input values for an 8-week flu epidemic, resulting in a moderate supply shock and demand spike (for example, from postponed elective surgeries), and different recruitment strategies. The input values are based in part on data from a regional blood center of the American Red Cross during 1996-2005. Our results from these scenarios suggest that the key to alleviating deficit effects of a system shock may be appropriate timing and duration of recruitment efforts, in turn depending critically on anticipating shocks and rapidly implementing recruitment efforts.     

The stochastic nature of biochemical networks

Cell behaviour and the cellular environment are stochastic. Phenotypes vary across isogenic populations and in individual cells over time. Here we will argue that to understand the abilities of cells we need to understand their stochastic nature. New experimental techniques allow gene expression to be followed in single cells over time and reveal stochastic bursts of both mRNA and protein synthesis in many different types of organisms. Stochasticity has been shown to be exploited by bacteria and viruses to decide between different behaviours. In fluctuating environments, cells that respond stochastically can out-compete those that sense environmental changes, and stochasticity may even have contributed to chromosomal gene order. We will focus on advances in modelling stochasticity, in understanding its effects on evolution and cellular design, and on means by which it may be exploited in biotechnology and medicine.     

Modeling biological systems using Dynetica--a simulator of dynamic networks

We present Dynetica, a user-friendly simulator of dynamic networks for constructing, visualizing, and analyzing kinetic models of biological systems. In addition to generic reaction networks, Dynetica facilitates construction of models of genetic networks, where many reactions are gene expression and interactions among gene products. Further, it integrates the capability of conducting both deterministic and stochastic simulations. AVAILABILITY AND SUPPLEMENTARY INFORMATION: Dynetica 1.0, example models, and the user's guide are available at http://www.its.caltech.edu/~you/Dynetica/Dynetica_page.htm     

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.