Gene Network Model Research Articles

New Computational Approaches for Analysis of cis-Regulatory Networks

The investigation and modeling of gene regulatory networks requires computational tools specific to the task. We present several locally developed software tools that have been used in support of our ongoing research into the embryogenesis of the sea urchin. These tools are especially well suited to iterative refinement of models through experimental and computational investigation. They include: BioArray, a macroarray spot processing program; SUGAR, a system to display and correlate large-BAC sequence analyses; SeqComp and FamilyRelations, programs for comparative sequence analysis; and NetBuilder, an environment for creating and analyzing models of gene networks. We also present an overview of the process used to build our model of the Strongylocentrotus purpuratus endomesoderm gene network. Several of the tools discussed in this paper are still in active development and some are available as open source.

Reverse engineering gene networks using singular value decomposition and robust regression.

We propose a scheme to reverse-engineer gene networks on a genome-wide scale using a relatively small amount of gene expression data from microarray experiments. Our method is based on the empirical observation that such networks are typically large and sparse. It uses singular value decomposition to construct a family of candidate solutions and then uses robust regression to identify the solution with the smallest number of connections as the most likely solution. Our algorithm has O(log N) sampling complexity and O(N(4)) computational complexity. We test and validate our approach in a series of in numero experiments on model gene networks.

Common pattern formation, modularity and phase transitions in a gene network model of morphogenesis

A model of biological morphogenesis is presented. The model is based on a gene network cell description and the interaction among the nearest cells. Here interactions between cells are due to diffusion-like mechanisms and also due to inductive, cell-to-cell interactions. An extensive analysis shows that (a) a small number of basic patterns are present, linked to a set of minimal gene nets (modules) with a small number of units and (b) spatial patterns are common in both types of interaction, but are much more common in the inductive case. These results support the idea (early conjectured by S. Kauffman) that evolution does not need to fine-tune through a high-dimensional parameter space, since spatial patterning is already a robust property of spatially extended gene networks displaying modular organization.

A numerical investigation of adaptation in populations of random boolean networks

We investigate the adaptation of random boolean networks that are a model for regulatory gene networks. The model considers a general genetic algorithm and a fitness function that takes into account the full network dynamical behavior. We propose a mathematical function to quantify the complexity catastrophe. We also find that the latter occurs when the task complexity increases, i.e., using networks with longer periods. Finally, we discuss a scenario that describes the adaptation on the proposed fitness landscape.

Symbolic dynamics and computation in model gene networks.

We analyze a class of ordinary differential equations representing a simplified model of a genetic network. In this network, the model genes control the production rates of other genes by a logical function. The dynamics in these equations are represented by a directed graph on an n-dimensional hypercube (n-cube) in which each edge is directed in a unique orientation. The vertices of the n-cube correspond to orthants of state space, and the edges correspond to boundaries between adjacent orthants. The dynamics in these equations can be represented symbolically. Starting from a point on the boundary between neighboring orthants, the equation is integrated until the boundary is crossed for a second time. Each different cycle, corresponding to a different sequence of orthants that are traversed during the integration of the equation always starting on a boundary and ending the first time that same boundary is reached, generates a different letter of the alphabet. A word consists of a sequence of letters corresponding to a possible sequence of orthants that arise from integration of the equation starting and ending on the same boundary. The union of the words defines the language. Letters and words correspond to analytically computable Poincare maps of the equation. This formalism allows us to define bifurcations of chaotic dynamics of the differential equation that correspond to changes in the associated language. Qualitative knowledge about the dynamics found by integrating the equation can be used to help solve the inverse problem of determining the underlying network generating the dynamics. This work places the study of dynamics in genetic networks in a context comprising both nonlinear dynamics and the theory of computation. (c) 2001 American Institute of Physics.

Global dynamics of neural nets with infinite gain

We consider a model of neural and gene networks where the nonlinearities in the system of differential equations are discontinuous and piecewise constant. We develop a framework for study of such systems. As a first step, we associate to the system a graph G on a hypercube and show how the collection of strongly connected components of G relates to the dynamics of the flow on the set of rays through the origin. In the second step, we discuss the relationship between the invariant sets of the ray flow and the invariant sets of the original flow. We provide a sufficient condition for a one-to-one correspondence between these sets. Finally, we study the class of binary networks within this framework. Under certain conditions, we can determine the structure of an invariant set corresponding to the lowest strongly connected component of the hypercube graph.

MADS‐BOX GENES: DEVELOPMENT AND EVOLUTION OF PLANT BODY PLANS

We review functional data on MADS‐box genes, recent phylogenetic analyses of these coding regions, and their roles in the development and evolution of key morphological innovations in plants. We map the origin of important morphological structures in particular diverse stages of the life cycle in different plant clades onto organismal phylogenies, and present relevant molecular genetic aspects of development related to the MADS‐box genes. We focus on reproductive structures of the sporophyte because most functional characterizations have been done of MADS‐box genes involved in flower development. We discuss MADS‐box evolution in flowering plants, but we also review studies in the other nonflowering vascular plants, gymnosperms (conifers and gnetales), and ferns and preliminary data from the algae. We suggest that floral (e.g. flowering time, inflorescence, and flower meristem identity) MADS‐box and nonfloral plant MADS‐box genes should be the focus of future comparative research. Cloning and functional analyses of MADS‐box genes in bryophytes, particularly in the experimental system Physcomitrella patens (Hedw.) B.S.G., are needed. The ABC model of floral organ specification is an excellent general representation of an important network of genes; however, formal analytical tools are required to integrate data on complex gene interaction in comparative analyses. This and other analytical approaches to constructing gene network models will help to frame homology hypotheses in an evolutionary and developmental framework.

Combinatorial explosion in model gene networks.

The explosive growth in knowledge of the genome of humans and other organisms leaves open the question of how the functioning of genes in interacting networks is coordinated for orderly activity. One approach to this problem is to study mathematical properties of abstract network models that capture the logical structures of gene networks. The principal issue is to understand how particular patterns of activity can result from particular network structures, and what types of behavior are possible. We study idealized models in which the logical structure of the network is explicitly represented by Boolean functions that can be represented by directed graphs on n-cubes, but which are continuous in time and described by differential equations, rather than being updated synchronously via a discrete clock. The equations are piecewise linear, which allows significant analysis and facilitates rapid integration along trajectories. We first give a combinatorial solution to the question of how many distinct logical structures exist for n-dimensional networks, showing that the number increases very rapidly with n. We then outline analytic methods that can be used to establish the existence, stability and periods of periodic orbits corresponding to particular cycles on the n-cube. We use these methods to confirm the existence of limit cycles discovered in a sample of a million randomly generated structures of networks of 4 genes. Even with only 4 genes, at least several hundred different patterns of stable periodic behavior are possible, many of them surprisingly complex. We discuss ways of further classifying these periodic behaviors, showing that small mutations (reversal of one or a few edges on the n-cube) need not destroy the stability of a limit cycle. Although these networks are very simple as models of gene networks, their mathematical transparency reveals relationships between structure and behavior, they suggest that the possibilities for orderly dynamics in such networks are extremely rich and they offer novel ways to think about how mutations can alter dynamics. (c) 2000 American Institute of Physics.

Mathematical modeling of gene networks.

The expression of clusters of genes can be regulated by stimulus-induced activation of signal transduction pathways that modulate the activity of transcription factors (TFs). TFs regulate transcription by binding to stretches of DNA known as responsive elements (reviewed by Karin 1994). Many genes are regulated by multiple TFs. Furthermore, genes coding for TFs are often activated or repressed by their own products as well as by other TFs. A large number—on the order of thousands—of such interactions together constitute the total array of genetic regulation in neurons and other cells. The term “gene network” can be used to refer to clusters of genes that satisfy two conditions. The expression of the genes in the cluster is affected in concert by specific stimuli, such as exposure to a hormone or neurotransmitter. Also, the protein products of some members of the cluster act as TFs to regulate the expression of other members.

Modeling Transcriptional Control in Gene Networks—Methods, Recent Results, and Future Directions

Mathematical models are useful for providing a framework for integrating data and gaining insights into the static and dynamic behavior of complex biological systems such as networks of interacting genes. We review the dynamic behaviors expected from model gene networks incorporating common biochemical motifs, and we compare current methods for modeling genetic networks. A common modeling technique, based on simply modeling genes as ON–OFF switches, is readily implemented and allows rapid numerical simulations. However, this method may predict dynamic solutions that do not correspond to those seen when systems are modeled with a more detailed method using ordinary differential equations. Until now, the majority of gene network modeling studies have focused on determining the types of dynamics that can be generated by common biochemical motifs such as feedback loops or protein oligomerization. For example, these elements can generate multiple stable states for gene product concentrations, state-dependent responses to stimuli, circadian rhythms and other oscillations, and optimal stimulus frequencies for maximal transcription. In the future, as new experimental techniques increase the ease of characterization of genetic networks, qualitative modeling will need to be supplanted by quantitative models for specific systems.

Quantitative Modeling of Gene Regulatory Network:Identifying the Network by Means of Genetic Algorithms

The progress on gene expression profiling technology has allowed us to venture into the underlying regulatory rules and suggest many gene network models. Among them, the quantitative models are probably the most potent to achieve the highest precision and sensitivity. But the practical limitation of the approach is the requirement of lengthy data points and vulnerability to noise in the data. With present DNA micro-array technology, the large data set is very costly, and the noise is inevitably significant in expression levels. We have focused on using a nonlinear matrix model to represent the network regulation, in which the regulatory input to a gene’s expression level is represented by the summation of the regulation state of other genes. We propose two approaches, which allow us to analyze the data sufficiently with noise and small amount of data, implemented with genetic algorisms. The method was applied to simulated data and Rat Cervical Spinal Cord development data to generate the analysis of the expression profile.

Delta-Notch lateral inhibitory patterning in the emergence of ciliated cells in Xenopus: experimental observations and a gene network model.

In diverse vertebrate and invertebrate systems, lateral inhibition through the Delta-Notch signaling pathway can lead to cells in initially uniform epithelial tissues differentiating in "salt-and-pepper", regular spacing patterns. In this paper we examine lateral inhibition during the emergence of ciliated cells in Xenopus embryonic skin, using experimental manipulations of the Delta-Notch pathway and a connectionist gene-network model of the process. The results of our model are in agreement with previous models of regular patterning through lateral inhibition and reproduce the observations of our experimental assays. Moreover, the model provides an account for the variability of embryonic responses to the experimental assays, points to a component of lateral inhibition that may be the chief source of this variability, and suggests ways to control it. Our model could thus serve as a tool to generate predictions about this and other regular patterning systems governed by lateral inhibition.

Dynamical Analysis of Gene Networks Requires Both mRNA and Protein Expression Information

One of the important goals of biology is to understand the relationship between DNA sequence information and nonlinear cellular responses. This relationship is central to the ability to effectively engineer cellular phenotypes, pathways, and characteristics. Expression arrays for monitoring total gene expression based on mRNA can provide quantitative insight into which gene or genes are on or off; but this information is insufficient to fully predict dynamic biological phenomena. Using nonlinear stability analysis we show that a combination of gene expression information at the message level and at the protein level is required to describe even simple models of gene networks. To help illustrate the need for such information we consider a mechanistic model for circadian rhythmicity which shows agreement with experimental observations when protein and mRNA information are included and we propose a framework for acquiring and analyzing experimental and mathematically derived information about gene networks.

Cellular automata model for gene networks

In order to study the overall behavior of gene networks, we propose a simple cellular automata (CA) model in which each binary gene is connected to K other inputs (including itself) interacting through asymmetric short- and long-range couplings. Using numerical simulations and mean-field calculations, collective dynamical properties of this CA model were investigated. It is shown that the CA exhibits three different dynamical regimes: a frozen, a marginal, and a chaotic phase, where an initial damage vanishes, remains limited, and grows to a finite fraction of the lattice sites, respectively. The results presented are also consistent with the observed biological scaling laws for the number of differentiated cells and cell length cycles as a function of the number of genes in an organism.

Transcriptional Analyses of Steroid-Regulated Gene Networks

It has been proposed that cell-specific responses to steroid action are the result of coordinate expression of steroid gene networks. Using three different cell systems, we have performed transcriptional analyses to determine if the observed hormone-induced alterations in gene expression are consistent with a limited number of potential target genes in any one cell type. Our results indicate that greater than 95% of the transcripts in dexamethasone-treated rat hepatoma (HTC), or mouse lymphoma (WEH17) cells, are similar to the mRNAs in untreated cells based on subtraction hybridization. In addition, we find that although the castration-induced expression of androgen-regulated transcripts in the rat ventral prostate (RVP) is significantly different between normal and castrated rats (19%), the majority of these mRNAs are accounted for by the over abundance of sulfated glycoprotein-2 sequences. Specifically, analysis of an RVP subtracted cDNA library revealed that sulfated glycoprotein-2 mRNA masked the presence of less abundant differentially expressed sequences, confirming that the actual size of the RVP androgen gene network is small. We conclude that steroid-mediated changes in transcription accurately reflect the expression of a few cell-specific target genes, and thus support the model of steroid gene networks. The potential to characterize key elements which determine both the time course and magnitude of cell-specific hormone responses is discussed.

Transsexualism: a medical perspective.

Transsexualism, a condition in which from earliest recollection the individual is unshakeably convinced he or she has been endowed with the wrong physical sexual body presents one of the most difficult problems as regards management and treatment in clinical medicine. The aetiology and treatment is discussed and the problems with which the medical practitioner may be faced in advising his transsexual patient which include change in social role and marriage and the difference between sex and gender.