Synchronization between Attractors: Genomic Mechanism of Cell-Fate Change.

Herein, we provide a brief overview of complex systems theory approaches to investigate the genomic mechanism of cell-fate changes. Cell trajectories across the epigenetic landscape, whether in development, environmental responses, or disease progression, are controlled by extensively coordinated genome-wide gene expression changes. The elucidation of the mechanisms underlying these coherent expression changes is of fundamental importance in cell biology and for paving the road to new therapeutic approaches. In previous studies, we pointed at dynamic criticality as a plausible characteristic of genome-wide transition dynamics guiding cell fate. Whole-genome expression develops an engine-like organization (genome engine) in order to establish an autonomous dynamical system, capable of both homeostasis and transition behaviors. A critical set of genes behaves as a critical point (CP) that serves as the organizing center of cell-fate change. When the system is pushed away from homeostasis, the state change that occurs at the CP makes local perturbation spread over the genome, demonstrating self-organized critical (SOC) control of genome expression. Oscillating-Mode genes (which normally keep genome expression on pace with microenvironment fluctuations), when in the presence of an effective perturbative stimulus, drive the dynamics of synchronization, and thus guide the cell-fate transition.

From Cell States to Cell Fates: Control of Cell State Transitions.

We examine the coordinated behavior of thousands of genes in cell fate transitions through genome expression as an integrated dynamical system using the concepts of self-organized criticality and coherent stochastic behavior. To quantify the effects of the collective behavior of genes, we adopted the flux balance approach and developed it in a new tool termed expression flux analysis (EFA). Here we describe this tool and demonstrate how its application to specific experimental genome-wide expression data provides new insights into the dynamics of the cell-fate transitions. Particularly, we show that in cell fate change, specific stochastic perturbations can spread over the entire system to guide distinct cell fate transitions through switching cyclic flux flow in the genome engine. Utilization of EFA enables us to elucidate a unified genomic mechanism for when and how cell-fate change occurs through critical transitions.

Temporal controls of the asymmetric cell division cycle in Caulobacter crescentus.

The asymmetric cell division cycle of Caulobacter crescentus is orchestrated by an elaborate gene-protein regulatory network, centered on three major control proteins, DnaA, GcrA and CtrA. The regulatory network is cast into a quantitative computational model to investigate in a systematic fashion how these three proteins control the relevant genetic, biochemical and physiological properties of proliferating bacteria. Different controls for both swarmer and stalked cell cycles are represented in the mathematical scheme. The model is validated against observed phenotypes of wild-type cells and relevant mutants, and it predicts the phenotypes of novel mutants and of known mutants under novel experimental conditions. Because the cell cycle control proteins of Caulobacter are conserved across many species of alpha-proteobacteria, the model we are proposing here may be applicable to other genera of importance to agriculture and medicine (e.g., Rhizobium, Brucella).

Computational analysis of dynamical responses to the intrinsic pathway of programmed cell death.

Multicellular organisms shape development and remove aberrant cells by programmed cell death ("apoptosis"). Because defective cell death (too little or too much) is implicated in various diseases (like cancer and autoimmunity), understanding how apoptosis is regulated is an important goal of molecular cell biologists. To this end, we propose a mathematical model of the intrinsic apoptotic pathway that captures three key dynamical features: a signal threshold to elicit cell death, irreversible commitment to the response, and a time delay that is inversely proportional to signal strength. Subdividing the intrinsic pathway into three modules (initiator, amplifier, executioner), we use computer simulation and bifurcation theory to attribute signal threshold and time delay to positive feedback in the initiator module and irreversible commitment to positive feedback in the executioner module. The model accounts for the behavior of mutants deficient in various genes and is used to design experiments that would test its basic assumptions. Finally, we apply the model to study p53-induced cellular responses to DNA damage. Cells first undergo cell cycle arrest and DNA repair, and then apoptosis if the damage is beyond repair. The model ascribes this cell-fate transition to a transformation of p53 from "helper" to "killer" forms.

A quantitative study of the division cycle of Caulobacter crescentus stalked cells.

Progression of a cell through the division cycle is tightly controlled at different steps to ensure the integrity of genome replication and partitioning to daughter cells. From published experimental evidence, we propose a molecular mechanism for control of the cell division cycle in Caulobacter crescentus. The mechanism, which is based on the synthesis and degradation of three "master regulator" proteins (CtrA, GcrA, and DnaA), is converted into a quantitative model, in order to study the temporal dynamics of these and other cell cycle proteins. The model accounts for important details of the physiology, biochemistry, and genetics of cell cycle control in stalked C. crescentus cell. It reproduces protein time courses in wild-type cells, mimics correctly the phenotypes of many mutant strains, and predicts the phenotypes of currently uncharacterized mutants. Since many of the proteins involved in regulating the cell cycle of C. crescentus are conserved among many genera of alpha-proteobacteria, the proposed mechanism may be applicable to other species of importance in agriculture and medicine.

Linking the genes: inferring quantitative gene networks from microarray data.

Modern microarray technology is capable of providing data about the expression of thousands of genes, and even of whole genomes. An important question is how this technology can be used most effectively to unravel the workings of cellular machinery. Here, we propose a method to infer genetic networks on the basis of data from appropriately designed microarray experiments. In addition to identifying the genes that affect a specific other gene directly, this method also estimates the strength of such effects. We will discuss both the experimental setup and the theoretical background.

HAUSP-regulated switch from auto- to p53 ubiquitination by Mdm2 (in silico discovery).

Stability of the 'guardian of the genome' tumor suppressor protein p53 is regulated predominantly through its ubiquitination. The ubiquitin-specific protease HAUSP plays an important role in this process. Recent experiments showed that p53 demonstrates a differential response to changes in HAUSP which nature and significance are not understood yet. Here a data-driven mathematical model of the Mdm2-mediated p53 ubiquitination network is presented which offers an explanation for the cause of such a response. The model predicts existence of the HAUSP-regulated switch from auto- to p53 ubiquitination by Mdm2. This switch suggests a potential role of HAUSP as a downstream target of stress signals in cells. The model accounts for a significant amount of experimental data, makes predictions for some rate constants, and can serve as a building block for the larger model describing a complex dynamic response of p53 to cellular stresses.

Gene networks: how to put the function in genomics.

An increasingly popular model of regulation is to represent networks of genes as if they directly affect each other. Although such gene networks are phenomenological because they do not explicitly represent the proteins and metabolites that mediate cell interactions, they are a logical way of describing phenomena observed with transcription profiling, such as those that occur with popular microarray technology. The ability to create gene networks from experimental data and use them to reason about their dynamics and design principles will increase our understanding of cellular function. We propose that gene networks are also a good way to describe function unequivocally, and that they could be used for genome functional annotation. Here, we review some of the concepts and methods associated with gene networks, with emphasis on their construction based on experimental data.

Exploring mechanisms of the DNA-damage response: p53 pulses and their possible relevance to apoptosis.

The transcription factor p53 plays a central role in maintaining genomic integrity. Recent experiments in MCF7 cells have shown that p53 protein level rises and falls in distinct pulses in response to DNA damage. The amplitudes of and intervals between pulses seem to be independent of the extent of damage, and some cells generate regular pulses of p53 over many days. Identifying the molecular mechanisms responsible for such interesting behavior is an important and challenging problem. This paper describes four dual-feedback mechanisms that combine both positive and negative feedback loops, which have been identified in the signaling network responsible for p53 regulation. Mathematical models of all four mechanisms are analyzed to determine if they are consistent with experimental observations and to characterize subtle differences among the possible mechanisms. In addition, a novel molecular mechanism is proposed whereby p53 pulses may induce, at first, cell cycle arrest and, if sustained, cell death. The proposal accounts for basic features of p53-mediated responses to DNA damage and suggests new experiments to probe the dynamics of p53 signaling.

Cell cycle control in bacteria and yeast: a case of convergent evolution?

Superficially similar traits in phylogenetically unrelated species often result from adaptation to common selection pressures. Examples of convergent evolution are known at the levels of whole organisms, organ systems, gene networks and specific proteins. The phenotypic properties of living things, on the other hand, are determined in large part by complex networks of interacting proteins. Here we present a mathematical model of the network of proteins that controls DNA synthesis and cell division in the alpha-proteobacterium, Caulobacter crescentus. By comparing the protein regulatory circuits for cell reproduction in Caulobacter with that in budding yeast (Saccharomyces cerevisiae), we suggest that convergent evolution may have created similar molecular reaction networks in order to accomplish the same purpose of coordinating DNA synthesis to cell division. Although the genes and proteins involved in cell cycle regulation in prokaryotes and eukaryotes are very different and (apparently) phylogenetically unrelated, they seem to be wired together in similar regulatory networks, which coordinate cell cycle events by identical dynamical principles.

Inferring gene networks from steady-state response to single-gene perturbations.

Inferring gene networks from gene expression data is an important step in understanding the molecular machinery of life. Three methods for establishing and quantifying causal relationships between genes based on steady-state measurements in single-gene perturbation experiments have recently been proposed: the regulatory strength method, the local regulatory strength method, and Gardner's method. The theoretical basis of these methods is presented here in a thorough and consistent fashion. In principle, for the same data set all three methods would generate identical networks, but they would quantify the strengths of connections in different ways. The regulatory strength method is shown here to be topology-dependent. It adopts the format of the data collected in gene expression microarray experiments and therefore can be immediately used with this technology. The regulatory strengths obtained by this method can also be used to compute local regulatory strengths. In contrast, Gardner's method requires both measurements of mRNA concentrations and measurements of the applied rate perturbations, which is not usually part of a standard microarray experimental protocol. The results generated by Gardner's method and by the two regulatory strengths methods differ only by scaling constants, but Gardner's method requires more measurements. On the other hand, the explicit use of rate perturbations in Gardner's approach allows one to address new questions with this method, like what perturbations caused given responses of the system. Results of the application of the three techniques to real experimental data are presented and discussed. The comparative analysis presented in this paper can be helpful for identifying an appropriate technique for inferring genetic networks and for interpreting the results of its application to experimental data.