Dynamic behavior in mathematical models of the tryptophan operon

In silico Determination of Some Conditions Leading to Glycolytic Oscillations and Their Interference With Some Other Processes in E. coli Cells

Autonomous oscillations of species levels in the glycolysis express the self-control of this essential cellular pathway belonging to the central carbon metabolism (CCM), and this phenomenon takes place in a large number of bacteria. Oscillations of glycolytic intermediates in living cells occur according to the environmental conditions and to the cell characteristics, especially the adenosine triphosphate (ATP) recovery system. Determining the conditions that lead to the occurrence and maintenance of the glycolytic oscillations can present immediate practical applications. Such a model-based analysis allows in silico (model-based) design of genetically modified microorganisms (GMO) with certain characteristics of interest for the biosynthesis industry, medicine, etc. Based on our kinetic model validated in previous works, this paper aims to in silico identify operating parameters and cell factors leading to the occurrence of stable glycolytic oscillations in the Escherichia coli cells. As long as most of the glycolytic intermediates are involved in various cellular metabolic pathways belonging to the CCM, evaluation of the dynamics and average level of its intermediates is of high importance for further applicative analyses. As an example, by using a lumped kinetic model for tryptophan (TRP) synthesis from literature, and its own kinetic model for the oscillatory glycolysis, this paper highlights the influence of glycolytic oscillations on the oscillatory TRP synthesis through the PEP (phosphoenolpyruvate) glycolytic node shared by the two oscillatory processes. The numerical analysis allows further TRP production maximization in a fed-batch bioreactor (FBR).

Optimal parameter values for the control of gene regulation

How does a transcription network arrive at the particular values of biochemical interactions defining it? These interactions define DNA-transcription factor interaction, degradation rates of proteins, promoter strengths, and communication of the environmental signal with the network. What is the structure of the fitness landscape that is defined by the space that these parameters can take on? To answer these questions, we simulate the simplest regulatory network: a transcription factor, R, and a target protein, T. We use a cost-benefit analysis to evolve the network and eventually arrive at values of parameters which maximize fitness. We show that for a given topology, multiple parameter sets exist which confer maximal fitness to the cell, and that pairwise correlations exist between parameters in optimal sets. In addition, our results indicate that in the parameter space defining the interactions in a topology, a highly rugged fitness landscape exists.

Revisiting demand rules for gene regulation

Starting with Savageau's pioneering work regarding demand rules for gene regulation from the 1970s, here, we choose the simplest transcription network and ask: how does the cell choose a particular regulatory topology from all available possibilities?

Mathematical modeling of gene expression: a guide for the perplexed biologist

The detailed analysis of transcriptional networks holds a key for understanding central biological processes, and interest in this field has exploded due to new large-scale data acquisition techniques. Mathematical modeling can provide essential insights, but the diversity of modeling approaches can be a daunting prospect to investigators new to this area. For those interested in beginning a transcriptional mathematical modeling project, we provide here an overview of major types of models and their applications to transcriptional networks. In this discussion of recent literature on thermodynamic, Boolean, and differential equation models, we focus on considerations critical for choosing and validating a modeling approach that will be useful for quantitative understanding of biological systems.

Towards an understanding of lineage specification in hematopoietic stem cells: a mathematical model for the interaction of transcription factors GATA-1 and PU.1

In addition to their self-renewal capabilities, hematopoietic stem cells guarantee the continuous supply of fully differentiated, functional cells of various types in the peripheral blood. The process which controls differentiation into the different lineages of the hematopoietic system (erythroid, myeloid, lymphoid) is referred to as lineage specification. It requires a potentially multi-step decision sequence which determines the fate of the cells and their successors. It is generally accepted that lineage specification is regulated by a complex system of interacting transcription factors. However, the underlying principles controlling this regulation are currently unknown. Here, we propose a simple quantitative model describing the interaction of two transcription factors. This model is motivated by experimental observations on the transcription factors GATA-1 and PU.1, both known to act as key regulators and potential antagonists in the erythroid vs. myeloid differentiation processes of hematopoietic progenitor cells. We demonstrate the ability of the model to account for the observed switching behavior of a transition from a state of low expression of both factors (undifferentiated state) to the dominance of one factor (differentiated state). Depending on the parameter choice, the model predicts two different possibilities to explain the experimentally suggested, stem cell characterizing priming state of low level co-expression. Whereas increasing transcription rates are sufficient to induce differentiation in one scenario, an additional system perturbation (by stochastic fluctuations or directed impulses) of transcription factor levels is required in the other case.

Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data

A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; beta-galactosidase, which is involved in the conversion of lactose to allolactose, glucose and galactose; the allolactose interactions with the lac repressor; and mRNA. The final model consists of five nonlinear differential delay equations with delays due to the transcription and translation process. We have paid particular attention to the estimation of the parameters in the model. We have tested our model against two sets of beta-galactosidase activity versus time data, as well as a set of data on beta-galactosidase activity during periodic phosphate feeding. In all three cases we find excellent agreement between the data and the model predictions. Analytical and numerical studies also indicate that for physiologically realistic values of the external lactose and the bacterial growth rate, a regime exists where there may be bistable steady-state behavior, and that this corresponds to a cusp bifurcation in the model dynamics.

Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations

Transcriptional regulation is an inherently noisy process. The origins of this stochastic behavior can be traced to the random transitions among the discrete chemical states of operators that control the transcription rate and to finite number fluctuations in the biochemical reactions for the synthesis and degradation of transcripts. We develop stochastic models to which these random reactions are intrinsic and a series of simpler models derived explicitly from the first as approximations in different parameter regimes. This innate stochasticity can have both a quantitative and qualitative impact on the behavior of gene-regulatory networks. We introduce a natural generalization of deterministic bifurcations for classification of stochastic systems and show that simple noisy genetic switches have rich bifurcation structures; among them, bifurcations driven solely by changing the rate of operator fluctuations even as the underlying deterministic system remains unchanged. We find stochastic bistability where the deterministic equations predict monostability and vice-versa. We derive and solve equations for the mean waiting times for spontaneous transitions between quasistable states in these switches.

Computational studies of gene regulatory networks: in numero molecular biology

Remarkable progress in genomic research is leading to a complete map of the building blocks of biology. Knowledge of this map is, in turn, setting the stage for a fundamental description of cellular function at the DNA level. Such a description will entail an understanding of gene regulation, in which proteins often regulate their own production or that of other proteins in a complex web of interactions. The implications of the underlying logic of genetic networks are difficult to deduce through experimental techniques alone, and successful approaches will probably involve the union of new experiments and computational modelling techniques.