Quantitative aspects of protein induction

Application of the Goodwin model to autoregulatory feedback for stochastic gene expression

In this paper we analyse stochastic expression of a single gene with its dynamics given by the classical Goodwin model with mRNA and protein contribution. We compare the effect of the presence of positive and negative feedback on the transcription regulation. In such cases we observe two qualitatively different types of asymptotic behaviour. In the case of a negative feedback loop, under sufficient conditions, one can find a stationary density for mRNA and protein molecules. In the case of a positive feedback loop we observe extinction of both types of molecules with time.

Time-Delayed Models of Gene Regulatory Networks

We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems.

Structural and dynamical analysis of biological networks

Biological networks are currently being studied with approaches derived from the mathematical and physical sciences. Their structural analysis enables to highlight nodes with special properties that have sometimes been correlated with the biological importance of a gene or a protein. However, biological networks are dynamic both on the evolutionary time-scale, and on the much shorter time-scale of physiological processes. There is therefore no unique network for a given cellular process, but potentially many realizations, each with different properties as a consequence of regulatory mechanisms. Such realizations provide snapshots of a same network in different conditions, enabling the study of condition-dependent structural properties. True dynamical analysis can be obtained through detailed mathematical modeling techniques that are not easily scalable to full network models.

Design of the lac gene circuit revisited

The lactose (lac) operon of Escherichia coli serves as the paradigm for gene regulation, not only for bacteria, but also for all biological systems from simple phage to humans. The details of the systems may differ, but the key conceptual framework remains, and the original system continues to reveal deeper insights with continued experimental and theoretical study. Nearly as long lasting in impact as the pivotal work of Jacob and Monod is the classic experiment of Novick and Weiner in which they demonstrated all-or-none gene expression in response to an artificial inducer. These results are often cited in claims that normal gene expression is in fact a discontinuous bistable phenomenon. In this paper, I review several levels of analysis of the lac system and introduce another perspective based on the construction of the system design space. These represent variations on a theme, based on a simply stated design principle, that captures the key qualitative features of the system in a largely mechanism-independent fashion. Moreover, this principle can be readily interpreted in terms of specific mechanisms to make predictions regarding monostable vs. bistable behavior. The regions of design space representing bifurcations are compared with the corresponding regions identified through bifurcation analysis. I present evidence based on biological considerations as well as modeling and analysis to suggest that induction of the lac system in its natural setting is a monostable continuously graded phenomenon. Nevertheless, it must be acknowledged that the lac stability question remains unsettled, and it undoubtedly will remain so until there are definitive experimental results.

Global signatures of protein and mRNA expression levels

Cellular states are determined by differential expression of the cell's proteins. The relationship between protein and mRNA expression levels informs about the combined outcomes of translation and protein degradation which are, in addition to transcription and mRNA stability, essential contributors to gene expression regulation. This review summarizes the state of knowledge about large-scale measurements of absolute protein and mRNA expression levels, and the degree of correlation between the two parameters. We summarize the information that can be derived from comparison of protein and mRNA expression levels and discuss how corresponding sequence characteristics suggest modes of regulation.

Common gene expression strategies revealed by genome-wide analysis in yeast

A comprehensive analysis of six variables characterizing gene expression in yeast, including transcription and translation, mRNA and protein amounts, reveals a general tendency for levels of mRNA and protein to be harmonized, and for functionally related genes to have similar values for these variables.

Background

Gene expression is a two-step synthesis process that ends with the necessary amount of each protein required to perform its function. Since the protein is the final product, the main focus of gene regulation should be centered on it. However, because mRNA is an intermediate step and the amounts of both mRNA and protein are controlled by their synthesis and degradation rates, the desired amount of protein can be achieved following different strategies.

Results

In this paper we present the first comprehensive analysis of the relationships among the six variables that characterize gene expression in a living organism: transcription and translation rates, mRNA and protein amounts, and mRNA and protein stabilities. We have used previously published data from exponentially growing Saccharomyces cerevisiae cells. We show that there is a general tendency to harmonize the levels of mRNA and protein by coordinating their synthesis rates and that functionally related genes tend to have similar values for the six variables.

Conclusion

We propose that yeast cells use common expression strategies for genes acting in the same physiological pathways. This trend is more evident for genes coding for large and stable protein complexes, such as ribosomes or the proteasome. Hence, each functional group can be defined by a 'six variable profile' that illustrates the common strategy followed by the genes included in it. Genes encoding subunits of protein complexes show a tendency to have relatively unstable mRNAs and a less balanced profile for mRNA than for protein, suggesting a stronger regulation at the transcriptional level.

Genomics and gene transcription kinetics in yeast

As an adaptive response to new conditions, mRNA concentrations in eukaryotes are readjusted after any environmental change. Although mRNA concentrations can be modified by altering synthesis and/or degradation rates, the rapidity of the transition to a new concentration depends on the regulation of mRNA stability. There are several plausible transcriptional strategies following environmental change, reflecting different degrees of compromise between speed of response and cost of synthesis. The recent development of genomic techniques now enables researchers to determine simultaneously (either directly or indirectly) the transcription rates and mRNA half-lifes, together with mRNA concentrations, corresponding to all yeast genes. Such experiments could provide a new picture of the transcriptional response, by enabling us to characterize the kinetic strategies that are used by different genes under given environmental conditions.

The incoherent feed-forward loop accelerates the response-time of the gal system of Escherichia coli

Complex gene regulation networks are made of simple recurring gene circuits called network motifs. One of the most common network motifs is the incoherent type-1 feed-forward loop (I1-FFL), in which a transcription activator activates a gene directly, and also activates a repressor of the gene. Mathematical modeling suggested that the I1-FFL can show two dynamical features: a transient pulse of gene expression, and acceleration of the dynamics of the target gene. It is important to experimentally study the dynamics of this motif in living cells, to test whether it carries out these functions even when embedded within additional interactions in the cell. Here, we address this using a system with incoherent feed-forward loop connectivity, the galactose (gal) system of Escherichia coli. We measured the dynamics of this system in response to inducing signals at high temporal resolution and accuracy by means of green fluorescent protein reporters. We show that the galactose system displays accelerated turn-on dynamics. The acceleration is abolished in strains and conditions that disrupt the I1-FFL. The I1-FFL motif in the gal system works as theoretically predicted despite being embedded in several additional feedback loops. Response acceleration may be performed by the incoherent feed-forward loop modules that are found in diverse systems from bacteria to humans.

Modeling of negative autoregulated genetic networks in single cells

We discuss recent developments in the modeling of negative autoregulated genetic networks. In particular, we consider the temporal evolution of the population of mRNA and proteins in simple networks using rate equations. In the limit of low copy numbers, fluctuation effects become significant and more adequate modeling is then achieved using the master equation formalism. The analogy between regulatory gene networks and chemical reaction networks on dust grains in the interstellar medium is discussed. The analysis and simulation of complex reaction networks are also considered.

Neural network model of gene expression

Many natural processes consist of networks of interacting elements that, over time, affect each other's state. Their dynamics depend on the pattern of connections and the updating rules for each element. Genomic regulatory networks are networks of this sort. In this paper we use artificial neural networks as a model of the dynamics of gene expression. The significance of the regulatory effect of one gene product on the expression of other genes of the system is defined by a weight matrix. The model considers multigenic regulation including positive and/or negative feedback. The process of gene expression is described by a single network and by two linked networks where transcription and translation are modeled independently. Each of these processes is described by different network controlled by different weight matrices. Methods for computing the parameters of the model from experimental data are discussed. Results computed by means of the model are compared with experimental observations. Generalization to a 'black box' concept, where the molecular processes occurring in the cell are considered as signal processing units forming a global regulatory network, is discussed.-Vohradský, J. Neural network model of gene expression.

Quantitative antisense dose-response relationships: mathematical modeling of antisense action under steady-state conditions

A quantitative theoretical analysis of antisense action is presented in which hyperbolic relationships between the logarithm of antisense oligodeoxynucleotide (AODN) ligand concentration, versus cognate messenger RNA (mRNA) and protein concentrations, are derived under conditions of steady state. This analysis incorporates a dual-compartment kinetic model of gene expression. The antisense dose-response functions yield an apparent equilibrium dissociation constant Kd (with the dimensions of concentration), which provides an index of binding affinity and AODN efficacy. Increases in Kd produce a parallel right shift in the theoretical dose-response curve. The dose ratio derived from the antisense concentrations that produce a 50% reduction in phenotypical response, or mRNA/protein level (i.e., the ED50) for two agents of differing efficacy, is shown to equal the Kd ratio for the respective agents. The parameter Kd provides a potentially useful and experimentally quantifiable constant for comparing AODN analog efficacy. Application of quantitative antisense dose-response relationships (QADRRs) and Kd should provide a more rigorous foundation for the experimental evaluation of antisense effects.

The kinetics of mammalian gene expression

When rates of transcription from specific genes change, delays of variable length intervene before the corresponding mRNAs and proteins attain new levels. For most mammalian genes, the time required to complete transcription, processing, and transport of mRNA is much shorter than the period needed to achieve a new, steady-state level of protein. Studies of inducible genes have shown that the period required to attain new levels of individual mRNAs and proteins is related to their unique half-lives. The basis for this is a physical principle that predicts rates of accumulation of particles in compartmental systems. The minimum period required to achieve a new level is directly proportional to product half-lives because rates of decay control the ratio between the rate of synthesis and the concentration of gene products at steady state. This kinetic model suggests that sensitivity of gene products to degradation by ribonucleases and proteinases is an important determinant of the time scale of gene expression.

Kinetics of biosynthesis of iron-regulated membrane proteins in Escherichia coli

Using biological iron chelators to control specifically iron availability to Escherichia coli K-12 in conjunction with radioactive pulse-labels, we examined the biosynthesis of six iron-regulated membrane proteins. Iron deprivation induced the synthesis of five proteins, which had molecular weights of 83,000 (83K), 81K (Fep), 78K (TonA), 74K (Cir), and 25K. The kinetics of induction were the same in entA and entA(+) strains, but were affected by the initial iron availability in the media. Iron-poor cells induced rapidly (half-time, 10 min), whereas iron-rich cells began induction after a lag and showed a slower induction half-time (30 min). Within this general pattern of induction after iron deprivation, several different kinetic patterns were apparent. The 83K, 81K, and 74K proteins were coordinately controlled under all of the conditions examined. The 78K and 25K proteins were regulated differently. The synthesis of a previously unrecognized 90K inner membrane protein was inhibited by iron deprivation and stimulated by iron repletion. Both ferrichrome and ferric enterobactin completely repressed 81K and 74K synthesis when the siderophores were supplied at concentrations of 5 muM in vivo (half-time, 2.5 min). At concentrations less than 5 muM, however, both siderophores repressed synthesis only temporarily; the duration of repression was proportional to the amount of ferric siderophore added. The half-lives of the 81K and 74K mRNAs, as measured by rifampin treatment, were 1.2 and 1.6 min, respectively. The results of this study suggest that enteric bacteria are capable of instantaneously detecting and reacting to fluctuations in the extracellular iron concentration and that they store iron during periods of iron repletion for utilization during periods of iron stress. Neither iron storage nor iron regulation of envelope protein synthesis is dependent on the ability of the bacteria to form heme.

Regulation of the deo operon in Escherichia coli: the double negative control of the deo operon by the cytR and deoR repressors in a DNA directed in vitro system

The synthesis of the four enzymes of the deo operon in Escherichia coli is known from in vivo experiments to be subject to a double negative control, exerted by the products of the cytR and deoR genes. A DNA-directed in vitro protein synthesizing system makes the deo enzymes (exemplified by thymidine phosphorylase) in agreement with in vivo results. Enzyme synthesis is stimulated by cyclic AMP and repressed by the cytR and deoR gene products. Repression by the cytR repressor is reversed by cytidine or adenosine in the presence of cyclic AMP, while repression by the deoR repressor is reversed by deoxyribose-5-phosphate. Assays for the presence of the cytR and deoR repressors were established by use of S-30 extracts prepared from the regulatory mutants. Dissociation constants for repressor-operator binding as well as for repressor-inducer interactions have been estimated from the results.

Regulation of phenylalanine ammonia-lyase activity in cell-suspension cultures of Petroselinum hortense. Apparent rates of enzyme synthesis and degradation

The time courses for induced changes in the phenylalanine ammonia-lyase activity at five different stages during the growth cycle of cell-suspension cultures from parsley (Petroselinum hortense Hoffm.) were investigated. Large increases in the enzyme activity, induced either by irradiation or by dilution of a cell culture into fresh medium, were followed by an expotential decline to the initial low level. The maximum inducible level of specific enzyme activity varied within a range of about six-fold, depending on the mode of induction and the growth stage of the cell culture.