Stochastic mechanisms in gene expression

Exercise and skeletal muscle gene expression

1. Skeletal muscle is a complex and heterogenous tissue capable of remarkable adaptation in response to exercise training. The role of gene transcription, as an initial target to control protein synthesis, is poorly understood. 2. Mature myofibres contain several hundred nuclei, all of which maintain transcriptional competency, although the localized responsiveness of nuclei is not well known. Myofibres are capable of hypertrophy. These processes require the activation and myogenic differentiation of mononuclear satellite cells that fuse with the enlarging or repairing myofibre. 3. A single bout of exercise in human subjects is capable of activating the expression of many diverse groups of genes. 4. The impact of repeated exercise bouts, typical of exercise training, on gene expression has yet to receive systematic investigation. 5. The molecular programme elicited by resistance exercise and endurance exercise differs markedly. Muscular hypertrophy following resistance exercise is dependent on the activation of satellite cells and their subsequent myogenic maturation. Endurance exercise requires the simultaneous activation of mitochondrial and nuclear genes to enable mitochondrial biogenesis. 6. Future analysis of the regulation of genes by exercise may combine high-throughput technologies, such as gene-chips, enabling the rapid detection and analysis of changes in the expression of many thousands of genes.

Control motifs for intracellular regulatory networks

A number of technological innovations are yielding unprecedented data on the networks of biochemical, genetic, and biophysical reactions that underlie cellular behavior and failure. These networks are composed of hundreds to thousands of chemical species and structures, interacting via nonlinear and possibly stochastic physical processes. A central goal of modern biology is to optimally use the data on these networks to understand how their design leads to the observed cellular behaviors and failures. Ultimately, this knowledge should enable cellular engineers to redesign cellular processes to meet industrial needs (such as optimal natural product synthesis), aid in choosing the most effective targets for pharmaceuticals, and tailor treatment for individual genotypes. The size and complexity of these networks and the inevitable lack of complete data, however, makes reaching these goals extremely difficult. If it proves possible to modularize these networks into functional subnetworks, then these smaller networks may be amenable to direct analysis and might serve as regulatory motifs. These motifs, recurring elements of control, may help to deduce the structure and function of partially known networks and form the basis for fulfilling the goals described above. A number of approaches to identifying and analyzing control motifs in intracellular networks are reviewed.

Robustness of circadian rhythms with respect to molecular noise

We use a core molecular model capable of generating circadian rhythms to assess the robustness of circadian oscillations with respect to molecular noise. The model is based on the negative feedback exerted by a regulatory protein on the expression of its gene. Such a negative regulatory mechanism underlies circadian oscillations of the PER protein in Drosophila and of the FRQ protein in Neurospora. The model incorporates gene transcription into mRNA, translation of mRNA into protein, reversible phosphorylation leading to degradation of the regulatory protein, transport of the latter into the nucleus, and repression of gene expression by the nuclear form of the protein. To assess the effect of molecular noise, we perform stochastic simulations after decomposing the deterministic model into elementary reaction steps. The oscillations predicted by the stochastic simulations agree with those obtained with the deterministic version of the model. We show that robust circadian oscillations can occur already with a limited number of mRNA and protein molecules, in the range of tens and hundreds, respectively. Entrainment by light/dark cycles and cooperativity in repression enhance the robustness of circadian oscillations with respect to molecular noise.

Bioengineering models of cell signaling

Strategies for rationally manipulating cell behavior in cell-based technologies and molecular therapeutics and understanding effects of environmental agents on physiological systems may be derived from a mechanistic understanding of underlying signaling mechanisms that regulate cell functions. Three crucial attributes of signal transduction necessitate modeling approaches for analyzing these systems: an ever-expanding plethora of signaling molecules and interactions, a highly interconnected biochemical scheme, and concurrent biophysical regulation. Because signal flow is tightly regulated with positive and negative feedbacks and is bidirectional with commands traveling both from outside-in and inside-out, dynamic models that couple biophysical and biochemical elements are required to consider information processing both during transient and steady-state conditions. Unique mathematical frameworks will be needed to obtain an integrated perspective on these complex systems, which operate over wide length and time scales. These may involve a two-level hierarchical approach wherein the overall signaling network is modeled in terms of effective "circuit" or "algorithm" modules, and then each module is correspondingly modeled with more detailed incorporation of its actual underlying biochemical/biophysical molecular interactions.

A new approach to decoding life: systems biology

Systems biology studies biological systems by systematically perturbing them (biologically, genetically, or chemically); monitoring the gene, protein, and informational pathway responses; integrating these data; and ultimately, formulating mathematical models that describe the structure of the system and its response to individual perturbations. The emergence of systems biology is described, as are several examples of specific systems approaches.

Canalization, developmental stability, and morphological integration in primate limbs

Canalization and developmental stability refer to the tendency of developmental processes to follow particular trajectories, despite external or internal perturbation. Canalization is the tendency for development of a specific genotype to follow the same trajectory under different conditions (different environments or different genetic backgrounds), while developmental stability is the tendency for the development of a specific genotype to follow the same trajectory under the same conditions. Morphological integration refers to the tendency for structures to show correlated variation because they develop in response to shared developmental processes or function in concert with other structures. All three phenomena are emergent properties of developmental systems that can affect the interaction of development and evolution. In this paper, we review the topics of canalization, developmental stability, and morphological integration and their relevance to primate and human evolution. We then test three developmentally motivated hypotheses about the patterning of variability components in the mammalian limb. We find that environmental variances and fluctuating asymmetries (FA) increase distally along the limb in adult macaques but not in fetal mice. We infer that the greater variability of more distal segments in macaques is due to postnatal mechanical effects. We also find that heritability and FA are significantly correlated when different limb measurements are compared in fetal mice. This supports the idea that the mechanisms underlying canalization and developmental stability are related. Finally, we report that the covariation structure of fore- and hindlimb skeletal elements shows evidence for morphological integration between serially homologous structures between the limbs. This is evidence for the existence of developmental modules that link structures between the limbs. Such modules would produce covariation that would need to be overcome by selection for divergence in hind- and forelimb morphology.

Explaining mortality rate plateaus

We propose a stochastic model of aging to explain deviations from exponential growth in mortality rates commonly observed in empirical studies. Mortality rate plateaus are explained as a generic consequence of considering death in terms of first passage times for processes undergoing a random walk with drift. Simulations of populations with age-dependent distributions of viabilities agree with a wide array of experimental results. The influence of cohort size is well accounted for by the stochastic nature of the model.

The dynamics of molecular networks: applications to therapeutic discovery

Recent advances in biomedical research, genomics and bioinformatics have given the pharmaceutical and biotechnology industries new promises and expectations: providing effective cures for complex diseases, discovering and prioritizing drug targets more efficiently, eliminating toxic and ineffective compounds earlier and delivering the right drug therapy to the appropriate patients. Ultimately, the biomedical information generated today must be transformed into integrated predictive models that can be consulted for decision-making in drug discovery, efficacy and toxicity screening and individualized therapy. Here we describe how models that capture different aspects of network dynamics can be generated and applied in disease pathway identification, drug screening, diagnostics and individualized therapy.

Synthetic cell biology

Synthesis of data into formal models of cellular function is rapidly becoming a necessary industry. The complexity of the interactions among cellular constituents and the quantity of data about these interactions hinders the ability to predict how cells will respond to perturbation and how they can be engineered for industrial or medical purposes. Models provide a systematic framework to describe and analyze these complex systems. In the past few years, models have begun to have an impact on mainstream biology by creating deeper insight into the design rules of cellular signal processing, providing a basis for rational engineering of cells, and for resolving debates about the root causes of certain cellular behaviors. This review covers some of the recent work and challenges in developing these "synthetic cell" models and their growing practical applications.

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.

Paternally inherited transgenes are down-regulated but retain low activity during early embryogenesis in Arabidopsis

We investigated the timing of transgene activation after fertilisation in Arabidopsis following crosses and using two transgenic promoters (from the AtCYCB1 and AtLTP1 genes). Using both a transactivation system and direct transcriptional fusion to drive beta-glucuronidase reporter expression, reciprocal crosses showed a lack of expression of the paternal components. This is consistent with a lack of paternal genome activity previously reported during early seed development in Arabidopsis [Viella-Calzada et al. (2000) Nature 404, 91-94]. However, transactivation experiments of the BARNASE gene gave evidence that at least some paternal loci retain transcriptional activity, though at a low level, during early embryogenesis.

Regulation of gene expression in flux balance models of metabolism

Genome-scale metabolic networks can now be reconstructed based on annotated genomic data augmented with biochemical and physiological information about the organism. Mathematical analysis can be performed to assess the capabilities of these reconstructed networks. The constraints-based framework, with flux balance analysis (FBA), has been used successfully to predict time course of growth and by-product secretion, effects of mutation and knock-outs, and gene expression profiles. However, FBA leads to incorrect predictions in situations where regulatory effects are a dominant influence on the behavior of the organism. Thus, there is a need to include regulatory events within FBA to broaden its scope and predictive capabilities. Here we represent transcriptional regulatory events as time-dependent constraints on the capabilities of a reconstructed metabolic network to further constrain the space of possible network functions. Using a simplified metabolic/regulatory network, growth is simulated under various conditions to illustrate systemic effects such as catabolite repression, the aerobic/anaerobic diauxic shift and amino acid biosynthesis pathway repression. The incorporation of transcriptional regulatory events in FBA enables us to interpret, analyse and predict the effects of transcriptional regulation on cellular metabolism at the systemic level.

Random monoallelic expression of three genes clustered within 60 kb of mouse t complex genomic DNA

Mammals achieve gene dosage control by (1) random X-chromosome inactivation in females, (2) parental origin-specific imprinting of selected autosomal genes, and (3) random autosomal inactivation. Genes belonging to the third category of epigenetic phenomenon are just now emerging, with only six identified so far. Here we report three additional genes, Nubp2, Igfals, and Jsap1, that show 50%-methylated CpG sites by Southern blot analyses and primarily monoallelic expression in single-cell allele-specific RT-PCR analysis of bone marrow stromal cells and hepatocytes. Furthermore, we show that, in contrast to X inactivation, alleles can switch between active and inactive states during the formation of daughter cells. These three genes are the first in their category to exist as a tight cluster, in the proximal region of mouse chromosome 17, providing a thus far unique example of a region of autosomal random monoallelic expression.

Stochastic kinetic analysis of the Escherichia coli stress circuit using sigma(32)-targeted antisense

A stochastic Petri net model was developed for simulating the sigma(32) stress circuit in E. coli. Transcription factor sigma(32) is the principal regulator of the response of E. coli to heat shock. Stochastic Petri net (SPN) models are well suited for kinetics characterization of fluxes in biochemical pathways. Notably, there exists a one-to-one mapping of model tokens and places to molecules of particular species. Our model was validated against experiments in which ethanol (inducer of heat shock response) and sigma(32)-targeted antisense (downward regulator) were used to perturb the sigma(32) regulatory pathway. The model was also extended to simulate the effects of recombinant protein production. Results show that the stress response depends heavily on the partitioning of sigma(32) within the cell; that is, sigma(32) becomes immediately available to mediate a stress response because it exists primarily in a sequestered, inactive form, complexed with chaperones DnaK, DnaJ, and GrpE. Recombinant proteins, however, also compete for chaperone proteins, particularly when folded improperly. Our simulations indicate that when the expression of recombinant protein has a low requirement for DnaK, DnaJ, and GrpE, the overall sigma(32) levels may drop, but the level of heat shock proteins will increase. Conversely, when the overexpressed recombinant protein has a strong requirement for the chaperones, a severe response is predicted. Interestingly, both cases were observed experimentally.

Contractile properties of adjacent segments of single human muscle fibers

A comparison of the contractile properties of adjacent segments of single human muscle fibers may help to explain the interaction among nuclear domains within the myofiber. Biopsy samples were obtained from the vastus lateralis muscle of 20 healthy untrained women (age 18-79 years). Single fibers (n = 38) were dissected and cut into halves (segments A and B). Segment diameter and depth were measured using an image analysis system. Maximal force (Po) was recorded during activation with calcium (pCa 4.5). Maximal unloaded shortening velocity (Vo) was calculated using the slack test. Myosin heavy chain (MyHC) expression was determined using sodium dodecyl sulphate polyacrylamide gel electrophoresis (SDS-PAGE). A significant difference ( approximately 7%) in Po was seen between adjacent segments expressing type I MyHC that could not be attributed to differences in fiber size. Significant differences were observed in Vo even after adjusting for fiber type. A positive correlation was seen in Po (concordance coefficient Rho_C = 0.803) and Vo (Rho_C = 0.690) between segments, but concordance was less than perfect in both cases. Possible explanations for nonuniformity of contractile properties include random variations in physiological systems or variability of protein expression among nuclear domains.

Blazing pathways through genetic mountains

It is now widely accepted that high-throughput data sources will shed essential understanding on the inner workings of cellular and organism function. One key challenge is to distill the results of such experiments into an interpretable computational form that will be the basis of a predictive model. A predictive model represents the gold standard in understanding a biological system and will permit us to investigate the underlying cause of diseases and help us to develop therapeutics. Here I explore how discoveries can be based on high-throughput data sources and discuss how independent discoveries can be assembled into a comprehensive picture of cellular function.

The evolution of controlled multitasked gene networks: the role of introns and other noncoding RNAs in the development of complex organisms

Eukaryotic phenotypic diversity arises from multitasking of a core proteome of limited size. Multitasking is routine in computers, as well as in other sophisticated information systems, and requires multiple inputs and outputs to control and integrate network activity. Higher eukaryotes have a mosaic gene structure with a dual output, mRNA (protein-coding) sequences and introns, which are released from the pre-mRNA by posttranscriptional processing. Introns have been enormously successful as a class of sequences and comprise up to 95% of the primary transcripts of protein-coding genes in mammals. In addition, many other transcripts (perhaps more than half) do not encode proteins at all, but appear both to be developmentally regulated and to have genetic function. We suggest that these RNAs (eRNAs) have evolved to function as endogenous network control molecules which enable direct gene-gene communication and multitasking of eukaryotic genomes. Analysis of a range of complex genetic phenomena in which RNA is involved or implicated, including co-suppression, transgene silencing, RNA interference, imprinting, methylation, and transvection, suggests that a higher-order regulatory system based on RNA signals operates in the higher eukaryotes and involves chromatin remodeling as well as other RNA-DNA, RNA-RNA, and RNA-protein interactions. The evolution of densely connected gene networks would be expected to result in a relatively stable core proteome due to the multiple reuse of components, implying that cellular differentiation and phenotypic variation in the higher eukaryotes results primarily from variation in the control architecture. Thus, network integration and multitasking using trans-acting RNA molecules produced in parallel with protein-coding sequences may underpin both the evolution of developmentally sophisticated multicellular organisms and the rapid expansion of phenotypic complexity into uncontested environments such as those initiated in the Cambrian radiation and those seen after major extinction events.

Whole-cell simulation: a grand challenge of the 21st century

Study of the cell will never be complete unless its dynamic behavior is understood. The complex behavior of the cell cannot be determined or predicted unless a computer model of the cell is constructed and computer simulation is undertaken. Rapid accumulation of biological data from genome, proteome, transcriptome and metabolome projects can bring us to the point where it is no longer purely speculative to discuss how to construct virtual cells in silico. This article describes attempts to construct whole cell models. The E-CELL project has completed a couple of virtual cell models, and computer simulations have revealed some biological surprises.

The future is noisy: the role of spatial fluctuations in genetic switching

A genetic switch may be realized by a certain operator sector on the DNA strand from which either genetic code, to the left or to the right of this operator sector, can be transcribed and the corresponding information processed. This switch is controlled by messenger molecules, i.e., they determine to which side the switch is flipped. Recently, it has been realized that noise plays an elementary role in genetic switching, and the effect of number fluctuations of the messenger molecules have been explored. Here we argue that the assumption of well stirredness taken in the previous models may not be sufficient to characterize the influence of noise: spatial fluctuations play a non-negligible part in cellular genetic switching processes.

Whole-cell biocomputing

The ability to manipulate systems on the molecular scale naturally leads to speculation about the rational design of molecular-scale machines. Cells might be the ultimate molecular-scale machines and our ability to engineer them is relatively advanced when compared with our ability to control the synthesis and direct the assembly of man-made materials. Indeed, engineered whole cells deployed in biosensors can be considered one of the practical successes of molecular-scale devices. However, these devices explore only a small portion of cellular functionality. Individual cells or self-organized groups of cells perform extremely complex functions that include sensing, communication, navigation, cooperation and even fabrication of synthetic nanoscopic materials. In natural systems, these capabilities are controlled by complex genetic regulatory circuits, which are only partially understood and not readily accessible for use in engineered systems. Here, we focus on efforts to mimic the functionality of man-made information-processing systems within whole cells.

Intrinsic noise in gene regulatory networks

Cells are intrinsically noisy biochemical reactors: low reactant numbers can lead to significant statistical fluctuations in molecule numbers and reaction rates. Here we use an analytic model to investigate the emergent noise properties of genetic systems. We find for a single gene that noise is essentially determined at the translational level, and that the mean and variance of protein concentration can be independently controlled. The noise strength immediately following single gene induction is almost twice the final steady-state value. We find that fluctuations in the concentrations of a regulatory protein can propagate through a genetic cascade; translational noise control could explain the inefficient translation rates observed for genes encoding such regulatory proteins. For an autoregulatory protein, we demonstrate that negative feedback efficiently decreases system noise. The model can be used to predict the noise characteristics of networks of arbitrary connectivity. The general procedure is further illustrated for an autocatalytic protein and a bistable genetic switch. The analysis of intrinsic noise reveals biological roles of gene network structures and can lead to a deeper understanding of their evolutionary origin.

Self-organisation and orderly processes by individual protein complexes in the bacterial cell

In the bacterial cell, individual multimeric proteins and multiprotein assemblies perform and control orderly processes. Individual motor enzyme complexes accomplish highly complex functions, such as nucleic acid and protein syntheses, with impressive efficiency and fidelity. Lac operon repression by the lac repressor is effectively controlled via a single molecular switch. There are only few copies of, for example, DNA polymerase holoenzyme and lac repressor and few specific target molecules/sites, with which these protein complexes interact, present in a single E. coli cell. These interactive processes take place in submicron-sized spaces characterised by extreme crowding (volume exclusion) of macromolecules and small molecules, heterogeneity and non-ideality. Recent evidence reinforces the fundamental difference of the cytoplasmic as compared with in vitro ("test tube") reaction conditions. This is reflected in the breakdown of the applicability of "bulk phase" thermodynamic, macroscopic chemical kinetic and diffusion laws to interactions of individual macromolecules and target sites in a single cell. Stochastic kinetic models and stochastic simulations enable the statistical description and analysis of biochemical reactions and binding processes which involve small numbers of reactants. New unifying concepts and models are required for the quantitative understanding of the microscopic self-organisation of multi-protein complexes and the dynamic order at the single-protein assembly and single-switch level in the living cell.

Early indicators of response in biologically based risk assessment for nongenotoxic carcinogens

The proposed existence of dose-response thresholds for nongenotoxic carcinogens has led to a major controversy in the risk extrapolation process. To resolve this debate, there has been a significant investment in mechanism-based risk assessment research. The ability to utilize this mechanistic research for risk assessment procedures is still limited and may not warrant the expense. Alternatively, an approach can be used to identify dose-response thresholds through the utilization of sensitive indicators of biological response. This approach does not rely upon a mechanistic framework for the development of pathology, is solely dependent on already existing technology, and takes into account the possibility of background levels of pathway activation. For this approach, sensitive biochemical responses need to be identified and linked to the introduction of the toxicant through dose response, by time of response, and, when possible, through a proposed biochemical mechanism. The weakness of this approach is that more sensitive unidentified responses may exist requiring that a safety factor of 10 be used to define a NOEL. For dioxin-like compounds, using a surrogate marker of response CYP1A1 induction, this approach yields an estimate of the acceptable daily intake of 5-50 fg/kg/day. This limit is remarkably similar to the results of the original EPA linear extrapolation (6 fg/kg/day). A similar approach can be used for other nongenotoxic carcinogens and the analysis can be completed within 1 year.

A power law for cells

Darwin observed that multiple, lowly organized, rudimentary, or exaggerated structures show increased relative variability. However, the cellular basis for these laws has never been investigated. Some animals, such as the nematode Caenorhabditis elegans, are famous for having organs that possess the same number of cells in all individuals, a property known as eutely. But for most multicellular creatures, the extent of cell number variability is unknown. Here we estimate variability in organ cell number for a variety of animals, plants, slime moulds, and volvocine algae. We find that the mean and variance in cell number obey a power law with an exponent of 2, comparable to Taylor's law in ecological processes. Relative cell number variability, as measured by the coefficient of variation, differs widely across taxa and tissues, but is generally independent of mean cell number among homologous tissues of closely related species. We show that the power law for cell number variability can be explained by stochastic branching process models based on the properties of cell lineages. We also identify taxa in which the precision of developmental control appears to have evolved. We propose that the scale independence of relative cell number variability is maintained by natural selection.

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.

The effect of transcription and translation initiation frequencies on the stochastic fluctuations in prokaryotic gene expression

The kinetics of prokaryotic gene expression has been modelled by the Monte Carlo computer simulation algorithm of Gillespie, which allowed the study of random fluctuations in the number of protein molecules during gene expression. The model, when applied to the simulation of LacZ gene expression, is in good agreement with experimental data. The influence of the frequencies of transcription and translation initiation on random fluctuations in gene expression has been studied in a number of simulations in which promoter and ribosome binding site effectiveness has been changed in the range of values reported for various prokaryotic genes. We show that the genes expressed from strong promoters produce the protein evenly, with a rate that does not vary significantly among cells. The genes with very weak promoters express the protein in "bursts" occurring at random time intervals. Therefore, if the low level of gene expression results from the low frequency of transcription initiation, huge fluctuations arise. In contrast, the protein can be produced with a low and uniform rate if the gene has a strong promoter and a slow rate of ribosome binding (a weak ribosome binding site). The implications of these findings for the expression of regulatory proteins are discussed.

Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits

Circuits and their involvement in complex dynamics are described in differential terms in Part I of this work. Here, we first explain why it may be appropriate to use a logical description, either by itself or in symbiosis with the differential description. The major problem of a logical description is to find an adequate way to involve time. The procedure we adopted differs radically from the classical one by its fully asynchronous character. In Sec. II we describe our "naive" logical approach, and use it to illustrate the major laws of circuitry (namely, the involvement of positive circuits in multistationarity and of negative circuits in periodicity) and in a biological example. Already in the naive description, the major steps of the logical description are to: (i) describe a model as a set of logical equations, (ii) derive the state table from the equations, (iii) derive the graph of the sequences of states from the state table, and (iv) determine which of the possible pathways will be actually followed in terms of time delays. In the following sections we consider multivalued variables where required, the introduction of logical parameters and of logical values ascribed to the thresholds, and the concept of characteristic state of a circuit. This generalized logical description provides an image whose qualitative fit with the differential description is quite remarkable. A major interest of the generalized logical description is that it implies a limited and often quite small number of possible combinations of values of the logical parameters. The space of the logical parameters is thus cut into a limited number of boxes, each of which is characterized by a defined qualitative behavior of the system. Our analysis tells which constraints on the logical parameters must be fulfilled in order for any circuit (or combination of circuits) to be functional. Functionality of a circuit will result in multistationarity (in the case of a positive circuit) or in a cycle (in the case of a negative circuit). The last sections deal with "more about time delays" and "reverse logic," an approach that aims to proceed rationally from facts to models. (c) 2001 American Institute of Physics.

Designer gene networks: Towards fundamental cellular control

The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational and analytical approaches relevant to nonlinear dynamics and statistical physics. We first review the relevant work on synthetic gene networks, highlighting the important experimental findings with regard to genetic switches and oscillators. We then present the derivation of a deterministic model describing the temporal evolution of the concentration of protein in a single-gene network. Bistability in the steady-state protein concentration arises naturally as a consequence of autoregulatory feedback, and we focus on the hysteretic properties of the protein concentration as a function of the degradation rate. We then formulate the effect of an external noise source which interacts with the protein degradation rate. We demonstrate the utility of such a formulation by constructing a protein switch, whereby external noise pulses are used to switch the protein concentration between two values. Following the lead of earlier work, we show how the addition of a second network component can be used to construct a relaxation oscillator, whereby the system is driven around the hysteresis loop. We highlight the frequency dependence on the tunable parameter values, and discuss design plausibility. We emphasize how the model equations can be used to develop design criteria for robust oscillations, and illustrate this point with parameter plots illuminating the oscillatory regions for given parameter values. We then turn to the utilization of an intrinsic cellular process as a means of controlling the oscillations. We consider a network design which exhibits self-sustained oscillations, and discuss the driving of the oscillator in the context of synchronization. Then, as a second design, we consider a synthetic network with parameter values near, but outside, the oscillatory boundary. In this case, we show how resonance can lead to the induction of oscillations and amplification of a cellular signal. Finally, we construct a toggle switch from positive regulatory elements, and compare the switching properties for this network with those of a network constructed using negative regulation. Our results demonstrate the utility of model analysis in the construction of synthetic gene regulatory networks. (c) 2001 American Institute of Physics.

Dynamic regulation of the tryptophan operon: a modeling study and comparison with experimental data

A mathematical model for regulation of the tryptophan operon is presented. This model takes into account repression, feedback enzyme inhibition, and transcriptional attenuation. Special attention is given to model parameter estimation based on experimental data. The model's system of delay differential equations is numerically solved, and the results are compared with experimental data on the temporal evolution of enzyme activity in cultures of Escherichia coli after a nutritional shift (minimal + tryptophan medium to minimal medium). Good agreement is obtained between the numeric simulations and the experimental results for wild-type E. coli, as well as for two different mutant strains.

Protein dynamics: implications for nuclear architecture and gene expression

Studies of nuclear architecture reveal that the dynamic properties of proteins in the nucleus are critical for their function. The high mobility of proteins ensures their availability throughout the nucleus; their dynamic interplay generates an ever-changing, but overall stable, architectural framework, within which nuclear processes take place. As a consequence, overall nuclear morphology is determined by the functional interactions of nuclear components. The observed dynamic properties of nuclear proteins are consistent with a central role for stochastic mechanisms in gene expression and nuclear architecture.

Computational cell biology in the post-genomic era

Rapid accumulation of biological data from novel high throughput technologies characteristic of genomic and proteomic research as well as advances in more traditional biological disciplines are leading to wider use of detailed and complex computational models of cell behavior. These models address a variety of dynamic intracellular processes ranging from interactions within a gene regulation network to intracellular and intercellular signal transduction. This review focuses on the current trends in computation cell biology, particularly emphasizing the role of experimental validation. The recent successes and future challenges facing computational cell biology are also discussed.

Why is DNA damage signaling so complicated? Chaos and molecular signaling

Molecular signaling in eukaryotic cells is accomplished by complex and redundant pathways converging on key molecules that are allosterically controlled by a limited number of signaling proteins. The p53-signaling pathway is an example of a complicated sequence of signals produced in response to DNA damage. This pattern of signaling may arise from chance occurrences at the origin of life and the necessities imposed on a nanomolar system. From this viewpoint, chaos theory may explain the origin, complexity, and convergence of these pathways.

Fluctuations in repressor control: thermodynamic constraints on stochastic focusing

The influence of fluctuations in molecule numbers on genetic control circuits has received considerable attention. The consensus has been that such fluctuations will make regulation less precise. In contrast, it has more recently been shown that signal fluctuations can sharpen the response in a regulated process by the principle of stochastic focusing (SF) (, Proc. Natl. Acad. Sci. USA. 97:7148-7153). In many cases, the larger the fluctuations are, the sharper is the response. Here we investigate how fluctuations in repressor or corepressor numbers can improve the control of gene expression. Because SF is found to be constrained by detailed balance, this requires that the control loops contain driven processes out of equilibrium. Some simple and realistic out-of-equilibrium steps that will break detailed balance and make room for SF in such systems are discussed. We conclude that when the active repressors are controlled by corepressor molecules that display large ("coherent") number fluctuations or when corepressors can be irreversibly removed directly from promoter-bound repressors, the response in gene activity can become significantly sharper than without intrinsic noise. A simple experimental design to establish the possibility of SF for repressor control is suggested.

Genetic and epigenetic regulation schemes: need for an alternative paradigm

Self-organization of living cells results from the tangle of positive and negative feedback developed to ensure their homeostasis and/or their differentiation. There are three major means cellular regulation operates: the genetic, the epigenetic, and the metabolic ones. The regulation type in each of them has been overviewed. Further examination of relations between complexity and developmental stability points out sui generis properties of feedback loops, which are redundancy and pleiotropy. Prototypical schemes for positive and negative regulation with redundant and pleiotropic (including multifunctional) proteins are presented. They stress a theoretical shift from the analytical to the systemic framework. The systemic paradigm appears to be of increasing interest and importance in the study of concepts for the representation of genetic and epigenetic regulations.

Fluctuations and quality of control in biological cells: zero-order ultrasensitivity reinvestigated

Living cells differ from most other chemical systems in that they involve regulation pathways that depend very nonlinearly on chemical species that are present in low copy numbers per cell. This leads to a variety of intracellular kinetic phenomena that elude macroscopic modeling, which implicitly assumes that cells are infinitely large and fluctuations negligible. It is of particular importance to assess how fluctuations affect regulation in cases where precision and reliability are required. Here, taking finite cell size and stochastic aspects into account, we reinvestigate theoretically the mechanism of zero-order ultrasensitivity for covalent modification of target enzymes ( Proc. Natl. Acad. Sci. USA. 78:6840-6844). Macroscopically, this mechanism can produce a very sharp transition in target concentrations for very small changes in the activity of the converter enzymes. This study shows that the transition is much more gradual in a finite cell or a population of finite cells. It also demonstrates that the switch is exactly analogous to a thermodynamic phase transition and that ultrasensitivity is inevitably coupled to random ultravariation. As a consequence, the average response in a large population of cells will often be much more gradual than predicted from macroscopic descriptions.

T cell effector function and anergy avoidance are quantitatively linked to cell division

We have shown previously that T cells activated by optimal TCR and CD28 ligation exhibit marked proliferative heterogeneity, and approximately 40% of these activated cells fail entirely to participate in clonal expansion. To address how prior cell division influences the subsequent function of primary T cells at the single cell level, primary CD4+ T cells were subjected to polyclonal stimulation, sorted based on the number of cell divisions they had undergone, and restimulated by ligation of TCR/CD28. We find that individual CD4+ T cells exhibit distinct secondary response patterns that depend upon their prior division history, such that cells that undergo more rounds of division show incrementally greater IL-2 production and proliferation in response to restimulation. CD4+ T cells that fail to divide after activation exist in a profoundly hyporesponsive state that is refractory to both TCR/CD28-mediated and IL-2R-mediated proliferative signals. We find that this anergic state is associated with defects in both TCR-coupled activation of the p42/44 mitogen-activated protein kinase (extracellular signal-related kinase 1/2) and IL-2-mediated down-regulation of the cell cycle inhibitor p27kip1. However, these defects are selective, as TCR-mediated intracellular calcium flux and IL-2R-coupled STAT5 activation remain intact in these cells. Therefore, the process of cell division or cell cycle progression plays an integral role in anergy avoidance in primary T cells, and may represent a driving force in the formation of the effector/memory T cell pool.

Heterogeneous distribution of lysine 6-aminotransferase during cephamycin C biosynthesis in Streptomyces clavuligerus demonstrated using green fluorescent protein as a reporter

The cellular distribution of the cephamycin biosynthetic enzyme lysine 6-aminotransferase (LAT) has been studied in Streptomyces clavuligerus hyphae by confocal microscopy using the S65T mutant of green fluorescent protein (GFP) as a reporter. LAT mediates the first committed step in the biosynthesis of the secondary metabolite cephamycin C by S. clavuligerus. The enzymic activity of LAT varies with time during the growth of S. clavuligerus in liquid medium. To investigate if this temporal variation occurs uniformly amongst all hyphae, S. clavuligerus was transformed with a plasmid containing the LAT-encoding gene translationally fused to the GFP-encoding gene. The LAT-GFP fusion product displayed fluorescence spectral characteristics of GFP, and showed similar temporal characteristics of LAT activity compared to the wild-type strain of S. clavuligerus. The transformed strain exhibited a heterogeneous distribution of fluorescence in mycelia grown in liquid cultures. This distribution varied significantly as the batch progressed: only a fraction of the mycelia fluoresced in the early growth phase, whereas nearly all hyphae fluoresced by the late growth phase. Thereafter, a non-uniform distribution of fluorescence was again observed in the declining growth phase. A large fraction of the non-fluorescent cells in the declining growth phase were found to be non-viable. Observations of S. clavuligerus colonies grown on solid agar also showed variation of LAT-GFP expression at different stages of growth. These observations in the solid phase can be explained in terms of nutrient deprivation and signalling molecules. The results suggest that physiological differentiation of S. clavuligerus mycelia leading to cephamycin C biosynthesis is both temporally and spatially distributed. The findings also revealed that the observed heterogeneity was independent of the position of individual cell compartments within the hypha. The potential of GFP as a reporter for the quantitative study of cephamycin biosynthesis at the cellular level has also been demonstrated.

Patterns of regulation from mRNA and protein time series

The rapid advance of genome sequencing projects challenges biologists to assign physiological roles to thousands of unknown gene products. We suggest here that regulatory functions and protein-protein interactions involving specific products may be inferred from the trajectories over time of their mRNA and free protein levels within the cell. The level of a protein in the cytoplasm is governed not only by the level of its mRNA and the rate of translation, but also by the protein's folding efficiency, its biochemical modification, its complexation with other components, its degradation, and its transport from the cytoplasmic space. All these co- and post translational events cause the concentration of the protein to deviate from the level that would result if we only accounted for translation of its mRNA. The dynamics of such deviations can create patterns that reflect regulatory functions. Moreover, correlations among deviations highlight protein pairs involved in potential protein-protein interactions. We explore and illustrate these ideas here using a genetically structured simulation for the intracellular growth of bacteriophage T7.

Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation

Many regulatory molecules are present in low copy numbers per cell so that significant random fluctuations emerge spontaneously. Because cell viability depends on precise regulation of key events, such signal noise has been thought to impose a threat that cells must carefully eliminate. However, the precision of control is also greatly affected by the regulatory mechanisms' capacity for sensitivity amplification. Here we show that even if signal noise reduces the capacity for sensitivity amplification of threshold mechanisms, the effect on realistic regulatory kinetics can be the opposite: stochastic focusing (SF). SF particularly exploits tails of probability distributions and can be formulated as conventional multistep sensitivity amplification where signal noise provides the degrees of freedom. When signal fluctuations are sufficiently rapid, effects of time correlations in signal-dependent rates are negligible and SF works just like conventional sensitivity amplification. This means that, quite counterintuitively, signal noise can reduce the uncertainty in regulated processes. SF is exemplified by standard hyperbolic inhibition, and all probability distributions for signal noise are first derived from underlying chemical master equations. The negative binomial is suggested as a paradigmatic distribution for intracellular kinetics, applicable to stochastic gene expression as well as simple systems with Michaelis-Menten degradation or positive feedback. SF resembles stochastic resonance in that noise facilitates signal detection in nonlinear systems, but stochastic resonance is related to how noise in threshold systems allows for detection of subthreshold signals and SF describes how fluctuations can make a gradual response mechanism work more like a threshold mechanism.

Random signal fluctuations can reduce random fluctuations in regulated components of chemical regulatory networks

Many intracellular components are present in low copy numbers per cell and subject to feedback control. We use chemical master equations to analyze a negative feedback system where species X and S regulate each other's synthesis with standard intracellular kinetics. For a given number of X-molecules, S-variation can be significant. We show that this signal noise does not necessarily increase X-variation as previously thought but, surprisingly, can be necessary to reduce it below a Poissonian limit. The principle resembles Stochastic Resonance in that signal noise improves signal detection.

Toggles and oscillators: new genetic circuit designs

Two recent papers report the de novo design of a functioning biological circuit using well-characterized genetic elements.(1,2) Gardner et al. designed and constructed a genetic toggle switch while Elowitz and Leibler built an oscillating genetic circuit. Both circuits were designed with the aid of mathematical models. These papers demonstrate progress towards the unification of theory and experiment in the study of genetic circuits. Comparison of the predicted and observed behavior of the circuits, however, shows that the models explain only some of the circuits' properties. Further study of the observed behaviors not predicted by the model would lead to new insight into the properties of genetic networks. BioEssays 22:507-509, 2000.