Simulation of prokaryotic genetic circuits

Nonlinear differential equation model for quantification of transcriptional regulation applied to microarray data of Saccharomyces cerevisiae

Microarray studies are capable of providing data for temporal gene expression patterns of thousands of genes simultaneously, comprising rich but cryptic information about transcriptional control. However available methods are still not adequate in extraction of useful information about transcriptional regulation from these data. This study presents a dynamic model of gene expression which allows for identification of transcriptional regulators using time series of gene expression. The algorithm was applied for identification of transcriptional regulators controlling 40 cell cycle regulated genes of Saccharomyces cerevisiae. The presented algorithm uses a dynamic model of time continuous gene expression with the assumption that the target gene expression profile results from the action of the upstream regulator. The goal is to apply the model to putative regulators to estimate the transcription pattern of a target gene using a least squares minimization procedure. The procedure iteratively tests all possible transcription factors and selects those that best approximate the target gene expression profile. Results were compared with independently published data and good agreement between the published and identified transcriptional regulators was found.

Frequency domain analysis of noise in simple gene circuits

Recent advances in single cell methods have spurred progress in quantifying and analyzing stochastic fluctuations, or noise, in genetic networks. Many of these studies have focused on identifying the sources of noise and quantifying its magnitude, and at the same time, paying less attention to the frequency content of the noise. We have developed a frequency domain approach to extract the information contained in the frequency content of the noise. In this article we review our work in this area and extend it to explicitly consider sources of extrinsic and intrinsic noise. First we review applications of the frequency domain approach to several simple circuits, including a constitutively expressed gene, a gene regulated by transitions in its operator state, and a negatively autoregulated gene. We then review our recent experimental study, in which time-lapse microscopy was used to measure noise in the expression of green fluorescent protein in individual cells. The results demonstrate how changes in rate constants within the gene circuit are reflected in the spectral content of the noise in a manner consistent with the predictions derived through frequency domain analysis. The experimental results confirm our earlier theoretical prediction that negative autoregulation not only reduces the magnitude of the noise but shifts its content out to higher frequency. Finally, we develop a frequency domain model of gene expression that explicitly accounts for extrinsic noise at the transcriptional and translational levels. We apply the model to interpret a shift in the autocorrelation function of green fluorescent protein induced by perturbations of the translational process as a shift in the frequency spectrum of extrinsic noise and a decrease in its weighting relative to intrinsic noise.

Synthetic biology: new engineering rules for an emerging discipline

Synthetic biologists engineer complex artificial biological systems to investigate natural biological phenomena and for a variety of applications. We outline the basic features of synthetic biology as a new engineering discipline, covering examples from the latest literature and reflecting on the features that make it unique among all other existing engineering fields. We discuss methods for designing and constructing engineered cells with novel functions in a framework of an abstract hierarchy of biological devices, modules, cells, and multicellular systems. The classical engineering strategies of standardization, decoupling, and abstraction will have to be extended to take into account the inherent characteristics of biological devices and modules. To achieve predictability and reliability, strategies for engineering biology must include the notion of cellular context in the functional definition of devices and modules, use rational redesign and directed evolution for system optimization, and focus on accomplishing tasks using cell populations rather than individual cells. The discussion brings to light issues at the heart of designing complex living systems and provides a trajectory for future development.

Host-pathogen systems biology

Unlike traditional biological research that focuses on a small set of components, systems biology studies the complex interactions between a large number of genes, proteins and other elements of biological networks and systems. Host-pathogen systems biology examines the interactions between the components of two distinct organisms, either a microbial or viral pathogen and its animal host or two different microbial species in a community. With the availability of complete genomic sequences of various hosts and pathogens, together with breakthroughs in proteomics, metabolomics and other experimental areas, the investigation of host-pathogen systems on a multitude of levels of detail has come within reach.

Qualitative simulation of the carbon starvation response in Escherichia coli

In case of nutritional stress, like carbon starvation, Escherichia coli cells abandon their exponential-growth state to enter a more resistant, non-growth state called stationary phase. This growth-phase transition is controlled by a genetic regulatory network integrating various environmental signals. Although E. coli is a paradigm of the bacterial world, it is little understood how its response to carbon starvation conditions emerges from the interactions between the different components of the regulatory network. Using a qualitative method that is able to overcome the current lack of quantitative data on kinetic parameters and molecular concentrations, we model the carbon starvation response network and simulate the response of E. coli cells to carbon deprivation. This allows us to identify essential features of the transition between exponential and stationary phase and to make new predictions on the qualitative system behavior following a carbon upshift.

Stochastic model of coliphage lambda regulatory network

The dynamic properties of the regulatory network governing the choice between lytic and lysogenic growths of coliphage lambda is studied using a Markov chain stochastic model. Our computer simulation confirms the finding by Li et al. [Proc. Natl. Acad. Sci. USA 101, 4781 (2004)] on the dynamics of budding yeast: that the biological stationary states are global attractors; the biological pathways of lytic and lysogenic growths are attracting trajectories; and the network functions are robustly designed against structural perturbations. In addition, our model shows the stochastic switch from lysogen to lytic growth, which has been observed in experiments. A definition of pseudoenergy is introduced in the network dynamics to reveal a transitionlike behavior in the system.

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.

Cross talking of network motifs in gene regulation that generates temporal pulses and spatial stripes

Gene regulatory networks contain several substructures called network motifs, which frequently exist throughout the networks. One of such motifs found in Escherichia coli, Saccharomyces cerevisiae, and Drosophila melanogaster is the feed-forward loop, in which an effector regulates its target by a direct regulatory interaction and an indirect interaction mediated by another gene product. Here, we theoretically analyze the behavior of networks that contain feed-forward loops cross talking to each other. In response to levels of the effecter, such networks can generate multiple rise-and-fall temporal expression profiles and spatial stripes, which are typically observed in developmental processes. The mechanism to generate these responses reveals the way of inferring the regulatory pathways from experimental results. Our database study of gene regulatory networks indicates that most feed-forward loops actually cross talk. We discuss how the feed-forward loops and their cross talks can play important roles in morphogenesis.

Modelling the evolution of genetic regulatory networks

An evolutionary model of genetic regulatory networks is developed, based on a model of network encoding and dynamics called the Artificial Genome (AG). This model derives a number of specific genes and their interactions from a string of (initially random) bases in an idealized manner analogous to that employed by natural DNA. The gene expression dynamics are determined by updating the gene network as if it were a simple Boolean network. The generic behaviour of the AG model is investigated in detail. In particular, we explore the characteristic network topologies generated by the model, their dynamical behaviours, and the typical variance of network connectivities and network structures. These properties are demonstrated to agree with a probabilistic analysis of the model, and the typical network structures generated by the model are shown to lie between those of random networks and scale-free networks in terms of their degree distribution. Evolutionary processes are simulated using a genetic algorithm, with selection acting on a range of properties from gene number and degree of connectivity through periodic behaviour to specific patterns of gene expression. The evolvability of increasingly complex patterns of gene expression is examined in detail. When a degree of redundancy is introduced, the average number of generations required to evolve given targets is reduced, but limits on evolution of complex gene expression patterns remain. In addition, cyclic gene expression patterns with periods that are multiples of shorter expression patterns are shown to be inherently easier to evolve than others. Constraints imposed by the template-matching nature of the AG model generate similar biases towards such expression patterns in networks in initial populations, in addition to the somewhat scale-free nature of these networks. The significance of these results on current understanding of biological evolution is discussed.

Advances in synthetic biology: on the path from prototypes to applications

Synthetic biology combines knowledge from various disciplines including molecular biology, engineering, mathematics and physics to design and build novel proteins, genetic circuits and metabolic networks. Early efforts aimed at altering the behavior of individual elements have now evolved to focus on the construction of complex networks in single-cell and multicellular systems. Recent achievements include the development of sophisticated non-native behaviors such as bi-stability, oscillations, proteins customized for biosensing, optimized drug synthesis and programmed spatial pattern formation. The de novo construction of such systems offers valuable quantitative insight into naturally occurring information processing activities. Furthermore, as the techniques for system design, synthesis and optimization mature, we will witness a rapid growth in the capabilities of synthetic systems with a wide-range of applications.

Rhythmic serotonin N-acetyltransferase mRNA degradation is essential for the maintenance of its circadian oscillation

Serotonin N-acetyltransferase (arylalkylamine N-acetyltransferase [AANAT]) is the key enzyme in melatonin synthesis regulated by circadian rhythm. To date, our understanding of the oscillatory mechanism of melatonin has been limited to autoregulatory transcriptional and posttranslational regulations of AANAT mRNA. In this study, we identify three proteins from pineal glands that associate with cis-acting elements within species-specific AANAT 3' untranslated regions to mediate mRNA degradation. These proteins include heterogeneous nuclear ribonucleoprotein R (hnRNP R), hnRNP Q, and hnRNP L. Their RNA-destabilizing function was determined by RNA interference and overexpression approaches. Expression patterns of these factors in pineal glands display robust circadian rhythm. The enhanced levels detected after midnight correlate with an abrupt decline in AANAT mRNA level. A mathematical model for the AANAT mRNA profile and its experimental evidence with rat pinealocytes indicates that rhythmic AANAT mRNA degradation mediated by hnRNP R, hnRNP Q, and hnRNP L is a key process in the regulation of its circadian oscillation.

Analyzing the biology on the system level

Although various genome projects have provided us enormous static sequence information, understanding of the sophisticated biology continues to require integrating the computational modeling, system analysis, technology development for experiments, and quantitative experiments all together to analyze the biology architecture on various levels, which is just the origin of systems biology subject. This review discusses the object, its characteristics, and research attentions in systems biology, and summarizes the analysis methods, experimental technologies, research developments, and so on in the four key fields of systems biology—systemic structures, dynamics, control methods, and design principles.

Optimizing genetic circuits by global sensitivity analysis

Artificial genetic circuits are becoming important tools for controlling cellular behavior and studying molecular biosystems. To genetically optimize the properties of complex circuits in a practically feasible fashion, it is necessary to identify the best genes and/or their regulatory components as mutation targets to avoid the mutation experiments being wasted on ineffective regions, but this goal is generally not achievable by current methods. The Random Sampling-High Dimensional Model Representation (RS-HDMR) algorithm is employed in this work as a global sensitivity analysis technique to estimate the sensitivities of the circuit properties with respect to the circuit model parameters, such as rate constants, without knowing the precise parameter values. The sensitivity information can then guide the selection of the optimal mutation targets and thereby reduce the laboratory effort. As a proof of principle, the in vivo effects of 16 pairwise mutations on the properties of a genetic inverter were compared against the RS-HDMR predictions, and the algorithm not only showed good consistency with laboratory results but also revealed useful information, such as different optimal mutation targets for optimizing different circuit properties, not available from previous experiments and modeling.

Reconstruction of cellular signalling networks and analysis of their properties

The study of cellular signalling over the past 20 years and the advent of high-throughput technologies are enabling the reconstruction of large-scale signalling networks. After careful reconstruction of signalling networks, their properties must be described within an integrative framework that accounts for the complexity of the cellular signalling network and that is amenable to quantitative modelling.

The JAK-STAT signaling network in the human B-cell: an extreme signaling pathway analysis

Large-scale models of signaling networks are beginning to be reconstructed and corresponding analysis frameworks are being developed. Herein, a reconstruction of the JAK-STAT signaling system in the human B-cell is described and a scalable framework for its network analysis is presented. This approach is called extreme signaling pathway analysis and involves the description of network properties with systemically independent basis vectors called extreme pathways. From the extreme signaling pathways, emergent systems properties of the JAK-STAT signaling network have been characterized, including 1), a mathematical definition of network crosstalk; 2), an analysis of redundancy in signaling inputs and outputs; 3), a study of reaction participation in the network; and 4), a delineation of 85 correlated reaction sets, or systemic signaling modules. This study is the first such analysis of an actual biological signaling system. Extreme signaling pathway analysis is a topologically based approach and assumes a balanced use of the signaling network. As large-scale reconstructions of signaling networks emerge, such scalable analyses will lead to a description of the fundamental systems properties of signal transduction networks.

Optimal identification of biochemical reaction networks

Advances in biotechnology and computer science are providing the possibility to construct mathematical models for complex biological networks and systematically understand their properties. Traditional network identification approaches, however, cannot accurately recover the model parameters from the noisy laboratory measurements. This article introduces the concept of optimal identification (OI), which utilizes a global inversion algorithm to extract the full distribution of parameters consistent with the laboratory data. In addition, OI integrates suitable computational algorithms with experimental capabilities in a closed loop fashion to maximally reduce the breadth of the extracted parameter distribution. The closed loop OI procedure seeks out the optimal set of control chemical fluxes and data observations that actively filter out experimental noise and enhance the sensitivity to the desired parameters. In this fashion, the highest quality network parameters can be attained from inverting the tailored laboratory data. The operation of OI is illustrated by identifying a simulated tRNA proofreading mechanism, in which OI provides superior solutions for all the rate constants compared with suboptimal and nonoptimal methods.

A genetic circuit amplifier: design and simulation

A genetic circuit amplifier is designed using an electronic inverting amplifier as a starting point. Two simulation methods are used to analyze circuit performance in terms of the impulse and sinusoidal responses of electrical engineering. The first method is an exact stochastic simulation based on a kinetic model of the circuit. The second method incorporates statistical thermodynamic analysis. The simulations are used to analyze amplifier performance in response to classical systems analysis stimuli: impulses and sine waves. Degradation reactions, analogous to leakage off circuit capacitors, are found to have considerable impact on circuit response. For the nonlinear gain element used in our exemplary circuit, the selection of bias level based on controlling protein degradation rate plays an important role in determining circuit behavior. A parameter without electronic analog, the circuit plasmid copy number, is crucial to circuit operation. These simulations suggest that the copy number must be less than 50 for desired circuit operation.

A proposal for using the ensemble approach to understand genetic regulatory networks

Understanding the genetic regulatory network comprising genes, RNA, proteins and the network connections and dynamical control rules among them, is a major task of contemporary systems biology. I focus here on the use of the ensemble approach to find one or more well-defined ensembles of model networks whose statistical features match those of real cells and organisms. Such ensembles should help explain and predict features of real cells and organisms. More precisely, an ensemble of model networks is defined by constraints on the "wiring diagram" of regulatory interactions, and the "rules" governing the dynamical behavior of regulated components of the network. The ensemble consists of all networks consistent with those constraints. Here I discuss ensembles of random Boolean networks, scale free Boolean networks, "medusa" Boolean networks, continuous variable networks, and others. For each ensemble, M statistical features, such as the size distribution of avalanches in gene activity changes unleashed by transiently altering the activity of a single gene, the distribution in distances between gene activities on different cell types, and others, are measured. This creates an M-dimensional space, where each ensemble corresponds to a cluster of points or distributions. Using current and future experimental techniques, such as gene arrays, these M properties are to be measured for real cells and organisms, again yielding a cluster of points or distributions in the M-dimensional space. The procedure then finds ensembles close to those of real cells and organisms, and hill climbs to attempt to match the observed M features. Thus obtains one or more ensembles that should predict and explain many features of the regulatory networks in cells and organisms.

Quantitative analysis of signaling networks

The response of biological cells to environmental change is coordinated by protein-based signaling networks. These networks are to be found in both prokaryotes and eukaryotes. In eukaryotes, the signaling networks can be highly complex, some networks comprising of 60 or more proteins. The fundamental motif that has been found in all signaling networks is the protein phosphorylation/dephosphorylation cycle--the cascade cycle. At this time, the computational function of many of the signaling networks is poorly understood. However, it is clear that it is possible to construct a huge variety of control and computational circuits, both analog and digital from combinations of the cascade cycle. In this review, we will summarize the great versatility of the simple cascade cycle as a computational unit and towards the end give two examples, one prokaryotic chemotaxis circuit and the other, the eukaryotic MAPK cascade.

Bifurcation analysis of a model of the budding yeast cell cycle

We study the bifurcations of a set of nine nonlinear ordinary differential equations that describe regulation of the cyclin-dependent kinase that triggers DNA synthesis and mitosis in the budding yeast, Saccharomyces cerevisiae. We show that Clb2-dependent kinase exhibits bistability (stable steady states of high or low kinase activity). The transition from low to high Clb2-dependent kinase activity is driven by transient activation of Cln2-dependent kinase, and the reverse transition is driven by transient activation of the Clb2 degradation machinery. We show that a four-variable model retains the main features of the nine-variable model. In a three-variable model exhibiting birhythmicity (two stable oscillatory states), we explore possible effects of extrinsic fluctuations on cell cycle progression.

Topological generalizations of network motifs

Biological and technological networks contain patterns, termed network motifs, which occur far more often than in randomized networks. Network motifs were suggested to be elementary building blocks that carry out key functions in the network. It is of interest to understand how network motifs combine to form larger structures. To address this, we present a systematic approach to define "motif generalizations": families of motifs of different sizes that share a common architectural theme. To define motif generalizations, we first define "roles" in a subgraph according to structural equivalence. For example, the feedforward loop triad--a motif in transcription, neuronal, and some electronic networks--has three roles: an input node, an output node, and an internal node. The roles are used to define possible generalizations of the motif. The feedforward loop can have three simple generalizations, based on replicating each of the three roles and their connections. We present algorithms for efficiently detecting motif generalizations. We find that the transcription networks of bacteria and yeast display only one of the three generalizations, the multi-output feedforward generalization. In contrast, the neuronal network of C. elegans mainly displays the multi-input generalization. Forward-logic electronic circuits display a multi-input, multi-output hybrid. Thus, networks which share a common motif can have very different generalizations of that motif. Using mathematical modeling, we describe the information processing functions of the different motif generalizations in transcription, neuronal, and electronic networks.

Insights into the relation between mRNA and protein expression patterns: I. Theoretical considerations

Translation is a central cellular process in every organism and understanding translation from the systems (genome-wide) perspective is very important for medical and biochemical engineering applications. Moreover, recent advances in cell-wide monitoring tools for both mRNA and protein levels have necessitated the development of such a model to identify parameters and conditions that influence the mapping between mRNA and protein expression. Experimental studies show a lack of correspondence between mRNA and protein expression profiles. In this study, we describe a mechanistic genome-wide model for translation that provides mapping between changes in mRNA levels and changes in protein levels. We use our model to study the system in detail and identify the key parameters that affect this mapping. Our results show that the correlation between mRNA and protein levels is a function of both the kinetic parameters and concentration of ribosomes at the reference state. In particular, changes in concentration of free and total ribosomes in response to a perturbation; changes in initiation and elongation kinetics due to competition for aminoacyl tRNAs; changes in termination kinetics; average changes in mRNA levels in response to the perturbation; and changes in protein stability are all important determinants of the mapping between mRNA and protein expression.

Computation in gene networks

Genetic regulatory networks have the complex task of controlling all aspects of life. Using a model of gene expression by piecewise linear differential equations we show that this process can be considered as a process of computation. This is demonstrated by showing that this model can simulate memory bounded Turing machines. The simulation is robust with respect to perturbations of the system, an important property for both analog computers and biological systems. Robustness is achieved using a condition that ensures that the model equations, that are generally chaotic, follow a predictable dynamics.

The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks

Recent analysis of the structure of transcription regulation networks revealed several "network motifs": regulatory circuit patterns that occur much more frequently than in randomized networks. It is important to understand whether these network motifs have specific functions. One of the most significant network motifs is the coherent feedforward loop, in which transcription factor X regulates transcription factor Y, and both jointly regulate gene Z. On the basis of mathematical modeling and simulations, it was suggested that the coherent feedforward loop could serve as a sign-sensitive delay element: a circuit that responds rapidly to step-like stimuli in one direction (e.g. ON to OFF), and at a delay to steps in the opposite direction (OFF to ON). Is this function actually carried out by feedforward loops in living cells? Here, we address this experimentally, using a system with feedforward loop connectivity, the L-arabinose utilization system of Escherichia coli. We measured responses to step-like cAMP stimuli at high temporal resolution and accuracy by means of green fluorescent protein reporters. We show that the arabinose system displays sign-sensitive delay kinetics. This type of kinetics is important for making decisions based on noisy inputs by filtering out fluctuations in input stimuli, yet allowing rapid response. This information-processing function may be performed by the feedforward loop regulation modules that are found in diverse systems from bacteria to humans.

Structure and function of the feed-forward loop network motif

Engineered systems are often built of recurring circuit modules that carry out key functions. Transcription networks that regulate the responses of living cells were recently found to obey similar principles: they contain several biochemical wiring patterns, termed network motifs, which recur throughout the network. One of these motifs is the feed-forward loop (FFL). The FFL, a three-gene pattern, is composed of two input transcription factors, one of which regulates the other, both jointly regulating a target gene. The FFL has eight possible structural types, because each of the three interactions in the FFL can be activating or repressing. Here, we theoretically analyze the functions of these eight structural types. We find that four of the FFL types, termed incoherent FFLs, act as sign-sensitive accelerators: they speed up the response time of the target gene expression following stimulus steps in one direction (e.g., off to on) but not in the other direction (on to off). The other four types, coherent FFLs, act as sign-sensitive delays. We find that some FFL types appear in transcription network databases much more frequently than others. In some cases, the rare FFL types have reduced functionality (responding to only one of their two input stimuli), which may partially explain why they are selected against. Additional features, such as pulse generation and cooperativity, are discussed. This study defines the function of one of the most significant recurring circuit elements in transcription networks.

Reconstructing metabolic flux vectors from extreme pathways: defining the alpha-spectrum

The move towards genome-scale analysis of cellular functions has necessitated the development of analytical (in silico) methods to understand such large and complex biochemical reaction networks. One such method is extreme pathway analysis that uses stoichiometry and thermodynamic irreversibly to define mathematically unique, systemic metabolic pathways. These extreme pathways form the edges of a high-dimensional convex cone in the flux space that contains all the attainable steady state solutions, or flux distributions, for the metabolic network. By definition, any steady state flux distribution can be described as a nonnegative linear combination of the extreme pathways. To date, much effort has been focused on calculating, defining, and understanding these extreme pathways. However, little work has been performed to determine how these extreme pathways contribute to a given steady state flux distribution. This study represents an initial effort aimed at defining how physiological steady state solutions can be reconstructed from a network's extreme pathways. In general, there is not a unique set of nonnegative weightings on the extreme pathways that produce a given steady state flux distribution but rather a range of possible values. This range can be determined using linear optimization to maximize and minimize the weightings of a particular extreme pathway in the reconstruction, resulting in what we have termed the alpha-spectrum. The alpha-spectrum defines which extreme pathways can and cannot be included in the reconstruction of a given steady state flux distribution and to what extent they individually contribute to the reconstruction. It is shown that accounting for transcriptional regulatory constraints can considerably shrink the alpha-spectrum. The alpha-spectrum is computed and interpreted for two cases; first, optimal states of a skeleton representation of core metabolism that include transcriptional regulation, and second for human red blood cell metabolism under various physiological, non-optimal conditions.

Inferring genetic networks and identifying compound mode of action via expression profiling

The complexity of cellular gene, protein, and metabolite networks can hinder attempts to elucidate their structure and function. To address this problem, we used systematic transcriptional perturbations to construct a first-order model of regulatory interactions in a nine-gene subnetwork of the SOS pathway in Escherichia coli. The model correctly identified the major regulatory genes and the transcriptional targets of mitomycin C activity in the subnetwork. This approach, which is experimentally and computationally scalable, provides a framework for elucidating the functional properties of genetic networks and identifying molecular targets of pharmacological compounds.

Dynamic responses of protein homeostatic regulatory mechanisms to perturbations from steady state

Nineteen hypothetical protein homeostatic regulatory mechanisms were constructed and analysed in terms of the rate at which they recovered from a perturbation in the steady-state concentration of any component. Systems were constructed to symbolize transcription/translation processes of the average protein from Escherichia coli (1000 copies of protein P along with 1 gene G per cell). In some model systems, G catalysed the synthesis of P directly, while in others G catalysed the synthesis of mRNA (called M), and M catalysed the synthesis of P in a subsequent step. Recovery rates for each regulatory mechanism were obtained by generating the corresponding system of differential equations, linearizing the system about the steady state, and determining eigenvalues of the associated coefficient matrix. The optimal rate of recovery for a given mechanism, R(D), was determined by combining random and gradient search approaches to find rate constants for which the system recovered fastest. Regulatory elements that improved dynamic regulation were identified. These consisted of negative feedback relationships that involved P binding to either G (to shut off the synthesis of P) or M (to stimulate its degradation). Regulation improved as increasing numbers of P's bound to either G or M; however, the binding to M was more effective. In other mechanisms PP dimers bound G. Dimer-binding mechanisms were roughly twice as effective in terms of regulation as those that bound P monomers. The effect of linking two regulatory "modules" was also investigated. Linking had no effect on R(D), but optimal rate constants for the linked system were similar to those of the unlinked modules, suggesting that it may be feasible to construct regulatory networks by linking individual modules of this type.

Response delays and the structure of transcription networks

Sensory transcription networks generally control rapid and reversible gene expression responses to external stimuli. Developmental transcription networks carry out slow and irreversible temporal programs of gene expression during development. It is important to understand the design principles that underlie the structure of sensory and developmental transcription networks. Cascades, which are chains of regulatory reactions, are a basic structural element of transcription networks. When comparing databases of sensory and developmental transcription networks, a striking difference is found in the distribution of cascade lengths. Here, we suggest that delay times in the responses of the network present a design constraint that influences the network architecture. We experimentally studied the response times in simple cascades constructed of well-characterized repressors in Escherichia coli. Accurate kinetics at high temporal resolution was measured using green fluorescent protein (GFP) reporters. We find that transcription cascades can show long delays of about one cell-cycle time per cascade step. Mathematical analysis suggests that such a delay is characteristic of cascades that are designed to minimize the response times for both turning-on and turning-off gene expression. The need to achieve rapid reversible responses in sensory transcription networks may help explain the finding that long cascades are very rare in databases of E.coli and Saccharomyces cerevisiae sensory transcription networks. In contrast, long cascades are common in developmental transcription networks from sea urchin and from Drosophila melanogaster. Response delay constraints are likely to be less important for developmental networks, since they control irreversible processes on the timescale of cell-cycles. This study highlights a fundamental difference between the architecture of sensory and developmental transcription networks.

On schemes of combinatorial transcription logic

Cells receive a wide variety of cellular and environmental signals, which are often processed combinatorially to generate specific genetic responses. Here we explore theoretically the potentials and limitations of combinatorial signal integration at the level of cis-regulatory transcription control. Our analysis suggests that many complex transcription-control functions of the type encountered in higher eukaryotes are already implementable within the much simpler bacterial transcription system. Using a quantitative model of bacterial transcription and invoking only specific protein-DNA interaction and weak glue-like interaction between regulatory proteins, we show explicit schemes to implement regulatory logic functions of increasing complexity by appropriately selecting the strengths and arranging the relative positions of the relevant protein-binding DNA sequences in the cis-regulatory region. The architectures that emerge are naturally modular and evolvable. Our results suggest that the transcription regulatory apparatus is a "programmable" computing machine, belonging formally to the class of Boltzmann machines. Crucial to our results is the ability to regulate gene expression at a distance. In bacteria, this can be achieved for isolated genes via DNA looping controlled by the dimerization of DNA-bound proteins. However, if adopted extensively in the genome, long-distance interaction can cause unintentional intergenic cross talk, a detrimental side effect difficult to overcome by the known bacterial transcription-regulation systems. This may be a key factor limiting the genome-wide adoption of complex transcription control in bacteria. Implications of our findings for combinatorial transcription control in eukaryotes are discussed.

Frequency domain analysis of noise in autoregulated gene circuits

We describe a frequency domain technique for the analysis of intrinsic noise within negatively autoregulated gene circuits. This approach is based on the transfer function around the feedback loop (loop transmission) and the equivalent noise bandwidth of the system. The loop transmission, T, is shown to be a determining factor of the dynamics and the noise behavior of autoregulated gene circuits, and this T-based technique provides a simple and flexible method for the analysis of noise arising from any source within the gene circuit. We show that negative feedback not only reduces the variance of the noise in the protein concentration, but also shifts this noise to higher frequencies where it may have a negligible effect on the noise behavior of following gene circuits within a cascade. This predicted effect is demonstrated through the exact stochastic simulation of a two-gene cascade. The analysis elucidates important aspects of gene circuit structure that control functionality, and may provide some insights into selective pressures leading to this structure. The resulting analytical relationships have a simple form, making them especially useful as synthetic gene circuit design equations. With the exception of the linearization of Hill kinetics, this technique is general and may be applied to the analysis or design of networks of higher complexity. This utility is demonstrated through the exact stochastic simulation of an autoregulated two-gene cascade operating near instability.

Constraints-based models: regulation of gene expression reduces the steady-state solution space

Constraints-based models have been effectively used to analyse, interpret, and predict the function of reconstructed genome-scale metabolic models. The first generation of these models used "hard" non-adjustable constraints associated with network connectivity, irreversibility of metabolic reactions, and maximal flux capacities. These constraints restrict the allowable behaviors of a network to a convex mathematical solution space whose edges are extreme pathways that can be used to characterize the optimal performance of a network under a stated performance criterion. The development of a second generation of constraints-based models by incorporating constraints associated with regulation of gene expression was described in a companion paper published in this journal, using flux-balance analysis to generate time courses of growth and by-product secretion using a skeleton representation of core metabolism. The imposition of these additional restrictions prevents the use of a subset of the extreme pathways that are derived from the "hard" constraints, thus reducing the solution space and restricting allowable network functions. Here, we examine the reduction of the solution space due to regulatory constraints using extreme pathway analysis. The imposition of environmental conditions and regulatory mechanisms sharply reduces the number of active extreme pathways. This approach is demonstrated for the skeleton system mentioned above, which has 80 extreme pathways. As regulatory constraints are applied to the system, the number of feasible extreme pathways is reduced to between 26 and 2 extreme pathways, a reduction of between 67.5 and 97.5%. The method developed here provides a way to interpret how regulatory mechanisms are used to constrain network functions and produce a small range of physiologically meaningful behaviors from all allowable network functions.

Genome-scale microbial in silico models: the constraints-based approach

Genome sequencing and annotation has enabled the reconstruction of genome-scale metabolic networks. The phenotypic functions that these networks allow for can be defined and studied using constraints-based models and in silico simulation. Several useful predictions have been obtained from such in silico models, including substrate preference, consequences of gene deletions, optimal growth patterns, outcomes of adaptive evolution and shifts in expression profiles. The success rate of these predictions is typically in the order of 70-90% depending on the organism studied and the type of prediction being made. These results are useful as a basis for iterative model building and for several practical applications.

An ensemble method for identifying regulatory circuits with special reference to the qa gene cluster of Neurospora crassa

A chemical reaction network for the regulation of the quinic acid (qa) gene cluster of Neurospora crassa is proposed. An efficient Monte Carlo method for walking through the parameter space of possible chemical reaction networks is developed to identify an ensemble of deterministic kinetics models with rate constants consistent with RNA and protein profiling data. This method was successful in identifying a model ensemble fitting available RNA profiling data on the qa gene cluster.

Genetic "code": representations and dynamical models of genetic components and networks

Dynamical modeling of biological systems is becoming increasingly widespread as people attempt to grasp biological phenomena in their full complexity and make sense of an accelerating stream of experimental data. We review a number of recent modeling studies that focus on systems specifically involving gene expression and regulation. These systems include bacterial metabolic operons and phase-variable piliation, bacteriophages T7 and lambda, and interacting networks of eukaryotic developmental genes. A wide range of conceptual and mathematical representations of genetic components and phenomena appears in these works. We discuss these representations in depth and give an overview of the tools currently available for creating and exploring dynamical models. We argue that for modeling to realize its full potential as a mainstream biological research technique the tools must become more general and flexible, and formal, standardized representations of biological knowledge and data must be developed.

Transcriptional regulation in constraints-based metabolic models of Escherichia coli

Full genome sequences enable the construction of genome-scale in silico models of complex cellular functions. Genome-scale constraints-based models of Escherichia coli metabolism have been constructed and used to successfully interpret and predict cellular behavior under a range of conditions. These previous models do not account for regulation of gene transcription and thus cannot accurately predict some organism functions. Here we present an in silico model of the central E. coli metabolism that accounts for regulation of gene expression. This model accounts for 149 genes, the products of which include 16 regulatory proteins and 73 enzymes. These enzymes catalyze 113 reactions, 45 of which are controlled by transcriptional regulation. The combined metabolic/regulatory model can predict the ability of mutant E. coli strains to grow on defined media as well as time courses of cell growth, substrate uptake, metabolic by-product secretion, and qualitative gene expression under various conditions, as indicated by comparison with experimental data under a variety of environmental conditions. The in silico model may also be used to interpret dynamic behaviors observed in cell cultures. This combined metabolic/regulatory model is thus an important step toward the goal of synthesizing genome-scale models that accurately represent E. coli behavior.

Model for a robust neural integrator

Integrator circuits in the brain show persistent firing that reflects the sum of previous excitatory and inhibitory inputs from external sources. Integrator circuits have been implicated in parametric working memory, decision making and motor control. Previous work has shown that stable integrator function can be achieved by an excitatory recurrent neural circuit, provided synaptic strengths are tuned with extreme precision (better than 1% accuracy). Here we show that integrator circuits can function without fine tuning if the neuronal units have bistable properties. Two specific mechanisms of bistability are analyzed, one based on local recurrent excitation, and the other on the voltage-dependence of the NMDA (N-methyl-D-aspartate) channel. Neither circuit requires fine tuning to perform robust integration, and the latter actually exploits the variability of neuronal conductances.

Computational cell biology: spatiotemporal simulation of cellular events

The field of computational cell biology has emerged within the past 5 years because of the need to apply disciplined computational approaches to build and test complex hypotheses on the interacting structural, physical, and chemical features that underlie intracellular processes. To meet this need, newly developed software tools allow cell biologists and biophysicists to build models and generate simulations from them. The construction of general-purpose computational approaches is especially challenging if the spatial complexity of cellular systems is to be explicitly treated. This review surveys some of the existing efforts in this field with special emphasis on a system being developed in the authors' laboratory, Virtual Cell. The theories behind both stochastic and deterministic simulations are discussed. Examples of respective applications to cell biological problems in RNA trafficking and neuronal calcium dynamics are provided to illustrate these ideas.

Modeling and simulation of genetic regulatory systems: a literature review

In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rule-based formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.