Workshop 2: Dynamics of signal transduction and of gene-protein regulatory networks: Titles & Abstracts
Modeling the dynamics of complex biological systems is challenging even when well-established biochemical frameworks are applicable. In the case of regulatory and signaling systems that include heterogeneous components and interactions, and/or are sparsely documented in terms of quantitative information, modeling is often thought impossible. This talk will argue for the usefulness of a discrete dynamic framework in incorporating qualitative interaction information into a predictive model. I will focus on a model of the signaling network responsible for the survival and long-term competence of cytotoxic T cells in the blood cancer T-LGL leukemia. Our model suggests that the persistence of IL-15 and PDGF is sufficient to reproduce all known deregulations in leukemic T-LGL. It also predicts the key nodes whose (in)activity is necessary to induce the apoptosis of T cells and reverse the disease. We experimentally validated several of these predictions. The model will be useful in identifying potential therapeutic targets for T-LGL leukemia and generating long-term competent CTL necessary for tumor and cancer vaccine development. The success of this and other similar models indicates that network-based discrete dynamic modeling is a promising framework that allows system-level analysis and predictions that would not be possible using traditional methods.
Reference: R. Zhang, M. V. Shah, J. Yang, S. B. Nyland, X. Liu, J. K. Yun, R. Albert and T. P. Loughran, Jr., Network Model of Survival Signaling in LGL Leukemia, PNAS 105, 16308-16313 (2008).
Along with the growth of technologies allowing accurate visualization of biochemical reactions to the scale of individual molecules has arisen an appreciation of the role of statistical fluctuations in intracellular biochemistry. The stochastic nature of metabolism can no longer be ignored. It can be probed empirically, and theoretical studies have established its importance. Traditional methods for modeling stochastic biochemistry are derived from an elegant and physically satisfying theory developed by Gillespie. However, although Gillespie's algorithm and its derivatives efficiently model small-scale systems, complex networks are harder to manage on easily available computer systems. Here we present a novel method of simulating stochastic biochemical networks using discrete events simulation techniques borrowed from manufacturing production systems. The method is very general and can be mapped to an arbitrarily complex network. As an illustration, we apply the technique to the glucose phosphorylation steps of the Embden-Meyerhof-Parnas pathway in E. coli. We show that a deterministic version of the discrete event simulation reproduces the behavior of an analogous deterministic differential equation model. The stochastic version of the same model predicts that catastrophic bottlenecks in the system are more likely than one would expect from deterministic theory.
The activity of a protein can be reversibly modulated by post-translational, covalent modifications, such as phosphorylation and dephosphorylation. In many cases, the modulated protein may be phosphorylated by the same kinase on many different amino acid residues. Such multisite phosphorylations may occur progressively (during a single binding event of kinase to substrate) or distributively (the kinase dissociates from its substrate after each phosphorylation reaction). If a protein is phosphorylated by a distributive multisite mechanism, then the net activity of a population of these protein molecules can be a highly nonlinear function of the ratio of activities of the kinase and phosphatase enzymes. If the multiply phosphorylated protein is embedded in a positive feedback loop with its kinase and/or phosphatase, then the network may exhibit robust bistable behavior. Using numerical simulations and bifurcation theory, we study the properties of a particular bistable reaction network motivated by the antagonistic relationship between cyclin-dependent kinase and its multiply phosphorylated target, Cdh1, which is involved in the degradation of cyclin molecules. We characterize the bistable switch in terms of (i) the mechanism of distributive phosphorylation (ordered or disordered), (ii) the number of phosphorylation sites on the target protein, (iii) the effect of phosphorylation on the target protein (abrupt or progressive inactivation), and (iv) the effects of stochastic fluctuations in small cells with limited numbers of kinase, phosphatase and target proteins.
Work done in collaboration with Orsolya Kapuy, Maria Rosa Domingo Sananes, John J. Tyson, and Bela Novak.
Why does the functioning of biological systems seem miraculous? One reason is that we do not know how to design systems that do what cells do, namely molecular computing. In contrast, we know how to design highly complex information systems. The fundamental reason for the successful evolution of information systems is the development of mathematical abstractions that enable efficient and robust design processes. In particular, Claude Shannon in his classical 1938 Master Thesis demonstrated that all Boolean functions can be computed by relay circuits, leading to the development of digital logic and resulting in computer chips with over a billion transistors. Motivated by the challenge of analyzing stochastic gene regulatory networks, we generalize the notion of logic design to probabilistic logic design. Specifically, we consider relay circuits where deterministic switches are replaced by probabilistic switches. We present efficient algorithms for synthesizing probabilistic relay circuits that can compute probability distributions.
The aim of this study is to construct a general mathematical model which can be applicable to study immune-surveillance of tissue specific tumors. Mathematical models of tumor-immune dynamics, built upon results from experiments on transgenic mice have added to our understanding of how host immune cells and cancerous cells evolve and interact. Our mathematical model describes immune-surveillance of tumors by cytotoxic T lymphocytes (CTLs). We use CTL numbers from three transgenic mice that can autonomously develop tumors by activation of specific promoters that lead to expression of the inserted Simian virus 40 (SV40) large T antigen (Tag). We use the qualitative information from experiments to develop a quantitative mathematical model in order to provide an insight into the rate constants of CTL activation and apoptosis leading to the tissue specific response and immune-dominance of CTL clones. We also study the dynamics of Tag transformed cells in wild-type mice as a control to our tumor simulations. Finally, we use our model to study the tolerance of CTLs in these mice.
Taking into account recent years' advances in the field of cellular biology, we have proposed to identify under what conditions Kauffmann’s hypothesis that living organism cells operate in a region bordering order and chaos holds. This property confers to living organisms both the stability to resist transcriptional errors and external disruptions, and, at the same time, the flexibility necessary to evolution. We studied two particular cases of genetic regulatory networks found in literature in terms of complex dynamical systems derived from the original RBN model. In order to do that, we compared the behavior of these systems under the original update function and the novel additive function that we believe is closer to the actual role of living organisms. We successfully identify contexts in which our model’s response can be interpreted as critical, thus most biologically plausible. Results of numerical simulations show that there exist values in both update functions that allow the models to operate in the critical region, and that these values are comparable in two different real-life GRNs.
Remodeling of the actin cytoskeleton is recognized to be an important process underlying eukaryotic cell motility. However, regulation of the spatio-temporal dynamics of actin is essential in order for the cell to orient and move correctly in response to chemoattractive stimuli. Here I will survey efforts in my group over the last years to understand this process. We show that a module of switch-like proteins (Rho GTPases) can set up robust cell polarity, leading to increased actin nucleation (via Arp2/3) at a cell "front" and increased contraction at the opposite pole ("rear"). A combination of 2D cell motility simulations and analytic treatment of reduced versions of the mathematical model lead to insights about the underlying mechanism. We also study how a membrane lipid module (phosphoinositides) interacts in the signaling network, and how this can fine-tune the response, eliminating confusion due to multiple conflicting stimuli. This talk represents work joint with Adriana Dawes, Alexandra Jilkine, Stan Maree, Yoichiro Mori, Veronica Grieneisen, and Ben Vanderlei.
An important property of Saccharomyces cerevisiae (yeast) is their ability to propagate as haploids. Haploid *a*- and /a/-cells secrete type-specific pheromones that promote cell fusion and the formation of an *a*//a/ diploid. Pheromone stimulation leads to a well-defined series of events required for mating, including readily-assayed responses, such as MAPK phosphorylation, new gene transcription and morphological changes. In particular, *a*-cells undergo chemotrophic growth in which they elongate in the direction of increasing pheromone concentration. Thus yeast is an attractive model system for studying cell differentiation and gradient sensing. We present recent computational and experimental investigations designed to elucidate the signaling events that lead to chemotrophic growth.
A coupled system is a network of interacting dynamical systems. In this talk we focus on networks where all nodes represent identical systems of differential equations and we discuss only time periodic solutions. For these networks we discuss those features of solutions that are the product of network architecture?
Cell cycle events in eukaryotes are regulated by periodic activation and inactivation of a family of cyclin–dependent kinases (Cdks). Entry into mitosis is initiated by accumulation of Cdk in complexes with B-type cyclins, and exit from mitosis requires inactivation of these Cdk-cyclin complexes and dephosphorylation of Cdk targets. In budding yeast, the Cdks are inactivated by Cdc20- and Cdh1-dependent proteolysis of Clb1 and Clb2 and by binding with inhibitors Sic1 and Cdc6. Cdc14 is an essential phosphatase promoting mitotic exit, it activates Cdh1 and it dephosphorylates Cdk targets. Cdc14 is kept inactive by forming a complex with Net1 protein in the nucleolus, and it is released from the complex when Net1 becomes phosphorylated upon mitotic exit. We have developed a deterministic ODE model for the control of Cdc14 release as budding yeast cells exit from mitosis. Our model provides a rigorous account of the factors affecting the dual exit pathways, called FEAR (Cdc14 early anaphase release) and MEN (mitotic exit network). The model captures the dynamics of mitotic exit in wild-type and in all 100+ mutant yeast cells studied up to date. We propose a novel mechanism for multiphosphorylation of Net1 by several kinases: Cdk, Cdc5 (Polo) and Dbf2/Mob1 (through activation by Cdc15). Understanding how Polo-like kinase fit into the exit pathway is important because Polo-like kinase is being actively pursued as a therapeutic target in the treatment of human cancer. The model also clarifies the mitotic exit functions of separase (Esp1): its non-catalytic function in inhibiting PP2A and thereby promoting activation of the FEAR pathway, and its catalytic function in degrading cohesins and thereby promoting sister chromatid separation at anaphase I, spindle elongation at anaphase II, and MEN activation in telophase.
Historically, intracellular signal transduction has been characterized in terms of linear pathways, exemplified by the canonical mitogen-activated protein kinase cascades; e.g., the Ras -> Raf -> MEK -> extracellular signal-regulated kinase (ERK) pathway in mammals. Our conceptual understanding of signal transduction networks now includes more complex interactions, including those between the classically defined pathways (crosstalk) and those responsible for feedback regulation or reinforcement; however, little has been done to move beyond hand-waving models of signaling networks to systematically quantify the relative magnitudes of classical, crosstalk, and feedback interactions.
Through quantitative measurements and computational modeling, we recently characterized crosstalk mechanisms in the platelet-derived growth factor (PDGF) receptor signaling network, in which phosphoinositide 3-kinase (PI3K) and Ras/ERK pathways are prominently activated [Wang C-C, Cirit M, Haugh JM. PI3K-dependent crosstalk interactions converge with Ras as quantifiable inputs integrated by Erk. Mol Syst Biol, 5: 246 (2009)]. Unique in its coverage of time, dose, and molecular perturbation conditions, our data set was comprised of >3,000 biochemical measurements, yielding > 150 processed data points that were used to constrain the accompanying model.
We have since refined this approach with additional measurements that push even further the boundary of data-driven kinetic modeling. With nearly double the number of data constraints, we have identified and parsed four distinct modes of negative regulation affecting ERK signaling and pinned down with even greater precision the magnitude of crosstalk from PI3K-dependent signaling to the Ras/ERK pathway. We further demonstrate that the current model is a predictive tool that successfully forecasts outcomes of experiments that perturb the feedback structure of the network. The goal now is to map the finer, molecular-level details (which have yet to be measured quantitatively) onto the dynamic, system-level properties that we have characterized.
Combinatorial regulation of gene expression is ubiquitous in eukaryotes with variety of inputs converging on regulatory control elements both adjacent and distant from the promoter. The dynamic properties of these elements are crucial for understanding the functionality of genetic networks regulating cell development and differentiation. We propose a method to quantitatively characterize the regulatory output of distant enhancers with a biophysical approach that recursively uses experimental results from transcriptional reporter libraries to determine free energies of protein-protein and protein-DNA interactions. We apply this method to model the Scl-Gata2-Fli1 triad - a network module playing an important role in cell fate specification of the hematopoietic stem cells. The model shows triad module is inherently bistable with irreversible transitions in the presence of physiologically relevant signals such as Notch, Bmp4 and Gata1. We use the model to predict the sensitivity of the network to mutations and indicate possible role of the triad architecture in filtering transient stimuli. These results lead us to a hypothesis about the role of the triad module in the hematopoietic gene regulatory network.
The kinetics and key controlling components of the Toll-Like Receptor 4(TLR4)-mediated innate immune response to infectious stimuli are poorly understood. Using computational modeling and live cell imaging, we investigated how different Lipopolysaccharide (LPS) dosage levels elicit different immune responses in individual immune cells. Due to the complexity of the TLR4 signaling pathways, our study was focused on the LPS-induced nucleo-cytoplasmic translocation dynamics of NF-kB, one of endpoint proteins in the TLR4 signaling pathways. An integrative approach of computational modeling and time-lapse fluorescence microscopy was employed to elucidate the kinetic mechanisms of NF-kB translocation dynamics in single cells. We built a stochastic model of NF-kB signaling pathway tightly regulated by multiple negative and positive feedback loops and stably constructed a green fluorescence reporter of RelA (a subunit of heterodimeric NF-kB) into murine macrophages for real time monitoring of the nulceo-cytoplasmic translocation of NF-kB in individual live cells. Computationally, we predicted that the NF-kB nucleo-cytoplasmic translocation would be oscillatory in LPS-stimulated individual cells, mainly due to intrinsic stochasticity in the circuitry of NF-κB signaling pathway. Our second prediction was that the extrinsic noise-originated cell-to-cell variability, modeled as the different kinetic conditions of the individual cells prior to the LPS stimulation, would diversify the shuttling patterns of NF-kB. Both of our model predictions were experimentally validated: Upon high LPS dosage stimulation, NF-kB translocation dynamics were predominantly oscillatory among the cells while upon low LPS dosage stimulation, NF-kB shuttling patterns were highly heterogeneous. While the biological functionality of NF-kB oscillatory shuttling remains to be proven, this present systems biology study of LPS-induced NF-kB dynamics revealed us the highly stochastic and heterogeneous/individualist nature of the immune response in single cells.
The DNA replication-division cycle of eukaryotic cells is controlled by a complex network of regulatory proteins, called cyclin-dependent kinases, and their activators and inhibitors. Although comprehensive and accurate deterministic models of the control system are available for yeast cells, reliable stochastic simulations have not been carried out because the full reaction network has yet to be expressed in terms of elementary reaction steps. As a first step in this direction, we present a simplified version of the control system that is suitable for exact stochastic simulation of intrinsic noise due to molecular fluctuations and extrinsic noise due to unequal division. The model is consistent with many characteristic features of noisy cell cycle progression in yeast populations, including the observation that mRNAs are present in very low abundance (approximately 1 mRNA molecule per cell for each expressed gene). For the control system to operate reliably at such low mRNA levels, some specific mRNAs in our model must have very short half-lives (< 1 min). If these mRNA molecules are longer lived (say, 2 min), then the intrinsic noise in our simulations is too large, and there must be some additional noise-suppression mechanisms at work in cells.
In cellular signal transduction, information in external stimulus is coded as temporal patterns of signaling activities; however, temporal coding mechanism has been poorly investigated. Here we show how the Akt pathway, involved in cell growth, serves as low-pass filters and specifically transfers temporal information of upstream signals to downstream. We modeled the epidermal growth factor (EGF)-dependent Akt pathway in PC12 cells based on experimental results. We found counterintuitive results that peak amplitudes of receptor and downstream phosphorylation are decoupled; weak sustained EGF receptor phosphorylation, rather than strong transient phosphorylation, strongly induced S6 phosphorylation, a downstream molecule of Akt. By use of frequency response analysis, we found that the Akt pathway exhibits low-pass filter characteristics, and that this characteristic of the Akt pathway can explain the decoupling effect of peak amplitudes between receptor and downstream phosphorylation. Because low-pass filter characteristic is an intrinsic feature of biochemical reactions, our finding raises a caution in interpreting biological data without temporal information.
Macrophages have built-in negative and positive regulatory loops that finely control the expression of pro- and anti-inflammatory genes. In particular, our laboratory has revealed that both feed forward and feedback controls exist in macrophages that regulate NFkB-mediated expression of pro-inflammatory cytokines, as well as nuclear-receptor (NR) mediated expression of anti-inflammatory genes. Furthermore, the cross-inhibition of NFkB pathway and NR pathway could potentially give rise to two bi-stable anti- and pro-inflammatory states. Knocking-out of several key molecular players can skew the bi-stable state to the direction of anti-inflammatory flavor, and serve as viable targets for the development of anti-inflammatory therapies.
In this talk, I will present a Goldbeter-Koshland type model to study the open signaling cascade with forward activation. Three different regimes related to the ultrasensitivity are clearly defined. When the cascade is sufficiently long, the steady states in the downstream cycles exhibit a limiting behavior. Meanwhile, a temporal switch-like behavior of OFF-ON-OFF type is revealed in the pre-ultrasensitivity regime without any feedback circuitry. A necessary condition for such a switch-like behavior is provided. The analytical results may provide a clue for experimentalist to design the experiments.
In the modeling and design of biological systems, one often wishes to capture aspects of qualitative dynamics which underlie the observed or desired physiology. For instance, in the context of building circadian rhythm models, one would like to capture aspects of the experimental data such as the phase relationship between the peaking times of the observed genes. In the context of synthetic biology, an example would be to build a genetic circuit for a multicellular system which when triggered by a diffusing input source could give rise to a desired spatial pattern. Within the context of disease modeling and therapeutics treatment, questions relating to qualitative dynamics enter as well: for instance, given a chronic stress condition manifested as an irreversibility of a bistable switch, one may ask what are the minimal interventions that would allow the system to revert from having a dynamical disease, to a healthy state?
Such questions of mapping qualitative dynamics to biochemical mechanisms are essentially problems of the inverse type, which often have the characteristics of being ill-posed as well as computationally demanding. For the above mentioned examples, we first show how to derive the appropriate forward and adjoint formulations which would allow for efficient solution techniques. Furthermore, in order to obtain reliable solutions we stabilize these inverse problems using sparsity-promoting regularization. This regularization strategy has the additional advantage of giving rise to sparse solutions, thereby identifying important "knobs" of the network which allow one to nagivate within a desired space of qualitative features.
Even the simplest biochemical networks often have more degrees of freedoms than one can (or should!) analyze. Can we ever hope to do the physicists' favorite trick of coarse-graining, simplifying the networks to a much smaller set of effective dynamical variables that still capture the relevant aspects of the kinetics? I will argue then that methods of statistical physics and statistical model selection provide hints at the existence of rigorous coarse-grained methodologies in modeling biological information processing systems, allowing to identify features of the systems that are relevant to their functions. While a general solution is still far away, I will focus on two specific examples illustrating the two approaches. First, for a general stochastic network exhibiting the kinetic proofreading behavior, I will show that the microscopic parameters of the system are largely important only to the extent that they contribute to a single aggregate parameter, the mean first passage time through the network. Thus a phenomenological model with a single parameter does a good job explaining all of the observable data generated by this complex system. Second, building an "as simple as possible, but not simpler" model of heat avoidance response of C. elegans, we show that a phenomenological model with a single hidden "memory" node is capable of reproducing all of the observed data, hinting strongly that the worm's thermotaxis behavior resembles that of a chemotaxing E. coli.
Integration of advances in genome sequencing and analysis, network biology, structural biology and computational chemistry may have the potential to revolutionize drug discovery and may allow customization of drug therapy. Here we describe an initial example for this potential using bacterial infections as a case study.
Computational and experimental studies together have yielded a compendium of insights into the signal transduction involved in eukaryotic cell cycle regulation. Our present work aims to describe the biochemical mechanisms that underlie mitotic progression, while also uncovering the molecular basis of the developmental transitions that accompany early embryogenesis. Some of these studies are focused upon understanding the dynamical behavior of the (cyclin-dependent kinase 1) CDK1 - (anaphase-promoting complex) APC oscillator - the driving force behind the rapid and unimpeded cleavages that occur prior to the midblastula transition (MBT) in the early embryo of Xenopus laevis. While protein synthesis, proteolysis, and phosphorylation-dephosphorylation events drive this system in general, it remains unclear how these inputs together confer the overall output of this oscillator. Indeed, current mathematical models do not reproduce all of the dynamic features observed during a CDK1 activity oscillation. A closer look at the Wee1-Cdc25-CDK1 module hints at the possible regulation by players that are involved in other aspects of mitotic control, and recent evidence has confirmed relationships between these regulators. Might the involvement of other M-phase kinases in the activation of CDK1 serve to tune the output of this kinase as a function of cyclin stimulus? To answer this question, we have initiated a systematic analysis of the activities of M-phase kinases in relation to the pattern of cyclin stimulus and CDK1 activity in Xenopus egg extracts. Our overall goal is to map and dissect experimentally the connections of the embryonic M-phase activation network, and to gather and apply these quantitative details towards the refinement of our mathematical model of the CDK1-APC oscillatory system.
Prior work on the dynamics of Boolean networks, including analysis of the state space attractors and the basin of attraction corresponding to each attractor, has mainly focused on synchronous update of the nodes’ states. Although the simplicity of synchronous updating makes it very attractive, it fails to take into account the variety of time scales associated with different types of biological processes. Asynchronous Boolean models overcome this limitation but add new levels of complexity. While several different asynchronous update methods have been proposed in the literature, there have not been any systematic comparisons of the dynamic behaviors displayed by the same system under different update methods. Here we fill this gap by carrying out a thorough comparative study on the dynamic behavior of a previously proposed Boolean model of the abscisic acid signal transduction network in plants. To this end, we compare the attractors obtained from synchronous and three different asynchronous updating schemes, both in the case of the unperturbed (wild-type) and perturbed (node-disrupted) systems. We find that the wild-type system possesses two limit cycles as well as a fixed point under synchronous update, whereas it has only a fixed point under random order and general asynchronous models. The deterministic asynchronous model, however, admits attractors other than fixed points. Interestingly, in the case of disruption of one particular node in the network the other two asynchronous models also lead to an extended attractor. Our study is a combination of theoretical analysis, such as solution of scalar equations and Markov chain techniques, and numerical simulations. Overall, our work provides a road map on how theoretical and computational analysis of Boolean network models can be combined to predict the dynamic patterns of a biological system under various internal and environmental perturbations.
In consideration of biological design principles, it is now generally recognized that a central role must be played by system robustness - that is, by the capacity for sustained and precise function even in the presence of environmental disruption. Lacking, however, is a clear picture of common network features that otherwise-different biochemical modules might incorporate to ensure the robustness required. Our general interest is in what we call absolute concentration-robustness (ACR): A biochemical system is said to exhibit ACR relative to an active molecular species if the concentration of that species is identical in every positive steady-state the system might admit. In this way, the function of an ACR-possessing system can be protected even against large changes in the overall supply of the system's components - changes that might arise from cell-to-cell variability or from variations in the same cell over time. Here, mathematics and chemistry come together to identify quite subtle structural attributes that will impart ACR to any mass action network possessing them. For example, these core network features provide a common source for the strong concentration robustness observed experimentally in the markedly-different E. coli EnvZ/OmpR osmoregulation and IDHKP/IDH glyoxylate-bypass-control systems. We believe that the same structural foundation will undergird a large variety of biochemical networks for which strong concentration robustness is essential.
Motile bacteria navigate in chemical gradients by performing temporal comparisons of ligand concentrations. In the adapted state with no gradients present, cells perform a random walk that consists of runs interrupted by short tumbles, which allows them to efficiently explore their environment. Such random work is ensured by a precise adjustment of the tumble signal, intracellular phosphorylation level of the response regulator CheY, to the sensitive range of flagellar motor. In presence of a gradient, the random walk becomes biased: an increase in attractant concentration - as experienced by cells swimming up the gradient - rapidly suppresses tumbles and thus results in longer runs in the favourable direction. This initial response is counteracted on a longer time scale by an adaptation system that regulates pathway activity through chemoreceptor methylation. Difference in the time scales of initial response and subsequent adaptation allows a swimming cell to compare concentrations at different points in the gradient.
Chemotactic performance of bacteria is affected by several types of noise, from stochastic ligand binding to Brownian motion to stochastic protein expression, and much of the pathway evolution appears to have been driven by the selection for robust signal processing under these conditions. We combined experiments, bioinformatics and computer modelling to investigate effects of the most prominent type of noise, stochastic variations in the levels of chemotaxis proteins in a population. We showed that such gene expression noise is compensated both by the robust pathway topology and by the chromosomal organization of chemotaxis genes. At the same time, the pathway also appears to utilize noise in the expression of adaptation enzymes to broaden the range of environmental gradients that a chemotactic population as a whole can follow.
The DNA replication-division cycle in eukaryotic cells is controlled by a complex network of regulatory proteins (called cyclin-dependent kinases, Cdk's) and their activators and inhibitors. A comprehensive deterministic model of Cdk regulation in budding yeast is available (Chen et al., 2004) that accurately accounts for the average phenotypic properties of wild-type cells and 150+ mutant strains. However, the deterministic model cannot account for the considerable variabilities in cell cycle properties that have been observed among genetically identical cells. These variabilities are due in large part to small numbers of molecules in yeast cells: 100's – 1000's of molecules of each specific protein and only 10's of molecules of each specific mRNA species per yeast cell. How can the cell cycle function reliably in the face of the large intrinsic molecular fluctuations implied by such numbers? We have addressed this question by constructing a realistic model (on the scale: toy < realistic < comprehensive) of Cdk regulation in budding yeast that is suitable for exact stochastic simulation by Gillepie's algorithm. The results of this model compare favorably to the extensive statistical properties of budding yeast cell cycle progression collected recently in Fred Cross's laboratory (Di Talia et al., 2007; Skotheim et al., 2008; Di Talia et al., 2009).
- Chen et al. (2004) Mol Biol Cell 15:3841.
- Di Talia et al. (2007) Nature 448:947.
- Di Talia et al. (2009) PLoS Biology, in press.
- Skotheim et al. (2008) Nature 454:291.
Modeling of glycolysis with energy transitions representing general metabolic processes including the adenylate kinase reaction shows a necessity for feedback on the glucose influx for stabilization of the system. Furthermore, stochastic influences can not be neglected.
Heterotrimeric G proteins mediate crucial and diverse signaling pathways in all eukaryotes. Here, we analyzed microarray data derived from guard cells and leaves of G protein subunit mutants of the model plant Arabidopsis thaliana, with or without treatment with the stress hormone, absicisc acid (ABA). While G-protein control of the transcriptome has received little attention to date in any system, transcriptome analysis allowed us to search for potentially uncommon yet significant signaling mechanisms. We first describe theoretical Boolean mechanisms of heterotrimer x hormone regulation, and then apply an approach based on pattern matching of gene expression profiles to Boolean models. We find that: (1) Classical mechanisms of G protein signaling are well supported. Conversely, some theoretical regulatory modes of the G protein are not supported. (2) A new mechanism, in which Gß regulates gene expression identically in the presence or absence of Ga, is supported. (3) Cell-specificity of G-protein signaling is revealed in that guard cells and leaves favor different G-protein modes in transcriptome regulation. Our method holds significant promise for analyzing analogous “switch-like” signal transduction events.
Signal transduction circuits have long been known to differentiate between signals by amplifying inputs to different levels1. Here, we describe a novel transcriptional circuitry that dynamically converts greater input levels into faster rates, without increasing the final equilibrium level (i.e. a level-to-rate converter circuit). We utilize time-lapse microscopy to study human herpesvirus (cytomegalovirus) infection of live cells in real time. Strikingly, our results show that transcriptional activators accelerate viral gene expression in single cells without amplifying the steady-state levels in these cells. This level-to-rate conversion operates by dynamically manipulating the traditional ‘gain-bandwidth’ feedback relationship from electrical circuit theory2 to convert greater input levels into faster rates, without increasing the final equilibrium level. Combining experimental approaches with mathematical modeling, we show that level-to-rate conversion results from a highly self-cooperative transcriptional auto-regulatory loop encoded by the virus’s essential transcriptional transactivator, IE23. There is a significant fitness advantage provided by level-to-rate conversion and abrogating IE2 auto-regulation eliminates level-to-rate conversion and severely impairs viral replication. Even minimal IE2 feedback circuits, lacking all other viral elements, maintain this fitness advantage via level-to-rate conversion. In general, level-to-rate converters may provide a mechanism for signal transduction circuits to rapidly respond to, and discriminate between, a diversity of signals without increasing steady-state levels of potentially cytotoxic molecules.
A protein undergoes conformational dynamics with multiple time scales, which results in fluctuating enzyme activities. Recent studies in single-molecule enzymology have observed this "age-old" dynamic disorder phenomenon directly. However, the single-molecule technique has its limitation. To be able to observe this molecular effect with real biochemical functions in situ, we propose to couple the fluctuations in enzymatic activity to noise propagations in small protein interaction networks such as a zeroth-order ultrasensitive phosphorylation-dephosphorylation cycle. We show that enzyme fluctuations can indeed be amplified by orders of magnitude into fluctuations in the level of substrate phosphorylation, a quantity of wide interest in cellular biology. Enzyme conformational fluctuations sufficiently slower than the catalytic reaction turnover rate result in a bimodal concentration distribution of the phosphorylated substrate. In return, this networkamplified single-enzyme fluctuation can be used as a novel biochemical "reporter" for measuring singleenzyme conformational fluctuation rates.
Development of nonequilibrium statistical physics theory is a grand challenge in physics. Most biological systems are far away from equilibrium. In this poster I will discuss some of my recent work. We will show how physical theories provide new insights and new methods for studying biological networks, and in turn how understanding biological networks lead to novel physical theory developments. First, I will show that a generic stochastic dynamic system can be mapped to a Hamiltonian system. The mapping makes many phenomena, such as noise-induced phase transition, critical slowing down, self-evident. It also allows well-established concepts and methods developed for Hamiltonian systems to apply to general dynamic systems. I will present generalization of the celebrated fluctuation-dissipation relations and application of the powerful Mori-Zwanzig projection technique to non-Hamiltonian systems (e.g., biological networks) far from equilibrium. I will discuss implications of the work on systems biology.
In this talk, we will discuss a detailed mathematical model for circadian timekeeping within the SCN. Our proposed model consists of a large population of SCN neurons, with each neuron containing a network of biochemical reactions involving the core circadian components. Using mathematical modeling, our results show that both intracellular molecular noise and intercellular coupling (nonlinear in nature) are required to sustain stochastic oscillations in the SCN oscillator network. Our work focuses on the problem of overcoming noise in oscillator systems, and our results highlight the importance of transcriptional noise in enhancing oscillations rather than dampening them. Surprisingly, our predictions from our model have been confirmed experimentally; we conclude with a short discussion of these results.
A simplified Ras-Raf-Mek-Erk model is simulated with a single growth factor receptor that acts as a switch. The transient and steady-state dynamics of the phosphorylated Erk formation and decay is investigated by a differential and a stochastic model.
