The estimation the connectivity structure of neuronal networks is hindered by one's inability to simultaneously and individually measure the activity of all neurons. Many unmeasured neurons could be interacting with the small set of measured neurons and corrupting estimates of connectivity in unknown ways. For example, a common connection from an unmeasured neuron could introduce correlations among two measured neurons, which might lead one to erroneously infer a connection between the measured neurons. We present a model-based approach to control for such effects of unmeasured neurons. We demonstrate the promise of this approach via simulations of small networks of neurons driven by a visual stimulus.

Cdc42 in yeast cells has the tendency to concentrate in polarized caps on the cell membrane, even when all other spatial cues have been deactivated. In order to understand what mechanism might be responsible for this tendency, we considered the simplest possible positive feedback model for the cytosol-membrane diffusion of Cdc42 in a yeast cell. We found that stochasticity and positive feedback were the only necessary ingredients to achieve polarization, and we observed that polarization can be switched on and off by regulating precisely one of the four parameters in the model. Predictions arising from the model have turned out to be consistent with experimental data.

Cis regulatory information comprises a key portion of genetic coding, yet despite the abundance of genomic sequences now available, identifying and characterizing this information remains a major challenge. We are pursuing a unique “bottom up” approach to understand the mechanistic processing of the regulatory elements (input codes) by the transcriptional machinery, using a well-defined and characterized set of repressors and activators in Drosophila blastoderm embryo. We are identifying quantitative values for parameters affecting transcriptional regulation in vivo, which are used to build and test mathematical models. The models will aid bioinformatics tools that predict the outputs of novel cis-regulatory elements in Drosophila and other organisms. Giant, Krüppel and Knirps are short-range transcriptional repressors involved in the developmental patterning of Drosophila blastoderm embryo. Using defined regulatory modules tested in germline transformed embryos, we are measuring quantitative parameters describing the effects of spacing, stoichiometry, arrangement, specificity and binding site affinities of these repressors on cassettes driven by Dorsal/Twist activator set. To develop predictive models, we modify the Fractional Site Occupancy Models (that are mainly used for prokaryotic gene regulation) by using part of our data set. This modified model is being used to predict the output of novel permutations of sites, which will allow us to test and refine parameters used for the model.

Central to development are the specification and maintenance of cell identity. We are using Systems Biology approaches to understand the regulatory networks underlying these processes at the resolution of individual cell types. We are also using novel mathematical descriptors to investigate the growth and response of the physical networks that roots make as they explore their environment.

This is a companion poster which complements the corresponding graphical results while the other one addresses the methodological part.

Protein interactomics represents a challenging field for complex network analysis, and extensive efforts are ongoing to model the topology. Both structure and dynamics are of interest, and while the former aspect is more studied, as single or multiple snapshots are available from many biological sources, the latter is still at its infancy stage. With regard to both aspects, we analyze the possible contribution coming from multiscale decompositions of some characterizing protein interactome features.

Morphogenic pathways such as those implicated in cell migration are regulated in space and time. Often they integrate mechanical signals with long-range effects and chemical signals with shorter range effects. One of the prime challenges in the analysis of pathways is to define the hierarchy and kinetics of signal transduction between spatially and temporally distributed pathway components. My lab is building a novel image analysis paradigm by which we multiplex image measurements across many experiments to register time courses of signaling events relative to cellular outputs. Indirectly, this defines also the sequence of activation of pathway components that are not simultaneously measured. Key to our multiplexing concept is the local analysis of constitutive stochastic fluctuations in pathways components with high resolution, i.e. below the diffusion radius of signaling molecules. Under these conditions, the correlation of time courses reveals precise information of the timing and of the spatial relationships between pathway activities, independent of intra-cellular and inter-cellular heterogeneity. From the timing, we can then infer causality and derive maps of the pathway hierarchy. In this presentation I will outline the idea of image fluctuation analysis and multiplexing and present first examples of pathway inference that underpin the potential of this data analysis approach.

Joint work with Yoichiro Kamimura, Meghdad Rahdar, Jane Borleis, Yu Long, Sandra de Keijzer, Jonathan Franca-Koh, Kristen Franson, Michelle Tang, and Stacey S. Willard (Department of Cell Biology, Johns Hopkins University, Baltimore, MD, USA 21205).

The mechanisms of sensing shallow gradients of extracellular signals is remarkably similar in Dictyostelium amoebae and mammalian leukocytes. An extensive series of studies have indicated that the upstream components and reactions in the signaling pathway are quite uniform while downstream responses such as PI (3,4,5)P₃ accumulation and actin polymerization are sharply localized towards the high side of the gradient. Uniform stimuli transiently recruit and activate PI3Ks and cause PTEN to be released from the membrane while gradients of chemoattractant cause PI3Ks and PTEN to bind to the membrane at the front and the back of the cell, respectively. This reciprocal regulation provides robust control of PIP₃ and leads to its sharp accumulation at the anterior. A similar PIP3-based "polarity circuit" plays a key role in cytokinesis where PI3Ks and PTEN move to and function at the poles and furrow, respectively, of the dividing cell. Disruption of PTEN broadens PI localization and actin polymerization in parallel, leading to vigorous extension of lateral pseudopodia; however, lowered levels of PIP3 do not greatly interfere with either chemotaxis or cytokinesis, suggesting that additional pathways act in parallel.

A screen to identify redundant pathways revealed a gene with homology to patatin-like phospholipase A₂. Loss of this gene did not alter PIP₃ regulation, but chemotaxis became sensitive to reductions in PI3K activity. Likewise, cells deficient in PI3K activity were more sensitive to inhibition of PLA₂ activity. Deletion of the PLA₂ homologue and two PI3Ks caused a strong defect in chemotaxis and a reduction in receptor-mediated actin polymerization. We propose that PLA₂ and PI3K signaling act in concert to mediate chemotaxis and arachidonic acid metabolites may be important mediators of the response.

Evidence has suggested that PKB signaling plays a role in cell motility and that TorC2 can regulate the actin cytoskeleton. We have recently shown that activation of TorC2 and PKB occurs at the leading edge of chemotaxing cells and plays a critical role in directed cell migration. Within seconds of stimulation of chemotactically sensitive cells, two PKB homologs, PKBA and PKBR1, transiently phosphorylate at least seven proteins. The enzymes are activated by phosphorylation of their hydrophobic motifs (HMs) through TorC2 and subsequent phosphorylation of their activation loops (ALs). Activation of PKBR1, a myristoylated form persistently bound to the membrane, does not require PI(3,4,5)P₃. Cells deficient in PKBR1 or TorC2, lack most of the phosphorylated substrates and are specifically impaired in directional sensing. Thus, temporal and spatial activation of PKB signaling by TorC2 is a critical event in directed cell migration that can act independently of localized PI(3,4,5)P₃.

Dorsal closure, an essential stage of Drosophila morphogenesis, provides a model system for tissue dynamics. Our research approach is based on modern genetics, in vivo imaging, laser microsurgery, digital image processing, and quantitative modeling to identify the mechanical forces that connect the genetic program of development to morphogenesis. Key to the dynamics of dorsal closure are four biological processes, involving three tissues, that are coordinated in space, synchronized in time, and remarkably resilient both to genetic perturbations and to laser perturbations. These processes can upregulate in response to laser perturbation, where there are spatial, kinematic, and dynamic asymmetries associated with upregulation. There also are asymmetries observed during non-perturbed, wild type closure, which are associated with the failure of dorsal closure in several mutant embryos. We are quantitatively characterizing emergent properties during dorsal closure, i.e., a velocity governor and the apparent coordination and synchronization of cell activities for these tissues.

Peralta et al. Upregulation of forces and morphogenic asymmetries in dorsal closure during Drosophila development. Biophysical Journal 92: 2583-2596 (2007).

Kiehart et al. 2005. Ultraviolet Laser Microbeam for Dissection of Drosophila Embryos. In Cell Biology: A Laboratory Handbook, Third Edition. J. E. Celis, editor. Elsevier, San Diego. 87-103 (2005).

Franke et al. Nonmuscle myosin II generates forces that transmit tension and drive contraction in multiple tissues during dorsal closure. Curr Biol. 15: 2208-2221 (2005).

Hutson et al. Forces for morphogenesis investigated with laser microsurgery and quantitative modeling. Science 300: 145-149 (2003).

Kiehart et al. Multiple forces contribute to cell sheet morphogenesis for dorsal closure in Drosophila. J. Cell Biol. 149: 471-490 (2000).

The idea of optimization is intimately connected with modern science. Pioneers like Galileo, Fermat, and Newton, were convinced that the world had been created by a benevolent god who had established the laws of nature as the most efficient way to achieve his purposes: in short, this is the best of all possible worlds, and it is the task of science to find out why and how. Gradually this view was overturned, leaving optimization as an important tool for the human-engineered world. More recently, game theory has come to replace optimization for describing situations where a multitude of individuals with conflicting interests make decisions based on imperfect information. In this lecture, Professor Ekeland will guide us along the path from Fermat to modern economic theory, and from optimization to game theory.

Joint work with Ahmet Ay², Evan Dayringer², Rupinder Sayal¹, Chichia Chiu², David N. Arnosti¹.

Cis regulatory information comprises a key portion of genetic coding, yet despite the abundance of genomic sequences now available, identifying and characterizing this information remains a major challenge. We are pursuing a unique “bottom-up” approach to understand the mechanistic processing of the regulatory elements (input codes) by the transcriptional machinery, using a well-defined and characterized set of repressor and activator transcription factors in Drosophila blastoderm embryos. We are identifying quantitative values for parameters affecting transcriptional regulation in vivo, which are used to build and test mathematical models that predict the outputs of novel cis-regulatory elements. Giant, Krüppel, Knirps are short-range transcriptional repressor proteins involved in the developmental patterning of Drosophila blastoderm embryo. Using defined regulatory modules tested in germline transformed embryos, we are measuring quantitative values of Giant protein (input) and lacZ mRNA (output) using confocal laser scanning microscopy technique. The expression of lacZ reporter gene is driven by Twist/Dorsal activator proteins. We build 3-scale mathematical models which consist of computer simulation of transcription factors (TF) dynamic, mathematical description of cis-regulatory elements (RE) along the DNA enhancer cassettes, and integration of TF and RE to predict transcription output. Our modeling at the DNA level will integrate all the key parameters of the binding sites including arrangement, spacing, stoichiometry, affinity, proximity to basal promoter and collaboration. We employ a nucleotide-base potential function for repressor and activator binding sites and partial differential equations to derive density functions representing the transcriptional map of clusters of binding sites. These models are being used to predict the output of novel permutations of binding sites, which will allow us to test and refine parameters used for the model. In one line of investigation, fluorescence quantitation of mRNA lacZ expression was used to measure the effect of moving Giant repressor binding sites from a position adjacent to Twist/Dorsal activator sites to a distal site 125bp upstream. Our mathematical model successfully predicted the distance effect of intermediate positions, such as 25, 50, 75 and 100bp compared to the experimental results. Enhancer cassettes with 1, 2 and 3 binding sites of Giant or Krüppel repressors upstream from Twist/Dorsal activator sites were analyzed for the effect of stoichiometry on lacZ expression. The in situ experimental results indicate a cooperative contribution within Giant and Krüppel repressor proteins on lacZ repression. Our model predicts a strong cooperativity within these repressor proteins. In other modules examined the effect of arrangement of Giant binding sites to the Twist/Dorsal activator sites, it showed a significant difference in transcriptional output providing a good evidence for the importance of modeling many key parameters of cis-transcriptional regulation. Extension of these predictive models to endogenous cis-elements will provide novel insights on regulatory element design and evolution, and should provide a bioinformatics tool for predicting quantitative output of novel regulatory elements.

¹Department of Biochemistry & Molecular Biology ²Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA.

Synechococcus elongatus, a single celled cyanobacterium, has a remarkably precise and robust circadian clock which has been reconstituted in vitro with just three proteins. Its simplicity makes it an ideal system for understanding dynamical functions that can arise from the kinetics of multiple phosphorylations. Recent experiments and theoretical analysis will be presented along with speculations on the evolutionary origins of this clock.

Uncovering the structure and function of gene regulatory networks has become one of the central challenges of the post-sequencing era. Theoretical models of protein-DNA feedback loops and gene regulatory networks have long been proposed, and recently, certain qualitative features of such models have been experimentally corroborated. For the first portion of the presentation, recent progress in constructing two synthetic gene oscillators will be discussed. These oscillators were built in accordance with design criteria that was developed with computational modeling. Both oscillators are robust, with all cells oscillating with a characteristic frequency that can be tuned with external inducers or temperature shifts. In the second part of the presentation, the response of metabolic gene regulation to periodic changes in the external carbon source will be discussed. The central finding is the metabolic regulatory system acts as a low-pass filter that reliably responds to a slowly changing environment, while effectively ignoring fluctuations that are too fast for the cell to mount an efficient response. Computational modeling calibrated with experimental data is used to determine that frequency selection in the system is controlled by the interaction of coupled positive feedback networks governing the signal transduction of alternative carbon sources. The simulations suggest that the feedback loops may confer a robustness to environmental fluctuations on cells regardless of deficiencies in network components. This prediction is validated with an experimental comparison of two cellular strains that exhibit the same filtering properties despite having markedly different induction characteristics. The underlying methodology highlights the utility of engineering-based methods in the exploration of gene regulatory networks.

Iron is necessary for cell growth, but through the Fenton reaction, excess iron can cause dangerous radicals. Hence, a cell's metabolism of iron is essential for survival. We present a model of iron metabolism in a generic epithelial cell created using CellDesigner, a diagram editor for creating biochemical or gene regulatory networks. This network includes all possible interactions found in the literature and includes reactions specific to intestinal epithelial cells (iron uptake) and hepatocyes (iron storage).

The developmental fate of cells depends upon the microenvironment provided by neighboring cells, growth factors, and the extracellular matrix. Subtle differences in the microenvironment can lead to heterogeneous phenotypes, even within isogenic cell populations that have been cultured uniformly. The genes and proteins linking microenvironment variability to cell outcomes are mostly unknown, because there has not been a way to systematically identify molecular differences among cells that otherwise appear identical. Here, I will present a new technique (called "stochastic sampling") that attempts to address this general problem. Stochastic sampling involves the repeated, random selection of very-small cell populations (~10 cells) followed by quantitative gene-expression profiling and simple statistical analysis. Comparing how transcripts are distributed across repeated samplings distinguishes molecular dichotomies (high expression in some cells, low expression in others) from biological noise. We combine laser-capture microdissection, a customized single-cell amplification protocol, and quantitative PCR to implement stochastic sampling in an in vitro model of mammary-gland morphogenesis. The distinct gene-expression patterns predicted by stochastic sampling were verified in situ by multicolor RNA FISH, identifying coregulated gene clusters that were completely obscured at the population level. Last, I will discuss preliminary work showing how our approach can be scaled up to the entire transcriptome by using oligonucleotide microarrays. These stochastic-profiling experiments have revealed unanticipated transcriptional dichotomies that may play critical roles during mammary-gland morphogenesis.

Any signalling network must be able to extract weak signals from a noisy environment and be robust against background perturbations, such as stochastic fluctuations in protein levels or variations in temperature and ambient stimulation. Our aim is to elucidate how these tasks have been solved in the evolutionary design of the chemotaxis pathway in E. coli, one of the best studied models for signal transduction. Combining fluorescence-based experimental analyses of spatial and temporal dynamics of the intracellular signal processing with quantitative computer modelling, we show that the robustness of chemotactic signalling is ensured at multiple levels, from gene expression to pathway topology to reaction rates.

Can genomics provide a new level of strategic intelligence about rapidly evolving pathogens? We have developed a new approach to measure the rates of all possible evolutionary pathways in a genome, using conditional Ka/Ks to estimate their "evolutionary velocity", and have applied this to several datasets, including clinical sequencing of 50,000 HIV-1 samples. Conditional Ka/Ks predicts the preferred order and relative rates of competing evolutionary pathways. We recently tested this approach using independent data generously provided by Shafer and coworkers (Stanford HIV Database), in which multiple samples collected at different times from each patient make it possible to track which mutations occurred first during this time-course. Out of 35 such mutation pairs in protease and RT, conditional Ka/Ks correctly predicted the experimentally observed order in 28 cases (p=0.00025). Conditional Ka/Ks data reveal specific accessory mutations that greatly accelerate the evolution of multi-drug resistance. Our analysis was highly reproducible in four independent datasets, and can decipher a pathogen's evolutionary pathways to multi-drug resistance even while such mutants are still rare. Analysis of samples from untreated patients shows that these rapid evolutionary pathways are specifically associated with drug treatment, and vanish in its absence.

Tumor necrosis factor alpha (TNF) is a pro-inflammatory cytokine that is released in response to trauma or infection. Binding of TNF to its receptor (TNFR) results in direct activation of caspase-8 and the apoptotic machinery via the intracellular death domain of TNFR. Healthy cells, however, are highly resistant to TNF-induced apoptosis owing to concurrent activation of nuclear factor kappa B (NF-kB), a pro-inflammatory, anti-apoptotic transcription factor. Recent studies suggest that the anti-apoptotic function of NF-kB may be mediated through cFLIP, whose pseudo-caspase domain prevents activation of caspase-8 by ligand-bound TNFR. To investigate the importance of this mechanism under various physiological conditions, we have constructed a mathematical model of TNF-induced NF-kB activation and regulation of the JNK pro-apoptotic pathway.

A basic unsolved question in cell biology is how the size of organelles is determined. Eukaryotic flagella (also known as cilia) are ideal organelles to study size control because they are linear structures and therefore require only a single number to specify size. Based on pulse-labeling and other experimental analyses, we have developed a simple model for flagellar length control based on the inherent length-dependence of intraflagellar transport. We compare the predicted dynamic behavior of the model, implemented by a series of increasingly complicated network implementations, with experimental observations of live cells. In order to further explore the functioning of this system, we have begun to measure biological noise in length control, and to couple experimental measurements of noise with predictions based on small-signal noise analysis of the model. These analyses allow us to deduce how mutations which affect length may change individual parameters within the model, as well as to predict novel phenotypes to be sought in future genetic screens. The approaches we are developing for studying flagellar length control should be applicable to other organelle size control problems.

Complex networks may be around us, and biologists have taken them to heart. Some of these networks exist in a real sense: a signal can be sent from an Internet address to other addresses, and perhaps from some cells in metazoan neural system to some other cells. But is there any physical sense of, say, protein-protein interaction network? For example, can anything be sent or propagated across it? Another question has to do with the quality of evidence. After the first round of claims that certain biological networks are scale-free, or small-world, or highly robust, we entered the stage of much more careful analysis, and many of these conclusions are being refined and sometimes even refuted. Finally, there is the "so what?" factor. Much attention has been given to the global properties of biological networks, e.g., their node-degree distribution - but, even when we finally describe such properties with some accuracy, which of them will be important for understanding of Life? My aspiration is to focus on what is real, and perhaps fundamental, about gene networks. My main claim is that any gene network is defined by the set of distances (or similarities) between each pair of genes, and by statistics that tells which of them are close enough to be of interest. Moreover, I speculate that if the network is directed, the directions of the edges can also be inferred from the distance matrix. Thus, understanding of the properties of distances between genes is a prerequisite for any "network biology."

Applying results from dynamical systems, control and optimization, we develop new approaches for designing experiments to elucidate the biochemical network structure of the chemotaxis mechanism in R. sphaeroides. Biological information and data is used to create initial models (model determination); an experiment is then designed in order to discriminate between these models; and a model invalidation procedure closes the loop. This way we can develop an understanding of the underlying biochemical network structure: a Synthetic Biology approach could then be used to redesign such networks for improved or modified functionality.

The vertebrate body can be subdivided along the antero-posterior (AP) axis into repeated structures called segments. This periodic pattern is established during embryogenesis by the somitogenesis process. Somites are generated in a rhythmic fashion from the paraxial mesoderm and subsequently differentiate to give rise to the vertebrae and skeletal muscles of the body. Somite formation involves an oscillator, the segmentation clock whose periodic signal is converted into the periodic array of somite boundaries. This clock drives the dynamic expression of cyclic genes in the presomitic mesoderm and requires Notch and Wnt signaling. Microarray studies of the mouse presomitic mesoderm transcriptome reveal that the segmentation clock drives the periodic expression of a large network of cyclic genes involved in cell signaling. Mutually exclusive activation of the Notch/FGF and Wnt pathways during each cycle, suggests that coordinated regulation of these three pathways underlies the clock oscillator. Whereas the segmentation clock is thought to set the pace of vertebrate segmentation, the translation of this pulsation into the reiterated arrangement of segment boundaries along the AP axis involves FGF and Wnt signaling. The FGF pathway controls the positioning of the wavefront, which corresponds to the level of the presomitic mesoderm where cells respond to the clock. fgf8 mRNA is only transcribed in tail bud precursors and it progressively decays in newly formed paraxial mesoderm cells, thus forming a dynamic mRNA gradient. This mRNA gradient is then translated into a graded FGF signaling response used to position the wavefront. This mechanism provides an efficient means to couple the spatio-temporal activation of segmentation to the posterior elongation of the embryo.

After the T cell receptor (TCR) has been formed on immature T cells in the thymus (thymocytes), they go through a process of selection in which the TCR is tested for its response against self-peptides. Thymocytes that either show very weak responses die through neglect (positive selection); those that show very strong responses die through apoptosis (negative selection). Defects in this selection process is an important component of predisposition towards T cell induced autoimmunity. Experiments have also shown that positive selection is a graded function of the strength of the signal received at the TCR while negative selection is a much sharper, almost digital function. Some point downstream of the TCR, weak signals appear to transduce along a different path of the signaling network than strong signals. The molecular origins of these differences have been a subject of much investigation in immunology. We have built a new explanation of the experiments based on a computational model of a module of the protein signaling pathway that describes the experimental observations qualitatively. Experiments are also underway to test the model.

Computer simulations based on the Hybrid Discrete-Continuous (HDC) mathematical model of cancer invasion (Anderson et al., Cell. 2006,127:905) predict that the degree of severity of the tumor microenvironment (tmE) directly impacts on the emergence of invasion. More precisely, harsh ME conditions (e.g., hypoxia, discontinuous matrix, inflammation) select for dominant aggressive clones that grow into a fingering, infiltrating mass. In contrast, in mild ME conditions (normoxia, homogenous matrix) selection for dominant aggressive clones is relaxed, so that they coexist with less aggressive ones and, together, they grow into a smooth-margin, noninvasive tumor mass. To populate HDC simulations with experimental data, we use a panel of cell lines, derived from the breast epithelial cell MCF10A. We have established a collection of variants of this platform cell line with distinct invasive potential, generated by transfection of oncogenes or passaging in vivo. We measured the following parameters: oxygen consumption/hypoxia, tumor cell proliferation, tumor cell survival, metabolic consumption, and matrix degrading enzyme activity. Initial simulations with these homogenous data indicate that invasion may require competition between phenotypes with distinct adaptive traits to the tmE. To validate these predictions in vitro, we have developed a novel Island Invasion Assay (IIA), which closely mimics the spatial arrangements of the HDC model. Preliminary results suggest that IIA supports the HDC predictions concerning invasion (fingering) under stressful tmE conditions. In addition, some unexpected results point to novel features that could be included in the HDC model to increase realism. This is an excellent example of synergistic interactions between modeling and experimentation, which will hopefully produce novel insights in the mechanisms underlying cancer invasion. For in vivo validation, we are comparing orthotopic (“mild ME”) versus subcutaneous (“harsh ME”) human breast cancer xenografts in mice (in vivo VICBC group, headed by Lisa McCawley). We utilized MCF-10 variant cell lines, CA1a and CA1d, shown to have distinct and consistent tumorigenic properties through repeated passage in immunocompromised mice. Several in vivo imaging modalities are being exploited to provide quantitative analysis of cellular parameters of the same tumor over time: Magnetic Resonance Imaging (MRI) analysis to distinguish tumor volume and necrotic tumor areas (i.e. nonoxygenated states) from viable (i.e. oxygenated) tissue; positron emission topography (PET) scan imaging of 18F-labeled-fluorodeoxyglucose(FDG) for metabolism; Optical imaging analysis of fluorogenic probes termed “proteolytic beacons” for matrix degrading protease activity (i.e. substrate hydrolysis). Tumor specimens are also biopsied at fixed volumes (0.5, 1 and 1.5 cm diameters) for further ex vivo analyses, including histology to assess invasion, immunohistochemistry and immunofluorescence to measure cellular proliferation (BrdU incorporation), apoptosis (TUNEL) and hypoxia (hypoxiprobe). Initial results from these analyses reveal advantages and limits of in vivo parameterization and validation. The main advantage is that relevant variables and parameters for tumor invasion can only be truly identified in a living organism, at least until convincing in vitro surrogates for spatial invasion, such as the IIA, are developed. The limits reflect largely the fact that conventional experimental biology has been seldom used for model validation, so that tools and approaches must be refined and adapted. These broad issues as well as intitial specific data will be discussed.

Classical studies show that for many proteins, the information required for specifying the tertiary structure is contained in the amino acid sequence. However, the potential complexity of this information is truly enormous, a problem that makes defining the rules for protein folding difficult through either computational or experimental methods. In the past few years, we have reported a new method (that we call the statistical coupling analysis or SCA) for estimating the conserved evolutionary constraints between sites on proteins through statistical analysis of large and diverse multiple sequence alignments1,2. Experiments in several protein systems demonstrate the functional importance of this evolution-based mapping of amino acid interactions1,3,4 and recently, the SCA information was shown to the necessary and sufficient to design functional artificial members of a small protein family in the absence of any structural or chemical information. These results support the hypothesis that in a purely statistical and mechanism-free way, the SCA captures the evolutionary rules for specifying natural-like proteins. In recent work, we have extended these results to the design of larger protein domains and are working on the physical mechanisms underlying the statistical coupling. The evolutionary constraints between residues are much more sparse and heterogeneous than traditional analyses of atomic structures would suggest, a finding that guides our thinking about potential general principles underlying the natural design of proteins.

[1] S.W. Lockless, R. Ranganathan, Science, 286, 295-9 (1999). [2] G. Suel et al., Nature Struct. Biol., 10., 59-69 (2003). [3] M.E. Hatley, et al., PNAS, 100: 14445-14450 (2003). [4] A.I. Shulman et al., Cell, 116: 417-429 (2004). [5] Socolich et al., Nature, 437: 512-518 (2005). [6] Russ et al., Nature, 437: 579-583 (2005).

Development of high throughput technologies including DNA microarrays has facilitated the study of cells and living organisms. The challenge is no longer to identify the genes or proteins that are diffentially expressed, but rather finding sub-systems that interact with each other in response to a given environmental condition. Study of these interacting sub-systems has provided an invaluable source of additional information that can be used to better understand the complex mechanisms of life. In this paper, we propose a latent variable model that directly incorporates the external information about the underlying network. We then use the theory of mixed linear models to present a general inference framework for the problem of testing the significance of subnetworks. Performance of the proposed model is evaluated on simulated and real data examples.

Chromosomal regions can adopt stable and heritable alternative states resulting in bistable gene expression without changes to the DNA sequence. Such epigenetic control is often associated with alternative covalent modifications of histones. The stability and heritability of the states are thought to involve positive feedback where modified nucleosomes recruit enzymes that similarly modify nearby nucleosomes. We developed a simplified stochastic model for dynamic nucleosome modification based on the silent mating-type region of the yeast Schizosaccharomyces pombe. We show that the mechanism can give strong bistability that is resistant both to high noise due to random gain or loss of nucleosome modifications and to random partitioning upon DNA replication. However, robust bistability required: (1) cooperativity, the activity of more than one modified nucleosome, in the modification reactions and (2) that nucleosomes occasionally stimulate modification beyond their neighbor nucleosomes, arguing against a simple continuous spreading of nucleosome modification.

Reference: Ian B. Dodd, Mille A. Micheelsen, Kim Sneppen and Geneviève Thon Cell, Vol 129, 813-822, 18 May 2007

Biomolecular networks, while exhibiting a rich variety of behaviors in signaling and regulation, would appear to be fairly well behaved as dynamical systems. Their (mathematical) models have solutions that tend to settle into well-defined steady states or periodic, but not "chaotic", behavior. This presents one major challenge to theoreticians: what is special about such networks, vis a vis general dynamical systems? A second challenge arises in the mathematical analysis itself: while on the one hand good qualitative, graph-theoretic, knowledge is frequently available, on the other hand it is often hard to experimentally validate the form of the nonlinearities used in reaction terms, and even when such forms are known, to accurately estimate coefficients (parameters, such as kinetic constants). This "data-rich/data-poor" dichotomy seems to be pervasive in systems biology.

This theory talk is concerned with both challenges. We approach the problem through the standard paradigm in control theory and signal processing, that of viewing larger systems as interconnections of input/output subsystems: provided that these subsystems are individually well-behaved, more complex behaviors arise from the global interconnection structure. This brings up a host of issues, from basic issues of modularity, retroactivity, and input and output "impedance", to the characterization of classes of appropriately "simple" components, to the question of what type of quantitative information suffices for obtaining precise conclusions regarding dynamics (such as the existence of multiple stable steady states, or oscillations).

As one specific example, we consider order-preserving (monotone) components, which enjoy particularly nice dynamical properties as well as robust responses to perturbations. Their interconnections may be, in principle, studied through a blend of qualitative and (relatively sparse) quantitative information, allowing one to draw conclusions about global dynamical behavior and the location of steady states. The talk will also present evidence suggesting that natural signaling and transcriptional regulation networks may be close to monotone, and that networks that are close to monotone are statistically better behaved than more arbitrary ones.

The website http://www.math.rutgers.edu/~sontag/ has references and online copies of papers with technical details.

Network inference algorithms, and in particular Bayesian networks algorithms, are being applied with growing regularity in computational molecular biology to recover gene regulatory networks from gene expression data. However, the basic task at hand -- to predict causal relationships based on repeated concurrent measurements of multiple variables -- -is not necessarily limited to the molecular realm. Here, I present my research on using Bayesian network inference algorithms to recover networks on several different levels of biological organization: genes, neurons, and ecosystems.

The quantitative relation between transcription factor concentrations and the rate of protein production from downstream genes is central to the function of genetic networks. I will describe a technique to measure this relation, the gene regulation function, in individual living cells. The gene regulation function is often a sigmoidal function, and I will show that, by interpreting genetic networks as inference modules, we can make predictions about why this sigmoidal function has different characteristics for different genetic networks. Our results should provide a basis for both understanding cellular decision-making and for designing synthetic genetic circuits.

Diverse organisms ranging from bacteria to mammalian stem cells undergo pluripotent differentiation where a single cell can commit to one out of several cell fates. How do underlying genetic circuits allow cells to “choose” a specific cell fate and execute the appropriate differentiation program? To address this question we investigate a simple bacterial differentiation system utilizing mathematical modeling and quantitative single cell measurements. In particular we are interested in elucidating the significance of circuit dynamics and stochastic behavior during cellular differentiation.

It is recognized that a biological systems should be characterized with multiscale and multi-modality imaging platforms such as using microarray gene expression and array CGH. While microarray gene expression analysis presents functional information, the array CGH analysis provides structural variations of genome using gene copy number changes. The integration of this complementary information is challenging. We view the gene expression and copy number variations as two different measurements of a biological system and apply the independent component analysis (ICA) to project the data into statistically independent biological processes, which are then integrated to identify variation patterns in two inputs. We apply the method to cluster genes according to the integrated data, resulting improved identification of genes that are statistically significant in both measurements (e.g., gene expression and aCGH). We also compared the approach with other approaches such as principal component analysis (PCA), and the generalized singular value decomposition (GSVD), demonstrating better performances.

Multistability (and steady-state behavior) is assumed to be a necessary feature of genetic ³on/off² switches (e.g. Lambda-phage lysis-lysogeny, E. coli lactose utilization, and human progenitor-cell differentiation). However, when one behavior of the switch is transient or destroys the cell, such as viral lysis, the underlying genetic circuit need not be bistable. Instead, transient excursions from a single monostable state may allow multiple behaviors, with switching arbitrated by the lifetime (decay) of the transient signal. I will discuss our recent work quantifying feedback strength in HIV by exploiting the stochastic noise inherent to gene-expression. Our results indicate that transcriptional positive-feedback extends transient gene-expression lifetime and thereby controls cell-fate in HIV.

The epidermal growth factor receptor (EGFR) is a central signal transduction pathway in epithelial cells and regulates diverse biological responses such as proliferation, migration and differentiation. Ligands for the EGFR, such as amphiregulin and TGFa are synthesized as membrane-anchored precursors and released by regulated proteolysis, leading to autocrine signaling. Ligand shedding is controlled by a number of different hormones and is responsible for EGFR “transactivation” or crosstalk. We have sought to understand the design principles of autocrine network in cells by using a combination of mathematical modeling and quantitative experimental approaches. We found that the core EGFR autocrine network can be modeled as three functional modules: ligand production, EGFR activation and ERK signaling. These three modules are linked in a recursive manner such that the output of the ERK module is linked to the input of the ligand production module. This positive feedback loop is shunted through the extracellular space, providing a mechanism by which the overall level of ERK signaling is linked to a cell’s environment. Each module in this circuit behaves as a linear control unit, apparently because of intramodule feedback. In contrast, intermodule feedback appears to control the overall level of signaling. Multiple growth factors feed into the EGFR autocrine circuit at different points, with consequent additive or synergistic effects. Despite the linearity of the overall autocrine circuit, internal module mechanisms can display nonlinear and even oscillatory behavior. In addition, consequent cellular outputs or decisions can be nonlinear or switch-like. We suggest that cell signaling networks are composed of a series of interconnected linear modules and that negative feedback is used extensively to increase module linearity and robustness. This structure likely evolved as a mechanism to facilitate module assembly into higher-order regulatory networks. However, the network can display non-linear properties at either the sub-module or supra-module level. Parsing signaling networks into their constituent modules is a potentially powerful approach for scaling signaling models to the multicellular level.

Dynamical system models of complex biochemical reaction networks are usually high-dimensional, nonlinear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for all values of the parameters in the model. In other cases multiple equilibria exist if and only if special relationships between these parameters are satisfied. We describe methods based on homotopy invariance of degree which allow us to determine the number of equilibria for complex biochemical reaction networks and how this number depends on parameters in the model. Joint work with G. Craciun and J. W. Helton.

By using a singularly perturbed system of integral differential equations as a reasonable realistic model, we show how a nonlinear nonlocal neuronal network can generate several stable traveling waves, including homoclinic orbits and heteroclinic orbits. All of these orbits serve as nontrivial local attractors of the dynamical systems. Furthermore, we establish relation between speed index functions and stability index functions whose zeros are necessary and sufficient to determine the stability of the brain waves.