## Workshop 2: Regulatory Networks

### Organizers

Ralf Bundschuh
Departments of Physics, Chemistry&Biochemistry, Division of Hematology, The Ohio State University
Jeff Hasty
Departments of Molecular Biology and Bioengineering, University of California, San Diego
Fernand Hayot
Department of Physics, The Ohio State University

It has been over 40 years since Monod and Jacob boldly predicted that such fundamental cellular processes as differentiation and protein regulation are accomplished through signaling pathways resident at the level of the gene. This prediction laid the foundation for the ensuing progress in describing the essential regulatory mechanisms in many specific genetic systems. With the development of the field of nonlinear dynamics and the concurrent advent of available computing, mathematical models describing gene regulation began to appear regularly in the 1970s. Implicit in these studies was the realization that the "wiring" of naturally-occurring gene regulatory networks would be too complex for qualitative descriptions devoid of mathematics. Though this realization proved to be ahead of its time, mainly due to the lack of experimentally deduced regulatory pathways in the "pre-genomic" era, recent experimental advances in both sequencing and genetic engineering have made the analysis and design of gene networks amenable to quantitative analysis. These advances have reignited interest in gene regulatory models that can be used to explain and predict behavior that emerges from gene regulatory networks.

In this workshop, we will focus on recent advances in utilizing mathematical models to describe gene regulatory networks. The workshop will begin by introducing mathematical modeling techniques, including boolean representations, classical kinetic theory, stochastic simulation methods and constraints-based models. This will be followed by descriptions of specific gene regulatory networks, such as those related to the lambda and T7 life cycles, drosophilia segmentation, and xenopus oocytes differentiation. The remainder of the workshop will be devoted to the construction and analysis of synthetic gene regulatory networks, including switches, oscillators, autoregulation, and noise analysis. The workshop will highlight the utility, which an accurate mathematical description of synthetic networks provides, in describing complex naturally-occurring networks.

### Accepted Speakers

Timothy Elston
Department of Mathematics, University of North Carolina, Chapel Hill
Daniel Forger
Department of Biology, New York University
Glaxo Smith Kline
Timothy Gardner
Biomedical Engineering, Boston University
Dan Gillespie
Biochemical Computing Consultant, Paisii Hilendarski'' University of Plovdiv
Terry Hwa
Department of Physics, University of California, San Diego
Jean-Christophe Leloup
Service de Chimie Physique, Faculte des Sciences, Universite Libre de Bruxelles
Ron Milo
Complex Systems/Molecular Cell Biology, The Weizmann Institute of Science
John Reinitz
Applied Mathematics and Statistics, Stony Brook University
Michael Savageau
Department of Biomedical Engineering, University of California, Davis
Luis Serrano
Biostructure and Biocomputing, European Molecular Biology Laboratory
Michael Simpson
Materials Science and Engineering, University of Tennessee
Ron Weiss
Electrical Engineering & Molecular Biology, Princeton University
Lingchong You
Chemistry and Chemical Engineering, California Institute of Technology
Monday, November 8, 2004
Time Session
09:30 AM
10:30 AM
Dan Gillespie - Stochastic Chemical Kinetics

The time evolution of a well-stirred chemically reacting system is traditionally modeled by a set of coupled ordinary differential equations called the reaction rate equation (RRE). The resulting picture of continuous deterministic evolution is, however, valid only for infinitely large systems. That condition is usually well approximated in macroscopic chemical systems. But in biological systems formed by single living cells, the small population numbers of some reactant species can result in dynamical behavior that is noticeably discrete rather than continuous, and stochastic rather than deterministic. In that case, a more accurate mathematical modeling is obtained by using the machinery of Markov process theory, specifically, the chemical master equation (CME) and the stochastic simulation algorithm (SSA). This talk will review the theoretical foundations of stochastic chemical kinetics, and then discuss some recent efforts to (1) approximate the SSA by a faster simulation procedure, and (2) establish the formal connection between the CME/SSA description and the RRE description.

11:00 AM
12:00 PM
Daniel Forger - Towards a Biologically Rigorous Model of the Mammalian Circadian Clock

Perhaps the best understood biochemical networks are those of the circadian (near 24-hour) clock within cells. A mathematical model of the mammalian circadian clock is developed which incorporates a wide range of experimental data, and is by far the most detailed mathematical model of a circadian clock yet derived. Despite its complexity, there is enough experimental data to estimate the parameters of the model as an inverse problem. The model is accurate in its predictions with respect to mutations and can be used to understand key questions about clock structure and phase resetting.

We then investigate the behavior of an earlier circadian clock model in the presence of molecular noise. Despite a previous report, we find very accurate rhythms from this model, and study the physiological causes of this robustness. Unfortunately, this model is not detailed enough to specify individual molecular interactions, which has lead to conflicting results in the literature.

Based on an experimental estimate of the number of molecules of key proteins within the mammalian circadian clock, we can directly, without ambiguity, simulate our model of the mammalian circadian clock with stochastic molecular interactions. Amazingly, interactions with promoters on the time scale of seconds are required for accurate 24-hour timekeeping. The stochasticity of our model follows the central limit theorem. Finally we find that non-redundant gene-duplication can increase immunity to molecular noise by allowing for more interactions with promoters. This work was conducted with Charles Peskin.

Work done in collaboration with Justin Blau.

Tuesday, November 9, 2004
Time Session
09:00 AM
10:00 AM
Michael Savageau - Discovery of System Design Principles and Construction of Gene Circuits

The ability to comprehensively and quantitatively monitor dynamic changes in gene expression, together with new genome-scale informatic methods, is enabling high-throughput characterization of genetic regulatory networks. In addition, methods of genetic engineering now allow synthetic regulatory circuits to be readily built. Attention is currently being turned towards manipulating genetic regulatory circuits for therapeutic and technological applications, which increases the need to understand the functional consequences of genetic manipulations and to discover principles that can guide the design process. This issue will be addressed by comparing and contrasting what has been learned about design principles for gene circuits in their complex natural setting and how these have been put to use in designing, constructing and analyzing simple synthetic gene circuits.

02:00 PM
03:00 PM
Luis Serrano - Engineering Gene Networks to Emulate Drosophila Embryonic Pattern Formation & In Silico Biological Validation of Protein Interaction Networks

To understand in a quantitative manner how biological systems operate we need to achieve several things. First we need accurate and meaningful data of biologically relevant interactions. Second, we need to have experimental methodologies that allow us to dissect the behavior of the network in a context free environment. Third, we need computer algorithms to explore and simulate many different parameters, proposing new experiments to do. Finally we need to be able to modify and design the properties of the target network based on the previous analysis. In my presentation I will deal with the first two points: How to validate biologically meaningful interactions and how to analyze the properties of a network in an "in theory" context free environment.

Biological Validation of Protein interaction Networks:

Protein interaction networks are an important part of the post-genomic effort to integrate a parts-list view of the cell into system-level understanding. Using a set of 11 yeast genomes we show that combining comparative genomics and secondary structure information can greatly increase consensus based prediction of SH3 targets. Careful benchmarking of our method against positive and negative standards gives 83% accuracy with 26% coverage. We demonstrate the concept of an optimal divergence time, for effective comparative genomics studies, by proving that genomes of species that diverged very recently from S. cerevisiae (S. mikatae, S. bayanus and S. paradoxus), or a long time ago (S. pombe) contain less information for accurate prediction of SH3 targets. Our findings highlight several novel S. cerevisiae SH3 protein-interactions and the importance of selection of optimal divergence times in comparative genomics studies.

Engineering Gene Networks to Emulate Drosophila Embryonic Pattern Formation:

Pattern formation is essential in the development of higher eukaryotes. For example, in the Drosophila embryo, maternal morphogen gradients establish gap gene expression domain patterning along the anterior-posterior axis, through linkage with an elaborate gene network. To understand better the evolution and behaviour of such systems, it is important to establish the minimal determinants required for patterning. We have therefore engineered artificial transcription/translation networks, that generate simple patterns, crudely analogous to the Drosophila gap gene system. The Drosophila syncytium was modelled using DNA-coated paramagnetic beads, fixed by magnets in an artificial chamber, forming a gene expression network. Transient expression domain patterns were generated using various levels of network connectivity. Generally, adding more transcription repression interactions increased the 'sharpness' of the pattern while reducing overall expression levels. An accompanying computer model for our system allowed us to search for parameter sets compatible with patterning. While it is clear that the Drosophila embryo is far more complex than our simplified model, several features of interest emerge. For example, the model suggests that simple diffusion may be too rapid for Drosophila-scale patterning, implying that sublocalization or 'trapping' is required. Secondly, we find that for pattern formation to occur under the conditions of our in vitro reaction-diffusion system, the activator molecules must propagate faster than the inhibitors. Thirdly, adding controlled protease degradation to the system stabilizes pattern formation over time.

Work done in collaboration with Mark Isalan, Caroline Lemerle, Pedro Beltrao, and Luis Serrano.

Wednesday, November 10, 2004
Time Session
09:00 AM
10:00 AM
Ron Milo - Searching for Building Blocks and Design Principles in the Genetic Regulatory Network of E. coli

Little is known about the design principles of transcriptional regulation networks that control gene expression in cells. Recent advances in data collection and analysis, however, are generating unprecedented amounts of information about gene regulation networks. To understand these complex wiring diagrams, we sought to break down such networks into basic building blocks. We generalized the notion of motifs, widely used for sequence analysis, to the level of networks. We define 'network motifs' as patterns of interconnections that recur in many different parts of a network at frequencies much higher than those found in randomized networks. We found such motifs in networks from biochemistry, neurobiology, sociology and engineering. One of the best-characterized regulation networks is that of direct transcriptional interactions in Escherichia coli. We find that much of the network is composed of repeated appearances of several highly significant motifs. Each network motif has a specific function in determining gene expression, such as generating temporal expression programs and governing the responses to fluctuating external signals. The talk will present the theoretical and experimental approaches used to detect, measure and analyze functional circuits in this genetic regulatory network.

10:30 AM
11:30 AM
John Reinitz - Regulatory Networks in the Drosophila Blastoderm

The fruit fly Drosophila is a premier system for investigating how animal embryos self-organize their body plan. The blueprint for the fly's body is created by networks of genes operating in an ellipsoidal shell of cell nuclei called the blastoderm. We create predictive models of this process using systems of ordinary or partial differential equations fit to gene expression data by simulated annealing and/or Lagrangian methods. In this talk I will discuss the entire pattern formation project, from colorful fluorescently stained embryos to image processing, new optimization algorithms, and finally to new biological results. Also, although the notion of 'cis-regulatory modules' central to modern molecular biology, I will show that our understanding of the function and organization of these entities is fundamentally insufficient for understanding developmental biology. I will propose a solution to this problem through a new theoretical approach in concert with quantitative data from promoter-reporter constructs.

02:00 PM
03:00 PM
Lingchong You - Homeostasis, Oscillations, and Ecological Interactions in Re-programmed Bacterial Populations

De novo engineering of gene circuits inside cells has emerged as a powerful approach to decoding 'design principles' of biological systems. Such circuits are also of great interest for their potential applications in computation, engineering, and medicine. However, it has been challenging to realize predictable and robust circuit performance due to some major hurdles, such as noise in gene expression and cell-to-cell variation in phenotype. We address these issues by using cell-cell communication to coordinate cellular behavior across the population. To establish cell-cell communication, we take advantage of 'quorum sensing' systems that many bacteria use to detect and respond to changes in the cell density. As a prototype example, we have built and characterized a 'population control' circuit in bacterium E. coli. This circuit autonomously regulates the cell density using a negative feedback loop acting on the entire population. With the circuit, the cell density is broadcasted and detected by a quorum sensing system, which modulates the expression of a killer gene. The killer gene in turn regulates the cell density by controlling the death rate. Upon activation, the circuit will lead to a stable steady state or sustained oscillations in terms of cell density and gene expression. This circuit lays down the conceptual foundation to program interactions among multiple cell populations - essentially creating 'synthetic ecosystems' from well-characterized genetic modules.

Thursday, November 11, 2004
Time Session
09:00 AM
10:00 AM
Michael Simpson - Probing Gene Circuit Structure and Function Using Noise

The study of gene circuits is similar to many other areas of biology in as much as the principal aim is to understand the relationships between structure and function. This is true not only of chemical (e.g. the sequences of bases) or physical (e.g., 3-D structure of proteins) structure, but also the informational structure of genetic circuits and networks. New insights are emerging from the top-down analysis of the biomolecular networks from which complex cellular function emerges. Network motifs have been found that occur significantly more often than would be expected in random networks, providing a rational basis to search for the structure-function relationships in these systems. However, topology alone does not define function, which is sensitive to the specifics of kinetic parameters and the structure and function of individual gene circuits which comprise the higher order networks. Unfortunately, these parameters are usually very difficult to measure or infer. The problem is exacerbated by the fact that we wish to measure these parameters within the context of the fully functioning system of the cell, especially as intracellular molecular crowding generates kinetics that are vastly different than those found from in vitro measurements.

Concurrent with this emphasis on the informational architecture of intracellular molecular networks, a new appreciation of the role of stochastic processes in decision making in biological systems has emerged. Efforts in this direction have developed analysis and simulation techniques; described the noise consequences of gene circuit structure; and have explored how stochastic processes may play a pivotal role in gene circuit functionality. However, the use of inherent noise as a gene circuit probe has been largely ignored. Stochastic fluctuations are a broad-spectrum input excitation, and the frequency-domain structure of the resulting output spectra reveal details about the underlying gene circuit structure and parameter values. In this talk I will describe the frequency-domain processing of stochastic fluctuations by genetic circuits, the measurement of the output noise spectral densities, and the use of these spectra to infer gene circuit structure and reaction rate constants.

10:30 AM
11:30 AM
Terry Hwa - Molecular Strategies for Control and Gain in Transcriptional Regulation

Molecular Strategies for Control and Gain in Transcriptional Regulation

02:00 PM
03:00 PM
Ron Weiss - Programming Collaborative Behavior and Pattern Formation in Bacterial Communities

Cell-cell communication is a pervasive activity common to both single cell and multicellular organisms, and is used in coordinating cell behavior for a variety of tasks ranging from quorum sensing in bacteria to embryogenesis in mammalian cells. Engineering synthetic multicellular communication systems to exhibit desired functions will improve our quantitative understanding of naturally occurring cell-cell communication, and will also have biotechnology applications in areas such as biosensing, biomaterial fabrication, and tissue engineering. Here we will present theoretical and experimental results from three synthetic multicellular communication systems implemented in bacteria that have been programmed to exhibit unique coordinated cell behavior. The first system is the pulse generator where sender cells communicate to nearby receiver cells, which then respond with a transient burst of gene expression whose amplitude and duration depends on the distance from the senders. In the second system, receiver cells have been engineered to respond to cell-cell communication signals only within prespecified ranges. We will demonstrate how this system can be used to generate a variety of interesting spatial patterns. In the third system, cells have been engineered to "play" Conway's Game of Life, where cells live or die based on the density of their neighbors. This system exhibits complex global emergent behavior that arises from the interaction of cells based on simple local rules. In this talk, we will correlate experimental results from observing the behavior of these systems with our quantitative spatiotemporal models.

Friday, November 12, 2004
Time Session
09:00 AM
10:00 AM
- Balancing Molecular Fluctuations and Cellular Stability at the Level of a Gene, Cell, and Cell Community

A living cell is a noisy biochemical reactor in which low reactant concentrations lead to significant statistical fluctuations, or noise, in molecule numbers and reaction rates. This noise is often perceived as being undesirable and unpredictable. However, living systems are inherently noisy and are optimized to function in the presence of stochastic fluctuations. Some organisms can exploit noise to introduce diversity into a population. In contrast, stability against fluctuations is essential in case of a gene regulatory cascade controlling cell differentiation in a developing embryo. Stability in biological systems is often obtained by feedback regulation in the underlying regulatory network. In this talk I will address how biological systems can tune the balance between stability and noise at the level of a gene, cell, and cell community.

10:30 AM
11:30 AM
Timothy Gardner - Inferring Gene Regulatory Network Structure and Function in Microbes via Expression Profiling

We have developed a systematic methods to infer regulatory structures and properties of gene networks using microarray expression data. The methods learn first-order models of regulatory influences using RNA expression profiles for a diverse set of treatments, including exogenous compounds, environmental stresses, genetic mutations, and RNA inhibition. We have successfully applied the methods in E. coli and yeast to infer networks of 10s to 1000s of genes. The resulting network models can be used to identify transcription factor interactions, critical regulatory hubs, and to predict the mode of action of compounds and metabolites. In yeast, for example, the method was applied to a microarray data set measuring 6000 RNAs in 300 treatments. The resulting network model was used correctly identify the gene target of terbinafine, itraconazole and several other drugs. This method may be similarly applied to identify the feedback interactions between metabolic compounds and regulatory genes. These regulatory models may improve the optimization of metabolic pathways for biotechnology applications and may create new opportunities for target identification and lead optimization in drug discovery.

02:00 PM
03:00 PM
Chetan Gadgil - Stochastic Reaction Engineering Analysis of Regulatory Networks

Regulatory processes, especially those involving reactions between species that exist at very low concentrations, are inherently stochastic in nature. It is presently not clear how the structure of the reaction network model affects the results from the (numerical) calculation of the distribution of species. As a step towards analyzing the time-dependent behavior of the concentration distribution of each species in a network, we derive analytical expressions for the mean and variance of the concentration of all species in an arbitrary network where all the interactions are zero-order production reactions or first order conversion, catalytic or degradation reactions. We find the surprising, and apparently unknown, result that the time evolution of the second moments is governed by linear combinations of the eigenvalues of the matrix for the evolution of the means.

We use this theoretical framework to analyze the effect of network topology on the evolution of the mean and variance of various species in the network. In particular, we analyze the slowest time-scales for relaxation of the mean and variance for networks that are linear, and those that have positive feedback or feedforward loops. For a stochastic analysis of diffusion-reaction processes, we derive a framework that facilitates the separation of the effects of domain geometry, diffusion, and reaction rates on the distribution of species. We discuss the use of various measures to describe the 'noise' in stochastic systems, and show that the choice of the noise measure can lead to completely different conclusions for the same system.

Name Email Affiliation
Agosto, Francisco agosto.6@osu.edu Biophysics Program, The Ohio State University
Alexandridis, Roxana roxana@stat.ohio-state.edu Department of Statistics, The Ohio State University
Bazaliy, Borys Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine
Best, Janet jbest@mbi.osu.edu Mathematics, The Ohio State University
Borisyuk, Alla borisyuk@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Brewer, Daniel d.brewer@ucl.ac.uk Institute of Child Health & CoMPLEX, University College London
Buechler, Steven buechler.1@nd.edu Department of Mathematics, University of Notre Dame
Bundschuh, Ralf bundschuh@mbi.osu.edu Departments of Physics, Chemistry&Biochemistry, Division of Hematology, The Ohio State University
Carl, Joe carl.30@osu.edu IBGP, The Ohio State University
Cracium, Gheorghe craciun@math.wisc.edu Dept. of Mathematics, University of Wisconsin-Madison
DiVentura, Barbara diventur@embl.de Structural Biology & Biocomputing, EMBL
Doss, Hani Department of Statistics, The Ohio State University
Dougherty, Daniel dpdoughe@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Edwards, David Department of Mathematical Sciences, University of Delaware
Elston, Timothy telston@amath.unc.edu Department of Mathematics, University of North Carolina, Chapel Hill
Erdal, Selnur erdal.3@osu.edu Department of Biophysics, The Ohio State University
Fang, Chih gt1091b@yahoo.com Molecular Virology, Immunology & Med Genetics, The Ohio State University
Foley, Catherine foley@math.mcgill.ca Mathematics and Statistics, McGill University, Macdonald Campus
Forger, Daniel forger@umich.edu Department of Biology, New York University
Frazier, John john.frazier@wpafb.af.mil Human Effectiveness Directorate, Wright-Patterson Air Force Base (WPAFB)
Gao, Jianbo gao@ece.ufl.edu Electrical & Computer Engineering, University of Florida
Gardner, Timothy gardner@amyris.com Biomedical Engineering, Boston University
Gillespie, Dan GillespieDT@mailaps.org Biochemical Computing Consultant, Paisii Hilendarski'' University of Plovdiv
Goel, Pranay goelpra@helix.nih.gov NIDDK, Indian Institute of Science Education and Research
Gokhale, Zoee gokhale.5@osu.edu Department of Biophysics, The Ohio State University
Grotewold, Erich grotewold.1@osu.edu Department of Plant Biology, The Ohio State University
Gu, Weisong weisong@osc.edu Ohio Supercomputer Center, The Ohio State University
Guo, Yixin yixin@math.drexel.edu Department of Psychology, The Ohio State University
Hassanali, Ali hassanali@osu.edu Department of Biophysics, The Ohio State University
Hasty, Jeff hasty@ucsd.edu Departments of Molecular Biology and Bioengineering, University of California, San Diego
Hayot, Fernand hayot@mps.ohio-state.edu Department of Physics, The Ohio State University
Hsu, Jason hsu.1@osu.edu Department of Statistics, The Ohio State University
Hu, Bei Department of Mathematics, University of Notre Dame
Huang, Yifan huang.338@osu.edu Department of Statistics, The Ohio State University
Hwa, Terry hwa@matisse.ucsd.edu Department of Physics, University of California, San Diego
Isaacson, Samuel isaacson@math.utah.edu Courant Institute of Mathematical Sciences, New York University
Jayaprakash, Ciriyam jay@mps.ohio-state.edu Department of Physics, The Ohio State University
Joseph-Souriraj, Irene joseph-souriraj.1@osu.edu Biophysics Program, The Ohio State University
Joyce, Andrew ajoyce@ucsd.edu Palsson Lab, PFBH 419, University of California, San Diego
Jung, Peter Quantitative Biology Institute, Ohio University
Kannan, Dan kannan@uga.edu Department of Mathematics, University of Georgia
Kuznetsov, Alexey alexey@bu.edu Department of Mathematics, Boston University
Lauria, Mario lauria@cis.ohio-state.edu Computer Science & Engineering, The Ohio State University
Lee, Yoonkyung Department of Statistics, The Ohio State University
Lee, Chang Heong chlee@math.umn.edu Department of Mathematics, University of Minnesota
Leloup, Jean-Christophe jleloup@ulb.ac.be Service de Chimie Physique, Faculte des Sciences, Universite Libre de Bruxelles
Lim, Sookkyung limsk@math.uc.edu Department of Mathematical Sciences, University of Cincinnati
Lin, Shili lin.328@osu.edu Department of Statistics, The Ohio State University
Lipniacki, Tomasz tlipnia@ippt.gov.pl, Institute of Fundamental Technological Research
Liu, Jun jliu@stat.harvard.edu Department of Statistics, Harvard University
Liu, Liang LiuLiang@stat.ohio-state.edu Department of Statistics, The Ohio State University
Melfi, Vincent melfi@mbi.osu.edu Mathematics, Michigan State University
Milo, Ron ron.milo@weizmann.ac.il Complex Systems/Molecular Cell Biology, The Weizmann Institute of Science
Nagaraja, Haikady Department of Statistics, The Ohio State University
Palaniswamy, Saranyan palaniswamy-1@medctr.osu.edu Human Cancer Genetics Program, The Ohio State University
Pohar, Twyla pohar-2@medctr.osu.edu Division of Human Cancer Genetics, The Ohio State University
Pol, Diego dpol@mbi.osu.edu Independent Researcher, Museo Paleontologico E. Feruglio
Rassoul-Agha, Firas firas@math.ohio-state.edu Department of Mathematics, University of Utah
Ray, William ray.29@osu.edu Pediatrics, The Ohio State University
Reinitz, John reinitz@odd.bio.sunysb.edu Applied Mathematics and Statistics, Stony Brook University
Rejniak, Katarzyna rejniak@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Santner, Thomas tjs@stat.ohio-state.edu Department of Statistics, The Ohio State University
Savageau, Michael masavageau@ucdavis.edu Department of Biomedical Engineering, University of California, Davis
Serrano, Luis serrano@embl-heidelberg.de Biostructure and Biocomputing, European Molecular Biology Laboratory
Simpson, Michael simpsonML1@ornl.gov Materials Science and Engineering, University of Tennessee
Singer, Greg gacsinger@gmail.com Human Cancer Genetics, The Ohio State University
Smolen, Paul paul.d.smolen@uth.tmc.edu Neurobiology and Anatomy, University of Texas Medical School at Houston
Stubna, Michael stubna@mbi.osu.edu Engineering Team Leader, Pulsar Informatics
Sun, Hao sun.143@osu.edu Human Cancer Genetics, The Ohio State University
Sun, Junfeng sun@stat.ohio-state.edu Department of Statistics, The Ohio State University
Tang, Fusheng fusheng-tang@uiowa.edu Department of Mathematics, University of Iowa
Terman, David terman@math.ohio-state.edu Mathemathics Department, The Ohio State University
Thomas, Rene rthomas@dbm.ulb.ac.be Biologie Moleculaire, Universite Libre de Bruxelles
Tian, Jianjun Paul tianjj@mbi.osu.edu Mathematics, College of William and Mary
Varbanov, Alex varbanov.ar@pg.com Department of Statistics, Proctor & Gamble
Verducci, Joseph verducci.1@osu.edu Department of Statistics, The Ohio State University
Volfson, Dmitri dvolfson@ucsd.edu Institute for Nonlinear Science, University of California, San Diego
Wang, Tao wangtao@stat.ohio-state.edu Department of Statistics, The Ohio State University
Wang, Zailong zlwang@mbi.osu.edu Integrated Information Sciences, Novartis
Wechselberger, Martin wm@mbi.osu.edu Mathematical Biosciences Insitute, The Ohio State University
Weiss, Ron rweiss@princeton.edu Electrical Engineering & Molecular Biology, Princeton University
Wright, Geraldine wright.572@osu.edu School of Biology, Newcastle University
Ye, Kenny kyeblue@yahoo.com Epidemiology & Population Health, Albert Einstein College of Medicine
Yin, Lijie yin.39@osu.edu Department of Pathology, The Ohio State University
You, Lingchong you@duke.edu Chemistry and Chemical Engineering, California Institute of Technology
Zhang, Xuan zhangx@cse.ohio-state.edu Computer Science & Engineering, The Ohio State University
Zhou, Jin jzhou@mbi.osu.edu Department of Mathematics, Northern Michigan University
Zhou, Penghui zhou.154@osu.edu Department of Molecular Genetics, The Ohio State University
Zinner, Bertram zinnebe@auburn.edu Mathematics and Statistics, Auburn University
Towards a Biologically Rigorous Model of the Mammalian Circadian Clock

Perhaps the best understood biochemical networks are those of the circadian (near 24-hour) clock within cells. A mathematical model of the mammalian circadian clock is developed which incorporates a wide range of experimental data, and is by far the most detailed mathematical model of a circadian clock yet derived. Despite its complexity, there is enough experimental data to estimate the parameters of the model as an inverse problem. The model is accurate in its predictions with respect to mutations and can be used to understand key questions about clock structure and phase resetting.

We then investigate the behavior of an earlier circadian clock model in the presence of molecular noise. Despite a previous report, we find very accurate rhythms from this model, and study the physiological causes of this robustness. Unfortunately, this model is not detailed enough to specify individual molecular interactions, which has lead to conflicting results in the literature.

Based on an experimental estimate of the number of molecules of key proteins within the mammalian circadian clock, we can directly, without ambiguity, simulate our model of the mammalian circadian clock with stochastic molecular interactions. Amazingly, interactions with promoters on the time scale of seconds are required for accurate 24-hour timekeeping. The stochasticity of our model follows the central limit theorem. Finally we find that non-redundant gene-duplication can increase immunity to molecular noise by allowing for more interactions with promoters. This work was conducted with Charles Peskin.

Work done in collaboration with Justin Blau.

Stochastic Reaction Engineering Analysis of Regulatory Networks

Regulatory processes, especially those involving reactions between species that exist at very low concentrations, are inherently stochastic in nature. It is presently not clear how the structure of the reaction network model affects the results from the (numerical) calculation of the distribution of species. As a step towards analyzing the time-dependent behavior of the concentration distribution of each species in a network, we derive analytical expressions for the mean and variance of the concentration of all species in an arbitrary network where all the interactions are zero-order production reactions or first order conversion, catalytic or degradation reactions. We find the surprising, and apparently unknown, result that the time evolution of the second moments is governed by linear combinations of the eigenvalues of the matrix for the evolution of the means.

We use this theoretical framework to analyze the effect of network topology on the evolution of the mean and variance of various species in the network. In particular, we analyze the slowest time-scales for relaxation of the mean and variance for networks that are linear, and those that have positive feedback or feedforward loops. For a stochastic analysis of diffusion-reaction processes, we derive a framework that facilitates the separation of the effects of domain geometry, diffusion, and reaction rates on the distribution of species. We discuss the use of various measures to describe the 'noise' in stochastic systems, and show that the choice of the noise measure can lead to completely different conclusions for the same system.

Inferring Gene Regulatory Network Structure and Function in Microbes via Expression Profiling

We have developed a systematic methods to infer regulatory structures and properties of gene networks using microarray expression data. The methods learn first-order models of regulatory influences using RNA expression profiles for a diverse set of treatments, including exogenous compounds, environmental stresses, genetic mutations, and RNA inhibition. We have successfully applied the methods in E. coli and yeast to infer networks of 10s to 1000s of genes. The resulting network models can be used to identify transcription factor interactions, critical regulatory hubs, and to predict the mode of action of compounds and metabolites. In yeast, for example, the method was applied to a microarray data set measuring 6000 RNAs in 300 treatments. The resulting network model was used correctly identify the gene target of terbinafine, itraconazole and several other drugs. This method may be similarly applied to identify the feedback interactions between metabolic compounds and regulatory genes. These regulatory models may improve the optimization of metabolic pathways for biotechnology applications and may create new opportunities for target identification and lead optimization in drug discovery.

Stochastic Chemical Kinetics

The time evolution of a well-stirred chemically reacting system is traditionally modeled by a set of coupled ordinary differential equations called the reaction rate equation (RRE). The resulting picture of continuous deterministic evolution is, however, valid only for infinitely large systems. That condition is usually well approximated in macroscopic chemical systems. But in biological systems formed by single living cells, the small population numbers of some reactant species can result in dynamical behavior that is noticeably discrete rather than continuous, and stochastic rather than deterministic. In that case, a more accurate mathematical modeling is obtained by using the machinery of Markov process theory, specifically, the chemical master equation (CME) and the stochastic simulation algorithm (SSA). This talk will review the theoretical foundations of stochastic chemical kinetics, and then discuss some recent efforts to (1) approximate the SSA by a faster simulation procedure, and (2) establish the formal connection between the CME/SSA description and the RRE description.

Molecular Strategies for Control and Gain in Transcriptional Regulation

Molecular Strategies for Control and Gain in Transcriptional Regulation

Searching for Building Blocks and Design Principles in the Genetic Regulatory Network of E. coli

Little is known about the design principles of transcriptional regulation networks that control gene expression in cells. Recent advances in data collection and analysis, however, are generating unprecedented amounts of information about gene regulation networks. To understand these complex wiring diagrams, we sought to break down such networks into basic building blocks. We generalized the notion of motifs, widely used for sequence analysis, to the level of networks. We define 'network motifs' as patterns of interconnections that recur in many different parts of a network at frequencies much higher than those found in randomized networks. We found such motifs in networks from biochemistry, neurobiology, sociology and engineering. One of the best-characterized regulation networks is that of direct transcriptional interactions in Escherichia coli. We find that much of the network is composed of repeated appearances of several highly significant motifs. Each network motif has a specific function in determining gene expression, such as generating temporal expression programs and governing the responses to fluctuating external signals. The talk will present the theoretical and experimental approaches used to detect, measure and analyze functional circuits in this genetic regulatory network.

Regulatory Networks in the Drosophila Blastoderm

The fruit fly Drosophila is a premier system for investigating how animal embryos self-organize their body plan. The blueprint for the fly's body is created by networks of genes operating in an ellipsoidal shell of cell nuclei called the blastoderm. We create predictive models of this process using systems of ordinary or partial differential equations fit to gene expression data by simulated annealing and/or Lagrangian methods. In this talk I will discuss the entire pattern formation project, from colorful fluorescently stained embryos to image processing, new optimization algorithms, and finally to new biological results. Also, although the notion of 'cis-regulatory modules' central to modern molecular biology, I will show that our understanding of the function and organization of these entities is fundamentally insufficient for understanding developmental biology. I will propose a solution to this problem through a new theoretical approach in concert with quantitative data from promoter-reporter constructs.

Discovery of System Design Principles and Construction of Gene Circuits

The ability to comprehensively and quantitatively monitor dynamic changes in gene expression, together with new genome-scale informatic methods, is enabling high-throughput characterization of genetic regulatory networks. In addition, methods of genetic engineering now allow synthetic regulatory circuits to be readily built. Attention is currently being turned towards manipulating genetic regulatory circuits for therapeutic and technological applications, which increases the need to understand the functional consequences of genetic manipulations and to discover principles that can guide the design process. This issue will be addressed by comparing and contrasting what has been learned about design principles for gene circuits in their complex natural setting and how these have been put to use in designing, constructing and analyzing simple synthetic gene circuits.

Engineering Gene Networks to Emulate Drosophila Embryonic Pattern Formation & In Silico Biological Validation of Protein Interaction Networks

To understand in a quantitative manner how biological systems operate we need to achieve several things. First we need accurate and meaningful data of biologically relevant interactions. Second, we need to have experimental methodologies that allow us to dissect the behavior of the network in a context free environment. Third, we need computer algorithms to explore and simulate many different parameters, proposing new experiments to do. Finally we need to be able to modify and design the properties of the target network based on the previous analysis. In my presentation I will deal with the first two points: How to validate biologically meaningful interactions and how to analyze the properties of a network in an "in theory" context free environment.

Biological Validation of Protein interaction Networks:

Protein interaction networks are an important part of the post-genomic effort to integrate a parts-list view of the cell into system-level understanding. Using a set of 11 yeast genomes we show that combining comparative genomics and secondary structure information can greatly increase consensus based prediction of SH3 targets. Careful benchmarking of our method against positive and negative standards gives 83% accuracy with 26% coverage. We demonstrate the concept of an optimal divergence time, for effective comparative genomics studies, by proving that genomes of species that diverged very recently from S. cerevisiae (S. mikatae, S. bayanus and S. paradoxus), or a long time ago (S. pombe) contain less information for accurate prediction of SH3 targets. Our findings highlight several novel S. cerevisiae SH3 protein-interactions and the importance of selection of optimal divergence times in comparative genomics studies.

Engineering Gene Networks to Emulate Drosophila Embryonic Pattern Formation:

Pattern formation is essential in the development of higher eukaryotes. For example, in the Drosophila embryo, maternal morphogen gradients establish gap gene expression domain patterning along the anterior-posterior axis, through linkage with an elaborate gene network. To understand better the evolution and behaviour of such systems, it is important to establish the minimal determinants required for patterning. We have therefore engineered artificial transcription/translation networks, that generate simple patterns, crudely analogous to the Drosophila gap gene system. The Drosophila syncytium was modelled using DNA-coated paramagnetic beads, fixed by magnets in an artificial chamber, forming a gene expression network. Transient expression domain patterns were generated using various levels of network connectivity. Generally, adding more transcription repression interactions increased the 'sharpness' of the pattern while reducing overall expression levels. An accompanying computer model for our system allowed us to search for parameter sets compatible with patterning. While it is clear that the Drosophila embryo is far more complex than our simplified model, several features of interest emerge. For example, the model suggests that simple diffusion may be too rapid for Drosophila-scale patterning, implying that sublocalization or 'trapping' is required. Secondly, we find that for pattern formation to occur under the conditions of our in vitro reaction-diffusion system, the activator molecules must propagate faster than the inhibitors. Thirdly, adding controlled protease degradation to the system stabilizes pattern formation over time.

Work done in collaboration with Mark Isalan, Caroline Lemerle, Pedro Beltrao, and Luis Serrano.

Probing Gene Circuit Structure and Function Using Noise

The study of gene circuits is similar to many other areas of biology in as much as the principal aim is to understand the relationships between structure and function. This is true not only of chemical (e.g. the sequences of bases) or physical (e.g., 3-D structure of proteins) structure, but also the informational structure of genetic circuits and networks. New insights are emerging from the top-down analysis of the biomolecular networks from which complex cellular function emerges. Network motifs have been found that occur significantly more often than would be expected in random networks, providing a rational basis to search for the structure-function relationships in these systems. However, topology alone does not define function, which is sensitive to the specifics of kinetic parameters and the structure and function of individual gene circuits which comprise the higher order networks. Unfortunately, these parameters are usually very difficult to measure or infer. The problem is exacerbated by the fact that we wish to measure these parameters within the context of the fully functioning system of the cell, especially as intracellular molecular crowding generates kinetics that are vastly different than those found from in vitro measurements.

Concurrent with this emphasis on the informational architecture of intracellular molecular networks, a new appreciation of the role of stochastic processes in decision making in biological systems has emerged. Efforts in this direction have developed analysis and simulation techniques; described the noise consequences of gene circuit structure; and have explored how stochastic processes may play a pivotal role in gene circuit functionality. However, the use of inherent noise as a gene circuit probe has been largely ignored. Stochastic fluctuations are a broad-spectrum input excitation, and the frequency-domain structure of the resulting output spectra reveal details about the underlying gene circuit structure and parameter values. In this talk I will describe the frequency-domain processing of stochastic fluctuations by genetic circuits, the measurement of the output noise spectral densities, and the use of these spectra to infer gene circuit structure and reaction rate constants.

Programming Collaborative Behavior and Pattern Formation in Bacterial Communities

Cell-cell communication is a pervasive activity common to both single cell and multicellular organisms, and is used in coordinating cell behavior for a variety of tasks ranging from quorum sensing in bacteria to embryogenesis in mammalian cells. Engineering synthetic multicellular communication systems to exhibit desired functions will improve our quantitative understanding of naturally occurring cell-cell communication, and will also have biotechnology applications in areas such as biosensing, biomaterial fabrication, and tissue engineering. Here we will present theoretical and experimental results from three synthetic multicellular communication systems implemented in bacteria that have been programmed to exhibit unique coordinated cell behavior. The first system is the pulse generator where sender cells communicate to nearby receiver cells, which then respond with a transient burst of gene expression whose amplitude and duration depends on the distance from the senders. In the second system, receiver cells have been engineered to respond to cell-cell communication signals only within prespecified ranges. We will demonstrate how this system can be used to generate a variety of interesting spatial patterns. In the third system, cells have been engineered to "play" Conway's Game of Life, where cells live or die based on the density of their neighbors. This system exhibits complex global emergent behavior that arises from the interaction of cells based on simple local rules. In this talk, we will correlate experimental results from observing the behavior of these systems with our quantitative spatiotemporal models.

Homeostasis, Oscillations, and Ecological Interactions in Re-programmed Bacterial Populations

De novo engineering of gene circuits inside cells has emerged as a powerful approach to decoding 'design principles' of biological systems. Such circuits are also of great interest for their potential applications in computation, engineering, and medicine. However, it has been challenging to realize predictable and robust circuit performance due to some major hurdles, such as noise in gene expression and cell-to-cell variation in phenotype. We address these issues by using cell-cell communication to coordinate cellular behavior across the population. To establish cell-cell communication, we take advantage of 'quorum sensing' systems that many bacteria use to detect and respond to changes in the cell density. As a prototype example, we have built and characterized a 'population control' circuit in bacterium E. coli. This circuit autonomously regulates the cell density using a negative feedback loop acting on the entire population. With the circuit, the cell density is broadcasted and detected by a quorum sensing system, which modulates the expression of a killer gene. The killer gene in turn regulates the cell density by controlling the death rate. Upon activation, the circuit will lead to a stable steady state or sustained oscillations in terms of cell density and gene expression. This circuit lays down the conceptual foundation to program interactions among multiple cell populations - essentially creating 'synthetic ecosystems' from well-characterized genetic modules.

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