Workshop 6: Algebraic Methods in Systems and Evolutionary Biology

(May 7,2012 - May 11,2012 )

Organizers


Reinhard Laubenbacher
Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University
Ilya Shmulevich
Department of Electrical Engineering, University of Washington
Seth Sullivant
Mathematics, North Carolina State University
Ruriko Yoshida
Statistics, University of Kentucky

Molecular networks drive many of the cellular and organismal processes that influence the phenotype of an organism, and have become a central focus of systems biology. To understand the complex dynamics underlying these processes, dynamic mathematical and computational models are needed. Several different approaches have been used successfully for this purpose. Beyond differential equations models, a range of discrete models has been used for this purpose, both deterministic and stochastic, for instance Boolean networks and their generalizations, and dynamic Bayesian networks. This workshop will focus on modeling of molecular networks, in particular gene regulatory networks, with an emphasis on discrete modeling approaches, including stochastic aspects of networks. In addition to models of specific molecular networks, it will explore questions such as the relationship between network structure and their dynamics, design principles of molecular networks, and the evolution of networks. Both mathematical and biological aspects of molecular network modeling will be discussed, and the workshop will open with tutorial talks on both.

Accepted Speakers

Eva Ackermann
Institut für Festkörperphysik, TU Darmstadt
Reka Albert
Department of Physics, Pennsylvania State University
Maximino Aldana
FAS Center for Systems Biology, Harvard University
Ziv Bar-Joseph
Computational biology, Carnegie-Mellon University
Gheorghe Craciun
Mathematics and Biomolecular Chemistry, University of Wisconsin-Madison
Aniruddha Datta
Electrical and Computer Engineering, Texas A & M University
Edward Dougherty
Electrical and Computer Engineering, Texas A & M University
Jeremy Gunawardena
Systems Biology, Harvard Medical School
Heather Harrington
Division of Molecular Biosciences,
David Haws
Department of Statistics, University of Kentucky
Monika Heiner
Computer Science, Brandenburgische Technische Universit""at Cottbus
Franziska Hinkelmann
MBI, The Ohio State University
Aziz Mithani
Department of Biology, School Of Science and Engineering, Lahore University of Management Sciences, Lahore, Pakistan
Elizabeth Remy
Institut de Mathématiques de Luminy, CNRS
Anne Shiu
Mathematics, University of Chicago
Joshua Socolar
Physics, Duke University
Alan Veliz-Cuba
Mathematics, University of Nebraska
Paola Vera-Licona
Bioinformatics and Computational Systems Biology of Cancer, Institut Curie
Monday, May 7, 2012
Time Session
04:00 PM
05:00 PM
Ruriko Yoshida, Franziska Hinkelmann, Joshua Socolar - Day One Discussion
Day One Discussion
Tuesday, May 8, 2012
Time Session
08:30 AM
09:30 AM
Reka Albert - Avenues toward simplified Boolean modeling of signal transduction networks
Over the past five years my group, in collaboration with wet-bench biologists, developed and validated asynchronous Boolean models of several signal transduction networks. Along the way we have encountered obstacles related to the lack of timing knowledge and the large size of the state space. In this talk I will present three methodologies we developed to overcome these obstacles. First, from a comparative analysis of several asynchronous update methods we concluded that updating a single, randomly selected node at each time instant offers the best combination of information and economy.

Second, we developed a two-step network reduction method which was able to reduce the number of variables by 90% in two different systems without affecting their dynamic behaviors. Third, we proposed an integration of Boolean rules into graph theoretical analysis and showed that this semi-structural method can identify critical signal mediators on par with dynamic models.
10:00 AM
11:00 AM
Aniruddha Datta - Cancer Therapy Design Based on Pathway Logic
Cancer encompasses various diseases associated with loss of cell-cycle control, leading to uncontrolled cell proliferation and/or reduced apoptosis. Cancer is usually caused by malfunction(s) in the cellular signaling pathways. Malfunctions occur in different ways and at different locations in a pathway. Consequently, therapy design should first identify the location and type of malfunction and then arrive at a suitable drug combination. We consider the growth factor (GF) signaling pathways, widely studied in the context of cancer. Interactions between different pathway components are modeled using Boolean logic gates. All possible single malfunctions in the resulting circuit are enumerated and responses of the different malfunctioning circuits to a 'test' input are used to group the malfunctions into classes. Effects of different drugs, targeting different parts of the Boolean circuit, are taken into account in deciding drug efficacy, thereby mapping each malfunction to an appropriate set of drugs.
11:00 AM
12:00 PM
Ziv Bar-Joseph - Linking the Signaling Cascades and Dynamic Regulatory Networks Controlling Cellular Responses
Transcriptional gene regulation is a dynamic process and its proper functioning is essential for all living organisms. By combining the abundant static regulatory data with time series expression data using an Input-Output Hidden Markov model (IOHMM) we were able to reconstruct a dynamic representations for these networks in multiple species. The models lead to testable temporal hypotheses identifying both new regulators and their time of activation. We have recently extended these models, by solving an optimization problem related to graph orientation, to connect signaling and regulatory networks. These reconstructed networks link receptors and proteins that directly interact with the environment to the observed expression outcome. I will discuss the application and experimental validation of predictions made by our methods focusing on stress response in yeast. I would also mention a number of other extensions for integrating microRNAs and discriminative motif search and their applications for studying mice development and response to pathogens in mammalian cells.
01:30 PM
02:30 PM
Heather Harrington - Non-parametric analysis of mass action models and data
How cells make decisions can be investigated using mathematical models. We describe a procedure to decide whether a model is compatible with steady-state data. This method requires no parameter values-- it is based on techniques from algebraic geometry, linear algebra, and optimization. Cellular decisions also depend on where they occur in the cell (e.g., nucleus or cytoplasm). We also find that cellular information processing can be altered by including spatial organization. Borrowing tools from chemical reaction network theory and dynamical systems, we show that the existence of distinct compartments plays a pivotal role in whether a system is capable of multistationarity.
02:30 PM
03:30 PM
Jeremy Gunawardena - Invariants � polynomial signatures of molecular networks
A network of biochemical reactions gives rise, under mass-action kinetics, to a polynomial dynamical system, the steady states of which form a real algebraic variety. Methods from computational algebraic geometry have begun to yield biological insights into such networks. Here, we review work on "invariants". An invariant is a polynomial expression in specified state variables that holds in any (positive) steady state of a network. Invariants characterise the behaviour of several model networks and concisely capture their salient behaviour. However, it remains challenging to calculate invariants and we do not yet understand why some networks have biologically-meaningful invariants while others, apparently, do not.
04:00 PM
05:00 PM
Reka Albert, Aniruddha Datta, Heather Harrington - Avenues toward simplified Boolean modeling of signal transduction networks
Over the past five years my group, in collaboration with wet-bench biologists, developed and validated asynchronous Boolean models of several signal transduction networks. Along the way we have encountered obstacles related to the lack of timing knowledge and the large size of the state space. In this talk I will present three methodologies we developed to overcome these obstacles. First, from a comparative analysis of several asynchronous update methods we concluded that updating a single, randomly selected node at each time instant offers the best combination of information and economy.

Second, we developed a two-step network reduction method which was able to reduce the number of variables by 90% in two different systems without affecting their dynamic behaviors. Third, we proposed an integration of Boolean rules into graph theoretical analysis and showed that this semi-structural method can identify critical signal mediators on par with dynamic models.
Wednesday, May 9, 2012
Time Session
12:00 AM
12:00 PM
Edward Dougherty - Intrinsically Bayesian Robust Structural Intervention and the Mean Objective Cost of Uncertainty in Gene Regulatory Networks
Standard operator optimization assumes a mathematical model and a family of operators on the model, defines an objective function to measure operator performance, and selects an optimal operator as one minimizing (maximizing) the objective function. With robust optimization the paradigm changes: the model is unknown and belongs to an uncertainty class of operators. If a prior distribution governs the uncertainty class, then an intrinsically Bayesian robust (IBR) operator is one that provides the minimum expectation of the objective function across the uncertainty class. The objective cost of uncertainty for any model in the uncertainty class is measured by the gain in performance from using an optimal operator for the model as opposed to using an IBR operator on the model. The overall cost of uncertainty is measured by the mean objective cost of uncertainty (MOCU) over the uncertainty class. Optimization is constrained by optimizing over the family of operators that are optimal for specific models in the uncertainty class. In this case, we refer to an optimal operator as a model-constrained Bayesian robust (MCBR) operator. Two general kinds of operational intervention have been considered for gene regulatory networks. Structural intervention involves a one-time alteration of the regulatory apparatus, which means a permanent change to the regulatory logic. Stationary intervention involves a time-invariant external control policy whose action at any time point depends on feedback from the system. In the presence of uncertainty, MCBR control has been treated for the stationary control of probabilistic Boolean networks in the framework of an objective cost of control and dynamic programming. This talk discusses IBR structural intervention for PBNs and the corresponding MOCU as it pertains to uncertain gene logic.
08:30 AM
09:30 AM
Monika Heiner - Coloured Petri Nets for Multiscale Systems Biology
This talk reports on our investigations to explore appropriate modelling and analysis techniques for processes evolving simultaneously over time and space, applied to biological systems. Current challenges for modelling in Systems Biology include those associated with issues of complexity and representing systems with multi-scale attributes. A drawback of current modelling approaches, including Petri nets, is their limitation to relatively small networks. We use Stochastic and Continuous Petri Nets to consider continuous time evolution as Markov process or system of Ordinary Differential Equations, and Coloured Petri Nets to statically encode finite discrete space. Combining both concepts yields Coloured Stochastic and Coloured Continuous Petri nets, which allow for directly executable models as well as computational experiments using standard analysis and simulation techniques over very large networks. We illustrate our approach by a couple of case studies, including gradient formation, multistrain bacterial colonies, and planar cell polarity signalling in Drosophila wing.
10:00 AM
11:00 AM
Ilya Shmulevich - Transcriptional Regulatory Networks from the Bottom Down
Regulatory networks of biomolecular interactions in cells govern virtually all cellular behaviors and functions. Modern measurement technologies are being used to generateinformation on many types of interactions, involving transcriptional and microRNA regulatory networks, signaling networks, and cytokine networks. Temporal measurements of gene and protein expression levels and chromatin modifications, coupled with data fusion strategies that incorporate computational predictions of regulatory mechanisms on the basis of other types of information, such as nucleic acid sequence, can be used to constructdynamical system models of these networks. The analysis and simulation of such models, in conjunction with experimental validation, sheds light on biological function and paves the way toward rational and systematic control strategies intended to drive a diseased system toward a desired state by means of targeted interventions. At the same time, such systems approaches permit new biological observables that reflect system-level behavior that cannot be understood by studying individual sets of interactions. Cellular decision making, maintenance of homeostasis and robustness, sensitivity to diverse types of information in the presence of environmental variability, and coordination ofcomplex macroscopic behavior are examples of such emergent systems-level behavior. Information theoretic approaches combined with elements of dynamical systems theory, such as phase transitions and structure dynamics relationships, are promising frameworks for studying fundamental principles governing living systems at all scales of organization.
Thursday, May 10, 2012
Time Session
08:30 AM
09:30 AM
Paola Vera-Licona - An Algebra-Based Method to Infer the Structure and Dynamics of Gene Regulatory Networks

The inference of molecular networks is an important problem in systems biology. This includes both the structure of the network in the form of its wiring diagram and its long-term dynamics. While there are many algorithms available that aim to infer network structure from experimental data, less emphasis has been placed on methods that utilize time series data effectively to infer both structure and dynamics. Since the network inference problem is typically underdetermined, it is important to also have the option of incorporating prior biological knowledge about the network into the process along with an effective description of the model search space. Finally, it is important to have an understanding of how a given inference method is affected by experimental and other noise in the data used for this purpose.

In this talk we will introduce a novel inference algorithm within the Boolean polynomial dynamical system (BPDS) framework, to meet all these requirements. The algorithm is able to use time series data, including network perturbations such as knock-out mutants and RNAi experiments. To infer wiring diagrams and dynamical models, it allows for the incorporation of prior biological knowledge while being robust to significant levels of noise in the data used for inference. It uses an evolutionary algorithm for local optimization with an encoding of models as BPDS. We will show how within this BPDS framework it is possible to give an effective representation of the model space to be searched to improve computational performance. We will show a validation of the algorithm with both an in silico network and with microarray expression profiles from a synthetic yeast network.

11:00 AM
12:00 PM
Aziz Mithani - A stochastic model for the evolution of metabolic network using neighbor dependence

The availability of genomes of many closely related bacteria with diverse metabolic capabilities offers the possibility of tracing metabolic evolution on a phylogeny relating the genomes to understand the evolutionary processes and constraints that affect the evolution of metabolic networks. Using simple (independent loss/gain of reactions) or complex (incorporating dependencies among reactions) stochastic models of metabolic evolution, it is possible to study how metabolic networks evolve over time. Here, we describe metabolic network evolution as a discrete space continuous time Markov process and introduce a neighbor-dependent model for the evolution of metabolic networks where the rates with which reactions are added or removed depend on the fraction of neighboring reactions present in the network. The model also allows estimation of the strength of the neighborhood effect during the course of evolution. We present Gibbs samplers for sampling networks at the internal node of a phylogeny and for estimating the parameters of evolution over a phylogeny without exploring the whole search space by iteratively sampling from the conditional distributions of the internal networks and parameters. The samplers are used to estimate the parameters of evolution of metabolic networks of bacteria in the genus Pseudomonas and to infer the metabolic networks of the ancestral pseudomonads. The results suggest that pathway maps that are conserved across the Pseudomonas phylogeny have a stronger neighborhood structure than those which have a variable distribution of reactions across the phylogeny, and that some Pseudomonas lineages are going through genome reduction resulting in the loss of a number of reactions from their metabolic networks.

01:30 PM
02:30 PM
Alan Veliz-Cuba - Reverse Engineering of Regulatory Networks Using Algebraic Geometry
Discrete models have been used successfully in modeling biological processes such as gene regulatory networks. When certain regulation mechanisms are unknown it is important to be able to identify the best model with the available data. In this context, reverse engineering of finite dynamical systems from partial information is an important problem. In this talk we will present a framework and algorithm to reverse engineer the possible wiring diagrams of a finite dynamical system from data. The algorithm consists on using an ideal of polynomials to encode all possible wiring diagrams, and choose those that are minimal using the primary decomposition. We will also show that these results can be applied to reverse engineer continuous dynamical systems.
02:30 PM
03:30 PM
Elizabeth Remy - Logical modelling of regulatory networks, results and challenges
The logical method proved useful for the modelling of regulatory networks and the analysis of their dynamical properties. It relies on two directed graphs: the regulatory graph, which represents the interactions between regulatory components, each associated with discrete levels of expression (or activity), and the state transition graph, which represents the discrete dynamics of such a model. This discrete modelling framework allows qualitative analyses of the behaviours driven by regulatory networks, based on analytical results or on simulation (i.e. construction of state transition graphs). Although this formalism abstracts and simplifies the biological reality, we still need to cope with challenging issues due to the complexity of ever increasing networks. We present here some results and tools that aim at facilitating the analysis of large networks. In particular, we will show how dynamical properties can be predicted from the presence of particular motifs in the regulatory graph, namely regulatory circuits and combination of such circuits. We will also discuss a method to reduce the model, yet keeping the main features of the dynamics. Finally, we will illustrate these approaches on a generic model of E2F1-dependent apoptosis and cell cycle entries.
04:00 PM
05:00 PM
Gheorghe Craciun , Alan Veliz-Cuba, Elizabeth Remy - Day Four Discussion
Day Four Discussion
Friday, May 11, 2012
Time Session
10:00 AM
11:00 AM
Anne Shiu - Chemical reaction systems with toric steady states
Chemical reaction networks taken with mass-action kinetics are dynamical systems governed by polynomial differential equations that arise in systems biology. In general, establishing the existence of (multiple) steady states is challenging, as it requires the solution of a large system of polynomials with unknown coefficients. If, however, the steady state ideal of the system is a binomial ideal, then we show that these questions can be answered easily. This talk focuses on systems with this property, and we say such systems have toric steady states. Our main result gives sufficient conditions for a chemical reaction system to admit toric steady states. Furthermore, we analyze the capacity of such a system to exhibit multiple steady states. An important application concerns the biochemical reaction networks networks that describe the multisite phosphorylation of a protein by a kinase/phosphatase pair in a sequential and distributive mechanism. No prior knowledge of chemical reaction network theory or binomial ideals will be assumed.

This is joint work with Carsten Conradi, Mercedes Pérez Millán, and Alicia Dickenstein.
Name Affiliation
Ackermann, Eva evachr@fkp.tu-darmstadt.de Institut für Festkörperphysik, TU Darmstadt
Adeyeye, John adeyeyej@wssu.edu Mathematics, Winston-Salem State University
Aggarwal, Nitish aggarwal.nitish@gmail.com Mathematics, The Ohio State University
Aguilar, Boris boaguilar@gmail.com Computer Science, Virginia Polytechnic Institute and State University
Albert, Reka ralbert@phys.psu.edu Department of Physics, Pennsylvania State University
Aldana, Maximino max@fis.unam.mx FAS Center for Systems Biology, Harvard University
Arat, Seda sedag@vt.edu Biosystems, Virginia Bioinformatics Institute
Bar-Joseph, Ziv zivbj@cs.cmu.edu Computational biology, Carnegie-Mellon University
Basu, Sukanya basus@gvsu.edu Mathematics, Wentworth Institute of Technology
Brandon, Madison mbrando1@vt.edu Mathematics, Virginia Polytechnic Institute and State University
Brunson, Jason jabrunso@vt.edu Mathematics, Virginia Polytechnic Institute and State University
Chifman, Julia jchifman@wakehealth.edu Cancer Biology, Wake Forest School of Medicine
Chossat, Pascal pascal.chossat@cirm.univ-mrs.fr Centre National de la Recherche Scientifique (CNRS)
Craciun, Gheorghe craciun@math.wisc.edu Mathematics and Biomolecular Chemistry, University of Wisconsin-Madison
Datta, Aniruddha datta@ee.tamu.edu Electrical and Computer Engineering, Texas A & M University
Dougherty, Edward edward@ece.tamu.edu Electrical and Computer Engineering, Texas A & M University
G. T. Zanudo, Jorge jgtz@psu.edu Physics, Pennsylvania State University
Ghezzi, Katherine Katherine.Ghezzi@birkhauser-science.com Editorial, Springer Science+Business Media
Gunawardena, Jeremy jeremy@hms.harvard.edu Systems Biology, Harvard Medical School
Harrington, Heather heather.harrington06@imperial.ac.uk Division of Molecular Biosciences,
Haws, David david.haws@uky.edu Department of Statistics, University of Kentucky
Heiner, Monika Monika.Heiner@informatik.tu-cottbus.de Computer Science, Brandenburgische Technische Universit""at Cottbus
Hinkelmann, Franziska fhinkel@vt.edu MBI, The Ohio State University
Hodge, Terrell terrell.hodge@wmich.edu College of Arts and Sciences, Western Michigan University
Hofmann, Ariane ariane.hofmann@googlemail.com Mathematics, Virginia Polytechnic Institute and State University
Huang, Lei lh389@cornell.edu Biological Statistics and Computational Biology, Cornell University
Jarrah, Abdul Salam ajarrah@aus.edu Mathematics and Statistics, American University of Sharjah
Johnston, Matthew mdjohnst@math.uwaterloo.ca Applied Mathematics, University of Waterloo
Joo, Jaewook jjoo1@utk.edu Physics, University of Tennessee
Kadelka, Claus cthomaskadelka@aol.com Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University
Laubenbacher, Reinhard reinhard@vbi.vt.edu Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University
Lee, Shernita shernita@vbi.vt.edu Genetics, Bioinformatics, and Computational Biology, Virginia Polytechnic Institute and State University
Li, Yuan yuanli7983@gmail.com Mathematics, Winston Salem State University
Macauley, Matthew macaule@clemson.edu Mathematical Sciences, Clemson University
Mithani, Aziz mithani@stats.ox.ac.uk Department of Biology, School Of Science and Engineering, Lahore University of Management Sciences, Lahore, Pakistan
Mohammed-Awel, Jemal jmohammedawel@valdosta.edu Mathematics and Computer Science, Valdosta State University
Murrugarra, David davidmur@vbi.vt.edu Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University
Oremland, Matthew moremlan@vt.edu Mathematics, Virginia Polytechnic Institute and State University
Remy, Elisabeth elisabeth.remy@univmed.fr Institut de Mathématiques de Luminy, CNRS
Robeva, Rayna (Raina) robeva@sbc.edu Mathematical Sciences, Sweet Briar College
Rong, Yongwu yongwurong@gmail.com Mathematics, George Washington University
Roualdes, Edward edward.roualdes@uky.edu Statistics, University of Kentucky
Shih, Yu-Keng shihy@cse.ohio-state.edu Computer Science and Engineering, The Ohio State University
Shiu, Anne annejls@math.uchicago.edu Mathematics, University of Chicago
Shmulevich, Ilya ilya.shmulevich@gmail.com Department of Electrical Engineering, University of Washington
Socolar, Joshua socolar@phy.duke.edu Physics, Duke University
Stigler, Brandilyn bstigler@smu.edu Mathematics, Southern Methodist University
Stillman, Mike mike@math.cornell.edu Mathematics, Cornell University
Sullivant, Seth smsulli2@ncsu.edu Mathematics, North Carolina State University
Swirydowicz, Katarzyna kswirydo@vt.edu Mathematics, Virginia Polytechnic Institute and State University
Veliz-Cuba, Alan aveliz-cuba2@unl.edu Mathematics, University of Nebraska
Vera-Licona, Paola paola.vera-licona@curie.fr Bioinformatics and Computational Systems Biology of Cancer, Institut Curie
Weyenberg, Grady gswe222@g.uky.edu Statistics, University of Kentucky
Yarahmadian, Shantia syarahmadian@math.msstate.edu Department of Mathematics, Mississippi State University
Yoshida, Ruriko ruriko.yoshida@uky.edu Statistics, University of Kentucky
Zhi, Weifeng wzhi@ms.uky.edu Department of Mathematics, University of Kentucky
Avenues toward simplified Boolean modeling of signal transduction networks
Over the past five years my group, in collaboration with wet-bench biologists, developed and validated asynchronous Boolean models of several signal transduction networks. Along the way we have encountered obstacles related to the lack of timing knowledge and the large size of the state space. In this talk I will present three methodologies we developed to overcome these obstacles. First, from a comparative analysis of several asynchronous update methods we concluded that updating a single, randomly selected node at each time instant offers the best combination of information and economy.

Second, we developed a two-step network reduction method which was able to reduce the number of variables by 90% in two different systems without affecting their dynamic behaviors. Third, we proposed an integration of Boolean rules into graph theoretical analysis and showed that this semi-structural method can identify critical signal mediators on par with dynamic models.
Day Two Discussion
Day Two Discussion
Linking the Signaling Cascades and Dynamic Regulatory Networks Controlling Cellular Responses
Transcriptional gene regulation is a dynamic process and its proper functioning is essential for all living organisms. By combining the abundant static regulatory data with time series expression data using an Input-Output Hidden Markov model (IOHMM) we were able to reconstruct a dynamic representations for these networks in multiple species. The models lead to testable temporal hypotheses identifying both new regulators and their time of activation. We have recently extended these models, by solving an optimization problem related to graph orientation, to connect signaling and regulatory networks. These reconstructed networks link receptors and proteins that directly interact with the environment to the observed expression outcome. I will discuss the application and experimental validation of predictions made by our methods focusing on stress response in yeast. I would also mention a number of other extensions for integrating microRNAs and discriminative motif search and their applications for studying mice development and response to pathogens in mammalian cells.
Day Four Discussion
Day Four Discussion
Cancer Therapy Design Based on Pathway Logic
Cancer encompasses various diseases associated with loss of cell-cycle control, leading to uncontrolled cell proliferation and/or reduced apoptosis. Cancer is usually caused by malfunction(s) in the cellular signaling pathways. Malfunctions occur in different ways and at different locations in a pathway. Consequently, therapy design should first identify the location and type of malfunction and then arrive at a suitable drug combination. We consider the growth factor (GF) signaling pathways, widely studied in the context of cancer. Interactions between different pathway components are modeled using Boolean logic gates. All possible single malfunctions in the resulting circuit are enumerated and responses of the different malfunctioning circuits to a 'test' input are used to group the malfunctions into classes. Effects of different drugs, targeting different parts of the Boolean circuit, are taken into account in deciding drug efficacy, thereby mapping each malfunction to an appropriate set of drugs.
Day Two Discussion
Day Two Discussion
Intrinsically Bayesian Robust Structural Intervention and the Mean Objective Cost of Uncertainty in Gene Regulatory Networks
Standard operator optimization assumes a mathematical model and a family of operators on the model, defines an objective function to measure operator performance, and selects an optimal operator as one minimizing (maximizing) the objective function. With robust optimization the paradigm changes: the model is unknown and belongs to an uncertainty class of operators. If a prior distribution governs the uncertainty class, then an intrinsically Bayesian robust (IBR) operator is one that provides the minimum expectation of the objective function across the uncertainty class. The objective cost of uncertainty for any model in the uncertainty class is measured by the gain in performance from using an optimal operator for the model as opposed to using an IBR operator on the model. The overall cost of uncertainty is measured by the mean objective cost of uncertainty (MOCU) over the uncertainty class. Optimization is constrained by optimizing over the family of operators that are optimal for specific models in the uncertainty class. In this case, we refer to an optimal operator as a model-constrained Bayesian robust (MCBR) operator. Two general kinds of operational intervention have been considered for gene regulatory networks. Structural intervention involves a one-time alteration of the regulatory apparatus, which means a permanent change to the regulatory logic. Stationary intervention involves a time-invariant external control policy whose action at any time point depends on feedback from the system. In the presence of uncertainty, MCBR control has been treated for the stationary control of probabilistic Boolean networks in the framework of an objective cost of control and dynamic programming. This talk discusses IBR structural intervention for PBNs and the corresponding MOCU as it pertains to uncertain gene logic.
Invariants � polynomial signatures of molecular networks
A network of biochemical reactions gives rise, under mass-action kinetics, to a polynomial dynamical system, the steady states of which form a real algebraic variety. Methods from computational algebraic geometry have begun to yield biological insights into such networks. Here, we review work on "invariants". An invariant is a polynomial expression in specified state variables that holds in any (positive) steady state of a network. Invariants characterise the behaviour of several model networks and concisely capture their salient behaviour. However, it remains challenging to calculate invariants and we do not yet understand why some networks have biologically-meaningful invariants while others, apparently, do not.
Non-parametric analysis of mass action models and data
How cells make decisions can be investigated using mathematical models. We describe a procedure to decide whether a model is compatible with steady-state data. This method requires no parameter values-- it is based on techniques from algebraic geometry, linear algebra, and optimization. Cellular decisions also depend on where they occur in the cell (e.g., nucleus or cytoplasm). We also find that cellular information processing can be altered by including spatial organization. Borrowing tools from chemical reaction network theory and dynamical systems, we show that the existence of distinct compartments plays a pivotal role in whether a system is capable of multistationarity.
Day Two Discussion
Day Two Discussion
Coloured Petri Nets for Multiscale Systems Biology
This talk reports on our investigations to explore appropriate modelling and analysis techniques for processes evolving simultaneously over time and space, applied to biological systems. Current challenges for modelling in Systems Biology include those associated with issues of complexity and representing systems with multi-scale attributes. A drawback of current modelling approaches, including Petri nets, is their limitation to relatively small networks. We use Stochastic and Continuous Petri Nets to consider continuous time evolution as Markov process or system of Ordinary Differential Equations, and Coloured Petri Nets to statically encode finite discrete space. Combining both concepts yields Coloured Stochastic and Coloured Continuous Petri nets, which allow for directly executable models as well as computational experiments using standard analysis and simulation techniques over very large networks. We illustrate our approach by a couple of case studies, including gradient formation, multistrain bacterial colonies, and planar cell polarity signalling in Drosophila wing.
Day One Discussion
Day One Discussion
A stochastic model for the evolution of metabolic network using neighbor dependence

The availability of genomes of many closely related bacteria with diverse metabolic capabilities offers the possibility of tracing metabolic evolution on a phylogeny relating the genomes to understand the evolutionary processes and constraints that affect the evolution of metabolic networks. Using simple (independent loss/gain of reactions) or complex (incorporating dependencies among reactions) stochastic models of metabolic evolution, it is possible to study how metabolic networks evolve over time. Here, we describe metabolic network evolution as a discrete space continuous time Markov process and introduce a neighbor-dependent model for the evolution of metabolic networks where the rates with which reactions are added or removed depend on the fraction of neighboring reactions present in the network. The model also allows estimation of the strength of the neighborhood effect during the course of evolution. We present Gibbs samplers for sampling networks at the internal node of a phylogeny and for estimating the parameters of evolution over a phylogeny without exploring the whole search space by iteratively sampling from the conditional distributions of the internal networks and parameters. The samplers are used to estimate the parameters of evolution of metabolic networks of bacteria in the genus Pseudomonas and to infer the metabolic networks of the ancestral pseudomonads. The results suggest that pathway maps that are conserved across the Pseudomonas phylogeny have a stronger neighborhood structure than those which have a variable distribution of reactions across the phylogeny, and that some Pseudomonas lineages are going through genome reduction resulting in the loss of a number of reactions from their metabolic networks.

Logical modelling of regulatory networks, results and challenges
The logical method proved useful for the modelling of regulatory networks and the analysis of their dynamical properties. It relies on two directed graphs: the regulatory graph, which represents the interactions between regulatory components, each associated with discrete levels of expression (or activity), and the state transition graph, which represents the discrete dynamics of such a model. This discrete modelling framework allows qualitative analyses of the behaviours driven by regulatory networks, based on analytical results or on simulation (i.e. construction of state transition graphs). Although this formalism abstracts and simplifies the biological reality, we still need to cope with challenging issues due to the complexity of ever increasing networks. We present here some results and tools that aim at facilitating the analysis of large networks. In particular, we will show how dynamical properties can be predicted from the presence of particular motifs in the regulatory graph, namely regulatory circuits and combination of such circuits. We will also discuss a method to reduce the model, yet keeping the main features of the dynamics. Finally, we will illustrate these approaches on a generic model of E2F1-dependent apoptosis and cell cycle entries.
Day Four Discussion
Day Four Discussion
Chemical reaction systems with toric steady states
Chemical reaction networks taken with mass-action kinetics are dynamical systems governed by polynomial differential equations that arise in systems biology. In general, establishing the existence of (multiple) steady states is challenging, as it requires the solution of a large system of polynomials with unknown coefficients. If, however, the steady state ideal of the system is a binomial ideal, then we show that these questions can be answered easily. This talk focuses on systems with this property, and we say such systems have toric steady states. Our main result gives sufficient conditions for a chemical reaction system to admit toric steady states. Furthermore, we analyze the capacity of such a system to exhibit multiple steady states. An important application concerns the biochemical reaction networks networks that describe the multisite phosphorylation of a protein by a kinase/phosphatase pair in a sequential and distributive mechanism. No prior knowledge of chemical reaction network theory or binomial ideals will be assumed.

This is joint work with Carsten Conradi, Mercedes Pérez Millán, and Alicia Dickenstein.
Transcriptional Regulatory Networks from the Bottom Down
Regulatory networks of biomolecular interactions in cells govern virtually all cellular behaviors and functions. Modern measurement technologies are being used to generateinformation on many types of interactions, involving transcriptional and microRNA regulatory networks, signaling networks, and cytokine networks. Temporal measurements of gene and protein expression levels and chromatin modifications, coupled with data fusion strategies that incorporate computational predictions of regulatory mechanisms on the basis of other types of information, such as nucleic acid sequence, can be used to constructdynamical system models of these networks. The analysis and simulation of such models, in conjunction with experimental validation, sheds light on biological function and paves the way toward rational and systematic control strategies intended to drive a diseased system toward a desired state by means of targeted interventions. At the same time, such systems approaches permit new biological observables that reflect system-level behavior that cannot be understood by studying individual sets of interactions. Cellular decision making, maintenance of homeostasis and robustness, sensitivity to diverse types of information in the presence of environmental variability, and coordination ofcomplex macroscopic behavior are examples of such emergent systems-level behavior. Information theoretic approaches combined with elements of dynamical systems theory, such as phase transitions and structure dynamics relationships, are promising frameworks for studying fundamental principles governing living systems at all scales of organization.
Day One Discussion
Day One Discussion
Reverse Engineering of Regulatory Networks Using Algebraic Geometry
Discrete models have been used successfully in modeling biological processes such as gene regulatory networks. When certain regulation mechanisms are unknown it is important to be able to identify the best model with the available data. In this context, reverse engineering of finite dynamical systems from partial information is an important problem. In this talk we will present a framework and algorithm to reverse engineer the possible wiring diagrams of a finite dynamical system from data. The algorithm consists on using an ideal of polynomials to encode all possible wiring diagrams, and choose those that are minimal using the primary decomposition. We will also show that these results can be applied to reverse engineer continuous dynamical systems.
Day Four Discussion
Day Four Discussion
An Algebra-Based Method to Infer the Structure and Dynamics of Gene Regulatory Networks

The inference of molecular networks is an important problem in systems biology. This includes both the structure of the network in the form of its wiring diagram and its long-term dynamics. While there are many algorithms available that aim to infer network structure from experimental data, less emphasis has been placed on methods that utilize time series data effectively to infer both structure and dynamics. Since the network inference problem is typically underdetermined, it is important to also have the option of incorporating prior biological knowledge about the network into the process along with an effective description of the model search space. Finally, it is important to have an understanding of how a given inference method is affected by experimental and other noise in the data used for this purpose.

In this talk we will introduce a novel inference algorithm within the Boolean polynomial dynamical system (BPDS) framework, to meet all these requirements. The algorithm is able to use time series data, including network perturbations such as knock-out mutants and RNAi experiments. To infer wiring diagrams and dynamical models, it allows for the incorporation of prior biological knowledge while being robust to significant levels of noise in the data used for inference. It uses an evolutionary algorithm for local optimization with an encoding of models as BPDS. We will show how within this BPDS framework it is possible to give an effective representation of the model space to be searched to improve computational performance. We will show a validation of the algorithm with both an in silico network and with microarray expression profiles from a synthetic yeast network.

Day One Discussion
Day One Discussion
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Transcriptional Regulatory Networks from the Bottom Down
Ilya Shmulevich Regulatory networks of biomolecular interactions in cells govern virtually all cellular behaviors and functions. Modern measurement technologies are being used to generateinformation on many types of interactions, involving transcriptional and microR

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A stochastic model for the evolution of metabolic network using neighbor dependence
Aziz Mithani

The availability of genomes of many closely related bacteria with diverse metabolic capabilities offers the possibility of tracing metabolic evolution on a phylogeny relating the genomes to understand the evolutionary processes and constraints tha

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Coloured Petri Nets for Multiscale Systems Biology
Monika Heiner This talk reports on our investigations to explore appropriate modelling and analysis techniques for processes evolving simultaneously over time and space, applied to biological systems. Current challenges for modelling in Systems Biology include tho

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Chemical reaction systems with toric steady states
Anne Shiu Chemical reaction networks taken with mass-action kinetics are dynamical systems governed by polynomial differential equations that arise in systems biology. In general, establishing the existence of (multiple) steady states is challenging, as it req

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Logical modelling of regulatory networks, results and challenges
Elisabeth Remy The logical method proved useful for the modelling of regulatory networks and the analysis of their dynamical properties. It relies on two directed graphs: the regulatory graph, which represents the interactions between regulatory components, each as

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Non-parametric analysis of mass action models and data
Heather Harrington How cells make decisions can be investigated using mathematical models. We describe a procedure to decide whether a model is compatible with steady-state data. This method requires no parameter values-- it is based on techniques from algebraic geomet

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Cancer Therapy Design Based on Pathway Logic
Aniruddha Datta Cancer encompasses various diseases associated with loss of cell-cycle control, leading to uncontrolled cell proliferation and/or reduced apoptosis. Cancer is usually caused by malfunction(s) in the cellular signaling pathways. Malfunctions occur in

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Avenues toward simplified Boolean modeling of signal transduction networks
Reka Albert Over the past five years my group, in collaboration with wet-bench biologists, developed and validated asynchronous Boolean models of several signal transduction networks. Along the way we have encountered obstacles related to the lack of timing know