SCIENTIFIC PROGRAMS AND ACTIVITIES

August 30, 2014
THE FIELDS INSTITUTE
FOR RESEARCH IN MATHEMATICAL SCIENCES
June 7, 2012
Guelph Biomathematics and Biostatistics Symposium

Frontiers in Networks: Models and Applications

Organizers
Chris Bauch, University of Guelph(Co-Chair, Mathematics)
Julie Horrocks, University of Guelph
(Co-Chair, Statistics)

Stefano Allesina, Department of Ecology and Evolution, University of Chicago
Interaction Type and the Stability of Large Ecological Networks


Forty years ago, May proved that large ecological networks would invariably be unstable and thus would not persist in time. May analysed large networks in which species interact at random. However, in natural systems pairs of species have well-defined interactions (for example predator–prey, mutualistic or competitive). Extending May's results to these cases, I find remarkable differences between predator–prey interactions, which are stabilizing, and mutualistic and competitive interactions, which are destabilizing. In mutualistic systems, nestedness is believed to have an important stabilizing effect. I show that this is not the case: nestedness, among all possible structures is the most destabilizing. To prove this result I develop an intuitive and robust characterization of nestedness in binary and quantitative ecological networks.

Shojaeddin Chenouri, Department of Statistics and Actuarial Sciences, University of Waterloo
A stochastic graph process for epidemic modelling

In this talk, a stochastic graph process with a Markov property is introduced to model the flow of an infectious disease over a known contact network. The model provides a probability distribution over unobserved infectious pathways. The basic reproductive number in compartmental models is generalized to a dynamic reproductive number based on the sequence of outdegrees in the graph process. The cumulative resistance and threat associated with each individual is also measured based on the cumulative indegree and outdegree of the graph process. The model is applied to the outbreak data from the 2001 foot-and-mouth (FMD) outbreak in the United Kingdom.

This is a joint work with Yasaman Hosseinkashi, Christopher G. Small and Rob Deardon.

Philip Kim
, Department of Molecular Genetics and Department of Computer Science, University of Toronto
Structure, Unstructure and Systems Biology

Genomics and systems biology have made great progress in recent years. At the same time, constant progress has been made in structural biology. Combining expertise from these fields can be very insightful and modern bioscience is increasingly becoming an integrative discipline. I will describe some recent progress on the boundary of the fields of protein structure (and unstructure) and systems biology. Many protein interactions, in particular those in signaling networks, are mediated by peptide recognition domains. These recognize short, linear amino acid stretches on
the surface of their cognate partners with high specificity. Residues in these stretches are usually assumed to contribute independently to binding, which has led to a simplified understanding of protein interactions. Conversely, in large binding peptide data sets different residue positions display highly significant correlations for many domains in three distinct families (PDZ, SH3 and WW). These correlation patterns reveal a widespread occurrence of multiple binding specificities and give novel structural insights into protein interactions. For example, a new binding mode of PDZ domains can be predicted and structurally rationalized for DLG1 PDZ1. While protein structure is very important for peptide binding domains, the
regions they bind are usually unstructured (intrinsically disordered). These regions are widespread, especially in proteomes of higher eukaryotes, and have been associated with a plethora of different cellular functions. Aside from general importance for signaling networks, they are also important for such diverse processes as protein folding or DNA binding. Leveraging knowledge from systems biology can help to structure the phenomenon. Strikingly, disorder can be partitioned into three biologically distinct phenomena: regions where disorder is conserved but with quickly evolving amino acid sequences (“flexible disorder”), regions of conserved disorder with also highly conserved amino acid sequence (“constrained disorder”) and, lastly, non-conserved disorder.

Eric Kolaczyk, Department of Mathematics & Statistics, Boston University
Network-based Statistical Models and Methods for Identification of Cellular Mechanisms of Action

Identifying biological mechanisms of action (e.g. biological pathways) that control disease states, drug response, and altered cellular function is a multifaceted problem involving a dynamic system of biological variables that culminate in an altered cellular state. The challenge is in deciphering the factors that play key roles in determining the cell's fate. In this talk I will describe some of the efforts by our group to develop statistical models and methods for identification of cellular mechanisms of action. More specifically, we assume gene expression data and treat the problem of determining mechanisms of action under perturbation (e.g., drug treatment, gene knockout, etc.) as a type of inverse problem. I will describe three approaches to solving this inverse problem. The first attempts to use only the gene expression data and to `filter' that data by an inferred network of gene regulatory interactions. The other two -- one testing-based and the other regression-based -- use gene expression data in conjunction with information from biological databases. More specifically, gene expression is modeled as deriving from a perturbed latent network of pathways, where the inter-connections among pathways is informed by shared biological function. Illustrations are given in the context of yeast experiments and human cancer.

Kevin McCann, Department of Integrative Biology, University of Guelph
The Stability of Ecological Networks: From Motifs to Whole Ecosystems

Here, we first show that the stability of one of the fundamental building blocks of ecological networks (i.e., the consumer-resource interaction) is dependent on whether the interaction strength between the two nodes/species is in an “excitable” domain (complex eigenvalues) or a “non-excitable” domain (entirely real eigenvalues). We then argue that a simple principle of relative interaction strength dictates whether other common ecological motifs are stabilized or destabilized by changes in relative interaction strength. Specifically, we argue that non-excitable interactions tend to be stabilized by increases in interaction strength whereas excitable interactions tend to be destabilized by increases in interaction strength. We end by then considering these ideas within the context of complex ecological networks to argue that these same rules gleaned from motifs appear to hold in complex networks.

Elisabeth Shiller, Department of Mathematics and Statistics, University of Guelph
Using evolution to locate contact networks for epidemics

This talk will explain a novel computational intelligence technology for fitting a network to data. Normally a contact network is generated using a statistical model or constructed from survey data. Presented is a technique that takes data about the number of individuals that become sick in a time period of an epidemic and then searches for contact networks that yield this behavior under an SIR model in which infection can only pass along links in the network. The technique used is an evolutionary algorithm using a generative representation that starts using an initial network with reasonable contact numbers for individuals and then evolves a sequence of editing commands. Quality of solutions is assessed by computing error of simulated epidemics on the network with the desired behavior. This is joint work with Dan Ashlock and Colin Lee.

Ali Shojaie, Department of Statistics, University of Washington
Network enrichment analysis: a framework for analysis of biological pathways in complex experiments

Advances in high throughput technologies have facilitated the simultaneous study of thousands of genes, proteins and metabolites. The challenge is no longer to identify the genes or proteins that are differentially expressed, but rather to find sub-systems that interact with each other in response to environmental conditions and/or are involved in disease progression and onset. Study of these interacting sub-systems has provided an invaluable source of additional information that can be used to better understand the complex mechanisms of life. I will discuss a model-based framework for analysis of biological pathways which directly incorporates available information on interactions among components of biological systems. The proposed approach uses recent developments in the graphical models, as well as the theory of mixed linear models to develop a rigorous and flexible framework for testing the effect of biological pathways in complex experimental settings. In silio and real data examples are used to demonstrate the efficiency of the proposed framework, and the advantages of incorporating the underlying network structure.

Shreyas Sundaram, Department of Electrical and Computer Engineering, University of Waterloo
Robustness of Complex Networks: Reaching Consensus Despite Adversaries

Complex networks (both natural and engineered) arise as a result of local interactions between various nodes (or agents). The efficacy of these networks is often predicated on their ability to diffuse information throughout the network, allowing the agents to reach consensus (or synchronize) on an appropriate quantity of interest. In this context, a key metric is the susceptibility of the network to a few individuals who wish to affect global decisions via their actions. This talk characterizes topological properties of networks that allow them to overcome adversarial behaviour of this form. We describe a natural class of diffusion dynamics where each node disregards its most extreme neighbours, and updates its own state to be a weighted average of the remaining neighbours' states. While this local rule is simple to describe, it turns out that traditional graph theoretic metrics (such as connectivity) are no longer sufficient to characterize the global behavior of this class of dynamics. Instead, we describe a new topological property termed "robustness", and show that networks with a sufficient degree of robustness can tolerate a variety of adversarial behaviour. We then show that several common random graph models for complex networks exhibit a threshold behaviour for robustness, and that well-connected complex networks also tend to be highly robust (a much stronger property).

 

 

 


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