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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