Title: On the Robustness of Cancer Networks: A Geometric Approach
Abstract: Cellular interactions can be modeled as complex dynamical systems represented by weighted graphs. The functionality of such networks, including measures of robustness, reliability, performance, and efficiency, are intrinsically tied to the topology and geometry of the underlying graph. Utilizing recently proposed geometric notions of curvature on weighted graphs, we investigate the features of gene co-expression networks derived from large-scale genomic studies of cancer. We find that the curvature of these networks reliably distinguishes between cancer and normal samples, with cancer networks exhibiting higher curvature than their normal counterparts. We establish a quantitative relationship between our findings and prior investigations of network entropy. Furthermore, we demonstrate how our approach yields additional, non-trivial pair-wise (i.e. gene-gene) interactions which may be disrupted in cancer samples. The mathematical formulation of our approach yields an exact solution to calculating pair-wise changes in curvature which was computationally infeasible using prior methods. As such, our findings lay the foundation for an analytical approach to studying complex biological networks.
Title: Optimal Resource Allocation to Control Epidemic Outbreaks in Networked Populations
Abstract: We study the problem of controlling epidemic outbreaks in networked populations by distributing protection resources throughout the nodes of the network. We assume that two types of protection resources are available: (i) Preventive resources able to defend individuals in the population against the spreading of the disease (such as vaccines or disease-awareness campaigns), and (ii) corrective resources able to neutralize the spreading (such as antidotes). We assume that both preventive and corrective resources have an associated cost and study the problem of finding the cost-optimal distribution of resources throughout the networked population. We analyze these questions in the context of a viral outbreak and study the following two problems: (i) Given a fixed budget, find the optimal allocation of preventive and corrective resources in the network to achieve the highest level of disease containment, and (ii) when a budget is not specified, find the minimum budget required to eradicate the disease. We show that both resource allocation problems can be efficiently solved for a wide class of cost functions. We illustrate our approach by designing optimal protection strategies to contain an epidemic outbreak that propagates through the air transportation network.
Speaker: Sahand Jamal Rahi, Rockefeller University
When:Tuesday February 14th, 2017 12:00pm
Where: Hill 260 (Busch Campus, Rutgers)
Title: Dynamics: Challenge and tool for understanding living systems
Abstract: A central challenge in biology is to predict system behavior in time, given incomplete knowledge, strong interactions, and noise. We have pursued multiple approaches to building predictive dynamical descriptions of biological systems, making progress toward general principles. We have focused on three specific problems: 1) The number of global oscillators controlling the 'cell cycle', the process by which cells replicate, had been unresolved. This left a number of fundamental questions unanswered: How do different processes sync up during the cell cycle? How can the cell cycle be arrested? We found that one central oscillator controls two major cell cycle processes, periodic phosphorylation/degradation and transcription, contradicting previous views. However, we also found exceptions to this rule; pursuing one such gene, we discovered a new, counter-intuitive genetic interaction between an inhibitor and a target, which violates the usual rules of genetics. 2) Can dynamic perturbations be used to identify molecular circuit topologies? We discovered dynamic 'response signatures' for specific circuit topologies and used them to solve previously hard-to-resolve questions: We identified the circuit responsible for timing robustness in yeast cell cycle control as well as a circuit leading to adaptation in the C. elegans olfactory sensory neuron AWA. 3) Do cell cycle checkpoints 'fail' in predictable patterns? A mathematically optimal checkpoint strategy, which we derived, predicts how cell cycle checkpoints fail as a function of the number of errors. Our preliminary experimental results agree with our predictions but challenge current views in the field; checkpoint failure may be a more common phenomenon than previously thought.
Title: Blind nonnegative source separation using biological neural networks
Abstract:Extraction of latent causes, or sources, from complex stimuli is essential for making sense of the world. Such stimuli could be mixtures of sounds, mixtures of odors, or natural images. If supervision, or ground truth, about the causes is lacking the problem is known as blind source separation. Here, we address a special and biologically relevant case of this problem when sources (but not the mixing matrix) are known to be nonnegative, for example, due to the physical nature of the sources. We search for the solution to this problem that can be implemented using biologically plausible neural networks. Specifically, we consider the online setting where the dataset is streamed to a neural network. The novelty of our approach is that we formulate blind nonnegative source separation as a similarity matching problem and derive neural networks from the similarity matching objective. Importantly, synaptic weights in our networks are updated per biologically plausible local learning rules. The resulting network architecture is reminiscent of the early stages of sensory processing in the brain.
Title:Genomic data analysis and dimensionality reduction in tree spaces
Abstract: Phylogenetic trees are arguably the most common representation of evolutionary processes. As genomic data has become more readily available, visualization and unsupervised statistical analysis of associated phylogenetic structures has gained significant complexity. Here, we introduce tree dimensionality reduction (TDR), a structured approach for reducing large and complex phylogenetic trees to a distribution of smaller ones, transforming questions about analysis of finite sets of trees to questions about comparisons and analysis of sets of point clouds of smaller trees. We show that using the metric geometry of tree spaces, point clouds of trees become amenable to statistical inference. We apply tree dimensionality reduction to 24 years of longitudinally collected H3N2 hemagglutinin sequences, and observe that the variance of the distributions produced from three to five seasons' sequence data correlates negatively with the influenza vaccine effectiveness in succeeding season. We show how tree distributions relate to antigenic clusters and choice of influenza vaccine, providing compelling evidence that TDR exposes links between genomic data of influenza A and important clinical observables, namely vaccine selection and efficacy.
Title:Quantitative biology of developmental metabolism and growth
Abstract:
This will be based on the work with two of my students, Jasmin Imran Alsous (growth) and Yonghyun Song (metabolism).
The first story is about differential growth, exploring how parts of a growing system change their size at different rates. We have a system where the number of parts is constant and small, only 16 cells, and they grow at very different rates. We track this differential growth by imaging and propose a simple 16-dimensional dynamical system for explaining the observed growth pattern. The second part of the talk will be about the first steps during the transformation of a single cell, a fertilized egg, into an embryo. In all animals, this process involves reductive cell divisions, accompanied by an exponential increase of the genomes. This requires tight control over the supply of dNTPs. We discovered that this supply is regulated by negative feedback system that ensures that the embryo makes just much dNTPs as it needs.