Seminars and Colloquia by Series

Modeling Stochasticity and Variability in Gene Regulatory Networks with Applications to the Development of Optimal Intervention Strategies

Series
Mathematical Biology Seminar
Time
Wednesday, September 25, 2013 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles Bld Room 005
Speaker
D. MurrugarraSoM, GaTech
Modeling stochasticity in gene regulation is an important and complex problem in molecular systems biology due to probabilistic nature of gene regulation. This talk will introduce a stochastic modeling framework for gene regulatory networks which is an extension of the Boolean modeling approach. This framework incorporates propensity parameters for activation and degradation and is able to capture the cell-to-cell variability. It will be presented in the context of finite dynamical systems, where each gene can take on a finite number of states, and where time is also a discrete variable. Applications using methods from control theory for Markov decision processes will be presented for the purpose of developing optimal intervention strategies. A background to stochastic modeling will be given and the methods will be applied to the p53-mdm2 complex.

Why the brain wiring's might use more than one decay scale

Series
Mathematical Biology Seminar
Time
Thursday, September 12, 2013 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
R.StoopInst. of Neuroinformatics, ETH, Zurich
We study to what extent cortical columns with their particular wiring, could boost neural computation. Upon a vast survey of columnar networks performing various real-world cognitive tasks, we detect no signs of the expected enhancement. It is on a mesoscopic?intercolumnar?scale that the wiring among the columns, largely irrespective of their inner organization, enhances the speed of information transfer and minimizes the total wiring length required to bind distributed columnar computations towards spatiotemporally coherent results. We suggest that brain efficiency may be related to a doubly fractal connectivity law, resulting in networks with efficiency properties beyond those by scale-free networks and we exhibit corroborating evidence for this suggestion. Despite the current emphasis on simpler, e.g., critical, networks, networks with more than one connectivity decay behavior may be the rule rather than the exception. Ref: Beyond Scale-Free Small-World Networks: Cortical Columns for Quick Brains Ralph Stoop, Victor Saase, Clemens Wagner, Britta Stoop, and Ruedi Stoop, PRL 108105 (2013)

Cascades and Social Influence on Networks

Series
Mathematical Biology Seminar
Time
Wednesday, August 28, 2013 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles Bld Room 005
Speaker
Mason PorterOxford, UK
I discuss "simple" dynamical systems on networks and examine how network structure affects dynamics of processes running on top of networks. I consider results based on "locally tree-like" and/or mean-field and pair approximations and examine when they seem to work well, what can cause them to fail, and when they seem to produce accurate results even though their hypotheses are violated fantastically. I'll also present a new model for multi-stage complex contagions--in which fanatics produce greater influence than mere followers--and examine dynamics on networks with hetergeneous correlations. (This talk discusses joint work with Davide Cellai, James Gleeson, Sergey Melnik, Peter Mucha, J-P Onnela, Felix Reed-Tsochas, and Jonathan Ward.)

Using semigroups to study coupled cell networks

Series
Mathematical Biology Seminar
Time
Wednesday, April 24, 2013 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
B.W. RinkVrije Univ. Amsterdam
Abstract: Dynamical systems with a coupled cell network structure arise in applications that range from statistical mechanics and electrical circuits to neural networks, systems biology, power grids and the world wide web. A network structure can have a strong impact on the behaviour of a dynamical system. For example, it has been observed that networks can robustly exhibit (partial) synchronisation, multiple eigenvalues and degenerate bifurcations. In this talk I will explain how semigroups and their representations can be used to understand and predict these phenomena. As an application of our theory, I will discuss how a simple feed-forward motif can act as an amplifier. This is joint work with Jan Sanders.

Generation and Synchronization of Oscillations in Synthetic Gene Networks

Series
Mathematical Biology Seminar
Time
Wednesday, April 17, 2013 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles Bldg, Room 006
Speaker
Lev TsimringUC San Diego, BIOCircuits Inst.
In this talk, I will describe our recent experimental and theoretical work on small synthetic gene networks exhibiting oscillatory behavior. Most living organisms use internal genetic "clocks" to govern fundamental cellular behavior. While the gene networks that produce oscillatory expression signals are typically quite complicated, certain recurring network motifs are often found at the core of these biological clocks. One common motif which may lead to oscillations is delayed auto-repression. We constructed a synthetic two-gene oscillator based on this design principle, and observed robust and tunable oscillations in bacteria. Computational modeling and theoretical analysis show that the key mechanism of oscillations is a small delay in the negative feedback loop. In a strongly nonlinear regime, this time delay can lead to long-period oscillations that can be characterized by "degrade and fire'' dynamics. We also achieved synchronization of synthetic gene oscillators across cell population as well as multiple populations using variants of the same design in which oscillators are synchronized by chemical signals diffusing through cell membranes and throughout the populations.

Long-Run Analysis of the Stochastic Replicator Dynamics in the Presence of Random Jumps

Series
Mathematical Biology Seminar
Time
Wednesday, January 30, 2013 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles Bld Room 005
Speaker
Andrew VlasicIndiana University
For many evolutionary dynamics, within a population there are finitely many types that compete with each other. If we think of a type as a strategy, we may consider this dynamic from a game theoretic perspective. This evolution is frequency dependent, where the fitness of each type is given by the expected payoff for an individual in that subpopulation. Considering the frequencies of the population, the logarithmic growth is given by the difference of the respective fitness and the average fitness of the population as a whole. This dynamic is Darwinian in nature, where Nash Equilibria are fixed points, and Evolutionary Stable Strategies are asymptotically stable. Fudenberg and Harris modified this deterministic dynamic by assuming the fitness of each type are subject to population level shocks, which they model by Brownian motion. The authors characterize the two strategy case, while various other authors considered the arbitrary finite strategy case, as well as different variations of this model. Considering how ecological and social anomalies affect fitness, I expand upon the Fudenberg and Harris model by adding a compensated Poisson term. This type of stochastic differential equation is no longer continuous, which complicates the analysis of the model. We will discuss the approximation of the 2 strategy case, stability of Evolutionary Stable Strategies and extinction of dominated strategies for the arbitrary finite strategy case. Examples of applications are given. Prior knowledge of game theory is not needed for this talk.

Time-varying dynamical networks

Series
Mathematical Biology Seminar
Time
Wednesday, November 28, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles Bldg Rm.005
Speaker
Igor BelykhGeorgia State
This talk focuses on mathematical analysis and modeling of dynamical systems and networks whose coupling or internal parameters stochastically evolve over time. We study networks that are composed of oscillatory dynamical systems with connections that switch on and off randomly, and the switching time is fast, with respect to the characteristic time of the individual node dynamics. If the stochastic switching is fast enough, we expect the switching system to follow the averaged system where the dynamical law is given by the expectation of the stochastic variables. There are four distinct classes of switching dynamical networks. Two properties differentiate them: single or multiple attractors of the averaged system and their invariance or non-invariance under the dynamics of the switching system. In the case of invariance, we prove that the trajectories of the switching system converge to the attractor(s) of the averaged system with high probability. In the non-invariant single attractor case, the trajectories rapidly reach a ghost attractor and remain close most of the time with high probability. In the non-invariant multiple attractor case, the trajectory may escape to another ghost attractor with small probability. Using the Lyapunov function method, we derive explicit bounds for these probabilities. Each of the four cases is illustrated by a specific technological or biological network.

Computational genomics and its challenges: From finding extreme elements to rearranging genomes

Series
Mathematical Biology Seminar
Time
Wednesday, September 19, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dmitry KorkinInformatics Institute and Department of Computer Science, University of Missouri-Columbia
We have recently witnessed the tremendous progress in evolutionary and regulatory genomics of eukaryotes fueled by hundreds of sequenced eukaryotic genomes, including human and dozens of animal and plant genomes and culminating in the recent release of The Encyclopedia of DNA Elements (ENCODE) project. Yet, many interesting questions about the functional and structural organization of the genomic elements and their evolution remain unsolved. Computational genomics methods have become essential in addressing these questions working with the massive genomic data. In this presentation, I will talk about two interesting open problems in computational genomics. The first problem is related to identifying and characterizing long identical multispecies elements (LIMEs), the genomic regions that were slowed down through the course of evolution to their extremes. I will discuss our recent findings of the LIMEs shared across six animal as well as six plant genomes and the computational challenges associated with expanding our results towards other species. The second problem is finding genome rearrangements for a group of genomes. I will present out latest approach approach that brings together the idea of symbolic object representation and stochastic simulation of the evolutionary graphs.

A NEW PARADIGM OF CANCER PROGRESSION AND TREATMENT DISCOVERED THROUGH MATHEMATICAL MODELING: WHAT MEDICAL DOCTORS WON’T TELL YOU

Series
Mathematical Biology Seminar
Time
Wednesday, April 25, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Leonid KhaninIdaho State University
Normal 0 false false false EN-US X-NONE X-NONE   Over the last several decades, cancer has become a global pandemic of epic proportions. Unfortunately, treatment strategies resulting from the traditional approach to cancer have met with only limited success. This calls for a paradigm shift in our understanding and treating cancer.    In this talk, we present an entirely mechanistic, comprehensive mathematical model of cancer progression in an individual patient accounting for primary tumor growth, shedding of metastases, their dormancy and growth at secondary sites. Parameters of the model were estimated from the age and volume of the primary tumor at diagnosis and volumes of detectable bone metastases collected from one breast cancer and 12 prostate cancer patients. This allowed us to estimate, for each patient, the age at cancer onset and inception of all detected metastasis, the expected metastasis latency time and the rates of growth of the primary tumor and metastases before and after the start of treatment. We found that for all patients: (1) inception of the first metastasis occurred very early when the primary tumor was undetectable; (2) inception of all or most of the surveyed metastases occurred before the start of treatment; (3) the rate of metastasis shedding was essentially constant in time regardless of the size of the primary tumor, and so it was only marginally affected by treatment; and most importantly, (4) surgery, chemotherapy and possibly radiation bring about a dramatic increase in the rate of growth of metastases. Although these findings go against the conventional paradigm of cancer, they confirm several hypotheses that were debated by oncologists for many decades. Some of the phenomena supported by our conclusions, such as the existence of dormant cancer cells and surgery-induced acceleration of metastatic growth, were first observed in clinical investigations and animal experiments more than a century ago and later confirmed in numerous modern studies. 

Computation of limit cycles and their isochrons: Applications to biology.

Series
Mathematical Biology Seminar
Time
Wednesday, April 18, 2012 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Gemma HuguetNYU
 In this talk we will present a numerical method to perform the effective computation of the phase advancement when we stimulate an oscillator which has not reached yet the asymptotic state (a limit cycle). That is we extend the computation of the phase resetting curves (the classical tool to compute the phase advancement) to a neighborhood of the limit cycle, obtaining what we call the phase resetting surfaces (PRS). These are very useful tools for the study of synchronization of coupled oscillators. To achieve this goal we first perform a careful study of the theoretical grounds (the parameterization method for invariant manifolds and the Lie symmetries approach), which allow to describe the isochronous sections of the limit cycle and, from them, to obtain the PRSs. In order to make this theoretical framework applicable, we design a numerical scheme to compute both the isochrons and the PRSs of a given oscillator. Finally, we will show some examples of the computations we have carried out for some well-known biological models. This is joint work with Toni Guillamon and R. de la Llave

Pages