Seminars and Colloquia by Series

Stochastic Discrete Dynamical Systems

Series
Mathematical Biology Seminar
Time
Wednesday, April 18, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
David MurrugarraVirginia Tech
Modeling stochasticity in gene regulation is an important and complex problem in molecular systems biology. This talk will introduce a stochastic modeling framework for gene regulatory networks. 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 a discrete variable. One of the new features of this framework is that it allows a finer analysis of discrete models and the possibility to simulate cell populations. A background to stochastic modeling will be given and applications will use two of the best known stochastic regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.

Multi-scale Model of CRISPR-induced Coevolutionary Dynamics: Diversification at the Interface of Lamarck and Darwin

Series
Mathematical Biology Seminar
Time
Wednesday, March 7, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Lauren ChildsBiology, Georgia Tech
The CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) system is a recently discovered immune defense in bacteria and archaea (hosts) that functions via directed incorporation of viral DNA into host genomes. Here, we introduce a multi-scale model of dynamic coevolution between hosts and viruses in an ecological context that incorporates CRISPR immunity principles. We analyze the model to test whether and how CRISPR immunity induces host and viral diversification and maintenance of coexisting strains. We show that hosts and viruses coevolve to form highly diverse communities through punctuated replacement of extant strains. The populations have very low similarity over long time scales. However over short time scales, we observe evolutionary dynamics consistent with incomplete selective sweeps of novel strains, recurrence of previously rare strains, and sweeps of coalitions of dominant host strains with identical phenotypes but different genotypes. Our explicit eco-evolutionary model of CRISPR immunity can help guide efforts to understand the drivers of diversity seen in microbial communities where CRISPR systems are active. 

Modeling angiogenesis from pathways to tissue

Series
Mathematical Biology Seminar
Time
Wednesday, February 29, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yi JiangGSU
Angiogenesis, growth of new blood vessels from existing ones, is animportant process in normal development, wound healing, and cancer development.  Presented with increasingly complex biological data and observations, the daunting task is to develop a mathematical model that is useful, i.e. can help to answer important and relevant questions, or to test a hypothesis, and/or to cover a novel mechanism. I will present two cell-based multiscale models focusing on biochemical (vescular endothelial growth factors) and biomechanical (extra-cellular matrix) interactions.  Our models consider intracellular signaling pathways, cell dynamics, cell-cell andcell-environment interactions. I will show that they reproduced someexperimental observations, tested some hypotheses, and generated more hypotheses.

Geometric flow for biomolecular solvation

Series
Mathematical Biology Seminar
Time
Wednesday, February 8, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Nathan BakerPacific Northwest National Laboratory
Implicit solvent models are important components of modern biomolecular simulation methodology due to their efficiency and dramatic reduction of dimensionality. However, such models are often constructed in an ad hoc manner with an arbitrary decomposition and specification of the polar and nonpolar components. In this talk, I will review current implicit solvent models and suggest a new free energy functional which combines both polar and nonpolar solvation terms in a common self-consistent framework. Upon variation, this new free energy functional yields the traditional Poisson-Boltzmann equation as well as a new geometric flow equation. These equations are being used to calculate the solvation energies of small polar molecules to assess the performance of this new methodology. Optimization of this solvation model has revealed strong correlation between pressure and surface tension contributions to the nonpolar solvation contributions and suggests new ways in which to parameterize these models. **Please note nonstandard time and room.**

Chemical reaction systems with toric steady states

Series
Mathematical Biology Seminar
Time
Wednesday, January 25, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anne ShiuUniversity of Chicago
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, are 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 P\'erez Mill\'an, and Alicia Dickenstein.)

CANCELED: (Geometric flow for biomolecular solvation)

Series
Mathematical Biology Seminar
Time
Wednesday, December 7, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nathan BakerPacific Northwest National Laboratory
Implicit solvent models are important components of modern biomolecular simulation methodology due to their efficiency and dramatic reduction of dimensionality. However, such models are often constructed in an ad hoc manner with an arbitrary decomposition and specification of the polar and nonpolar components. In this talk, I will review current implicit solvent models and suggest a new free energy functional which combines both polar and nonpolar solvation terms in a common self-consistent framework. Upon variation, this new free energy functional yields the traditional Poisson-Boltzmann equation as well as a new geometric flow equation. These equations are being used to calculate the solvation energies of small polar molecules to assess the performance of this new methodology. Optimization of this solvation model has revealed strong correlation between pressure and surface tension contributions to the nonpolar solvation contributions and suggests new ways in which to parameterize these models.

CANCELLED (Multi-scale Model of CRISPR-induced Coevolutionary Dynamics -- Diversification at the Interface of Lamarck and Darwin)

Series
Mathematical Biology Seminar
Time
Wednesday, November 16, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Lauren ChildsBiology, Georgia Tech
The CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) system is a recently discovered immune defense in bacteria and archaea (hosts) that functions via directed incorporation of viral DNA intohost genomes. Here, we introduce a multi-scale model of dynamic coevolution between hosts and viruses in an ecological context that incorporates CRISPR immunity principles. We analyze the model to test whether and how CRISPR immunity induces host and viral diversification and maintenance of coexisting strains. We show that hosts and viruses coevolve to form highly diverse communities through punctuated replacement of extant strains. The populations have very low similarity over long time scales. However overshort time scales, we observe evolutionary dynamics consistent with incomplete selective sweeps of novel strains, recurrence of previously rare strains, and sweeps of coalitions of dominant host strains with identical phenotypes but different genotypes. Our explicit eco-evolutionary model of CRISPR immunity can help guide efforts to understand the drivers of diversity seen in microbial communities where CRISPR systems are active.

Discrimination of binary patterns by perceptrons with binary weights

Series
Mathematical Biology Seminar
Time
Wednesday, November 9, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Andrei OliferGeorgia Gwinnett College
Information processing in neurons and their networks is understood incompletely, especially when neuronal inputs have indirect correlates with external stimuli as for example in the hippocampus. We study a case when all neurons in one network receive inputs from another network within a short time window. We consider it as a mapping of binary vectors of spiking activity ("spike" or "no spike") in an input network to binary vectors of spiking activity in the output network. Intuitively, if an input pattern makes a neuron spike then the neuron should also spike in response to similar patterns - otherwise, neurons would be too sensitive to noise. On the other hand, neurons should discriminate between sufficiently different input patterns and spike selectively. Our main goal was to quantify how well neurons discriminate input patterns depending on connectivity between networks, spiking threshold of neurons and other parameters. We modeled neurons with perceptrons that have binary weights. Most recent results on perceptron neuronal models are asymptotic with respect to some parameters. Here, using combinatorial analysis, we complement them by exact formulas. Those formulas in particular predict that the number of the inputs per neuron maximizes the difference between the neuronal and network responses to similar and distinct inputs. A joint work with Jean Vaillant (UAG).

“What’s Eating You?” Quantifying Proteolytic Activity in Health and Disease with Novel Assays and Computational Models

Series
Mathematical Biology Seminar
Time
Wednesday, October 19, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Manu O. PlattCoulter Department of Biomedical Engineering, Georgia Institute of Technology & Emory University
Cathepsins are enzymes that can cleave collagen and elastin, major structural proteins of tissue and organs, and participate in tissue-destructive disease progression seen in osteoporosis, arthritis, atherosclerosis, and cancer metastasis. Detection of mature cathepsins and quantification of specific activity have proven difficult due to instability of the mature, active enzyme extracellularly, which has led to them being overlooked in a number of diseases. During this seminar, Dr. Platt will discuss the important development of a reliable, sensitive method to detect the activity of mature cathepsins K, L, S, and V. Then he will focus on their progress towards developing a comprehensive computational model of cathepsin-mediated degradation of extracellular matrix, based on systems of ordinary differential equations. From the computational model and experimental results, a general assumption of inertness between familial enzymes was shown to be invalid as it failed to account for the interaction of these proteases among themselves and within their microenvironment. A consequence of this was significant overestimation of total degradative potential in multiple cathepsin reaction systems. After refining the system to capture the cathepsin interactive dynamics and match the experimental degradation results, novel mechanisms of cathepsin degradation and inactivation were revealed and suggest new ways to inhibit their activity for therapeutic benefit.

Modeling and measuring different interferon resistance of HCV quasispecies (Math Biology)

Series
Mathematical Biology Seminar
Time
Wednesday, October 12, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Pavel SkumsCDC
Hepatitis C virus (HCV) infects 2.2% of the world's population and is a major cause of liver disease worldwide. There is no vaccine against HCV and current interferon and ribavirin (IFN/RBV) therapy is effective in 50%-60% of patients. Since the interferon therapy is the expansive and painful for the patient process, it is very important to predict its outcome before starting full course of treatment. HCV exists in infected patients as a large viral population of intra-host variants (quasispecies), which form the certain topological structure (sequence space) and may be differentially resistant to interferon treatment. We present a method for measuring differential interferon resistance of HCV quasispecies based on the mathematical modeling and analysis of HCV population dynamics during the first hours of interferon therapy. The analysis of the model allowed us to accurately predict the long-term outcome of the interferon therapy on the test group of patients.

Pages