Seminars and Colloquia by Series

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

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).

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