Quantitative Biology Institute

QBI Seminars

MAY 28, 2008

Irvine 159 4:10-5:00PM

Sonya Bahar, Center for Neurodynamics, Department of Physics & Astronomy

University of Missouri at St. Louis

"Synchronization in the brain: from epilepsy to traumatic brain injury"

Abstract:

I will discuss the application of stochastic phase synchronization analysis to two pathological situations: (1) neural synchronization imaged in the rat cortex in vivo during focal seizures, and (2) synchronization between eye and target in human traumatic brain injury. In the first study, we perform in vivo voltage sensitive dye imaging of the rat cortex during 4-aminopyridine induced seizures. We find a sharp increase in synchronization between all areas of seizure activity during the duration of the seizure, supporting the hypothesis that seizure activity correlates with massive over-synchronization of neural firing in the affected brain area. In the traumatic brain injury study, we investigate the effect of brain injury on smooth pursuit eye movement, in which human subjects are asked to visually track a target moving in a circular path. We find that age, injury, and cognitive load all affect the subject's ability to track the target.

MAY 16, 2008 seminar

Irvine Hall 159, 2:10-3:00 PM

Jeffrey R Groff, College of William and Mary

Title: "Markov chain model of calcium puffs and sparks"

Abstract. Localized cytosolic Ca²⁺ elevations known as puffs and sparks are important regulators of cellular function that arise due to the cooperative activity of Ca²⁺-regulated inositol 1,4,5-trisphosphate receptors (IP₃Rs) or ryanodine receptors (RyRs) co-localized at Ca²⁺ release sites on the surface of the endoplasmic reticulum or sarcoplasmic reticulum. Theoretical studies have demonstrated that the cooperative gating of a cluster of Ca²⁺-regulated Ca²⁺ channels modeled as a continuous-time discrete-state Markov chain may result in dynamics reminiscent of Ca²⁺ puffs and sparks. In such simulations, individual Ca²⁺-release channels are coupled via a mathematical representation of the local [Ca²⁺] and exhibit “stochastic Ca²⁺ excitability” where channels open and close in a concerted fashion.

In this seminar, I will present results of simulations involving Markov chain models of Ca²⁺ release sites composed of channels that are both activated and inactivated by Ca²⁺. These simulations help to clarify the role of Ca²⁺ inactivation in the generation and termination of puffs and sparks. It is found that when the average fraction of inactivated channels is significant, puffs and sparks are often less sensitive to variations in the number of channels at release sites and the strength of Ca²⁺ coupling between channels. Importantly, we found that Ca²⁺ inactivation may be an important negative feedback mechanism contributing to puff/spark termination even when its time constant is much greater than the duration of puffs and sparks. I will also present results of simulations that investigate the dynamics of puffs and sparks exhibited by release site models that include both Ca²⁺ coupling and nearest-neighbor allosteric coupling between channels. It is observed that allosteric interactions that energetically stabilize neighboring channel pairs (when both channels are in the same state) often promote puffs and sparks. Interestingly, the dynamics of puffs and sparks are somewhat insensitive to the spatial aspect of allosteric interactions leading to a computationally efficient “mean-field” approximation to the full spatially explicit release site model.

MARCH 13, 2008 seminar (Joint CMMS/QBI)

Walter Hall 245, 4:10-5:00 PM

Ulrike Feudal, UC Santa Barbara and Carl von Ossietyky University,Oldenburg, Germany

Title: "Spatio-temporal patterns in simple models of marine systems"

Abstract. Spatio-temporal patterns in marine systems are a result of the interaction of population dynamics with physical transport processes. These physical transport processes can be either diffusion processes in marine sediments or advection of biological species in the water column. We study in a simplified model the dynamics of one population of bacteria and its nutrient in sediments, taking into account that the considered bacteria possess an active as well as an inactive state, where activation is processed by signal molecules. Furthermore the nutrients are transported actively by bioirrigation and passively by diffusion. It is shown that under certain conditions Turing patterns can occur which yield heterogeneous spatial patterns of species. The influence of bioirrigation on Turing patterns leads to the emergence of "hot spots," i.e. localized regions of enhanced bacterial activity. In the water column advection is the dominant physical process. We study the influence of mesoscale hydrodynamic structures on biological growth processes in the wake of an island. Using a stream function approach for the velocity field we show how the upwelling of nutrients away from the island affects the evolution of plankton close to it. In particular we show that mesoscale vortices act as incubators for planktongrowth leading to localized plankton blooms within vortices.

FEBRUARY 6, 2008 seminar

Irvine Hall 159, 4:10-5:00 PM

Greg Smith, Department of Applied Science, The College of William and Mary.

"Modeling local control of calcium-induced calcium release in cardiac myocytes"

Abstract. I will present a probability density approach to modeling localized Ca influx via L-type Ca channels and Ca-induced Ca release mediated by clusters of ryanodine receptors during excitation-contraction coupling in cardiac myocytes. Coupled advection-reaction equations are derived relating the time-dependent probability density of subsarcolemmal subspace and junctional sarcoplasmic reticulum [Ca] conditioned on "Ca release unit" state. When these equations are solved numerically using a high-resolution finite difference scheme and the resulting probability densities are coupled to ordinary differential equations for the bulk myoplasmic and sarcoplasmic reticulum [Ca], a realistic but minimal model of cardiac excitation-contraction coupling is produced. Modeling Ca release unit activity using this probability density approach avoids the computationally demanding task of resolving spatial aspects of global Ca signaling, while accurately representing heterogeneous local Ca signals in a population of diadic subspaces and junctional sarcoplasmic reticulum depletion domains. The probability density approach is validated for a physiologically realistic number of Ca release units and benchmarked for computational efficiency by comparison to traditional Monte Carlo simulations. [This is joint work with George S. B. Williams, Marco A. Huertas, Eric A. Sobie, and M. Saleet Jafri.]

OCTOBER 30, 2007 seminar

Irvine Hall 159, 4:10-5:00 PM.

Visiting Professor Fabio Marchesoni from the Dipartimento di Fisica, Universita' di Camerino, Italy will give the third of three seminars on "STOCHASTIC PHENOMENA IN BIOLOGY" on "SINGLE MOLECULE EXPERIMENTS: A physicist’s interpretation" on October 30 in Irvine 159 at 4:10 PM.

OCTOBER 23, 2007

Robin Snyder, Department of Biology, Case Western Reserve University.

"Duration and behavior of transient dynamics in a spatially extended system: plant population responses to altered disturbance regimes".

Irvine Hall 159 at 4:10 PM.

Abstract. The disturbance regimes on which many plant communities depend can be changed by, e.g., changes in fire suppression or grazing practices or alterations in weather patterns due to climate change. Most work on environmental variation has focused on populations' ultimate fates via their long-run growth rates, implicitly assuming that transient dynamics are short-lived. I present an analytic study of transient dynamics in a spatial model of competing annual plants. I find that the traits which promote species segregation also increase reactivity (the tendency for perturbations to grow initially) and transient duration.

OCTOBER 16, 2007 seminar

Irvine Hall 159, 4:10-5:00 PM.

Visiting Professor Fabio Marchesoni from the Dipartimento di Fisica, Universita' di Camerino, Italy will give the second of three seminars on "STOCHASTIC PHENOMENA IN BIOLOGY" on "Molecular Motors" on October 16 in Irvine 159 at 4:10 PM.

OCTOBER 2007

STOCHASTIC PHENOMENA IN BIOLOGY

Visiting Professor Fabio Marchesoni from the Department of Physics at the University of Camerino, Italy will give a series of three seminars on "STOCHASTIC PHENOMENA IN BIOLOGY" on alternate Tuesdays in October in Irvine 159 at 4:10 PM.

Topics are:
"Stochastic Resonance" (October 2),
"Molecular Motors" (October 16) and
"Extracting Information from Biological Data" (October 30).

OCTOBER 2, 2007 STOCHASTIC RESONANCE

Abstract

Conventional wisdom teaches us that the transmission and detection of signals is hindered by noise. However, during the last two decades, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, addition of the appropriate amount of noise can boost a signal and hence facilitate its detection in a noisy environment. Due to its simplicity and robustness, SR can work on almost every scale, thus attracting interdisciplinary interest from physicists, geologists, engineers, biologists and medical doctors, who nowadays use it as an instrument for their specific purposes.

At the present time, there exist a lot of diversified models of SR. Moreover, different characterizations of SR have been proposed in order to make such a mechanism more accessible to experimenters. This presentation relies mostly on the two-state model of SR, which is general enough to exhibit the main features of SR. Finally, we also discuss some situations that go beyond the generic SR scenario but are still characterized by a constructive role of noise.

(Abstracts for the October 16 and October 30 seminars will be available soon)

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May 30, 2007 Morton 320 4:10-5:00 PM

(Applied Math Seminar)

German Enciso, Ohio State University, MBI

“Moving in the right direction: A model of direction selectivity in the retina”

Abstract. A neuron in the retina, called directionally selective ganglion cell, has long been known to fire a signal to the brain only when it detects a light signal moving towards a specific direction. It has been an open problem for the past 50 years to determine the mechanism behind this 'direction selectivity', which is now believed to involve neighboring radially symmetric neurons called starburst amacrine cells (SAC).

After giving a general introduction to the subject, I will describe a tentative computational model for this process using a tightly interconnected, compartmental network of SACs. I will discuss the ability of this model to reproduce several basic experimental measurements, including the interesting propagation of a wave of inhibition in the SAC network. I will also stress the role in this model of so-called ion contransporters, which were recently shown to be present in SACs by Stuart Mangel and collaborators at Ohio State University.

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May 16, 2007 Clippinger 259 4:10-5:00 PM

(Joint with Biophysics Seminar Series)

Andrey Shilnikov, Dept. Mathematics, Georgia State University

“Routes to bursting in neuronal models”

Abstract. A single neuron can demonstrate different spiking and bursting patterns which can be elicited naturally depending on a modulation status or artificially due to disturbances caused by distinct recording technique. Transitions between oscillatory spiking patterns are in general non-local and could not be understood using only a local analysis of the neuron's rest states, but the nonlocal theory tools including the Poincar\'e return mapping technique. The mappings constructed then predict thetemporal characteristics of the spiking and bursting patterns and allows one to study transitions between them. The origin of spike adding in bursting activity is so studied in the interneuron model. We show that as the activation kinetics of the slow potassium current is shifted towards depolarized membrane potential values, the bursting phase accommodates incrementally more spikes into the train. This phenomenon is attested to be caused by the homoclinic bifurcations of a saddle periodic orbit setting the threshold between the tonic spiking and quiescent phases of the bursting.

May 9, 2007 Clippinger 259 4:10-5:00 PM

(Joint with Biophysics Seminar Series)

Tatiana Engel, Dept. Physics, Humboldt University, Berlin

“Firing statistics in neurons as non-Markovian first passage time problem”

Abstract. Subthreshold membrane potential resonances of single neurons influence the rhythmic activity of entire neuronal networks. As the fast signaling between neurons is largely dependent on action potentials, it is vital to understand how the subthreshold properties of a cell influence its ability to generate spikes. We therefore aim to establish the quantitative relationship between the subthreshold dynamics and spike patterns generated by neurons. In particular, we investigate differences in spike patterns of resonant and nonresonant neurons. The former exhibit subthreshold resonance and subthreshold oscillations, the latter lack both. Complex spike patterns, reflected in multipeak densities of interspike intervals (ISI), are characteristic for resonant neurons, whereas ISI densities in nonresonant neurons are monomodal. We derive several analytical approximations for the multipeak ISI distributions in neurons with subthreshold frequency preference. We aplly these theoretical results to explore spike patterns in stellate (resonant) and pyramidal (nonresonant) cells in the entorhinal cortex in rat. ISI densities observed experimentally in these cells are in excellent agreement with the analytical model predictions, which explains the mechanisms shaping the spike patterns in these cortical neurons.

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February 28, 2007 Grosvenor West 111 4:10-5:00 PM

(Joint with Biophysics Seminar Series)

Jong-Hoon Nam, University of Wisconsin-Madison, Dept. of Physiology

“A virtual hair cell: Computational study on the structure, dynamics and mechanoelectric transduction of vestibular hair cell”

Abstract. The hair cell, a specialized cell in the inner ear, is responsible for hearing and balance. The hair cell is an exquisite sensor that captures mechanical stimuli and generates neurosensory signals. A theory called gating theory has been widely used to analyze the experimental data of hair cell transduction. Despite increasing knowledge about molecular structures of hair cells, the mechanical model in the gating theory remained simple. Efforts to make the most of the recent findings regarding the hair cell structures led to the development of hair cell finite element (FE) model. I have extended this approach by adding channel kinetics and structural dynamics to the hair cell bundle FE model.

My computational study features the most detailed hair cell structural model and includes up-to-date knowledge of the hair cell structure such as the stereocilia and various extracellular links.   In addition to these structural features, I added channel kinetics such as the fast and slow adaptation. In my study, the Ca²⁺ kinetics plays a key role in the hair cell adaptations. The Ca²⁺ association rate to the fast adaptation modulator is postulated to govern the fast and slow adaptation. I assumed that two factors—the tip link tension and the Ca²⁺ concentration at the tip of stereocilia govern the hair cell mechanoelectric transduction. Developed hair cell computational model enables us (1) to study how the hair cells’ morphological variations are related to their function; (2) to investigate the hair cell mechanoelectric transduction at the single channel level, in silico, as opposed to the statistical approach; (3) to test the response of hair cells under in situ force boundary conditions.

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February 21, 2007 Morton 320 2:10-3:00 PM

(Jointly sponsored with Applied Math)

German Enciso, Ohio State University, MBI

“Monotone systems: stability and oscillations”

Abstract. Monotone systems are dynamical systems with strong stability properties, and they are strongly associated with positive feedback interactions. The recent work by E. Sontag and collaborators suggests that the theory of monotone dynamical systems can be used to model the behavior of various gene regulatory networks in molecular biology.

   In this talk, I will provide an overview of some of the main results of this theory, which fall into two categories. The first result, known as a 'small gain theorem', guarantees the global asymptotic stability of various dynamical systems under negative feedback, even with the addition of time delays. A second type of result describes the emergence of oscillatory behavior in different biological contexts.

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February 20, 2007 Baker Center 239 4:10-5:00 PM

Gregg Hartvigsen, Biology Department, SUNY Geneseo (currently on sabbatical at MBI), will present a talk entitled

"How I learned to stop worrying and love influenza"

Abstract. There is growing interest in understanding and controlling the spread of diseases through realistically structured host populations. We investigate how network structures, ranging from circulant, through small-world networks, to random networks, and vaccination strategy and effort interact to influence the proportion of the population infected, the size and timing of the epidemic peak, and the duration of the epidemic.

We found these three factors, and their higher-order interactions, significantly influenced epidemic development and extent. Increasing vaccination effort (from 0 - 90%) decreased the number of hosts infected while increasing network randomness worked to increase disease spread. On average, vaccinating hosts based on degree (hubs) resulted in the smallest epidemics while vaccinating hosts with the highest clustering coefficient resulted in the largest epidemics. In a targeted test of five vaccination strategies on a small-world network (probability of rewiring edges = 5%) with 10% vaccination effort we found that vaccinating hosts preferentially with high-clustering coefficients (similar to some real-world strategies) resulted in twice the number of hosts infected as random vaccinations and nearly a 30-fold higher number of cases than our strategy targeting hubs (highest degree hosts). Our model suggests how vaccinations might be implemented to minimize the extent of an epidemic (e.g., duration and total number infected) as well as the timing and number of hosts infected at a given time over a wide range of structured host networks.

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January 12, 2007 Morton 126 4:10-5:00

Refreshments at 3:30 in Morton 325

Avner Friedman, Ohio State University. Dr. Friedman is President-elect of the Society for Mathematical Biology, a member of the National Academy of Sciences, and Director of the Mathematical Biosciences Institute. He will speak on:

“Mathematical Models of Tumor Growth”

Abstract. The talk will describe how tumor growth can be modeled by partial differential equations. What makes the problem a real challenge is that the tumor domain, where the equations are to hold, varies in time. Such problems are called free boundary problems. In addition, more recent “multiscale” models of tumors will also be described.

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November 8, 2006 (Joint with EEB colloquium)

Irvine 114 12:10-1:00

Will Wilson, Duke University, “Ecological Patterns for Mechanistic Processes”

Will’s interests span theoretical evolutionary ecology, and his approaches include both mathematics and individual-based simulation models. Along these lines, he’s examined a variety of single- and multiple-species systems to understand how spatial extensions affect population-level dynamics. An ongoing interest of his is the connection of theoretical and empirical systems. Specific research topics include resource-consumer interactions; animal grouping; hermaphroditism-dioecy mating system models; and obligate mutualism-exploiter systems.

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October 25, 2006 (Math department colloquium of interest to QBI folks) Morton 322 3:10-4:00

Martin Feinburg, Chemical Engineering and Mathematics, Ohio State,

“Understanding Bistability in Complex Enzyme-Driven Reaction Networks”

The talk will be non-technical and accessible to graduate and advanced undergraduate students.

Abstract. In nature there are millions of distinct networks of chemical reactions that might present themselves for study at one time or another. Each network gives rise to its own system of differential equations. These are usually large and almost always nonlinear. Nevertheless, the reaction network induces the corresponding differential equations (up to parameter values) in a precise way. This raises the possibility that qualitative properties of the induced differential equations might be tied directly to reaction network structure.

        Chemical reaction network theory has as its goal the development of powerful but readily implementable tools for connecting reaction network structure to the qualitative capacity for certain phenomena. The theory goes back at least to the 1970s. It has not been specific to biology, but, for obvious reasons, there is now growing interest in biological applications. Very recent work (with Gheorghe Craciun) has been dedicated specifically to biochemical networks driven by enzyme-catalyzed reactions. In particular, it is now known that there are remarkable and quite subtle connections between properties of reaction diagrams of the kind that biochemists normally draw and the capacity for biochemical switching. My aim in this talk will be to explain, for an audience unfamiliar with chemical reaction network theory, those tools that have recently become available.

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October 18, 2006 (Joint with Applied Math/Computational Mathematics) Morton 320 at 3PM.

Brandilyn Stigler, “Reverse engineering of network topology”

Abstract: Advances in bioinformatics technologies and computational modeling methods are launching biology into a new paradigm of quantitative, predictive science. The emerging field of systems biology is focused on the integration of biological information at multiple levels of living organization into descriptive and predictive mathematical models. One primary approach in the systems-biology framework is to build models from time series of experimental data, often obtained by measuring the response of a biological system to certain types of perturbations. This approach, commonly referred to as reverse engineering, is an important step in elucidating features of such systems, including network topology and dynamics. We consider the problem of reverse engineering network topology for systems of interacting biochemicals. In this setting network topology is encoded in a directed graph, called a wiring diagram, which represents the causal relationships between system variables. We present an algorithm which computes all possible minimal wiring diagrams for a given data set of measurements from a biochemical network and scores the diagrams. The algorithm uses computational algebra, namely primary decomposition of monomial ideals, as the principal tool. An application to the reverse-engineering of two gene regulatory networks is included.

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September 27, 2006 Morton 320 at 4PM.

Andrew Nevai, “A mathematical model of plant competition for sunlight”