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QBI Seminars


APRIL 19, 2016  QBI Seminar

Irvine 159 3:00-3:55 PM


Maxim Bazhenov

Division of Pulmonary, Critical Care and Sleep Medicine

UC San Diego, School of Medicine

“Role of Sleep in Memory Consolidation”  


Abstract:  Memory depends on three general processes: encoding, consolidation and retrieval. Although the vast majority of research has been devoted to understanding encoding and retrieval, recent novel approaches have been developed in both human and animal research to probe mechanisms of consolidation. A story is emerging in which important functions of consolidation occur during sleep and that specific features of sleep appear critical for successful retrieval across a range of memory domains, tasks, and species. In my talk I will first discuss the neuronal and network level mechanisms behind major sleep EEG rhythms and experimental data on memory consolidation. I will then present our new results, obtained in computer simulations with large-scale network models, to reveal the neural substrates of memory consolidation involving preferential replay of memory specific sequences of spikes.


NOVEMBER 20, 2014  QBI Seminar

Morton 219 5:00-5:45 PM

Kie Van Ivanky Saputra

Visiting Fullbright Scholar, partially supported by QBI

Head of Dept. of Mathematics, University of Pelita Harapan, Indonesia
“Dynamics of an HIV-1 infection model with Cytotoxic T-Lymphocytes (CTL) responses”


Abstract:  As an example of dynamical systems having a co-dimension one invariant manifold, this talk will discuss the dynamics of an HIV-1 infection model with CTL responses. Detailed analysis will show that the system has three equilibrium solutions, namely the disease-free equilibrium, an endemic equilibrium without CTL response, and an endemic equilibrium with CTL response. The model exhibits transcritical and Hopf bifurcations. The model also addresses how treatment is related to varying model parameters. The findings show how treatment would allow our immune system to control the virus in the long run.


SEPTEMBER 15, 2014  QBI Seminar

Morton 318 4:10-5:10 PM


Joan Saldaña

Dept. Informàtica, Matemàtica Aplicada i Estadística 
Edifici P-IV, Campus de Montilivi
Universitat de Girona

“Analysis of a class of epidemic models with awareness”  


Abstract:  Recent formulations of epidemic models consider human behavioral responses. In the analysis of these models, the influence of these responses on the prevention of epidemic spreading is measured from the stability analysis of the disease-free equilibrium. One of these works considers a network epidemic model where individuals are classified as susceptible (S), aware (A), and infectious (I), and assumes no decay in awareness. For this SAIS model, it was proven the existence of a die-out threshold (different from the classic disease-invasion one) defining a region of slow epidemic extinction.


By means of an equivalent mean-field model defined on regular random networks, we analyze the dynamics of this network model, especially for very low values of the awareness decay, and show that the continuum of equilibria arising from the absence of awareness decay collapses into a unique equilibrium when awareness decay is assumed. For this modified model, the resulting bifurcation from the disease-free equilibrium turns out to be equivalent to that of classic epidemic models and those minor outbreaks observed in the slow die-out epidemic regime are now replaced by dumped oscillations around an endemic equilibrium. Continuous-time stochastic simulations are carried out on networks of size 1000 for both models. They show good agreement with the mean-field predictions when the network degree is not very low.


APRIL 21, 2014  QBI Seminar

Morton 326 4:10-5:10 PM


Valentin Afraimovich

Glidden Visiting Professor


 " Heteroclinic Sequences and Neuronal Networks"


Abstract:  Robustness and reproducibility of sequential spatio-temporal responses is an essential feature of many neural circuits in sensory and motor systems of animals. The most common mathematical images of dynamical regimes in neural systems are fixed points, limit cycles, chaotic attractors, and continuous attractors (attractive manifolds of neutrally stable fixed points). These are not suitable for the description of reproducible transient sequential neural dynamics. In this talk we present the concept of a stable heteroclinic sequence (SHS), which is not an attractor. SHS opens the way for understanding and modeling of transient sequential activity in neural circuits. We show that this new mathematical object can be used to describe robust and reproducible sequential neural dynamics. Using the framework of a generalized high-dimensional LotkaVolterra model, that describes the dynamics of firing rates in an inhibitory network, we present analytical results on the existence of the SHS in the phase space of the network and generalizations that we have been pursuing this year at Ohio.


MARCH 17, 2014  QBI Seminar

Morton 326 4:10-5:10 PM


Igor Belykh

Department of Mathematics, Neurosciences Institute

Georgia State University


 "When repulsive inhibition induces synchrony in excitatory networks of bursting neurons"


Abstract:  Synchrony has been broadly observed in pathological brain states, especially during epilepsy and Parkinson's tremors. In this talk, we will discuss the influence of coupling strength and network topology on synchronization in neuronal networks with fast excitatory and inhibitory connections. We will show that the addition of repulsive inhibition to excitatory networks induces bursting synchrony, in contrast to one's expectations.  We will discuss the  mechanism of this purely synergetic phenomenon and show that it originates from the transition between two distinct types of bursting. Our study suggests that promoting inhibition in an attempt to destabilize the abnormal synchronous state can have a counterproductive effect.


OCTOBER 29, 2013  QBI/CMSS Seminar

Walter Hall 245 4:10-5:10 PM


Hans Braun

Neurodynamics Group, Institute of Physiology, Philipps University, Marburg, Germany


“Nonlinear Dynamics, Oscillations, Chaos and Noise:

From Shark Electroreceptors to Mental Disorders


Abstract:  Biological functions typically include nonlinearities and time delays and often are organized in circular, positive and negative feedback loops which easily can lead to oscillations and even chaotic behvior. Moreover, biological systems are notoriously noisy which can induce significant alterations of the system dynamics compared to the deterministic situation.


Consequences of these particular properties will be illustrated by experimental recording from hypothalamic neurons and sensory receptors of the skin with focus on temperature sensitive electroreceptors of sharks that are endowed with a most exquisite stimulus sensitivity. The experimental data will be accomplished by computer simulations for the elucidation of the underlying dynamics.


Remarkably, similar functional principles can be applied to model the time course of manic-depressive disorders - in this case, however, with rather detrimental than beneficial effects: sensitivity turns into vulnerability. Implications of these apparently general principles of biological functions will be discussed, - also in comparison to technical systems. The question arises whether biological systems are still more flexible and adaptable then any technical system not despite but because of these technically mostly undesired properties. 


OCTOBER 23, 2013  Applied Math and QBI Seminar

Morton Hall 122 4:10-5:10 PM


Kendrick Shaw

MD-PhD Medical Scientist Training Program, Case Western Reserve University


“Dynamical Architectures for Controlling Feeding in Aplysia californica


Abstract:  For behaviors such as swallowing, walking, and swimming, the nervous system must reliably generate sequences of motor behavior.  Two competing models have been proposed for how this task is accomplished - chain reflex theory and central pattern generator theory.  Chain reflex theory posits that the nervous system contains a sequence of reflexes, so that the action of one reflex creates the sensory input required to trigger the next.  In contrast, central pattern generator theory posits that the nervous system is capable, in the absence of sensory input, of generating motor patterns that closely resemble the motor patterns during behavior.  When modeling these behaviors with systems of differential equations, these two ideas correspond to a collection of stable nodes, in the case of the chain reflex theory, and a stable limit cycle, in the case of central pattern generator theory.  Many systems can exhibit motor patterns in the absence of sensory input, violating the predictions of chain reflex theory, but those patterns are very distorted compared to in vivo behaviors, violating the assumptions of central pattern generator theory.  In this talk, we will explore a third hypothesis, known as a heteroclinic channel, where a trajectory slows dramatically in small regions as it passes near saddle points, creating local regions of sensitivity.  We explore the implications of these dynamics by building a neuromechanical model of swallowing in Aplysia californica which can be changed from a stable heteroclinic channel to a limit cycle by changing a single parameter, and then compare the behavior within these two regimes to the behavior seen in vivo.  The stable heteroclinic channel provides a better match for what is seen in vivo, seemingly due to its timing sensitivity.  We then analytically explored the basis for this sensitivity by studying a tractable heteroclinic channel and deriving a closed-form expression for its infinitesimal phase response curve. The qualitative behavior of the tractable model is present in more complex models, including the Morris-Lecar neuron model as it approaches the homoclinic bifurcation.




MARCH 11, 2013  Applied Math and QBI Seminar

Morton Hall 226 4:10-5:10 PM


S. Lee Hong
Department of Biomedical Sciences, Ohio University


“Entropy Conservation in Brain and Behavior”



Patterns of brain activity as well as cognitive and motor behavior are known to be highly variable.  Despite being variable, behavioral patterns are extremely flexible and adaptable to different task demands and environmental conditions.  This prompts a question of whether “rules” exist to guide the process of adaptation.  In this talk, I will present results from a range of different experiments that test the hypothesis of “entropy conservation” in brain and behavior.  First, we will explore the phenomenon of entropy conservation in task, behavior, and environment during adaptations of muscle force control under different conditions.  Next, we will examine the effects of stimulus uncertainty on visual search strategies and cognitive responses.  Finally, I will present data from a study of neural activity obtained from mice actively exploring a maze.  The common finding across all of these studies was compensatory tradeoffs in entropy:  whenever there is an increase in entropy in one dimension, there are observed decreases in others.  The results of all of these studies provide initial evidence that entropy conservation guides the process of harnessing variability for functional adaptation in brain and behavior.


AUGUST 24, 2012  QBI Seminar

Clippinger 259 12:00-1:00 PM

Benjamin Lindner

Bernstein Center for Computational Neuroscience, Berlin and Physics Department of the Humboldt University Berlin


“Neural information transmission with dynamic synapses”


Abstract: Many synapses display short-term plasticity (STP): upon repetitive stimulation, synaptic efficacies can either increase (facilitation) or decrease (depression). In my talk I discuss the effect of STP on the neural encoding of information about time-dependent stimuli. Specifically, I address under which conditions integrate-and-fire neurons with dynamic synapses encode preferentially slow components (low-pass information filter) or fast components (high-pass information filter) of one or more signals. Considered are a homogeneous setup, in which all synapses of the postsynaptic cell are of the same kind and a heterogeneous setup, in which facilitating and depressing synapses coexist and are driven by distinct signals.



MARCH 28, 2012  QBI Seminar

ARC 102  4:10-5:00 PM

Gabor Balazsi

Department of Systems Biology

The University of Texas, MD Anderson Cancer Center


“Networks, noise and fitness: Lessons from synthetic gene circuits”


Abstract.  Genes are templates for protein synthesis. Proteins determine how cells behave. Therefore, genes should determine how cells behave. However, genes do not act in isolation: they alter each other’s protein producing capacity through complex regulatory networks. Moreover, genes and proteins are present in small numbers and move around stochastically inside minuscule cellular volumes, giving rise to stochastic reactions. These reactions can affect cell division rates, thereby modulating fitness. Therefore, the connection between genes and cell behavior is complex and non-deterministic. I will illustrate how we apply mathematical and computational methods to design synthetic gene networks that control biological noise, providing insights into microbial drug resistance.


JANUARY 19, 2012  QBI Seminar

Irvine Hall 159  4:10-5:00 PM

Bard Ermentrout

Department of Mathematics

University of Pittsburgh


“Flicker Phosphenes: How to get your visual kicks in a drug free world”


Abstract.  When the human visual system is subjected to diffuse flickering light in the range of 5-25 Hz, many subjects report beautiful swirling colorful geometric patterns. In the years since Jan Purkinje first described them, there have been many qualitative and quantitative analyses of the conditions in which they occur. Here, we use a simple excitatory-inhibitory neural network to explain the dynamics of these fascinating patterns. We employ a combination of computational and mathematical methods to show why these patterns arise. We demonstrate that the geometric forms of the patterns are intimately tied to the frequency of the flickering stimulus.


Bard is the author/developer of the free differential equations solving software XPP/XPPAUT, which runs on many platforms, including the iPad, ( .  Bard is also the co-author (with David Terman) of the book “Mathematical Foundations of Neuroscience”. 



SEPTEMBER 26, 2011  QBI Seminar

Morton Hall 218  4:10-5:00 PM

Valentin Afraimovich

Universidad Autónoma de San Luis Potosí, S.L.P., México.

“Transient Dynamics in Neural Networks”



The observed forms of electrical activity in neural systems are quite varied. Neurophysiological experiments show that some neural processes are accompanied by short-time activity of individual neurons or small groups of neurons. For some models, for instance the generalized Lotka-Volterra systems, a mathematical description of such a transient activity is based on the existence of a collection of metastable invariant sets joined by heteroclinic trajectories in the phase space, the heteroclinic network. So, the motion can be thought of a process of successive switchings among these metastable sets. In the simple situation when these sets are just saddle equilibrium points, the full description of transient behavior can be adequately described, including a mechanism of binding between different information modalities. However, sequential activity is not always directly related to the existence of heteroclinic networks. For such situations an approach suggested by D. Terman et al (2008) appeared that allows us to reduce the study of some neural networks to a simple discrete dynamics in the form of cellular automata. V. Nekorkin et al (2011) have applied this approach to networks of Morris-Lecar and Hodgkin-Huxley neurons joint by chemical synapses possessing the short-term plasticity property.  In the present talk, we suppose to discuss all these problems.


Two seminars by QBI folk.


APRIL 27, 2011  New Professor Lecture Series

Baker 242, 4-5 PM

Todd Young, Department of Mathematics


“Clustering in the Cell Cycle of Yeast.  How a Dynamical Systems Viewpoint can be Useful for Biology”



APRIL 28, 2011 Math Awareness Month

Morton 115, 4:10-5:00 PM

Winfried Just, Department of Mathematics


“Unraveling Complex systems: What do brains, the internet, and ant colonies have in common?


ABSTRACT:  We are surrounded by complex systems: Power grids, transportation systems, administrative structures, hurricanes, biological systems from cells through organs to ecosystems. The list goes on.  Scientists from a variety of disciplines are trying to understand and predict the behavior of such systems.  How can mathematics contribute to these efforts?  Which mathematical tools are needed for the study of complex systems?  Will existing mathematical tools give us the answers we are seeking, or do we need to develop  new areas of mathematics?  The talk will address these questions at a level accessible to a general audience.




FEBRUARY 18, 2011

Morton Hall 318, 4-5 PM

Horst Malchow

Institute of Environmental Systems Research, Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany


“Noise and Diffusion in Models of Population Dynamics”


Abstract.   The dynamics of spatial and spatiotemporal pattern formation in nonlinear systems far from equilibrium are of continuous interest and many mechanisms of structure generation are not known yet.  Here, the fascinating variety of spatiotemporal patterns in such systems and the governing mechanisms of their generation and further dynamics are described and related to plankton communities.  The formation and spread of spatiotemporal structures in a simple predation-diffusion model with Holling type II or III predator is demonstrated.  The analysis of the local system yields a number of stationary and/or oscillatory regimes.  Correspondingly interesting is the spatiotemporal behaviour, modeled by reaction-diffusion equations.  Spatial spread will be presented as well as competition of concentric and/or spiral population waves with non-oscillatory subpopulations for space, and long transients to spatially homogeneous population distributions.  Environmental fluctuations are modeled as parametric as well as external multiplicative noise, using stochastic partial differential equations.  The noise can enhance the survival of a population that would go extinct in a deterministic environment. In the parameter range of excitability and slow-fast dynamics of prey and predator, respectively, noise can induce local and global oscillations as well as local coherence resonance and global synchronization.  Stationary patterns have been observed, too.  Furthermore, it is shown that noise can suppress periodic travelling waves and the onset of chaos.  The results are related to plankton dynamics, partly with viral infections of the prey population [1–4].



[1] H. Malchow, S.V. Petrovskii, E. Venturino, Spatiotemporal patterns in ecology and epidemiology:  Theory, models, simulations,  CRC Mathematical and Computational Biology Series, CRC Press, Boca Raton, 2008.

[2] M. Sieber, H. Malchow, S.V.Petrovskii, Noise-induced suppression of periodic travelling waves in oscillatory reaction-diffusion systems, Proceedings of the Royal Society A466(2010) 1903-1917.

[3] M. Sieber, H. Malchow, Oscillations vs. chaotic waves: Attractor selection in bistable stochastic reaction-diffusion systems, The European Physical Journal–Special Topics 187(2010) 95-99.

[4] S. Petrovskii, A. Morozov, H. Malchow, M. Sieber, Noise can prevent onset of chaos in spatiotemporal population dynamics, The European Physical Journal B78(2010) 253–264.


JANUARY 19, 2011

Irvine Hall 159, 4-5 PM

 Angela Blisset

Biophysics Program, Ohio State University


“Extracellular Matrix Regulation by Discoidin Domain Receptors (DDR1 and DDR2)”


Abstract: Bone strength is dependent upon the material composition and the microarchitectural structure of bone tissue. The underlying mechanisms that regulate bone material composition and microarchitectural structure are not well understood. Since collagen type 1 is the major component of bone, it is evident that processes regulating collagen deposition and structure are bound to impact bone quality. Discoidin domain receptors (DDRs) are ubiquitously expressed, unique tyrosine kinase receptors that bind to and get activated by collagens, including collagen type I.  Our lab has recently discovered a novel mechanism of collagen regulation by the extracellular domain (ECD) of DDR1 and DDR2 in an in vitro study.  Using stably transfected MC 3T3 pre-osteoblast cell lines, transfected with DDR1 and DDR2 protein constructs absent of the kinase domain, we have elucidated that expression of DDR ECDs results in alterations of endogenous matrix laid down by cells.  Evaluation by transmission electron microscopy (TEM) analysis revealed that expression of DDR ECDs results in collagen fibers with smaller fiber diameters, disrupted banded structures, reduced matrix deposition, delayed rate of fibrillogenesis and increased amount of matrix mineralization.  The goal of our current study is to elucidate the role of DDR1 in bone morphology to elucidate its effect on mechanical integrity of bone. Using bone tissue from DDR1 knock out mice and their wildtype littermates we assess both cortical and trabecular bone morphology in the adult mouse by µ-CT analysis.  Further, using isolated monocytes cultured in the presence of differentiation media we aim to elucidate the role of DDR1 in osteoclast differentiation and function in-vitro via various cell based techniques.  This pilot study on adult DDR1 knockout mice will pave the way for further studies to understand how the DDR1 receptor is involved in matrix remodeling events in different pathological situations and aging.


OCTOBER 7, 2010 QBI Colloquium

Morton 322, 2:10-3:00 PM
Valentin Afraimovich

Universidad Autónoma de San Luis Potosí, S.L.P., México.

“Modeling of sequential dynamics in networks of active elements.”

Abstract:  In neural networks, central pattern generators, cognitive systems, etc. people have been observing a special kind of dynamics that is characterized by an alternate activation of different elements or clusters of elements. Such dynamics is said to be sequential. In the phase space of a mathematical model it corresponds to a successive switching among metastable states along heteroclinic trajectories joining the metastable sets. In this talk we present some theoretical and numerical results related to the case where the mathematical image of a metastable state is just a saddle equilibrium point.



MAY 6, 2010  Distinguished Lecture in Quantitative Biology

Morton Hall 115 4:10-5:00 PM

Martin Golubitsky

Distinguished Professor of Mathematics and Physical Sciences, Director of the Mathematical Biosciences Institute, Ohio State University


”Symmetry-Breaking; Synchrony Breaking"


Abstract:  A coupled cell system is a network of interacting dynamical systems.  Coupled cell models assume that the output from each cell is important and that signals from two or more cells can be compared so that patterns of synchrony can emerge.  We ask: which part of the qualitative dynamics observed in coupled cells is the product of network architecture and which part depends on the specific equations?


In our theory, local network symmetries replace symmetry as a way of organizing network dynamics, and synchrony-breaking replaces symmetry-breaking as a basic way in which transitions to complicated dynamics occur. Background on symmetry-breaking and pattern formation will be presented.



Dr. Golubitsky is a Fellow of the American Academy of Arts and Sciences, the American Association for the Advancement of Science (AAAS), and the Society for Industrial and Applied Mathematics (SIAM). He is also the 1997 recipient of the University of Houston Esther Farfel Award, the 2001 co-recipient of the Ferran Sunyer i Balaguer Prize (for / The Symmetry Perspective/) and the recipient of the 2009 Moser Lecture Prize of the SIAM Dynamical Systems Activity Group. He has been elected to the Councils of the Society for Industrial and Applied Mathematics (SIAM), AAAS, and the American Mathematical Society. Dr. Golubitsky was the founding Editor-in-Chief of the /SIAM Journal on Applied Dynamical Systems/ and has served as President of SIAM (2005-06).  He has co-authored four graduate texts, one undergraduate text, and two nontechnical trade books, (/Fearful Symmetry: Is God a Geometer/ with Ian Stewart and / Symmetry in Chaos/ with Michael Field) and over 100 research papers.



MARCH 4, 2010

Walter Hall 245 4:10-5:00 PM

Jainwei Shuai

Department of Physics

Xiamen University, China

"The stochastic dynamics of hierarchical intracellular calcium signals"



NOVEMBER 18, 2009

Morton Hall 318 4:10-5:00 PM

Edy Soewono

Department of Mathematics

Institut Teknologi Bandung

"A harm reduction model for controlling the spread of HIV/AIDS among injecting drug users"


The spread of HIV/AIDS, especially among injecting drug users (IDUs), has becomes an alarming issue all over the world in the last few decades. One of the recommended programs believed to be safe and effective in controlling the spread of HIV/AIDS is called Harm Reduction Program. In this program, two strategic methods are implemented. The first method is called the Needle and Syringe Program, in which syringes and needles are distributed for free among IDUs upon the return of used needles. The second program is Methadone Therapy, in which methadone is given at a reduced price in several designated hospitals and clinics. Due to limited government budgets, a practical question to be answered is how one can determine the size of action such that the Harm Reduction Program is still effective within a given period. Here in this presentation a new mathematical model for controlling the spread of HIV/AIDS among IDUs is considered. Basic reproduction ratios for both actions and for a combination of the two actions are obtained. Optimum portions of treated compartments which give the largest harm reduction are shown.


MARCH 11, 2009

Walter Hall 245 4:10-5:00 PM

Brent Doiron

Department of Mathematics

University of Pittsburgh

"Unlocking temporal rhythms with spatial keys"

Stimulus evoked rhythms in neural populations are observed in many sensory systems.  The basic interactions between populations of excitatory and inhibitory cells that subtend network rhythms are somewhat understood.  In contrast, the mechanisms by which stimuli modulate rhythms are virtually unknown.  Using characterized circuitry in both the electrosensory system and the auditory cortex I show how the spatial extent of a driving input can gate rhythmic activity.  In both cases mean field theory for populations of simple integrate-and-fire neurons is developed and captures the essential mechanisms.  Overall the work points to a general theory whereby the spatial structure of sensory networks into feature-based topologies permits select stimuli to recruit network oscillations. This suggests that neural rhythms may be useful in sensory coding, consistent with their frequent occurrence in sensory evoked neural dynamics.


FEBRUARY 9, 2009 Joint QBI and Applied Math Seminar 

Irvine 159  4:10-5:00PM

Erik Boczko

Vanderbilt University

"Talking Yeast"



Cell cycle position and age are often dispersed in a culture of budding yeast and can confound measured population averages. We have been exploring methods to describe and to manipulate the population structure of different yeast strains with modeling and data. Our work has resulted in a filtration protocol to extend the maintenance of cell cycle synchrony, and a model of the population structure that develops under autonomous oscillations. We will describe the development and application of these ideas and their relation to quorum sensing.

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"



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.




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).



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)



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.


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.


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.


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.


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.


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.


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.


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.


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.


September 27, 2006  Morton 320 at 4PM.

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




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