Second Young Researchers Workshop in Mathematical Biology

(March 27,2006 - March 30,2006 )

To provide a forum for young mathematical biologists to interact with their peers, the Mathematical Biosciences Institute hosted the Second Young Researchers Workshop in Mathematical Biology. The workshop brang together approximately 45 young researchers in mathematical biology to broaden their scientific perspective and to develop connections that will be important for their future careers.

We cordially invited postdoctoral researchers and junior faculty to apply for participation in this workshop. A limited number of advanced graduate students were also accepted.

Each participant presented a poster of current research and gave a five-minute advertisement of the poster. The workshop also featured working group discussions on broad issues relevant to researchers in mathematical biology.

Plenary talks were given by leading researchers in mathematical biology:

  • Catherine Carr, University of Maryland
  • Leah Edelstein-Keshet, University of British Columbia
  • Bard Ermentrout, University of Pittsburgh
  • Philip Maini, Oxford University
  • Hans Othmer, University of Minnesota
  • Timothy Secomb, University of Arizona
  • Arthur Sherman, National Institutes of Health
  • Kristin Swanson, University of Washington

Accepted Speakers

Catherine Carr
Biology, University of Maryland at Baltimore
Leah Edelstein-Keshet
Mathematics Department, University of British Columbia
Bard Ermentrout
Department of Mathematics, University of Pittsburgh
Hans Othmer
School of Mathematics, University of Minnesota
Tim Secomb
Physiology, University of Arizona
Artie Sherman
National Institutes of Health
Kristin Swanson
Department of Pathology, University of Washington
Raimond Winslow
Department of Biomedical Engineering, Johns Hopkins University
Monday, March 27, 2006
Time Session
09:15 AM
10:15 AM
Artie Sherman - Metabolic and Electrical Oscillations in Insulin-Secreting Pancreatic Beta-Cells

The first generation of models for electrical activity in pancreatic beta-cells focused on ionic mechanisms. Negative feedback by calcium, directly onto calcium-activated potassium channels and indirectly onto ATP-sensitive potassium channels and sodium pumps, is the main type of mechanism considered in current models. Such models do a good job of accounting for the oscillations on a wide range of time scales, ranging from 10 seconds to about 2 minutes. However, even slower oscillations, with periods of 4 or even 10 minutes are often observed, and these often appear with the faster oscillations layered on top. This suggests that there is an additional mechanism for oscillations, which we have proposed is based on oscillations of glycolysis. We will discuss how two relatively simple oscillators, which can be off, oscillating, or tonically on, depending on stimulation level, can be combined to account for the great diversity of observed patterns. We will also consider the impact of metabolic oscillations on synchronization of beta-cells within the islet of Langerhans. Diffusion of glycolytic metabolites provides an important mechanism for secretion, but can also lead to oscillator death and a source of bistability.

02:00 PM
03:00 PM
Catherine Carr - Evolution of Sound Localization Circuits

Animals, including humans, use interaural time differences (ITDs) that arise from of different sound path lengths to the two ears, as a cue of horizontal sound source location. The nature of the neural code for ITD is still controversial. Current models advocate either a map-like place code of ITD along an array of neurons, consistent with a large body of data in the barn owl, or a rate-based population code, consistent with data from small mammals. Recently, it was proposed that these different codes reflect an optimal coding strategy that depends on head size and sound frequency. The chicken makes an excellent test case because its physical prerequisites are similar to small mammals, yet it shares a more recent common ancestry with the owl. We show here that, like in the barn owl, the brainstem nucleus laminaris in mature chickens displayed the major features of a place code of ITD. The physiological range of ITDs was systematically represented in the maximal responses of neurons along each isofrequency band. This is in contrast to the predictions from optimal coding theory and thus re-opens the question as to what determines the neural coding strategies for ITDs, including which code might be implemented by the human brain.

Tuesday, March 28, 2006
Time Session
09:00 AM
10:00 AM
Bard Ermentrout - What makes a neuron spike? Phase resetting and intrinsic dynamics

What aspects of a stimulus cause a neuron to fire? How do stimuli affect the time of spikes? In this talk, I will discuss what we can learn about neuronal firing patterns by regarding neurons as nonlinear oscillators. The spike-triggered average or reverse correlation method is a common approach for determining what kinds of stimuli make a neuron fire. The poststimulus time histogram is another experimental measurement for describing the affect of a stimulus on the firing pattern of a neuron. The latter can be related to the former by using some optimality arguments. Both of these curves should be affected by the membrane properties of the individual neuron of interest. Since this is a huge-dimensional space, we will focus on one property of neurons which has been shown to be tightly coupled to neuronal dynamics: the phase resetting curve (PRC). The PRC describes the shift in the timing of a spike due to a brief stimulus as a function of the time since the last spike. We show that under certain circumstances there is a 1:1 mapping between the STA, the PSTH, and the PRC. Thus, we connect internal dynamics of neurons with their preferred stimuli and their population responses. This work is joint with Boris Gutkin, Alex Reyes, Nathan Urban, Roberto Galan, and Nicolas Fourcaud.

01:30 PM
02:30 PM
Leah Edelstein-Keshet - Models for the Role of the Biopolymer Actin in Cell Motility

I will describe some recent work in our group on the dynamics of the actin cytoskeleton in relation to the movement of a motile cell. First, I will describe work (joint with Adriana Dawes, Eric Cytrynbaum, and Bard Ermentrout) on a simple 1D spatial model of a cell. We show how the branching of actin filaments and the forces they exert on the cell membrane account for the protrusion velocity and characteristic actin density profiles. (This work is partly analytical and partly numerical.) We use this model to understand how branching rates and other biochemical parameters control cell speed by studying the relevant travelling wave solutions.


I will also describe efforts (joint with AFM Maree, Alexandra Jilkine, Adriana Dawes and Veronica Grieneisen) at assembling a more detailed 2D spatial model of a crawling cell, in which we take into account the regulatory role of a set of signalling proteins (Cdc42, Rac, Rho). We show how the interplay between these and the actin cytoskeleton accounts for the ability of the cell to self-organize, polarize, maintain a stable shape and speed, and respond to new external signals.

02:45 PM
03:45 PM
Tim Secomb - Mathematical Modeling of the Microcirculation

The main function of the circulatory system is to transport and exchange substances throughout the body. Delivery of oxygen is a particularly demanding function, because oxygen is relatively insoluble in water. Within blood vessels, oxygen is carried convectively by hemoglobin molecules within red blood cells. Oxygen exchange with tissue occurs by diffusion in the microcirculation, an extensive branching network of microscopic vessels that brings blood close to all oxygen-consuming tissues. The microcirculation regulates blood flow according to changing local demands over short and long time scales. Mathematical models can be used to gain insight into these processes. Models will be described for the mechanics of blood flow in capillaries, for oxygen exchange between blood and tissues and for structural adaptation of blood vessels. Applications to disease states including cancer will be discussed.

Wednesday, March 29, 2006
Time Session
09:00 AM
10:00 AM
- TBA

TBA

Thursday, March 30, 2006
Time Session
09:00 AM
10:00 AM
Kristin Swanson - Applications of Quantitative Modeling in the Clinical Imaging of Invasive Brain Tumors

Gliomas account for over half of all primary brain tumors and have been studied extensively for decades. Even with increasingly sophisticated medical imaging technologies, gliomas remain uniformly fatal lesions. A significant gap remains between the goal of designing effective therapy and the present understanding of the dynamics of glioma progression. It has become increasingly clear that, along with the proliferative potential of these neoplasms, it is the subclinically diffuse invasion of gliomas that most contributes to their resistance to treatment. That is, the inevitable recurrence of these tumors is the result of diffusely invaded but practically invisible tumor cells peripheral to the abnormal signal on medical imaging and to the limits of surgical, radiological and chemical treatments.


In this presentation, I will demonstrate how quantitative modeling can not only shed light on the spatio-temporal growth of gliomas but also can have specific clinical application in real patients. Integration of our quantitative model with the T1-weighted and T2-weighted magnetic resonance (MR) imaging characteristics of gliomas can provide estimates of the extent of invasion of glioma cells peripheral to the imaging abnormality. Additionally, further insight can be gained from parametric mapping of kinetic model parameters derived from positron emission tomography (PET) with novel tracers. In summary, although current imaging techniques remain woefully inadequate in accurately resolving the true extent of gliomas, quantitative modeling provides a new approach for the dynamic assessment of real patients and helps direct the way to novel therapeutic approaches.

10:15 AM
11:15 AM
Hans Othmer - Deterministic and Stochastic Models of Actin Dynamics

This lecture will be devoted to a discussion of some of the basic problems in modeling actin dynamics. Actin polymerization and network formation are key processes in cell motility. Numerous actin binding proteins controlling the dynamic properties of actin networks have been studied and models such as the dendritic nucleation scheme have been proposed for the functional integration of at least a minimal set of such regulatory proteins. However, a complete understanding of actin network dynamics is still lacking. Even at the actin-filament level, the dynamics of the distribution of filament lengths and nucleotide profiles are still not fully understood. We will describe recent work on the evolution of the distribution of filament lengths and nucleotide profiles of actin filaments, both from a deterministic and a stochastic viewpoint. If time permits we will discuss work aimed at integrating microscopic models of actin dynamics into cell-level descriptions of motility.

Name Email Affiliation
Achuthan, Srisairam sachutha@mail.math.fsu.edu Mathematics, Florida State University and NHMFL
Allen, Linda linda.j.allen@ttu.edu Mathematics and Statistics, Texas Tech University
An , Jung-ha jan@ima.umn.edu Institute for Mathematics and its Applications, University of Minnesota
Andries, Erik andriese@unm.edu Pathology Department MSC08 4640 , University of New Mexico
Baker, Tanya tibaker@uchicago.edu Biology, University of Chicago
Best, Janet jbest@mbi.osu.edu
Bolker, Ben bolker@zoo.ufl.edu Zoology, University of Florida
Boushaba, Khalid boushaba@iastate.edu Mathematics, Iowa State University
Brassil, Chad brassilc@kbs.msu.edu W.K. Kellogg Biological Station, Michigan State University
Calder, Catherine calder@stat.ohio-state.edu Statistics, The Ohio State University
Carr, Catherine cc117@umail.umd.edu Biology, University of Maryland at Baltimore
Chan, David dmchan@mail1.vcu.edu Mathematics, Virginia Commonwealth University
Craciun, Gheorghe craciun@math.wisc.edu Mathematics and Biomolecular Chemistry, University of Wisconsin-Madison
Cressie, Noel ncressie@stat.ohio-state.edu Statistics, The Ohio State University
Dimitrova, Elena edimit@clemson.edu Mathematics, Virginia Tech
Djordjevic, Marko mdjordjevic@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Dougherty, Daniel doughe57@msu.edu Lyman Briggs School of Science, Michigan State University
Drover , Jonathan drover@njit.edu Mathematics, New Jersey Institute of Technology
Edelstein-Keshet, Leah keshet@math.ubc.ca Mathematics Department, University of British Columbia
Enciso, German German_Enciso@hms.harvard.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Eriksson, Nicholas eriksson@math.berkeley.edu Mathematics , UC Berkeley
Ermentrout, Bard bard@pitt.edu Department of Mathematics, University of Pittsburgh
Fall, Chris fall@uic.edu Anatomy and Cell Biology/Psychiatry, University of Illinois at Chicago
Forde , Jonathan forde@math.utah.edu Mathematics, University of Utah
Goel, Pranay goelpra@helix.nih.gov Mathematical Biosciences Institute (MBI), The Ohio State University
Grajdeanu, Paula pgrajdeanu@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Griffith , Boyce boyceg@gmail.com Courant Institute of Mathematical Sciences, New York University
Guan, Bo guan@math.ohio-state.edu Mathematics, The Ohio State University
Guan, Bo guan@math.ohio-state.edu Mathematics, The Ohio State University
Guan, Bo guan@math.ohio-state.edu Department of Mathematics, The Ohio State University
Heuett, William wheuett@gmail.com Physics, University of Colorado, Boulder
Hurdal, Monica mhurdal@math.fsu.edu Department of Mathematics, Florida State University
Jalics, Jozsi jalics@math.ysu.edu Mathematics and Statistics, Boston University
Jourquin, Jerome jerome.jourquin@vanderbilt.edu Cancer Biology , Vanderbilt University
Just, Winfried just@math.ohio.edu Math, Ohio University
Kane, Abdoul kane.abdoul@utoronto.ca Physiology, University of Toronto
Krogh-Madsen, Trine trk2002@med.cornell Medicine , Weill Medical College of Cornell University
Kuznetsov , Alexey alexey@math.iupui.edu Mathematical Sciences , IUPUI
Kuznetsova, Anna anna@math.iupui.edu Mathematical Sciences , Indiana University--Purdue University
Lim, Sookkyung limsk@math.uc.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Lin, Shili lin.328@osu.edu Statistics, The Ohio State University
Loladze, Irakli iloladze@math.unl.edu MBI, The Ohio State University
Lou, Yuan lou@math.ohio-state.edu Mathematics, The Ohio State University
Macaba, Joyce macabea@molsci.org Molecular Sciences, Molecular Sciences Institute
Martins , Ana Margarida Virginia Bioinformatics Institute, Virginia Tech
Milescu, Lorin milescul@ninds.nih.gov Laboratory of Neural Control, National Institutes of Health
Miller , Laura miller@math.utah.edu Mathematics , University of Utah
Mincheva , Maya mincheva@cs.uleth.ca Chemistry , University of Lethbridge
Mitchell , Colleen mtchll@math.uiowa.edu Mathematics, University of Iowa
Mubayi, Anuj anujmubayi@yahoo.com Mathematics, Arizona State University
Nevai, Andrew anevai@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Nguyen , Hoan hknguyen@ncsu.edu Mathematics , North Carolina State University
Nguyen, Baochi bnguyen@math.uci.edu Mathematics, University of California, Irvine
Osan, Remus osan@bu.edu Pharmacology; Biomedical Engineering, Boston University
Othmer, Hans othmer@math.umn.edu School of Mathematics, University of Minnesota
Pol, Diego dpol@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Potter, Dustin potter.153@osu.edu MBI, The Ohio State University
Raghib Moreno , Michael mraghib@math.princeton.edu Applied and Computational Mathematics, Princeton University
Rios-Soto , Karen krr22@cornell.edu Department of Mathematics and Statistics, Arizona State University
Rubchinsky, Leonid leo@math.iupui.edu Math. Sciences&StarkNeurosciencesResInst , Indiana University
Schugart, Richard richard.schugart@wku.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Secomb, Timothy secomb@u.arizona.edu Physiology, University of Arizona
Sherman, Arthur asherman@nih.gov National Institutes of Health
Sirito, Gabriele gabriele.sirito@nottingham.ac.uk Math. Sciences, Theoretical Mechanics, University of Nottingham
Srinivasan, Partha p.srinivasan35@csuohio.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Stigler, Brandy bstigler@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Swanson, Kristin swanson@amath.washington.edu Department of Pathology, University of Washington
Thomas, Peter pjthomas@cwru.edu neuroscience, Oberlin College
Tian, Paul tianjj@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Timofeeva, Yulia yulia.timofeeva@nottingham.ac.uk Mathematical Sciences, University of Nottingham
Vera-Licona, Martha (Paola) mveralic@vbi.vt.edu Mathematics & Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University
Wagner , John wagnerjo@us.ibm.com Functional Genomics and Systems Biology , IBM Thomas J. Watson Research Center
Winslow, Raimond rwinslow@jhu.edu Department of Biomedical Engineering, Johns Hopkins University
Yang, Xingzhou xyang4@tulane.edu Center for Computational Science , Tulane University
Zhou, Jin jzhou@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Evolution of Sound Localization Circuits

Animals, including humans, use interaural time differences (ITDs) that arise from of different sound path lengths to the two ears, as a cue of horizontal sound source location. The nature of the neural code for ITD is still controversial. Current models advocate either a map-like place code of ITD along an array of neurons, consistent with a large body of data in the barn owl, or a rate-based population code, consistent with data from small mammals. Recently, it was proposed that these different codes reflect an optimal coding strategy that depends on head size and sound frequency. The chicken makes an excellent test case because its physical prerequisites are similar to small mammals, yet it shares a more recent common ancestry with the owl. We show here that, like in the barn owl, the brainstem nucleus laminaris in mature chickens displayed the major features of a place code of ITD. The physiological range of ITDs was systematically represented in the maximal responses of neurons along each isofrequency band. This is in contrast to the predictions from optimal coding theory and thus re-opens the question as to what determines the neural coding strategies for ITDs, including which code might be implemented by the human brain.

Models for the Role of the Biopolymer Actin in Cell Motility

I will describe some recent work in our group on the dynamics of the actin cytoskeleton in relation to the movement of a motile cell. First, I will describe work (joint with Adriana Dawes, Eric Cytrynbaum, and Bard Ermentrout) on a simple 1D spatial model of a cell. We show how the branching of actin filaments and the forces they exert on the cell membrane account for the protrusion velocity and characteristic actin density profiles. (This work is partly analytical and partly numerical.) We use this model to understand how branching rates and other biochemical parameters control cell speed by studying the relevant travelling wave solutions.


I will also describe efforts (joint with AFM Maree, Alexandra Jilkine, Adriana Dawes and Veronica Grieneisen) at assembling a more detailed 2D spatial model of a crawling cell, in which we take into account the regulatory role of a set of signalling proteins (Cdc42, Rac, Rho). We show how the interplay between these and the actin cytoskeleton accounts for the ability of the cell to self-organize, polarize, maintain a stable shape and speed, and respond to new external signals.

What makes a neuron spike? Phase resetting and intrinsic dynamics

What aspects of a stimulus cause a neuron to fire? How do stimuli affect the time of spikes? In this talk, I will discuss what we can learn about neuronal firing patterns by regarding neurons as nonlinear oscillators. The spike-triggered average or reverse correlation method is a common approach for determining what kinds of stimuli make a neuron fire. The poststimulus time histogram is another experimental measurement for describing the affect of a stimulus on the firing pattern of a neuron. The latter can be related to the former by using some optimality arguments. Both of these curves should be affected by the membrane properties of the individual neuron of interest. Since this is a huge-dimensional space, we will focus on one property of neurons which has been shown to be tightly coupled to neuronal dynamics: the phase resetting curve (PRC). The PRC describes the shift in the timing of a spike due to a brief stimulus as a function of the time since the last spike. We show that under certain circumstances there is a 1:1 mapping between the STA, the PSTH, and the PRC. Thus, we connect internal dynamics of neurons with their preferred stimuli and their population responses. This work is joint with Boris Gutkin, Alex Reyes, Nathan Urban, Roberto Galan, and Nicolas Fourcaud.

Deterministic and Stochastic Models of Actin Dynamics

This lecture will be devoted to a discussion of some of the basic problems in modeling actin dynamics. Actin polymerization and network formation are key processes in cell motility. Numerous actin binding proteins controlling the dynamic properties of actin networks have been studied and models such as the dendritic nucleation scheme have been proposed for the functional integration of at least a minimal set of such regulatory proteins. However, a complete understanding of actin network dynamics is still lacking. Even at the actin-filament level, the dynamics of the distribution of filament lengths and nucleotide profiles are still not fully understood. We will describe recent work on the evolution of the distribution of filament lengths and nucleotide profiles of actin filaments, both from a deterministic and a stochastic viewpoint. If time permits we will discuss work aimed at integrating microscopic models of actin dynamics into cell-level descriptions of motility.

Mathematical Modeling of the Microcirculation

The main function of the circulatory system is to transport and exchange substances throughout the body. Delivery of oxygen is a particularly demanding function, because oxygen is relatively insoluble in water. Within blood vessels, oxygen is carried convectively by hemoglobin molecules within red blood cells. Oxygen exchange with tissue occurs by diffusion in the microcirculation, an extensive branching network of microscopic vessels that brings blood close to all oxygen-consuming tissues. The microcirculation regulates blood flow according to changing local demands over short and long time scales. Mathematical models can be used to gain insight into these processes. Models will be described for the mechanics of blood flow in capillaries, for oxygen exchange between blood and tissues and for structural adaptation of blood vessels. Applications to disease states including cancer will be discussed.

Metabolic and Electrical Oscillations in Insulin-Secreting Pancreatic Beta-Cells

The first generation of models for electrical activity in pancreatic beta-cells focused on ionic mechanisms. Negative feedback by calcium, directly onto calcium-activated potassium channels and indirectly onto ATP-sensitive potassium channels and sodium pumps, is the main type of mechanism considered in current models. Such models do a good job of accounting for the oscillations on a wide range of time scales, ranging from 10 seconds to about 2 minutes. However, even slower oscillations, with periods of 4 or even 10 minutes are often observed, and these often appear with the faster oscillations layered on top. This suggests that there is an additional mechanism for oscillations, which we have proposed is based on oscillations of glycolysis. We will discuss how two relatively simple oscillators, which can be off, oscillating, or tonically on, depending on stimulation level, can be combined to account for the great diversity of observed patterns. We will also consider the impact of metabolic oscillations on synchronization of beta-cells within the islet of Langerhans. Diffusion of glycolytic metabolites provides an important mechanism for secretion, but can also lead to oscillator death and a source of bistability.

Applications of Quantitative Modeling in the Clinical Imaging of Invasive Brain Tumors

Gliomas account for over half of all primary brain tumors and have been studied extensively for decades. Even with increasingly sophisticated medical imaging technologies, gliomas remain uniformly fatal lesions. A significant gap remains between the goal of designing effective therapy and the present understanding of the dynamics of glioma progression. It has become increasingly clear that, along with the proliferative potential of these neoplasms, it is the subclinically diffuse invasion of gliomas that most contributes to their resistance to treatment. That is, the inevitable recurrence of these tumors is the result of diffusely invaded but practically invisible tumor cells peripheral to the abnormal signal on medical imaging and to the limits of surgical, radiological and chemical treatments.


In this presentation, I will demonstrate how quantitative modeling can not only shed light on the spatio-temporal growth of gliomas but also can have specific clinical application in real patients. Integration of our quantitative model with the T1-weighted and T2-weighted magnetic resonance (MR) imaging characteristics of gliomas can provide estimates of the extent of invasion of glioma cells peripheral to the imaging abnormality. Additionally, further insight can be gained from parametric mapping of kinetic model parameters derived from positron emission tomography (PET) with novel tracers. In summary, although current imaging techniques remain woefully inadequate in accurately resolving the true extent of gliomas, quantitative modeling provides a new approach for the dynamic assessment of real patients and helps direct the way to novel therapeutic approaches.