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

Monday, March 27, 2006 | |
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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 | |
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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 | |
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Time | Session |

09:00 AM 10:00 AM | - TBA TBA |

Thursday, March 30, 2006 | |
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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 | 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 | ||

Bolker, Ben | 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 | 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 | 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 | 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 | 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 | 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 | 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 |

Macabéa, 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 | Mathematics, Northern Illinois University |

Mitchell, Colleen | mtchll@math.uiowa.edu | Mathematics, University of Iowa |

Mubayi, Anuj | anujmubayi@yahoo.com | Mathematics, Arizona State University |

Nevai, Andrew | 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 | neuroscience, Oberlin College | |

Tian, Paul | tianjj@mbi.osu.edu | Mathematical Biosciences Institute (MBI), The Ohio State University |

Timofeeva, Yulia | 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 |

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.

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 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.

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.

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.

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.

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.