The workshop is intended to broaden the scientific perspective of young researchers in mathematical biology and to encourage interactions with other scientists.

Workshop activities include plenary talks and poster sessions, as well as group discussions on issues relevant to mathematical biologists. Several abstracts will be chosen for short talks as well as to be presented as a poster.

We cordially invite young mathematical biologists to participate.

### Accepted Speakers

Monday, August 30, 2010 | |
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Time | Session |

09:00 AM 10:00 AM | James Keener - Mechanisms of length regulation of flagella in Salmonella The construction of flagellar motors in motile bacteria such as Salmonella is a carefully regulated genetic process. Among the structures that are built are the hook and the filament. The length of the hook is tightly controlled while the length of filaments is less so. However, if a filament is broken off it will regrow, while a broken hook will not regrow. The question that will be addressed in this talk is how Salmonella detects and regulates the length of these structures. This is related to the more general question of how physical properties (such as size or length) can be detected by chemical signals and what those mechanisms are. In this talk, I will present mathematical models for the regulation of hook and filament length. The model for hook length regulation is based on the hypothesis that the hook length is determined by the rate of secretion of the length regulatory molecule FliK and a cleavage reaction with the gatekeeper molecule FlhB. A stochastic model for this interaction is built and analyzed, showing excellent agreement with hook length data. The model for filament length regulation is based on the hypothesis that the growth of filaments is diffusion limited and is measured by negative feedback involving the regulatory protein FlgM. Thus, the model includes diffusion on a one-dimensional domain with a moving boundary, coupled with a negative feedback chemical network. The model shows excellent qualitative agreement with data, although there are some interesting unresolved issues related to the quantitative results. |

10:40 AM 11:00 AM | Casian Pantea - Persistence of mass-action biochemical reaction networks In the generic class of biological population models, the notion of persistence (impossibility of species extinction) is often of central interest. Persistence has an intrinsic importance in the study of animal population dynamics and in the analysis of infections spread. Moreover, in certain general settings, it has been shown that persistence precludes bistable, switch-like or oscillatory behavior of the model; this fact is of major significance to biochemical interaction networks models (e.g. metabolic pathways), where a great deal of attention has been paid recently to devising criteria that determine the possibility of such behaviors. In this work we show that a large class of two-dimensional biological interaction network models is persistent. This result is robust, in the sense that it holds independently of the choice of parameters in the model. More precisely, we prove that any two-dimensional, endotactic, k-variable mass-action system is persistent. A k-variable mass-action system is a generalized mass-action system where rate constants are allowed to vary with time. A system is endotactic if its underlying network satisfies an easily-checked geometric property. The class of endotactic networks encompasses the well-known class of weakly reversible networks. In the end, we use our persistence result to prove the three-dimensional case of the Global Attractor Conjecture for biochemical reaction networks, a long-standing conjecture originating in the work of Horn, Jackson and Feinberg. This is joint work with George Craciun. |

11:00 AM 12:00 PM | Reinhard Laubenbacher - Algebraic models in systems biology Progress in systems biology relies on the use of mathematical and statistical models for system level studies of biological processes. Several different modeling frameworks have been used successfully, including traditional differential equations based models, a variety of stochastic models, agent-based models, and Boolean networks, to name some common ones. This talk will focus on several types of discrete models, and will describe a common mathematical approach to their comparison and analysis, which relies on computer algebra. Hence, we refer to such models as "algebraic models." The talk will present specific examples of biological systems that can be modeled and analyzed in this way. |

02:00 PM 03:00 PM | Peter Bates - Kinesin-Microtubule Interactions: Transport and Spindle Formation This talk consists of two parts: Pattern formation in families of microtubules under the action of kinesin and the detailed motion of kinesin along a microtubule. Microtubules are long cylindrical structures (lengths being tens of microns and diameter approximately 25 nm) comprised of tubulin dimers, which self-assemble, 13 protofilaments being required side-to-side to form the circular cross section. In the first set of results, microtubules are represented as stiff, polar rods which are subject to diffusion in position and orientation and also subject to pair-wise interaction, mediated by kinesin molecular motors. The concentration of kinesin is represented by a parameter that feeds into the probability of an interaction occurring when two microtubules collide. The probability of an interaction also depends on the location of the collision point along the lengths of the microtubules, because kinesin accumulates at the positive end of each microtubule. With collision rules in place, Monte-Carlo simulations for large numbers of freely moving microtubules are performed, adjusting parameters for concentration of kinesin and polarity of the microtubules. From these studies, a phase diagram is produced, indicating thresholds for phase change to occur. Simulation results are compared to those from in vitro experiments. The second part of the talk involves modeling the fine scale dynamics of a kinesin motor as it walks along a microtubule. The two heads of the kinesin molecule alternately bind and unbind to the microtubule with certain mechanisms providing a directional bias to the Brownian motion expected. One bias is the shape of the head and the shape of the binding site, along with the companion electrostatic charges. The second bias is that, utilizing ATP capture and transferal of phosphors for energy, part of the polymeric leg (neck-linker) of the bound head becomes attached towards the front of that head (the lqlq zipped q q state). The trailing head detaches from the microtubule. It then becomes subject to the biased entropic force due to the zipped state of the leading head and also preferentially (because of shape orientation) attaches in front of the currently attached head at which time ADP is released and a conformational change occurs, strengthening the binding. This motion is modeled using stochastic a differential equation. Simulations are performed with different lengths of neck-linkers and the mean speeds of progression obtained. These are compared with experimental results |

03:00 PM 03:20 PM | Thomas Woolley - Asymmetric stable droplets in a fish patterning model. Soliton like structures called "stable droplets" are found to exist within a paradigm reaction diffusion model which can be used to describe the patterning in a number of fish species. It is straightforward to analyse this phenomenon in the case when two non-zero stable steady states are symmetric, however the asymmetric case is more challenging. We use a recently developed perturbation technique to investigate the weakly asymmetric case. |

04:00 PM 04:20 PM | Rosalyn Rael - Evolution of body size in food webs Body size has been shown to be a significant factor in shaping the structure of food webs, which are network models of the flow of energy in an ecosystem. Recent studies have shown that body size constraints can influence food web dynamics through prey preference and foraging behavior, and can thereby influence the stability of these ecosystem models. Because of its significance, we use body size as the species strategy in an evolutionary game theory approach to studying the influence of predation at individual trophic levels on evolutionarily stable strategies (ESS) in food webs. We systematically construct small (3-5 species) food webs, and combine ecological and evolutionary dynamics using differential equation models to show how the addition of each trophic level impacts the equilibrium strategies of other species. The strategy in our model influences the intrinsic growth rate and carrying capacity of the basal (plant) species, and the interaction rates across species. We show that when a consumer is introduced, the equilibrium strategy of the basal species evolves toward a value that increases the intrinsic growth rate; however, the strength of this effect is mediated by predator species at the third trophic level. We also show how size-based prey preference can influence strategy dynamics and population sizes over long time scales. These results suggest that understanding evolution of body size is important for understanding the trophic interactions that form the basis for large-scale food web structure and function. |

04:20 PM 04:40 PM | William Sherwood - Modeling Neural Circuitry for Early Olfactory Processing The neuronal networks of the olfactory system transduce and transform complex mixtures of odorant molecules into patterns of the neural activity representing smells. We explore two important aspects of how this process works, at the cellular and the neural circuit level, in modeling studies that produce experimental testable predictions. 1) It has long been known that (in rodents) initial synaptic olfactory processing occurs in the olfactory bulb (OB) glomeruli, but the roles of various juxtaglomerular neurons is still not well understood. Recent experimental studies indicate that endogenously bursting external tufted (ET) cells -- which connect olfactory receptor neurons (ORN; OB input) to mitral cells (MC; OB output) -- play a central role in coordinating intraglomerular activity. We develop a biophysically realistic, Hodgkin-Huxley-style ET cell model that includes membrane currents known to be essential for bursting. We use specialized smooth optimization methods to study the (local) sensitivity of its functional characteristics (e.g. burst duration, interburst interval) to parameters, and statistical analyses to characterize the (global) influence of different currents. 2) Odorant-evoked input to and output from the OB is temporally dynamic, and these dynamics are important in shaping odor perception. Inhalation-evoked input bursts of ORN activity occur with durations, latencies, and amplitudes that vary across glomeruli (for the same odorant) and also in individual glomeruli for different odorants, and similarly diverse activity patterns occur at the MC level. We investigate these dynamics using biophysical models of the ORN-MC and ORN-ET-MC circuits. The modelsâ€™ inputs are taken from recordings of ORN calcium signals of head-fixed rats exposed to odorants and closely reproduce signals received by the real neurons. With this data-driven dynamical modeling approach, we are able to explore how the circuitsâ€™ response dynamics vary for different odorants, synaptic strengths, and intrinsic cellular parameters. |

04:50 PM 05:30 PM | Folashade Agusto, Sharon Bewick, James Caffrey - Poster Previews Poster Previews |

Tuesday, August 31, 2010 | |
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Time | Session |

09:00 AM 10:00 AM | John Lowengrub - Feedback, lineages and cancer A multispecies continuum model is developed to simulate the dynamics of cell lineages in solid tumors. The model accounts for spatiotemporally varying cell proliferation and death mediated by the heterogeneous distribution of oxygen and soluble chemical factors. Together, these regulate the rates of self-renewal and differentiation of the different cells within the lineages. As demonstrated in the talk, the feedback processes are found to play a critical role in tumor progression and the development of morphological instability. |

10:30 AM 12:00 PM | Orly Alter - Discovery of Mechanisms from Mathematical Modeling of DNA Microarray Data: Computational Prediction and Experimental Verification molecular biological data, such as DNA microarray data, just as Kepler discovered the laws of planetary motion by using mathematics to describe trends in astronomical data [1]. In this talk, I will demonstrate that mathematical modeling of DNA microarray data can be used to correctly predict previously unknown mechanisms that govern the activities of DNA and RNA. First, I will describe the computational prediction of a mechanism of regulation, by developing generalizations of the matrix and tensor computations that underlie theoretical physics and using them to uncover a genome-wide pattern of correlation between DNA replication initiation and RNA expression during the cell cycle [2,3]. Second, I will describe the recent experimental verification of this computational prediction, by analyzing global expression in synchronized cultures of yeast under conditions that prevent DNA replication initiation without delaying cell cycle progression [4]. Third, I will describe the use of the singular value decomposition to uncover "asymmetric Hermite functions," a generalization of the eigenfunctions of the quantum harmonic oscillator, in genome-wide mRNA lengths distribution data [5]. These patterns might be explained by a previously undiscovered asymmetry in RNA gel electrophoresis band broadening and hint at two competing evolutionary forces that determine the lengths of gene transcripts. Finally, I will describe ongoing work in the development of tensor algebra algorithms (as well as visual correlation tools), the integrative and comparative modeling of DNA microarray data (as well as rRNA sequence data), and the discovery of mechanisms that regulate cell division, cancer and evolution. 1) Alter, PNAS 103, 16063 (2006). 2) Alter & Golub, PNAS 101, 16577 (2004). 3) Omberg, Golub & Alter, PNAS 104, 18371 (2007). 4) Omberg, Meyerson, Kobayashi, Drury, Diffley & Alter, Nature MSB 5, 312 (2009). 5) Alter & Golub, PNAS 103, 11828 (2006). |

03:40 PM 04:00 PM | Sijia Liu - Novel clustering methods for the analysis of biological data The need to interpret and extract possible inferences from high-dimensional datasets has led over the past decades to the development of dimensionality reduction and data clustering techniques. Scientific and technological applications of clustering methodologies include among others biomedical imaging, data mining and bioinformatics. Current research in data clustering focuses on identifying and exploiting information on dataset geometry and on developing robust algorithms for noisy datasets. Recent approaches based on spectral graph theory have been devised to efficiently handle dataset geometries exhibiting a manifold structure, and fuzzy clustering methods have been developed that assign cluster membership probabilities to data that cannot be readily assigned to a specific cluster. In this talk, we develop a novel fuzzy spectral clustering algorithm that combines seamlessly the strengths of spectral approaches to clustering with various desirable properties of fuzzy methods. We also discuss examples of gene expression datasets for which the developed methodology outperforms other frequently used algorithms. |

04:00 PM 04:20 PM | Delphine Picart - Optimal control on insect pest population In this work, a multi-stage age-structured population dynamics model is used to determine the most efficient and least expensive procedures to reduce the population size of a vine pest. Egg and larval pesticides are often used by wine makers to contain this pest. Making the decision to apply these products or not is sometimes not easy because it depends on several variables, for example weather, price or field observations. Here, we focus on three constraints that are the action mode, the price and the efficiency of pesticides and, we determine according to them the best treatment during the pest life cycle to maximum reduce the population size of this insect. To get the optimal control on this population we study an optimization problem with constraints. |

04:20 PM 04:40 PM | Michael Cortez - Understanding how rapid evolution affects predator-prey systems using fast-slow dynamical systems Evidence of rapid evolution in ecological communities has accumulated in the last thirty years, yet theory explaining the interplay between ecological and evolutionary processes on comparable time scales has not kept pace. This disparity between experiments and theory is partially due to the intractability of high dimensional systems of ordinary differential equations - even systems with two evolving species must be of at least dimension four. I will present work focusing on how the theory of slow-fast dynamical systems can be used to study predator-prey system exhibiting rapid evolution. This approach not only reduces our system back down to two dimensions, but also yields graphical techniques with predictive power about the (potentially new) qualitative dynamics a given predator-prey system can exhibit. |

04:50 PM 05:30 PM | Andrey Dovzhenok, Souvik Bhattacharya, Jiafen Gong, Andrea Barreiro - Poster Preview II Poster Preview II |

Wednesday, September 1, 2010 | |
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Time | Session |

10:00 AM 11:00 AM | Van Savage - Scaling in Vascular Networks: Curvature, Finite-Size Effects, and Applications to Tumor Angiogenesis and Growth Metabolic rate, heart rate, and lifespan depend on body size according to scaling relationships that extend over ~21 orders of magnitude and that represent diverse taxa and environments. These relationships for body mass have long been approximated by power laws, but there has been intense debate about the values of exponents (e.g., 1/4 versus 1/3). I will show for mammals that these scaling relationships exhibit systematic curvature in logarithmic space. This curvature explains why different studies find different power-law exponents. I will also show how existing optimal network theory can be modified using finite-size corrections and hydrodynamical considerations to predict curvature. I will distinguish among potential physiological mechanisms by comparing model predictions for the direction and magnitude of the curvature with results from empirical data. For the final half of the talk, I will develop modified network models to describe tumor angiogenesis and vascular structure. These new models will help to compare tumor with normal vasculature, to understand different phases (pre- and post-angiogenesis) of tumor growth, and to describe the formation of a necrotic core. |

11:20 AM 11:40 AM | Sarah Iams - Leg based control of mosquito flight Mosquitoes are agile, yet surprisingly stable fliers. In the air, their long, slender legs are a visually compelling feature of their body plan. Since legs are so prominent in flight, it is unsurprising that they have long been conjectured to serve as a secondary flight control system (with the primary system being subtle modulations in wing motion). This idea has remained speculative for nearly a century. Using high speed video to capture leg, body and wing dynamics, we develop mathematically based tracking and classification techniques to identify in-flight leg activity. By combining functional data analysis methods with a physical model-based understanding of flight force generation, we examine the importance of leg activity to in-flight maneuvering. We estimate the impact of leg activity on overall flight dynamics, examining how mosquito leg motion effects mosquito stability and turning manuevers. |

11:40 AM 12:00 PM | Christina Hamlet - Modeling and computation of fluid structure interactions near the bell of upside-down jellyfish This work focuses on describing the scaling effects on fluid flow near the bell of the upside down jellyfish (Cassiopeia sp.) using computational fluid dynamics and live experiments. The immersed boundary method is used to simulate the bell of a jellyfish as an flexible structure coupled with a porous boundary. The porous boundary represents the oral arms which protrude over the bell, altering the flow. The effect of the oral arms on vortex formation and on volumetric flow rates are analyzed across a range of Reynolds numbers. |

01:30 PM 01:50 PM | - Dan Siegal-Gaskins' Presentation at WYRMB 2010 Dan Siegal-Gaskins' Presentation at WYRMB 2010 |

01:50 PM 02:10 PM | Holger Perfahl - Holger Perfahl Lecture Holger Perfahl Lecture |

02:30 PM 02:50 PM | Kevin Sanft - Model reduction in stochastic simulation of the enzyme-substrate reaction set Michaelis-Menten kinetics are often used to describe enzyme-catalyzed reactions in biochemical models. The Michaelis-Menten approximation has been rigorously derived in the context of traditional differential equation models. In many biochemical processes, however, stochastic effects due to the random interaction of chemical species present in small numbers play an important role. To capture these effects one has to move away from differential equation models, which are continuous and deterministic, to a discrete stochastic representation. The theory underlying Gillespie stochastic simulation algorithm (SSA) provides a physical justification for stochastic models comprised of elementary reactions. Solving for the evolution of the chemical species distributions exactly is intractable for most models. Typically, the SSA is used to generate an ensemble of trajectories to establish an estimate of the distribution. The slow-scale stochastic simulation algorithm (ssSSA) uses model reduction to improve the performance of the SSA. However, the ssSSA suggests an approximation that differs from the Michaelis-Menten rate for certain enzymatic reactions. First-passage time analysis is used to examine some of these differences. The Michaelis-Menten approximation is shown to be applicable under a set of validity criteria in discrete stochastic models. |

Name | Affiliation | |
---|---|---|

Agusto, Folashade | agusto@nimbios.org | NIMBIOS, University of Tennessee |

Alter, Orly | orlyal@mail.utexas.edu | Scientific Computing & Imaging Institute, University of Utah |

Barreiro, Andrea | akb6@washington.edu | Applied Mathematics, University of Washington |

Bates, Peter | bates@math.msu.edu | Department of Mathematics, Michigan State University |

Bewick, Sharon | sharon_bewick@hotmail.com | NIMBioS, University of Tennessee |

Bhattacharya, Souvik | souvik@ufl.edu | Mathematics, University of Florida |

Byrne, Erin | erin.byrne@colorado.edu | Applied Mathematics, University of Colorado |

Caffrey, James | jcaffrey@ms.unimelb.edu.au | Mathematics and Statistics, University of Melbourne |

Cortez, Michael | mhc37@cornell.edu | Center for Applied Mathematics, Cornell University |

Dovzhenok, Andrey | adovzhen@iupui.edu | Mathematical Sciences, Indiana University--Purdue University |

Dunmyre, Justin | mathemagician@gmail.com | Mathematics Department, University of Pittsburgh |

Eager, Eric | s-eeager1@math.unl.edu | Mathematics, University of Nebraska |

Frank, Dennis | dofrank@ncsu.edu | Department of Mathematics, North Carolina State University |

Fuhrman, Kseniya | fuhrman@msoe.edu | Mathematics, Milwaukee School of Engineering |

Gadelha, Hermes | gadelha@maths.ox.ac.uk | Centre for Mathematical BIology, University of Oxford |

Gong, Jiafen | jgong@math.ualberta.ca | Mathematical and Statstical Science, University of Alberta |

Govinder, Kesh | govinder@ukzn.ac.za | School of Mathematical & Statistical Sciences, University of Kwazulu-Natal |

Gutierrez, Juan | j.gutierrez@math.miami.edu | Department of Mathematics, University of Miami |

Hamlet, Christina | chamlet@email.unc.edu | Mathematics, University of North Carolina, Chapel Hill |

Hammond, Jason | hammonjf@colorado.edu | Applied Math, University of Colorado |

Hao, Wenrui | whao@nd.edu | Department of Applied and Computational Mathematics and Statistics, University of Notre Dame |

Hinkelmann, Franziska | fhinkel@vt.edu | Mathematics, University of Virginia |

Hosoi, Anette | peko@mit.edu | Mechanical Engineering, Massachusetts Institute of Technology |

Hower, Valerie | vhower@math.berkeley.edu | Mathematics, University of Miami |

Iams, Sarah | smi6@cornell.edu | Center for Applied Mathematics, Cornell University |

Jin, Yu | yujin@math.ualberta.ca | Mathematical and Statistical Sciences, University of Alberta |

Keener, James | keener@math.utah.edu | Dept of Math, University of Utah |

Khain, Evgeniy | khain@oakland.edu | Physics, Oakland University |

Kilpatrick, Zachary | kilpatri@math.utah.edu | Mathematics, University of Pittsburgh |

Laubenbacher, Reinhard | betsyw@vbi.vt.edu | Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University |

Li, Dong | mpdongli@gmail.com | Mathematics, University of Iowa |

Liu, Sijia | sijialiu@iastate.edu | Mathematics, Iowa State University |

Long, Byron | bl6@rice.edu | Bioengineering, Rice University |

Lowengrub, John | lowengrb@math.uci.edu | Mathematics, University of California, Irvine |

Meyer, Kim | meyer.kimberly@gmail.com | Mathematics, University of Louisville |

Pantea, Casian | pantea@math.wisc.edu | Mathematics, University of Wisconsin |

Park, Jun-Koo | jkpark@iastate.edu | Department of Mathematics, Iowa State University |

Perfahl, Holger | holger.perfahl@ibvt.uni-stuttgart.de | Center Systems Biology, University of Stuttgart |

Picart, Delphine | delphine.picart@asu.edu | Mathematics and Statistical Sciences, Arizona State University |

Price, Ian | imp5@pitt.edu | Mathematics, University of Pittsburgh |

Prokopiou, Sotiris | pmxsp@nottingham.ac.uk | School of Biosciences, University of Nottingham |

Rael, Rosalyn | rrael@umich.edu | Ecology and Evolutionary Biology, University of Michigan |

Robinson, Nathaniel | robinson.1146@osu.edu | Molecular Genetics and Mathematics, The Ohio State University |

Sanft, Kevin | kevin@kevinsanft.com | Computer Science, University of California, Santa Barbara |

Savage, Van | vsavage@ucla.edu | Department of Biomathematics, University of Southern California |

Shah, Aalok | ashah@math.arizona.edu | Applied Mathematics, University of Arizona |

Sherwood, William | wesher@bu.edu | Mathematics Dept. & Center for BioDynamics, Boston University |

Shlizerman, Eli | shlizee@uw.edu | Applied Mathematics, University of Washington |

Shtylla, Blerta | shtyllab@math.utah.edu | Mathematics Department, University of Utah |

Sit, Atilla | atillast@gmail.com | Department of Mathematics, Iowa State University |

Solomon, Bill | billsolo@sbcglobal.net | Blue Valley High School |

Srinivasan, Partha | p.srinivasan35@csuohio.edu | Mathematics, Cleveland State University |

Trenado, Carlos | trenado@cdb-unit.de | Comp. Diagnostics and Biocybernetics Unit, Saarland University Hospital |

Vilela, Marco | marco.vilela@mail.chem.tamu.edu | Chemistry, Texas A & M University |

Wang, Qixuan | wangx825@umn.edu | Mathematics, University of Minnesota |

Woolley, Thomas | woolley@maths.ox.ac.uk | Centre for Mathematical Biology, University of Oxford |

Zheng, Likun | zhen0107@math.umn.edu | School of Mathematics, University of Minnesota |

First, I will describe the computational prediction of a mechanism of regulation, by developing generalizations of the matrix and tensor computations that underlie theoretical physics and using them to uncover a genome-wide pattern of correlation between DNA replication initiation and RNA expression during the cell cycle [2,3].

Second, I will describe the recent experimental verification of this computational prediction, by analyzing global expression in synchronized cultures of yeast under conditions that prevent DNA replication initiation without delaying cell cycle progression [4].

Third, I will describe the use of the singular value decomposition to uncover "asymmetric Hermite functions," a generalization of the eigenfunctions of the quantum harmonic oscillator, in genome-wide mRNA lengths distribution data [5]. These patterns might be explained by a previously undiscovered asymmetry in RNA gel electrophoresis band broadening and hint at two competing evolutionary forces that determine the lengths of gene transcripts.

Finally, I will describe ongoing work in the development of tensor algebra algorithms (as well as visual correlation tools), the integrative and comparative modeling of DNA microarray data (as well as rRNA sequence data), and the discovery of mechanisms that regulate cell division, cancer and evolution.

1) Alter, PNAS 103, 16063 (2006).

2) Alter & Golub, PNAS 101, 16577 (2004).

3) Omberg, Golub & Alter, PNAS 104, 18371 (2007).

4) Omberg, Meyerson, Kobayashi, Drury, Diffley & Alter, Nature MSB 5, 312 (2009).

5) Alter & Golub, PNAS 103, 11828 (2006).

Microtubules are long cylindrical structures (lengths being tens of microns and diameter approximately 25 nm) comprised of tubulin dimers, which self-assemble, 13 protofilaments being required side-to-side to form the circular cross section. In the first set of results, microtubules are represented as stiff, polar rods which are subject to diffusion in position and orientation and also subject to pair-wise interaction, mediated by kinesin molecular motors. The concentration of kinesin is represented by a parameter that feeds into the probability of an interaction occurring when two microtubules collide. The probability of an interaction also depends on the location of the collision point along the lengths of the microtubules, because kinesin accumulates at the positive end of each microtubule. With collision rules in place, Monte-Carlo simulations for large numbers of freely moving microtubules are performed, adjusting parameters for concentration of kinesin and polarity of the microtubules. From these studies, a phase diagram is produced, indicating thresholds for phase change to occur. Simulation results are compared to those from in vitro experiments.

The second part of the talk involves modeling the fine scale dynamics of a kinesin motor as it walks along a microtubule. The two heads of the kinesin molecule alternately bind and unbind to the microtubule with certain mechanisms providing a directional bias to the Brownian motion expected. One bias is the shape of the head and the shape of the binding site, along with the companion electrostatic charges. The second bias is that, utilizing ATP capture and transferal of phosphors for energy, part of the polymeric leg (neck-linker) of the bound head becomes attached towards the front of that head (the lqlq zipped q q state). The trailing head detaches from the microtubule. It then becomes subject to the biased entropic force due to the zipped state of the leading head and also preferentially (because of shape orientation) attaches in front of the currently attached head at which time ADP is released and a conformational change occurs, strengthening the binding. This motion is modeled using stochastic a differential equation. Simulations are performed with different lengths of neck-linkers and the mean speeds of progression obtained. These are compared with experimental results

Using high speed video to capture leg, body and wing dynamics, we develop mathematically based tracking and classification techniques to identify in-flight leg activity. By combining functional data analysis methods with a physical model-based understanding of flight force generation, we examine the importance of leg activity to in-flight maneuvering. We estimate the impact of leg activity on overall flight dynamics, examining how mosquito leg motion effects mosquito stability and turning manuevers.

The question that will be addressed in this talk is how Salmonella detects and regulates the length of these structures. This is related to the more general question of how physical properties (such as size or length) can be detected by chemical signals and what those mechanisms are.

In this talk, I will present mathematical models for the regulation of hook and filament length. The model for hook length regulation is based on the hypothesis that the hook length is determined by the rate of secretion of the length regulatory molecule FliK and a cleavage reaction with the gatekeeper molecule FlhB. A stochastic model for this interaction is built and analyzed, showing excellent agreement with hook length data. The model for filament length regulation is based on the hypothesis that the growth of filaments is diffusion limited and is measured by negative feedback involving the regulatory protein FlgM. Thus, the model includes diffusion on a one-dimensional domain with a moving boundary, coupled with a negative feedback chemical network. The model shows excellent qualitative agreement with data, although there are some interesting unresolved issues related to the quantitative results.

In this work we show that a large class of two-dimensional biological interaction network models is persistent. This result is robust, in the sense that it holds independently of the choice of parameters in the model. More precisely, we prove that any two-dimensional, endotactic, k-variable mass-action system is persistent. A k-variable mass-action system is a generalized mass-action system where rate constants are allowed to vary with time. A system is endotactic if its underlying network satisfies an easily-checked geometric property. The class of endotactic networks encompasses the well-known class of weakly reversible networks.

In the end, we use our persistence result to prove the three-dimensional case of the Global Attractor Conjecture for biochemical reaction networks, a long-standing conjecture originating in the work of Horn, Jackson and Feinberg.

This is joint work with George Craciun.

We systematically construct small (3-5 species) food webs, and combine ecological and evolutionary dynamics using differential equation models to show how the addition of each trophic level impacts the equilibrium strategies of other species. The strategy in our model influences the intrinsic growth rate and carrying capacity of the basal (plant) species, and the interaction rates across species. We show that when a consumer is introduced, the equilibrium strategy of the basal species evolves toward a value that increases the intrinsic growth rate; however, the strength of this effect is mediated by predator species at the third trophic level. We also show how size-based prey preference can influence strategy dynamics and population sizes over long time scales. These results suggest that understanding evolution of body size is important for understanding the trophic interactions that form the basis for large-scale food web structure and function.

1) It has long been known that (in rodents) initial synaptic olfactory processing occurs in the olfactory bulb (OB) glomeruli, but the roles of various juxtaglomerular neurons is still not well understood. Recent experimental studies indicate that endogenously bursting external tufted (ET) cells -- which connect olfactory receptor neurons (ORN; OB input) to mitral cells (MC; OB output) -- play a central role in coordinating intraglomerular activity. We develop a biophysically realistic, Hodgkin-Huxley-style ET cell model that includes membrane currents known to be essential for bursting. We use specialized smooth optimization methods to study the (local) sensitivity of its functional characteristics (e.g. burst duration, interburst interval) to parameters, and statistical analyses to characterize the (global) influence of different currents.

2) Odorant-evoked input to and output from the OB is temporally dynamic, and these dynamics are important in shaping odor perception. Inhalation-evoked input bursts of ORN activity occur with durations, latencies, and amplitudes that vary across glomeruli (for the same odorant) and also in individual glomeruli for different odorants, and similarly diverse activity patterns occur at the MC level. We investigate these dynamics using biophysical models of the ORN-MC and ORN-ET-MC circuits. The modelsĂ˘â‚¬â„˘ inputs are taken from recordings of ORN calcium signals of head-fixed rats exposed to odorants and closely reproduce signals received by the real neurons. With this data-driven dynamical modeling approach, we are able to explore how the circuitsĂ˘â‚¬â„˘ response dynamics vary for different odorants, synaptic strengths, and intrinsic cellular parameters.

**Modeling Neural Circuitry for Early Olfactory Processing**

William Sherwood The neuronal networks of the olfactory system transduce and transform complex mixtures of odorant molecules into patterns of the neural activity representing smells. We explore two important aspects of how this process works, at the cellular and the

**Scaling in Vascular Networks: Curvature, Finite-Size Effects, and Applications to Tumor Angiogenesis and Growth**

Van Savage Metabolic rate, heart rate, and lifespan depend on body size according to scaling relationships that extend over ~21 orders of magnitude and that represent diverse taxa and environments. These relationships for body mass have long been approximated b

**Algebraic models in systems biology**

Reinhard Laubenbacher Progress in systems biology relies on the use of mathematical and statistical models for system level studies of biological processes. Several different modeling frameworks have been used successfully, including traditional differential equations bas

**Kinesin-Microtubule Interactions: Transport and Spindle Formation**

Peter Bates This talk consists of two parts: Pattern formation in families of microtubules under the action of kinesin and the detailed motion of kinesin along a microtubule.

Microtubules are long cylindrical structures (lengths being tens of micr

**Asymmetric stable droplets in a fish patterning model.**

Thomas Woolley Soliton like structures called "stable droplets" are found to exist within a paradigm reaction diffusion model which can be used to describe the patterning in a number of fish species. It is straightforward to analyse this phenomenon in the

**Evolution of body size in food webs**

Rosalyn Rael Body size has been shown to be a significant factor in shaping the structure of food webs, which are network models of the flow of energy in an ecosystem. Recent studies have shown that body size constraints can influence food web dynamics through pr