• Tuesday Seminars
• Postdoc Seminars
• Neuroscience Journal Club
• Postdoctoral Research Forum

In populations of synapses, long-term potentiation and long-term depression reflect the sum of many individual plasticity events. We have found that at individual hippocampal CA3-CA1 synapses, upward or downward transitions in strength are all-or-none and sudden, thus allowing each synapse two levels of strength. Under native conditions, three-fourths of synapses begin in a low-strength state. Downward transitions are reversible, but after upward transitions synapses can be locked quickly into a high-strength state. Upward and downward transitions could be isolated by blocking or saturating potentiation or depression. This resolves plasticity into component processes that, when recombined, yield the native learning rule. Under realistic spiking conditions, these processes have activity- and timing-dependence predicting that when a rat runs through a place field the only possible form of plasticity is LTP. A three-state model (low, high and locked-in) accounts for our observations and for a variety of previous physiological, pharmacological and genetic manipulations.

In many situations, cell-cell adhesion is mediated by multiple ligand-receptor pairs. For example, the interaction between T cells and antigen-presenting cells of the immune system is mediated not only by T cell receptors and their ligands (peptide-major histocompatibility complex) but also by binding of intracellular adhesion molecules. Interestingly, these binding pairs have different resting lengths. Fluorescent labelling reveals segregation of the longer adhesion molecules from the shorter T cell receptors in this case. We explore the thermal equilibrium of a general cell-cell interaction mediated by two ligand-receptor pairs to examine competition between the elasticity of the cell wall, non-specific intercellular repulsion and bond formation, leading to segregation at equilibrium. We make detailed predictions concerning the relationship between physical properties of the membrane and ligand-receptor pairs and equilibrium pattern formation and suggest experiments to refine our understanding of the system. We demonstrate our model by application to the T cell-antigen-presenting-cell system and natural killer cell-target cell adhesion. Our results underline the importance of active, energy-consuming processes in this system.

New insights in such diverse topics as RNA to protein ratio in cells, predator-prey interactions, and effects of globally rising CO2 on humans come from mathematical models that rely on biological stoichiometry. Biological stoichiometry is founded on rigorous scale-invariant principles such as mass balance law and the fact that for all life forms, from viruses to humans, carbon (C), nitrogen (N) and phosphorus (P) are essential. The rigor and the universality of these principles provide a framework that is particularly appealing to mathematicians that want to venture into mathematical biology. In this talk, I will present three examples of stoichiometrically based ODE models together with their mathematical analysis and biological implications.

The time evolution of influenza A virus is linked to a non-fixed landscape driven by tight co-evolutionary interactions between hosts and competing influenza strains. Herd-immunity, cross-immunity and age-structure are among the factors that have been shown to support strain coexistence and/or disease oscillations. In this study, we put two influenza strains under various levels of (interference) competition. We establish that cross-immunity and host isolation lead to periodic epidemic outbreaks (sustained oscillations) in this multi-strain system. We compute the basic reproductive number for each strain independently, as well as for the full system and show that when the basic reproductive number of both strains is less than 1, the disease dies out. Sub-threshold coexistence driven by cross-immunity is possible even when the basic reproductive number of one strain is below one. Conditions that guarantee a winning type or coexistence are established in general. Oscillatory coexistence is established via Hopf-bifurcation theory and numerical simulations using realistic parameter values.

The dynamics of continuous cultures (or bioreactors) has been a problem of considerable interest to many mathematicians. The standard modeling approach was developed following the pioneering work of J. Monod. Models of this class include only extracellular variables such as cell and substrate concentrations. These simple unstructured models typically fail to accurately describe the transient behavior of bioreactors. Understanding such transients is crucial for such applications as waste water treatment and food processing where bioreactors are widely used.

In this talk, I will report on our recent progress in formulating and analyzing structured models of microbial growth which explicitly consider intracellular variables that determine the physiological state of the cell. Specifcally, I will discuss such topics as: 1) General description and formualtion of structured models; 2) The role of transport enzymes; 3) Dynamics of single and mixed cultures; and 4) Connections between theory and experiments.

References:
• Shoemaker, J., Reeves, G.T., Gupta, S., Pilyugin, S.S., Egli, T., & Narang, A. (2003). The dynamics of single-substrate continuous cultures: The role of transport enzymes. J. Theor. Biol., 222, 307-322.
• Reeves, G.T., Narang, A., & Pilyugin, S.S. (2003). Growth of mixed cultures on mixtures of substitutable substrates: The operating diagram for a structured model. Journal of Theoretical Biology, 226 (2), 143-157.
• Pilyugin, S.S., Reeves, G.T., & Narang, A. Stability of mixed microbial cultures: connecting theory and experiments. Part 1. Unstructured model. Manuscript submitted for publication.
• Pilyugin, S.S., Reeves, G.T., & Narang, A. Stability of mixed microbial cultures: connecting theory and experiments. Part 2. Structured model. Manuscript submitted for publication.

Specifcally, the talk will include: 1) Formulation and stability analysis of the variable yield model; 2) A subcritical bifurcation lemma, divergence criterion; 3) Several examples involving the divergence criterion; and 4) Examples of complicated dynamics for two competitors, period-doubling cascades, Neimark-Sacker bifurcation.

References:
• Pilyugin, S.S., & Waltman, P. (2003). Multiple limit cycles in the chemostat with variable yield. Math. Biosci., 182 , 151-166.
• Pilyugin, S.S., & Waltman, P. (2003). Divergence criterion for generic planar systems. SIAM Journal on Applied Mathematics, 64 (1), 81-93.
• Arino, J., Pilyugin, S.S., & Wolkowicz, G. S. K. Considerations on yield, nutirent uptake, cellular growth, and competition in chemostat models. Manuscript submitted for publication.

The classical Monod model of microbial growth in a chemostat assumes that the yield coecient, dened as the ratio of biomass production to nutrient consumption, is constant. In this talk, I will discuss the generalization of the Monod model to the case where the yield coeffcient is an increasing function of the nutrient concentration. In contrast to the Monod model, the variable yield model exhibits sustained oscillations. Moreover, the variable yield model may undergo a subcritical Hopf bifurcation and feature multiple limit cycles. I will present the mathematical methods that were derived to analyze this model. I will also discuss the implications of variable yield for the coexistence of two competing populations.

The dynamic nature of immune responses requires the development of appropriate experimental and theoretical tools to quantitatively estimate the division and death rates which determine the turnover of immune cells. A number of papers have used experimental data from BrdU and D-glucose labels together with a simple random birth-death model to quantify the turnover of immune cells focusing on HIV/SIV infections.

In this talk, I will discuss how the uncertainties in the assumptions of the random birth-death model may lead to substantial errors in the parameters estimated. I will show how more accurate estimates can be obtained from the more recent CFSE data which allow to track the number of divisions each cell has undergone.

Specifcally, the talk will include:
• Biological background;
• Description of a mathematical model;
• Several examples;
• Analysis of the Smith-Martin model;
• Method of rescaling;
• Application to experimental datasets;
• Discussion.

References:
• Pilyugin, S.S., Ganusov, V. V., Murali-Krishna, K., Ahmed, R., & Antia, R. (2003). The rescaling method for quantifying the turnover of cell populations. J. Theor. Biol., 225, 275-283.
• Ganusov, V.V., Pilyugin, S.S., de Boer, R., Murali-Krishna, K., Ahmed, R., & Antia, R. Quantifying the cell turnover using CFSE data. Manuscript submitted for publication.

The living world is filled with striped and mottled patterns of contrasting colors; with sculptural equivalents of those patterns realized as surface crests and troughs; with patterns of organization and behavior even among individual organisms. People have long been tempted to find some obscure "intelligence" behind all these biological patterns. In the early twentieth century the Belgian Symbolist playwright Maurice Maeterlinck, pondering the efficient organization of bee and termite colonies, asked:

"What is it that governs here? What is it that issues orders, foresees the future, elaborates plans and preserves equilibrium, administers, and condemns to death?"

The natural world, it turns out, is replete with patterns and processes that exhibit organization without an organizer, coordination without a coordinator.

For some people who come to appreciate this point, it then becomes tempting to attribute such complex patterns and processes to innate behaviors, instincts, or genetic information encoded deep within the chromosomes of the organism. But such "simple explanations" are not likely and, in the best of cases, they merely sweep the question under the carpet. What then is the origin of all this stunning complexity?

Excerpted from: http://www.naturalhistorymag.com/0603/0603_feature.html

A polymorphism is a trait which shows variability in a population (e.g., the blood type): without polymorphisms, we would all look the same! The possible values of the trait are called alleles.

At genomic level, a polymorphism is a DNA region (string of A, T, C and Gs) whose content varies in a population. The smallest such polymorphism consists of a single base, and is called Single Nucleotide Polimorphism (SNP, pronounced "snip").

Trying to determine the allele values for a set of SNPs, for either an individual or an entire population, gives rise to several nice and challenging combinatorial problems. These problems, called "haplotyping" problems, have been extensively studied in the last few years. In this talk, we will illustrate the most important haplotyping problems and mention the results that have been obtained for their solution. In particular, some of such problems have been proved NP-hard and solved by (worst case) exponential-time algorithms, while others are solvable in polynomial time.

Spatial patterns of glomerular activity in the vertebrate olfactory bulb and arthropod antennal lobe are believed to reflect an important component of the first-order olfactory representation and contribute to odorant identification. Higher-concentration odorant stimuli evoke broader glomerular activation patterns, resulting in greater spatial overlap among different odor representations. However, behavioral studies demonstrate results contrary to what these data might suggest: honeybees are more, not less, able to discriminate among odorants when they are applied at higher concentrations. Using a computational model of the honeybee antennal lobe, we here show that changes in synchronization patterns among antennal lobe projection neurons, as observed electrophysiologically in response to odor stimuli of different concentrations, could parsimoniously underlie these behavioral observations. We suggest that "stimulus salience," as defined behaviorally, is directly correlated with the degree of synchronization among second-order olfactory neurons.

Recently, direct electrical coupling between inhibitory neurons has been found to be widespread in the brain. The effects of electrical coupling between neurons has been the focus of much experimental and theoretical work, however the functional role that electrical coupling plays in neuronal networks remains unclear. It has been suggested that electrical coupling can help coordinate synchronous oscillatory behavior in inhibitory networks, which has been hypothesized to be important for sensory and cognitive processes. However, it has been shown that electrical coupling can desynchronize activity as well. Previous theoretical studies have examined the effects of electrical coupling on synchronization patterns between single-compartment model neurons. The applicability of these studies to dynamics in real inhibitory neuronal networks depends on whether or not a single-compartment description is a sufficient model. Single-compartment models neglect the spatial structure of neurons, and when neurons are not sufficiently electrotonically compact, the spatial structure cannot be ignored. In this talk, I will discuss how the spatial structure of neurons (dendritic processing) can affect network dynamics and I will show how the location of electrical coupling influences phase-locking in networks of neurons.

Angiogenesis, the formation of new blood vessels, is required for several normal physiological process including development and wound healing. Angiogenesis also contributes to the progression of several diseases because it is a mechanism for providing diseased tissue with the nutrients required for cellular viability. For example, angiogenesis is required for tumors to grow beyond 1 mm in size. Pharmaceuticals that target angiogenesis block tumor growth in animal models and certain of these drugs are currently under clinical evaluation.

Angiogenesis is a complex physiological process that is mediated by the endothelial cells that form existing blood vessels. Component of this process include the degradation of the extracellular matrix, endothelial cell migration, cell proliferation, and vessel formation. These cellular activities are activated by extracellular stimuli, and both growth factors and the extracellular matrix regulate cell function. These activators do not enter the endothelial cells, but instead activate cell surface receptors triggering intracellular cell signal transduction pathways.

Vascular Endothelial Growth Factor (VEGF) has received considerable attention as a potent angiogenic growth factor. This is due in part to the observations that inhibition of VEGF function blocks both angiogenesis and tumor growth in animal models. VEGF binding to its high affinity receptor activates multiple signal transduction pathways and endothelial cell activities. Clarification of these signaling pathways may allow for the identification of new pharmaceutical targets and the development of more efficacious inhibitors.

Echolocation -- "seeing" using sound -- is a remarkable ability bats (and toothed whales) have and we don't. We know some of what bats can do with echolocation but are still in a fairly unenlightened state when in comes to explaining how they do it. This talk will focus on some of what we have learned from bats in psychophysical experiments that raise questions about their signal-processing strategy.

Sudden cardiac death resulting from disturbance in the normal rhythmic beating of the heart (i.e., ventricular fibrillation) remains the leading cause of death in industrially developed countries, accounting for between 300,000 and 500,000 deaths each year in the United States. Yet, despite the enormity of this problem, the mechanisms responsible for these lethal changes in the cardiac rhythm remain largely to be determined. Alterations in the autonomic neural regulation of heart may play a critical role in sudden cardiac death, particularly during myocardial ischemia. It is now generally accepted that the activation of cardiac sympathetic nerves reduce cardiac electrical stability, while the activation of parasympathetic nerves may counteract sympathetic activation and protect against ventricular fibrillation. However, the mechanisms by which alterations in cardiac autonomic activity provoke these lethal cardiac rhythm disturbances remain to be determined. Ultimately, transmitter substances released from the autonomic nerve terminals must bind to post-synaptic receptors triggering a cascade of intracellular events that, in turn, provoke changes in the flux of ions across the cell membrane. These changes in ion flux may reduce cardiac electrical stability and increase the probability for catastrophic rhythm disturbances. For over 20 years, I have used a canine model of sudden cardiac death to investigate the role alterations in the autonomic control of the heart and the resulting changes in intracellular and extracellular cations play in the induction of ventricular fibrillation during myocardial ischemia.

E. coli and Salmonella swim using several flagella, each of which consist of a rotary motor, a universal joint known as the hook, and a helical filament which acts a propeller. For propulsion, the filaments wrap into a bundle when the motors turn counter-clockwise. We built a scale model to study the interplay of hydrodynamics and elasticity in this process. Our model shows how the filaments wrap around each other, and allows us to determine which characteristic timescales govern bundling. The filament is normally left-handed in the absence of external stress, but undergoes mechanical phase transitions to other helical states ("polymorphs") in response to external torque. The filament is made of identical flagellin protein subunits which are organized into eleven protofilaments which wind around the filament. We develop an effective theory in which the flagellin subunits and their connections along the protofilaments are modeled with a non-convex potential. A helical spring represents the other connections of the subunits, and introduces a twist-stretch coupling and an element of frustration in our model. We solve for the ground states and the phase diagram for filament shapes.

I'll begin with a brief discussion of the physiology of intracellular calcium signalling, and then present a model of calcium oscillations in secretory epithelial cells. I'll show how we used the model to address one particular controversy in the field, that of how calcium oscillations are affected by membrane calcium transport. I'll briefly describe how we used the model to make a number of predictions, and the experiments we did to test the predictions.

We present a mathematical model for the tumor vascularization theory of tumor growth proposed by Judah Folkman in the early 70's and subsequently established experimentally by him and his coworkers. In the simplest version of this model, an avascular tumor secretes a tumor growth factor, (TGF) which is transported across an extracellular matrix (ECM) to a neighboring vasculature where it stimulates endothelial cells to produce a protease that acts as a catalyst to degrade the bronectin of the capillary wall and the ECM. The endothelial cells then move up the TGF gradient back to the tumor, proliferating and forming a new capillary network.

In this, we include two mechanisms for the action of angiostatin. In the first mechanism, substantiated experimentally, the angiostatin acts as a protease inhibitor. A second mechanism for the production of protease inhibitor from angiostatin by endothelial cells is proposed to be of Michaelis- Menten type. Mathematically, this mechanism includes the former as a sub case.

Our model is different from other attempts to model the process of tumor angiogenesis in that it focuses (1) on the biochemistry of the process at the level of the cell; (2) the movement of the cells is based on the theory of reinforced random walks; (3) standard transport equations for the diffusion of molecular species in porous media.

One consequence of our numerical simulations is that we obtain very good computational agreement with the time of the onset of vascularization and the rate of capillary tip growth observed in rabbit cornea experiments. Furthermore, our numerical experiments agree with the observation that the tip of a growing capillary accelerates as it approaches the tumor.

Immunological memory - the ability to "remember" previously encountered pathogens and respond faster upon re-exposure is a central feature of the immune response of vertebrates. We use models to consider the role of different factors such as exposure to pathogens, cross-reactive and bystander stimulation and homeostasis on the longevity of memory in the CD8 T cell population. We show that the longevity of memory, defined as the decline in the population of memory cell lineages is governed by the following rules:

• The average loss of cells in memory lineages is proportional to the number of cells of new (memory) specities generated following stimulation by new pathogens and inversely proportional to the size of the memory compartment.
• Cross reactive stimulation (i) reduces the average rate of loss of memory by reducing the magnitude of expansion of new naive lineages; (ii) the variation in the rate of decline in the populations of cells to different lineages is greatest at intermediate levels of cross-reactivity.
• The loss of memory is independent of bystander stimulation and the precise mechanism for the maintenance of homeostasis.

Natural selection acts on viruses at a variety of levels: within cells, within hosts, and between hosts. We examine how viruses can optimise their behavior within a host under pressure from the immune system, and how this optimal within-host behavior may not be ideal from the point of view of transmission between hosts. This is a preliminary presentation of ongoing work with Michael Gilchrist (University of Tennessee) and Alan Perelson (LANL).

Models that incorporate host dynamics to study the evolving nature of pathogens such as influenza face major computational challenges. We develop a mathematical model that allows for the study of several strain structures and show how these may influence disease dynamics. In particular, partial cross-immunity to next-to-kin strains leaves hosts less likely to be infected by antigenically similar strains while providing no immunity against all other strains. The status of the host is determined by immune-competence levels corresponding to all the strains that each host has immunity to. Immunity of the host population is captured by an index-set notation where the index specifies the immune-competence level against each particular strain. In contrast to previous modeling approaches, the population here is structured into non-intersecting subclasses. That is, since multiple infection with influenza strains is uncommon, we do not imbed superinfection with the same or different strains as part of our model. We provide threshold quantities that allows us to determine conditions for the invasion of a single strain or multiple co-existence of strains. Furthermore we provide stability conditions for the disease-free and endemic state equilibrium.

Adrenal Zona Fasciculata (AZF) cells release the hormone Cortisol in conditions of physical or psychological stress. Cortisol release is governed by the action of ion channels expressed in the AZF cells. Using the method of patch clamp, the ion channels expressed in bovine AZF cells were analyzed. Modeling of these ion channels will involve fitting mathematical equations that describe the empirical data. Creating a mathematical model that mimics the behavior of these ion channels will provide a unique understanding of the process of cortisol release and will help in predicting the possibility of membrane excitability of the AZF cells.

We consider the existence and the stability of standing pulse solutions of an integro-differential equation used to describe the activity of neuronal networks. The network consists of a single-layer of neurons with non-saturating piecewise linear gain function, synaptically coupled by lateral inhibition. The existence condition for pulses can be reduced to the solution of an algebraic system and using this condition we map out the shape of the pulses for different weight kernels and gains. We also find conditions for the existence of pulse with a 'dimple' on top and for a double-pulse. For a fixed gain and connectivity, we find two single-pulse solutions-a ``large'' one and a ``small'' one. We derive conditions to show that the large one is stable and the small one is unstable. Using the same conditions, we also show that the dimple-pulse is stable. More importantly, the large single-pulse and the dimple pulse are bistable with the all-off state. This bistable localized activity may have strong implications for the mechanism underlying of working memory.

When an elastic filament spins in a viscous incompressible fluid at varying angular frequency it may undergo a whirling instability and a bifurcation occurs, as studied asymptotically by Wolgemuth, Powers, Goldstein. We use the Immersed Boundary (IB) method to study the interaction between the elastic filament and the surrounding viscous incompressible fluid as governed by the Navier-Stokes equations, and to determine the nature of the bifurcation, which turns out to be subcritical. This allows the study of the whirling motion when the shape of the filament is very different from the unperturbed straight state. The numerical method shows two dynamical motions of the rotating elastic filament depending on the angular frequency and also on the initial bend. These are in which the filament rotates in place around a straight axis, and in which the axis of the filament becomes drastically bent and precesses about the symmetry axis of the system.

Ran is a small GTPase with functions in nuclear transport, spindle formation, and nuclear envelope re-assembly. It exists in two forms, Ran-GTP and Ran-GDP, which are interconverted by the activity of two proteins. RanGAP turns RanGTP into RanGDP while RCC1 turns RanGDP into RanGTP. The spatial separation of RanGAP and RCC1 in the cell leads to the establishment of a gradient between Ran-GTP and Ran-GDP, which is important for the function of Ran. During interphase, RanGAP is cytoplasmic while RCC1 is located in the nucleus. This establishes a gradient of RanGTP to RanGDP across the nuclear envelope, which is involved in the directionality of transport between nucleus and cytoplasm. During animal mitosis, RCC1 remains bound to the chromosomes while RanGAP migrates to the spindle apparatus. The resulting mitotic gradient of Ran has been shown by imaging methods in live cells. We have found that like animal RanGAP, plant RanGAP is associated with the nuclear envelope during interphase. However, during mitosis, it appears at the newly forming cell plate, a structure unique to plants. A specific N-terminal domain of plant RanGAP is necessary and sufficient for targeting the protein to the plant nuclear envelope in interphase and to the cell plate in mitosis. We conclude that the spatial re-organization of the Ran gradient during mitosis differs in plants and animals. We are interested in measuring and possibly modeling the gradient in plant cells.

Complex biological systems containing tissue immersed in a viscous incompressible fluid are ubiquitous. Understanding the dynamics of such systems is crucial in a vast array of scientific and engineering problems, such as the function of the heart, the mechanism of hearing, the dynamics of biological membranes, cell morphology and insect flight, to name a few. In such systems the tissue may be elastic or active, and it may posess complicated internal structure. Its interaction with the fluid is often coupled with other physical processes, such as biochemical reactions, electrical currents and heat diffusion. In this talk I will survey my work on large-scale computer modeling of such systems using the immersed boundary method. I will discuss the application of this work to modeling the fluid dynamics of the heart and (in more detail) the construction of a computational model of the cochlea (the inner ear).

Ca2+ ions play a very important role in cellular function, ranging from contraction, differentiation, secretion to transcriptional regulation and programmed cell death. My lab focuses on studying the structure and functional regulation of Ca2+ permeable channels, which are essential for increasing intracellular Ca2+ concentrations. Molecular cloning and genome sequencing have revealed the existence of a novel family of Ca2+ permeable cation channels formed by homologues of transient receptor potential (TRP) protein initially identified from eyes of fruit flies. The TRP superfamily currently consists of several subfamilies including TRPC, TRPV and TRPM, each of which contains multiple family members. These channels are involved in many important physiological functions ranging from taste transduction, vision, muscle contraction, synaptic transmission fertilization to temperature, pressure, and pain sensations. The TRP channels have been the main focus of my research. Here, I will present two topics concerning with the functions of TRPV channels. First, I will describe a naturally occurring dominant-negative isoform of TRPV1, also know as vanilloid receptor type 1. Then I will discuss a number of potential activation signals for TRPV3. Both channels are considered to be thermal sensitive channels involved in inflammatory and nociceptive pain pathways of the somatosensory system. Integration of signals coming from various thermal sensitive channels could be an area for mathematical modeling. In the last third of my talk, I will present our study on the regulation of Cav2.1 voltage-gated channel by L7/Pcp2, a cerebellar specific protein known to regulate Gi/o family of the heterotrimeric G proteins. Our data suggest that L7/Pcp2 regulates the activity of the Ca2+ channel in a dose dependent manner. This type of regulation is likely to occur in the cerebellar Purkinje cells in consequence to the activity-dependent local synthesis L7 proteins and thus implicated in learning and memory. Mathematical modeling is commonly used to predict cerebellar output associated with changes in the activity of different ion channels in Purkinje cells.

Complex and interconnected signaling networks allow cells to integrate information that regulates growth, differentiation, cell division or programmed cell death. Plants can sense levels of nutrients such as carbon and nitrogen and accordingly adjust gene expression, which in turn affects metabolic and cellular activities. Numerous physiological studies have demonstrated that the availability and ratio of carbon and nitrogen are key determinants for plant growth and development. While this nutrient response is critical, our understanding of the molecular mechanisms underlying sugar or nitrogen signal transduction in plants is obscure. To begin unraveling complex sugar signaling networks in plants, DNA microarray analysis was used to determine the effects of glucose and nitrate on gene expression on a global scale in model plant Arabidopsis. Under the conditions used, glucose is a much more potent signal in regulating transcription than inorganic nitrogen, and that other than genes associated with nitrate assimilation, glucose had a greater effect in regulating nitrogen metabolic genes than nitrogen itself. Glucose also regulated a broader range of genes, including genes associated with carbohydrate metabolism, transcriptional regulation, and metabolite transport. Cluster analysis revealed significant interaction between glucose and nitrogen in regulating gene expression, because a combination of glucose and nitrogen could modulate the expression of many genes responsive either to glucose or nitrogen individually. A large number of genes associated with stress response were induced by glucose-we postulate that glucose signaling regulates these genes either via crosstalk with stress hormone ABA or ethylene signaling or via independent signal transduction mechanisms. Using cycloheximide, an inhibitor of protein synthesis, we have found that glucose repression appears to be a primary response while glucose induction is largely a secondary response requiring de novo protein synthesis. We conclude that glucose and inorganic nitrogen have dual roles in plants, acting as both metabolites and effective signaling molecules. Our long-term goal is to reveal the transcriptional cascades underlying sugar regulated gene expression in plants.

At the molecular core of the circadian clock lies a transcription/translation autoregulatory feedback loop. Cyclic expression of at least some of the components of the circadian central oscillator is essential to maintain circadian rhythmicity. High amplitude cycling of mRNA and protein abundance, protein phosphorylation and nuclear/cytoplasmic shuttling have all been implicated in the maintenance of circadian period. We have used a newly characterized Arabidopsis suspension cell culture to establish that the rhythmic changes in the levels of the novel clock-associated F-box protein, ZEITLUPE, are post-transcriptionally controlled through different circadian phase-specific degradation rates. This proteolysis is proteasome dependent, implicating ZTL itself as substrate for ubiquitination. This demonstration of circadian phase-regulated degradation of an F-box protein, which itself controls circadian period, suggests a novel regulatory feedback mechanism among known circadian systems. Evidence for an additional level of light- and dark-dependent control of ZTL function will also be presented.

My lab has a long-standing interest in understanding how signaling pathways elicit selective changes in gene transcription in mammalian cells. We use a combination of genetic mouse models, molecular genetics, biochemistry and cell biology to attack these problems. Most recently, we have become interested in understanding interactions between signaling pathways locating in the different cell types involved in complex biological processes of cancer cell progression and normal cellular differentiation. For example, in vertebrate animals, bone is formed through the interactions between two cell types, cells that make bone (the osteoblasts) and cells that remodel bone (the osteoclast). There is exquisite communication between these cell types throughout life, and upsetting this balance results in disease states, for example, osteoporosis in humans. Understanding and targeting such intercellular networks of communication holds great promise for new advances in the diagnosis and treatment of many human diseases. Recent advances in genomics and functional genomics makes it possible to begin studying such complex networks of interaction that control the overall behavior of different cell types. It is clear that computational and statistical tools will be necessary to model these complex interactions.

• Nicolelis,M.A.L. (2003). Brain-machine interfaces to restore motor function and probe neural circuits. Nature Reviews Neuroscience, 4, 417-422.
• Chapin, J.K., Moxon, K.A., Markowitz, R.S., & Nicolelis, M.A.L. (1999). Real-time control of a robot arm using simultaneously recorded neurons in the motor cortex. Nature Neuroscience, 2, 664-670.

• Brainard, M.S. & Doupe, A.J. (2000). Auditory feedback in learning and maintenance of vocal behavior. Nature Reviews Neuroscience, 1, 31-40.
• Brainard, M.S. & Doupe, A.J. (2000). Interruption of a basal ganglia-forebrain circuit prevents plasticity of learned vocalizations. Nature, 404, 762-766.

• Schultz W, Dayan P, Montague PR. A neural substrate of prediction and reward. Science. 1997 Mar 14;275(5306):1593-9. Review.
• Fiorillo CD, Tobler PN, Schultz W. Discrete coding of reward probability and uncertainty by dopamine neurons. Science. 2003 Mar 21;299(5614):1898-902.

• The beginning (FIRST 5.5 PAGES - up to 'summation') of Pearce, JM. (2002). Evaluation and development of a connectionist theory of configural learning. Animal learning and behavior, 30(2), 73-95.
• Review: Menzel, R. (2001). Searching for the memory trace in a mini-brain, the honeybee. Learning and memory, 8, 53-62.
• Menzel, R. & Giurfa, M. (2001). Cogntitive architecture of a mini-brain: the honeybee. Trends in Cognitive Sciences, 5(2), 62-71.
• Fanselow, MS. (1998). Pavlovian conditioning, negative feedback, and blocking: mechanisms that regulate association formation. Neuron, 20, 625-627.

My research involves using mathematical methods such as ordinary and partial differential equations to model biological phenomena, including the development and analysis of mean field models arising from spatially explicit or agent-based models. I will describe examples of biological problems for which these approaches are useful.

Our laboratories are using several techniques including immunohistochemistry, physiology, electron microscopy,tissue culture and HPLC to better understand the role of the cerebellum in controling and coordinating both motor activity and higher cognitive functions. Currently, we are carrying out 2 research projects. In one, we are defining the role of a peptide called corticotropin releasing factor (CRF) in adult and developing animals. In the adult CRF acts to modulate neuronal activity, whereas in the embryonic and early postnatal brain it appears to play a developmental role in establishing circuits and insuring survival of neurons. We will continue our analysis of CRF and its interactions with its 2 known receptors defined as the type 1 and type 2 CRF receptor. In a second series of studies, we are determining if damage to the cerebellum is associated with the loss of cognitive functions, in particular those associated with autism. Our initial studies indicate that use of a drug that is associated with a high incidence of autism in the human population induces changes in the morphological and physiological characteristics of a specific population of neurons in the cerebellum.

We describe three different types of challenges for dynamical system modeling in biology.

In the first case we look at large networks of enzymatic reactions in the cell. A mathematical model is easy to write, but there is not enough experimental data to determine the parameters in the model. We show that we are still able to derive qualitative information about the system.

In the second case we look at fast and slow axonal transport. Experimental data is available, but there is no confirmed model. We design a mathematical model, and attempt to validate it based on the experimental data.

In the third case we are interested in the distribution of ionic channels along dendrites. Both experimental data and a model are available, but we run into computational difficulties when we try to use the model to compute the distribution of channels. We design a new computational method, applicable to that specific model and input data.

In this short talk, a methodology known as hierarchical statistical modeling is presented. I show how it could be applied in a spatial setting that links ambient air pollution to human health outcomes.

My research interests are in the field of Bioinformatics & Computational Biology. My group is currently working on (i) Development of computational tools to annotate transcriptional regulatory regions in mammalian genomes (ii) Development of pattern recognition methods and statistical models to identity transcription factor binding sites, model transcriptional modules and networks in hematopoiesis cell lineages (iii) Development of robust databases and visualization tools for genomic data and annotations. We provide the annotations of promoter regions and first exons in the human genome to the UCSC genome browser, in collaboration with Zhang lab in Cold Spring Harbor Laboratory. Three major projects we are currently working on are:

MPromDb: Transcription in mammalian cells is a highly complex process that involves multiple layers of general and gene-specific transcription factors (TFs). MPromDb (Mammalian Promoter Database) is an information resource of mammalian gene regulatory regions. The current version contains 23,931 experimentally supported and 25,940 computationally annotated promoters, and mapping of 5,831 experimentally known TF binding sites. We are currently working on annotating other functional elements by combining comparative genomics approaches with pattern recognition methods.

HemoPDb: Hematopoiesis is the process by which blood cells of different lineages are formed throughout normal life, and abnormalities in this developmental program lead to blood cell diseases including leukemia. From analysis of mice deficient in transcription factor (TF) genes and from the characterizations of chromosome breakpoints in human leukemias, it has become evident that altered transcriptional regulation is a major contributor to the neoplastic characteristics of most tumor cells. We are developing computational tools to annotate promoters of genes that are expressed in hematopoietic cell-lineages, statistical models to model combinatorial association of TFs and transcriptional regulatory networks inovolved in hematopoietic cell-lineages.

AGRIS: AGRIS stands for Arabidopsis gene regulatory information server, being developed in collaboration with Grotewold Laboratory, Dept. of Plant Biology and Plant Biotechnology Center. AGRIS is an information resource of Arabidopsis promoter sequences, transcription factors and their target genes. AGRIS currently contains two databases, AtTFDB (Arabidopsis thaliana transcription factor database) and AtcisDB (Arabidopsis thaliana cis-regulatory database). The long-term goal of AGRIS is to develop a genome-wide map of cis-regulatory elements in Arabidopsis, by combining bioinformatics approaches with highthroughput experimental technologies.

I am interested in developing statistical and mathematical approaches useful in predicting the behavior of cellular systems. In my work in predictive microbiology I have applied techniques such as dynamical systems modeling, robust non-parametric regression and chemical systems modeling. Current work focuses on developing new approaches for studying complex diseases such as coronary artery disease and cancer.

Gene expressions may differ in different cell types (e.g., normal and diseased tissues) even for genes not involved in the disease process such as housekeeping genes. We recommend (negative) control genes be included in microarray experiments, and their observed differential expressions be used to normalize the observed differentials of the target genes. This project of selecting suitable housekeeping genes as control genes will make use of my experience developing statistical methods that are in use in clinical "equivalence" trials.

Alzheimer's disease (AD) is the major dementing illness of the elderly, with prevalence expected to reach over 10 million cases in the U.S. in the coming decades. The disease is characterized pathologically by the appearance of hallmark lesions in select regions of the brain. Lesion appearance correlates temporally with neurodegeneration, and is the major surrogate marker for disease diagnosis.

Because of these considerations, we focus on intracellular lesion formation as a target for diagnostic and therapeutic discovery. Above all, we seek to clarify the protein misfolding events that accompany lesion formation. We have begun by developing methods for modeling protein misfolding biochemically using purified components. We have also selected small, drug like inhibitors of the model reaction, which may have therapeutic potential. We seek to clarify the mechanism of these reactions in detail, and to determine the feasibility of our approach for treatment of AD.

Three aspects of our work would benefit from mathematical modeling. First, the model reaction, which is a logistic process, must be cast in the form of elementary rate constants. This will allow us to test hypotheses concerning events that initiate or accelerate the reaction. Second, the interaction of drug-like inhibitors with the system must be modeled so that hypotheses concerning mechanism can be tested. This is essential for assessing the feasibility of our therapeutic strategy. Finally, we seek to model lesion formation at the whole brain level, so that utility of various inhibitory mechanisms for treatment of authentic disease can be predicted.

This is a "chalk" talk in which I will briefly describe Folkman's idea for tumor growth and show how this idea may be modeled, at least in part. The model derives from the biochemical observation that growth factors expressed by an avascular tumor in response to hypoxia can stimulate endothelia in neighboring capillaries to grow branches that vascularize the tumor and relieve the hypoxia, thus stimulating rapid vascular tumor growth as well as encouraging such unpleasant side effects as metastasis.

My research interests are in statistical genetics, genetic epidemiology, and bioinformatics. I focus on the development and applications of statistical and computational methods for linkage analysis, association mapping, and analysis of microarray gene expression data. The sort of data that render conventional methods infeasible, such as data from large families with complex relationships, is of a long-standing interest of mine. Other important issues in mapping, such as crossover interference, genetic heterogeneity, multiple testing, and haplotype analysis, are also of particular interest. More recently, I have also delved into issues in functional genomics and bioinformatics, in particular in cancer type and subtype classification based on gene expression data. I also enjoy working on applied projects, including collaborative research with medical doctors on genetic epidemiological studies.

My lab has a long-standing interest in understanding how signaling pathways elicit selective changes in gene transcription in mammalian cells. We use a combination of genetic mouse models, molecular genetics, biochemistry and cell biology to attack these problems. Most recently, we have become interested in understanding interactions between signaling pathways locating in the different cell types involved in complex biological processes of cancer cell progression and normal cellular differentiation. For example, a breast tumor is composed not only of the epithelial-cell derived tumor cell, but also stromal cells, endothelial cells, and immune cells including macrophages, B-cells and T-cells. It is the interaction of these cell types through complex signaling networks that are likely to be important for tumor cell progression and metastasis, and not just the action of individual signaling pathways within the epithelial tumor cell. Understanding and targeting such intercellular networks of communication holds great promise for new advances in the diagnosis and treatment of cancer. Recent advances in genomics and functional genomics makes it possible to begin studying such complex networks of interaction that control the overall behavior of different cell types. It is clear that computational and statistical tools will be necessary to model these complex interactions.

My research involves the use of computational techniques, such as the immersed boundary method, to gain insight into the mechanism of growth and development of various biological tissues. Several computer simulations will be presented, including development of abnormal invaginations in the placental trophoblast bilayer; formation of cardinal lobes in the rat cerebellum; growth of cancer cells in the breast ductal system.

The goal of pharmacogenomics is to design novel drugs and improve existing therapies by exploiting genetic differences between individual patients. The term 'genomics' indicates that this field of science encompasses integration of all genes present in the human genome. This leads to numerous complex problems that require advanced mathematical modeling and statistics to resolve questions relevant to therapy. These include the interpretation of mRNA microarrays, network analysis of interacting genes and chemicals (drugs), stratification of patient populations with the use of haplotypes (phased polymorphisms in the same gene) in multiple candidate genes, genome-wide association studies, utilization of large databases, and the discovery of novel drug targets through modeling of cellular systems. The new OSU Program in Pharmacogenomics (http://pharmacogenomics.osu.edu/section1.html) encompasses multiple investigators with highly integrated research projects, both in basic sciences and clinical applications.

Most of my past and current research projects are concerned with understanding the formation of patterns and the dynamics of nonlinear waves in spatially extended systems modelled typically by partial differential equations on unbounded domains. Nonlinear waves correspond to interfaces, or defects, that are formed between co-existing patterns. Examples are the transmission of signals in optical fibers, the formation of hexagonal and stripe patterns in fluid convection, and the generation of spiral waves in catalytic chemical reactions. Motivated by experiments and numerical simulations, I aim to understand when and how patterns and defects are formed, how they behave under small perturbations, what other patterns or waves with a more complicated spatio-temporal behaviour can bifurcate from them, and how they interact with each other or with domain boundaries. To answer these questions, I use a mixture of analytical and geometric dynamical-systems techniques, and I have also developed numerical algorithms for the computation of waves and their bifurcations.

Advances in protein separation techniques, mass spectroscopy, and bioinformatics has enabled the examination of the proteome, the protein complement of the genome. We utilize proteomics approaches including MALDI-TOF mass spectrometry to examine changes in protein expression during differentiation of mammalian neuronal cells in culture, to define protein-protein interactions following inhibition of nucleologenesis, and to identify phosphoproteins involved in cell cycle regulation. New SELDI-TOF mass spectrometry equipment available to the lab will be applied to these studies as well as to clinical based studies designed to discover and validate disease biomarkers from patient samples. Enormous amounts of data can be generated from these studies, and appropriate methods of data analysis and interpretation are required. This provides an opportunity for coordinated efforts between life scientists and computer scientists to design innovative methods for the acquisition and analysis of proteomic information.

Chemical databases often encode the structure of molecules in long binary string s called fingerprints. A general goal is to use these fingerprints to predict s ome specific biological activity of a molecule, such as its ability to kill cert ain cancer cells. It is well known that different classes of chemicals interact with cells via different mechanisms, and that small structural differences with in a class can produces large changes in biological activity. Under these circu mstances, simple implementations of support vector machines do not perform well. However, recent work (Wilton, et al. 2002) suggests that some specialized kernel smoothers may work well in distinguishing biologically active molecules.

Our approach is first to form localized regions using the Jacard-Tanimoto metric, which is sensitive to the relative number of mismatched features, and then use "weighted triples" kernels within local neighb orhood. These utilize low order interactions of binary features in creating the underlying kernel function. The technique is illustrated by identifying key feature-combinations of a subclass of colchicines with high activity against H23 lung cancer cells.

I will outline research done in my lab on computational modeling of auditory scene analysis - the perceptual process of separating a target sound source from a sound mixture that may contain many acoustic intrusions. In particular, speech segregation will be highlighted, and neural machanisms for computational auditory scene analysis will be discussed.

In my presentation, I will summarize my current work in progress with respect to my recordings in the antennal lobe of insects. One problem that I face using the type of electrophysiological recording technique that I am using in Brian Smith's lab is being able to identify which spiking events belong to which neurons. I have tried a few different spike sorting techniques, and have encountered difficulties arising from the ability to identify spiking events before they are classified. I will present what I am planning to do to solve my current problems with spike sorting.

Our research involves the use of computational approaches, based on both bioinformatics and molecular biology, to study the structure and function of human genome and proteome. We combine biology and computational science with the goal of understanding the sequence, structural, and molecular basis of a wide range of biological phenomena. This work includes fundamental theoretical research, the design of effective algorithms, development of software tools, and applications to problems of biological significance. We are currently interested in the use of comparative genomics to identify disease-related genes, protein structure prediction, the study of protein-protein and protein-ligand interactions; the development of computational methods to identify protein function based on protein structure; and the use of these methods to characterize families of proteins and their specific biological functions.

Protein Structure Prediction: Much of our recent effort has been devoted to the development of new tools for homology modeling as well as fold recognition. Reliable homology models are essential for many of our studies on the structural origins of specificity in protein-protein interactions. Good homology models require good sequence alignments, and to this end we have developed a new position-specific scoring matrix that take three-dimensional context into account. This has allowed accurate fold recognition for distantly related proteins. Here we applied principle component analysis, and biophysical estimations for various molecular interactions. In addition, we developed metric-based indexing scheme to classify all known substructural elements necessary to reduce the redundancies in the selection of known structural templates. We also applied graph theory to both represent and model 3D protein structures again with the aim to detect similar substructures. Our goal in the coming year is the design of a fully automated structure prediction system for the entire genome.

Protein-Protein Interactions: The analysis of protein-protein interactions involves the recognition of features on protein surfaces that are involved in binding to other proteins. We are particularly interested in delineating features that dictate specificity versus affinity in binding interactions and in deriving general rules that may aid in the identification of interacting surfaces when there is no available structure of a complex. In this context, we used Hough transformation to index both geometric and biological critical points associated with the formation of protein complexes. We have assessed the contribution of individual amino acids to binding based on both structural and sequence profiling analysis. Specifically, residues important in protein-protein interactions are conserved and exhibit similar evolutionary constraints, which are weighted into the transformation. When this method is combined with our structure-based alignment tools, we are able to cluster protein families into functional subgroups and to detect novel sequence/structure/function relationships. We hope that our combined bioinformatics/molecular approach will yield new general insights, new methods, and new approaches toward the understanding of the structural basis of biological specificity.

Genome Analysis: The recent release of the complete human genome provides an unprecedented opportunity to integrate human genes and their functions in a complete positional context. However, at least three significant technical hurdles remain: first, to assemble a complete and nonredundant human transcript index; second, to accurately place the individual transcript indices on the human genome; and third, to functionally annotate all human genes. We assembled existing transcripts into gene-oriented transcript contigs. Each resulting assembly is aligned to the human genome as evidence of experimentally supported gene. This provides a physical map with annotations for a majority of the human transcripts. Such information can be immediately applied to the discovery of new genes and the identification of candidate genes for positional cloning.

Molecular cloning and genome sequencing have revealed the existence of a novel family of cation channels formed by homologues of transient receptor potential (TRP) protein initially identified from eyes of fruit flies. The TRP superfamily currently consists of several subfamilies including TRPC, TRPV and TRPM, each of which contains multiple family members. These channels are involved in many important physiological functions ranging from taste transduction, vision, muscle contraction, synaptic transmission fertilization to temperature, pressure, and pain sensations. Our work has focused on the structure and function of TRPC proteins. Using heterologous expression, intracellular Ca2+ imaging, patch-clamp recording, and protein binding studies, we have demonstrated that TRPC proteins form agonist-stimulated non-selective Ca2+ cation channels. They are activated by binding to inositol-trisphosphate receptors and inactivated by binding to calmodulin. More recently, we have identified multiple calmodulin binding sites from TRPC, as well as TRPV and TRPM proteins. Related Ca2+ binding proteins such as CaBP1 also bind to TRPs and prevent their activation. Thus multiple Ca2+ sensing proteins are associated with TRP channels at various sites, fine-tuning the activities of these channels.