Seminars 2003-2004

September 23, 2003 3:30 - 4:30PM
Abstract

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

October 07, 2003 3:00 - 4:30PM
Abstract

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.

October 09, 2003 11:30 - 12:30PM
Abstract

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.

October 14, 2003 3:00 - 4:00PM
Abstract

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.

October 16, 2003 11:30 - 12:30PM
Abstract

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.

October 28, 2003 3:30 - 4:30PM
Abstract

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.

October 30, 2003 11:30 - 12:30PM
Abstract

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.

December 31, 1969 7:00 - 7:00PM
Abstract

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.

December 31, 1969 7:00 - 7:00PM
Abstract

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.

TBA
November 04, 2003 2:30 - 3:30PM
Abstract

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.

November 25, 2003 3:30 - 4:30PM
Abstract

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.

December 02, 2003 3:30 - 4:30PM
Abstract

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.

February 12, 2004 1:30 - 2:30PM
Abstract

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).

February 19, 2004 11:30 - 12:30PM
Abstract

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.

December 31, 1969 7:00 - 7:00PM
Abstract

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.

February 23, 2004 2:30 - 3:30PM
Abstract

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.

February 26, 2004 11:30 - 12:30PM
Abstract

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.

March 29, 2004 11:30 - 12:30PM
Abstract

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.

April 15, 2004 11:30 - 12:30PM
Abstract

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.

April 19, 2004 3:30 - 4:30PM
Abstract

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.

December 31, 1969 7:00 - 7:00PM
Abstract

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.

December 31, 1969 7:00 - 7:00PM
Abstract

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.

December 31, 1969 7:00 - 7:00PM
Abstract

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.

April 23, 2004 2:00 - 5:00PM
Abstract

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.

April 29, 2004 11:30 - 12:30PM
Abstract

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.

December 31, 1969 7:00 - 7:00PM
Abstract

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.

May 03, 2004 3:30 - 4:30PM
Abstract

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.

May 25, 2004 3:30 - 4:30PM
Abstract

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.

May 27, 2004 11:30 - 12:30PM
Abstract

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.

December 31, 1969 7:00 - 7:00PM
Abstract

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.

June 08, 2004 3:30 - 4:30PM
Abstract

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.

June 10, 2004 11:00 - 12:00PM
Abstract

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).

December 31, 1969 7:00 - 7:00PM
Abstract

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).

June 16, 2004 3:30 - 4:30PM
Abstract

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.

June 18, 2004 11:00 - 12:00PM
Abstract

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.

December 31, 1969 7:00 - 7:00PM
Abstract

mmunological 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.