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Abstracts for 2009 Mathematical Biology Seminars
Speaker: Eldon Emberly
Title: Optimization of Mutual Information in Genetic Networks
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Abstract:
Cellular decisions rely upon a cell making some measurement of its surroundings and then regulating its behaviour based on this measurement. For many cellular processes this decision is regulated by the transcriptional output of a gene which is regulated by a single input which may exist in several possible states. Given the noise inherent in the input signal and the chemical processes coupling the input to the output, how well can the input states be measured by the genetic network and is the genetic network optimized to maximize the likelihood of determining the correct input state? Recently, this problem has been analyzed in the context of mutual information. I will discuss the application of mutual information to the problem of morphogen readout in developing organisms, and will compare the predicted optimal morphogen gradient for the early drosophila factor Bcd to its experimental profile. Lastly, I will show how optimizing mutual information for an organism that needs to infer a two state environment which varies, leads to an optimal transcriptional response with biologically realistic kinetic parameters.
Speaker: Prof. Pik-Yin Lai
Title: Synchronization of cardiac cells growing in culture.
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Abstract:
Synchronization of heterogeneous systems consisted of oscillatory and passive elements are studied in cardiac myocytes (CM)/fibroblasts (FB) co-cultures. It is found that beating clusters of CM surrounded by FB will be formed. The beatings of the CM clusters are not correlated at early times but get synchronized as the cultures mature. This synchronization can be understood by a Kuramoto model with a time increasing coupling strength. Our findings show that the growth of the coupling strength between clusters is linear while the overall wave dynamics of the system is controlled by the passive FB in the system which presumably is growing exponentially. The variations of the frequencies towards synchronization are also modeled b y the "frequency enhancement" effect for coupled excitable/oscillatory elements.
Speaker: David Drubin
Title: A mechanochemical model for endocytic vesicle formation
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Abstract:
Formation of endocytic vesicles is a complex, dynamic process that couples sequential protein recruitment and lipid modifications with dramatic shape transformations of the plasma membrane. How the proper timing and coordination of these events is achieved, and the vesicle scission mechanism, are not understood. We address these questions by constructing an integrated mathematical model based on four key ideas: (1) membrane curvature and PI(4,5)P2 hydrolysis are mechanochemically coupled; (2) curvature-sensing and curvature-deforming activities constitute a positive feedback loop for BAR domain protein recruitment; (3) the mechanochemical coupling of events ensures the proper and robust temporal and spatial sequence of endocytic events; and (4) vesicle scission is the result of an interfacial force that develops at a lipid phase boundary. The model quantitatively recapitulates the endocytic events in budding yeast in a coherent manner, and explains key aspects of endocytosis in mammalian cells.
Speaker: Anmar Khadra
Title: Investigating the role of IGRP-specific low avidity T cells in the protection against T1D
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Abstract:
Recent experimental observations have revealed that during the onset of autoimmune Type 1 Diabetes (T1D), different clones of T cells with various T cell avidities and protein specificities are naturally generated in diabetic animal models. One particular protein, IGRP, is considered to be the most dominant autoantigen, responsible for activating low and high avidity IGRP-specific T cells via APCs. Although high avidity T cells destroy ~90% of beta cell repertoire, leading to the abolishment of insulin secretion crucial for glucose metabolism, low avidity T cells appear to play a protective role. Several hypotheses concerning the kinetics of these low avidity T cells and the effects of certain drug treatments on this populations have been suggested. In this talk, we shall present series of mathematical models that investigate these hypotheses and the outcome of certain drug treatments. We shall examine the experimental data available so far and explain certain features exhibited by the various clones of T cells.
Speaker: Nessy Tania
Title: Mathematical models of calcium regulation in cardiac cells
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Abstract:
Calcium is a ubiquitous signaling molecule involved in the regulation of a wide range of processes. In cardiac cells, calcium plays a key role in mediating the electrical-excitation and contraction processes. Three mathematical models of calcium regulation are derived and analyzed. Using a simplified model, we first show that release localization, diffusion, and single-channel activity modulate the onset of calcium oscillations. These factors are of particular importance in cardiac cells where calcium release is spatially inhomogeneous and inherently stochastic. However, models that take these effects into account are computationally expensive to simulate. Using a variety of asymptotic approximations, we derive a simplified yet reliable model of stochastic calcium flux through a release unit. Finally, we use a whole-cell model to explore the role of calcium oscillations in the generation of periodic action potentials based on recent experimental studies on the sinoatrial node and embryonic cardiac cells.
Speaker: Kurt Haas
Title: Imaging single neuron growth and circuit activity in the awake developing brain: How does activity sculpt structure and function?
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Abstract:
Using techniques to label individual neurons within intact brains and in vivo two-photon rapid time-lapse microscopy we image dynamic growth of neuronal dendritic arbors in awake Xenopus tadpoles. Our result suggest a strong role of neuronal transmission in directing dendrite growth by influencing synapse formation, which in turn, stabilize new dynamic dendritic branches. By loading the entire brain with calcium sensitive dyes, we find that brain neuron responses to sensory stimuli can be increased or decreased by training with sensory input. Combining single neuron morphometric and network activity analysis we hope to understand how neuronal transmission and developmental experience influences brain circuit form and function.
Speaker: Scott Grandison
Title: It's tough at the tip: Mechanical models of polar growth.
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Abstract:
From cell morphogenesis to protein docking, shape and shape dynamics have a vital role to play in our understanding of biological systems. In this talk we will discuss a novel method for extracting important shape information based on image processing, minimum energy surfaces and the calculus of variations which allows us to infer some of the mechanical properties of a tip growing Arabidopsis root hair from time-lapse image data. We have developed a computer simulation, based on a network of interconnected springs which enable our formulation to be validated against further experimental data.
Speaker: Paul Tian
Title: Mathematical Study of Brain Tumor Therapies.
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Abstract:
Glioma is the most serious malignant brain tumor. In order to improve the efficacy of therapies, it is important to understand its progression with therapies and its genesis. In this talk, I will first present our effort in understanding of glioma progression with different therapies in terms of mathematical models. The first model is about virotherapy of glioma, which is a free boundary problem with five nonlinear partial differential equations. Virotherapy is a promising treatment for malignant solid tumors, and it is now in animal experimental stage. In order to treat human glioma by virotherapy, it is critical to understand all factors involved in the therapy. Our model finds an important factor burst size of virus, and the effect of immunosuppression drug cyclophosphamide in animal experiments. The model prediction has been verified by experimental results. The second model is about radiotherapy plus chemotherapy after surgical resection, which is a two-component free boundary problem. After surgery, the tumor progression depends on the degree of resection and radiation, and a particular drug. We use human data to estimate parameter values, and the model can predict the mean survival times of patients who undergo different protocols of treatments.
Speaker: Pik-Yin Lai
Title: Synchronized Bursting and Growth of cultured neuronal network: experiments & model.
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Abstract:
Synchronized bursting is observed in cortical neuronal cultures in vitro when the neuronal network is incubated for a sufficiently period of time. The synchronized bursting frequency of the network is found to be much slower than the characteristic time scale of a neuron and increases with the network connectivity. We present a detailed analysis and theoretical growth models to account for the experimental data on the growth of cortical neuronal networks. The bursting frequency (f) during SF of the networks is found to be an increasing function of k. In particular, the special form of P(k)~ exp(-k/ko) gives the experimental observed result that f is characterized by a critical age tc and a critical frequency (fc) as: f = fc + fo log(t/tc). The growth of the network is consistent with the model of an early enhanced growth of connection, but followed by a retarded growth once the synchronized cluster is formed. Our electrophysiological measurements using double-patch techniques reveal that even though the bursting frequencies are synchronized, the intra-burst spikes are not. We present a mean field model of the neural network that combines a Fitz-Hugh Nagumo (FHN) model with an additional dynamic variable. This new variable is slower than those in the FHN model. It enables the neuron firing to be inhibited and generates inter-spike intervals (ISI) with long time scales resulting in bursting.
Speaker: Geoff Wasteneys
Title: Dynamic Properties of Microtubules in Plant Cells, with Implications for Spatial Organization, Growth and Development.
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Abstract:
Microtubules are dynamic polymers found in all eukaryotic organisms that build the cellular machines that separate chromosomes, polarize the cytoplasm, direct expansion and divide cells. Interestingly, plant cells lack the central microtubule-organizing centres common in animal cells but still manage to organize microtubules into complex arrays.

The research in my laboratory explores how the dynamic properties of microtubules, which we can now quantify in live cells using fluorescent reporter proteins, help to determine the spatial organization of microtubule arrays, and how these arrays in turn control the growth, morphology and performance of plants. I will outline how genetic approaches to identify key accessory proteins that modulate microtubule dynamics are generating experimental tools for understanding the mechanisms that drive organization of the microtubule arrays. Comparing the dynamic behaviour of microtubules in mutant lines that are defective in one or more of these accessory proteins enables us to test models of the molecular mechanisms that drive microtubule organization. We are currently using this knowledge to explore the role microtubules play in the mechanical properties of the cellulosic cell wall, the helical handedness of elongating organs, and even the polar transport of the hormone auxin.
Speaker: Matthew Onsum
Title: Analysis of immune cell chemotaxis and signal integration
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Abstract:
In response to an injury, immune cells are recruited to fight off infecting microbes and clear cellular damage. A number of chemicals, called chemoattractants, are produced at or near sites of infection and inflammation and diffuse into the surrounding tissue. Immune cells sense these chemoattractants and move in the direction where their concentration is greatest, a process termed chemotaxis, and thus locate the source of the attractants and associated targets. In this talk I will present my work using mathematical modeling and experiments to understand how immune cells detect and interpret multiple chemoattractants and convert these signals into directed migration. I will conclude my talk by discussing the application of this work, and mathematical modeling in general, to the drug discovery process in the pharmaceutical industry.
Speaker: Ryan Gutenkunst
Title: Sloppiness in biochemical modeling and evolution
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Abstract:
The dynamics of complex biochemical networks typically depend on many parameters (e.g. reaction rate constants). I show that mathematical models of such networks exhibit a universal "sloppy" pattern of parameter sensitivities; their dynamics are exponentially more sensitive to changes in some combinations of parameters than others. For model builders this suggests that predictions will be much more efficiently constrained by fitting parameters than by directly measuring them. I also explore the evolutionary consequences of sloppiness in the context of Fisher's geometrical model. Sloppiness has little affect on the first step in an adaptive walk, but it may substantially slow the long-term pace of adaptation.
Speaker: Vered Rom-Kedar
Title: Novel strategies for G-CSF support of severe prolonged neutropenia.
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Abstract:
We develop, in an axiomatic fashion, structurally stable mathematical equations that describe the G-CSF-neutrophil dynamics (the majority of the white blood cells are neutrophils. G- CSF is a factor that may be injected to help patients produce more neutrophils). We then show that a variant of this model adequately describes the neutrophils dynamics after chemotherapy treatments with various support protocols. A grading for neutropenia (the dangerous drop in the neutrophil's level) and corresponding tailored G-CSF treatments are proposed and are shown to be robust to parameter variability. Our results clarify and revise the current American Society of Clinical Oncology recommendations for G-CSF administration in neutropenia following intensive chemotherapy regimens. As all our recommendations correspond to clinically available protocols, a framework for a prospective randomized clinical trial is proposed.
Speaker: Babak Pourbohloul
Title: Emerging Infectious Disease, Pandemic Preparedness and Mathematical Models: How to Prepare When We Don't Know the Enemy?
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Abstract:
The underlying contact structure among individuals that determines the pattern of disease transmission and the progression in time of this pattern are two crucial elements in understanding and controlling communicable disease spread within a social setting. Mathematical models of infectious disease that are in principle analytically tractable, have taken two general approaches in incorporating these elements. The first approach, generally known as compartmental models, addresses the time evolution of disease spread at the expense of simplifying the pattern of transmission. On the other hand, the second approach - contact networks - incorporates detailed information of underlying contact structure among individuals. While providing accurate estimates on the final size of outbreak/epidemics, this approach in its current formalism, loses track of the time progression of outbreaks. So far, the only alternative to integrate both aspects of disease spread simultaneously, has been to abandon the analytical approach and rely on computer simulations. Although, powerful modern computers can perform an enormous amount of simulations at an incredibly rapid pace, the complex structure of `realistic' contact networks along with the stochastic nature of disease spread pose a serious challenge to the ability of the computational techniques to the robust analysis of disease spread in large populations in real time. An analytical alternative to this approach is lacking. We offer a new analytical framework, which incorporates both complexity of contact network structure and time progression of disease spread. Furthermore, we demonstrate that this framework works equally effective for finite- and `infinite'-size networks.
Speaker: Nick Hill
Title: Modelling Abdominal Aortic Aneurysms
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Abstract:
This is the first mathematical model to account for the evolution of the abdominal aortic aneurysm. The artery is treated as a two-layer, cylindrical membrane using nonlinear elasticity and a physiologically realistic constitutive model. It is subject to a constant systolic pressure and a physiological axial prestretch. The development of the aneurysm is assumed to be a consequence of the remodelling of its material constituents. Microstructural recruitment and fibre density variables for the collagen are introduced into the strain energy density functions. This enables the remodelling of collagen to be addressed as the aneurysm enlarges. An axisymmetric aneurysm, with axisymmetric degradation of elastin and linear differential equations for the remodelling of the fibre variables, is simulated numerically. Using physiologically determined parameters to model the abdominal aorta and realistic remodelling rates for its constituents, the predicted dilations of the aneurysm agree with those observed in vivo. An asymmetric aneurysm with spinal contact is also considered, and the stress distributions are consistent with previous studies. Additionally, the dynamic properties of the AAA are calculated for different stages in its development, and the evolution of clinically measurable mechanical properties compare well with published physiological data. Watton, P.N., Hill, N.A. & Heil, M. ``A mathematical model for the growth of the abdominal aortic aneurysm.'' Biomechanics and Modeling in Mechanobiology, 3, pp. 98-113, 2004 Watton, P.N. & Hill, N.A. ``Evoloving mechanical properties of a model of abdominal aortic aneurysm.'' Biomechanics and Modeling in Mechanobiology, 2007, DOI: 10.1007/s10237-007-0115-9
Speaker: Xiaoyu Luo
Title: Dynamic simulation of mitral valve using the immersed boundary method
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Abstract:
The dynamic behaviour of a novel chorded mitral prosthesis is studied using an immersed boundary model. To investigate the mechanical behaviour of the mitral design under physiological flow conditions without having to model the left ventricle, we make use of in vivo magnetic resonance images of the left ventricle. The relative motion of the mitral annulus and the papillary muscle regions of the ventricle determined from these MRI images is then used as a prescribed boundary condition for the chorded mitral valve in a dynamic cycle. Results show that without the proper functioning of the papillary muscle, the mitral prosthesis can suffer from an intolerable over-stretch during systole compared with laboratory tests in which the mitral chordae are fixed in space. This turns out to be the key weakness of the current design. The mechanical performance of the prosthesis is compared with recent studies of native porcine valves; differences in mechanical behaviour are observed. Potential improvements for the design and future research projects are also discussed.
Speaker: Angela Reynolds
Title: Mathematical Models of Acute Inflammation
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Abstract:
Acute inflammation involves both pro- and anti- inflammatory components. The balance between these responses is key to the survival of an insult. In severe cases, unbalance can result in multiple organ dysfunction (MODS). MODS is characterized by sequential organ failure caused by an overactive immune system that persists despite treatment of the initial insult. In order to explore treatments for MODS we have developed multiple models of acute inflammation.
These models were constructed through a modular approach where the dynamics of multiple subsystems were analyzed. The subsystems were then merged to form the full model. This approach ensures that known dynamical features of component interactions, such as bistability, excitability, and bifurcation structures, are present in the model dynamics.
We will consider three models accounting for various aspects of acute inflammation. The first will focus on the dynamics between pro- and anti-inflammation. The second models the communication between the tissue and blood, which is essential in mounting a successful response to pathogen. The third models acute inflammation in the lung and its effects on gas exchange. Creating these models is the first step in simulating the spread of inflammation between organs.
Speaker: Richard Allen
Title: Modelling the Endothelial Cell Response to Fluid Flow
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Abstract:
Following the onset of shear stress due to fluid flow endothelial cells polarise and elongate in the direction of flow. How the mechanical signal is transformed into an organised and directed response is poorly understood. A multi-scale cellular Potts model promises to aid investigation of this question. A 3D virtual cell defines the fluid flow via a boundary integral representation, solution of which gives the force over the surface of the cell. A framework of how to link this to models of Rho GTPase interaction, actin filament alignment and Arp2/3 induced actin polymerisation will be described.
Speaker: Jessica Conway
Title: Superlattice Patterns in Oscillatory Systems Forced at Multiple Resonant Frequencies
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Abstract:
Superlattice patterns and quasipatterns have been well-studied in waves on the surface of vertically vibrated viscous fluids (Faraday waves). We show that such patterns, comprised of 4 or more Fourier modes at different orientation, can also be obtained in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations if they are exposed to a spatially homogeneous forcing with judiciously chosen time dependence with frequencies near the 1:1-, 1:2-, and 1:3-resonance. For weak forcing such systems can be described by a suitably extended complex Ginzburg-Landau equation with time periodic coefficients. Using Floquet theory and weakly nonlinear analysis we obtain the amplitude equations for simple patterns (comprised of 1, 2, or 3 modes) as well as superlattice patterns comprised of more modes. Exploiting spatiotemporal resonances we stabilize subharmonic 4- and 5-mode patterns. We confirm our analysis through direct numerical simulations of the Ginzburg-Landau equation. We also show the possibility of such complex patterns in the laboratory setting by using system parameters reported for experiments on the oscillatory Belousov-Zhabotinsky reaction and explicitly demonstrating that the forcing parameters can be tuned such that 4-mode patterns are the preferred patterns.
Speaker: Ben Vanderlei
Title: Error Estimates for Numerical Solutions of Interface Problems
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Abstract:
In order to make numerical approximations more useful in application settings it is important to understand and, if possible, to quantify the error introduced by approximating the solution of the problem using numerical methods. I will discuss the results of applying a modification of the Method of Nearby Problems to compute error estimates. I will present first the results for a continuous problem and then discuss interface problems. The model interface problem will be an elliptic PDE with a coefficient which is discontinuous across an internal boundary. I will present the Immersed Interface solution of this problem and the development of an error estimate. We will also look at solutions obtained using regularization methods and the additional error introduced by regularizing the problem.
Speaker:Somdatta Sinha
Title: Collective Behaviour in Multi-cell Systems
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Abstract:
Robust synchronized functional dynamics are commonly observed in biological cell populations and spatially extended biological systems, e.g., tissues. These are fascinating examples of collective behaviour. To investigate the roles of local cellular dynamics and interaction strength in the spatiotemporal dynamics of cell-collectives of different sizes, we studied a model system consisting of a ring of coupled cells incorporating an auto-regulated, three-step biochemical pathway. The isolated individual cells can display complex dynamics as a result of the nonlinear interactions common in cellular processes. On coupling the cells to nearest neighbours, through diffusion of the pathway end product, the ring of cells yields a host of interesting and unusual dynamical features for varying interaction strengths and system sizes. But robust complete synchronization can be induced in these coupled cells with a small degree of random coupling among them even where regular coupling yielded only intermittent synchronization. The example of beta cell dynamics in pancreatic islets will be discussed.
Speaker: Sido Nagano
Title: Receptors as a master key for synchronization of rhythms -amoebae know the strategy of the crystal growth?
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Abstract:
Unicellular amoeba called Dictyostelium discoideum has attracted a lot of atten tion recently as a model system for the study of multicellular morphogenesis and pattern form ation. When starved, they aggregate and form a multicellular organism. During the aggregati on process, amoebae communicate by periodically producing and relaying cAMP signals (chemic al signals). From the modeling study of Dictyostelium's survival strategy, we have derived a simple, but general scheme to achieve synchronization of rhythms, and clarified that biolog ical receptors work as apparatuses that can convert external stimulus to the form of nonlinear interaction within individual oscillators. The derived scheme is very simple mathematically , but surprisingly powerful. We can apply an essence of Dictyostelium's survival strategy not only to other biological systems (for example, pancreas), but also to crystal growth and elec tric circuit design.
Speaker: Gideon Ngwa
Title: The population dynamics of the malaria vector
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Abstract:
A deterministic differential equation model for the population dynamics of the human malaria vector is derived and studied. Conditions for the existence and stability of a non-zero steady state vector population density are derived. These reveal that a threshold parameter, the vectorial basic reproduction number, exist and the vector can established itself in the community if and only if this parameter exceeds unity. When a non-zero steady state population density exists, it can be stable but it can also be driven to instability via a Hopf Bifurcation to periodic solutions, as a parameter is varied in parameter space. By considering a special case, an asymptotic perturbation analysis is used to derive the amplitude of the oscillating solutions for the full non-linear system. The present modelling exercise and results show that it is possible to study the population dynamics of disease vectors, and hence oscillatory behaviour as it is often observed in most indirectly transmitted infectious diseases of humans, without recourse to external seasonal forcing. In this communication, we derive and study a simple model for the dynamics of the human malaria vector based on the simple idea that the mosquito has a human biting habit. Since it is the mosquito that actively seeks and bites human beings, this assumption, which has been used successfully to model the dynamics of malaria transmission Ngwa et al. [1, 2, 3], may be seen as a restricted form of homogeneous mixing based on the idea that the mosquito has a human biting habit. The concept of the existence of a basic reproduction number, R0, in models has been addressed by Porphyre et al. [4], Diekmann et. al. [5]. In our formulation, R0 depends on a mass action contact rate tau* as well as on the probability of the mosquito obtaining a successful blood meal p in the sense that R0 goes to 0 whenever p goes to 0 or tau* goes to 0, and saturates to a positive non-zero value when p goes to 1 and tau* becomes infinite .

[1] Ngwa, G. A., Modelling the dynamics of endemic malaria in growing populations. Discrete and Continuous Dynamical SystemsđSeries B Vol 4 No. 4 (2004), 11731202. [2] Ngwa, G. A., Ngonghala, C. Ngeh and Sama Wilson, N.B, A model for endemic malaria with delay and variable populations. Journal of the Cameroon Academy of Sciences, Vol. 1 No. 3 (2001), 168-186. [3] Ngwa, G. A and Shu, W. S., A mathematical model for endemic malaria with variable human and mosquito populations. Math. and Comp. Modelling, 32(7-8) (2000), 747763. [4] Porphyre T. Bicout D. J., Sabatier P., Modelling the abundance of mosquito vectors versus flooding dynamics. Ecological Modelling 183 (2005) 173-181. [5] Diekmann O., Heesterbeek J.A.P and Metz J.A.J. On the definition and computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28 (1990), 365-382.


Speaker: Heather Hardway
Title: Modeling Genetic Networks in the Fruit Fly
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Abstract:
Over the past century, the Drosophila melanogaster (fruit fly) gene network has become one of the most studied and well understood. This is especially true of the genes involved in the anterior-posterior axis specification, the first step in spatially organizing the developing embryo. However, a new feature of this system was recently discovered: positional noise filtering. Gene products were shown to have high specificity with respect to positional location, despite receiving noisy information from upstream regulators. I will discuss reaction-diffusion models for this system and the results of a parameter search for such robust networks. In addition, I will present some unexpected nonlinear phenomenon possible in these gene networks, including tango waves in an activator-inhibitor system.
Speaker: Caz Taylor
Title: Finding optimal behavior using decision rules in an individual-based model
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Abstract:
We describe a modeling approach in which individuals are able to use information about their state and the environment to formulate behavioural rules that optimize fitness. We model the decision probability as a function of weighted input or state variables. We then use a search optimization algorithm (simulated annealing) to find the rule weights so that a series of decisions made by an individual maximize a known fitness function. The advantage of this individual rule-based approach is that we can optimize behaviour in an environment that includes complex interactions, such as density-dependence. We apply this approach to the migration behavior of Western Sandpipers (Calidris mauri), moving sequentially through a set of stopover sites along the North American Pacific coast and optimizing arrival time at the breeding grounds. The departure probability of each individual at each stopover site is a function of four state variables (i) whether or not the individual is on time, (ii) the individual fuel load, (iii) availability of food, and (iv) risk of predation. The latter two variables depend not only on the individual but on the density of conspecifics and therefore on the behavior of all other individuals. We investigate how different types of density dependence affects the patterns of migration.
Speaker: Sally Otto and Rich FitzJohn
Title: Inferring the past for traits that alter speciation and extinction rates
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Abstract:
We will describe work by ourselves and co-authors Wayne Maddison and Peter Midford to build a likelihood-based approach to infer how speciation and extinction rates depend on the state of a particular character. The phylogenetic tree of a group of species contains information about character transitions and about diversification: higher speciation rates, for example, give rise to shorter branch lengths. The likelihood method that we have developed uses all of the information contained in a phylogeny and integrates over all possible evolutionary histories to infer the speciation and extinction rates for species with different character states. Our method can be used to provide more detailed information than previous methods, allowing us to disentangle whether a particular character state is rare because species in that state are prone to extinction, are unlikely to speciate, or tend to move out of that state faster than they move in.
Speaker: Jana Gevertz
Title: Multi-scale Mathematical Modeling of Heterogeneous Tumor Growth
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Abstract:
An in silico tool that can be utilized in the clinic to predict neoplastic progression and propose individualized treatment strategies is the holy grail of computational tumor modeling. As we have the long-term goal of developing such a simulation tool, we have worked over the years to address a number of tumor-related questions using variations of one theoretical model. In this talk, I will focus on both the implementation of, and the results drawn from, several of the model variants. Questions we have addressed through our modeling efforts include: 1. How do we develop a minimalistic quantitative model of tumor progression? 2. What effects do organ geometry and topology have on tumor size, shape and spread? 3. How does an evolving vasculature impact tumor dynamics? 4. What effects do genetic mutations have on patient prognosis? After looking at a set of model variants that allows us to answer each of these questions, I talk about recent efforts to merge these models into one comprehensive cancer simulation tool. I use the merged model to highlight biological features that must be considered in a clinically-relevant tumor growth algorithm and to test the impact of vascular-targeting treatment strategies.
Speaker: Yue-Xian Li
Title: Modeling Hormonal Rhythms in a Network of Endocrine Neurons
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Abstract:
The regulation of reproductive function and fertility is ultimately controlled by a pulsatile signal of gonadotropin-releasing hormone (GnRH). GnRH is synthesized and secreted by a few hundred GnRH neurons in the hypothalamus that work in synchrony to produce this pulsatile rhythm. The mysteries surrounding the rhythmogenesis in GnRH neurons remain defiant to any conventional knowledge of rhythm-generation in neuronal networks. Efforts to crack this puzzle have been pushing the frontier of classical neuroscience that traditionally only focused on ionotropic channel events with time scales of milliseconds to the inclusion of metabotropic receptors, second messengers, vesicle transportation and docking, autocrine/parcrine regulations, as well as genetic events. Mathematical modeling of this rhythm gives rise to challenging nonlinear mathematical problems one has never encountered before. This talk will present a brief summary of important progress in recent years including our own contributions to solving this puzzle.
Speaker: Alexander Verkhovsky
Title: Organization and dynamics of motile machinery in a simple cell
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Abstract:
Understanding cell migration as an integrated physical phenomenon requires a combination of experimental and theoretical studies, and appropriate model systems. Fish epidermal keratocytes exhibit a simple and regular organization and motion pattern and therefore represent a favorable system to understand how the molecular machinery is orchestrated to produce coordinated behavior at a cellular level. We use a combination of experimental imaging, micromanipulation, and computational approaches to evaluate structural and dynamical parameters of actin network, map assembly and motion of actin and myosin II during migration, and to investigate the relationship between cytoskeletal dynamics and generation of motile forces. The results indicate the mechanism of generation of contractile forces and suggest several redundant modes of cell migration.
Speaker: Gareth Leng
Title: Modeling a model system; bursts and pulses in neuroendocrine neurones
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Abstract:
Peptides in the hypothalamus are not like conventional neurotransmitters; their release is not particularly associated with synapses, and their long half-lives mean that they can diffuse to distant targets. Peptides can act on their cells of origin to facilitate the development of patterned electrical activity, they can act on their neighbours to bind the collective activity of a neural population into a coherent signalling entity, and the co-ordinated population output can transmit waves of peptide secretion that act as a patterned hormonal analogue signal within the brain. At their distant targets, peptides can re-programme neural networks, by effects on gene expression, synaptogenesis, and by functionally rewiring connections by priming activity-dependent release.

My lab has studied mainly the oxytocin and vasopressin neurones of the hypothalamus, these neurones fire in distinctive patterns that govern and in turn are governed by the peptide secretion that they induce. Oxytocin cells display remarkable synchronised bursts, that arise through emergent properties of an interactive network; vasopressin cells also burst, but asynchronously in a very different way and for very different reasons. In their different ways, these two neuronal systems have become important model systems in neuroscience; in this talk I will talk about modelling these model systems.

(1) Leng G, Brown C, Sabatier N, Scott V (2008) Population dynamics in vasopressin neurons. Neuroendocrinology PMID: 18667805. (2) Leng G, Ludwig M (2008) Neurotransmitters and peptides: whispered secrets and public announcements. Journal of Physiology Oct 9. [Epub ahead of print]. (3) Rossoni E, Feng J, Tirozzi B, Brown D, Leng G, Moos F (2008) Emergent synchronous bursting of oxytocin neuronal network. PLoS Computational Biology Jul 18;4(7):e1000123.PMID: 18636098. (4) Leng G, Macgregor D (2008) Mathematical modelling in neuroendocrinology Journal of Neuroendocrinology 20: 713-718 PMID: 18513205.
Speaker: Sohrab Shah
Title: Model based approaches to array CGH data analysis
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Abstract:
DNA copy number alterations (CNAs) are genetic changes that can produce adverse effects in numerous human diseases, including cancer. CNAs are segments of DNA that have been deleted or amplified and can range in size from one kilobases to whole chromosome arms. Development of array comparative genomic hybridization (aCGH) technology enables CNAs to be measured at sub-megabase resolution using tens of thousands of probes. However, aCGH data are noisy and result in continuous valued measurements of the discrete CNAs. Consequently, the data must be processed through algorithmic and statistical techniques in order to derive meaningful biological insights. We introduce model-based approaches to analysis of aCGH data and develop state-of-the-art solutions to three distinct analytical problems. In the simplest scenario, the task is to infer CNAs from a single aCGH experiment. We apply a hidden Markov model (HMM) to accurately identify CNAs from aCGH data. We show that borrowing statistical strength across chromosomes and explicitly modeling outliers in the data, improves on baseline models. In the second scenario, we wish to identify recurrent CNAs in a set of aCGH data derived from a patient cohort. These are locations in the genome altered in many patients, providing evidence for CNAs that may be playing important molecular roles in the disease. We develop a novel hierarchical HMM profiling method that explicitly models both statistical and biological noise in the data and is capable of producing a representative profile for a set of aCGH experiments. We demonstrate that our method is more accurate than simpler baselines on synthetic data, and show our model produces output that is more interpretable than other methods. Finally, we develop a model based clustering framework to stratify a patient cohort, expected to be composed of a fixed set of molecular subtypes. We introduce a model that jointly infers CNAs, assigns patients to subgroups and infers the profiles that represent each subgroup. We show our model to be more accurate on synthetic data, and show in two patient cohorts how the model discovers putative novel subtypes and clinically relevant subgroups in two types of lymphoma.
Speaker: Vipul Periwal
Title: Dynamics of Adipose Tissue Growth
Abstract:
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Adipose tissue grows by two mechanisms: hyperplasia (cell number increase) and hypertrophy (cell size increase). Genetics and diet affect the relative contributions of these two mechanisms to the growth of adipose tissue in obesity. To address adipose tissue growth precisely, we developed a mathematical model describing the evolution of the adipose cell-size distributions as a function of the increasing fat pad mass, instead of the increasing chronological time. Our model describes the recruitment of new adipose cells and their subsequent development in different strains, and with different diet regimens, with common mechanisms, but with diet- and genetics-dependent model parameters. Hyperplasia is enhanced by high-fat diet in a strain-dependent way, suggesting a synergistic interaction between genetics and diet. Moreover, high-fat feeding increases the rate of adipose cell size growth, independent of strain, re▀ecting the increase in calories requiring storage. Additionally, high-fat diet leads to a dramatic spreading of the size distribution of adipose cells in both strains; this implies an increase in size ▀uctuations of adipose cells through lipid turnover.

Speaker: Will Heuett
Title: Modeling Metabolism in Pancreatic Beta-Cell Mitochondria
Abstract:
Pancreatic beta-cells sense the ambient blood-glucose concentration and secrete insulin to signal other tissues to take up glucose. Mitochondria play a key role in this response as they metabolize nutrients to produce ATP and reactive oxygen species (ROS), both of which are involved in insulin secretion signaling. I will present a model of beta-cell mitochondrial respiration, ATP synthesis, and ROS production in response to glucose and fatty acid stimulation, based on available data in the literature and mathematical models derived from first principles. The model explains experimental observations of the non-ohmic rise in the passive proton-leak rate at high membrane potential and its dependence on increased ROS production. It also predicts that glucose-stimulated insulin secretion is inhibited by long-term fatty acid exposure, but can be enhanced by inhibiting uncoupling protein activation and promoting mitochondrial biogenesis. Using glucose and fatty acid profiles from individuals, I will show that there is a negative correlation between the amount of ROS produced per ATP, as predicted by the model, and the individual insulin sensitivities. Finally, I will discuss how the model can be used to predict the c-peptide and insulin secretion rate and provide a quantitative description of beta-cell function for a single individual. Return to seminar page


Speaker: Joe Yuichiro Wakano
Title: Origin of culture: an evolutionary model of social learning
Abstract:
Social learning is an important ability seen in a wide range of animals. Especially, humans developed the advanced social learning ability such as language, which triggered rapid cultural evolution. On the other hand, many species, such as viruses, rely on genetic evolution to adapt to environmental fluctuations. Here we propose an evolutionary game model of competition among three strategies; social learning, individual learning, and genetic determination of behavior. We identify the condition for learning strategies to evolve.

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