Applied & Biological Contemporary Mathematics Program

The ABC program is intended to foster and promote interdisciplinary research linking mathematics with the life sciences. It is also intended to be supportive of other College and Institute initiatives - specifically the emerging Integrative Biological Systems thrust. Due to its clear interdisciplinary focus, the success of the ABC program will come from clear and effective communications and research partnerships with our life sciences colleagues.

Initially, a broad range of faculty from the School of Mathematics will be affiliated with the ABC program, although this is expected in time to extend to faculty from other units on campus.

The ABC program will support:

• A research seminar in Mathematical Biology and Ecology
• Conferences and Workshops
• Graduate student support

Activities in 2008-2009

11:00 am Wednesday, April 8, 2009
Mathematical Biology & Ecology Seminar: Synchrony in tritrophic food chain metapopulations
by Igor Belykh (University of Georgia) Skiles 255

11:00 am Wednesday, April 8, 2009
Mathematical Biology & Ecology Seminar: Socially-induced Synchronization of Avian Ovulation Cycles
by Shandelle Henson (Andrews University) Skiles 255

Oscillator synchrony can occur through environmental forcing or as a phenomenon of spontaneous self-organization in which interacting oscillators adjust phase or period and begin to cycle together. Examples of spontaneous synchrony have been documented in a wide variety of electrical, mechanical, chemical, and biological systems, including the menstrual cycles of women. Many colonial birds breed approximately synchronously within a time window set by photoperiod. Some studies have suggested that heightened social stimulation in denser colonies can lead to a tightened annual reproductive pulse (the Fraser Darling effect). It has been unknown, however, whether avian ovulation cycles can synchronize on a daily timescale within the annual breeding pulse. We will discuss socially-stimulated egg-laying synchrony in a breeding colony of glaucous-winged gulls using Monte Carlo analysis and a discrete-time dynamical system model.

CANCELLED 11:00 am Wednesday, April 1, 2009
Mathematical Biology & Ecology Seminar: Mathematical and experimental considerations of density and physiological state effects on antimicrobial susceptibility
by Klas Udekwu (Emory University) in Skiles 255

The treatment of bacterial infections with antibiotics is universally accepted as one of (if not THE) most significant contributions of medical intervention to reducing mortality and morbidity during last century. Despite their widespread use over this extended period however, basic knowledge about how antibiotics kill or prevent the growth of bacteria is only just beginning to emerge. The dose and term of antibiotic treatment has long been determined empirically and intuitively by clinicians. Only recently have antibiotic treatment protocols come under scrutiny with the aim to theoretically and experimentally rationalize treatment protocols. The aim of such scrutiny is to design protocols which maximize antibiotics efficacy in clearing bacterial infections and simultaneously prevent the emergence of resistance in treated patients. Central to these endeavors are the pharmacodynamics, PD (relationship between bug and drug), and the pharmacokinetics, PK (the change antibiotic concentration with time) of each bacteria : drug : host combination. The estimation of PD and PK parameters is well established and standardized worldwide and although different PK parameters are commonly employed for most of these considerations, a single PD parameter is usually used, the minimum inhibitory concentration (MIC). MICs, also utilized as the criteria for resistance are determined under conditions that are optimal to the action of the antibiotic; low densities of bacteria growing exponentially. The method for estimating MICs which is the only one officially sanctioned by the regulatory authority (Clinical and Laboratory Standards Institute) defines conditions that rarely obtain outside of the laboratory and virtually never in the bacteria infecting mammalian hosts. Real infections with clinical symptoms commonly involve very high densities of bacteria, most of which are not replicating. These populations are rarely planktonic but rather reside as colonies or within matrices called biofilms which sometimes include other species of bacteria.

In the first part of my talk, I will present newly published data that describes the pharmacodynamic relationship between the sometimes pathogenic bacterium Staphylococcus aureus and antibiotics of six classes and the effects of cell density on MICs. By including density dependent MIC in a standard mathematical model of antibiotic treatment (from our lab), I show that this density-dependence may explain why antibiotic treatment fails in the absence of inherited resistance. In the second part of my talk I will consider the effects of the physiological state of clinical isolates of S. aureus on their susceptibility to different antibiotics. I present preliminary data which suggests that the duration of an infection may contribute adversely to an antibiotics chance of clearing the infection. I conclude with a brief discussion of the implications of the theoretical and experimental results for the development of antibiotic treatment protocols. As a special treat, I will outline problems of antibiotic treatment that could well be addressed with some classy mathematics.

11:00 am Wednesday, March 25, 2009
Mathematical Biology & Ecology Seminar: Stabilization of multimeric enzymes: structural adaptation to stress conditions
by Ruslan Rafikov (Medical College of Georgia) in Skiles 255

The stress condition calls for an adequate activity of key enzymatic systems of cellular defense. Massive protein destabilization and degradation is occurring in stressed cells. The rate of protein re-synthesis (DNA->RNA->protein) is inadequate to adapt to rapidly changing environment. Therefore, an alternative mechanism should exist maintaining sufficient activity of defense enzymes. Interestingly, more than 50% of enzymes consist of identical subunits which are forming multimeric interface. Stabilization of multimers is important for enzymatic activity. We found that it can be achieved by the formation of inter-subunit covalent bridges in response to stress conditions. It shows an elegance of the structure design that directs selective subunits linkage and increases enzyme's robustness and chances of cell survival during the stress. In contrast, modification of aminoacids involved in linkage leads to protein destabilization, unfolding and degradation. These results describe a new instantaneous mechanism of structural adaptation that controls enzymatic system under stress condition.

11:00 am Wednesday, March 11, 2009
Mathematical Biology & Ecology Seminar: "Feel Sick? Follow the money!" - New Perspectives on Global Human Mobility and Disease Dynamics
by Dirk Brockmann (Northwestern University) in Skiles 255

Human Mobility in our globalised world has reached a complexity and volume of unprecedented degree. More than 60 million people travel billions of kilometres on more than 2 million international flights each week. Hundreds of millions of people commute on a complex web of highways and railroads most of which operate at their maximum capacity. Human mobility is responsible for the geographical spread of emergent human infectious diseases and plays a key role in human mediated bioinvasion, the dominant factor in the global biodiversity crisis. I will report on the recent discovery of scaling laws in global human traffic (obtained from online bill-tracking at www.wheresgeorge.com) and mathematical models that can account for it. I will present a complex network perspective on multi-scale human traffic networks, report on their statistical properties and show that they can be used to identify geographically coherent communities that only vaguely resemble administrative ones. The approach provides an operational segmentation of maps into a hierarchical set of effective regions and boundaries based on human behavior. I will briefly talk about European transportation networks, geocaching and trackable items.

11:00 am Wednesday, March 4, 2009
Mathematical Biology & Ecology Seminar: Modeling Age Structure Via Delay Differential Equations
by Sean Ellermeyer (Kennesaw State University) in Skiles 255

11:00 am Wednesday, February 25, 2009
Mathematical Biology & Ecology Seminar: Nonlinear effect of copy number variation on gene expression
by Yuriy Mileyko (School of Biology, Georgia Tech) in Skiles 255

The expression dynamics of interacting genes depends on the topology of the regulatory network, the quantitative nature of feedbacks and interactions between DNA, RNA and proteins, and the biochemical state of the intracellular and surrounding environment. In this talk we show that dynamics of a gene regulatory network can also depend sensitively on the copy number of genes and promoters. Genetic regulatory networks include an overrepresentation of subgraphs commonly known as network motifs. We consider positive feedback, bistable feedback, and toggle switch motifs and show that variation in gene copy number can cause a sequence of saddle-node bifurcations in the corresponding differential equations models, which leads to multiple orders of magnitude change in gene expression. A similar analysis of a 3-gene motif with successive inhibition (the ``repressilator'') reveals that changes in gene copy number can also cause a Hopf bifurcation, thus leading to a qualitative switch in system behavior among oscillatory and equilibrium dynamics. Importantly, we show that these bifurcations exist over a wide range of parameter values, thus reinforcing our claim that copy number is a key control parameter in the expression dynamics of regulatory networks.

11:00 am Wednesday, January 28, 2009
Mathematical Biology & Ecology Seminar: Ecological feedbacks in the evolution of resistance and tolerance to infectious disease
by Mike Boots (University of Sheffield) in Skiles 255

11:00 am Wednesday, December 3, 2008
Mathematical Biology & Ecology Seminar: Transient (Electro)Chemical Imaging of Reacting Interfaces: Physical Concepts and Mathematical Challenges
by Andrei Fedorov (School of Mechanical Engineering, Georgia Tech) in Skiles 255

In this presentation I will outline physical principles of two analytical techniques, the Scanning ElectroChemical Microscopy (SECM) and Scanning Mass Spectrometry (SMS), which can be used to obtain the spatially resolved images of (bio/electro)chemically active interfaces. The mathematical models need to be employed for image interpretation and mapping measured quantities (e.g., an electrode current in SECM) to biochemically relevant quantities (e.g., kinetics of exocytotic signaling events in cellular communications), and I will review the key ideas/assumptions used for the model formulation and the main results of analysis and simulations. In conclusion, an alternative approach to spatially-resolved imaging based on the multi-probe array will be introduced along with intriguing opportunities and challenges for mathematical interpretation of such images.

11:00 am Wednesday, November 12, 2008
Mathematical Biology & Ecology Seminar: TBA
by Benjamin Ridenhour (CDC/CCID/NCIRD, CTR) in Skiles 255

11:00 am Wednesday, November 5, 2008
Mathematical Biology & Ecology Seminar: Eat your spinach? The role of buffering reactions in clearing hydrogen
by Melissa Kemp (Dept of Biomedical Engineering, Georgia Tech) in Skiles 255

Hydrogen peroxide has been long considered a harmful reactive oxygen species, but is increasingly appreciated as a cellular signaling molecule. The mechanism by which the cell buffers against intracellular H2O2 accumulation during periods of oxidative stress is not fully understood. I will introduce a detailed network model of the known redox reactions and cellular thiol modifications involved in H2O2 buffering. The model includes anti-oxidative contributions of catalase, glutathione peroxidase, peroxiredoxin, and glutaredoxin, in addition to the cytoplasmic redox buffers, thioredoxin and glutathione. Based on ordinary differential equations, the model utilizes mass action kinetics to describe changes in concentration and redox state of cytoplasmic proteins upon exposure to physiologically relevant concentrations of extracellular H2O2. Simulations match experimental observations of a rapid and transient oxidation of thioredoxin upon exposure to extracellular peroxide. The increase in the concentration of oxidized proteins predicted by the model is simultaneously accompanied by an increase in protein S-glutathionylation, possibly regulating signal transduction in cells undergoing oxidative stress. Ultimately, this network analysis will provide insight into how to target antioxidant therapies for enhanced buffering without impacting the necessary protein oxidation used by cells for signaling purposes.

11:00 am Wednesday, October 22, 2008
Mathematical Biology & Ecology Seminar: Data-driven methods in protein engineering: new ways to utilize sequence and structures of proteins
by Andy Bommarius (School of Chemistry & Biochemistry, Georgia Tech) in Skiles 255

After rational protein design and combinatorial protein engineering (directed evolution), data-driven protein engineering emerges as a third generation of techniques for improving protein properties. Data-driven protein engineering relies heavily on the use of mathematical algorithms. In the first example, we developed a method for predicting the positions in the amino acid sequence that are critical for the catalytic activity of a protein. With nucleotide sequences of both functional and non-functional variants and a Support Vector Machine (SVM) learning algorithm, we set out to narrow the interesting sequence space of proteins, i.e. find the truly relevant positions. Variants of TEM-1 -lactamase were created in silico using simulations of both mutagenesis and recombination protocols. The algorithm was shown to be able to predict critical positions that can tolerate up to two amino acids. Pairs of amino acid residues are known to lead to inactive sequences, unless mutated jointly. In the second example, we combine SVM, Boolean learning (BL), and the combination of the two, BLSVM, to find such interactive residues. Results on interactive residues in two fluorescent proteins, Discosoma Red Fluorescent Protein (Ds-Red) and monomeric Red Fluorescent Protein (mRFP), will be presented.

11:00 am Wednesday, October 15, 2008
Mathematical Biology & Ecology Seminar: Dynamics and implications of some models of hepatitis B virus infection
by Yang Kuang (Arizona State University) in Skiles 255

Chronic HBV infection affects 350 million people and can lead to death through cirrhosis-induced liver failure or hepatocellular carcinoma. We present the rich dynamics of two recent models of HBV infection with logistic hepatocyte growth and a standard incidence function governing viral infection. One of these models also incorporates an explicit time delay in virus production. All model parameters can be estimated from biological data. We simulate a course of lamivudine therapy and find that the models give good agreement with clinical data. Previous models considering constant hepatocyte growth have permitted only two dynamical possibilities: convergence to a virus free or an endemic steady state. Our models admit periodic solutions. Minimum hepatocyte populations are very small in the periodic orbit, and such a state likely represents acute liver failure. Therefore, the often sudden onset of liver failure in chronic HBV patients can be explained as a switch in stability caused by the gradual evolution of parameters representing the disease state.

11:00 am Wednesday, October 8, 2008
Mathematical Biology & Ecology Seminar: A population model of influenza designed to evaluate projected pandemic vaccine production in Taiwan
by John Glasser (CDC/CCID/NCIRD) in Skiles 255

Background: We endeavor to reproduce historical observations and to identify and remedy the cause of any disparate predictions before using models to inform public policy-making. We have no finely age- and time-stratified observations from historical pandemics, but prior exposure of older adults to a related strain is among the more compelling hypotheses for the w-shaped age-specific mortality characterizing the 1918 pandemic, blurring the distinction between annual and pandemic influenza.
Methods: We are attempting to reproduce patterns in annual influenza morbidity and mortality via a cross-classified compartmental model whose age class sojourns approximate the longevity of clusters of closely-related strains. In this population model, we represent effective inter-personal contacts via a generalization of Hethcote's formulation of mixing as a convex combination of contacts within and between age groups. Information about mixing has been sought in face-to-face conversations, a surrogate for contacts by which respiratory diseases might be transmitted, but could also be obtained from household and community transmission studies. We reanalyzed observations from several such studies to learn about age-specific preferences, proportions of contacts with others the same age. And we obtained age-specific forces of infection from proportions reporting illness in a prospective study of household transmission during the 1957 influenza pandemic, which we gamma distributed to correct for misclassification. Then we fit our model to weekly age-specific hospitalizations from Taiwan's National Health Insurance Program, 2000-07, by adjusting a) age-specific coefficients of harmonic functions by which we model seasonality and b) probabilities of hospitalization given influenza.
Results: While our model accounts for only 30% of the temporal variation in hospitalizations, estimated conditional probabilities resemble official health resource utilization statistics. Moreover, younger and older people are most likely to be hospitalized and elderly ones to die of influenza, with modeled deaths 10.6% of encoded influenza or pneumonia mortality.
Conclusions: Having satisfactorily reproduced recent patterns in influenza morbidity and mortality in Taiwan via a deterministic model, we will switch to a discrete event-time simulator and - possibly with different initial conditions and selected parameters - evaluate the sufficiency of projected pandemic vaccine production. Joint work with Denis Taneri, and Jen-Hsiang Chuang

11:00 am Wednesday, October 1, 2008
Mathematical Biology & Ecology Seminar: Demographic stochasticity and the Daphnia model
by John Drake (University of Georgia) in Skiles 255

11:00 am Wednesday, September 24, 2008
Mathematical Biology & Ecology Seminar: Algebraic models in systems biology
by Reinhard Laubenbacher (Virginia Bioinformatics Institute and Department of Mathematics, Virginia Tech) in Skiles 255

Since John von Neumann introduced cellular automata in the 1950s to study self-replicating systems, algebraic models of different kinds have increased in popularity in network modeling in systems biology. Their common features are that the interactions between network nodes are described by "rules" and that the nodes themselves typically take on only finitely many states, resulting in a time-discrete dynamical system with a finite state space. Some advantages of such qualitative models are that they are typically intuitive, can accommodate noisy data, and require less information about a variety of kinetic and other parameters than differential equations models. Yet they can capture essential network features in many cases. This talk will discuss examples of different types of algebraic models of molecular networks and a common conceptual framework for their analysis.

The evolution of sociality represented one of the major transition points in biological history. Highly social animals such as social insects dominate ecological communities because of their complex cooperative and helping behaviors. We are interested in understanding how evolutionary processes affect social systems and how sociality, in turn, affects the course of evolution. Our research focuses on understanding the social structure and mating biology of social insects. In addition, we are interested in the process of development in the context of sociality. We have found that some social insect females mate with multiple males, and that this behavior affects the structure of colonies. We have also found that colonies adjust their reproductive output in a coordinated and adaptive manner. Finally, we are investigating the molecular basis underlying the striking differences between queens and workers in highly social insects. Overall, our research provides insight into the function and evolutionary success of highly social organisms.

In the ocean, coherent vortices account for a large portion of the ocean turbulent kinetic energy and their presence significantly affects the dynamics and the statistical properties of ocean flows, with important consequences on transport processes. Mesoscale vortices also affect the population dynamics of phyto- and zooplankton, and are associated with secondary currents responsible for localized vertical fluxes of nutrients. The fact that the nutrient fluxes have a fine spatial and temporal detail, generated by the eddy field, has important consequences on primary productivity and the horizontal velocity field induced by the eddies has been suggested to play an important role in determining plankton patchiness. Owing to their trapping properties, vortices can also act as shelters for temporarily less-favoured planktonic species. In this contribution, I will review some of the transport properties associated with coherent vortices and their impact on the dynamics of planktoni ecosystems, focusing on the simplified conceptual model provided by two-dimensional turbulence.

Activities in 2007-2008

Activities in 2006-2007

Affiliated Faculty

• Leonid Bunimovich Director
• Silas Alben
• Yuri Bakhtin
• Jeffrey Geronimo
• Guillermo Goldsztein
• Serge Guillas
• Christine Heitsch
• Vladimir Koltchinskii
• Heinrich Matzinger
• Liang Peng
• Maria Westdickenberg
• Prasad Tetali
• Howard Weiss
• Joshua Weitz
• Hao Min Zhou

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