We study a spatial extension of the classical predator
– prey model with an independent source of prey in
the context of lymphocyte  pathogen dynamics. We found
the regimes,where the mean field theory is wrong. We show
using stochastic simulations that such regimes exist and
study the mechanism leading to the stabilization of the
point with zero prey density in regions of parameter space
where the mean field prediction is that the coexistence
fix point is the stable one. Understanding the formation of the arabidopsis root
epidermis through an intimate collaboration between modeling
and experiment Our model modifies the MeinhardtGierer model of activatorinhibitor
interaction to study the role of position cues, such as
those produced by SCM in Arabidopsis Thaliana, on the production
of heterogeneous steadystates patterns. In A. thaliana,
the WER/MYB23 complex acts as a nonmobile activator and
CPC/TRY as the mobile inhibitor. Using sensitivity analysis
and parameter identification techniques, we look to see
if the application of the position cues will produce the
wildtype pattern observed in nature. Using experimental
techniques, we look for the criteria for differentiation
into the pattern of hair and nonhair fates and examine
the ability of the model to reproduce this pattern. A. thaliana,
a variety of mustard plant, is an ideal organism for study
because of its fully sequenced genome and its short growth
period. Experimental evidence suggests that an epidermal
cell of A. thaliana differentiates into a haircell when
the activator to inhibitor ratio is sufficiently high and
this ratio inside the cell is 10x magnitude higher than
the activator to inhibitor ratio in neighboring cells. An Investigation of Tyrosine Kinase Tnk1 Substrates
and Function Protein tyrosine kinases (PTKs) play essential roles in many aspects of cell signaling (1). PTKs are utilized during a wide diversity of multicellular functions including; cell growth, differentiation, adhesion, motility, and apoptosis (2). Tnk1 is a nonreceptor tyrosine kinase apart of the Ack protein family (3). It was originally cloned from human umbilical cord blood hematopoietic stem/progenitor cells (3). Tnk1 is expressed broadly in fetal tissues while expression in adults is limited to select tissues (3). The majority of signaling pathways involving Tnk1 have not been identified (4). However, Tnk1 is known to interact with Phospholipase C?1 by means of its SH3 domain to inhibit the transactivation of nuclear factor?B via tumornecrosisfactora (TNFa), allowing TNFa induced apoptosis to take place (5). Unpublished data revels that Tnk1 is capable of inducing phosphorylation in a number of substrates (6). We aim to identify these substrates and define if Tnk1 phosphorylates these substrates in primary neurons during fetal brain development.
2. Robinson, D. R., Wu, Y.M., and Lin, S.F. (2000). The protein tyrosine kinase family of the human genome. Oncogene, 19(49):55485557. 3. Hoehn, G. T., Stokland, T., Amin, S., Ramírez, M., Hawkins, A. L., Griffin, C. A., Small, D., and Civin, C. I. (1996). Tnk1: a novel intracellular tyrosine kinase gene isolated from human umbilical cord blood cd34+/lin/cd38 stem/progenitor cells. Oncogene, 12(4):903913. 4. Felschow, D. M., Civin, C. I., and Hoehn, G. T. (2000). Characterization of the tyrosine kinase tnk1 and its binding with phospholipase c[gamma]1. Biochemical and Biophysical Research Communications, 273(1):294301. 5. Azoitei, N., Brey, A., Busch, T., Fulda, S., Adler, G., and Seufferlein, T. Thirtyeightnegative kinase 1 (tnk1) facilitates tnfainduced apoptosis by blocking nf?b activation. Oncogene, aop(current). 6. Lionel Arnold (Unpublished results). Simulating the growth patterns of Bacillus subtilis
with a cellular automaton We introduce a cellularautomaton based model for the description
of the migration and growth patterns of colonies of Bacillus
subtilis. The two phases, associated to processes of migration
and consolidations, are described by appropriate rules for
the update of the automaton. We show that it is possible
to reproduce the patterns present in the morphological diagram
for Bacillus subtilis and in particular the ringlike structure
that the colonies adopt in the case of a not very hard medium
and under nutrient abundance. In this presentation, we consider a parabolic system incorporating treatment terms of effector cells and cytokine interleukin2(IL2) in the dynamics among tumor cells, immuneeffector cells and IL2. In this system, we investigate sufficient conditions that the tumor cell could be eliminated. These phenomena can be interpreted by the effect of treatment terms. Furthermore, we demonstrate a numerical simulation to present the mathematical results. A statistical approach to population studies of Chagas
Disease Chagas Disease is an endemic in the South American countries that has affected millions of people. It is transmitted by the vector Triatoma infestans which feeds at night when the victims are caught unaware. It may take several years for the disease to present itself with heart disease, megaesophogus, and megacolon. In this study, we used micro satellite markers with the help of cluster analysis to determine the clonal distribution of the parasite, T. cruzi. Along with the micro satellites, we used the blood meals of the vectors to determine the lineage of the parasite. We used artificial neural networks and contingency test to look for association of the parasite cloned particular feeding types.  A model of cardiac action potential: incorporating the
caveolaeassociated sodium current The contraction of a cardiac cell is initiated by a transient
depolarization of the cell membrane called an action potential.
Action potentials result from the rapid movement of ions
across the membrane through pores called ion channels. Recent
electrophysiological data regarding caveolae, small invaginations
of the cell membrane, reveal that caveolae are reservoirs
of ‘recruitable’ sodium ion channels. As such,
caveolar ion channels constitute a substantial and previously
unrecognized source of sodium current that can significantly
influence action potential morphology. While many mathematical
models of cardiac action potential exist, none take into
account this caveolaeassociated sodium current. In this
talk, a threecompartment ODE model of cardiac action potential
incorporating a caveolar component will be introduced. I
will demonstrate that this model yields results that are
consistent with experimental data and that this model promises
to offer insight into the composition of the caveolar membrane
at the molecular level and into the biophysical mechanisms
underlying some cardiac arrhythmias. Analysis of a DrugDrug Interaction Problem from Pharmacokinetic A two drug interaction is usually predicted by individual
drug pharmacokinetic. An improved drugdrug interaction
prediction method based on a threelevel hierarchical Bayesian
metaanalysis model uses Monte Carlo Markov chain pharmacokinetic
parameter estimation procedure. Underlying present the parameter
estimation procedure is a fast integration method of the
stiff pharmacokinetic equations. In this presentation, we
report the establishment and computation of some lower and
upper bounds using quasi linearization method. We are able
to prove the existence and uniqueness of the solution by
using the perturbation theory of a two real autonomous system.
We discuss the interrelation and the interaction between
the Monte Carlo Markov Chain Pharmacokinetic parameter estimation
procedure and the numerical integration scheme. A metapopulation model for the growth of nassella tussock Nassella tussock is a major pest plant in Australia and
New Zealand. In the Hurunui area of NZ Nassella is managed
by over 800 individual property owners by grubbing (manual
removal) of plants. We develop a metapopulation model of
growth on each property. We show that a mean field model
is not a suitable simplification and variation between properties,
particularly for some model parameters is essential for
realistic results. We present some ideas for management
and control strategies. A Model of the BMP4 and FGF Signaling Pathways in Embryonic
Xenopus laevis A mathematical model of the BMP4 and FGF signaling pathways
during the neural and epidermal development of Xenopus laevis
is presented in this talk. The model consists of a system
of coupled, nonlinear ordinary differential equations. By
using linear stability analysis and bifurcation theory,
the properties of this model are described. Numerical computations
include bifurcation studies, which may be helpful in elucidating
the interactions within the biochemical signaling network
in embryonic Xenopus laevis. Modeling a cell population with intracellular threshold
dependent differentiation The maintenance of a stable stem cell population in the
epidermis is important for the constant regeneration of
the stratified epithelium. Stable cell population size is
regulated by intracelluar proteins e.g. cMyc, and also
by secreted diffusible extracellular signalling molecules
e.g. TGFb. Extracelluar molecules are produced by the
cell population and directly regulate the intracellular
proteins. In this talk we focus on the intracelluar protein,
cMyc, with a threshold value that allows cell differentiation.
A structured model incorporating both levels of regulation
will be presented, and the balance between growth and differentiation
will be discussed. An SIR epidemic model with partial temporary immunity
modeled with delay The SIRepidemic model for disease dynamics considers recovered
individuals to be permanently immune, while the SISepidemic
model considers recovered individuals to be immediately
resusceptible. We study the case of temporary immunity in
an SIRbased model with delayed coupling between the susceptible
and removed classes, which results in a coupled set of delaydifferential
equations. We find conditions for which the endemic steady
state becomes unstable to periodic outbreaks. We then use
analytical and numerical bifurcation analyses, specialized
for delaydifferential equations, to describe the severity
and period of the recurrent epidemics. Modeling of gene dispersal in a natural forest system Due to the growth of using genetically modified plants,
the drastic decline in bee populations, and increase in
habitat fragmentation understanding the movement in genes
via insect pollinators is vital. Using an agentbased model
we examine various biological parameters (e.g. turning probabilities,
target perception, pollen carryover, etc.) and physical
parameters (e.g. target density, target size, flower density,
etc.) on the effects of gene dispersal. We study how these
affect measurements of expected distance, search area covered,
and genetic dispersal within the population. Robust Cell Polarization Cells localize (polarize) internal components to specific locations in response to external signals such as spatial gradients. For example, yeast cells form a mating projection toward the source of mating pheromone. There are specific challenges associated with cell polarization including amplification of shallow external gradients of ligand to produce steep internal gradients of protein components (e.g. localized distribution), response over a broad range of ligand concentrations, and tracking of moving signal sources. In this talk, we will propose models that investigate the tradeoffs among these performance objectives. With our models, strategies for balancing the tradeoffs will be presented. We will also highlight the critical role of lateral diffusion of proteins in the membrane on the robustness of polarization.  The Role of Flightin in Drosophila Native Thick Filament
Flexural Rigidity and Assembly Drosophila Indirect Flight Muscle (IFM), responsible for wing movement, is widely considered among the most powerful muscles in the animal kingdom. Power output of the muscle is highly dependent upon the muscle’s stiffness due to the process of stretch activation. Muscle stiffness is reliant upon the primary proteins in muscle; myosin and actin. We isolated native thick filaments from wildtype Drosophila melanogaster as well as mutants lacking the thick filament accessory protein flightin (fln0). Atomic Force Microscopy images of these filaments were evaluated with an automated analysis algorithm that precisely identifies filament position and shape. The curvature of these filaments was analyzed using statistical polymer chain mechanics in order to ascertain their specific persistence length (SPL), which is an index of filament flexural rigidity. Our data suggests the presence of flightin yields a significant increase (p<.05) in SPL (fln0:1,301µm ?1,805µm, wildtype: 2,446µm ?2,450µm) for newly eclosed flies. The same trend (p<.05) is also seen in 25 day old flies (fln0: 637µm ?557µm, wildtype: 1,672µm ?1,660µm). Our data also shows differences in filament length between the wildtype and fln0 newly eclosed flies (fln0: 3.90µm ?1.33µm, wildtype: 3.00µm ?0.38µm), which suggests that flightin has a role in the assembly of thick filaments. These results raise the possibility that thick filaments are a major contributor to the high resting stiffness of IFM, a characteristic feature of this muscle that underlies Drosophila’s ability to be activated by stretch and oscillate at high wing beat frequencies. A model of CA1 hippocampal neurons with astrocytic input Over time astrocytes have been thought to function in an
auxiliary manner, providing neurons with metabolic and structural
support. However, recent research suggests they may play
a fundamental role in the generation and propagation of
focal epileptic seizures by causing synchronized electrical
bursts in neurons. It would be helpful to have a simple
mathematical model that represents this dynamic and incorporates
these updated experimental results. We have used ordinary
differential equations to create a twocompartment model
of a typical neuron found in the hippocampal CA1 region,
an area often thought to be the origin of these seizures.
The focus is on properly modelling the astrocytic input
to examine the pathological excitation of these neurons
and subsequent transmission of the signals. Parameter Estimation and Data Analysis in an Ecosystem
Model of College Drinking Recently we developed a model composed of five impulsive differential equations that describes the changes in drinking patterns amongst college students. Many of the model parameters cannot be measured directly from data; thus, an inverse problem approach, which chooses the set of parameters that results in the “best” model to data fit, is crucial for using this model as a predictive tool. Here we present a procedure for parameter estimation in this model. The results show that our model provides a good fit to survey data for 32 campuses.  Determining the Correlation between Temporal Changes
in Gravitropism and Auxin Sensitivity in Flax (Linum usitatissimum)
Roots: A Mathematical Approach The successful development of plants depends on the downward
growth of the emerging root, and the upward growth of the
shoot. Such orientation of plant organs in response to the
gravity vector is known as gravitropism. The gravityinduced
spatial configuration is essential for plant growth and
development since it establishes a root system for anchorage,
water acquisition and mineral uptake from the soil, and
a shoot system for the capture of sunlight for photosynthesis
aboveground. We observed that both the gravity response
and sensitivity of flax seedlings deteriorates as roots
age, and we examined the potential correlation with changes
in the sensitivity of root tissue to auxin. Roots of different
ages were tested for their elongation rate, gravitropic
response, and gravitropic sensitivity under a wide range
of auxin concentrations. For curvature measurements, roots
were isolated using image segmentation techniques, and the
angles of curvature were obtained using methods from differential
geometry of curves on the Blum medial axis of the roots.
Accurate characterization of gravity perception and response
under varying conditions would allow us to further investigate
the gravisensing machinery in plant roots. Systems Properties of Signaling pathways in CVB3infected
Cardiomyocytes Background: Coxsackievirus serotype B3 (CVB3), a small nonenveloped singlestranded RNA enterovirus in the Picornaviridae family, is the most significant causative agent of viral myocarditis. The intimate relationship between virus and host makes it difficult to discuss one without considering the other. Viruses must extensively manipulate host cell machinery to support viral replication. Meanwhile, infected cells induce an array of defence mechanisms to battle the invader. We and others have already shown how distinct signaling pathways are exploited by virus or infected cells. Now, we speculate cell signaling pathways are not autonomous units, but conjoined networks. Many hostvirus events are mediated by interaction and crosscorrelation between cellular signaling cascades. Hypothesis: Crosstalk between signaling pathways determines the fate of CVB3infected cardiomyocytes and enable CVB3 to progress through its life cycle. Methods: Murine cardiomyocytes were pretreated and infected with signaling inhibitors and CVB3, respectively, at various timepoints. Viral protein synthesis and progeny release were determined by Western blot and plaque assay, respectively. Virusinduced cell death was assessed by cell viability assay and caspase activity assay. Host protein phosphorylation status was determined by individual phosphoELISA kits. We generated 3dimensional data: 1) components: ten signaling molecules, four host apoptotic responses, and two virus replication indicators; 2) timepoints: shaminfected cells [0h postinfection (p.i.)], viral receptor interaction (0.17h p.i.), internalization (1h p.i.), viral RNA synthesis (8h p.i.), viral protein synthesis (16h p.i.) and virion progeny release (24h p.i.), and 3) 23 different experimental conditions. We utilized the following computational tools: 1) Least Angle Regression Analysis (LARS); 2) Principal Components Analysis (PCA), and 3) Gaussian Graphical Modeling (GeneNet ®), to process generated data. Results: 1) At 0h p.i., the only crosstalk between signaling pathways that we detected was a negative correlation between JNK and NFkB; 2) at 0.17h and 1h p.i., we did not detect a correlation between any of other signaling components ; 3) at 8h p.i., there was a negative correlation between JNKNFkB and positive correlation between AktNFkB, JNKp38 MAPK, AktJNK; both GSK3b and ERK1/2 share CREB as a transcription factor; 3) at 16 h p.i., there were positive correlations between NFkBGSk3b, ??p38 MAPKGSk3b, p38 MAPKNFkB, ERK1/2GSk3b ??and? negative correlation between Aktp38 MAPK, JNKNFkB, and 4) at 24 h p.i., there was a positive correlation between ERK1/2GSk3b ?and a negative correlation between AktHsp27. On the one hand, GSK3b and p38 MAPK merged on CREB as transcription factor; on the other hand, p38 MAPK, JNK and Hsp27 share ATF2 as a substrate. Conclusion: The systematic cataloging of signaling pathways allows us to understand the behaviour of signaling networks in CVB3infected cardiomyocytes. We determined that some of signaling components played more interactive roles than others for instance, NFkB, GSK3b ?and JNK. Applying a systems approach to study complex interactions in signaling networks is yielding novel insights into the interplay between virus and host, and allows for the generation of new hypotheses.  Estimating mutational pathways of carcinogenesis The development of cancer is thought to be a multistep
process of accumulating mutations. We describe this process
by an exponential waiting time model in which the chronology
of events is constrained by a partial order. This mathematical
structure defines the conjunctive Bayesian network, a probabilistic
model accounting for multiple pathways of carcinogenesis.
We introduce a censored version of this model and estimate
model parameters and the underlying partial order from observed
mutation data by an EM algorithm. The expected waiting time
of a given mutational pattern measures the genetic progression
of the tumor and presents a marker of disease progression.
We apply our model to comparative genomic hybridization
(CGH) data from different cancer types revealing characteristic
mutagenetic pathways. Furthermore we evaluate the prognostic
value of the genetic progression score using patient survival
data. Growing Heterogeneous Tumors in Silico 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. Considering the highly complex nature of cancer progression, a multitude of intertumor processes and host tumorinteractions must be incorporated into any computational model that will be of use in a clinical setting. With this goal in mind, we have developed a novel twodimensional hybrid cellular automaton model of cancer growth that incorporates two distinct types of interactions between the tumor and the host. First, the algorithm couples the remodeling of the microvasculature with the evolution of the tumor mass. Second, the algorithm considers the impact that organimposed physical confinement and heterogeneity have on tumor growth. By incorporating the effects of tissue structure, tumor shape and spread is more accurately predicted than when radially symmetric growth is assumed. Finally, we illustrate how genetic mutations can be incorporated into the model and explore the likelihood that different advantageous and deleterious mutations survive in the tumor cell population. Together, this algorithm is a first step in the direction of developing a clinically relevant cancer simulation tool that can be used to test how perturbing certain aspects of the tumor system impact its growth and survival.  Individual based model of factors influencing the territorial
boundary between the harvester ant Pogonomyrmex spp. and
related hybrid lineages Hybridization between species can lead to speciation if
the hybrids are able to successfully compete ecologically
with their parent species. Interbreeding between harvester
ants Pogonomyrmex rugosus and P. barbatus has produced hybrid
lineages whose geographic ranges meet with both parent species
at contact zones. An individual based model will be developed
to investigate the local characteristics of the boundaries
between the parent and hybrid lineages and determine which
biotic and abiotic factors may influence their ecological
success. The model will be validated against distribution
patterns observed in the field. If the model reproduces
the same types of distributions as seen in the field, the
processes included in the model may be important in the
competition between the hybrid and parent lineages. The geometry of bursting in the dualoscillator model
of pancreatic betacells. The rapid increase in the occurrence of Type 2 Diabetes
Mellitus (T2DM) is a major health concern throughout the
developed nations, and most of the world. Impaired insulin
secretion from the endocrine betacells of the pancreatic
Islets of Langerhans is central to the development of T2DM
and is the subject of much investigation. Despite great
advances in the field, the mechanism underlying the pulsatility
of insulin secretion continues to remain controversial.
The work of Artie Sherman et al. has been systematically
elucidating the biophysical basis of secretion for over
two decades. In a recent development, calcium and metabolism
have been proposed as being jointly implicated in controlling
the intracellular dynamics leading to hormone release. A
mathematical model, termed the DualOscillator Model (DOM),
has been put forward that successfully explains much available
data on islet bursting activity.
Habitat segregation between two species of Harvest Ants
and their interspecific hybrids For hybridization to lead to persistent hybrid populations,
there must be some niche differentiation between the hybrids
and parental species. However, hybrid harvester ant populations
originally derived from Pogonomyrmex rugosus and P. barbatus
cooccur regularly with their parental species in the southwestern
region of the United States. In this study we examined a
variety of abiotic and biotic factors that may be involved
in niche differentiation between parental species and hybrid
lineages on a microgeographic scale using six contact sites,
three for each parent species, where both a parental species
and hybrid lineage cooccur in comparable numbers. The parental
and hybrid lineages clustered geographically in patterns
predictable by the environmental factors examined in this
study. Our results suggest that habitat variability may
allow for hybridization to act as a mechanism of speciation. Models for Robust Protein Gradients in the Drosophila
Embryo In early Drosophila development, one of the first specifications
made in determining cell location is the formation of the
anteriorposterior axis, and this event is carried out with
incredible precision, despite many variations of the genetic
regulatory network and environmental fluctuations. My focus
is on the first step in this process, where the protein,
Hunchback (Hb), forms a very sharp boundary at the midpoint
of the embryo, despite receiving ‘noisy’ information
from its known upstream regulator, Bicoid (Bcd). Using systems
of partial differential equations to model the gene network,
we seek an answer to the following inverse problem: given
the ‘robust’ Hb boundary, what conditions does
this place on the regulatory network? While a simple answer
does not likely exist, we provide examples of such networks,
as the result of both numeric searches and analytic techniques,
and an interpretation of the conditions in terms of the
biological system. Simulation of spatially inhomogenous cellular reaction
networks on unstructured meshes Stochastic simulation of reactiondiffusion processes inside living cells are computationally very expensive. We extend an existing algorithm in two ways. First, by making connections to the finite element method (FEM) we are able to conduct simulations on unstructured meshes. The jump propensities can be conveniently obtained by using existing FEM software, and thus the treatment of complicated geometries is made possible. Secondly, in the spatially homogeneous case, hybrid methods have been introduced to facilitate the study of stiff models. We propose a hybrid method for the reactiondiffusion master equation where the diffusion is treated deterministically, when appropriate, for some or all of the species. The connection to FEM has the potential of making this approach highly efficient by utilizing the capabilities of state of the art solvers. We show that the method qualitatively reproduces results obtained with an existing software (mesoRD) that uses Cartesian meshes. In a first Matlab implementation, the hybrid approach is three orders of magnitude faster for a model problem. The results suggest that the method will be an efficient alternative to pure stochastic simulation. Ongoing work includes the integration of the method with finite element software in order to obtain a generic, easytouse framework for both stochastic and hybrid simulation of reactiondiffusion models.  Modeling the dependence of radial oxygen losses from
arterioles on hematocrit Erythrocyte O2 saturation levels at the entrances to capillaries are known to be substantially lower than arterial values. A number of proposed mechanisms for this phenomenon exist, such as the effect of radial O2 losses from arterioles. The goal of this model is to attempt to quantify these radial oxygen losses that take place at the arteriolar level. In particular, three effects were studied for their influence on radial oxygen losses: 1) Spatial distribution of hemoglobin, 2) P50 value of the hemoglobinoxygen dissociation curve, and 3) PO2 of the surrounding tissue. This was modeled by considering a timedependent diffusion equation with a nonlinear source term. The model was studied numerically, through the use of a finite difference approach, with steady state cases evaluated analytically through the use of Green's functions. Using this model, the dependence of oxygen saturation levels on hematocrit was found. In future work, this result will be used in conjunction with an existing model to study the regulation of capillary O2 delivery. This work was supported by NIH grant HL089125.  The Importance of Simulation in Freshman Education Since 1998, studies using models in scientific literature
have increased by more than a fourfold (Keeling and Rohani,
2007). We predict that the strongest effect of math on biology
and biology education will be the extensive use of models
and simulations. Today, integrated platforms and information
systems ranging from Visual Cell to Netlogo and others provide
templates where data, models, simulations, theories, mechanisms,
different pieces of qualitative and quantitative knowledge
are represented in a uniform and transparent fashion, which
makes it easy to experiment, form and evaluate models and
alternative hypotheses. Students without knowledge of advanced
math are able to access and experiment quantitative biology
problems and acquire skills and understanding of basic math
problems. We provide examples of research projects we did
with freshman biology students to introduce them into interdisciplinary
research. These methods are particularly prone to study
the dynamics of such complex and socially important phenomena
as diseases where experimentation is not possible. Indirect relations in ecosystems: An individual based
approach A common way to represent an ecosystem is to build a graph
(or a digraph), where vertices represent compartments and
edges represent specific relations, such as flow of biomass
or energy. However, two disconnected compartments can still
be highly correlated, as they might have multiple common
neighbors. Therefore a graph representation of an ecosystem
may provide a misleading visualization of the actual relation
strength among compartments. There has been efforts to quantify
these so called indirect relations, mostly through linear
algebraic arguments that aggregate flows among all compartments.
Here, we present a novel way to compute the indirect effects
precisely, using a stochastic individual based algorithm.
Particle Tracking Simulation (PTS), a highly capable numerical
algorithm, enables us to track individual particles that
flow in the system, providing very detailed information
on ecosystem organization and function. PTS results are
compatible with the differential equation representation
of the ecosytem, providing an accurate comparison between
our method and currently available measures for indirect
relations. This work is applicable to a wide range of ecosystem
models, as long as the currency is a conserved entity, such
as biomass, energy, N, C, P, etc. Optimal Control Model for Cancer Chemotherapy Subject
to Drug Resistance Optimal control techniques are used to optimize a chemotherapy
treatment regime. Cell cyclespecific chemotherapy is examined
when drug resistance reduces the effectiveness of treatment
over time, and toxicity levels place limitations on the
course of treatment. The governing state equations are developed
from a compartmental model that shows the development of
resistance over time. The optimal control is characterized
for the system, allowing for some numerical simulations. Glioma invasion in vitro Multicellular tumor spheroids (MCTS) have been used as a model system because of their remarkable ability of reproducing the properties of tumors in vivo. Glioma cells, already at an early growth of the tumor, tend to migrate from the primary tumor into the surrounding tissue in different patterns. For example, cells from U87 cellline have been shown to disperse in a radially symmetric fashion from a spherical tumor, whereas mutant U87DeltaEGFR cells form branching patterns similar spokes from a hub. Several models have been suggested to explain the different modes of migration, but none of them, so far, has explored the important role of cellcell adhesion. The present paper develops a mathematical model which includes the role of adhesion and provides an explanation for the various patterns of cell migration. It is shown that, depending on critical adhesion and chemotactic parameters, the migration patterns exhibit a gradual shift from branching to dispersion, as observed in experiments.  Bifurcation analysis of a system of MorrisLecar neurons
with time delayed gap junctional coupling We consider a system of two identical MorrisLecar neurons coupled via electrical coupling. We focus our study on the effects that the coupling strength, g, and the coupling time delay, t, cause on the dynamics of the system. For small g we use the phase model reduction technique to analyze the system behavior. We determine the stable states of the system with respect to g and t using the appropriate phase models, and we estimate the regions of validity of the phase models in the g, t plane using both analytical and numerical analysis.  Separating the Effects of Genetic Drift and Natural
Selection Using a Modification of Tajima's D Statistic A number of statistical measures have been devised to infer
past evolutionary forces from patterns of genetic diversity
in sequence data. One of these measures, Tajima's D statistic,
detects changes in overall genetic diversity, but cannot
distinguish between the impacts of genetic drift versus
natural selection. By analyzing synonymous (Dsyn) and nonsynonymous
(Dnon) mutations separately, we can isolate the effects
of these two evolutionary forces. For codons bearing only
a single observed mutation, that mutation can be easily
classified as synonymous or nonsynonymous. However, this
classification becomes ambiguous for codons in which multiple
mutations have occurred. In this talk, we explore three
strategies for resolving this issue of ambiguity: (i) the
Nei & Gojobori method, which extrapolates synonymous:nonsynonymous
ratios from singlemutation codons to ambiguous codons;
(ii) a genetic codebased method that employs expected frequencies
based on the observed set of codons; and (iii) a mutation
pathwaybased method that averages the number of synonymous
and nonsynonymous mutations over all possible pathways connecting
observed codon pairs. Distributions for Dsyn and Dnon will
be generated under models of specific evolutionary and demographic
scenarios and will then be used to measure our method's
ability to correctly infer the population's history. Mathematical Modeling of the Transcriptional Network
Controlling the Cold Shock Response in Saccharomyces cerevisiae Gene expression is a complex biological process in which cells translate their genetic code into proteins. In this process, cells first transcribe their DNA into an intermediary code known as mRNA, and then the cell translates mRNA into proteins. Involved in this process are transcription factors, which are proteins that increase or decrease the rate at which a cell transcribes a gene. We used mathematical modeling to describe the interactions between transcription factors thought to play a role in controlling the environmental stress response in Saccharomyces cerevisiae. We created a network of 15 active transcription factors that regulate one another, a model that we analyzed by running forward simulations in MATLAB. The concentrations of the individual transcription factors are modeled using ordinary differential equations, which we solved as a system in order to identify the optimal combination of parameters. Each transcription factor’s equation includes a production rate and a degradation rate. The production rate for each gene depends nonlinearly on other genes influencing its production. This nonlinear function is parameterized with a sigmoidal response. The production rates and degradation rates were inferred from experimental data, and the remaining parameters in the sigmoidal response were optimized using a leastsquares algorithm that compares yeast coldshock microarray data to the mathematical model. We performed sensitivity analysis on the model by running the forward simulations with systematically perturbed parameters. We also compared the fold changes of each gene in the original model to fold changes generated when a transcription factor is deleted from the model. This may predict the behavior of a mutant strain of yeast (a strain with the same transcription factor deleted) to cold shock.  Mathematical Modelling of Blood Flow Through Magnetic
Effects In this paper a two layered blood flow model is investgated.
The flow of blood and plasma take place in the core and
peripheral regions respectively. In the present study the
effect of a magnetic field on the blood flow is investigated
using the equation of a magnetic fluid model.The governing
equations are solved by the finite difference method. The
influence of the magnetic field on blood flow in the core
region affects the flow of non magnetic plasma in the peripheral
regions. Use path analysis and regression for wheat characterizes
in dry land condition Key word : path analysis , regression , correlation , wheat,
dry land Models for Antigen Receptor Gene Rearrangement: CDR3
Length Despite the various processing steps involved in V(D)J
recombination, which could potentially introduce many biases
in the length distribution of complementarity determining
region 3 (CDR3) segments, the observed CDR3 length distributions
for complete repertoires are very close to a normal like
distribution. This raises the question of whether this distribution
is simply a result of the random steps included in the process
of gene rearrangement, or has been optimized during evolution.
We have addressed this issue by constructing a simulation
of gene rearrangement, which takes into account the DNA
modification steps included in the process, namely hairpin
opening, nucleotide additions, and nucleotide deletions.
We found that the nearGaussian shape of CDR3 length distribution
can only be obtained under a relatively narrow set of parameter
values, and thus our model suggests that specific biases
govern the rearrangement process. In both Bcell receptor
(BCR) heavy chain and Tcell receptor beta chain, we obtained
a Gaussian distribution using identical parameters, despite
the difference in the number and the lengths of the D segments.
Hence our results suggest that these parameters most likely
reflect the optimal conditions under which the rearrangement
process occurs. We have subsequently used the insights gained
in this study to estimate the probability of occurrence
of two exactly identical BCRs over the course of a human
lifetime. Whereas identical rearrangements of the heavy
chain are highly unlikely to occur within one human lifetime,
for the light chain we found that this probability is not
negligible, and hence the light chain CDR3 alone cannot
serve as an indicator of Bcell clonality. Interdisciplinary Training in Mathematical Biology at
Truman State University Truman State University's new program in Mathematical Biology
trains students to work at the intersection of the life
and mathematical sciences through a combination of coursework
and undergraduate research, with an emphasis on the latter.
This poster will describe the program with an emphasis on
some of its more novel aspects, including its summer research
community, its minor degree, and its field trip program. Recurrent intrahost epidemics in a model of Malaria
with binary immune response We study the intrahost immune response to infection by a single species of the Malaria parasite by considering a mathematical model that accounts for both variantspecific and crossreactive immune response. We first determine the biological conditions that lead to damped oscillations in the host's viral load, which corresponds to recurring but weakening bouts of sickness. In particular, we find that the ratio of the efficacy of the variantspecific immune response to the crossreactive immune response is critical in determining the characteristics of the disease dynamics. We then find that a slow responding immune system, modelled with a fixed delay, can lead to undamped and persistent oscillations in the viral load. We use analytical and numerical bifurcation analyses, specialized for delaydifferential equations, to describe the severity and period of the recurrent intrahost epidemics, i.e., bouts of highviral load and sickness.  Analysis of tumor vascular networks using nonlinear
dynamic. Angiogenesis is a process that involves the growth of new
vascular networks in tumor malignant, Stochastic simulation of interphase microtubule dynamics
in plant systems Microtubules (MT) are a critical component of the cytoskeleton. They serve as structural components within cells and are involved in many cellular processes including mitosis, cytokinesis, and vesicular transport. Plant cells create highly structured MT arrays at the cell cortex without a central organizing center to anchor the microtubule ends. Microtubules are created by polymerization of tubulin. In vivo imaging of individual microtubules in Arabidopsis plants revealed that new microtubules exhibit dynamics at both ends. Polymerization biased dynamic instability at one end and slow depolymerization at the other end constitute a hybrid treadmilling mechanism(1) that results in sustained microtubule migration across the cell cortex. Using the measured polymerization and depolymerization rates and estimated tubulin concentrations, the dynamic properties of the plant interphase array will be simulated. In order to test the organization of the cortical microtubule array, we require an accurate model for the dynamics of the individual MT polymers. Here, we present the results of a dynamic engine that accurately recapitulates the dynamic properties of the MTs as they have been measured in live cells. References:
Mathematical model of interactions between cell volume
regulation and transport in cortical TAL cells We develop a mathematical model of a cortical thick ascending limb (cTAL) cell to study the interactions between ion transport and cell volume (CV) regulation. Because the Na+K+2Cl cotransporter (NKCC2) mediates the Na+ uptake, and its activity is regulated by CVdependent kinases, we hypothesize that transportrelated CV changes should result in compensatory regulation of NKCC2 activity and Na+ reabsorption. The cTAL cell model is based on mass conservation and includes models for the Na+K+ATPase, the Na+H+ exchanger, Cl_HCO3 exchanger, the NKCC2 (A isoform), the K+Cl cotransporter (KCC1), and passive ion fluxes. CVsensitive regulation of the activities of NKCC2 and KCC1 is represented with empirical functions. Model parameters were chosen to yield potentials, cytosolic concentrations, and ionic fluxes consistent with published data. To test our hypothesis, we simulated published experiments which measured the relationship between short circuit current (Isc) and luminal [Cl]. Simulations were done with and without NKCC12 and KCC1 regulation. The agreement between the predicted and measured responses was significantly improved, particularly at luminal [Cl] greater than 75mM, by inclusion of NKCC2 and KCC1 regulation. Moreover, the gain that provided the best fit to the Isc curve yielded regulatory volume decreases consistent with published data. These findings support the idea that CV regulatory responses modulate Na+ transport in cTAL cells.
An Application of Mutational Analysis to Cancer Morphology We use JeanPierre Aubin's theory of mutational equations to develop spatial models of cancer growth. As an initial investigation, we consider a model of a single solid tumor growth in the avascular phase as well as a model of solid tumor growth in the presence of a nearby vascular supply to model the vascular phase.  Linear assumption or dynamic system  A study to sex
ratio in China The sex ration in human population is often assumed to
be equal in the study of sexually transmitted disease (STD).
It is not always true in developing country like China.
A mathematical model is constructed to describe the change
of human population. The simulation shows that the growth
of male and female population in sexually mature stage could
be estimated linearly while the total population and other
sexgender groups behave differently. Efficient combination of antiangiogenic therapy and
chemotherapy: A mathematical modeling approach Recent experimental and clinical studies have shown that the combination of cytotoxic therapies and antiangiogenic agents will probably be the most effective strategy in the treatment of malignant tumors. However, there are vastly different outcomes based on, at least partially, dosages and treatment times. A mathematical model may help to better predict the results of a wide array of possible combinations. In this direction, we have developed a simple model including tumor cells and blood vasculature, as well as proangiogenic and antiangiogenic factors. The antiangiogenic therapy is considered either to be blocking/deactivating proangiogenic factors or removing endothelial cells directly while the chemotherapeutic agent attacks tumor cells. We also discuss nanocells that include both forms of treatment in one delivery system with appropriate drug release profiles.  Cofilin, a protein that severs actin filaments to create
new barbed and pointed ends, has long been identified as
a regulator of steady state cytoskeleton dynamics by increasing
the turnover of Gactin monomers. Recent work indicates
that cofilin activity in carcinoma cells is stimulated by
a transient phospholipase(PLC)dependent response to a chemoattractant
gradient, such as EGF. This cofilin pathway is responsible
for an early peak of barbed ends at the leading edge of
a cell which is further amplified by a coupled Arp2/3 pathway
to sustain directional movement. Cofilin has then emerged
as a key player in the directional sensing of invasive tumour
cells and its overall activity is hypothesized as a major
determinant of the metastatic phenotype of tumour cells.
We propose several models of the dynamics of the cofilin
pathway; the eventual objective being to work with existing
cell polarity models in order to predict possible tumour
cell phenotypes. Estimation of growth parameters of the Drosophila's
wing disc development from a sequence of micrographs using
the Growth as Random Iterated Diffeomorphisms Model According to a mathematical model for biological growth,
called GRID, growth patterns are composed of smaller, local
deformations, each resulting from elementary biological
events (e.g.,cell division). A large number of such biological
events, each ocurring randomly and independently from one
another, results in a visible growth pattern or biological
shape changes observed from the image data. Given a sequence
of micrographs reflecting the dynamics of Wingless expression
pattern in the growing Drosophila's wing disc we estimate
the underlying optimal diffeomorphic transformation using
a visible growth law derived from the GRID Model. We demonstrate
the estimation of the GRID parameter, called growth power
directly from the image data of biological growth. Then
the growth induced transformation is obtained from the estimated
growth power distribution in the growing wing disc. Harmful Mating Strategies in Hermaphrodites Cost to females due to damaging male mating behaviour is
commonly associated with sperm competition and conflict,
but the precise function is not well understood. This conflict
between male and female is especially important in hermaphrodites,
because individuals can simultaneously take both sexual
roles. We consider the hypothesis that harm inflicted during
mating is a negative side effect of a trait that benefits
the male function. Here, we generalise an existing model
for sperm competition to encompass the harmful mating tactics
that are commonly found in simultaneous hermaphrodites.
Harm is modelled by a probability of death for the sperm
recipient following a mating. We calculate Evolutionary
Stable Strategies (ESS) for the level of harm, along with
resource allocation to male and female functions. We observe
that harmful mating should be associated with multiplymating
species in which ability to displace sperm, without the
use of a harmful mating tactic, is low. Alternatively, if
the harmful mating tactic is more efficient at promoting
sperm displacement, the ability to displace sperm without
the use of a harmful mating tactic becomes less important.
It has been previously shown that resource allocation to
male and female function can tend to equality in hermaphrodites.
An unexpected outcome is that the model predicts that harmful
mating tactics favour a considerably more female biased
resource allocation. Although Bateman's principle implies
that an increased allocation to female function should increase
the number of offspring produced and hence the fitness of
the population, the model instead shows that harmful mating
tactics more than countercompensate, so leading to reduced
fitness and a greater possibility of extinction when competing
with other species for a limited resource. Parallel Biological Simulations on the Graphics Processing
Unit Electrophysiological simulations and parameter estimation
are areas where massively parallel simulations can have
a profound impact. One method for massively parallel simulations
is a network of computers. Here we describe an alternative
method for massively parallel biological simulations using
the Graphics Processing Unit (GPU). We are able to run excitable
cell systems with thousands of cells in parallel on the
GPU at a fraction of the time required for serial simulations
on a workstation. We will discuss applications of the GPU
to areas such as parameter searching and simulations of
networks of coupled neurons. Spatial patterns in stagestructured populations with
densitydependent dispersal Spatial segregation among life cycle stages has been observed
to occur in some stagestructured species, including species
of the flour beetle Tribolium. We explore stagestructured,
integrodifference equation models that incorporate densitydependent
dispersal and investigate the mechanisms that can lead to
spatial patterns in a homogeneous habitat, including patterns
that have separated life cycle stages. Methods to analyse nucleotide sequence data on HIV retroviral
recombination. Retroviral recombination plays an important role in the
evolution of HIV1 by diversifying the viral quasispecies.
Recombination can accelerate escape from immune pressure
and antiretroviral therapy, which can lead to treatment
failure. Previous experimental approaches to measuring recombination
have often employed large gene insertions, and measured
gene activation or inactivation rates. We have developed
a novel HIV1 marker system by making a small number of
codon modifications in gag and pol, to mimic the recombination
between closely related viral quasispecies in an infected
individual, where viral genome sequences and structure are
highly related. We can thus obtain direct sequence data
showing recombination over multiple gene segments. We formulate
statistical tools to calculate an öptimal recombination
rate" that reproduces experimental recombination frequencies,
taking into account the length over which recombination
is measured and the possibility of multiple template switches.
We used a bootstrapping approach to give a robust estimate
of recombination rates using 248 and 268 sequences for gag
and pol respectively. Our system of multiple markers allows
recombination rates to be estimated along different regions
of the genes. We compared the optimal recombination rate
over the entire gene to rates within specific gene segments
to determine the existence of recombination hotspots. Although
our preliminary results suggest that recombination rates
may vary along the genes, this was not significant. We also
investigated the effects of specific conditions and gene
modification, and found that deletion of the dimerization
initiation site (DIS) significantly reduced the recombination
rate in gag (p < 0.05), and that recombination is significantly
higher in macrophages than in lymphocytes in both gag and
pol (p < 0.05 for both). The Dynamics of a OnePredator TwoPrey Model for Integrated
Pest Management We present a onepredator twoprey model for integrated
pest management. Features of this model include stage structure
for the predator species and one of the prey species and
a birth pulse (rather than continuous growth) for the stage
structured prey species. We demonstrate the existence of
total pest eradication solutions and permanent solutions.
We also investigate the effects of model parameters through
the analysis of bifurcation diagrams. Inverted fish biomass pyramid in coral reefs Global warming and fishing have made a negative impact
on coral reefs around the world. The diversity and biomass
of coral reef fish is directly connected to the magnitude
of coral reef cover in their local environment. It has been
recently observed in pristine coral reefs that the biomass
of fish is dominated by carnivorous fishes. This inversion
of the fish biomass pyramid is in contrast to coral reefs
where commercial fishing is practiced. We provide a predatorprey
model which shows the connection between the size of coral
reefs and biomass pyramid of coral reef fishes. Modelling of the population dynamics with complex structure Many species of animals produce a small number of offspring and take care of them. This phenomenon is natural for many species of mammals and birds and forms the main difference between the behavior of a population taking care of offspring and that of a population without maternal or parental duties. Mammals and birds feed, warm, and defend their young offspring from enemies. If one of these natural duties is not realized, young offspring die, and the population vanishes. For many species of mammals only females take care of their young offspring. Some species of mammals and birds care of their offsprings in couples. We discuss a discrete newborn setbased deterministic model
taking into account age, number of offsprings, and care
of them. The model consists of integropartial differential
equations subject to the conditions of integral type. The
number of these equations depends on the biologically possible
maximal newborn number of the same generation produced by
an individual. Analytical and numerical results will be
discussed. Analyzing, Mining and Modeling Medical Therapeutic Data
for Quantification and Reproducibility Osteopathic manipulative medicine has been used for over
100 years to treat an array of medical conditions. Anecdotal
reporting in osteopathic literature indicates significant
therapeutic benefit; however, there has been little quantitative
research conducted to verify these claims. Current work
at the A.T. Still Research Institute focuses on providing
a strong evidence base for manipulative diagnosis and treatment
essential to the future of osteopathic practice. To assess
the validity and accuracy of osteopathic diagnostic tests,
specialized digital cameras and pressuresensitive pads
are used to collect precise threedimensional coordinates
of specific points on the practitioner's hands as well as
the forces applied during palpation. This new instrumentation
generates vast amounts of raw data available for mining,
analysis and visualization, far too much to be processed
by hand. Key challenges in this work include signal processing
of the raw data and merging of multiple data streams into
a coherent information stream, pattern recognition in the
information stream to identify palpation session milestones,
and data visualization strategies. Current work has focused
primarily on signal processing, pattern recognition and
visualization of the threedimensional camera data stream
during a diagnostic session. A system was developed to allow
practitioners to visualize the threedimensional movement
of their hands and select points at where palpations begin
and end. Visualization of those sections of data is then
produced along with reports including displacement, duration
between a single palpation, as well as the specific location
of each identified landmark along the body. Future work
aims to incorporate the pressure data stream. Carnivore Hunting Mode and Plant Species Coexistence Indirect effects of top predators is increasingly being invoked as an important determinant of plant community structure and attendant ecosystem function. Topdown effects of predators on plants can be mediated by herbivore prey in two general ways that are related to predator hunting mode. Actively hunting predators cause largely densitymediated indirect effects by direct lowering the abundance of herbivores impacting plants. Sitandwait ambush predators largely cause traitmediated indirect effects by causing herbivore foraging shifts to avoid predation risk. We explore here, using a series of dynamical systems models, the implications of indirect effects propagated by carnivore hunting mode on plant species coexistence. We then examine how these effects singly (i.e., an identity effect) and in combination (i.e., a multiple predator effect) influence plant species coexistence.  Simulation of mRNA Migration in Subnuclear Environment We study a mathematical model for mRNA translocation in
the nucleus from the site of synthesis to a nuclear pore
where it is exported to the cytoplasm. The free diffusion
model which has been the dominant hypothesis for quite some
time is compared to one in which the nuclear skeleton and
chromatins confine the mRNA movement. The results show that
chromatin serves as a barrier to mRNA movement away from
the nuclear pore complex, hence enhancing early exit but
keeping entrapped particles for longer; on the other hand,
a bias towards diffusing in the directions perpendicular
to the nuclear envolope, simulating the effect of a proposed
nuclear skeleton, has little effect on the exit time. A Mathematical Model of Erythropoiesis Subject to Malaria
Infection There have been numerous mathematical studies on the dynamics
of erythropoiesis. The same can be said of the dynamics
of malaria infection within a particular host. Surprisingly,
there are no detailed mathematical studies on how these
processes affect each other. In this study, we develop a
mathematical model of erythropoiesis under the influence
of malaria infection. The model takes the form of six coupled
equations. Two are firstorder, hyberbolic, partial differential
equations describing the precursor and mature erythrocyte
populations. The remaining four are ordinary differential
equations describing the erythrpoietin concentration, the
parasite population, the infected erythrocyte population,
and the body's immune response. Modeling the Effects of Genetic Drift and Natural Selection
with Discrete Simulation To obtain distributions against which to compare our calculated
Dsyn and Dnon values, we constructed a simulation that models
the effects of selection and genetic drift over time. This
software provides the capability to integrate and model
several different evolutionary patterns such as natural
selection, genetic drift, or any combination of these. A
modelspecific function determines the reproductive fitness
of each individual, and a realvalued matrix controls both
the degree of reproductive isolation of subpopulations and
changes in population size. By combining these parameters,
we can simulate both simple and more complex scenarios;
for example, directional selection occurring within partially
isolated subpopulations. After many model runs under a specific
scenario, we acquire statistical distributions of our modified
D statistics. Using Bayesian analysis, we then calculate
the likelihood of the observed D statistics under each of
the evolutionary scenarios to infer the population’s
demographic and evolutionary history. Although our model
was constructed to reflect specific biological features
of HIV evolution, we anticipate that our extension of Tajima’s
analysis will have broad applicability. The Interaction Between Influenza Hemagglutinin (HA)
Fusion Peptides and a Lipid Bilayer Membrane The microscopic level interaction between influenza Hemagglutinin
(HA) fusion peptides and a lipid bilayer membrane is important
for the membrane fusion process, which is a key step of
the viral infection. We use a coarsegrained molecular dynamics
(CGMD) simulation method to study the interaction between
HA fusionpeptides and a phospholipid bilayer membrane.
With CGMD, we have been able to simulate a relatively large
piece of membrane for a sufficiently long time period and
with more than one peptide embedded in the membrane. We
obtained a kinkedshaped conformation of the peptide with
the kink at the level of phosphate group, consistent with
experimental NMR study. A presence of fusion peptides inside
the membrane may cause bilayer thinning and lipid molecule
disorder, which are required for the fusion activity. Peptides
tend to come close to each other required for forming clusters
as seen in many experiments. Analytical methods for comparing samples of the T cell
receptor repertoire The hyperbolic effect of density and strength of interbeta
cell cell coupling in islet bursting The insulin producing beta cells reside in pancreatic islets, with tight interbeta cell couplings. Each human islet contains several thousands of beta cells. Synchronized bursting from all beta cells in each islet is the basis of regulated insulin release. Increasing evidence is indicating the importance of islet morphology in its function, and the need for quantitative investigation. In this study we utilized a new 3D hexagonal closest packing (HCP) cell cluster model to examine islet bursting characteristics and the cluster architectural parameters including number of beta cells n_beta, number of interbeta cell couplings each cell has nc, and the coupling strength gc. We simulated beta cell clusters of different sizes ranging from 1343, gc spanning from 01000 pS, and nc varying between 012. From the resultant betacell responses, we quantified three significant functional measures – fraction of bursting ?cells fb, synchronization index lambda and bursting period Tb. Our results suggest that the bursting characteristics depend quantitatively on the cluster architecture in a nonlinear fashion. Specifically, we investigated the role of nc and gc, as these are impaired under pathological conditions like diabetes. We discovered a hyperbolic response to the combined stimulus of nc and gc. Based on this we defined a “cluster coupling index” or CCI. CCI describes the mechanical integrity of gap junctions among betacells and is critical to the robustness of islet oscillation and synchronization. We propose CCI as an important functional islet predictor
that has the potential of providing insight into the compensatory
mechanism of islets during the onset of diabetes and disease
progression. It may also hold the key to targeted drug delivery
for altering either gc or nc to preserve islet functionality. Fast diffusion prevent blow up in chemotaxis In this work, we propose a new mechanism to prevent blow
up in a chemotaxis model. Based on biological relevance,
we show that fast diffusion in chemotaxis can generate pattern
formation and solutions of the resulting model stay bounded.
We will show both numerical and theorectical results. Heterogeneity and HIV drug resistance The emergence of drug resistance for HIV patients has led to the development of a range of drug types, each targeting a different stage in the production of viral particles within the body. Amongst the most common drugs are reverse transcriptase inhibitors which reduce the infection rate of susceptible cell targets and protease inhibitors which reduce the production rate of virus particles from infected cells (Gazzard, 2006). In addition to selection pressure on HIV to produce drug resistance strains, the wild type virus has an unusually large mutation rate in the absence of any drugs (Larder et al., 2001) which significantly complicates the problem of developing drug regimes to minimize viral load in a patient. When considering viral loads within the body, it is often useful to use a compartmental model which can distinguish loads in the blood stream and in key body organs. Previous models which have taken a compartmental approach have demonstrated the possibility for different viral loads in different compartments in the presence of drugs (Calloway and Perelson, 2002). Here we extend this idea using the standard viral dynamic model of Nowak and May (2000) and demonstrate that drugs are not necessary to obtain such heterogeneity. Instead, by considering different cell target types in the different compartments, heterogeneity in viral load can emerge. Parameter estimates obtained from published data are used to demonstrate this behaviour numerically. We extend the idea to consider the competition of different viral strains within the body. We discuss the results of this modeling, in particular focusing on the way in which drug and cellular heterogeneity affect the proportions of wild type and resistant strains within the body. References
 A SemiAutomated Procedure for Segmenting
Early Embryogenesis in Caenorhabditis elegans
by Alexandra Wehrman Truman State University Coauthors: Kurt Warnhoff, Dr. Scott Thatcher, and Dr. Tim Walston An understanding of the forces acting on cells
in the early embryo can provide important information for
how cells interact to determine their shapes, movements and
fates. These forces can be physical and genetic, as well as
intracellular or extracellular. The early Caenorhabditis elegans
embryo provides an excellent environment to explore the forces
acting during embryogenesis and to develop techniques and
models that can be applied later to more advanced biological
events. We report the continued development of a fourdimensional
GGH (GlazierGranierHogeweg) model to simulate the fourcell
stage of embryogenesis. In addition, a semiautomated procedure
for the segmentation of fourdimensional differential interference
contrast (DIC) microscopic data has been developed. A precise
and accurate segmentation scheme offers many opportunities
for the quantitative analysis of early embryogenesis and other
cellular systems. Our segmentation technique incorporates
a combination of level set and watershed methods to properly
delineate cells and cellular components of the embryo in DIC
micrographs. Segmented data serves as an input into the current
GGH code and data from many embryos are needed as a source
of calibration and validation for the model. This segmentation
technique for DIC images of the C. elegans embryo should also
be applicable to DIC images of other embryos or biological
samples.
Date received: June 27, 2008
 Inside GIS: Habitat Parameterization and
Metapopulation Modeling of a Rare Winter Annual
by Brett L. Wiley Truman State University Coauthors: Jonathan D. Vollmer, Truman State University; Dr. Michael J. Adams, Truman State University; Dr. Michael I. Kelrick, Truman State University Metapopulation models have become standard
tools for biological conservation. These models require knowledge
of both occupancy and flux of individuals among patches of
suitable habitat. For animal species, estimation of these
parameters is reasonably straightforward. However, for plants,
it is impracticable to follow seed fates, and therefore difficult
to build realistic metapopulation models. Even so, we are
assembling a metapopulation model for the federally threatened,
rare, winter annual plant species, the microhabitat endemic
Missouri bladderpod (Lesquerella filiformis). Our model simulates
a permanent grid of 963 5 X 5m cells. Using a Geographic
Information System approach, we used four years’ empirical
data characterizing percent cover of cells’ habitat attributes
to classify a cell as one of four subjectively defined microhabitats
for which microhabitatspecific demographic data had been
collected, or to exclude it from the simulation. Microhabitatspecific
vital rates are computed by intraannual data that have been
combined to form interannual transition values that preserve
measurement error associated with the field data collection.
Through model simulations incorporating environmental stochasticity
we can produce a distilled probabilistic projection of the
time trajectories of population size of the entire grid. Our
model incorporates a novel approach to simulating seed dispersal
and habitat conditions, such as removing young cedars, to
provide land management prescriptions for suitable L. filiformis
habitat.
Date received: June 30, 2008
 Game theory of female guarding: the role
of female choice
by Lev Yampolsky East Tennessee State University Coauthors: Mahul Chakraborty, Daniel Scantlebury, Jing Zhu and Tracy Ivy We present a game theory model of the evolution
of monogyny in the form of female guarding by males, in the
situation in which guarding is not 100% efficient and females
can therefore exercise at least some choice. Investment of
time and effort into guarding of a single female at the expense
of future copulations is not beneficial unless there is some
factor impeding polygynous males' fertilization success. Previous
models, developed mostly to describe monogyny in redback spiders
(Fromhage et al., 2005, 2008), focused on malebiased sex
ratio and male mortality between matings as factors limiting
success of polygynous males. We consider a situation in which
females evaluate mates and the probability of mating depends
on the duration of courtship, giving the advantage to femaleguarding
monogynous males. We also assume that females can mate more
than once, so both monogynous and polygynous males can experience
sperm competition. While applicable to a variety of organisms,
the model is tailored to describe mateguarding in gammarids.
Unlike spiders, in which monogamy is enforced after mating,
gammarid males have to guard a female before mating can occur.
In a twoperson game with pure strategies (monogyny, or "guard"
and polygyny, or "seek"), depending on the shape
of relationship between courship time and mating probability,
either both or neither "guard" and "seek"
strategies may be the ESS. Accelerating returns on courtship
time create an advantage for the "guard" strategy,
while diminishing returns benefit the "seekers".
A multiplayer mixed strategy game, however, never predicts
a mixed ESS, suggesting that female choicemediated guarding
evolves under a restricted set of circumstances as an allornothing
strategy.
 Teaching Math to Biologists and Biology
to Mathematicians: When Needed and As Much As Needed
by Lev Yampolsky East Tennessee State University Coauthors: Istvan Karsai, Edith Seyer, Karl Joplin, Laura Catron and Brandy Warner Traditional biology curriculum leaves a gap
between introduction of mathematical concepts within Calculus
and Probability courses and application of these concepts
to biological situations. Likewise, a Math major willing to
get exposed to biological applications will have to survive
a lot of biology before mathematical tools and ideas can be
put to work. Even less likely is a typical undergraduate student
to have a chance to apply mathematical concepts in research
situations. This results in poor retention of knowledge and,
more generally, lack of a common language for collaboration
between traditionally educated biologists and mathematicians.
We report here two concurrent interacting projects unfolding
at ETSU: an NSFfunded undergraduate research program Talent
Expansion in Quantitative Biology and an HHMIfunded curriculum
development project aiming at creating a three semester integrated
Biology and Math course (SYMBIOSIS I, II, III) to replace
introductory Biology, Statistics and Calculus classes traditionally
taught to Biology majors. In the SYMBIOSIS curriculum, the
students get credit for both the Biology and Statistics (SYMBIOSIS
I) or Biology and Calculus (SYMBIOSIS II) in the same class.
Traditional order of presentation of biological material has
been significantly changed to accommodate the more logical
order of introducing mathematical concepts, from algebra and
probabilities, to elementary calculus, to differential equations
and linear algebra. In Talent Expansion program emphasis is
on application of mathematical tools to problemsolving situations.
We present examples of research and exam problem highlighting
this integrated approach.
Date received: June 24, 2008
 A Mathematical Model to Relate SerumMediated
Bacterial Killing with Anaphylatoxin Elaboration
by Suellen Yin, Alex Jacobson University of Michigan Coauthors: Suellen Yin, Alex Jacobson, Patrick W. Nelson, John G. Younger Our study aims to quantitatively analyze the
kinetics of the Complement Cascade, the human body’s
way of destroying foreign pathogens. The bacteria used in
this study, Klebsiella Pneumoniae, are commonly found as a
cause of blood infections. Using fluorescently labeled bacteria
and enzymelinked immunoassays, a reaction mixture of bacteria
and human sera was created to obtain highresolution measurements
of bacterial growth and complement protein binding. This data
and several assumptions about the interactions of the immune
system were combined to develop and fit parameters for a pharmacokinetic
mathematical model.
 Quantifying the fitness of influenza drugresistant
mutants from plaque assay data
by Karen Yip Department of Physics, Ryerson University Coauthors: Catherine Beauchemin, Ryerson University, and Guy Boivin, CHUQCHUL and Universite Laval An increasing fraction of circulating and
emerging influenza strains are resistant to antiflu drugs.
To assist in developing public health measures to contain
a potential flu pandemic, epidemiological modellers will need
to make accurate predictions of the size and rapidity of emergence
of drugresistant mutant strain populations. This requires
accurate quantitative measures of the parameters responsible
for the fitness impairments/enhancements of these mutants.
Differences in fitness between strains is typically assessed by comparing the diameter of the plaques produced by different strains in infection plaque assay experiments. The aim of our work is to develop a tool which could translate differences in plaque diameter to a difference in a parameter controlling viral reproduction in these strains (e.g., viral attachment rate, production rate, or release rate). Here, we present the first step of this project which consisted in developing an agentbased model to mimic an in vitro infection plaque assay setup. Our approach should also be applicable to other infection systems (e.g., SARS, metapneumovirus), and could be used to rapidly quantify the virulence of emerging strains. Date received: June 26, 2008
 Mathematical modeling of animal morphogenesis;
pattern formation on the cellbased growing field
by Eiichi Yoshimoto Nagoya University Coauthors: Shigeru Kondo (Nagoya University) There are many mathematical models proposed
to explain the pattern formation of animal development. In
many cases, the numerical simulation studying these models
was done in the fixed and continuous fields. However, in the
real morphogenesis, the field (embryo) is the aggregate of
the cells, and the size and the shape of the field changes
by the division, death and migration of the cells. To do a
more realistic simulation of the animal morphogenesis, we
need to incorporate these phenomena into the simulation of
the pattern formation. On this purpose, we developed a platform
of the simulation that deals the behavior of the cells and
calculates the whole embryo shape automatically. This system
enables us to simulate the morphological changes in more realistic
condition. By applying a reactiondiffusion model to this
system, it is possible to reproduce the early development
of some animal species.
Date received: June 28, 2008
 To Investigate the Genetic Variability
and Spatial Distribution of Tubifex tubifex
by Jiaxin Yu University of Vermont Coauthors: Lori Stevens (University of Vermont) Nilanjan Lodh (University of Vermont) Max Droppman (University of Vermont) The objective of this research is to compare
the prevalence of Myxobolus cerebralis infection in worms
collected from Montana vs. Vermont, and to use GIS to determine
if the spatial distribution of Tubifex tubifex in Vermont
is different than in Montana. The Batten Kill in Manchester,
Vermont was previously tested positive for Myxobolus cerebralis,
and five sites on the river were chose as sample collection
sites. During sample collection, streams will be divided into
100m sections, and samples will be collected using kicknets.
Twenty worms will be collected from each site. Habitat assessment
will also be carried out on each site. Nested PCR for 18S
rDNA of M. cerebralis and gel electrophoresis are used to
screen the T. tubifex to determine whether they are positive
for the parasite. GIS will be used to compile habitat information
to determine whether there are similarities of habitat characteristics
between Montana and Vermont. This research is still ongoing,
samples from Montana have been analyzed, the results are yet
to compile.
 A New View of CDC's Plan of Elimination
of Syphilis
by Ruijun Zhao Purdue University The CDC launched the National Plan to Eliminate
Syphilis from US in October 1999. In order to reach their
goal, a good understanding of transmission dynamics of the
disease is necessary. Breben et al. supported the plan by
showing that no cycling occurs for syphilis based on a SIRS
model. We study three suboptimal models, taking care of partial
immunity, vaccination, and relapse of secondary lesions. Our
models suggest that a backward bifurcation very likely occurs
using the estimated epidemiological parameters for syphilis,
which may explain the resurgence of syphilis after mass treatment.
Occurrence of backward bifurcation brings a new challenge
for the CDC's plan  a balance between treatment of primary
and secondary infection and vaccination development and health
education. Our models support the premise that development
of effective vaccine and health education enhancing biological
and behavioral protection against infection in risky populations
is amongst the best ways to achieve the goal of elimination
of syphilis from US.

cmm@fields.utoronto.ca

