Poster Session
04:45 - 05:05

Baek, Seunghyeon (Mathematics, Korea University, South Korea)
-Authors: Inkyung Ahn, Wonlyul Ko and Seunghyeon Baek, Korea University, South Korea
-Title: Stationary pattern and stability in a tumor-immune interaction model with immunotherapy
A diffusive tumor-immune system with immunotherapy is investigated under homogeneous Neumann boundary conditions. The large time behavior of nonnegative equilibria and the persistence of the solution in the time-dependent system are studied. Especially, a sufficient condition for the tumor-free states is provided. Furthermore, for this coupled reaction-diffusion system, we obtain the results for the existence of nonconstant positive steady state solutions in case that the parameter for immunotherapy effect is small.

Byun, Jonghyuk (Mathematics, University of Cincinnati)
-Authors: Donald A. French, Jonghyuk Byun, M.Kupferle, Nick G. Cogan, Sookkyung Lim
-Title: Fluid motion in an urban pipe with various surfaces
-Abstract: We investigate the motion of the fluid dynamics in an urban pipe system in which the geometry of the pipe surfaces varies. The fluid motion is compared in two different types of surfaces, cylindrical surface and curved surfaces. We expect the shear force near the surface to be influenced by the fluid motion and hence the wall shear stress may affect on the thickness of the bioflim along the pipe surface.

Chen, Duan (Department of Mathematics, Michigan State University)
-Title: Multiscale Modeling and Simulation for Proton Translocation in the Ion Channel
Aiming at the special properties of the proton and unique transport mechanism, a general multiscale partial differential equations model, containing classical and quantum mechanical theories, is proposed to simulate the translocation of protons in the ion channel with reasonable biological assumptions and approximations. Several associated numerical schemes are employed to solve the model numerically with high accuracy and efficiency. At last, the validity of this model is tested through a specific proton channel, the well-known Gramicidin A, by the channel electrostatic profile and conductance. With parameters taken in the physiological ranges, the simulation results agree with the experimental data well. The limitation of this model will be addressed in future work.

Du, Huijing (Mark Alber group, Mathematics, University of Notre Dame)
-Authors: Hujing Du, Mark Alber, Zhiliang Xu
-Title: Multiscale Models of Bacterial Swarming
We present an off lattice stochastic model which incorporates the different motility engines and the reversing capability to examine the swarming of M. Xanthus. The model also accounts for the interactions of individual cells with the slime on the surface left by other cells. Simulations involving the variation of cell density, aspect ratio, and reversing period were made and we present some of the results including the optimization of M. Xanthus reversing period at eight minutes which was observed experimentally.

Holmes, William (Mathematics, Indiana University)
-Title: A 3D computational model of the Mammalian Cochlea with Asymptotics
We seek to build a computational model for the simplified Mammalian Cochlea with the standard coupled fluid-plate equations as our base. Physiological data shows a clear wave nature in the response of the basilar membrane to stimulus. We seek to explain the presence of this wave nature and use it as inspiration for a 3D numerical solver. The results of simulations along with asymptotic arguments suggest a relationship between the form and function of the cochlea which we compare to physiological data.

Hengenius, James (Gribskov and Rundell Labs, Agricultural and Biological Engineering, Purdue University)
-Authors: James Hengenius (*), Ann E. Rundell, Michael Gribskov, and David M. Umulis
-Title: Effects of a realistic 3D domain on models of Drosophila melanogaster gap gene regulation
The fruit fly Drosophila melanogaster is a model organism for studying spatio-temporal dynamics of animal development. In the gap gene regulatory network, an initial non-uniform distribution of the transcription factor Bicoid controls downstream expression of additional interacting transcription factors. This leads to the formation of non-uniform protein distributions along the anterior-posterior axis of the embryo. Previous studies have considered gap gene regulation as a reaction-diffusion system in one dimension, fitting models to protein expression data from a limited lateral region of the embryo. While these models agree with data in the sampled lateral region, the embryo has a complex three-dimensional geometry. Because poor agreement over the full embryo geometry would indicate incomplete understanding of gap gene regulation, we evaluated existing model structures over this domain. Additionally, we optimized model parameters on the 3D domain. We first implemented a full 3D model using the finite element method with a mesh derived embryonic nuclei positions. Model output was fit to expression data from the Quantitative Spatiotemporal Gene Atlas (Fowlkes et al., 2008) by minimizing a sum-of-squared-error function. Model outputs from the best parameter sets were compared to results using previously published 1D model parameters. While previously published parameter values recapitulated data in the lateral region, the model deviated from data over most of the 3D domain. Our parameter optimization recovered parameter sets that fit the full 3D model better than previously published parameters. Our findings indicate that the current models of gap gene regulation are incomplete and must be revised to account for geometric effects and possible genetic interactions occurring outside the lateral region.

Im, Jeong Sook (Mathematics, Ohio State University)
-Title: Boundary integral method for shallow water and evaluation of the KdV equation in random wave field
Consider the two-dimensional incompressible, inviscid and irrotational fluid flow of finite depth bounded above by a free interface. Ignoring viscous and surface tension effects, the fluid motion is governed by the Euler equations and suitable interface boundary conditions. A boundary integral technique(BIT) which has an an advantage of reducing the dimension by one is used to solve the Euler equations. For convenience, the bottom boundary and interface are assumed to be 2pi-periodic. The complex potential is composed of two integrals, one along the free surface and the other along the rigid bottom. When evaluated at the surface, the integral along the surface becomes weakly singular and must be taken in the principal-value sense. The other integral along the boundary is not singular but has a rapidly varying integrand, especially when the depth is very shallow. This rapid variation requires high resolution in the numerical integration. By removing the nearby pole, this difficulty is removed. In situations with long wavelengths and small amplitudes, one of the approximations for the Euler equations is the KdV equation. I compare the numerical solution of Euler equation and the solution of KdV equation and calculate the error in the asymptotic approximation. For larger amplitudes, there is significant disagreement. Indeed, the waves tend to break and the boundary integral technique still works well. The comparison is also done in random wave field. The strong nonlinearity has made a huge difference in the power spectrum between Euler equation and KdV equation.

Jordan, Benjamin (Department of Organismic & Evolutionary Biology, Harvard University)
-Title: Coupling tissue growth and reaction kinetics to model chick limb development
The limb of the chicken (G. gallus ) is a model organism in developmental biology used to study the patterning of tissues, cell specication, and cell fates. The developing limb bud tissue responds to protein-gradients in a concentration-specic manner. Amongst the myriad cellular responses to these signals, division, dierentiation, death, and changes to the extracellular matrix are crucial to our understanding. These responses feed back into both the chemical interactions and the material properties of the growing limb bud. To understand the interplay between growth and patterning, we have developed a model that couples the production, diusion, reaction and advection of the relevant chemical species to the growing tissue domain. By assuming that growth is a plastic-process which occurs beyond some given yielding threshold, we model the tissue as a viscous free-boundary uid with a volumetric source, which is in turn dependent on the concentration of specic growth factors included in the kinetics network. In this poster, I describe the mathematical model, discuss the parametrization, and explain the algorithm for the numerical solution. Specically, details on the remeshing, convection, and split-time stepping are discussed. Preliminary results suggest that both the shape and protein distribution can be described accurately by such a model, and the next steps of this work are discussed.

Karim, Mohammad Shahriar (Electrical and Computer Engineering, Purdue University)
-Authors: Mohammad Shahriar Karim(*), Gregery T. Buzzard, and David M. Umulis
-Title: Secreted, receptor-associated BMP regulators reduce stochastic noise intrinsic to many extracellular morphogen distributions
Morphogens specify cell-fate in a concentration dependent manner. Intriguingly, recent measurements of ligand-receptor binding suggest that many morphogens saturate receptors at concentrations less than 1nM or less than 20 molecules/cell. Low molecule number, combined with slow binding kinetics leads to a noisy interpretation of extracellular concentration that fluctuates on the time-scale of hours, however many morphogen patterning networks are remarkably robust. To investigate mechanisms of biological robustness and signal interpretation we developed a stochastic model of the local ligand-receptor dynamics and extended this work to consider spatial patterning and measure the errors in positional information expected for each local regulatory mechanism. We find that if a secreted non-receptor such as Crossveinless-2 (Cv-2) partially regulates ligand-receptor interactions, the amplitude of ligand-receptor fluctuations can be reduced by about 2-folds depending on specific parameter values and non-receptor concentration. Receptor-ligand regulation by secreted factors can also modify the binding dynamics to increase the frequency of fluctuations, which can be buffered out immediately downstream by the intracellular network if the time-scale for intracellular dynamics are slow relative to ligand-receptor fluctuations. This phenomenon of non-receptor imitates performance of a simple low pass filter for the system. Together, these data indicate that one of the benefits of receptor-ligand regulation by secreted non-receptors may be greater reliability of morphogen patterning mechanisms and we are developing experiments to test these conclusions.

Kim, Jae Kyoung (Mathematics, University of Michigan-Ann Arbor)
-Title: Modeling the Interaction between Circadian and Metabolic Regulation.
Recent experimental evidence has discovered strong links between circadian timekeeping and metabolic regulation. Because of the complexity of the biochemical networks that underlie these systems, mathematical modeling has the potential to help clarify experimental results and predict new phenomena. Here we review mathematical models that can be used to understand the links between circadian and metabolic regulation. We present a preliminary model for the role of SIRT1 in circadian rhythms. This model predicts experimental findings that can be used to understand the link between circadian regulation and metabolism. Further modeling can account for other links beyond these systems; one current interest is how circadian rhythm affect cancer through metabolism.

Lee, Sang-hun (Agricultural and Biological Engineering, Purdue University)
-Authors: Sang-hun Lee (*), and David M. Umulis
-Title: Dynamic simulation of Bone Morphogenetic Protein patterning in a 3D finite-element model of the Danio rerio embryo
Zebrafish development relies on the spatiotemporal distribution of molecules called morphogens that pattern anterior/posterior (AP) and dorsal/ventral (DV) axes in a concentration-dependent manner. Numerous secreted regulators control the spatiotemporal distributions of BMP signaling along the DV axis, however, the mechanisms of dynamic regulation of BMP signaling remain unclear. To determine the relative contributions of the Alk8 receptors, Chordin, Tolloid-like molecules, and Sizzled, we developed and tested a full 3D mathematical model of a developing zebrafish embryo. We developed an image registration algorithm to assign point-cloud experimental data to a reference set and determine both the stage of development and the orientation of the embryo. Following development of the image registration methodology, we converted the point-cloud reference into 3D finite element meshes for each 1.5 minute time-point during growth from early blastula through gastrula stages (200-500 minutes post fertilization (MPF)). We then developed a seamless modeling strategy to test alternative hypotheses regarding the mechanism of BMP-mediated patterning on the dynamically evolving mesh and found that Sizzled-mediated regulation of Tld leads to robust mechanism to regulate gradient shape of BMP activity. We also investigated mechanisms of dynamic morphogen scale-invariance in zebrafish embryos and present a summary of these findings.

Lioi, Josh (Mark Alber group, Mathematics, University of Notre Dame)
-Authors: Joshua Lioi(1), Zhiliang Xu(1), Malgorzata M. Kamocka(3), Danny Z. Chen(2), Elliot D. Rosen(3), Mark Alber(1) ((1) Department of Mathematics, University of Notre Dame, (2) Computer Science University of Notre Dame, (3) Medical and Molecular Genetics, Indiana University School of Medicine )
- Title: Study of the role of Factor VII in Venous Thrombus Formation Using a Combination of a Multiscale Model and Experiment
- Abstract:
We extend a two-dimensional multiscale model of thrombus formation by including surface-mediated control of the coagulation pathway. The model was used to simulate thrombus formation in normal or limited levels Factor VII (FVII). Simulation predictions were compared with experimental results involving thrombogenesis following laser-induced injury of venules in wild type and FVII deficient mice. It is shown that low levels of FVII in blood results in a significant delay in thrombin production demonstrating that FVII plays an active role in promoting thrombus development at an early stage.

Liu, Sijia (Mathematics, Iowa State University)
- Title : Novel clustering methods for the analysis of biological data
- Abstract:
The need to interpret and extract possible inferences from high-dimensional datasets has led over the past decades to the development of dimensionality reduction and data clustering techniques. In this poster, we present a novel family of clustering algorithms that combine seamlessly the strengths of existing spectral approaches to clustering with various desirable properties of fuzzy methods. We discuss examples of gene expression datasets for which the developed methodology outperforms other frequently used algorithms.

Liu, Yuan (Mathematics, University of Notre Dame)
- Title : A preliminary study of two models on angiogenesis
- Abstract:
We are studying two PDE models regarding to angiogenesis. One model is proposed by G. Serini in [1], in which the cell population is described by a continuous distribution of density and velocity. The other one is a PDE system derived from a two-dimensional stochastic cellular Potts model (CPM) describing cell moving in a medium and reacting to each other through direct contact, cell-cell adhesion, and long-range chemotaxis [2]. In the first system, we successfully solved the hyperbolic system in third order finite difference weno scheme and third order finite volume weno scheme on triangular mesh., in both way, we could observe the formation of blood vessel networks similar to those observed in the experiments. We also quantitatively studied the relationship between the endothelial cell number, the range of activity of chemo-attractant and the vascular network formation and size. However, the numerical simulation will blow up as is expected. In the model derived from CPM, the networks are also observed. And the numerical solutions of the model with/without the excluded volume indicate that the excluded volume interactions are important in the chosen range of values of parameters. Contrary to classical Keller-Segel model, solutions of this one do not collapse in finite time.
[1] G. Serini, D. Ambrosi, E. Giraudo, A. Gamba, L. Preziosi and F. Bussolino, Modeling the early stages of vascular network assembly, The EMBO Journal, Vol.22, No.8, (2003), pp1771-1779.
[2] P. Lushnikov, N. Chen and M. Alber, Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact, Phys. Rev. E. 78, 061904.

Luterek, Adam ( Brad Roth Group , Physics, Oakland University)
- Authors : Adam Luterrek and Bradley J. Roth
- Title : Studying the Movement of Nerve Axons Under the Influence of Strong Magnetic Fields
- Abstract:
We extend a model introduced by Roth and Basser (Magn. Reson. Med., 61:59-64, 2009) to study the movement of a nerve during magnetic resonance imaging. When exposed to a magnetic field, neural action currents are subjected to a Lorentz force that moves the nerve. Roth and Basser considered action currents that were uniform along the length of the nerve. In our study, we examine the full three-dimensional distribution of current. We calculate the nerve displacement for the case of the nerve perpendicular to the magnetic field. Additionally, if the magnetic field is parallel to the nerve, it may be possible for the axon to twist due to the Lorentz force.

Pargett, Michael (Weldon School of Biomedical Engineering, Purdue University)
-Title: Brat-mediated bi-stability and cell-competition autoregulate stem cell number in the Drosophila germarium
-Authors: Michael Pargett, Robin Harris, Hillary Ashe, and David Umulis
Complex organisms must maintain stable populations of stem cells to remain healthy and support somatic tissues. In the germline stem cells (GSC) of the Drosophila ovary, Bone Morphogenetic Protein (BMP) signaling regulates the decision between stem cell self renewal or differentiation. Our collaborators have elucidated key players in the intracellular network that regulates cell-receptivity to extracellular BMPs, however the interaction between the intra- and extracellular regulation of BMP distributions and interpretations remains unknown. To determine the relative contribution of intra- and extracellular control of BMP regulation we developed a local model for a single cell receiving an extracellular cue and a 3D extracellular model of the germarium. The proposed intracellular feedback mechanism exhibits bistabilty in response to levels of BMP signaling, making cells refractory to additional signal. By combining intracellular and extracellular regulation in the 3D multi-cell model, we find that cell-mediated competition for limiting amounts of ligand leads to autoregulation of stem cell number in the niche. Competition, combined with the bistable intracellular system supports the maintenance of the constrained stem cell population, causing differentiation of extraneous GSCs and repopulating if GSCs are lost.

Srivastava, Prashant (IIT Kanpur, INDIA)
-Title: Dynamical Model of HIV and CD4+ T cell with drug therapy
Here we shall propose and analyse a dynamical model of HIV and CD 4+ T cells under the influence of drugs Reverse transcriptase inhibitor and protease inhibitor. The infection develops as HIV infects CD4+ T cells. Infected cells are divided into two sub classes: infected cells before completion of reverse transcription and infected cells after reverse transcription. It is assumed that a fraction of infected cells revert back to uninfected class. We performed stability and also solved model numerically to analyse the analytical results.

Stevens, Joshua B. (School of Medicine, Wayne State University)
-Authors: Joshua B. Stevens, Guo Liu, Steven Bremer, Christine J Ye, Henry H. Heng
-Title: Dynamics of Somatic Cell Evolution During Cancer Progression
For decades cancer progression has been believed to be a linear process that was driven by stepwise accumulation of a small number of common gene mutations. Identification of these gene mutations and subsequent drug targeting of their functions promised to cure cancer. However, recent large scale cancer genome sequencing projects have failed to detect these expected common gene mutations. Similarly we have show that on the chromosomal level, there is no recurrent pattern of change which has lead to the development of the genome theory of cancer which states that cancer progression is a stochastic process driven by system replacement manifested by chromosomal change. During cancer progression population diversity increases during periods of stress such as prior to immortalization and during chemotherapy. This diversity increases the probability that a cell (or number of cells) will survive the stress, promoting further progression. Despite the recent success of the genome theory, many questions still exist. These questions include: What level (gene, epigenetic, or genome) has the most utility in predicting cancer progression, and how can measurements at all levels be integrated? Are there more or less favorable types of diversity? How do responses of populations of cells react to differing circumstances if one population is largely genomically homogenous and one is heterogeneous, but both populations share a similar level of some molecular marker? Answering these important questions will require a bio-mathematic approach to integrate these new cancer progression findings into clinically applicable models and treatment designs.

Wang, Xiaoxia (Mathematics, Case Western Reserve University)
Multiple factors affect schistosomiasis transmission in distributed meta-population systems including age, behavior, and environment. Traditional modeling approach to macroparasite transmission often exploits ``mean worm burden formulation'' (MWB) for human hosts. Such approach oversimplifies the system, and can give wrong predictions for control interventions. Typical worm distribution in humans is overdispersed, and classic models either ignore it or make ad-hoc assumptions about its pattern (e.g. `negative binomial'). We propose a new modeling approach to macro-parasite transmission by stratifying human populations according to burden, and replacing MWB dynamics with that of `population strata'. The Stratified Worm Burden (SWB) approach offers many advantages; it accounts naturally for overdispersion, and accommodates other important factors and measures of human infection and demographics. We developed the calibration procedure for such extended (multi-component) systems, and run it for a specific data set collected in the Msabweni region of Eastern Kenya. The calibrated model was validated against additional data, and applied to study control interventions (drug treatment). In particular, we simulated several control strategies proposed by WHO and examined their long term outcomes. We believe our model can provide useful information and tools for future WHO policies on eradication of schistosomiasis.

Xu, Dan ( Brad Roth Group , Physics, Oakland University)
- Authors : Dan Xu and Bradley J Roth
- Title: The Magnetic Field Produced by the Heart and Its influence on MRI
- Abstract:
Recently, much work has been done to detect neuronal activation by using the magnetic field produced by biocurrents. In general, these magnetic fields are too tiny to measure by magnetic resonance imaging. However, the heart is the source of the largest biocurrents in the body, so it may be easier to detect cardiac action currents using MRI compared to neural action currents. There are two sources that produce a magnetic field in cardiac tissue. One is the intracellular current in the tissue with the "return" current through an adjacent volume conductor; the other is the anisotropy of the tissue. In this study, we examine a simplified "spherical heart" model with a simple transmembrane potential distribution and calculate the resulting action currents and magnetic field, and estimate their impact on an MRI signal. This research was supported by the National Institutes of Health Grant R01EB008421.