** Speaker: **
Giordano Tierra, University of Notre Dame

** Title: **
Mathematical modeling of bacterial communities: Swarming processes and mechanical behavior of biofilms.

** Abstract: **
Bacterial biofilms are structured cellular communities that represent the dominant bacterial growth state for both environmental and clinical scenarios. There is great interest to understand biofilm assembly, as infections resulting from biofilms are notoriously resistant to antibiotic treatments. Treatment of a broad spectrum of human health issues, ranging from lethal infections from opportunistic pathogens such as those in cystic fibrosis patients, to catastrophic failure of prosthetic implants, could improve with a greater understanding of biofilm formation. Among the biofilm development steps for which we lack understanding is the ability of bacteria to first colonize host surfaces. Bacterial swarming motility has been shown to be important to biofilm formation, where cells act not as individuals, but as coordinated groups to move across surfaces, often within a thin-liquid film. In this talk two models are presented. The first one focuses on simulating the swarming process for Pseudomonas aeruginosa bacterial communities, whose spread is aided by the production of a surfactant that lowers surface tension of the liquid film to improve bacterial motility. The second model simulates the mechanical behavior of biofilms. In particular, deformation and detachment produced by interaction with liquid flow is studied by using a multi-component complex fluid formulation.

** Speaker: **
Ken Weiss, Penn State University

** Title: **
Genes must predict biological traits, mustn't they? Then why is it so difficult to understand how? (a non-mathematical, philosophical view of biological causation and evolution)

** Abstract: **
It’s widely assumed that genes determine who we are. But the genetic basis of human traits often turns out to be perplexingly complicated. We face the same problem in trying to understand normal traits, disease, and even behavior—and their evolution. Genomic determinism is at the heart of some of the key problems in modern biology. Computer simulation may be useful here, if we do not build in what we want to learn.

** Speaker: **
Ephraim M. Hanks Ephraim Hanks, Penn State University

** Title: **
Random Walks, Circuits, and Spatial Statistical Models for Gene Flow in Heterogeneous Landscapes

** Abstract: **
Genetic data collected over space are commonly used to study how landscape features such as mountains, rivers, and roads affect connectivity in animal species. One approach correlates observed genetic distance with the circuit-theoretic resistance distance of a graph representation of the landscape. We examine links between this circuit modeling approach and random walk models for gene flow in heterogeneous environments. We show that a Gaussian Markov random field model can be constructed which matches the spatial structure implied by circuits and by the equilibrium state of a random walk model. This provides a spatial statistical model with links to a spatio-temporal data generating process.

** Speaker: **
Yoichiro Mori, Mathematics, University of Minnesota

** Title: **
Modeling Electrodiffusion and Osmosis in Physiological Systems

** Abstract: **
Electrolyte and cell volume regulation is essential in physiological systems. After a brief introduction to cell volume control and electrophysiology, I will discuss the classical pump-leak model of electrolyte and cell volume control. I will then generalize this to a PDE model that allows for the modeling of tissue-level electrodiffusive and osmotic phenomena. This model will then be applied to the study of cortical spreading depression, a pathophysiological phenomenon in the brain that is thought to underlie migraine aura and other pathologies.

** Speaker: ** Duan Chen, University of North Carolina at Charlotte

** Title: ** Proton transport and its role in cancer research

** Abstract: ** Tumors have distinct properties from normal tissues, such as lower oxygen tension, stronger acidity and faster reducing rate. These biomarkers exist in a wide range of solid tumors and the corresponding microenvironment is critical for tumor development and design of anti-cancer treatments. Multiscale mathematical models are necessary to discover the macroscopic tumor growth at the tissue level and microscopic molecular interactions. Aiming at the tumor acidity, in this talk I will first introduce a quantum dynamic model for proton transport through membrane proteins and related numerical algorithms for simulation challenges. Then I will introduce a free boundary problem based tumor growth model for interactions among cancer cells and immune system at the tissue level. These two type of models and computational tools are fundamental building blocks for future multiscale model of tumor growth with complicated microenvironmental changes.

** Speaker: ** Weihua Geng, Southern Methodist University

** Title: ** Accurate and Efficient Interface Methods for Implicitly Solvated Biomolecular Simulation

** Abstract: **
The Poisson-Boltzmann (PB) model is an effective implicit solvent approach for simulating solvated biomolecular systems. By treating the solvent with a mean field approximation and capturing the mobile ions with the Boltzmann distribution, the PB model largely reduces the degree of freedom and computational cost. However, solving the PB equation suffers many numerical difficulties arising from interface jump conditions, complex geometry, charge singularities, and boundary conditions at infinity. In order to overcome these difficulties, two interface methods with different formulation and discretization are investigated.

The first approach is the matched interface and boundary (MIB) method. This finite difference meshed method repeatedly uses interface jump conditions to capture the non-smoothness of solutions, adaptively applies local interpolation to characterize the complex geometry, and analytically takes Green's function based decomposition to regularize the singularities of the source terms. By computing a series of benchmark tests, the MIB-PB solver shows a solid 2nd order convergence thus stands out among Cartesian grid based PB solvers.

The second approach is the treecode-accelerated boundary integral (TABI) method, which adopts a well-conditioned boundary integral formulation to handle aforementioned difficulties while accelerates the Krylov subspace based iterative methods such as GMRES with Cartesian treecode. This treecode is an O(N*logN) scheme with properties of easy implementation, efficient memory usage, infrequent communication, and straightforward parallelization. In addition, the treecode/boundary integral scheme can be conveniently implemented on GPUs. Numerical tests show 100+ times speed-up on a single GPU card, potentially making it possible to run PB model based molecular dynamics simulation for billions of time-steps.

** Speaker: ** Samit Bhattacharyya, Penn State University

** Title: ** Strain interactions and erratic periodicity of Whooping Cough

** Abstract: **
Whooping cough has a very unpredictable dynamics with global periodicity 2-5 years. Several studies, in recent years, proposed different hypotheses such as stochasticity in transmission, boosting immunity, vaccination, and demographic factors to explain this erratic periodicity of whooping cough. In this study, we are modelling whooping cough outbreak dynamics as combination of two of its etiological serotypes B. pertussis and B. parapertussis, where these two strains interact with each other by ecological competition, namely temporary removal or quarantine (via age dependent disease severity). We hypothesize that variable dynamics of whooping cough is due to coexistence of multiple attractors emerging from the interaction of these two serotypes. We are developing a stage-structured compartmental model of multi-pathogen system and exploring how the age-specific pattern of quarantine impacts the interaction of two pathogens. We also discuss how vaccination of one strain impacts the dynamics of the other in this framework of age-specific competition.

** Speaker: ** William Nelson, Queen's University

** Title: ** Scaling from life-cycles to population dynamics: insights from combining models & empirical biology

** Abstract: **

Many biological organisms has strong ontogenetic stage-structure that impacts the instantaneous rates of development, mortality and reproduction. In this seminar, I will discuss two systems where the combination of mathematical modelling and experimentation/empirical observation has been used to gain insight into the effect that stage-structure has on population dynamics.

** Speaker: ** Dezhe Z. Jin, Department of Physics, Penn State University

** Title: ** Dynamics of Neural Networks and Birdsong Syntax

** Abstract: **
Songbirds learn to sing like humans learn to speak. The songs of many species consist of sequences of discrete syllables. The sequences follow syntactical rules that have some rudimentary similarities to grammars in human language. Experimental and computational works have converged to unveil how the collective dynamics of connected neurons in the songbird brain controls the syntax. Neurons form unidirectional chain networks that drive the syllables. The chains are connected into branched networks. Neural activity flows along the branched pathway to produce syllable sequences. At a branching point, one of the connected chains is selected to carry on the activity, producing a probabilistic syllable transition. These results may shed light on how human speech is encoded in the brain.