Mathematical Biology Seminar
Department of Mathematical Sciences

New Jersey Institute of Technology

Spring 2014

All seminars are 11:40-12:40, in Cullimore Hall Room 611 (Math Conference Room) unless noted otherwise.  If you have any questions about a particular seminar, please contact the person hosting the speaker. The Math Department also hosts a number of other seminars and colloquia which can be accessed here: DMS Seminar Listing

Date	Speaker and Title	Host
Tuesday  January 21	APPLIED MATH SEMINAR AT 2:30
Tuesday January 28	APPLIED MATH SEMINAR AT 2:30
Tuesday February 4	APPLIED MATH SEMINAR AT 2:30
Tuesday February 11 11:30 AM	APPLIED MATH SEMINAR AT 2:30
Tuesday February 18 11:30 AM	Haroon Anwar - Rutgers University at Newark Determinants of intracellular calcium levels in dendrites
Tuesday February 25 11:30 AM	Carlos Luna - University of Maryland Physical properties of lamprey spinal cord regeneration: Adaptive vs. Maladaptive recovery	Gal Haspel
Tuesday March 4 11:30 AM	Mohammad Rahimi - Princeton University Shape dynamics and lipid hdrodynamics of bilayer membranes	Yuan-Nan Young
Tuesday March 11
Tuesday March 18	No Seminar - Spring Break
Tuesday March 25 11:30 AM	Casey Diekman - NJIT Multi-Level Organization of the Mammalian Circadian Clock
Tuesday April 1 11:30 AM	No seminar
Tuesday April 8 11:30 AM	- James R Kozloski - IBM T.J. Watson Research Center Scalable Reaction Diffusion Calculations over Gap Junction Coupled, Branched Neuron Topologies in Neural Tissue Simulations of the Inferior Olive	Casey Diekman
Tuesday   April 15   11:30 AM	Haroon Anwar - Rutgers University at Newark
Tuesday   April 22   11:30 AM	Jana Gevertz - The College of New Jersey Predictive Mathematical Modeling of Tumor-Host Interactions  with Implications for Treatment	Amit Bose
Tuesday   April 29 10:00 AM	Zeynep Akcay- NJIT Thesis Defense

Abstracts

Mohammad Rahimi

Princeton University

Shape dynamics and lipid hdrodynamics of bilayer membranes

Biological membranes are continuously brought out of equilibrium, as they shape organelles, package and transport cargo, or respond to external actions. Even the dynamics of plain lipid membranes in experimental model systems are very complex due to the tight interplay between the bilayer architecture, the shape dynamics, and the rearrangement of the lipid molecules. We formulate and numerically implement a continuum model of the shape dynamics and lipid hydrodynamics, which describes the bilayer by its midsurface and by a lipid density field for each monolayer. The viscoelastic response of bilayers is determined by the stretching and curvature elasticity, and by the interonolayer friction and the membrane interfacial shear viscosity. While the bilayer equilibria are well-understood theoretically, dynamical calculations have relied on simplified continuum approaches of uncertain transferability, or on molecular simulations reaching very limited length and time scales. Our approach incorporates the main physics, is fully nonlinear, does not assume predefined shapes, and can access a wide range of time and length scales. We use this model to examine the dynamics of confined bilayers, of bilayers exposed to stimuli changing locally the lipid density, or to study the mobility of inclusions and the fluctuations in curved membranes.

Haroon AnwPredictive Mathematical Modeling of Tumor-Host Interactions 
with Implications for Treatmentar

Rutgers University at Newark

Determinants of intracellular calcium levels in dendrites

Calcium is the most important signaling factor in dendrites. Calcium entering through voltage-gated calcium channels and various receptors give rise to cytosolic alcium levels, which in turn control calcium-activated potassium channels and may activate signaling pathways underlying synaptic plasticity. Several molecular and morphological components are involved in the maintenance of calcium levels, which include spatially distributed discrete (stochastic) ion channels, calcium buffers, diffusion of calcium and buffers, pumps, intracellular stores and dendritic morphology. Using a biophysical model of Purkinje cell dendritic excitability, first I will show how the calcium buffering mechanisms shape the temporal characteristics of calcium levels that differentially control different calcium-activated potassium channels. Interestingly, the effect of dendritic diameter on calcium levels is so robust that, even in the presence of buffers and pumps, local changes in dendritic diameter maintain gradients of calcium levels. Additionally, the calcium levels are stronPredictive Mathematical Modeling of Tumor-Host Interactions 
with Implications for Treatmentgly influenced by the stochastic activity of discrete and spatially distributed ion channels. Altogether, these results indicate that the experimentally observed variability in calcium levels and spiking activity is not only due to measurement noise but also contains intrinsic variability due to dendritic morphology, discrete and stochastic nature of ion channels and spatial distribution of ion channels.

James Kozloski

Carlos Luna

University of Maryland

Physical properties of lamprey spinal cord regeneration: Adaptive vs. Maladaptive recovery

Spinal cord injury (SCI) is a physical trauma that can result in paralysis and even death; to date no treatment exists to promote adaptive recovery. In this work, we studied the larvae lamprey (Petromyzon Marinus), an animal model with dual regenerative capabilities. Spinal cord regeneration at room/warm temperature (23⁰C) resulted in adaptive behavior, but when placed at their native/cold temperature (10⁰C) recovery was maladaptive. Through the use of thisPredictive Mathematical Modeling of Tumor-Host Interactions 
with Implications for Treatment animal model, we sought to understand the physical factors that influence adaptive recovery and used them to enhance regeneration in maladaptive animals. In the first part of this work, we measured nerve regeneration and blood clot formation early after SCI, for adaptive and maladaptive conditions. In the second part, we analyzed the mechanical and structural properties of the spinal cord and notochord using in vivo X-ray imaging and tensile loading testing. We found that animals in cold temperature failed to recover normal mechanical properties of both spinal cord and notochord. Furthermore, clot formation blocks nerve regeneration of animals in cold but not in warm temperature. Using those lessons learned from adaptive animals, we removed the clot of animals in cold temperature early after injury. We measured the locomotion of animals with clot removal and found an enhancement from maladaptive to adaptive recovery; a simple but very importantconclusion that will contribute greatly to SCI research.

Casey Diekman

NJIT

Multi-level organization of the mammalian circadian clock

Circadian (~24-hour) rhythms offer one of the clearest examples of the interplay between different levels of nervous system organization, with dynamic changes in gene expression leading to daily rhythms in neural activity, physiology and behavior. The main output signal of the master circadian clock in mammals has long been believed to be a simple day/night difference in the firing rate of neurons within the suprachiasmatic nucleus (SCN). Our recent findings challenge this theory, and demonstrate that a substantial portion of SCN neurons exhibit a more complex and counterintuitive set of electrical state transitions throughout the day/night cycle. In this talk, I will attempt to provide a mathematical understanding of these daily transitions in SCN electrical state and the Jana Gevertzfunctional roles they play in the mammalian circadian clock.

James Kozloski

IBM

Scalable Reaction Diffusion Calculations over Gap Junction Coupled, Branched Neuron Topologies in Neural Tissue Simulations of the Inferior Olive

We developed a novel tissue volume decomposition, and a hybrid branched cable equation solver for performing large-scale simulations of neural tissue (2011). The decomposition divides the simulation into regular tissue blocks and distributes them on a parallel multithreaded machine. The solver computes neurons that have been divided arbitrarily across blocks and can be considered a tunable hybrid of Hines’ fully implicit method (1984), and the explicit predictor-corrector method of Rempe and Chopp (2006). We demonstrate thread, strong, and weak scaling of our approach on a machine of 4,096 nodes with 4 threads per node. Scaling synapses to physiological numbers had little effect on performance, since our decomposition approach generates synapses that are almost always computed locally. We then extended the capabilities of the simulator to generate arbitrary neuron morphologies, compose them into tissues, and solve different “compartment variables” over shared topological constraints imposed by the tissue. Using these capabilities, we demonstrate a simultaneous calculation of transmembrane voltage and calcium concentrations in a simulated Inferior Olive tissue.  We introduce gap junctions that exchange both current and calcium among compartments in our model, and solve these without fixed point iteration beyond our two step predictor-corrector method. Robust synchronization across neurons in the tissue is achieved via these currents and calcium diffusion across coupled dendrites. Kozloski, J. and Wagner, J. (2011). Front. Neuroinform. 5:15.
Rempe, M. J., and Chopp, D. L. (2006). SIAM J. Sci. Comput. 28, 2139–2161. Hines, M. (1984). Int. J. Biomed. Comput. 15, 69–76.

Jana Gevertz

The College of New Jersey

Predictive Mathematical Modeling of Tumor-Host Interactions with Implications for Treatment

Mathematical modeling techniques are now widely employed in the field of cancer research.  In this talk, a computational tool is presented that seeks to provide a theoretical basis for helping drug design teams assess the most promising drug targets and design optimal cancer treatment strategies.  The tool is grounded in a previously-validated hybrid cellular automaton model of tumor growth in a vascularized environment.  I will demonstrate how computer simulations of the mathematical model can be used to study the anti-tumor activity of several vascular-targeting compounds, as well as a chemotherapeutic agent.   When possible, simulation results will be directly compared to preclinical and clinical data.  Further, I will illustrate how techniques from optimization theory can be employed to identify a dosing protocol that minimizes the number of cancer cells remaining after treatment with a vascular-disrupting and chemotherapeutic drug.  The treatment regimen identified can successfully halt simulated tumor growth, even after the cessation of therapy.  I will end with some ongoing modeling work exploring the reciprocal relationship between cancer growth, invasion, and the density/structure of the surrounding host microenvironment.  Preliminary results on how tumor shape, size and spread are impacted by varying density microenvironments will be presented, and the implications of these results for patient prognosis will be explored.