Mathematical Biology Seminar
Department of Mathematical Sciences

New Jersey Institute of Technology

Spring 2013
 

All seminars are 4:00 - 5:00 p.m., in Cullimore Hall Room 611 (Math Conference Room) unless noted otherwise. Refreshments are usually served at 3:30 p.m., and talks start at 4:00 p.m. 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 22
 
4:00PM

Katherine Newhall - New York University
Synchronous Firing Events in Stochastic Neuronal Network Models

Amit Bose

Thursday
January 24
11:30 AM


Xaq Pitkow -
University of Rochester

Mike Siegel

Tuesday
January 29
4:00PM


Marian Gidea -  Institute of Advanced Studies

Topology and Dynamics: From Mechanical to Biological Systems

Amit Bose

Tuesday
February 5
4:00PM

Joyce Lin - University of Utah

Modeling the Electrical Activity in Cardiac Tissue

Mike Siegel

Tuesday
February 12
4:00PM

Casey Diekman - Ohio State University

Linking Gene Expression Rhythms to Membrane Dynamics in the Circadian Clock

Mike Siegel

 Thursday
 February 14
 11:30 AM

Michael Chevalier - University of California at San Francisco

Quantifying stochastic and spatio-temporal effects in biological signaling pathways


    Mike Siegel

Tuesday
February 19
4:00PM

Peter Thomas - Case Western University

Noise and the Single Neuron

Amit Bose

 Wednesday
 February 20
 4:00PM

Sridhar Raghavachari - Duke University

Quantifying negative feedback regulation by microRNAs

    Amit Bose

Tuesday
February 26
4:00PM


No Seminar


Tuesday
March 5
4:00PM

Sorinel Oprisan - College of Charleston

How does the brain keep track of time?

Farzan Nadim

Tuesday
March 12
4:00PM


No Seminar


Tuesday
March 19
4:00PM

No Seminar - Spring Break


Tuesday
March 26
4:00PM

Sarah Muldoon - INSERM, France

The structure of synchrony in chronically epileptic 

networks: a multi-scale approach

Horacio Rotstein

Tuesday
April 2
4:00PM


Miranda I. Teboh-Ewungkem - Lafayette College

Complex Dynamics in a Model for the Vector-Borne Disease Malaria

Amit Bose

 Tuesday
 April 9
 4:00PM

No Seminar  

 Tuesday
  April 16
  4:00PM

Yuriy Polyakov - US PolyResearch

Amit Bose

 Tuesday
  April 23
 4:00PM

 Josh Chang - Ohio State University

Gaussian integrals for inverse problems


 Robert Miura

 

Abstracts


Katherine Newhall, New York University

Synchronous Firing Events in Stochastic Neuronal Network Models

Synchrony manifests itself in a variety of forms in noisy biological systems.  Within computational neuronal models, even with the desynchronizing effect of noisy input, the excitatory coupling between neurons can cause the network to synchronize, or oscillate, over a large range of model parameters.  I will discuss synchrony in the context of pulse-coupled Integrate-and-Fire models where cascading firing events cause multiple neurons to fire at the exact same instance in time.  I will describe the synchronizing mechanism and present methods for computing the probability distribution for the number of neurons firing together, as well as the probability the system maintains a synchronous firing state.  These results can potentially be combined with population based simulation methods to efficiently simulate interacting excitatory and inhibitory neuron populations in biologically relevant regimes.

Xaq Pitkow, Rochester University
Efficient coding and beyond in the early visual system

The brain uses its past experience to draw conclusions from new sense data. We can quantify this idea using statistical principles that enable us to generate predictions about neural circuitry. One highly influential theory, efficient coding, applies this idea to visual processing. It proposes that the retina compresses natural images using center-surround receptive fields to remove natural correlations. I test this prediction and demonstrate that the spike trains of retinal ganglion cells are indeed decorrelated compared to the visual input. However, most of the decorrelation is accomplished not by the receptive fields, but by nonlinear processing. I show that these nonlinearities provide nearly optimal information transmission for noisy neurons. Extending the efficient coding theory to a nonlinear code thus provides a better explanation for the observed structure of retinal spike trains. I will conclude by discussing the role of statistics in neural computation more generally. I will contrast computation with information transmission, and emphasize the importance of nonlinearities and recurrent connectivity in extracting relevant information. As a concrete example I will describe my recent progress modelling contextual inference in the primary visual cortex.

Marian Gidea, Institute for Advanced Studies, Princeton University
Topology and Dynamics: From Mechanical to Biological Systems

We will start with an overview of some topological and geometric methods that are used to study stability and instability in mechanical systems. These include normal hyperbolicity, KAM theory, Aubry-Mather sets, and homology algebra.  Then we will provide some applications of these methods to analyze stability/instability in biological systems. We will focus on a ‘genotypic-phenotypic quality’ single species population model, and on the electrical activity of the heart. We will also discuss some novel applications of topological data analysis to validation of macromolecular models derived from three dimensional electron microscopy, and to detection of critical transitions in gene regulatory systems.


Joyce Lin, University of Utah
Modeling the Electrical Activity in Cardiac Tissue

Electrical stimulation of cardiac cells causes an action potQuantifying negative feedback regulation by microRNAsential wave to propagate through myocardial tissue, resulting in muscular contraction and pumping blood through the body. Approximately two thirds of unexpected, sudden cardiac deaths, presumably due to ventricular arrhythmias, occur without recognition of cardiac disease. While conduction failure has been linked to arrhythmia, the major players in conduction have yet to be well established. Additionally, recent experimental studies have shown that ephaptic coupling, or field effects, occurring in microdomains may be another method of communication between cardiac cells, bringing into question the classic understanding that action potential propagation occurs primarily through gap junctions. In this talk, I will introduce the mechanisms behind cardiac conduction, give an overview of previously studied models, and present and discuss results from a new model for the electrical activity in cardiac cells with simplifications that afford more efficient numerical simulation, yet capture complex cellular geometry and spatial inhomogeneities that are critical to ephaptic coupling.



Casey Diekman, Ohio State University
Linking Gene Expression Rhythms to Membrane Dynamics in the Circadian Clock

 
Daily rhythms in the behavior and physiology of mammals are coordinated by a group of neurons that constitute the central circadian (~24-hour) clock. Clock neurons contain molecular feedback loops that lead to rhythmic expression of clock-related genes. Much progress has been made in the past two decades to understand the genetic basis of the molecular circadian clock. However, the relationship between the molecular clock and the primary output of clock neurons—their electrical activity—remains unclear. In this talk, I will explore this relationship using a mathematical model of an unusual electrical state that clock neurons enter at a certain time of day. The model predicts that this state causes high levels of calcium ions inside clock neurons, which activates transcription of clock genes. I will then demonstrate that this additional feedback promotes gene expression rhythms. Thus, I propose that electrical activity is not just an output of the clock, but also part of the core circadian timekeeping mechanism that plays an important role in health and disease.

Michael Chevalier,  California at San Francisco
Quantifying stochastic and spatio-temporal effects in biological signaling pathways

Genetically identical cells under the same environmental conditions can exhibit different phenotypes across a population. This stochastic behavior, uncovered by recent advances in quantitative single cell measurements, necessitates the development of new analysis and modeling tools. Inspired from recent dynamic measurements of the unfolded protein response (UPR) signaling pathway in yeast and exocytosis on dendrites, I will describe the development of a set of quantitative biological modeling tools which address the multi-scale, stochastic nature of biochemical systems and general spatio-temporal processes in biology such as diffusion-reactions on membranes. Results from data analysis and modeling of the unfolded protein response will be also be discussed, specifically, how the protein folding chaperone BiP modulates the UPR’s master signal transducer Ire1.

Peter Thomas,  Case Western University
Noise and the single neuron

A deep understanding of neural function at the single cell level requires consideration of both determinstic and stochastic dynamical models.  I will review several approaches to understanding the entrainment of individual neurons by fluctuating injected currents, and discuss the implications of the resulting "spike time patterns" for neural coding.  In the second half of the talk, I will discuss current work on hybrid discrete/continuous Markov process models for neural dynamics in the presence of random ion channel gating.  Within this framework I will propose a novel way of defining the "asymptotic phase" of a noisy limit cycle, as a step towards extending the classical theory of synchronization and entrainment of neural oscillators to the stochastic case.


Sridhar Raghavachari,  Duke University
Quantifying negative feedback regulation by microRNAs

Micro-RNAs (miRNAs), evolutionarily conserved non-protein coding messenger RNAs, play a critical role in post-transcriptional gene regulation by pairing with target mRNAs to repress protein production. It has been shown that over one-third of human genes are targeted by miRNA. Although hundreds of miRNAs have been identified in mammalian genomes, the function of miRNA-based repression in the context of gene regulation networks remains unclear. Here we present two mathematical models of negative feedback regulation by miRNAs -- 1) a stochastic model of a gene network that controls the maturation and function of dopamine neurons in the brain and 2) a deterministic model of a gene network comprised of cancer-inducing and tumor suppressor genes regulated by miRNA. We show that the mode of repression plays a central role in the dynamics of the network. In the developmental network, if miRNAs catalytically suppress translational rates, the protein fluctuations can be strongly suppressed by negative feedback, as conventionally expected. However, if miRNAs and mRNAs are co-degraded, the protein fluctuations are enhanced relative to theoretically predicted levels. In the cancer network, the mode of repression leads to oscillations in the levels of miRNA and the repressed target. We discuss the functional implications of the modes of repression.

Sorinel Oprisan,  College of Charleston
How does the brain keep track of time?

Time perception in the supra-second range is crucial for fundamental cognitive processes like decision making, rate calculation, and planning.  In the vast majority of species, behavioral and neurophysiological manipulations, interval timing is scale invariant: the time-estimation errors are proportional to the estimated duration.  The origin and mechanisms of this fundamental property are unknown. We investigated the computational properties of a circuit consisting of a large number of (input) neural oscillators projecting on a small number of (output) coincidence detector neurons, which allows time to be coded by the pattern of coincidental activation of its inputs. We showed that time-scale invariance emerges from the neural noise ubiquitous in the form of small fluctuations in the firing patterns of its input neurons and in the errors with which information is encoded and retrieved by its output neurons. In this architecture, time-scale invariance is ubiquitous (resistant to manipulations) as it depends neither on the details of the input population, nor on the distribution probability of noise.

Sarah Muldoon, INSERM, France
The structure of synchrony in chronically epileptic networks: a multi-scale approach

Epilepsy is a disorder typically characterized by synchronous neuronal activity.  While many studies have focused on understanding macro-level network activity using electrophysiological approaches, less is known about the underlying spatiotemporal dynamics at the micro-level of individual cells.  I will present data obtained from simultaneous two-photon calcium imaging of the activity of hundreds of individual neurons in acute slices from chronically epileptic mice.  Under hyperexcitable conditions, these slices display recurrent synchronous network level activity.  In order to probe the structure of this synchronous activity, we employed a functional clustering algorithm to compute the functional network structure at the scale of individual neuronal activity.  This analysis revealed that the observed macro-level synchronizations are actually composed of the co-activation of subsets of spatially localized neuronal clusters.  Furthermore, different combinations of clusters are active during each event, meaning that although the events appear similar when viewed at the macro-level of network synchronization, they are in fact quite variable and display little repetition in the micro-level structure of events.


Miranda Teboh-Ewungkem, Lafayette College
Complex Dynamics in a Model for the Vector-Borne Disease Malaria

Chaotic dynamics have rarely been reported in deterministic continuous time mathematical models for malaria, unless when seasonal forcing is included in the model. Backward bifurcation, another complex dynamic, is often associated with immune response, disease induced death, the use of an imperfect vaccine, or a more nonlinear incidence function in deterministic models. We showed that when focus is placed on the mosquito vector in the malaria transmission process, so that the mosquito feeding patterns, demography and reproduction habits are explicitly incorporated in the transmission dynamics, and the reproductive gains that accrue to the mosquito's population as a result of its interaction with the human population accounted for, complex dynamics can be observed. In particular, a non-seasonally forced mass action Susceptible-Exposed-Infectious (SIS) continuous time deterministic malaria model was shown to be oscillatory, and it exhibited the phenomenon of backward bifurcation. When a more nonlinear birthrate function for the mosquito population was considered, chaotic dynamics were observed as well. We posit that mathematical models for malaria and other vector-borne diseases should be modeled to account for the reproductive gains to the vector's population as a result of its interaction with the human or host population. 

Yuriy Polyakov, UsPoly Research
Analysis of Brain Activity Signals: Application to the Diagnosis of Schizophrenia and Photosensitive Epilepsy

Frequency and phase synchronization, existence of specific correlations between characteristic frequencies and phases of the excitations in different parts of the cortex (specific neural ensembles), and synchronization of the excitation amplitudes are the necessary conditions for the brain to function as an integral system. A normally functioning brain responds to external actions on the human organism by establishing a certain optimal level of such synchronization. A significant deviation from this optimal level, such as an anomalously high level of synchronization or lack of synchronization, may be considered as an indicator of a pathology in brain activity. In this talk, I will discuss my two recent studies where quantitative characteristics of such deviation are used as new diagnostic markers for photosensitive epilepsy and schizophrenia. The parameters are found from the cross-correlation analysis of magnetoencephalogram (photosensitive epilepsy) and electroencephalogram (schizophrenia) signals by flicker-noise spectroscopy, an original set of mathematical tools for statistical signal analysis.

Josh Chang, Ohio State University
Gaussian intergrals for inverse problems

Inverse problems often require the use of ``regularization" tricks, particularly when they are ill-posed or ill-conditioned. A common technique for regularization, Tikhonov regularization, has a Bayesian statistical interpretation. This interpretation has a some advantages. First, it provides a guideline for choosing the regularization -- this interpretation suggests that one should use regularizing terms that are consistent with prior knowledge. Second, it allows one to estimate the uncertainty in the solution of an inverse problem. Third, it
suggests the use of functional integration methods in solving such problems. In this talk, I will present first Tikhonov regularization in a discrete interface-tracking problem, where the speed of a spreading depression wave in the brain in optical intrinsic signal images is regularized according to a-priori assumptions of its spatial correlation. I will then talk about regularization incontinuous inverse problems, where Feynman's path integral method provides exact solutions for linear problems such as interpolation of bacterial membranes from cyro-EM images,  and perturbative approximations to nonlinear problems like the inversion of Poisson's equation to recover a dielectric field,
which is used in biological imaging applications.