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
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 microRNAs
ential 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.