University of Houston
June 11 - August 3, 2012 (8 weeks)
UH - Department of Mathematics
(interacts with existing summer research fellowship program)
Topic 1:
Correlations between the responses of neurons - Krešimir Josić
Project Description:
Correlations between the responses of neurons can strongly affect the coding of stimuli in the collective response of a neural population. Whether these effects improve or degrade stimulus representations depends on how correlations are distributed across a population. It is therefore important to understand how a stimulus, the context within which it appears, or the internal state of an organism modulates the correlations in the neural response. An analysis of the impact of correlations is needed for patterns of correlations that arise as a result of such modulations.
Students in Dr. Josić' lab will examine the structure of correlations in the responses obtained in an experimental setting obtained from experimental collaborators. Information theoretic methods will be used to examine the impact of correlations on the neural representation of a stimulus under different conditions. For instance, the encoding of the orientation of a stimulus will be examined in the presence and absence of an adapting stimulus. To further explore these effects, synthetic data with predefined correlation structure will be generated using algorithms developed by Dr. Josić' group.
Pre-requisites:
Some familiarity with Matlab. Courses in linear algebra and differential equations.
Topic 2:
Testing the limits of deterministic and stochastic delay models of gene regulation - Krešimir Josić and Will Ott
Project Description:
An essential function of biochemical signaling pathways and genetic networks is to process and respond to incoming signals. This frequently requires the integration of information from different sources. The impact of delays on this type of computation becomes evident when engineering biochemical circuits. As in the logical gates inside computers, such biological circuits require different pieces of information to arrive nearly synchronously. To understand information processing in living systems it is therefore essential to account for the non-instantaneous nature of information transfer.
Dr Ott and Dr. Josic work on developing a new mathematical framework for modeling delay in gene network dynamics. The goal of this project will be to test the limits of deterministic and stochastic delay models of gene regulation. We have already shown that stochastic models that incorporate delay can behave very differently from standard nonlinear ODE models favored in the literature. The traditional mathematical approaches used in the analysis of gene networks, such as methods of bifurcation theory and stochastic differential equations, will have to be extended and complemented. We will discuss analytical techniques to handle the delayed dynamics of gene networks and take into account the finite times necessary for signals to propagate. We aim to verify the conclusions of this analysis in an experimental setting.
Pre-requisites:
Linear algebra, differential equations, probability and some familiarity with Matlab.
