Research Area

Applied Mathematics, Biophysics and Computational Biology.
I use mathematics, physics and computing to study biology at molecular, cellular and systems levels.  This research benefits greatly from experimental collaborations.  I am also interested in various aspects of applied mathematics itself.

Current Research Topics

•  Molecular Basis of Neurotransmitter Release and its Functional Significance in Neural Computation
•  Neural Mechanism of Robust Locomotion in Nerve-Muscle-Body-Environment Interactions

Recent Results

A Benefit of Randomness in Synaptic Vesicle Release: Noise is not only a source of disturbance, but it also can be beneficial for neuronal information processing. The release of neurotransmitter vesicles in synapses is an unreliable process, especially in the central nervous system. Recently, we showed that the probabilistic nature of neurotransmitter release directly influences the functional role of a synapse, and that a small probability of release per docked vesicle helps reduce the error in the reconstruction of desired signals from the time series of vesicle release events. Link to our paper.

Neural Mechanism of Optimal Limb Coordination: Despite the general belief that neural circuits have evolved to optimize behavior, few studies have clearly identified the neural mechanisms underlying optimal behavior. The distinct limb coordination in crustacean swimming and the relative simplicity of the neural coordinating circuit have allowed us to show that the interlimb coordination in crustacean swimming is biomechanically optimal and how the structure of underlying neural circuit robustly gives rise to this coordination. Thus, we provided a concrete example of how an optimal behavior arises from the anatomical structure of a neural circuit. Furthermore, our results suggested that the connectivity of the neural circuit underlying limb coordination during crustacean swimming may be a consequence of natural selection in favor of more effective and efficient swimming. Link to our paper.

Robust Phase-Waves in CPG Networks: Many neuronal circuits driving coordinated locomotion are composed of chains of half-center oscillators (HCOs) of various lengths. The HCO is a common motif in central pattern generating circuits (CPGs); an HCO consists of two neurons, or two neuronal populations, connected by reciprocal inhibition. To maintain appropriate motor coordination for effective locomotion over a broad range of frequencies, chains of CPGs must produce approximately constant phase-differences in a robust manner. Here, we studied phase-locking in chains of nearest-neighbor coupled HCOs and examined how the circuit architecture can promote phase-constancy, i.e., inter-HCO phase-differences that are frequency-invariant. Link to our paper.

Positions Held

8/2016 - present    Assistant Professor
Department of Mathematics, University of Arizona
9/2013 - 8/2016    Assistant Professor / Courant Instructor
Courant Institute of Mathematical Sciences, New York University