Oscillations and Synchrony: How do neurons synchronize their activity? How are pacemaking and bursting oscillations generated and modulated?

My major area of research interest is computational neuroscience, specifically the nonlinear dynamics of neurons and small networks, synchronization, oscillation, central pattern generation, bursting neurons, midbrain dopaminergic neurons, and the regulation of the firing pattern in neurons.

I have pursued two lines of research during my career. The first is the synchronization and phase locking of small networks of neurons. One application of this research is a better understanding of central pattern generating networks for respiration, locomotion, and other repetitive motor activities. I have utilized primarily a technique called phase resetting, or phase response curves. This technique can be applied to any cyclical process, and was developed initially to better understand circadian rhythms. I have contributed to the application of these methods to neural oscillators, which have additional complications such as threshold behavior and pulsatile coupling. I have published many original proofs regarding the synchronization of neural oscillators. These proofs utilize both nonlinear systems theory (manifested as phase resetting) and linear systems theory (manifested as stability analyses) applied to neural networks. Currently, I am collaborating with invertebrate electrophysiologists to test these methods in hybrid circuits comprised of one biological neuron and one computational model neuron using a technique called the dynamic clamp. One goal of this work is to generalize to larger oscillatory networks such as those observed in mammalian cortex.

  The second line of research involves the biophysical basis of different firing patterns in neurons, such as regular pacemaker firing, burst firing and irregular firing. My initial work was on neuron R15 in Aplysia, but my current research focuses on the dopaminergic neurons of the mammalian midbrain. These neurons exhibit a wide variety of electrical activity both in a slice preparation and in the intact animal. In collaboration with electro-physiologists, this line of research focuses on how the intrinsic currents generate the firing pattern, and how they interact with synaptic currents and neuromodulators to produce alterations in the firing pattern. Dysfunctional dopaminergic signaling has been implicated in a number of diseases, and the firing pattern in these neurons, in particular the timing of burst firing, is thought to have important functional consequences. I utilize techniques from the mathematical field of nonlinear dynamics, including bifurcation theory, as well as computational techniques to simulate multi-compartment neurons, in order to synthesize the experimental data into a theoretical model of dopamine neurons. One goal of this research is to predict the effect of different types of plasticity as well as various pharmaceutical agents on the electrical activity of dopamine neurons.

Current Research

    The work in my lab is computational in nature. Funded collaborations, generally use the Dynamic Clamp to integrate theory and experiment, and currently include the following experimental labs: Dr. Robert Butera (Georgia Tech), Dr. Astrid Prinz (Emory), Dr. Paul Shepard (Maryland Psychiatric Research Institute), Dr. Edwin Levitan (Pittsburgh Medical School), and Dr. John A. White (University of Utah).  Synchronization of neural activity is one unifying theme of the research conducted in my lab. Synchronization in its broadest sense encompasses the generation of the phase locked patterns exhibited by the central pattern generators responsible for rhythmic activity such as respiration and locomotion. Hence we have developed general criteria under which such lockings can occur in oscillators in which the duration of the postsynaptic potential is short compared to a cycle period.  Synchronized oscillations are also thought to underlie many aspects of cognition. Rapid, internally generated synchronization between distal regions in the brain that relies on intrinsic oscillation has been shown to be important for encoding, retention, and retrieval of information and proposed to underlie binding and conscious perception. Cross frequency synchronization between theta and gamma has been suggested to match the information stored in working memory with incoming sensory information, and synchronization between alpha and theta has been suggested as a mechanism for retrieving items from long-term memory and loading them in working memory. Synchronization of brain rhythms is known to be affected in most psychiatric disorders.  We have recently produced a novel proof that synchrony is a generic solution of identical pulse coupled oscillators separated by a conduction delay, and shown that the robustness of the near synchronous solution in the presence of heterogeneity increases with coupling strength. We have also recently established existence and stability criteria for N:1 cross frequency lockings for pulse coupled oscil-lators. Another focus area is the oscillatory dynamics of bursting and pacemaking rhythms. The dopaminergic neurons of the mammalian midbrain have been extensively modeled in my lab. The coupled oscillator theory of the dopamine neurons holds that the spiking rate is usually driven by slow calcium oscillations in the soma and larger dendrites but during bursting the activation of distal NMDA receptors allows the smaller dendrites to dominate. Recently we have shown that in the presence of spiking activity, the intuition that the natural frequency of the smaller dendrites is faster does not hold. We have also recently suggested critical roles for the L-type calcium current and the SK potassium current in bursting activity, as well as a role for the ether a-go-go related potassium current in relieving depolarization block. Abnormal dopaminergic signaling has been implicated in Parkinson's, schizophrenia, and drug abuse.