Neurons represent information about relevant biological signals in patterns of electrical spiking activity. Statistical modeling and dynamical systems theory represent two distinct approaches to modeling the activity of neurons, which have largely been developed separately. However, the neural code is both stochastic and dynamic. This research and education program provides a link between modeling and data analysis by developing a robust framework for the statistical analysis of neural spiking data. This research is partially motivated by the increasing recognition that dynamics related to rhythmic and oscillatory brain signals play an important role in many cognitive states such as attention, memory, perception, and language, while abnormalities in these rhythms are associated with neurological diseases such as schizophrenia, Parkinson's, and Alzheimer's disease.
The fundamental objective of this research is to develop a framework for the analysis of neural spike train data that incorporates dynamical state models of neural and other biological signals. This objective will be achieved by a combination of theoretical development of dynamical models and mathematical algorithms, and the application of this theory to the analysis of recorded neural data at multiple scales, including individual neurons, small microcircuits, and larger networks across brain regions. The theoretical component of this research project will extend earlier results using point process methods to more accurately describe and more efficiently extract information from spike trains. New stochastic neural models that include dynamic state variables will be explored, and estimation algorithms based on point process likelihoods and posterior distributions will be derived. This framework will then be applied to problems of relating spiking activity to dynamic oscillatory signals in spiny stellate cells from the medial entorhinal cortex of the rat and in subthalamic nucleus in patients with Parkinson's disease. The theory will inform the applications by providing methods for neural estimation and model evaluation, while these applications will inform the theory by promoting the development of new physiologically relevant neural models.
This project established an integrated research and education plan to study the information contained in the electrical impulses, or spikes, in the brain. We developed new statistical methods to capture how populations of neurons in various brain areas work together to represent features of the outside world, and perform computations to respond to outside stimuli. At the heart of this approach is the notion of modeling the instantaneous probability that any neuron will spike as a function of its own past activity, the past activity of other neurons, and as a function of the stimuli that drive activity in the given brain region. These models use specific nonlinear structures and classes of probability distributions that we have shown to accurately represent neural activity in a wide variety of brain regions, both in humans and in animals. We developed new techniques to model neural spike data, to test scientific and statistical hypotheses about this data, to evaluate the quality of our models, and to decode biological stimuli and predict future behavior using neural spike activity. We applied these methods to a variety of important neuroscience problems. We helped develop models to elucidate how the hippocampus, the brain region most associated with memory storage and recall, is able to simultaneously represent time and space. In that same brain area, we have also developed models to understand how neurons use differential activity to select between possible future behavioral actions. This work has helped us understand neural mechanisms of memory function and tasks like navigation. We have also applied these methods to the study of human physiology and of disease processes. We have applied our statistical models to activity in deep brain structures related to movement in patients with Parkinson’s disease in order to understand the pathological activity that leads to motor deficits in this disease. We found that minor changes in the influence of past activity on the spiking probability in these structures that likely arise due to dysregulation of the brain network in these deep areas leads to pathological, uncontrolled rhythmic activity across a wide range of brain areas. Manipulating the spiking activity in the proper location with electric or other forms of stimulation has the capacity to restore normal spiking patterns and alleviate motor deficits. This research has provided the preliminary findings for a current study on Parkinson’s disease therapy with the goal of improving deep brain stimulation for the motor symptoms of Parkinson’s disease, by using recorded activity to improve electrode placement. Recently, we have also used these methods to study how spiking activity in the sympathetic nervous system is used to control the cardiac rhythm. We have constructed models to characterize the precise spiking patterns associated with changing heart rate as a simple exercise is used to excite the sympathetic nervous system. This research represents an important step towards understanding mechanisms of human sympathetic control of the cardiovascular system. We have constructed models of neural connections in a subset of neurons from the crab stomach using their spiking activity. As opposed to standard modeling techniques, which have been previously shown to fail to capture the correct connectivity patterns and mechanisms for rhythmic activity in this system, we were able to accurately reconstruct known anatomical features and mechanisms within this system. Finally, we developed a method to combine computational, mechanistic models of the activity of individual neurons with statistical techniques to estimate model components directly from data. Classically, mechanistic neural models are estimated through a laborious process of hand tuning. Our results suggest that this approach could be replaced in the future by automated methods that are able to successfully uncover ionic currents and mechanisms that lead to both healthy and pathological activity across a variety of neural cell types. This work has also led a variety of new educational initiatives. We have developed curricula and taught two completely new statistics classes at Boston University, one at the undergraduate level focused on modeling methods for spiking data, and one at the graduate level focused on advanced statistical methods for computational research. These classes have integrated new techniques and datasets that were developed as part of this research. This research has also led to the training in neuroscience data analysis techniques of four undergraduate students, five graduate students, and one post-doctoral researcher. This work has been disseminated to the neuroscience and statistics research communities through presentations at 36 meetings and conferences and has led to the publication of 19 peer-reviewed journal articles. As new neuroscience research, with increasingly large datasets from multiple brain regions, is conducted, statistical methods such as these are becoming critical. The modeling approach at the center of this research project that we helped pioneer is now becoming standard practice for the analysis of neural spiking data.
