Contributions to statistical analysis methods for neural spiking activity

With the technical advances in neuroscience experiments in the past few decades, we have seen a massive expansion in our ability to record neural activity. These advances enable neuroscientists to analyze more complex neural coding and communication properties, and at the same time, raise new challenges for analyzing neural spiking data, which keeps growing in scale, dimension, and complexity. This thesis proposes several new statistical methods that advance statistical analysis approaches for neural spiking data, including sequential Monte Carlo (SMC) methods for efficient estimation of neural dynamics from membrane potential threshold crossings, state-space models using multimodal observation processes, and goodness-of-fit analysis methods for neural marked point process models. In a first project, we derive a set of iterative formulas that enable us to simulate trajectories from stochastic, dynamic neural spiking models that are consistent with a set of spike time observations. We develop a SMC method to simultaneously estimate the parameters of the model and the unobserved dynamic variables from spike train data. We investigate the performance of this approach on a leaky integrate-and-fire model. In another project, we define a semi-latent state-space model to estimate information related to the phenomenon of hippocampal replay. Replay is a recently discovered phenomenon where patterns of hippocampal spiking activity that typically occur during exploration of an environment are reactivated when an animal is at rest. This reactivation is accompanied by high frequency oscillations in hippocampal local field potentials. However, methods to define replay mathematically remain undeveloped. In this project, we construct a novel state-space model that enables us to identify whether replay is occurring, and if so to estimate the movement trajectories consistent with the observed neural activity, and to categorize the content of each event. The state-space model integrates information from the spiking activity from the hippocampal population, the rhythms in the local field potential, and the rat's movement behavior. Finally, we develop a new, general time-rescaling theorem for marked point processes, and use this to develop a general goodness-of-fit framework for neural population spiking models. We investigate this approach through simulation and a real data application

Modelling the effect of genes on the dynamics of probabilistic spiking neural networks for computational neurogenetic modelling

Computational neuro-genetic models (CNGM) combine two dynamic models – a gene regulatory network (GRN) model at a lower level, and a spiking neural network (SNN) model at a higher level to model the dynamic interaction between genes and spiking patterns of activity under certain conditions. The paper demonstrates that it is possible to model and trace over time the effect of a gene on the total spiking behavior of the SNN when the gene controls a parameter of a stochastic spiking neuron model used to build the SNN. Such CNGM can be potentially used to study neurodegenerative diseases or develop CNGM for cognitive robotics.

Evaluation of dynamic causal modelling and Bayesian model selection using simulations of networks of spiking neurons

Inferring the mechanisms underlying physiological and pathological processes in the brain from recorded electrical activity is challenging. Bayesian model selection and dynamic causal modelling aim to identify likely biophysical models to explain data and to fit the model parameters. Here, we use data generated by simulations to investigate the effectiveness of Bayesian model selection and dynamic causal modelling when applied at steady state in the frequency domain to identify and fit Jansen-Rit models. We first investigate the impact of the necessary assumption of linearity on the dynamics of the Jansen-Rit model. We then apply dynamic causal modelling and Bayesian model selection to data generated from simulations of linear neural mass models, non-linear neural mass models, and networks of discrete spiking neurons. Action potentials are a characteristic feature of neuronal dynamics but have not previously been explicitly included in simulations used to test Bayesian model selection or dynamic causal modelling. We find that the assumption of linearity abolishes the qualitative transitions seen as a function of the connectivity parameter in the original Jansen-Rit model. As with previous work, we find that the recovery procedures are effective when applied to data from linear Jansen-Rit neural mass models, however, when applying them to non-linear neural mass models and networks of discrete spiking neurons we find that their effectiveness is significantly reduced, suggesting caution is required when applying these methods.Comment: 18 pages, 15 figure

A unified approach to linking experimental, statistical and computational analysis of spike train data

A fundamental issue in neuroscience is how to identify the multiple biophysical mechanisms through which neurons generate observed patterns of spiking activity. In previous work, we proposed a method for linking observed patterns of spiking activity to specific biophysical mechanisms based on a state space modeling framework and a sequential Monte Carlo, or particle filter, estimation algorithm. We have shown, in simulation, that this approach is able to identify a space of simple biophysical models that were consistent with observed spiking data (and included the model that generated the data), but have yet to demonstrate the application of the method to identify realistic currents from real spike train data. Here, we apply the particle filter to spiking data recorded from rat layer V cortical neurons, and correctly identify the dynamics of an slow, intrinsic current. The underlying intrinsic current is successfully identified in four distinct neurons, even though the cells exhibit two distinct classes of spiking activity: regular spiking and bursting. This approach – linking statistical, computational, and experimental neuroscience – provides an effective technique to constrain detailed biophysical models to specific mechanisms consistent with observed spike train data.Published versio

Integration of continuous-time dynamics in a spiking neural network simulator

Contemporary modeling approaches to the dynamics of neural networks consider two main classes of models: biologically grounded spiking neurons and functionally inspired rate-based units. The unified simulation framework presented here supports the combination of the two for multi-scale modeling approaches, the quantitative validation of mean-field approaches by spiking network simulations, and an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes. While most efficient spiking simulations rely on the communication of discrete events, rate models require time-continuous interactions between neurons. Exploiting the conceptual similarity to the inclusion of gap junctions in spiking network simulations, we arrive at a reference implementation of instantaneous and delayed interactions between rate-based models in a spiking network simulator. The separation of rate dynamics from the general connection and communication infrastructure ensures flexibility of the framework. We further demonstrate the broad applicability of the framework by considering various examples from the literature ranging from random networks to neural field models. The study provides the prerequisite for interactions between rate-based and spiking models in a joint simulation