Dissertations, Theses, and Capstone Projects

Date of Degree

2-2024

Document Type

Dissertation

Degree Name

Ph.D.

Program

Biology

Advisor

Asohan Amarasingham

Committee Members

Ekaterina Likhtik

Lucas Parra

Horacio Rotstein

Samuel McKenzie

Subject Categories

Applied Statistics | Biological and Chemical Physics | Computational Neuroscience | Dynamical Systems | Systems Neuroscience

Keywords

causal inference, spike trains, functional connectivity, neuroscience, biophysics

Abstract

Since the 1960s, neuroscientists have worked on the problem of estimating synaptic properties, such as connectivity and strength, from simultaneously recorded spike trains. Recent years have seen renewed interest in the problem coinciding with rapid advances in experimental technologies, including an approximate exponential increase in the number of neurons that can be recorded in parallel and perturbation techniques such as optogenetics that can be used to calibrate and validate causal hypotheses about functional connectivity. This thesis presents a mathematical examination of synaptic inference from two perspectives: (1) using in vivo data and biophysical models, we ask in what cases the biophysical properties of neurons render identifiable monosynaptic causal effects, and (2) primarily within identifiable regimes, we search for robust statistical assumptions for estimating causal effects. In the first part, synaptically-coupled biophysical model neurons are fit to in vivo perturbation data and the statistical identification of synaptic properties from spike trains is studied as a function of dynamical parameters of the fitted models. Using these observations to narrow the investigation, a semi-parametric statistical framework is then outlined for estimating the causal effect of excitatory synapses. In the second part, a more comprehensive causal inference framework for pairwise causal effects between spike trains is developed, providing proofs of theorems for unbiased point estimation and exact confidence intervals for excitatory and inhibitory interactions. Through the lens of this framework, the link between biophysical parameters and a statistical definition of causality between spike trains is examined in more generality and across a greater spectrum of dynamical systems. Some additional investigations include studying the effect of neural perturbations (e.g., optogenetics) on biophysical model neurons, designing experiments that can quantitatively test the causal inference framework with perturbations, providing experimental predictions for alternative hypotheses (specifically, the implications of misinterpreting synaptic common input correlations as monosynaptic connections), and a sketch of an ensemble approach that uses model-guided deep learning to combine distinct forms of evidence, including inferences from the causal inference framework, to estimate causal effects between spike trains. We conclude with remarks on how a deeper purpose of the work is to bridge dynamical and statistical descriptions of neural circuits in ways relevant to neural coding.

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