Inferring phenomenological models of biological systems Open Access

Rivera, Catalina (Fall 2020)

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Biological systems and processes are complex. They are governed by a large number of units interacting with each other in many different ways and on many different time scales. Thus, constructing mechanistically accurate models capable of explaining the emergent macroscopic behavior of these system and making non-trivial predictions based on such models is often infeasible. To alleviate this problem, new approaches are needed to infer functional, phenomenological models of biological systems directly from data. Here, we develop and apply tools capable of doing this, using statistical inference to automatically construct phenomenological models for different types of biological processes across multiple spatio-temporal scales. Our approach is enabled by the increases in computational power and the development of statistical inference and machine learning methods on the one hand, and the high-throughput biological experimental techniques on the other, which we have experienced over the last decades. First, we focus on inferring phenomenological models for studying systems that can be seen as First Passage Processes---where a relevant or observable biological phenomenon happens after a certain state is achieved in a series of stochastic transitions among internal states of the system. We develop a phenomenological approach where simple models get refined (rather than complex models getting coarse-grained), adding progressively more details until the experimental first passage time distribution is well approximated. In this way, our approach avoids the pitfalls of having to build a detailed, mechanistically accurate model first, in route to phenomenological, functional understanding. In particular, we infer models explaining Purkinje Cells (a type of a neuron) spike generation and single-enzyme turnover times distribution. We show that our inferred models allow us to uncover minimal constraints on more mechanistically accurate models of the involved phenomena. Our second set of phenomenological model inference tools revolves around developing a mathematical framework to study animal behavioral evolution. In particular, we study the behavioral evolution of six closely related species of fruit flies. We show that, by reconstructing ancestral behavioral repertoires, a very simple model describing the stochasticity in behavioral evolution lets us infer the nature of the intra- vs inter-species variability. Our approach provides a new framework to study behavioral evolution and to develop an understanding of its genetic basis. All of the phenomenological inference approaches proposed in this Dissertation show the potential of using statistical inference tools to help us achieve physics-level model-based  understanding of various functions of complex biological systems.

Table of Contents

1 Introduction 1

2 Inferring Phenomenological models of First Passage processes 8

2.1 Introduction 8

2.2 Results 11

2.3 Discussion 26

2.4 Materials and Methods 29

3 Inferring phenomenological models for biochemical reactions 37

3.1 Introduction 37

3.2 Single enzyme reaction times 39

3.3 Results 42

3.4 Discussion 54

4 A framework for studying behavioral evolution by reconstructing ancestral repertoires 57

4.1 Introduction 57

4.2 Experiments and behavioral quantification 60

4.3 Reconstructing Ancestral Behavioral Repertoires 64

4.4 Individual variability and long timescale correlations 66

4.5 Identifying phylogenetically linked behaviors 71

4.6 Discussion 73

4.7 Materials and Methods 76

5 Conclusions 80

Appendix A 84

Appendix B 87

Appendix C 88

Bibliography 92

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