Simon Fraser University Undergraduate Collection

In stochastic biological systems, it is difficult to predict how the state of the system will evolve in response to a dynamic environment. Various attempts have been proposed in different literature. Some papers contain extreme simplicity in the system or suggest a potentially misleading method. In this study, we propose methodology to infer properties of the environment in which an observed system may have evolved: “reverse ecology”. Here, the system can be a cell, and the environment can be everything else other than the cell. We aim to understand the success of a given system compared to all other possible systems in the given environment. From this, we infer the environment that is the most likely one for the system to have arisen in. This Bayesian approach is applied as an inference method that is different from the existing methods. Two different model systems, Poisson distributions and negative binomial distributions, are applied to infer the evolutionary environment from an observed system.

We investigate a model that allows us to look at electron transfer in the fast-hopping regime. Using recent developments in the study of non-equilibrium processes, we compute optimal protocols which minimize the excess work required to drive the system from one control parameter value to another. Using these protocols, we evolve the system using Fokker-Planck dynamics to calculate how successful these protocols are over a variety of parameter values. We find that in using these protocols there is a trade-off between reducing the dissipation and successfully transferring the electron.

The standard cosmological model, known as the ΛCDM model, is the simplest model that accurately describes a variety of aspects of the Universe, including the cosmic microwave background (CMB), large scale structure, and accelerated expansion. Independent observational data, including data from the CMB, baryon acoustic oscillations (BAO), and supernovae type Ia (SNe Ia) provide significant statistical support for the ΛCDM model. Despite this support the Hubble expansion rate determined from these observations is inconsistent with direct measurements, presenting a tension of over 4σ. In this examination we attempt to alleviate this tension by looking at an important assumption of the ΛCDM model, the assumption that the energy densities of the different cosmic fluid components evolve independently. To test this we consider pairwise interactions between dark sector cosmic fluid components by introducing terms which allow for energy exchange between components to the right hand side of the Friedmann fluid equations. Making use of Markov Chain Monte Carlo methods we find that energy exchange between cold dark matter (CDM) and dark energy can correct for the discrepancy between CMB measurements of the Hubble expansion rate and direct measurements, but that adding the BAO measurements to the analysis prevents this tension from being fully alleviated. Our findings suggest dark sector cosmic fluid interactions are a strong candidate for physics beyond ΛCDM and warrant additional research.

Cellular networks in biological systems are complex and as such, identifying the molecular interactions that give rise to the complex behavior observed can require an immense amount of data. Often, statistical and machine learning techniques are used to analyze this data and extract a global picture of network dynamics. One of the challenges of network analysis in systems biology is finding the connections between genes, proteins, or both, and predicting additional ones that have not yet been detected experimentally. This problem is easily mappable to the inverse problem of statistical physics: inferring the microscopic particle-particle interactions given macroscopic observations of a system. In particular, the focus of this work is to investigate whether perturbations can be introduced into the system so as to improve the output data quality. Specifically, we explore how perturbations in the form of magnetic field can be used to improve the inference of interactions for a three-spin Ising system. Utilizing a maximum likelihood approach, we empirically show that there exists an optimal field where learning is most ecient. Such a field seems to counteract the individual interactions between spins, allowing for optimal inference.

A stochastic system under the influence of a stochastic environment will become correlated with both present and future states of the environment. Such a system can be seen as a predictive model of future environmental states. The non-predictive model complexity in such a model has been shown in a recent paper to be fundamentally equivalent to thermodynamic dissipation. In this dissertation, this abstract result is explored in concrete models in order to illustrate how it emerges in realistic systems. In steady-state, this model complexity is found to be the dominant form of dissipation when the system is strongly driven and quick to relax back to equilibrium. Model complexity being the dominant form of dissipation is shown to be equivalent to the rate at which the system learns about its environment being large compared to the heat dissipation.

Biological processes are inherently stochastic, and to achieve directionality, consume free energy. In most cases, the total free energy for a single cycle is fixed. We investigate how this fixed free energy can be allocated throughout different states to maximize the probability flux. We adopt a formalism based on the master equation to find exact solutions to the probability distribution for a specific state at a given time in Laplace space. With this analytical expression for probability distributions, we can calculate the probability flux for a 2-state and 3-state systems using two different energy landscapes, forward=labile, and reverse-labile schemes. We find the optimal allocation of free energy is unevenly distributed to compensate for slower transitions rates in the cycle.

To study how gene-gene interactions may be controlled, and driven toward particular gene states, an Ising model has been proposed to model genes as binary interacting spins. To determine the effect of ‘clamping’ the states of particular genes requires accounting for the other interactions in the network through the renormalization scheme proposed in this thesis.

In recent years, the amount of data available on biological systems such as genetic regulatory networks and neural networks has increased exponentially, thanks to improvements in experimental methods such as drop-seq [1], which enables biologists to simultaneously analyze RNA expression in thousands of cells. To keep pace with the available data, modern machine learning requires efficient methods for using this data to develop predictive models about the natural world. Using a canonical statistical physics example, the Inverse Ising problem, we ask how physical factors such as temperature affect the learning efficiency. In a network governed by a Hamiltonian with spin-spin interactions, we construct a linear system of equations based on equilibrium observations of spin states, and use linear algebra to solve for the underlying spin-spin couplings. We show that there exists an optimal temperature Topt for which learning is most efficient. Furthermore, we discuss several physical correlates for the scaling of Topt with network size for a simple uniform-coupling network and discuss the extension to more general distributions of couplings. The Fisher information, which depends strongly on the variance of the spin-spin alignment, is shown to predict this scaling most accurately.

Recent experimental advancements have allowed for the precise spatial and temporal control of chemical potentials between proteins in the vicinity of one another through optogenetic techniques [3]. This new technique allows for the investigation of cell signalling. Cells communicate by sending chemical signals to induce changes in chemical potentials which then leads to a change of cellular state. In this thesis we apply non-equilibrium theory [6] to model the response of cells to changes in chemical potential, then, by assuming cells want to minimize wasted energy we derive the optimal protocol for cells to change their cellular state through changes in chemical potential. We provide the theoretical framework to derive this optimal protocol for three separate two state chemical reactions: a discrete open system attached to a bath of proteins, a discrete closed system where the total number of proteins is fixed and a continuous closed system where we consider both the spatial and temporal dependence. Although the theory developed is applicable to these reactions for any transition rates, we assume a specific form which closely resembles cell signalling. The resistance to changes in chemical potential is shown to increase exponentially with chemical potential for an open system, to increase exponentially then decay slowly with chemical potential for a closed system and decreases as 1/r where r is the distance from the change. From this we find the optimal protocol and compare the excess work required to change the cellular state using the optimal and naive (constant velocity) protocols. For an open system the optimal protocol is much better than the naive if the chemical potential is varied across a large distance. For a closed system we find similar behaviour for smaller chemical potentials but the improvement then peaks and decreases slowly for very large distances. The spatial dependence of the continuous system has the added effect of decreasing the improvement and smoothing out the peak. We show that our results are consistent with one another in the limiting cases. From this we conclude that cells which require changes in chemical potential within the peak region to change their cellular state will gain the largest benefit from the optimal protocols derived. The optimal protocol has a simple logarithmic form in time µ(t) = ln(ct + b), with c and b constants, for the open system, for the closed and continuous systems it has a more complex shape. Proof of concept of directly simulating the system for comparison is shown, and issues with simulation are discussed.