Intermittency as metastability: a predictive approach to evolution in disordered environments

Many systems across the sciences evolve through a combination of multiplicative growth and diffusive transport. In the presence of disorder, these systems tend to form localized structures which alternate between long periods of relative stasis and short bursts of activity. This behaviour, known as intermittency in physics and punctuated equilibrium in evolutionary theory, is difficult to forecast; in particular there is no general principle to locate the regions where the system will settle, how long it will stay there, or where it will jump next. Here I introduce a predictive theory of linear intermittency that closes these gaps. I show that any positive linear system can be mapped onto a generalization of the "maximal entropy random walk", a Markov process on graphs with non-local transition rates. This construction reveals the localization islands as local minima of an effective potential, and intermittent jumps as barrier crossings in that potential. My results unify the concepts of intermittency in linear systems and Markovian metastability, and provide a generally applicable method to reduce, and predict, the dynamics of disordered linear systems. Applications span physics, evolutionary dynamics and epidemiology.Comment: Extension of arXiv:1912.0589

On the Use of Coarse-Grained Thermodynamic Landscapes to Efficiently Estimate Folding Kinetics for RNA Molecules

Thesis advisor: Peter CloteRNA folding pathways play an important role in various biological processes, such as 1) the conformational switch in spliced leader RNA from Leptomonas collosoma, which controls transsplicing of a portion of the 5’ exon, and 2) riboswitches–portions of the 5’ untranslated region of mRNA that regulate genes by allostery. Since RNA folding pathways are determined by the thermodynamic landscape, we have developed a number of novel algorithms—including FFTbor and FFTbor2D—which efficiently compute the coarse-grained energy landscape for a given RNA sequence. These energy landscapes can then be used to produce a model for RNA folding kinetics that can compute both the mean first passage time (MFPT) and equilibrium time in a deterministic and efficient manner, using a new software package we call Hermes. The speed of the software provided within Hermes—namely FFTmfpt and FFTeq—present what we believe to be the first suite of kinetic analysis tools for RNA sequences that are suitable for high throughput usage, something we believe to be of interest in the field of synthetic design.Thesis (PhD) — Boston College, 2015.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Biology