Summary of a thesis. Felce, Catherine (2026). "Biophysical Modeling for Gene Expression and Evolution". PhD thesis, California Institute of Technology. Defended December 10, 2025. (original). Rights: all rights reserved — not reproduced. This is a short account of it in our own words; the work itself is not reproduced here.
Biophysical Modeling for Gene Expression and Evolution¶
What this covers¶
A Caltech physics PhD thesis building biophysically motivated stochastic models for single-cell genomics data, and separately developing exact mathematical analogies between physics and evolutionary/ecological theory. It speaks to computational biology and theoretical evolutionary biology, asking where mechanistic models of transcription, translation and chromatin dynamics can replace heuristic analyses of single-cell data, and where correspondences between physical and biological theory can sharpen evolutionary argument rather than just decorate it.
The question¶
Single-cell gene-expression analysis has mostly relied on heuristics — differential expression, dimension reduction, clustering — without reference to the molecular mechanisms of transcription, translation and decay. As single-cell measurement expanded beyond mRNA to chromatin accessibility (ATAC-seq) and surface protein (CITE-seq), the thesis asks whether these modalities can instead be described jointly with RNA through stochastic chemical-master-equation models, and what such models reveal about mechanism and data quality. A parallel question concerns evolution: comparative studies of expression divergence between species have used bulk mRNA level as the evolving trait, which obscures which biophysical process — burst size, burst frequency, decay rate — is actually under selection. More broadly, the thesis asks whether analogies between physical theory (statistical mechanics, Newtonian mechanics) and evolutionary/ecological theory (the Price equation, population cycles) can be made exact rather than left as metaphor.
The approach¶
Each central chapter builds a chemical master equation (CME) for molecular counts, solved via generating-function methods, coupled either to real single-cell data or to a model of evolutionary change. Chromatin accessibility at neighbouring ATAC-seq peaks is modeled as a 1-D Ising-like chain, with one parameter tuning the preference of adjacent loci to share open/closed states, combined with constitutive transcription to give a joint chromatin/RNA distribution. An existing nascent/mature-RNA bursting model is extended with translation and protein decay, giving a joint CME for unspliced RNA, spliced RNA and protein (with Meichen Fang). Per-gene biophysical parameters (burst size, splicing rate, decay rate) estimated separately across six vertebrate species are treated as continuous traits evolving along the species tree under competing multivariate Ornstein-Uhlenbeck models, each encoding a different hypothesis about which quantity is under stabilizing selection. Finally, the time-averaged continuous Price equation is shown identical to the virial theorem under a dictionary mapping population size to momentum and trait value to position, then used to extend an ecological maternal-effect model of population cycles to interacting, spatially separated subpopulations.
What it found¶
In the chromatin chapter, an eight-parameter Ising-like model (independent on/off rates per site plus a shared neighbour-correlation term) beat a six-parameter independent-sites model by BIC at most tested six-peak loci across three 10x ATAC-seq datasets (26/30 PBMC, 7/7 mouse cortex, 14/14 human-mouse mixture), supporting real positive correlation between neighbouring sites. It also showed that downstream transcript correlations can exceed the correlation of the parent DNA states, and that registered and unregistered scATAC+scRNA data give comparable power to identify the correlation parameter for a fixed budget, with scATAC-seq alone the most cost-efficient single modality.
In the RNA-protein chapter, simulations recovered all five parameters (burst size, splicing rate, RNA decay, translation rate, protein decay) accurately for most of 46 simulated genes; because real unspliced counts were too sparse, a reduced model fit to spliced RNA and protein alone remained identifiable, with some loss of accuracy in splicing rate. Fit to two 10x CITE-seq PBMC datasets, it reproduced observed joint mRNA-protein distributions for marker genes (CD14, CD45, IL7R).
In the phylogenetics chapter, fitting the competing models to parameters estimated across six species' spleen data, the decay-rate-constrained model — selection on mRNA decay, with burst size free to adapt and hold mean expression at its optimum — fit much better by AIC (2,124) than an independent model (2,726) or a burst-size-constrained model (3,186). Selection strength on decay rate also increased with expression level, matching dN/dS patterns for the same genes, suggesting mRNA decay is the more constrained process and bursting the more flexible lever.
In the physics-analogy chapter, the Price-equation/virial-theorem identity supports reading the covariance ("selection") term as a selection rate, and suggests selection corresponds to a rate of change of fitness — a force — rather than being a constant force itself. Applied to the extended maternal-effect model, it yields closed-form simple-harmonic-motion solutions for population cycles, a "universality" result that combining such subpopulations can reproduce arbitrary periodic dynamics, and, for spatially distributed competing subpopulations, a wave equation for trait evolution in space.
Limits and context¶
These are presented as first, deliberately minimal models rather than finished biological accounts. The Ising-chromatin model does not explain the mechanistic origin of neighbour correlations and is limited by ATAC-seq sparsity. The RNA-protein model treats surface protein as a direct, instantaneous proxy for intracellular protein, and the full three-modality fit was unreliable on real data because of noisy unspliced counts, hence the reduced two-modality fit used in practice. The phylogenetic model assumes genome-wide-shared evolutionary rates and treats per-gene variability as either following the shared model or white noise, resting on only six species and one tissue. The physics analogies are flagged as formal correspondences, not shared causal mechanism — the resemblance of the ecological oscillator to a mass on a spring is called "optical only" — and the author favours the "statistical" interpretation of evolutionary theory over a "dynamical" one that treats selection as a literal force. Throughout, the thesis argues against treating ad hoc heuristics as adequate once single-cell, multi-modal data make mechanistic modeling possible.
Citation¶
Felce, Catherine (2026). "Biophysical Modeling for Gene Expression and Evolution". PhD thesis, California Institute of Technology. Defended December 10, 2025. Available at https://thesis.library.caltech.edu/17880/.