Summary of a thesis. Fang, Meichen (2025). "A biophysical approach to normalization and trajectory inference in single-cell RNA sequencing data analysis." PhD thesis, California Institute of Technology. Defended May 28, 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.
A biophysical approach to normalization and trajectory inference in single-cell RNA sequencing data analysis¶
What this covers¶
A PhD thesis in biological engineering arguing that two routine steps of single-cell RNA sequencing (scRNA-seq) analysis, normalization and trajectory inference, should be built on explicit stochastic models of gene expression rather than the heuristic procedures that dominate current pipelines.
The question¶
Early single-cell studies of gene expression, before scRNA-seq existed, fitted mechanistic stochastic models — the telegraph and bursty promoter models, solved via the chemical master equation (CME) — to small numbers of genes measured by imaging. The author frames this, after Breiman's "two cultures" of statistical modeling, as a data model culture: positing a stochastic mechanism and prioritizing interpretability. Once scRNA-seq made genome-wide profiling possible, the field's standard workflow — filter by total counts, normalize by dividing by a cell's total counts, apply a \(\log(1+x)\) transform, select variable genes, embed and infer pseudotime from distances — largely abandoned that grounding for an algorithmic culture, chosen because it scales and predicts well rather than because it describes how the data arose. The thesis asks what is gained by returning to an explicit generative model for these two steps: what normalization and "pseudotime" actually mean once a mechanism and a measurement model are stated, and what static snapshot data can and cannot support as a result.
The approach¶
A background chapter reviews the CME and its standard large-volume approximations (system-size expansion/linear noise approximation, WKB), recounting the known result that their infinite-time and infinite-volume limits do not commute, so neither holds uniformly in time. It then sketches a preliminary, explicitly incomplete attempt, via the positive Poisson representation, to build an approximation for bimolecular reactions valid uniformly in time.
The normalization chapter models the variability across cells and genes as the product of a per-cell biological scaling factor (cell size, cycle phase, similar global effects) and a technical factor from Bernoulli sampling of transcripts during library preparation. This gives an algebraic identity linking the normalized covariance between genes, this combined "extrinsic noise," and the overdispersion seen in genes whose counts are intrinsically close to Poisson. The identity lets near-Poisson "control" genes be identified from data alone and used, rather than total counts over all genes, as a principled cell-size factor.
The trajectory chapter introduces Chronocell, which places each cell at a latent (lineage, process time) position on a directed graph of discrete states, each with its own constant transcription rate; nascent and mature RNA counts follow the known analytic solution of a constant-rate birth-death CME, with a sequencing-noise layer on top. Parameters and process time are fit by variational inference, competing topologies are compared by AIC/BIC, and a per-gene goodness-of-fit check flags genes the model does not capture — replacing the usual fit-then-test pipeline, which the thesis argues is circular because it tests genes against a pseudotime built from those same genes.
What it found¶
The CME chapter's time-uniform approximation is left unfinished: it shows a stable fixed point cannot exist off the real axis in the complex-domain rate equation, but does not complete the construction.
The normalization model, validated on synthetic dilution data, was applied to human-mouse mixing experiments, where ambient mRNA from the other species gave an independent read on technical noise. Biological and technical extrinsic noise were both substantial and comparable (e.g. technical noise around 0.15 against total noise around 0.24 in one dataset), and often under a fifth of genes had mature-mRNA counts consistent with Poisson statistics. Size factors built from these genes correlated closely with conventional total-count size factors (\(r \approx 0.99\)) in one dataset but diverged, with consequences for differential expression, when cell-type composition was skewed. The Bernoulli assumption held for mature mRNA in several 10x datasets but failed on a STORM-seq dataset, so the model needs validating per protocol.
Chronocell recovered simulated ground-truth process time to within about 5% of trajectory duration, estimated the fast-switching transcription rate more accurately than splicing and degradation rates, correctly selected the true topology over wrong alternatives by AIC/BIC, and correctly flagged non-dynamic genes. On real data it recovered a cyclic topology for a cell-cycle dataset, with degradation-rate estimates moderately correlated with two metabolic-labeling techniques, and on a time-stamped neuron dataset its process time tracked experimental time better than four widely used alternatives, only one of which captured the trend at all. Comparator methods failed on data simulated under Chronocell's own assumptions; on more generic simulations Chronocell was comparable to or better, though no method recovered exact timing.
A short closing chapter argues both models are deliberately simplified — a single scalar biological noise factor, bursting-free piecewise-constant transcription — and calls for closing the loop between mechanistic modeling and experimental design, so scRNA-seq technical variability could eventually be characterized as reproducibly as a physical constant.
Limits and context¶
The thesis states that its CME approximation is unfinished, that its normalization model collapses biological extrinsic noise into one per-cell number and cannot be checked where Bernoulli sampling fails, and that Chronocell's transcription model undershoots real transcriptional noise and assumes a trajectory topology chosen by model selection rather than discovered from scratch. It argues against purely similarity/distance-based pseudotime, which it says cannot be given a physical interpretation, and against testing gene association with a pseudotime inferred from the same data, calling that circular. It does not claim a comprehensive benchmark, since comparisons across methods built on different generative assumptions are not strictly like for like.
Citation¶
Fang, Meichen (2025). A biophysical approach to normalization and trajectory inference in single-cell RNA sequencing data analysis. PhD thesis, California Institute of Technology. Defended May 28, 2025. DOI: 10.7907/asek-t904. Available from the Caltech Thesis Library.