Counting-based inference of mutant growth rates from pooled sequencing across growth regimes

Time-resolved sequencing of pooled mutants is widely used to track their frequencies under selection pressure, thereby revealing variants that are enriched or depleted. Here, we address how to quantify variant growth rates by analyzing the temporal dimension of the counts data through a model of growth. For exponential growth, we first study weighted least-squares fitting and show that non-linear fitting based on the softmax transformation exhibits more favorable properties than the currently employed linear regression. We then argue that direct maximization of the likelihood of the noise model should be preferred over least-squares fitting. For a multinomial model of counting noise, we adopt variational Bayesian inference to additionally quantify uncertainties in the estimated growth rates. We provide closed-form expressions for the experimentally practical case of sequencing only at the beginning and at the end of the experiment. Finally, we extend maximum-likelihood estimation and variational Bayesian inference to logistic and Gompertz growth, which serve as illustrative examples of general, non-exponential growth models formulated in terms of a small number of parameters per variant. The ability to incorporate arbitrary growth models within the developed inference framework opens new opportunities for high-throughput estimation of diverse biochemical parameters that influence growth. Author summarySimultaneously tracking the relative abundances of thousands of genetically distinct cellular variants over time is now possible through deep sequencing and other counting-based methods. This capability provides a quantitative window into increasingly broad regions of the combinatorial fitness landscape--well beyond those explored by natural evolution. While identifying a few engineered variants that survive under extreme selection is valuable, quantitative mapping of the fitness landscape requires accurate inference of growth rates for the entire variant population. Here, we revisit three approaches for estimating growth rates from sequencing count data: least-squares fitting, maximum likelihood estimation, and variational Bayesian inference. By clearly delineating the probabilistic model of counting noise and the deterministic model of variant growth--both jointly required for inferring growth rates from time-resolved sequencing counts--we show how exponential growth can be replaced by any alternative growth model. Applying the developed analysis framework to models in which growth rates are expressed in terms of microscopic biochemical parameters will enable the high-throughput inference of fundamental kinetic and biophysical constants from sequencing data.