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.