Translation of mRNA into protein is a fundamental yet complex biological process with multiple factors that can potentially affect its efficiency. Here, we study a stochastic model describing the traffic flow of ribosomes along the mRNA (namely, the inhomogeneous -TASEP), and identify the key parameters that govern the overall rate of protein synthesis, sensitivity to initiation rate changes, and efficiency of ribosome usage. By analyzing a continuum limit of the model, we obtain closed-form expressions for stationary currents and ribosomal densities, which agree well with Monte Carlo simulations. Furthermore, we completely characterize the phase transitions in the system, and by applying our theoretical results, we formulate design principles that detail how to tune the key parameters we identified to optimize translation efficiency. Using ribosome profiling data from S. cerevisiae, we shows that its translation system is generally consistent with these principles. Our theoretical results have implications for evolutionary biology, as well as synthetic biology.

Direct comparison of bulk gene expression profiles is complicated by distinct cell type mixtures in each sample that obscure whether observed differences are actually caused by changes in the expression levels themselves or are simply a result of differing cell type compositions. Single-cell technology has made it possible to measure gene expression in individual cells, achieving higher resolution at the expense of increased noise. If carefully incorporated, such single-cell data can be used to deconvolve bulk samples to yield accurate estimates of the true cell type proportions, thus enabling one to disentangle the effects of differential expression and cell type mixtures. Here, we propose a generative model and a likelihood-based inference method that uses asymptotic statistical theory and a novel optimization procedure to perform deconvolution of bulk RNA-seq data to produce accurate cell type proportion estimates. We show the effectiveness of our method, called RNA-Sieve, across a diverse array of scenarios involving real data and discuss extensions made uniquely possible by our probabilistic framework, including a demonstration of well-calibrated confidence intervals.

Translation of mRNA into protein is a fundamental yet complex biological process with multiple factors that can potentially affect its efficiency. In particular, different genes can have quite different initiation rates, while site-specific elongation rates can vary substantially along a given transcript. Here, we analyze a stochastic model of translation dynamics to identify the key parameters that govern the overall rate of protein synthesis and the efficiency of ribosome usage. The mathematical model we study is an interacting particle system that generalizes the Totally Asymmetric Simple Exclusion Process (TASEP), where particles correspond to ribosomes. While the TASEP and its variants have been studied for the past several decades through simulations and mean field approximations, a general analytic solution has remained challenging to obtain. By analyzing the so-called hydrodynamic limit, we here obtain exact closed-form expressions for stationary currents and particle densities that agree well with Monte Carlo simulations. In addition, we provide a complete characterization of phase transitions in the system. Surprisingly, phase boundaries depend on only four parameters: the particle size, and the first, last and minimum particle jump rates. Relating these theoretical results to translation, we formulate four design principles that detail how to tune these parameters to optimize translation efficiency in terms of protein production rate and resource usage. We then analyze ribosome profiling data of S. cerevisiae and demonstrate that its translation system is generally efficient, consistent with the design principles we found. We discuss implications of our findings on evolutionary constraints and codon usage bias.

Direct comparison of bulk gene expression profiles is complicated by distinct cell type mixtures in each sample which obscure whether observed differences are actually due to changes in expression levels themselves or simply cell type compositions. Single-cell technology has made it possible to measure gene expression in individual cells, achieving higher resolution at the expense of increased noise. If carefully incorporated, such single-cell data can be used to deconvolve bulk samples to yield accurate estimates of the true cell type proportions, thus enabling one to disentangle the effects of differential expression and cell type mixtures. Here, we propose a generative model and a likelihood-based inference method that uses asymptotic statistical theory and a novel optimization procedure to perform deconvolution of bulk RNA-seq data to produce accurate cell type proportion estimates. We demonstrate the effectiveness of our method, called RNA-Sieve, across a diverse array of scenarios involving real data and discuss several extensions made uniquely possible by our probabilistic framework, including general hypotheses tests and confidence intervals.

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