Basin Mapping Method for Extracting Comparative Assessments of Protein Phase Behavior from In Vivo Measurements

Abstract

To uncover sequence-encoded driving forces for and the mechanisms of protein-specific phase transitions, we require knowledge of the underlying phase diagram, the degree of supersaturation, and the distance from critical point. Recent technological developments [1] based on Distributed Amphifluoric FRET (DAmFRET) allow the quantitative tracking of phase transitions as a function of protein expression in yeast. These in vivo experiments afford unprecedented throughput while enabling quantitative comparisons of protein-specific phase behavior. For a given protein, the DAmFRET dataset provides 2-dimensional histograms of AmFRET values and expression levels. Here, we adapt advances from energy landscape theory, specifically the inherent structure formalism of Stillinger and coworkers [2], to uncover protein-specific free energy functionals that underlie the phase behavior observed in DAmFRET measurements. We have developed and deployed a hybrid steepest-descent basin mapping method that identifies and quantifies major expression level dependent basins using the 2-dimensional histograms extracted from DAmFRET measurements. This approach identifies; (i) basins, which are envelopes in the 2-dimensional histograms; (ii) the relative weights of basins, and (iii) the centers of basins as defined by the steepest descent mapping. Results from the basin mapping procedure are used to infer protein-specific free energy functionals and these free energy functionals are used to reconstruct phase diagrams. Our analysis enables quantitative comparisons of phase transitions encoded by different protein sequences in a model cellular system. 1. T. Khan et al., (2018), Molecular Cell, 71: 155-168. 2. F. H. Stillinger, Energy Landscapes, Inherent Structures, and Condensed Matter Phenomena, Princeton University Press, 2016.