A mean-field theory for predicting single polymer collapse induced by neutral crowders

Macromolecular crowding can induce the collapse of a single long polymer into a globular form due to depletion forces of entropic nature. This phenomenon has been shown to play a significant role in compacting the genome within the bacterium Escherichia coli into a well-defined region of the cell known as the nucleoid. Motivated by the biological significance of this process, numerous theoretical and computational studies have searched for the primary determinants of the behavior of polymer-crowder phases. However, our understanding of this process remains incomplete and there is debate on a quantitatively unified description. In particular, different simulation studies with explicit crowders have proposed different order parameters as potential predictors for the collapse transition. In this work, we present a comprehensive analysis of published simulation data obtained from different sources. Based on the common behavior we find in this data, we develop a unified phenomenological model that we show to be predictive. Finally, to further validate the accuracy of the model, we conduct new simulations on polymers of various sizes, and investigate the role of jamming of the crowders.