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

Abstract

Crowding by macromolecules in the surrounding environment can collapse a single long polymer to globular form through depletion forces of entropic nature. For instance, the genomic DNA of the bacterium Escherichia coli can be compacted by crowding, and the current consensus is that crowding is needed in order to fold it into the "nucleoid", occupying a well defined region of the cell. Motivated by the biological importance of this problem, numerous theoretical and computational investigations have been conducted to ascertain the primary factors influencing the phases of polymer-crowder systems. Despite numerous candidate order parameters predicting this transition have been proposed, a singular quantitative description of the collapse transition in polymers driven by the presence of crowders is still elusive. Here, integrating results from molecular simulations of polymer chains in explicit crowders, we derive a unifying phenomenological model based on an effective monomer-monomer interaction potential. We demonstrate the predictive power of the new theory through an investigation of polymers with varying lengths, crowders of different sizes in a range spanning from low-density to high-density conditions. Finally, we address the role of jamming by crowders.

Molecular Crowding: The History and Development of a Scientific Paradigm

“…The authors found a compaction of all four proteins upon increase of PEG content, and, at a given PEG content, a gradual compaction of the proteins with increasing size of the PEG molecules. The latter results, which covered a broader range of crowder sizes, are in contrast to the trend observed in computer simulations. , However, both simulation techniques applied hard sphere crowders, , whereas Soranno and co-workers used flexible macromolecules as crowders, stressing the relevance not only of the size asymmetry ratio but equally important, of the nature of the crowder …”

“…The latter results, which covered a broader range of crowder sizes, are in contrast to the trend observed in computer simulations. 106,107 However, both simulation techniques applied hard sphere crowders, 105,106 whereas Soranno and co-workers used flexible macromolecules as crowders, stressing the relevance not only of the size asymmetry ratio but equally important, of the nature of the crowder. 108 In 2017, Alfano et al addressed the question of whether and what is the optimal size of crowders.…”

“…In the cited study, the crowder was equal to or larger than the probe molecule Cytochrome b 562 . The same trend was observed in Wang–Landau simulations published by Taylor and co-workers on CP mixtures covering size values of the crowder from the size of a monomer to the size of the collapsed polymer, and by computer simulations by Scolari et al, which extends to a size of the colloids to a regime even smaller than the length of a monomeric unit of the macromolecules. The authors revealed an increase of the temperature for the coil-to-globule transition with decreasing crowder size with the effect gradually disappearing as the crowder size approached the size of the native protein.…”

Two-way feedback between chromatin compaction and histone modification state explains Saccharomyces cerevisiae heterochromatin bistability

“…Within the simple framework of the Flory mean-field theory for polymers ( 46 , 47 ), one can write a mean-field free energy for a real polymer whose minimization gives the equilibrium value of the radius of gyration. In the silenced state, the locus is compact and highly deacetylated.…”