Abstract
Cells possess non-membrane-bound bodies, many of which are now understood as phase-separated condensates. One class of such condensates is composed of two polymer species, where each consists of repeated binding sites that interact in a one-to-one fashion with the binding sites of the other polymer. Biologically-motivated modeling revealed that phase separation is suppressed by a “magic-number effect” which occurs if the two polymers can form fully-bonded small oligomers by virtue of the number of binding sites in one polymer being an integer multiple of the number of binding sites of the other. Here we use lattice-model simulations and analytical calculations to show that this magic-number effect can be greatly enhanced if one of the polymer species has a rigid shape that allows for multiple distinct bonding conformations. Moreover, if one species is rigid, the effect is robust over a much greater range of relative concentrations of the two species.
Highlights
Cells possess non-membrane-bound bodies, many of which are understood as phaseseparated condensates
Previous results from modeling the Rubisco-EPYC1 system, which established the concept of the magic-number effect, can be summarized as follows: the A4:B8R system forms stable trimers and compared to the A3:B8R or A5:B8R systems, requires a substantially higher total monomer concentration for the formation of large clusters, assuming equal total stoichiometry of A and B monomers[7]
Confirming the visual impression that the observed large clusters arise from phase separation, rather than arising as percolation clusters from homogeneous gelation[23], we found that for strong enough specific interactions ( ≥ 4kBT) the internal cluster density remains approximately constant above the transition, as expected for phase separation but not for clusters formed by percolation (Supplementary Fig. 4)
Summary
Cells possess non-membrane-bound bodies, many of which are understood as phaseseparated condensates. The algal pyrenoid, is a carbon-fixation organelle, in which the two components essential for assembly[11] are the rigid oligomer Rubisco (the active enzyme in CO2 fixation) and EPYC1, an unstructured linker protein[12] Another multivalent system, PML (promyelocytic leukemia) nuclear bodies that repair DNA damage[13], relies on the Small Ubiquitin-like Modifier (SUMO) domain that interacts with the SUMO Interacting Motif (SIM) to form droplets[14,15,16]. PML (promyelocytic leukemia) nuclear bodies that repair DNA damage[13], relies on the Small Ubiquitin-like Modifier (SUMO) domain that interacts with the SUMO Interacting Motif (SIM) to form droplets[14,15,16] This system inspired in vitro experiments with engineered polySUMO and polySIM of various valences[10], and, phase separation was observed with increasing concentrations of the two polymers. While many intracellular condensates are held together by weak interactions of multiple types (e.g., charged, aromatic, and hydrophobic[18], as well as pi–cation[19], and pi–pi interactions20) natural protein–protein, protein–RNA, or protein–peptide interactions such as SUMOSIM10 or synthetic interactions, e.g., based on DNA hybridization[21,22], can readily reach the strong-binding regime required to observe the magic-number effect
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