Random-phase-approximation theory for sequence-dependent, biologically functional liquid-liquid phase separation of intrinsically disordered proteins

Abstract

Intrinsically disordered proteins (IDPs) are typically low in nonpolar/hydrophobic but relatively high in polar, charged, and aromatic amino acid compositions. Some IDPs undergo liquid-liquid phase separation in the aqueous milieu of the living cell. The resulting phase with enhanced IDP concentration can function as a major component of membraneless organelles that, by creating their own IDP-rich microenvironments, stimulate critical biological functions. IDP phase behaviors are governed by their amino acid sequences. To make progress in understanding this sequence-phase relationship, we report further advances in a recently introduced application of random-phase-approximation (RPA) heteropolymer theory to account for sequence-specific electrostatics in IDP phase separation. Here we examine computed variations in phase behavior with respect to block length and charge density of model polyampholytes of alternating equal-length charge blocks to gain insight into trends observed in IDP phase separation. As a real-life example, the theory is applied to rationalize/predict binodal and spinodal phase behaviors of the 236-residue N-terminal disordered region of RNA helicase Ddx4 and its charge-scrambled mutant for which experimental data are available. Fundamental differences are noted between the phase diagrams predicted by RPA and those predicted by mean-field Flory-Huggins and Overbeek-Voorn/Debye-Hückel theories. In the RPA context, a physically plausible dependence of relative permittivity on protein concentration can produce a cooperative effect in favor of IDP-IDP attraction and thus a significant increased tendency to phase separate. Ramifications of these findings for future development of IDP phase separation theory are discussed.

Charge pattern matching as a ‘fuzzy’ mode of molecular recognition for the functional phase separations of intrinsically disordered proteins

“…and G k G k 12 21 = ( )ˆ( ). As in our previous studies [61,62], we consider a simple formulation in which all IDPs are modeled as Gaussian chains without excluded volume within the RPA formalism [66]. In this approximation, there is no correlation between the positions of different chains; hence G k G k 0 12 21 = = ( )ˆ( ) and One phase is concentrated in seq2 but dilute in seq1 (top), the other phase is concentrated in seq1 but dilute in seq2 (bottom).…”

“…being the i j , element of the bare two-body correlation matrix G k of all possible sequence-sequence correlations [62],…”

“…In contrast, if the bulk state is in a concave-downward region, the state is thermodynamically unstable because a phase-separated state allows for a lower free energy. Accordingly, the system undergoes phase separation to multiple coexisting phases with different protein volume fractions [62].…”

Sequence determinants of protein phase behavior from a coarse-grained model

“…Jacobs and Frenkel used Monte Carlo simulations to study 37 multiple-component phase separation and found that the phase boundary is very 38 sensitive to intermolecular interactions, but less dependent on the number of 39 components in the system [36]. Lin and Chan applied the random phase approximation 40 to treat electrostatic interactions [37] and Flory Huggins theory for mixing entropy and 41 other interactions. They were able to capture the sequence specificity of charged amino 42 acids and found that the dependence of the phase boundary of the IDP Ddx4 on salt 43 concentration can be explained by considering only electrostatic screening in their 44 model [38].…”

“…To understand the mechanism of such dependence, we apply Flory-Huggins 430 theory [79,80], which has previously been used to understand IDP phase 431 separation [9,37,38], to fit the phase transition properties obtained by molecular 432 dynamics simulations when varying the chain length N . If we assume that each solvent 433 molecule occupies one lattice position, then the the critical temperature 434 T c ∝ N/( √ N + 1) 2 and the critical concentration ρ c ∝ 1/( √ N + 1).…”