The Analytical Flory Random Coil Is a Simple-to-Use Reference Model for Unfolded and Disordered Proteins

Abstract

Denatured, unfolded, and intrinsically disordered proteins (collectively referred to here as unfolded proteins) can be described using analytical polymer models. These models capture various polymeric properties and can be fit to simulation results or experimental data. However, the model parameters commonly require users’ decisions, making them useful for data interpretation but less clearly applicable as stand-alone reference models. Here we use all-atom simulations of polypeptides in conjunction with polymer scaling theory to parameterize an analytical model of unfolded polypeptides that behave as ideal chains (ν = 0.50). The model, which we call the analytical Flory random coil (AFRC), requires only the amino acid sequence as input and provides direct access to probability distributions of global and local conformational order parameters. The model defines a specific reference state to which experimental and computational results can be compared and normalized. As a proof-of-concept, we use the AFRC to identify sequence-specific intramolecular interactions in simulations of disordered proteins. We also use the AFRC to contextualize a curated set of 145 different radii of gyration obtained from previously published small-angle X-ray scattering experiments of disordered proteins. The AFRC is implemented as a stand-alone software package and is also available via a Google Colab notebook. In summary, the AFRC provides a simple-to-use reference polymer model that can guide intuition and aid in interpreting experimental or simulation results.

SOURSOP: A Python Package for the Analysis of Simulations of Intrinsically Disordered Proteins

“…While our analysis is necessarily retrospective and correlative, it is in line with prior experimental work. ,− To explore this observation further, we performed all-atom simulations using the ABSINTH implicit solvent model of the p53 − with three phosphomimetic mutations (S15E, T18E, and S20E) and compared the result to previous simulations of the wildtype sequence (Figure A) . While glutamic acid is an imperfect analogue for the phosphate group, the results revealed that relatively modest changes in linear charge density can cause local and long-range changes in the...…”

“…Comparison of changes in local and global dimensions for wildtype vs phosphomimetic versions of p53. (A) Scaling maps where inter-residue distances for the phosphomimetic version of the p53 N-terminal domain (p53 − ) are normalized by distances for the wildtype protein. Despite differing by only three residues in the N-terminal quarter of the protein, the phosphomimetic version of p53 shows substantial differences in long-range and local dimensions, as shown by the emergence of both attractive (blue) and repulsive (red) interactions.…”

“…An alternative normalization approach is using polymer models as reference states or considering additional polymeric parameters that report on the global chain dimensions ( e.g. , hydrodynamic radius, end-to-end distance, or the apparent polymer scaling exponent). − All of these can be calculated in SOURSOP (get_radius_of_gyration­(), get_hydrodynamic_radius­(), get_end_to_end_distance­(), and get_scaling_exponent­()). For convenience, we focus here on t and on the normalized radius of gyration, although other metrics would likely report similar conclusions.…”

“…For convenience, we focus here on t and on the normalized radius of gyration, although other metrics would likely report similar conclusions. To normalize the radius of gyration, we make use of an analytical model (the analytical Flory random coil, AFRC) that provides the expected radius of gyration if the chain behaved as a polymer in a theta solvent …”

Excluded Volume and Weak Interactions in Crowded Solutions Modulate Conformations and RNA Binding of an Intrinsically Disordered Tail

“…Previous efforts have contributed to building a general theoretical framework for understanding the impact of crowding on disordered proteins, linking the protein response to fundamental properties of the sequence, such as the scaling exponent. While the scaling exponent reflects the monomer–solvent and monomer–monomer interactions, and therefore depends on the primary structure of the protein, different disordered proteins may attain the same scaling exponent through completely different sequence compositions. − Sequence-specific effects are relatively unexplored, but they can encode for nonspecific affinities for crowding agents, modulate conformations across different length scales, and even introduce transient secondary structure motifs. Furthermore, the contribution of macromolecular crowding has been previously tested only for full-length IDPs.…”