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Abstract The preponderance of intrinsically disordered proteins (IDPs) in the eukaryotic proteome, and their ability to interact with each other, and with folded proteins, RNA, and DNA for functional purposes, have made it important to quantitatively characterize their biophysical properties. Toward this end, we developed the transferable self‐organized polymer (SOP‐IDP) model to calculate the properties of several IDPs. The values of the radius of gyration () obtained from SOP‐IDP simulations are in excellent agreement (correlation coefficient of 0.96) with those estimated from SAXS experiments. For AP180 and Epsin, the predicted values of the hydrodynamic radii () are in nearly quantitative agreement with those from fluorescence correlation spectroscopy (FCS) experiments. Strikingly, the calculated SAXS profiles for 36 IDPs are also nearly superimposable on the experimental profiles. The dependence of and the mean end‐to‐end distance () on chain length, , follows Flory's scaling law, ( and ), suggesting that globally IDPs behave as synthetic polymers in a good solvent. This finding depends on the solvent quality, which can be altered by changing variables such as pH and salt concentration. The values of and are 0.20 and 0.48 nm, respectively. Surprisingly, finite size corrections to scaling, expected on theoretical grounds, are negligible for and . In contrast, only by accounting for the finite sizes of the IDPs, the dependence of experimentally measurable on can be quantitatively explained using . Although Flory scaling law captures the estimates for , , and accurately, the spread of the simulated data around the theoretical curve is suggestive of of sequence‐specific features that emerge through a fine‐grained analysis of the conformational ensembles using hierarchical clustering. Typically, the ensemble of conformations partitions into three distinct clusters, having different equilibrium populations and structural properties. Without any further readjustments to the parameters of the SOP‐IDP model, we also obtained nearly quantitative agreement with paramagnetic relaxation enhancement (PRE) measurements forα‐synuclein. The transferable SOP‐IDP model sets the stage for several applications, including the study of phase separation in IDPs and interactions with nucleic acids. 

Protein domains, such as ENTH (epsin N-terminal homology) and BAR (bin/amphiphysin/rvs), contain amphipathic helices that drive preferential binding to curved membranes. However, predicting how the physical parameters of these domains control this ‘curvature sensing’ behavior is challenging due to the local membrane deformations generated by the nanoscopic helix on the surface of a large sphere. We here use a deformable continuum model that accounts for the physical properties of the membrane and the helix insertion to predict curvature sensing behavior, with direct validation against multiple experimental datasets. We show that the insertion can be modeled as a local change to the membrane's spontaneous curvature, c ins0, producing excellent agreement with the energetics extracted from experiments on ENTH binding to vesicles and cylinders, and of ArfGAP helices to vesicles. For small vesicles with high curvature, the insertion lowers the membrane energy by relieving strain on a membrane that is far from its preferred curvature of zero. For larger vesicles, however, the insertion has the inverse effect, de-stabilizing the membrane by introducing more strain. We formulate here an empirical expression that accurately captures numerically calculated membrane energies as a function of both basic membrane properties (bending modulus κ and radius R ) as well as stresses applied by the inserted helix ( c ins0 and area A ins ). We therefore predict how these physical parameters will alter the energetics of helix binding to curved vesicles, which is an essential step in understanding their localization dynamics during membrane remodeling processes. 

Many critical biological events, including biochemical signaling, membrane traffic, and cell motility, originate at membrane surfaces. Each such event requires that members of a specific group of proteins and lipids rapidly assemble together at a specific site on the membrane surface. Understanding the biophysical mechanisms that stabilize these assemblies is critical to decoding and controlling cellular functions. In this article, we review progress toward a quantitative biophysical understanding of the mechanisms that drive membrane heterogeneity and organization. We begin from a physical perspective, reviewing the fundamental principles and key experimental evidence behind each proposed mechanism. We then shift to a biological perspective, presenting key examples of the role of heterogeneity in biology and asking which physical mechanisms may be responsible. We close with an applied perspective, noting that membrane heterogeneity provides a novel therapeutic target that is being exploited by a growing number of studies at the interface of biology, physics, and engineering.