Dimension conversion and scaling of disordered protein chains

Small-Angle X-ray Scattering Signatures of Conformational Heterogeneity and Homogeneity of Disordered Protein Ensembles

An accurate account of disordered protein conformations is of central importance to deciphering the physicochemical basis of biological functions of intrinsically disordered proteins and the folding-unfolding energetics of globular proteins. Physically, disordered ensembles of nonhomopolymeric polypeptides are expected to be heterogeneous, i.e., they should differ from those homogeneous ensembles of homopolymers that harbor an essentially unique relationship between average values of end-to-end distance R_EE and radius of gyration R_g. It was posited recently, however, that small-angle X-ray scattering (SAXS) data on conformational dimensions of disordered proteins can be rationalized almost exclusively by homopolymer ensembles. Assessing this perspective, chain-model simulations are used to evaluate the discriminatory power of SAXS-determined molecular form factors (MFFs) with regard to homogeneous versus heterogeneous ensembles. The general approach adopted here is not bound by any assumption about ensemble encodability, in that the postulated heterogeneous ensembles we evaluated are not restricted to those entailed by simple interaction schemes. Our analysis of MFFs for certain heterogeneous ensembles with more narrowly distributed R_EE and R_g indicates that while they deviate from MFFs of homogeneous ensembles, the differences can be rather small. Remarkably, some heterogeneous ensembles with asphericity and R_EE drastically different from those of homogeneous ensembles can nonetheless exhibit practically identical MFFs, demonstrating that SAXS MFFs do not afford unique characterizations of basic properties of conformational ensembles in general. In other words, the ensemble to MFF mapping is practically many-to-one and likely nonsmooth. Heteropolymeric variations of the R_EE-R_g relationship were further showcased using an analytical perturbation theory developed here for flexible heteropolymers. Ramifications of our findings for interpretation of experimental data are discussed.

Allostery of multidomain proteins with disordered linkers

Intrinsically disordered regions are often involved in allosteric regulation of multidomain proteins. They can act as disordered linkers to connect and interact with domains, resulting in rather complex allosteric mechanism and novel protein behavior. Therefore, it is necessary to analyze the diverse functions of disordered linkers in order to better understand allostery and relevant regulation process. Here we summarize recent advances in understanding the function of linkers and the advantages of adopting mutlidomain architecture with disorder linkers. It was shown that linkers between domains enhance the local domain concentration and make the allosteric regulation of weakly interacting partners possible, while linkers with only one tethered end cause an entropy effect to reduce binding affinity and prevent aggregation.

Disordered linkers in multidomain allosteric proteins: Entropic effect to favor the open state or enhanced local concentration to favor the closed state?

There are many multidomain allosteric proteins where an allosteric signal at the allosteric domain modifies the activity of the functional domain. Intrinsically disordered regions (linkers) are widely involved in this kind of regulation process, but the essential role they play therein is not well understood. Here, we investigated the effect of linkers in stabilizing the open or the closed states of multidomain proteins using combined thermodynamic deduction and coarse-grained molecular dynamics simulations. We revealed that the influence of linker can be fully characterized by an effective local concentration [B]₀ . When K_d is smaller than [B]₀ , the closed state would be favored; while the open state would be preferred when K_d is larger than [B]₀ . We used four protein systems with markedly different domain-domain binding affinity and structural order/disorder as model systems to understand the relationship between [B]₀ and the linker length as well as its flexibility. The linker length is the main practical determinant of [B]₀ . [B]₀ of a flexible linker with 40-60 residues was determined to be in a narrow range of 0.2-0.6 mM, while a too short or too long length would dramatically decrease [B]₀ . With the revealed [B]₀ range, the introduction of a flexible linker makes the regulation of weakly interacting partners possible.

Thermodynamically driven assemblies and liquid-liquid phase separations in biology

The sustenance of life depends on the high degree of organization that prevails through different levels of living organisms, from subcellular structures such as biomolecular complexes and organelles to tissues and organs. The physical origin of such organization is not fully understood, and even though it is clear that cells and organisms cannot maintain their integrity without consuming energy, there is growing evidence that individual assembly processes can be thermodynamically driven and occur spontaneously due to changes in thermodynamic variables such as intermolecular interactions and concentration. Understanding the phase separation in vivo requires a multidisciplinary approach, integrating the theory and physics of phase separation with experimental and computational techniques. This paper aims at providing a brief overview of the physics of phase separation and its biological implications, with a particular focus on the assembly of membraneless organelles. We discuss the underlying physical principles of phase separation from its thermodynamics to its kinetics. We also overview the wide range of methods utilized for experimental verification and characterization of phase separation of membraneless organelles, as well as the utility of molecular simulations rooted in thermodynamics and statistical physics in understanding the governing principles of thermodynamically driven biological self-assembly processes.

A comprehensive ensemble model for comparing the allosteric effect of ordered and disordered proteins

Intrinsically disordered proteins/regions (IDPs/IDRs) are prevalent in allosteric regulation. It was previously thought that intrinsic disorder is favorable for maximizing the allosteric coupling. Here, we propose a comprehensive ensemble model to compare the roles of both order-order transition and disorder-order transition in allosteric effect. It is revealed that the MWC pathway (order-order transition) has a higher probability than the EAM pathway (disorder-order transition) in allostery, suggesting a complicated role of IDPs/IDRs in regulatory proteins. In addition, an analytic formula for the maximal allosteric coupling response is obtained, which shows that too stable or too unstable state is unfavorable to endow allostery, and is thus helpful for rational design of allosteric drugs.

Allosteric effect is an important regulation mechanism in biological processes, where the binding of a ligand at one site of a protein influences the function of a distant site. Conventionally, allostery was thought to originate from structural transition. However, in recent years, intrinsically disordered proteins (IDPs) were found to be widely involved in allosteric regulation in despite of their lack of ordered structure under physiological condition. It is still a mystery why IDPs are prevalent in allosteric proteins and how they differ from ordered proteins in allostery. Here, we propose a comprehensive ensemble model which includes both ordered and disordered states of a two-domain protein, and investigate the role of various state combinations in allosteric effect. By sampling the parameter space, we conclude that disordered proteins are less competitive than ordered proteins in performing allostery from a thermodynamic point of view. The prevalence of IDPs in allosteric regulation is likely determined by all their advantage, but not only by their capacity in endowing allostery.

Single Molecule FRET: A Powerful Tool to Study Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are often modeled using ideas from polymer physics that suggest they smoothly explore all corners of configuration space. Experimental verification of this random, dynamic behavior is difficult as random fluctuations of IDPs cannot be synchronized across an ensemble. Single molecule fluorescence (or Förster) resonance energy transfer (smFRET) is one of the few approaches that are sensitive to transient populations of sub-states within molecular ensembles. In some implementations, smFRET has sufficient time resolution to resolve transitions in IDP behaviors. Here we present experimental issues to consider when applying smFRET to study IDP configuration. We illustrate the power of applying smFRET to IDPs by discussing two cases in the literature of protein systems for which smFRET has successfully reported phosphorylation-induced modification (but not elimination) of the disordered properties that have been connected to impacts on the related biological function. The examples we discuss, PAGE4 and a disordered segment of the GluN2B subunit of the NMDA receptor, illustrate the great potential of smFRET to inform how IDP function can be regulated by controlling the detailed ensemble of disordered states within biological networks.

A critical comparison of coarse-grained structure-based approaches and atomic models of protein folding

Structure-based coarse-grained Gō-like models have been used extensively in deciphering protein folding mechanisms because of their simplicity and tractability. Meanwhile, explicit-solvent molecular dynamics (MD) simulations with physics-based all-atom force fields have been applied successfully to simulate folding/unfolding transitions for several small, fast-folding proteins. To explore the degree to which coarse-grained Gō-like models and their extensions to incorporate nonnative interactions are capable of producing folding processes similar to those in all-atom MD simulations, here we systematically compare the computed unfolded states, transition states, and transition paths obtained using coarse-grained models and all-atom explicit-solvent MD simulations. The conformations in the unfolded state in common Gō models are more extended, and are thus more in line with experiment, than those from all-atom MD simulations. Nevertheless, the structural features of transition states obtained by the two types of models are largely similar. In contrast, the folding transition paths are significantly more sensitive to modeling details. In particular, when common Gō-like models are augmented with nonnative interactions, the predicted dimensions of the unfolded conformations become similar to those computed using all-atom MD. With this connection, the large deviations of all-atom MD from simple diffusion theory are likely caused in part by the presence of significant nonnative effects in folding processes modelled by current atomic force fields. The ramifications of our findings to the application of coarse-grained modeling to more complex biomolecular systems are discussed.

Conformational Heterogeneity and FRET Data Interpretation for Dimensions of Unfolded Proteins

A mathematico-physically valid formulation is required to infer properties of disordered protein conformations from single-molecule Förster resonance energy transfer (smFRET). Conformational dimensions inferred by conventional approaches that presume a homogeneous conformational ensemble can be unphysical. When all possible-heterogeneous as well as homogeneous-conformational distributions are taken into account without prejudgment, a single value of average transfer efficiency 〈E〉 between dyes at two chain ends is generally consistent with highly diverse, multiple values of the average radius of gyration 〈R_g〉. Here we utilize unbiased conformational statistics from a coarse-grained explicit-chain model to establish a general logical framework to quantify this fundamental ambiguity in smFRET inference. As an application, we address the long-standing controversy regarding the denaturant dependence of 〈R_g〉 of unfolded proteins, focusing on Protein L as an example. Conventional smFRET inference concluded that 〈R_g〉 of unfolded Protein L is highly sensitive to [GuHCl], but data from SAXS suggested a near-constant 〈R_g〉 irrespective of [GuHCl]. Strikingly, our analysis indicates that although the reported 〈E〉 values for Protein L at [GuHCl] = 1 and 7 M are very different at 0.75 and 0.45, respectively, the Bayesian R_g² distributions consistent with these two 〈E〉 values overlap by as much as 75%. Our findings suggest, in general, that the smFRET-SAXS discrepancy regarding unfolded protein dimensions likely arise from highly heterogeneous conformational ensembles at low or zero denaturant, and that additional experimental probes are needed to ascertain the nature of this heterogeneity.