Molecular Transfer Model for pH Effects on Intrinsically Disordered Proteins: Theory and Applications

Intrinsic stiffness and Θ-solvent regime in intrinsically disordered proteins: Implications for liquid-liquid phase separation

Liquid-liquid phase separation (LLPS) exhibited by intrinsically disordered proteins (IDPs) depends on the solvation state around the Θ-regime, which separates good from poor solvent. Experimentally, the Θ-solvent regime of the finite length (N) IDPs, as probed by small angle X-ray scattering (SAXS) and single molecular fluorescence resonance energy transfer (smFRET), is in disagreement. Using computer simulations of a coarse-grained IDP model, we address the effect of chain length on the Θ-regime of IDPs with polar side chains (polyglutamine) and hydrophobic side chains (polyleucine) subject to varying concentrations of cosolvents [ C ] , urea (denaturant) or trimethylamine N-oxide (protective osmolyte) in water. Due to their intrinsic stiffness, these IDPs are always expanded on short-length scales, independent of the solvent quality. As a result, for short IDP sequences ( ≈ 10 to 25 residues), their propensity to exhibit LLPS cannot be inferred from single-chain properties. Further, for finite-size IDPs, the cosolvent concentration to attain the Θ-regime ( [ C Θ ] ) extracted from the structure factor emulating SAXS and pair distances mimicking smFRET differs. They converge to the same cosolvent concentration only at large N, indicating that finite size corrections vary for different IDP properties. We show that the radius of gyration ( R g ) of the IDPs in the Θ-solvent regime satisfies the scaling relation R g 2 = N f ( c N ) , which can be exploited to accurately extract [ C Θ ] ( c = ( [ C ] / [ C Θ ] - 1 ) ). We demonstrate the importance of finite size aspects originating from the chain stiffness and thermal blob size in analyzing IDP properties to identify the Θ-solvent regime.

Impact of Guanidinium Hydrochloride on the Shapes of Prothymosin-α and α-Synuclein Is Dramatically Different

The effects of guanidinium hydrochloride (GdmCl) on two intrinsically disordered proteins (IDPs) are investigated using simulations of the self-organized polymer-IDP (SOP-IDP) model. The impact of GdmCl is taken into account using the molecular transfer model (MTM). We show that due to the dramatic reduction in the stiffness of the highly charged Prothymosin-α (ProTα) with increasing concentration of GdmCl ([GdmCl]), the radius of gyration (Rg) decreases sharply until about 1.0 M. Above 1.0 M, ProTα expands, caused by the swelling effect of GdmCl. In contrast, Rg of α-Synuclein (αSyn) swells as continuously as [GdmCl] increases, with most of the expansion occurring at concentrations less than 0.2 M. Strikingly, the amplitude of the small-angle X-ray scattering (SAXS) profiles for ProTα increases until [GdmCl] ≈ 1.0 M and decreases beyond 1.0 M. The [GdmCl]-dependent SAXS profiles for αSyn, which has a pronounced bump at small wave vector (q ∼ 0.5 nm-1) at low [GdmCl] (≤0.2 M), monotonically decrease at all values of [GdmCl]. The contrasting behavior predicted by the combination of MTM and SOP-IDP simulations may be qualitatively understood by modeling ProTα as a strongly charged polyelectrolyte with nearly uniform density of charges along the chain contour and αSyn as a nearly neutral polymer, except near the C-terminus, where the uncompensated negatively charged residues are located. The precise predictions for the SAXS profiles as a function of [GdmCl] can be readily tested.

Biological and thermodynamic stabilization of lipid-based delivery systems through natural biopolymers; controlled release and molecular dynamics simulations

Nowadays, the use of lipid-based nanocarriers for the targeted and controlled delivery of a variety of hydrophobic and hydrophilic bioactive-compounds and drugs has increased significantly. However, challenges such as thermodynamic instability, oxidation, and degradation of lipid membranes, as well as the unintended release of loaded compounds, have limited the use of these systems in the food and pharmaceutical industries. Therefore, the present study reviews the latest achievements in evaluating the characteristics, production methods, challenges, functional, and biological stabilization strategies of lipid-based carriers (including changes in formulation composition, structural modification, membrane-rigidity, and finally monolayer or multilayer coating with biopolymers) in different conditions, as well as molecular dynamics simulations. The scientists' findings indicate the effect of natural biopolymers (such as chitosan, calcium alginate, pectin, dextran, xanthan, caseins, gelatin, whey-proteins, zein, and etc.) in modifying the external structure of lipid-based carriers, improving thermodynamic stability and resistance of membranes to physicochemical and mechanical tensions. However, depending on the type of bioactive compound as well as the design and production goals of the delivery-system, selecting the appropriate biopolymer has a significant impact on the stability of vesicles and maintaining the bioaccessibility of the loaded-compounds due to the stresses caused by the storage-conditions, formulation, processing and gastrointestinal tract.

pH Induced Switch in the Conformational Ensemble of Intrinsically Disordered Protein Prothymosin-α and Its Implications for Amyloid Fibril Formation

Aggregation of intrinsically disordered proteins (IDPs) can lead to neurodegenerative diseases. Although there is experimental evidence that acidic pH promotes IDP monomer compaction leading to aggregation, the general mechanism is unclear. We studied the pH effect on the conformational ensemble of prothymosin-α (proTα), which is involved in multiple essential functions, and probed its role in aggregation using computer simulations. We show that compaction in the proTα dimension at low pH is due to the protein's collapse in the intermediate region (E41-D80) rich in glutamic acid residues, enhancing its β-sheet content. We observed by performing dimer simulations that the conformations with high β-sheet content could act as aggregation-prone (N*) states and nucleate the aggregation process. The simulations initiated using N* states form dimers within a microsecond time scale, whereas the non-N* states do not form dimers within this time scale. This study contributes to understanding the general principles of pH-induced IDP aggregation.

The Dynamic Range of Acidity: Tracking Rules for the Unidirectional Penetration of Cellular Compartments

Labeled ammonium cations with pKa ∼7.4 accumulate in acidic organelles because they can be neutralized transiently to cross the membrane at cytosolic pH 7.2 but not at their internal pH<5.5. Retention in early endosomes with less acidic internal pH was achieved recently using weaker acids of up to pKa 9.8. We report here that primary ammonium cations with higher pKa 10.6, label early endosomes more efficiently. This maximized early endosome tracking coincides with increasing labeling of Golgi networks with similarly weak internal acidity. Guanidinium cations with pKa 13.5 cannot cross the plasma membrane in monomeric form and label the plasma membrane with selectivity for vesicles embarking into endocytosis. Self-assembled into micelles, guanidinium cations enter cells like arginine-rich cell-penetrating peptides and, driven by their membrane potential, penetrate mitochondria unidirectionally despite their high inner pH. The resulting tracking rules with an approximated dynamic range of pKa change ∼3.5 are expected to be generally valid, thus enabling the design of chemistry tools for biology research in the broadest sense. From a practical point of view, most relevant are two complementary fluorescent flipper probes that can be used to image the mechanics at the very beginning of endocytosis.

A Transfer Free Energy Based Implicit Solvent Model for Protein Simulations in Solvent Mixtures: Urea-Induced Denaturation as a Case Study

We developed a method for implicit solvent molecular dynamics simulations of proteins in solvent mixtures (model with implicit solvation thermodynamics, MIST). The MIST method introduces experimental group transfer free energies to the generalized Born formulation for generating molecular trajectories without the need for developing rigorous explicit-solvent force fields for multicomponent solutions. As a test case, we studied the urea-induced denaturation of the Trp-cage miniprotein in water. We demonstrate that our method allows efficient exploration of the conformational space of the protein in only a few hundreds of nanoseconds of all-atom unbiased simulations. Furthermore, selective implementation of the transfer free energies of specific peptide groups, backbone, and side chains enables us to decouple their specific energetic contributions to the conformational changes of the protein. The approach herein developed can readily be extended to the investigation of complex matrices as well as to the characterization of protein aggregation. The MIST method is implemented in Plumed (ver. 2.8) as a separate module called SASA.

Quantifying charge state heterogeneity for proteins with multiple ionizable residues

Ionizable residues can release and take up protons and this has an influence on protein structure and function. The extent of protonation is linked to the overall pH of the solution and the local environments of ionizable residues. Binding or unbinding of a single proton generates a distinct charge microstate defined by a specific pattern of charges. Accordingly, the overall partition function is a sum over all charge microstates and Boltzmann weights of all conformations associated with each of the charge microstates. This ensemble-of-ensembles description recast as a q-canonical ensemble allows us to analyze and interpret potentiometric titrations that provide information regarding net charge as a function of pH. In the q-canonical ensemble, charge microstates are grouped into mesostates where each mesostate is a collection of microstates of the same net charge. Here, we show that leveraging the structure of the q-canonical ensemble allows us to decouple contributions of net proton binding and release from proton arrangement and conformational considerations. Through application of the q-canonical formalism to analyze potentiometric measurements of net charge in proteins with repetitive patterns of Lys and Glu residues, we determine the underlying mesostate pKa values and, more importantly, we estimate relative mesostate populations as a function of pH. This is a strength of using the q-canonical approach that cannot be replicated using purely site-specific analyses. Overall, our work shows how measurements of charge equilibria, decoupled from measurements of conformational equilibria, and analyzed using the framework of the q-canonical ensemble, provide protein-specific quantitative descriptions of pH-dependent populations of mesostates. This method is of direct relevance for measuring and understanding how different charge states contribute to conformational, binding, and phase equilibria of proteins.

How much can physics do for protein design?

Physics and physical chemistry are an important thread in computational protein design, complementary to knowledge-based tools. They provide molecular mechanics scoring functions that need little or no ad hoc parameter readjustment, methods to thoroughly sample equilibrium ensembles, and different levels of approximation for conformational flexibility. They led recently to the successful redesign of a small protein using a physics-based folded state energy. Adaptive Monte Carlo or molecular dynamics schemes were discovered where protein variants are populated as per their ligand-binding free energy or catalytic efficiency. Molecular dynamics have been used for backbone flexibility. Implicit solvent models have been refined, polarizable force fields applied, and many physical insights obtained.