Configurational entropy of protein: A combined approach based on molecular simulation and integral-equation theory of liquids

Aggregation propensities of proteins with varying degrees of disorder

The hydration thermodynamics of a globular protein (AcP), three intrinsically disordered protein regions (1CD3, 1MVF, 1F0R) and a fully disordered protein (α-synuclein) is studied by an approach that combines an all-atom explicit water molecular dynamics simulations and three-dimensional reference interaction site model (3D-RISM) theory. The variation in hydration free energy with percentage disorder of the selected proteins is investigated through its nonelectrostatic and electrostatic components. A decrease in hydration free energy is observed with an increase in percentage disorder, indicating favorable interactions of the disordered proteins with the solvent. This confirms the role of percentage disorder in determining the aggregation propensity of proteins which is measured in terms of the hydration free energy in addition to their respective mean net charge and mean hydrophobicity. The hydration free energy is decoupled into energetic and entropic terms. A residue-wise decomposition analysis of the hydration free energy for the selected proteins is evaluated. The decomposition shows that the disordered regions contribute more than the ordered ones for the intrinsically disordered protein regions. The dominant role of electrostatic interactions is confirmed from the residue-wise decomposition of the hydration free energy. The results depict that the negatively charged residues contribute more to the total hydration free energy for the proteins with negative mean net charge, while the positively charged residues contribute more for proteins with positive mean net charge.

Site-Specific Backbone and Side-Chain Contributions to Thermodynamic Stabilizing Forces of the WW Domain

The native structure of a protein is stabilized by a number of interactions such as main-chain hydrogen bonds and side-chain hydrophobic contacts. However, it has been challenging to determine how these interactions contribute to protein stability at single amino acid resolution. Here, we quantified site-specific thermodynamic stability at the molecular level to extend our understanding of the stabilizing forces in protein folding. We derived the free energy components of individual amino acid residues separately for the folding of the human Pin WW domain based on simulated structures. A further decomposition of the thermodynamic properties into contributions from backbone and side-chain groups enabled us to identify the critical residues in the secondary structure and hydrophobic core formation, without introducing physical modifications to the system as in site-directed mutagenesis methods. By relating the structural and thermodynamic changes upon folding for each residue, we find that the simultaneous formation of the backbone hydrogen bonds and side-chain contacts cooperatively stabilizes the folded structure. The identification of stabilizing interactions in a folding protein at atomic resolution will provide molecular insights into understanding the origin of the protein structure and into engineering a more stable protein.

Dissecting the Conformational Free Energy of a Small Peptide in Solution

The free energy surface of a small peptide was analyzed based on an unbiased microsecond molecular dynamics simulation. The peptide sampled disordered conformational ensembles of distinct compactness, and its free energy was decomposed into separate contributions from the intramolecular potential energy, conformational entropy, and solvation free energy. The latter was further broken down into enthalpic and entropic contributions due to peptide-water and water-water interactions. This decomposition was enabled by a generalized linear response relation between the peptide-water interaction energy and the solvation free energy, which was empirically parametrized by explicit solvation free energy calculations for representative peptide conformations. This full dissection of the peptide free energy identifies individual contributions that stabilize and destabilize compact and extended peptide conformational ensembles and reveals the origin of a free energy barrier associated with transitions between them.

Hydration Thermodynamics of Familial Parkinson's Disease-Linked Mutants of α-Synuclein

The hydration thermodynamics of different mutants of α-synuclein (α-syn) related to familial Parkinson's disease (PD) is explored using a computational approach that combines both molecular dynamics simulations in water and integral equation theory of molecular liquids. This analysis focuses on the change in conformational entropy, hydration free energy (HFE), and partial molar volume of α-syn upon mutation. The results show that A53T, A30P, E46K, and H50Q mutants aggregate more readily and display increased HFE and less negative interaction volume than the wild-type α-syn. In contrast, an opposite trend is observed for the G51D mutant with a lower experimental aggregation rate. The residuewise decomposition analysis of the HFE highlights that the dehydration/hydration of the hydrophilic residue-rich N- and C-termini of α-syn majorly contributes to the change upon mutation. The hydration shell contributions of different residues to the interaction volume are consistent with its increase/decrease upon mutation. This work shows that both HFE and interaction volume determine the aggregation kinetics of α-syn upon mutation and may serve as an appropriate benchmark for the treatment of PD.

Computational Screening of a Functional Cyclodextrin Derivative for Suppressing a Side Effect of Doxorubicin

The binding affinity of the beta-cyclodextrin (β-CyD) derivatives with Doxorubicin (Dox) is evaluated by means of the 3D-RISM/KH theory combined with the molecular dynamics simulation in order to screen the compounds for suppressing a side-effect of the cancer drug. A protocol revised for the external and conformational entropies of the host-guest system is employed to calculate the binding free energy. It is found that the direct interactions of CyD with Dox and the desolvation free-energies of the both compounds largely cancel out to leave moderate contributions to the affinity, which are comparable to those from the entropies. The results shed light on the entropy terms for determining the binding affinity, although the external-entropy terms are essentially constant over all the compounds examined and do not affect the screening. The theoretical result is compared with the experimental data of the association constant for a CyD derivative which was predicted to be the best compound by the preliminary calculation without the entropy terms.

Hydration Thermodynamics of the N-Terminal FAD Mutants of Amyloid-β

The hydration thermodynamics of amyloid-β (Aβ) and its pathogenic familial Alzheimer's disease (FAD) mutants such as A2V, Taiwan (D7H), Tottori (D7N), and English (H6R) and the protective A2T mutant is investigated by a combination of all-atom, explicit water molecular dynamics (MD) simulations and the three-dimensional reference interaction site model (3D-RISM) theory. The change in the hydration free energy on mutation is decomposed into the energetic and entropic components, which comprise electrostatic and nonelectrostatic contributions. An increase in the hydration free energy is observed for A2V, D7H, D7N, and H6R mutations that increase the aggregation propensity of Aβ and lead to an early onset of Alzheimer's disease, while a reverse trend is noted for the protective A2T mutation. An antiphase correlation is found between the change in the hydration energy and the internal energy of Aβ upon mutation. A residue-wise decomposition analysis shows that the change in the hydration free energy of Aβ on mutation is primarily due to the hydration/dehydration of the side-chain atoms of the negatively charged residues. The decrease in the hydration of the negatively charged residues on mutation may decrease the solubility of the mutant, which increases the observed aggregation propensity of the FAD mutants. Results obtained from the theory show an excellent match with the experimentally reported data.

Delineating elastic properties of kinesin linker and their sensitivity to point mutations

We analyze free energy estimators from simulation trials mimicking single-molecule pulling experiments on a neck linker of a kinesin motor. For that purpose, we have performed a version of steered molecular dynamics (SMD) calculations. The sample trajectories have been analyzed to derive distribution of work done on the system. In order to induce stretching of the linker, we have applied a constant pulling force to the molecule and allowed for a subsequent relaxation of its structure. The use of fluctuation relations (FR) relevant to non-equilibrium systems subject to thermal fluctuations allows us to assess the difference in free energy between stretched and relaxed conformations. To further understand effects of potential mutations on elastic properties of the linker, we have performed similar in silico studies on a structure formed of a polyalanine sequence (Ala-only) and on three other structures, created by substituting selected types of amino acid residues in the linker’s sequence with alanine (Ala) ones. The results of SMD simulations indicate a crucial role played by the Asparagine (Asn) and Lysine (Lys) residues in controlling stretching and relaxation properties of the linker domain of the motor.

Examining a Thermodynamic Order Parameter of Protein Folding

Dimensionality reduction with a suitable choice of order parameters or reaction coordinates is commonly used for analyzing high-dimensional time-series data generated by atomistic biomolecular simulations. So far, geometric order parameters, such as the root mean square deviation, fraction of native amino acid contacts, and collective coordinates that best characterize rare or large conformational transitions, have been prevailing in protein folding studies. Here, we show that the solvent-averaged effective energy, which is a thermodynamic quantity but unambiguously defined for individual protein conformations, serves as a good order parameter of protein folding. This is illustrated through the application to the folding-unfolding simulation trajectory of villin headpiece subdomain. We rationalize the suitability of the effective energy as an order parameter by the funneledness of the underlying protein free energy landscape. We also demonstrate that an improved conformational space discretization is achieved by incorporating the effective energy. The most distinctive feature of this thermodynamic order parameter is that it works in pointing to near-native folded structures even when the knowledge of the native structure is lacking, and the use of the effective energy will also find applications in combination with methods of protein structure prediction.

A Systematic Analysis of the Binding Affinity between the Pim-1 Kinase and Its Inhibitors Based on the MM/3D-RISM/KH Method

A systematic study of the binding affinities of 16 lead compounds targeting the Pim-1 kinase based on the 3D-RISM/KH theory and MD simulations is reported. The results show a correlation coefficient R = 0.69 between the theoretical and experimental values of the binding free energy. This demonstrates that the method is applicable to the problem of compound screening and lead optimization, for which relative values of the free energy among the compounds have significance. We elucidate the contribution of the ligand fragments to the binding free energy. Our results indicate that the interactions between the residues and the triazolo[4,3-b]pyridazine scaffold as well as the phenyl ring of the ligand molecule make significant contributions to stabilization of the complex. Using the 3D-RISM/KH theory, we further analyze the probability distribution of a ligand fragment around the protein-ligand complex in which the substituent around the phenyl ring is removed from the ligand. The results demonstrate that the 3D-RISM/KH theory is capable of predicting the position of substitution on a ligand that has a higher affinity to a target protein.

Dynamics of Hydration Water Plays a Key Role in Determining the Binding Thermodynamics of Protein Complexes

Interfacial waters are considered to play a crucial role in protein–protein interactions, but in what sense and why are they important? Here, using molecular dynamics simulations and statistical thermodynamic analyses, we demonstrate distinctive dynamic characteristics of the interfacial water and investigate their implications for the binding thermodynamics. We identify the presence of extraordinarily slow (~1,000 times slower than in bulk water) hydrogen-bond rearrangements in interfacial water. We rationalize the slow rearrangements by introducing the “trapping” free energies, characterizing how strongly individual hydration waters are captured by the biomolecular surface, whose magnitude is then traced back to the number of water–protein hydrogen bonds and the strong electrostatic field produced at the binding interface. We also discuss the impact of the slow interfacial waters on the binding thermodynamics. We find that, as expected from their slow dynamics, the conventional approach to the water-mediated interaction, which assumes rapid equilibration of the waters’ degrees of freedom, is inadequate. We show instead that an explicit treatment of the extremely slow interfacial waters is critical. Our results shed new light on the role of water in protein–protein interactions, highlighting the need to consider its dynamics to improve our understanding of biomolecular bindings.

Computer Simulations of Intrinsically Disordered Proteins

The investigation of intrinsically disordered proteins (IDPs) is a new frontier in structural and molecular biology that requires a new paradigm to connect structural disorder to function. Molecular dynamics simulations and statistical thermodynamics potentially offer ideal tools for atomic-level characterizations and thermodynamic descriptions of this fascinating class of proteins that will complement experimental studies. However, IDPs display sensitivity to inaccuracies in the underlying molecular mechanics force fields. Thus, achieving an accurate structural characterization of IDPs via simulations is a challenge. It is also daunting to perform a configuration-space integration over heterogeneous structural ensembles sampled by IDPs to extract, in particular, protein configurational entropy. In this review, we summarize recent efforts devoted to the development of force fields and the critical evaluations of their performance when applied to IDPs. We also survey recent advances in computational methods for protein configurational entropy that aim to provide a thermodynamic link between structural disorder and protein activity.

Distinct role of hydration water in protein misfolding and aggregation revealed by fluctuating thermodynamics analysis

Protein aggregation in aqueous cellular environments is linked to diverse human diseases. Protein aggregation proceeds through a multistep process initiated by conformational transitions, called protein misfolding, of monomer species toward aggregation-prone structures. Various forms of aggregate species are generated through the association of misfolded monomers including soluble oligomers and amyloid fibrils. Elucidating the molecular mechanisms and driving forces involved in the misfolding and subsequent association has been a central issue for understanding and preventing protein aggregation diseases such as Alzheimer's, Parkinson's, and type II diabetes. In this Account, we provide a thermodynamic perspective of the misfolding and aggregation of the amyloid-beta (Aβ) protein implicated in Alzheimer's disease through the application of fluctuating thermodynamics. This approach "dissects" the conventional thermodynamic characterization of the end states into the one of the fluctuating processes connecting them, and enables one to analyze variations in the thermodynamic functions that occur during the course of protein conformational changes. The central quantity in this approach is the solvent-averaged effective energy, f = Eu + Gsolv, comprising the protein potential energy (Eu) and the solvation free energy (Gsolv), whose time variation reflects the protein dynamics on the free energy landscape. Protein configurational entropy is quantified by the magnitude of fluctuations in f. We find that misfolding of the Aβ monomer when released from a membrane environment to an aqueous phase is driven by favorable changes in protein potential energy and configurational entropy, but it is also accompanied by an unfavorable increase in solvation free energy. The subsequent dimerization of the misfolded Aβ monomers occurs in two steps. The first step, where two widely separated monomers come into contact distance, is driven by water-mediated attraction, that is, by a decrease in solvation free energy, harnessing the monomer solvation free energy earned during the misfolding. The second step, where a compact dimer structure is formed, is driven by direct protein-protein interactions, but again it is accompanied by an increase in solvation free energy. The increased solvation free energy of the dimer will function as the driving force to recruit another Aβ protein in the approach stage of subsequent oligomerizations. The fluctuating thermodynamics analysis of the misfolding and dimerization of the Aβ protein indicates that the interaction of the protein with surrounding water plays a critical role in protein aggregation. Such a water-centric perspective is further corroborated by demonstrating that, for a large number of Aβ mutants and mutants of other protein systems, the change in the experimental aggregation propensity upon mutation has a significant correlation with the protein solvation free energy change. We also find striking discrimination between the positively and negatively charged residues on the protein surface by surrounding water molecules, which is shown to play a crucial role in determining the protein aggregation propensity. We argue that the protein total charge dictates such striking behavior of the surrounding water molecules. Our results provide new insights for understanding and predicting the protein aggregation propensity, thereby offering novel design principles for producing aggregation-resistant proteins for biotherapeutics.

Effects of Zn2+ binding on the structural and dynamic properties of amyloid β peptide associated with Alzheimer's disease: Asp1 or Glu11?

Extensive experimental and computational studies have suggested that multiple Zn(2+) binding modes in amyloid β (Aβ) peptides could exist simultaneously. However, consistent results have not been obtained for the effects of Zn(2+) binding on Aβ structure, dynamics, and kinetics in particular. Some key questions such as why it is so difficult to distinguish the polymorphic states of metal ions binding to Aβ and what the underlying rationale is, necessitate elucidation. In this work, two 3N1O Zn(2+) binding modes were constructed with three histidines (His(6), His(13), and His(14)), and Asp(1)/Glu(11) of Aβ40 coordinated to Zn(2+). Results from molecular dynamics simulations reveal that the conformational ensembles of different Zn(2+)-Aβ40 complexes are nonoverlapping. The formation of turn structure and, especially, the salt bridge between Glu(22)/Asp(23) and Lys(28) is dependent on specific Zn(2+) binding mode. Agreement with available NMR observations of secondary and tertiary structures could be better achieved if the two simulation results are considered together. The free energy landscape constructed by combining both conformations of Aβ40 indicates that transitions between distinct Aβ40 conformations thar are ready for Zn(2+) binding could be possible in aqueous solution. Markov state model analyses reveal the complex network of conformational space of Aβ40 modeulated by Zn(2+) binding, suggesting various misfolding pathways. The binding free energies evaluated using a combination of quantum mechanics calculations and the MM/3D-RISM method suggest that Glu(11) is the preferred oxygen ligand of Zn(2+). However, such preference is dependent on the relative populations of different conformations with specific Zn(2+) binding modes, and therefore could be shifted when experimental or simulation conditions are altered.

Impact of chemical heterogeneity on protein self-assembly in water

Hydrophobicity is thought to underlie self-assembly in biological systems. However, the protein surface comprises hydrophobic and hydrophilic patches, and understanding the impact of such a chemical heterogeneity on protein self-assembly in water is of fundamental interest. Here, we report structural and thermodynamic investigations on the dimer formation of full-length amyloid-β proteins in water associated with Alzheimer's disease. Spontaneous dimerization process--from the individual diffusive regime at large separations, through the approach stage in which two proteins come close to each other, to the structural adjustment stage toward compact dimer formation--was captured in full atomic detail via unguided, explicit-water molecular dynamics simulations. The integral-equation theory of liquids was then applied to simulated protein structures to analyze hydration thermodynamic properties and the water-mediated interaction between proteins. We demonstrate that hydrophilic residues play a key role in initiating the dimerization process. A long-range hydration force of enthalpic origin acting on the hydrophilic residues provides the major thermodynamic force that drives two proteins to approach from a large separation to a contact distance. After two proteins make atomic contacts, the nature of the water-mediated interaction switches from a long-range enthalpic attraction to a short-range entropic one. The latter acts both on the hydrophobic and hydrophilic residues. Along with the direct protein-protein interactions that lead to the formation of intermonomer hydrogen bonds and van der Waals contacts, the water-mediated attraction of entropic origin brings about structural adjustment of constituent monomer proteins toward the formation of a compact dimer structure.

Amyloid-β peptide structure in aqueous solution varies with fragment size

Various fragment sizes of the amyloid-β (Aβ) peptide have been utilized to mimic the properties of the full-length Aβ peptide in solution. Among these smaller fragments, Aβ16 and Aβ28 have been investigated extensively. In this work, we report the structural and thermodynamic properties of the Aβ16, Aβ28, and Aβ42 peptides in an aqueous solution environment. We performed replica exchange molecular dynamics simulations along with thermodynamic calculations for investigating the conformational free energies, secondary and tertiary structures of the Aβ16, Aβ28, and Aβ42 peptides. The results show that the thermodynamic properties vary from each other for these peptides. Furthermore, the secondary structures in the Asp1-Lys16 and Asp1-Lys28 regions of Aβ42 cannot be completely captured by the Aβ16 and Aβ28 fragments. For example, the β-sheet structures in the N-terminal region of Aβ16 and Aβ28 are either not present or the abundance is significantly decreased in Aβ42. The α-helix and β-sheet abundances in Aβ28 and Aβ42 show trends--to some extent--with the potential of mean forces but no such trend could be obtained for Aβ16. Interestingly, Arg5 forms salt bridges with large abundances in all three peptides. The formation of a salt bridge between Asp23-Lys28 is more preferred over the Glu22-Lys28 salt bridge in Aβ28 but this trend is vice versa for Aβ42. This study shows that the Asp1-Lys16 and Asp1-Lys28 regions of the full length Aβ42 peptide cannot be completely mimicked by studying the Aβ16 and Aβ28 peptides.

Atomic decomposition of the protein solvation free energy and its application to amyloid-beta protein in water

We report the development of an atomic decomposition method of the protein solvation free energy in water, which ascribes global change in the solvation free energy to local changes in protein conformation as well as in hydration structure. So far, empirical decomposition analyses based on simple continuum solvation models have prevailed in the study of protein-protein interactions, protein-ligand interactions, as well as in developing scoring functions for computer-aided drug design. However, the use of continuum solvation model suffers serious drawbacks since it yields the protein free energy landscape which is quite different from that of the explicit solvent model and since it does not properly account for the non-polar hydrophobic effects which play a crucial role in biological processes in water. Herein, we develop an exact and general decomposition method of the solvation free energy that overcomes these hindrances. We then apply this method to elucidate the molecular origin for the solvation free energy change upon the conformational transitions of 42-residue amyloid-beta protein (Aβ42) in water, whose aggregation has been implicated as a primary cause of Alzheimer's disease. We address why Aβ42 protein exhibits a great propensity to aggregate when transferred from organic phase to aqueous phase.