Disassembling solvation free energies into local contributions—Toward a microscopic understanding of solvation processes

Entropy Tug-of-War Determines Solvent Effects in the Liquid-Liquid Phase Separation of a Globular Protein

Liquid-liquid phase separation (LLPS) plays a key role in the compartmentalization of cells via the formation of biomolecular condensates. Here, we combined atomistic molecular dynamics (MD) simulations and terahertz (THz) spectroscopy to determine the solvent entropy contribution to the formation of condensates of the human eye lens protein γD-Crystallin. The MD simulations reveal an entropy tug-of-war between water molecules that are released from the protein droplets and those that are retained within the condensates, two categories of water molecules that were also assigned spectroscopically. A recently developed THz-calorimetry method enables quantitative comparison of the experimental and computational entropy changes of the released water molecules. The strong correlation mutually validates the two approaches and opens the way to a detailed atomic-level understanding of the different driving forces underlying the LLPS.

DFT, ADME studies and evaluation of the binding with HSA and MAO-B inhibitory potential of protoberberine alkaloids from Guatteria friesiana: theoretical insights of promising candidates for the treatment of Parkinson's disease

CONTEXT

Parkinson's disease is a chronic neurodegenerative condition that has no cure, characterized by the progressive degeneration of specific brain cells responsible for producing dopamine, a crucial neurotransmitter for controlling movement and muscle coordination. Parkinson's disease is estimated to affect around 1% of the world's population over the age of 60, but it can be diagnosed at younger ages. One of the treatment strategies for Parkinson's disease involves the use of drugs that aim to increase dopamine levels or simulate the action of dopamine in the brain. A class of commonly prescribed drugs are the so-called monoamine oxidase B (MAO-B) inhibitors due to the fact that this enzyme is responsible for metabolizing dopamine, thus reducing its levels in the brain. Studies have shown that berberine-derived alkaloids have the ability to selectively inhibit MAO-B activity, resulting in increased dopamine availability in the brain. In this context, berberine derivatives 13-hydroxy-discretinine and 7,8-dihydro-8-hydroxypalmatine, isolated from Guatteria friesiana, were evaluated via density functional theory followed by ADME studies, docking and molecular dynamic simulations with MAO-B, aiming to evaluate their anti-Parkinson potential, which have not been reported yet. Docking simulations with HSA were carried out aiming to evaluate the transport of these molecules through the circulatory system.

METHODS

The 3D structures of the berberine-derived alkaloids were modeled via the DFT approach at B3LYP-D3(BJ)/6-311 + + G(2df, 2pd) theory level using Gaussian 09 software. Solvation free energies were determined through Truhlar's solvation model. MEP and ALIE maps were generated with Multiwfn software. Autodock Vina software was used for molecular docking simulations and analysis of the interactions in the binding sites. The 3D structure of MAO-B was obtained from the Protein Data Bank website under PDB code 2V5Z. For the interaction of studied alkaloids with human serum albumin (HSA) drug sites, 3D structures with PDB codes 2BXD, 2BXG, and 4L9K were used. Molecular dynamics simulations were carried out using GROMACS 2019.4 software, with the GROMOS 53A6 force field at 100 ns simulation time. The estimation of the ligand's binding free energies was obtained via molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method.

Driving forces of the complex formation between highly charged disordered proteins

Highly disordered complexes between oppositely charged intrinsically disordered proteins present a new paradigm of biomolecular interactions. Here, we investigate the driving forces of such interactions for the example of the highly positively charged linker histone H1 and its highly negatively charged chaperone, prothymosin α (ProTα). Temperature-dependent single-molecule Förster resonance energy transfer (FRET) experiments and isothermal titration calorimetry reveal ProTα-H1 binding to be enthalpically unfavorable, and salt-dependent affinity measurements suggest counterion release entropy to be an important thermodynamic driving force. Using single-molecule FRET, we also identify ternary complexes between ProTα and H1 in addition to the heterodimer at equilibrium and show how they contribute to the thermodynamics observed in ensemble experiments. Finally, we explain the observed thermodynamics quantitatively with a mean-field polyelectrolyte theory that treats counterion release explicitly. ProTα-H1 complex formation resembles the interactions between synthetic polyelectrolytes, and the underlying principles are likely to be of broad relevance for interactions between charged biomolecules in general.

Thermodynamic forces from protein and water govern condensate formation of an intrinsically disordered protein domain

Liquid-liquid phase separation (LLPS) can drive a multitude of cellular processes by compartmentalizing biological cells via the formation of dense liquid biomolecular condensates, which can function as membraneless organelles. Despite its importance, the molecular-level understanding of the underlying thermodynamics of this process remains incomplete. In this study, we use atomistic molecular dynamics simulations of the low complexity domain (LCD) of human fused in sarcoma (FUS) protein to investigate the contributions of water and protein molecules to the free energy changes that govern LLPS. Both protein and water components are found to have comparably sizeable thermodynamic contributions to the formation of FUS condensates. Moreover, we quantify the counteracting effects of water molecules that are released into the bulk upon condensate formation and the waters retained within the protein droplets. Among the various factors considered, solvation entropy and protein interaction enthalpy are identified as the most important contributions, while solvation enthalpy and protein entropy changes are smaller. These results provide detailed molecular insights on the intricate thermodynamic interplay between protein- and solvation-related forces underlying the formation of biomolecular condensates.

Spatial Layouts of Low-Entropy Hydration Shells Guide Protein Binding

Protein-protein binding enables orderly biological self-organization and is therefore considered a miracle of nature. Protein‒protein binding is driven by electrostatic forces, hydrogen bonding, van der Waals force, and hydrophobic interactions. Among these physical forces, only hydrophobic interactions can be considered long-range intermolecular attractions between proteins due to the electrostatic shielding of surrounding water molecules. Low-entropy hydration shells around proteins drive hydrophobic attraction among them that essentially coordinate protein‒protein binding. Here, an innovative method is developed for identifying low-entropy regions of hydration shells of proteins by screening off pseudohydrophilic groups on protein surfaces and revealing that large low-entropy regions of the hydration shells typically cover the binding sites of individual proteins. According to an analysis of determined protein complex structures, shape matching between a large low-entropy hydration shell region of a protein and that of its partner at the binding sites is revealed as a universal law. Protein‒protein binding is thus found to be mainly guided by hydrophobic collapse between the shape-matched low-entropy hydration shells that is verified by bioinformatics analyses of hundreds of structures of protein complexes, which cover four test systems. A simple algorithm is proposed to accurately predict protein binding sites.

Prevalence and mechanism of synergistic carboxylate-cation-water interactions in halophilic proteins

The cytoplasmic proteins of some halophilic organisms remain stable and functional at multimolar concentrations of KCl, i.e., under conditions that most mesophilic proteins cannot withstand. Their stability arises from their unusual amino acid composition. The most dramatic difference between halophilic and mesophilic proteins is that the former are rich in acidic amino acids. It has been proposed that one of the evolutionary driving forces for this difference is the occurrence of synergistic interactions between multiple acidic amino acids at the surface of the protein, the potassium cations in solution, and water. We investigate this possibility with molecular dynamics simulations, using high-quality force fields for the protein-water, protein-ion, and ion-ion interactions. We create a rigorous thermodynamic definition of interactions between acidic amino acids on proteins that can be used to distinguish between synergistic, noninteracting and interfering interactions. Our results demonstrate that synergistic interactions between neighboring acidic amino acids in halophilic proteins are frequent at multimolar KCl concentration. Synergistic interactions have an electrostatic origin, and are associated with stronger water-to-carboxylate hydrogen bonds than for acidic amino acids without synergistic interactions. Synergistic interactions are not observed in minimal systems of carboxylates, indicating that the protein environment is critical for their emergence. Our results demonstrate that synergistic interactions are neither associated with rigid amino acid orientations nor with highly structured and slow moving water networks, as had been originally proposed. Moreover, synergistic interactions can also be found in unfolded protein conformations. However, because these conformations are only a small subset of the unfolded state ensemble, synergistic interactions should contribute to the net stabilization of the folded state.

Understanding dynamics in coarse-grained models. I. Universal excess entropy scaling relationship

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.

Total free energy analysis of fully hydrated proteins

The total free energy of a hydrated biomolecule and its corresponding decomposition of energy and entropy provides detailed information about regions of thermodynamic stability or instability. The free energies of four hydrated globular proteins with different net charges are calculated from a molecular dynamics simulation, with the energy coming from the system Hamiltonian and entropy using multiscale cell correlation. Water is found to be most stable around anionic residues, intermediate around cationic and polar residues, and least stable near hydrophobic residues, especially when more buried, with stability displaying moderate entropy-enthalpy compensation. Conversely, anionic residues in the proteins are energetically destabilized relative to singly solvated amino acids, while trends for other residues are less clear-cut. Almost all residues lose intraresidue entropy when in the protein, enthalpy changes are negative on average but may be positive or negative, and the resulting overall stability is moderate for some proteins and negligible for others. The free energy of water around single amino acids is found to closely match existing hydrophobicity scales. Regarding the effect of secondary structure, water is slightly more stable around loops, of intermediate stability around β strands and turns, and least stable around helices. An interesting asymmetry observed is that cationic residues stabilize a residue when bonded to its N-terminal side but destabilize it when on the C-terminal side, with a weaker reversed trend for anionic residues.

Diclofenac Ion Hydration: Experimental and Theoretical Search for Anion Pairs

Self-assembly of organic ions in aqueous solutions is a hot topic at the present time, and substances that are well-soluble in water are usually studied. In this work, aqueous solutions of sodium diclofenac are investigated, which, like most medicinal compounds, is poorly soluble in water. Classical MD modeling of an aqueous solution of diclofenac sodium showed equilibrium between the hydrated anion and the hydrated dimer of the diclofenac anion. The assignment and interpretation of the bands in the UV, NIR, and IR spectra are based on DFT calculations in the discrete-continuum approximation. It has been shown that the combined use of spectroscopic methods in various frequency ranges with classical MD simulations and DFT calculations provides valuable information on the association processes of medical compounds in aqueous solutions. Additionally, such a combined application of experimental and calculation methods allowed us to put forward a hypothesis about the mechanism of the effect of diclofenac sodium in high dilutions on a solution of diclofenac sodium.

Spatially Resolved Hydration Thermodynamics in Biomolecular Systems

Water is essential for the structure, dynamics, energetics, and thus the function of biomolecules. It is a formidable challenge to elicit, in microscopic detail, the role of the solvation-related driving forces of biomolecular processes, such as the enthalpy and entropy contributions to the underlying free-energy landscape. In this Perspective, we discuss recent developments and applications of computational methods that provide a spatially resolved map of hydration thermodynamics in biomolecular systems and thus yield atomic-level insights to guide the interpretation of experimental observations. An emphasis is on the challenge of quantifying the hydration entropy, which requires characterization of both the motions of the biomolecules and of the water molecules in their surrounding.

Spatially resolved free-energy contributions of native fold and molten-globule-like Crambin

The folding stability of a protein is governed by the free-energy difference between its folded and unfolded states, which results from a delicate balance of much larger but almost compensating enthalpic and entropic contributions. The balance can therefore easily be shifted by an external disturbance, such as a mutation of a single amino acid or a change of temperature, in which case the protein unfolds. Effects such as cold denaturation, in which a protein unfolds because of cooling, provide evidence that proteins are strongly stabilized by the solvent entropy contribution to the free-energy balance. However, the molecular mechanisms behind this solvent-driven stability, their quantitative contribution in relation to other free-energy contributions, and how the involved solvent thermodynamics is affected by individual amino acids are largely unclear. Therefore, we addressed these questions using atomistic molecular dynamics simulations of the small protein Crambin in its native fold and a molten-globule-like conformation, which here served as a model for the unfolded state. The free-energy difference between these conformations was decomposed into enthalpic and entropic contributions from the protein and spatially resolved solvent contributions using the nonparametric method Per|Mut. From the spatial resolution, we quantified the local effects on the solvent free-energy difference at each amino acid and identified dependencies of the local enthalpy and entropy on the protein curvature. We identified a strong stabilization of the native fold by almost 500 kJ mol-1 due to the solvent entropy, revealing it as an essential contribution to the total free-energy difference of (53 ± 84) kJ mol-1. Remarkably, more than half of the solvent entropy contribution arose from induced water correlations.

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.

Dielectrophoresis of proteins: experimental data and evolving theory

The ability to selectively move and trap proteins is core to their effective use as building blocks and for their characterization. Analytical and preparative strategies for proteins have been pursued and modeled for nearly a hundred years, with great advances and success. Core to all of these studies is the separation, isolation, purification, and concentration of pure homogeneous fractions of a specific protein in solution. Processes to accomplish this useful solution include biphasic equilibrium (chromatographies, extractions), mechanical, bulk property, chemical equilibria, and molecular recognition. Ultimately, the goal of all of these is to physically remove all non-like protein molecules-to the finest detail: all atoms in the full three-dimensional structure being identical down the chemical bond and bulk structure chirality. One strategy which has not been effectively pursued is exploiting the higher order subtle electrical properties of the protein-solvent system. The advent of microfluidic systems has enabled the use of very high electric fields and well-defined gradients such that extremely high resolution separations of protein mixtures are possible. These advances and recognition of these capabilities have caused a re-evaluation of the underlying theoretical models and they were found to be inadequate. New theoretical descriptions are being considered which align more closely to the total forces present and the subtlety of differences between similar proteins. These are focused on the interfacial area between the protein and hydrating solvent molecules, as opposed to the macroscale assumptions of homogeneous solutions and particles. This critical review examines all data which has been published that place proteins in electric field gradients which induce collection of those proteins, demonstrating a force greater than dispersive effects or countering forces. Evolving theoretical constructs are presented and discussed, and a general estimate of future capabilities using the higher order effects and the high fields and precise gradients of microfluidic systems is discussed. Graphical abstract.

The Partner Does Matter: The Structure of Heteroaggregates of Acridine Orange in Water

Self-assembly of organic molecules in aqueous solutions is governed by a delicate entropy/enthalpy balance. Even small changes in their intermolecular interactions can cause critical changes in the structure of the aggregates and their spectral properties. The experimental results reported here demonstrate that protonated cations of acridine orange, acridine, and acridin-9-amine form stable J-heteroaggregates when in water. The structures of these aggregates are justified by the homonuclear ¹H cross-relaxation nuclear magnetic resonance (NMR). The absorption and fluorescence of these aggregates deviate characteristically from the known H-homoaggregates of the protonated cations of acridine orange. The latter makes acridine orange a handy optical sensor for soft matter studies.