PDB2ENTROPY and PDB2TRENT: Conformational and Translational–Rotational Entropy from Molecular Ensembles

Assessing nanobody interaction with SARS-CoV-2 Nsp9

The interaction between SARS-CoV-2 non-structural protein Nsp9 and the nanobody 2NSP90 was investigated by NMR spectroscopy using the paramagnetic perturbation methodology PENELOP (Paramagnetic Equilibrium vs Nonequilibrium magnetization Enhancement or LOss Perturbation). The Nsp9 monomer is an essential component of the replication and transcription complex (RTC) that reproduces the viral gRNA for subsequent propagation. Therefore preventing Nsp9 recruitment in RTC would represent an efficient antiviral strategy that could be applied to different coronaviruses, given the Nsp9 relative invariance. The NMR results were consistent with a previous characterization suggesting a 4:4 Nsp9-to-nanobody stoichiometry with the occurrence of two epitope pairs on each of the Nsp9 units that establish the inter-dimer contacts of Nsp9 tetramer. The oligomerization state of Nsp9 was also analyzed by molecular dynamics simulations and both dimers and tetramers resulted plausible. A different distribution of the mapped epitopes on the tetramer surface with respect to the former 4:4 complex could also be possible, as well as different stoichiometries of the Nsp9-nanobody assemblies such as the 2:2 stoichiometry suggested by the recent crystal structure of the Nsp9 complex with 2NSP23 (PDB ID: 8dqu), a nanobody exhibiting essentially the same affinity as 2NSP90. The experimental NMR evidence, however, ruled out the occurrence in liquid state of the relevant Nsp9 conformational change observed in the same crystal structure.

Significance of the Disulfide Bridge in the Structure and Stability of Metalloprotein Azurin

Metalloproteins make up a class of proteins that incorporate metal ions into their structures, enabling them to perform essential functions in biological systems, such as catalysis and electron transport. Azurin is one such metalloprotein with copper cofactor, having a β-barrel structure with exceptional thermal stability. The copper metal ion is coordinated at one end of the β-barrel structure, and there is a disulfide bond at the opposite end. In this study, we explore the effect of this disulfide bond in the high thermal stability of azurin by analyzing both the native S-S bonded and S-S nonbonded (S-S open) forms using temperature replica exchange molecular dynamics (REMD). Similar to experimental observations, we find a 35 K decrease in denaturation temperature for S-S open azurin compared to that of the native holo form (420 K). As observed in the case of native holo azurin, the unfolding process of the S-S open form also started with disruptions of the α-helix. The free energy surfaces of the unfolding process revealed that the denaturation event of the S-S open form progresses through different sets of conformational ensembles. Subsequently, we compared the stabilities of individual β-sheet strands of both the S-S bonded and the S-S nonbonded forms of azurin. Further, we examined the contacts between individual residues for the central structures from the free energy surfaces of the S-S nonbonded form. The microscopic origin of the lowering in the denaturation temperature is further supplemented by thermodynamic analysis.

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.

Conformational and Thermodynamic Differences Underlying Wild-Type and Mutant Eleven-Nineteen-Leukemia YEATS Domain Specificity for Epigenetic Marks

Histone post-translational modifications (PTMs) are interpreted by multiple reader domains and proteins to regulate gene expression. The eleven-nineteen-leukemia (ENL) YEATS domain is a prototypical PTM reader that recognizes multiple lysine acetylation marks on the histone H3 tails as a way of recruiting chromatin remodellers. Two ENL YEATS mutations have been identified which have been linked with leukemia, Wilms tumor, and other forms of cancer and result in either an insertion or deletion of residues in the loop connecting beta sheets distant from the protein active site. In vitro experiments have shown that these mutations modulate the selectivities of YEATS domains for various lysine acetylation marks, although different experiments have provided contrasting views on the abilities of the insertion and deletion mutants to discern specific PTMs. Here, we have performed multiple molecular dynamics simulations of wild-type and insertion and deletion mutant YEATS domains free from and in complex with two PTM peptides: one that is acetylated at K9 of H3 and the other that is acetylated at residue K27 of H3. Results show that these two peptides have distinct flexibilities and binding energetics when bound to YEATS domains and that these properties are affected by interactions with residues within and outside of the peptide consensus motif. Furthermore, these properties are modulated by the YEATS insertion and deletion mutants, which results in disparate binding effects in these systems. Together, these results suggest that only the partial exposure of histone tails is sufficient in the context of nucleosomes for YEATS-mediated recognition of acetylation marks on histone tails. They also caution against the overinterpretation of results obtained from experiments on reader domain-histone peptide binding in isolation and not in the full-length nucleosome context.

Solvent quality and solvent polarity in polypeptides

Using molecular dynamics and thermodynamic integration, we report on the solvation process of seven polypeptides (GLY, ALA, ILE, ASN, LYS, ARG, GLU) in water and in cyclohexane. The polypeptides are selected to cover the full hydrophobic scale while varying their chain length from tri- to undeca-homopeptides, providing indications on possible non-additivity effects as well as the role of the peptide backbone in the overall stability of the polypeptides. The use of different solvents and different polypeptides allows us to investigate the relation between solvent quality - the capacity of a given solvent to fold/unfold a given biopolymer often described on a scale ranging from "good" to "poor"; and solvent polarity - related to the specific interactions of any solvent with respect to a reference solvent. Undeca-glycine is found to be the only polypeptide to have a stable collapse in water (polar solvent), with the other hydrophobic polypeptides displaying repeated folding and unfolding events in water, with polar polypeptides presenting even more complex behavior. By contrast, all polypeptides are found to keep an extended conformation in cyclohexane, irrespective of their polarity. All considered polypeptides are also found to have favorable solvation free energy independent of the solvent polarity and their intrinsic hydrophobicity, clearly highlighting the prominent stabilizing role of the peptide backbone - with the solvation process largely enthalpically dominated in polar polypeptides and partially entropically driven for hydrophobic polypeptides. Our study thus reveals the complexity of the solvation process of polypeptides defying the common view "like dissolves like", with the solute polarity playing the most prominent role. The absence of mirror symmetry upon the inversion of polarities of both the solvent and the polypeptides is confirmed.

Effects of Conformational Constraint on Peptide Solubility Limits

Liquid-liquid phase separation of proteins preferentially involves intrinsically disordered proteins or disordered regions. Understanding the solution chemistry of these phase separations is key to learning how to quantify and manipulate systems that involve such processes. Here, we investigate the effect of cyclization on the liquid-liquid phase separation of short polyglycine peptides. We simulated separate aqueous systems of supersaturated cyclic and linear GGGGG and observed spontaneous liquid-liquid phase separation in each of the solutions. The cyclic GGGGG phase separates less robustly than linear GGGGG and has a higher aqueous solubility, even though linear GGGGG has a more favorable single molecule solvation free energy. The versatile and abundant interpeptide contacts formed by the linear GGGGG stabilize the condensed droplet phase, driving the phase separation in this system. In particular, we find that van der Waals close contact interactions are enriched in the droplet phase as opposed to electrostatic interactions. An analysis of the change in backbone conformational entropy that accompanies the phase transition revealed that cyclic peptides lose significantly less entropy in this process as expected. However, we find that the enhanced interaction enthalpy of linear GGGGG in the droplet phase is enough to compensate for a larger decrease in conformational entropy.

Toward Reliable and Insightful Entropy Calculations on Flexible Molecules

The absolute entropy of a flexible molecule can be approximated by the sum of a rigid-rotor-harmonic-oscillator (RRHO) entropy and a Gibbs-Shannon entropy associated to the Boltzmann distribution for the occupation of the conformational energy levels. Herein, we show that such partitioning, which has received renewed interest, leads to accurate entropies of single molecules of increasing size provided that the conformational part is estimated by means of a set of discretization and expansion techniques that are able to capture the significant correlation effects among the torsional motions. To ensure a reliable entropy estimation, we rely on extensive sampling as that produced by classical molecular dynamics simulations on the microsecond time scale, which is currently affordable for small- and medium-sized molecules. According to test calculations, the gas-phase entropy of simple organic molecules is predicted with a mean unsigned error of 0.9 cal/(mol K) when the RRHO entropies are computed at the B3LYP-D3/cc-pVTZ level. Remarkably, the same protocol gives small errors [<1 cal/(mol K)] for the extremely flexible linear alkane molecules (C_nH_2n+2, n = 14, 16, and 18). Similarly, we obtain well-converged entropies for a more challenging test of drug molecules, which exhibit more pronounced correlation effects. We also perform equivalent entropy calculations on a 76 amino acid protein, ubiquitin, by taking advantage of the cutoff-dependent formulation of an expansion technique (correlation-consistent multibody local approximation, CC-MLA), which incorporates genuine correlation effects among the neighboring dihedral angles. Moreover, we show that insightful descriptors of the coupled torsional motions can be obtained with the CC-MLA approach.

Data Structures and Algorithms for k-th Nearest Neighbours Conformational Entropy Estimation

Entropy of multivariate distributions may be estimated based on the distances of nearest neighbours from each sample from a statistical ensemble. This technique has been applied on biomolecular systems for estimating both conformational and translational/rotational entropy. The degrees of freedom which mostly define conformational entropy are torsion angles with their periodicity. In this work, tree structures and algorithms to quickly generate lists of nearest neighbours for periodic and non-periodic data are reviewed and applied to biomolecular conformations as described by torsion angles. The effect of dimensionality, number of samples, and number of neighbours on the computational time is assessed. The main conclusion is that using proper data structures and algorithms can greatly reduce the complexity of nearest neighbours lists generation, which is the bottleneck step in nearest neighbours entropy estimation.

Thermal Unfolding of the Human Serotonin Transporter: Differential Effect by Stabilizing and Destabilizing Mutations and Cholesterol on Thermodynamic and Kinetic Stability

Folding-deficient mutants of solute carrier 6 (SLC6) family members have been linked to human diseases. The serotonin transporter [(SERT)/SLC6A4] is an important drug target in the treatment of depression, anxiety, and obsessive-compulsive disorders and-with structural information in several conformational states-one of the best understood transporters. Here, we surmised that thermal unfolding offered a glimpse on the folding energy landscape of SLC6 transporters. We carried out molecular dynamic (MD) simulations to understand the mechanistic basis for enhanced and reduced stability, respectively, of the thermostabilized variant SERT-Y110A/I291A/T439S, which had previously been used for crystallization of human SERT in the outward-facing state, and of the folding-deficient SERT-P601A/G602A. We also examined the hydrophobic mismatch caused by the absence of cholesterol to explore the contribution of cholesterol to protein stability. When compared with wild type SERT, the thermodynamic and kinetic stability of SERT-Y110A/I291A/T439S was enhanced. In the other instances, changes in these two components were not correlated: the mutations in SERT-P601A/G602A led to a drop in thermodynamic but an increase in kinetic stability. The divergence was even more pronounced after cholesterol depletion, which reduced thermodynamic stability but increased the kinetic stability of wild type SERT to a level comparable to that of SERT-Y110A/I291A/T439S. We conclude that the low cholesterol content of the endoplasmic reticulum facilitates progression of the folding trajectory by reducing the energy difference between folding intermediates and the native state. SIGNIFICANCE STATEMENT: Point mutations in solute carrier 6 (SLC6) family members cause folding diseases. The serotonin transporter [(SERT)/SLC6A4] is a target for antidepressants and the best understood SLC6. This study produced molecular dynamics simulations and examined thermal unfolding of wild type and mutant SERT variants to understand their folding energy landscape. In the folding-deficient SERT-P012A/G602A, changes in kinetic and thermodynamic stability were not correlated. Similarly, cholesterol depletion lowered thermodynamic but enhanced kinetic stability. These observations allow for rationalizing the action of pharmacochaperones.

Phospholipids dock SARS-CoV-2 spike protein via hydrophobic interactions: a minimal in-silico study of lecithin nasal spray therapy

Understanding the physical and chemical properties of viral infections at molecular scales is a major challenge for the scientific community more so with the outbreak of global pandemics. There is currently a lot of effort being placed in identifying molecules that could act as putative drugs or blockers of viral molecules. In this work, we computationally explore the importance in antiviral activity of a less studied class of molecules, namely surfactants. We employ all-atoms molecular dynamics simulations to study the interaction between the receptor-binding domain of the SARS-CoV-2 spike protein and the phospholipid lecithin (POPC), in water. Our microsecond simulations show a preferential binding of lecithin to the receptor-binding motif of SARS-CoV-2 with binding free energies significantly larger than [Formula: see text]. Furthermore, hydrophobic interactions involving lecithin non-polar tails dominate these binding events, which are also accompanied by dewetting of the receptor binding motif. Through an analysis of fluctuations in the radius of gyration of the receptor-binding domain, its contact maps with lecithin molecules, and distributions of water molecules near the binding region, we elucidate molecular interactions that may play an important role in interactions involving surfactant-type molecules and viruses. We discuss our minimal computational model in the context of lecithin-based liposomal nasal sprays as putative mitigating therapies for COVID-19.

Thermodynamic Compensation in Peptides Following Liquid-Liquid Phase Separation

Liquid-liquid phase separation of proteins often incorporates intrinsically disordered proteins or those with disordered regions. Examining these processes via the entropy change is desirable for establishing a quantitative foundation with which to probe and understand these phase transitions. Of interest is the effect of residue sequence on the entropy of the peptide backbone. In this work we model these systems via all atom simulations of liquid-liquid phase separation of peptides. Systems of supersaturated pentapeptides separate into a peptide-dense liquid droplet phase as well as a dilute (saturated) aqueous phase. An analysis of the change in backbone conformational entropy associated with the phase transition was performed. We examined systems of four different pentapeptides (GGGGG, GGQGG, GGNGG, and GGVGG) in order to explore the effect of sequence variation on the conformational entropy, as well as the effect of side chain variation on the physical characteristics of the droplet phases. We find that the loss of conformational entropy that accompanies aqueous → droplet transitions is more than compensated by a decrease in interaction enthalpy as contributions to the free energy change for the process.

Entropy of Two-Molecule Correlated Translational-Rotational Motions Using the kth Nearest Neighbor Method

The entropy associated with rotations, translations, and their coupled motions provides an important contribution to the free energy of many physicochemical processes such as association and solvation. The kth nearest neighbor method, which offers a convenient way to estimate the entropy in high-dimensional spaces, has been previously applied for translational-rotational entropy estimation. Here, we explore the possibility of extending the kth nearest neighbor method to the computation of the entropy of correlated translation-rotations of two molecules, i.e., in the product space of two translation-rotations, both referred to the same independent reference system, which is relevant for all cases in which the correlated translational-rotational motion of more than two molecules is involved. Numerical tests show that, albeit the relatively high dimensionality (12) of the space, the kth nearest neighbor approach provides an accurate estimate for the entropy of two correlated translational-rotational motions, even when computed from a limited number of samples.

Calculating Transfer Entropy from Variance-Covariance Matrices Provides Insight into Allosteric Communication in ERK2

We develop an approach by which reliable estimates of the transfer entropy can be obtained from the variance-covariance matrix of atomic fluctuations, which converges quickly and retains sensitivity to the full chemical profile of the biomolecular system. We validate our method on ERK2, a well-studied kinase involved in the MAPK signaling cascade for which considerable computational, experimental, and mutation data are available. We present the results of transfer entropy analysis on data obtained from molecular dynamics simulations of wild-type active and inactive ERK2, along with mutants Q103A, I84A, L73P, and G83A. We show that our method is systematically consistent within the context of other approaches for calculating transfer entropy, and we provide a method for interpreting networks of interconnected residues in the protein from a perspective of allosteric coupling. We introduce new insights about possible allosteric activity of the extreme N-terminal region of the kinase, and we describe evidence that suggests that activation may occur by different paths or routes in different mutants. Our results highlight systematic advantages and disadvantages of each method for calculating transfer entropy and show the important role of transfer entropy analysis for understanding allosteric behavior in biomolecular systems.

Entropy of Proteins Using Multiscale Cell Correlation

A new multiscale method is presented to calculate the entropy of proteins from molecular dynamics simulations. Termed Multiscale Cell Correlation (MCC), the method decomposes the protein into sets of rigid-body units based on their covalent-bond connectivity at three levels of hierarchy: molecule, residue, and united atom. It evaluates the vibrational and topographical entropy from forces, torques, and dihedrals at each level, taking into account correlations between sets of constituent units that together make up a larger unit at the coarser length scale. MCC gives entropies in close agreement with normal-mode analysis and smaller than those using quasiharmonic analysis as well as providing much faster convergence. Moreover, MCC provides an insightful decomposition of entropy at each length scale and for each type of amino acid according to their solvent exposure and whether they are terminal residues. While the residue entropy depends weakly on solvent exposure, there is greater variation in entropy components for larger, more polar amino acids, which have increased conformational entropy but reduced vibrational entropy with greater solvent exposure.

Interplay between Conformational Entropy and Solvation Entropy in Protein-Ligand Binding

Understanding the driving forces underlying molecular recognition is of fundamental importance in chemistry and biology. The challenge is to unravel the binding thermodynamics into separate contributions and to interpret these in molecular terms. Entropic contributions to the free energy of binding are particularly difficult to assess in this regard. Here we pinpoint the molecular determinants underlying differences in ligand affinity to the carbohydrate recognition domain of galectin-3, using a combination of isothermal titration calorimetry, X-ray crystallography, NMR relaxation, and molecular dynamics simulations followed by conformational entropy and grid inhomogeneous solvation theory (GIST) analyses. Using a pair of diastereomeric ligands that have essentially identical chemical potential in the unbound state, we reduced the problem of dissecting the thermodynamics to a comparison of the two protein-ligand complexes. While the free energies of binding are nearly equal for the R and S diastereomers, greater differences are observed for the enthalpy and entropy, which consequently exhibit compensatory behavior, ΔΔ H°(R - S) = -5 ± 1 kJ/mol and - TΔΔ S°(R - S) = 3 ± 1 kJ/mol. NMR relaxation experiments and molecular dynamics simulations indicate that the protein in complex with the S-stereoisomer has greater conformational entropy than in the R-complex. GIST calculations reveal additional, but smaller, contributions from solvation entropy, again in favor of the S-complex. Thus, conformational entropy apparently dominates over solvation entropy in dictating the difference in the overall entropy of binding. This case highlights an interplay between conformational entropy and solvation entropy, pointing to both opportunities and challenges in drug design.

How phosphorylation influences E1 subunit pyruvate dehydrogenase: A computational study

Pyruvate (PYR) dehydrogenase complex (PDC) is an enzymatic system that plays a crucial role in cellular metabolism as it controls the entry of carbon into the Krebs cycle. From a structural point of view, PDC is formed by three different subunits (E1, E2 and E3) capable of catalyzing the three reaction steps necessary for the full conversion of pyruvate to acetyl-CoA. Recent investigations pointed out the crucial role of this enzyme in the replication and survival of specific cancer cell lines, renewing the interest of the scientific community. Here, we report the results of our molecular dynamics studies on the mechanism by which posttranslational modifications, in particular the phosphorylation of three serine residues (Ser-264-α, Ser-271-α, and Ser-203-α), influence the enzymatic function of the protein. Our results support the hypothesis that the phosphorylation of Ser-264-α and Ser-271-α leads to (1) a perturbation of the catalytic site structure and dynamics and, especially in the case of Ser-264-α, to (2) a reduction in the affinity of E1 for the substrate. Additionally, an analysis of the channels connecting the external environment with the catalytic site indicates that the inhibitory effect should not be due to the occlusion of the access/egress pathways to/from the active site.