Grid inhomogeneous solvation theory for cross-solvation in rigid solvents.

Grid Inhomogeneous Solvation Theory (GIST) has proven useful to calculate localized thermodynamic properties of water around a solute. Numerous studies have leveraged this information to enhance structure-based binding predictions. We have recently extended GIST toward chloroform as a solvent to allow the prediction of passive membrane permeability. Here, we further generalize the GIST algorithm toward all solvents that can be modeled as rigid molecules. This restriction is inherent to the method and is already present in the inhomogeneous solvation theory. Here, we show that our approach can be applied to various solvent molecules by comparing the results of GIST simulations with thermodynamic integration (TI) calculations and experimental results. Additionally, we analyze and compare a matrix consisting of 100 entries of ten different solvent molecules solvated within each other. We find that the GIST results are highly correlated with TI calculations as well as experiments. For some solvents, we find Pearson correlations of up to 0.99 to the true entropy, while others are affected by the first-order approximation more strongly. The enthalpy-entropy splitting provided by GIST allows us to extend a recently published approach, which estimates higher order entropies by a linear scaling of the first-order entropy, to solvents other than water. Furthermore, we investigate the convergence of GIST in different solvents. We conclude that our extension to GIST reliably calculates localized thermodynamic properties for different solvents and thereby significantly extends the applicability of this widely used method.

Explicit solvation thermodynamics in ionic solution: extending grid inhomogeneous solvation theory to solvation free energy of salt-water mixtures.

Hydration thermodynamics play a fundamental role in fields ranging from the pharmaceutical industry to environmental research. Numerous methods exist to predict solvation thermodynamics of compounds ranging from small molecules to large biomolecules. Arguably the most precise methods are those based on molecular dynamics (MD) simulations in explicit solvent. One theory that has seen increased use is inhomogeneous solvation theory (IST). However, while many applications require accurate description of salt-water mixtures, no implementation of IST is currently able to estimate solvation properties involving more than one solvent species. Here, we present an extension to grid inhomogeneous solvation theory (GIST) that can take salt contributions into account. At the example of carbazole in 1 M NaCl solution, we compute the solvation energy as well as first and second order entropies. While the effect of the first order ion entropy is small, both the water-water and water-ion entropies contribute strongly. We show that the water-ion entropies are efficiently approximated using the Kirkwood superposition approximation. However, this approach cannot be applied to the water-water entropy. Furthermore, we test the quantitative validity of our method by computing salting-out coefficients and comparing them to experimental data. We find a good correlation to experimental salting-out constants, while the absolute values are overpredicted due to the approximate second order entropy. Since ions are frequently used in MD, either to neutralize the system or as a part of the investigated process, our method greatly extends the applicability of GIST. The use-cases range from biopharmaceuticals, where many assays require high salt concentrations, to environmental research, where solubility in sea water is important to model the fate of organic substances.

X-Entropy: A Parallelized Kernel Density Estimator with Automated Bandwidth Selection to Calculate Entropy.

X-Entropy is a Python package used to calculate the entropy of a given distribution, in this case, based on the distribution of dihedral angles. The dihedral entropy facilitates an alignment-independent measure of local protein flexibility. The key feature of our approach is a Gaussian kernel density estimation (KDE) using a plug-in bandwidth selection, which is fully implemented in a C++ backend and parallelized with OpenMP. We further provide a Python frontend, with predefined wrapper functions for classical coordinate-based dihedral entropy calculations, using a 1D approximation. This makes the package very straightforward to include in any Python-based analysis workflow. Furthermore, the frontend allows full access to the C++ backend, so that the KDE can be used on any binnable one-dimensional input data. In this application note, we discuss implementation and usage details and illustrate potential applications. In particular, we benchmark the performance of our module in calculating the entropy of samples drawn from a Gaussian distribution and the analytical solution thereof. Further, we analyze the computational performance of this module compared to well-established python libraries that perform KDE analyses. X-Entropy is available free of charge on GitHub (https://github.com/liedllab/X-Entropy).

Conformational Ensembles of Antibodies Determine Their Hydrophobicity.

A major challenge in the development of antibody biotherapeutics is their tendency to aggregate. One root cause for aggregation is exposure of hydrophobic surface regions to the solvent. Many current techniques predict the relative aggregation propensity of antibodies via precalculated scales for the hydrophobicity or aggregation propensity of single amino acids. However, those scales cannot describe the nonadditive effects of a residue's surrounding on its hydrophobicity. Therefore, they are inherently limited in their ability to describe the impact of subtle differences in molecular structure on the overall hydrophobicity. Here, we introduce a physics-based approach to describe hydrophobicity in terms of the hydration free energy using grid inhomogeneous solvation theory (GIST). We apply this method to assess the effects of starting structures, conformational sampling, and protonation states on the hydrophobicity of antibodies. Our results reveal that high-quality starting structures, i.e., crystal structures, are crucial for the prediction of hydrophobicity and that conformational sampling can compensate errors introduced by the starting structure. On the other hand, sampling of protonation states only leads to good results when combined with high-quality structures, whereas it can even be detrimental otherwise. We conclude by pointing out that a single static homology model may not be adequate for predicting hydrophobicity.

Hydration thermodynamics of cytosolic phospholipase A2 GIVA predict its membrane-associated parts and its highly hydrated binding site.

During biological events, the water molecules associated with the protein are re-oriented to adapt to the new conditions, inducing changes in the system's free energy. The characterization of water structure and thermodynamics may facilitate the prediction of certain biological events, such as the binding of a ligand and the membrane-associated parts of a protein. In this computational study, we calculated the hydration thermodynamics of cytosolic phospholipase A2 group IV (GIVA cPLA2) to study the hydration properties of the protein's surface and binding pocket. Hydrophobicity scales and the Grid Inhomogeneous Solvation Theory (GIST) tool were employed for the calculations. The hydrophobic areas of the protein's surface were predicted more accurately with the GIST method rather than with the hydrophobicity scales. Based on this, a model of the protein-membrane complex was constructed. In addition, the calculation revealed the highly hydrated binding pocket that further contribute to our understanding of the ligands' binding. Communicated by Ramaswamy H. Sarma.

Polarizable and non-polarizable force fields: Protein folding, unfolding, and misfolding.

Molecular dynamics simulations are an invaluable tool to characterize the dynamic motions of proteins in atomistic detail. However, the accuracy of models derived from simulations inevitably relies on the quality of the underlying force field. Here, we present an evaluation of current non-polarizable and polarizable force fields (AMBER ff14SB, CHARMM 36m, GROMOS 54A7, and Drude 2013) based on the long-standing biophysical challenge of protein folding. We quantify the thermodynamics and kinetics of the ß-hairpin formation using Markov state models of the fast-folding mini-protein CLN025. Furthermore, we study the (partial) folding dynamics of two more complex systems, a villin headpiece variant and a WW domain. Surprisingly, the polarizable force field in our set, Drude 2013, consistently leads to destabilization of the native state, regardless of the secondary structure element present. All non-polarizable force fields, on the other hand, stably characterize the native state ensembles in most cases even when starting from a partially unfolded conformation. Focusing on CLN025, we find that the conformational space captured with AMBER ff14SB and CHARMM 36m is comparable, but the ensembles from CHARMM 36m simulations are clearly shifted toward disordered conformations. While the AMBER ff14SB ensemble overstabilizes the native fold, CHARMM 36m and GROMOS 54A7 ensembles both agree remarkably well with experimental state populations. In addition, GROMOS 54A7 also reproduces experimental folding times most accurately. Our results further indicate an over-stabilization of helical structures with AMBER ff14SB. Nevertheless, the presented investigations strongly imply that reliable (un)folding dynamics of small proteins can be captured in feasible computational time with current additive force fields.

Protein-Protein Binding as a Two-Step Mechanism: Preselection of Encounter Poses during the Binding of BPTI and Trypsin.

Biomolecular recognition between proteins follows complex mechanisms, the understanding of which can substantially advance drug discovery efforts. Here, we track each step of the binding process in atomistic detail with molecular dynamics simulations using trypsin and its inhibitor bovine pancreatic trypsin inhibitor (BPTI) as a model system. We use umbrella sampling to cover a range of unbinding pathways. Starting from these simulations, we subsequently seed classical simulations at different stages of the process and combine them to a Markov state model. We clearly identify three kinetically separated states (an unbound state, an encounter state, and the final complex) and describe the mechanisms that dominate the binding process. From our model, we propose the following sequence of events. The initial formation of the encounter complex is driven by long-range interactions because opposite charges in trypsin and BPTI draw them together. The encounter complex features the prealigned binding partners with binding sites still partially surrounded by solvation shells. Further approaching leads to desolvation and increases the importance of van der Waals interactions. The native binding pose is adopted by maximizing short-range interactions. Thereby side-chain rearrangements ensure optimal shape complementarity. In particular, BPTI's P1 residue adapts to the S1 pocket and prime site residues reorient to optimize interactions. After the paradigm of conformation selection, binding-competent conformations of BPTI and trypsin are already present in the apo ensembles and their probabilities increase during this proposed two-step association process. This detailed characterization of the molecular forces driving the binding process includes numerous aspects that have been discussed as central to the binding of trypsin and BPTI and protein complex formation in general. In this study, we combine all these aspects into one comprehensive model of protein recognition. We thereby contribute to enhance our general understanding of this fundamental mechanism, which is particularly critical as the development of biopharmaceuticals continuously gains significance.

Solvation Thermodynamics in Different Solvents: Water-Chloroform Partition Coefficients from Grid Inhomogeneous Solvation Theory.

Reliable information on partition coefficients plays a key role in drug development, as solubility decisively affects bioavailability. In a physicochemical context, the partition coefficient of a solute between two different solvents can be described as a function of solvation free energies. Hence, substantial scientific efforts have been made toward accurate predictions of solvation free energies in various solvents. The grid inhomogeneous solvation theory (GIST) facilitates the calculation of solvation free energies. In this study, we introduce an extended version of the GIST algorithm, which enables the calculation for chloroform in addition to water. Furthermore, GIST allows localization of enthalpic and entropic contributions. We test our approach by calculating partition coefficients between water and chloroform for a set of eight small molecules. We report a Pearson correlation coefficient of 0.96 between experimentally determined and calculated partition coefficients. The capability to reliably predict partition coefficients between water and chloroform and the possibility to localize their contributions allow the optimization of a compound's partition coefficient. Therefore, we presume that this methodology will be of great benefit for the efficient development of pharmaceuticals.

Macrocycle Cell Permeability Measured by Solvation Free Energies in Polar and Apolar Environments.

The relation of surface polarity and conformational preferences is decisive for cell permeability and thus bioavailability of macrocyclic drugs. Here, we employ grid inhomogeneous solvation theory (GIST) to calculate solvation free energies for a series of six macrocycles in water and chloroform as a measure of passive membrane permeability. We perform accelerated molecular dynamics simulations to capture a diverse structural ensemble in water and chloroform, allowing for a direct profiling of solvent-dependent conformational preferences. Subsequent GIST calculations facilitate a quantitative measure of solvent preference in the form of a transfer free energy, calculated from the ensemble-averaged solvation free energies in water and chloroform. Hence, the proposed method considers how the conformational diversity of macrocycles in polar and apolar solvents translates into transfer free energies. Following this strategy, we find a striking correlation of 0.92 between experimentally determined cell permeabilities and calculated transfer free energies. For the studied model systems, we find that the transfer free energy exceeds the purely water-based solvation free energies as a reliable estimate of cell permeability and that conformational sampling is imperative for a physically meaningful model. We thus recommend this purely physics-based approach as a computational tool to assess cell permeabilities of macrocyclic drug candidates.

Charge Anisotropy of Nitrogen: Where Chemical Intuition Fails.

For more than half a century computer simulations were developed and employed to study ensemble properties of a wide variety of atomic and molecular systems with tremendous success. Nowadays, a selection of force-fields is available that describe the interactions in such systems. A key feature of force-fields is an adequate description of the electrostatic potential (ESP). Several force-fields model the ESP via point charges positioned at the atom centers. A major shortcoming of this approach, its inability to model anisotropies in the ESP, can be mitigated using additional charge sites. It has been shown that nitrogen is the most problematic element abundant in many polymers as well as large molecules of biological origin. To tackle this issue, small organic molecules containing a single nitrogen atom were studied. In performing rigorous scans of the surroundings of these nitrogen atoms, positions where a single extra charge can enhance the ESP description the most were identified. Significant improvements are found for ammonia, amines, and amides. Interestingly, the optimal location for the extra charge does not correlate with the chemically intuitive position of the nitrogen lone pair. In fact, the placement of an extra charge in the lone-pair location does not lead to significant improvements in most cases.

Catalytic Site pKa Values of Aspartic, Cysteine, and Serine Proteases: Constant pH MD Simulations.

Enzymatic function and activity of proteases is closely controlled by the pH value. The protonation states of titratable residues in the active site react to changes in the pH value, according to their pKa, and thereby determine the functionality of the enzyme. Knowledge of the titration behavior of these residues is crucial for the development of drugs targeting the active site residues. However, experimental pKa data are scarce, since the systems' size and complexity make determination of these pKa values inherently difficult. In this study, we use single pH constant pH MD simulations as a fast and robust tool to estimate the active site pKa values of a set of aspartic, cysteine, and serine proteases. We capture characteristic pKa shifts of the active site residues, which dictate the experimentally determined activity profiles of the respective protease family. We find clear differences of active site pKa values within the respective families, which closely match the experimentally determined pH preferences of the respective proteases. These shifts are caused by a distinct network of electrostatic interactions characteristic for each protease family. While we find convincing agreement with experimental data for serine and aspartic proteases, we observe clear deficiencies in the description of the titration behavior of cysteines within the constant pH MD framework and highlight opportunities for improvement. Consequently, with this work, we provide a concise set of active site pKa values of aspartic and serine proteases, which could serve as reference for future theoretical as well as experimental studies.

Sodium-induced population shift drives activation of thrombin.

The equilibrium between active E and inactive E* forms of thrombin is assumed to be governed by the allosteric binding of a Na+ ion. Here we use molecular dynamics simulations and Markov state models to sample transitions between active and inactive states. With these calculations we are able to compare thermodynamic and kinetic properties depending on the presence of Na+. For the first time, we directly observe sodium-induced conformational changes in long-timescale computer simulations. Thereby, we are able to explain the resulting change in activity. We observe a stabilization of the active form in presence of Na+ and a shift towards the inactive form in Na+-free simulations. We identify key structural features to quantify and monitor this conformational shift. These include the accessibility of the S1 pocket and the reorientation of W215, of R221a and of the Na+ loop. The structural characteristics exhibit dynamics at various timescales: Conformational changes in the Na+ binding loop constitute the slowest observed movement. Depending on its orientation, it induces conformational shifts in the nearby substrate binding site. Only after this shift, residue W215 is able to move freely, allowing thrombin to adopt a binding-competent conformation.

pH-Induced Local Unfolding of the Phl p 6 Pollen Allergen From cpH-MD.

Susceptibility to endosomal degradation is a decisive contribution to a protein's immunogenicity. It is assumed that the processing kinetics of structured proteins are inherently linked to their probability of local unfolding. In this study, we quantify the impact of endosomal acidification on the conformational stability of the major timothy grass pollen allergen Phl p 6. We use state of the art sampling approaches in combination with constant pH MD techniques to profile pH-dependent local unfolding events in atomistic detail. Integrating our findings into the current view on type 1 allergic sensitization, we characterize local protein dynamics in the context of proteolytic degradation at neutral and acidic pH for the wild type protein and point mutants with varying proteolytic stability. We analyze extensive simulation data using Markov state models and retrieve highly reliable thermodynamic and kinetic information at varying pH levels. Thereby we capture the impact of endolysosomal acidification on the structure and dynamics of the Phl p 6 mutants. We find that upon protonation at lower pH values, the conformational flexibilities in key areas of the wild type protein, i.e., T-cell epitopes and early proteolytic cleavage sites, increase significantly. A decrease of the pH even leads to local unfolding in otherwise stable secondary structure elements, which is a prerequisite for proteolytic cleavage. This effect is even more pronounced in the destabilized mutant, while no unfolding was observed for the stabilized mutant. In summary, we report detailed structural models which rationalize the experimentally observed cleavage pattern during endosomal acidification.

Solvation Free Energy as a Measure of Hydrophobicity: Application to Serine Protease Binding Interfaces.

Solvation and hydrophobicity play a key role in a variety of biological mechanisms. In substrate binding, but also in structure-based drug design, the thermodynamic properties of water molecules surrounding a given protein are of high interest. One of the main algorithms devised in recent years to quantify thermodynamic properties of water is the grid inhomogeneous solvation theory (GIST), which calculates these features on a grid surrounding the protein. Despite the inherent advantages of GIST, the computational demand is a major drawback, as calculations for larger systems can take days or even weeks. Here, we present a GPU accelerated version of the GIST algorithm, which facilitates efficient estimates of solvation free energy even of large biomolecular interfaces. Furthermore, we show that GIST can be used as a reliable tool to evaluate protein surface hydrophobicity. We apply the approach on a set of nine different proteases calculating localized solvation free energies on the surface of the binding interfaces as a measure of their hydrophobicity. We find a compelling agreement with the hydrophobicity of their substrates, i.e., peptides, binding into the binding cleft, and thus our approach provides a reliable description of hydrophobicity characteristics of these biological interfaces.

Molecular Dynamics Gives New Insights into the Glucose Tolerance and Inhibition Mechanisms on ß-Glucosidases.

ß-Glucosidases are enzymes with high importance for many industrial processes, catalyzing the last and limiting step of the conversion of lignocellulosic material into fermentable sugars for biofuel production. However, ß-glucosidases are inhibited by high concentrations of the product (glucose), which limits the biofuel production on an industrial scale. For this reason, the structural mechanisms of tolerance to product inhibition have been the target of several studies. In this study, we performed in silico experiments, such as molecular dynamics (MD) simulations, free energy landscape (FEL) estimate, Poisson-Boltzmann surface area (PBSA), and grid inhomogeneous solvation theory (GIST) seeking a better understanding of the glucose tolerance and inhibition mechanisms of a representative GH1 ß-glucosidase and a GH3 one. Our results suggest that the hydrophobic residues Y180, W350, and F349, as well the polar one D238 act in a mechanism for glucose releasing, herein called "slingshot mechanism", dependent also on an allosteric channel (AC). In addition, water activity modulation and the protein loop motions suggest that GH1 ß-Glucosidases present an active site more adapted to glucose withdrawal than GH3, in consonance with the GH1s lower product inhibition. The results presented here provide directions on the understanding of the molecular mechanisms governing inhibition and tolerance to the product in ß-glucosidases and can be useful for the rational design of optimized enzymes for industrial interests.

CDR-H3 loop ensemble in solution - conformational selection upon antibody binding.

We analyzed pairs of protein-binding, peptide-binding and hapten-binding antibodies crystallized as complex and in the absence of the antigen with and without conformational differences upon binding in the complementarity-determining region (CDR)-H3 loop. Here, we introduce a molecular dynamics-based approach to capture a diverse conformational ensemble of the CDR-H3 loop in solution. The results clearly indicate that the inherently flexible CDR-H3 loop indeed needs to be characterized as a conformational ensemble. The conformational changes of the CDR-H3 loop in all antibodies investigated follow the paradigm of conformation selection, because we observe the experimentally determined binding competent conformation without the presence of the antigen within the ensemble of pre-existing conformational states in solution before binding. We also demonstrate for several examples that the conformation observed in the antibody crystal structure without antigen present is actually selected to bind the carboxyterminal tail region of the antigen-binding fragment (Fab). Thus, special care must be taken when characterizing antibody CDR-H3 loops by Fab X-ray structures, and the possibility that pre-existing conformations are present should always be considered.

Electrostatic recognition in substrate binding to serine proteases.

Serine proteases of the Chymotrypsin family are structurally very similar but have very different substrate preferences. This study investigates a set of 9 different proteases of this family comprising proteases that prefer substrates containing positively charged amino acids, negatively charged amino acids, and uncharged amino acids with varying degree of specificity. Here, we show that differences in electrostatic substrate preferences can be predicted reliably by electrostatic molecular interaction fields employing customized GRID probes. Thus, we are able to directly link protease structures to their electrostatic substrate preferences. Additionally, we present a new metric that measures similarities in substrate preferences focusing only on electrostatics. It efficiently compares these electrostatic substrate preferences between different proteases. This new metric can be interpreted as the electrostatic part of our previously developed substrate similarity metric. Consequently, we suggest, that substrate recognition in terms of electrostatics and shape complementarity are rather orthogonal aspects of substrate recognition. This is in line with a 2-step mechanism of protein-protein recognition suggested in the literature.

Late-Stage Functionalization of Drug-Like Molecules Using Diversinates.

Late-stage functionalization (LSF) is a powerful method to quickly generate new analogues of a lead structure without resorting to de novo synthesis. We have leveraged Baran Diversinates to carry out late-stage functionalizations on lead structures from internal drug discovery projects and accurately predicted regioselectivities using computational methods. Our functionalization successfully afforded specific regioisomers which were in line with our predictions. To enhance reactivity, decrease reaction time, and increase reaction yields, we have developed new functionalization conditions involving iron(III) catalysis. Finally, we demonstrate how our LSF reactions using Baran Diversinates can lead to new analogues with improved in vitro DMPK parameters.

Characterizing the Diversity of the CDR-H3 Loop Conformational Ensembles in Relationship to Antibody Binding Properties.

We present an approach to assess antibody CDR-H3 loops according to their dynamic properties using molecular dynamics simulations. We selected six antibodies in three pairs differing substantially in their individual promiscuity respectively specificity. For two pairs of antibodies crystal structures are available in different states of maturation and used as starting structures for the analyses. For a third pair we chose two antibody CDR sequences obtained from a synthetic library and predicted the respective structures. For all three pairs of antibodies we performed metadynamics simulations to overcome the limitations in conformational sampling imposed by high energy barriers. Additionally, we used classic molecular dynamics simulations to describe nano- to microsecond flexibility and to estimate up to millisecond kinetics of captured conformational transitions. The methodology represents the antibodies as conformational ensembles and allows comprehensive analysis of structural diversity, thermodynamics of conformations and kinetics of structural transitions. Referring to the concept of conformational selection we investigated the link between promiscuity and flexibility of the antibodies' binding interfaces. The obtained detailed characterization of the binding interface clearly indicates a link between structural flexibility and binding promiscuity for this set of antibodies.