On the Structure, Stability, and Cell Uptake of Nanostructured Lipid Carriers for Drug Delivery.

The efficacy of nanostructured lipid carriers (NLC) for drug delivery strongly depends on their stability and cell uptake. Both properties are governed by their compositions and internal structure. To test the effect of the lipid composition of NLC on cell uptake and stability, three kinds of liquid lipids with different degrees of unsaturation are employed. After ensuring homogeneous size distributions, the thermodynamic characteristics, stability, and mixing properties of NLC are characterized. Then the rates and predominant pathways of cell uptake are determined. Although the same surfactant is used in all cases, different uptake rates are observed. This finding contradicts the view that the surface properties of NLC are dominated by the surfactant. Instead, the uptake rates are explained by the structure of the nanocarrier. Depending on the mixing properties, some liquid lipids remain inside the nanocarrier, while other liquid lipids are present on the surface. Nanocarriers with liquid lipids on the surface are taken up more readily by the cells. This shows that the engineering of efficient lipid nanocarriers requires a delicate balance of interactions between all components of the nanocarrier on the molecular level.

Rational prioritization strategy allows the design of macrolide derivatives that overcome antibiotic resistance.

Antibiotic resistance is a major threat to global health; this problem can be addressed by the development of new antibacterial agents to keep pace with the evolutionary adaptation of pathogens. Computational approaches are essential tools to this end since their application enables fast and early strategical decisions in the drug development process. We present a rational design approach, in which acylide antibiotics were screened based on computational predictions of solubility, membrane permeability, and binding affinity toward the ribosome. To assess our design strategy, we tested all candidates for in vitro inhibitory activity and then evaluated them in vivo with several antibiotic-resistant strains to determine minimal inhibitory concentrations. The predicted best candidate is synthetically more accessible, exhibits higher solubility and binding affinity to the ribosome, and is up to 56 times more active against resistant pathogens than telithromycin. Notably, the best compounds designed by us show activity, especially when combined with the membrane-weakening drug colistin, against Acinetobacter baumanii, Pseudomonas aeruginosa, and Escherichia coli, which are the three most critical targets from the priority list of pathogens of the World Health Organization.

Mechanistic details of the actinobacterial lyase-catalyzed degradation reaction of 2-hydroxyisobutyryl-CoA.

Actinobacterial 2-hydroxyacyl-CoA lyase reversibly catalyzes the thiamine diphosphate-dependent cleavage of 2-hydroxyisobutyryl-CoA to formyl-CoA and acetone. This enzyme has great potential for use in synthetic one-carbon assimilation pathways for sustainable production of chemicals, but lacks details of substrate binding and reaction mechanism for biochemical reengineering. We determined crystal structures of the tetrameric enzyme in the closed conformation with bound substrate, covalent postcleavage intermediate, and products, shedding light on active site architecture and substrate interactions. Together with molecular dynamics simulations of the covalent precleavage complex, the complete catalytic cycle is structurally portrayed, revealing a proton transfer from the substrate acyl Cß hydroxyl to residue E493 that returns it subsequently to the postcleavage Cα-carbanion intermediate. Kinetic parameters obtained for mutants E493A, E493Q, and E493K confirm the catalytic role of E493 in the WT enzyme. However, the 10- and 50-fold reduction in lyase activity in the E493A and E493Q mutants, respectively, compared with WT suggests that water molecules may contribute to proton transfer. The putative catalytic glutamate is located on a short α-helix close to the active site. This structural feature appears to be conserved in related lyases, such as human 2-hydroxyacyl-CoA lyase 2. Interestingly, a unique feature of the actinobacterial 2-hydroxyacyl-CoA lyase is a large C-terminal lid domain that, together with active site residues L127 and I492, restricts substrate size to ≤C5 2-hydroxyacyl residues. These details about the catalytic mechanism and determinants of substrate specificity pave the ground for designing tailored catalysts for acyloin condensations for one-carbon and short-chain substrates in biotechnological applications.

Relative free-energy calculations for scaffold hopping-type transformations with an automated RE-EDS sampling procedure.

The calculation of relative free-energy differences between different compounds plays an important role in drug design to identify potent binders for a given protein target. Most rigorous methods based on molecular dynamics simulations estimate the free-energy difference between pairs of ligands. Thus, the comparison of multiple ligands requires the construction of a "state graph", in which the compounds are connected by alchemical transformations. The computational cost can be optimized by reducing the state graph to a minimal set of transformations. However, this may require individual adaptation of the sampling strategy if a transformation process does not converge in a given simulation time. In contrast, path-free methods like replica-exchange enveloping distribution sampling (RE-EDS) allow the sampling of multiple states within a single simulation without the pre-definition of alchemical transition paths. To optimize sampling and convergence, a set of RE-EDS parameters needs to be estimated in a pre-processing step. Here, we present an automated procedure for this step that determines all required parameters, improving the robustness and ease of use of the methodology. To illustrate the performance, the relative binding free energies are calculated for a series of checkpoint kinase 1 inhibitors containing challenging transformations in ring size, opening/closing, and extension, which reflect changes observed in scaffold hopping. The simulation of such transformations with RE-EDS can be conducted with conventional force fields and, in particular, without soft bond-stretching terms.

Ensembler: A Simple Package for Fast Prototyping and Teaching Molecular Simulations.

Ensembler is a Python package that enables method prototyping using 1D and 2D model systems and allows deepening of the understanding of different molecular dynamics (MD) methods, starting from basic techniques to enhanced sampling and free-energy approaches. The ease of installing and using the package increases shareability, comparability, and reproducibility of scientific code developments. Here, we describe the implementation and usage of the package and provide an application example for free-energy calculation. The code of Ensembler is freely available on GitHub at https://github.com/rinikerlab/Ensembler.

An Alternative to Conventional λ-Intermediate States in Alchemical Free Energy Calculations: λ-Enveloping Distribution Sampling.

Alchemical free energy calculations typically rely on intermediate states to bridge between the relevant phase spaces of the two end states. These intermediate states are usually created by mixing the energies or parameters of the end states according to a coupling parameter λ. The choice of the procedure has a strong impact on the efficiency of the calculation, as it affects both the encountered energy barriers and the phase space overlap between the states. The present work builds on the connection between the minimum variance pathway (MVP) and enveloping distribution sampling (EDS). It is shown that both methods can be regarded as special cases of a common scheme referred to as λ-EDS, which can also reproduce the behavior of conventional λ-intermediate states. A particularly attractive feature of λ-EDS is its ability to emulate the use of soft core potentials (SCP) while avoiding the associated computational overhead when applying efficient free energy estimators such as the multistate Bennett's acceptance ratio (MBAR). The method is illustrated for both relative and absolute free energy calculations considering five benchmark systems. The first two systems (charge inversion and cavity creation in a dipolar solvent) demonstrate the use of λ-EDS as an alternative coupling scheme in the context of thermodynamic integration (TI). The three other systems (change of bond length, change of dihedral angles, and cavity creation in water) investigate the efficiency and optimal choice of parameters in the context of free energy perturbation (FEP) and Bennett's acceptance ratio (BAR). It is shown that λ-EDS allows larger steps along the alchemical pathway than conventional intermediate states.

A Comparison of QM/MM Simulations with and without the Drude Oscillator Model Based on Hydration Free Energies of Simple Solutes.

Maintaining a proper balance between specific intermolecular interactions and non-specific solvent interactions is of critical importance in molecular simulations, especially when predicting binding affinities or reaction rates in the condensed phase. The most rigorous metric for characterizing solvent affinity are solvation free energies, which correspond to a transfer from the gas phase into solution. Due to the drastic change of the electrostatic environment during this process, it is also a stringent test of polarization response in the model. Here, we employ both the CHARMM fixed charge and polarizable force fields to predict hydration free energies of twelve simple solutes. The resulting classical ensembles are then reweighted to obtain QM/MM hydration free energies using a variety of QM methods, including MP2, Hartree⁻Fock, density functional methods (BLYP, B3LYP, M06-2X) and semi-empirical methods (OM2 and AM1 ). Our simulations test the compatibility of quantum-mechanical methods with molecular-mechanical water models and solute Lennard⁻Jones parameters. In all cases, the resulting QM/MM hydration free energies were inferior to purely classical results, with the QM/MM Drude force field predictions being only marginally better than the QM/MM fixed charge results. In addition, the QM/MM results for different quantum methods are highly divergent, with almost inverted trends for polarizable and fixed charge water models. While this does not necessarily imply deficiencies in the QM models themselves, it underscores the need to develop consistent and balanced QM/MM interactions. Both the QM and the MM component of a QM/MM simulation have to match, in order to avoid artifacts due to biased solute⁻solvent interactions. Finally, we discuss strategies to improve the convergence and efficiency of multi-scale free energy simulations by automatically adapting the molecular-mechanics force field to the target quantum method.

Absolute binding free energies for octa-acids and guests in SAMPL5 : Evaluating binding free energies for octa-acid and guest complexes in the SAMPL5 blind challenge.

As part of the SAMPL5 blind prediction challenge, we calculate the absolute binding free energies of six guest molecules to an octa-acid (OAH) and to a methylated octa-acid (OAMe). We use the double decoupling method via thermodynamic integration (TI) or Hamiltonian replica exchange in connection with the Bennett acceptance ratio (HREM-BAR). We produce the binding poses either through manual docking or by using GalaxyDock-HG, a docking software developed specifically for this study. The root mean square deviations for our most accurate predictions are 1.4 kcal mol-1 for OAH with TI and 1.9 kcal mol-1 for OAMe with HREM-BAR. Our best results for OAMe were obtained for systems with ionic concentrations corresponding to the ionic strength of the experimental solution. The most problematic system contains a halogenated guest. Our attempt to model the σ-hole of the bromine using a constrained off-site point charge, does not improve results. We use results from molecular dynamics simulations to argue that the distinct binding affinities of this guest to OAH and OAMe are due to a difference in the flexibility of the host. We believe that the results of this extensive analysis of host-guest complexes will help improve the protocol used in predicting binding affinities for larger systems, such as protein-substrate compounds.

Absolute binding free energy calculations of CBClip host-guest systems in the SAMPL5 blind challenge.

Herein, we report the absolute binding free energy calculations of CBClip complexes in the SAMPL5 blind challenge. Initial conformations of CBClip complexes were obtained using docking and molecular dynamics simulations. Free energy calculations were performed using thermodynamic integration (TI) with soft-core potentials and Bennett's acceptance ratio (BAR) method based on a serial insertion scheme. We compared the results obtained with TI simulations with soft-core potentials and Hamiltonian replica exchange simulations with the serial insertion method combined with the BAR method. The results show that the difference between the two methods can be mainly attributed to the van der Waals free energies, suggesting that either the simulations used for TI or the simulations used for BAR, or both are not fully converged and the two sets of simulations may have sampled difference phase space regions. The penalty scores of force field parameters of the 10 guest molecules provided by CHARMM Generalized Force Field can be an indicator of the accuracy of binding free energy calculations. Among our submissions, the combination of docking and TI performed best, which yielded the root mean square deviation of 2.94 kcal/mol and an average unsigned error of 3.41 kcal/mol for the ten guest molecules. These values were best overall among all participants. However, our submissions had little correlation with experiments.

Correcting for the free energy costs of bond or angle constraints in molecular dynamics simulations.

BACKGROUND: Free energy simulations are an important tool in the arsenal of computational biophysics, allowing the calculation of thermodynamic properties of binding or enzymatic reactions. This paper introduces methods to increase the accuracy and precision of free energy calculations by calculating the free energy costs of constraints during post-processing. The primary purpose of employing constraints for these free energy methods is to increase the phase space overlap between ensembles, which is required for accuracy and convergence. METHODS: The free energy costs of applying or removing constraints are calculated as additional explicit steps in the free energy cycle. The new techniques focus on hard degrees of freedom and use both gradients and Hessian estimation. Enthalpy, vibrational entropy, and Jacobian free energy terms are considered. RESULTS: We demonstrate the utility of this method with simple classical systems involving harmonic and anharmonic oscillators, four-atomic benchmark systems, an alchemical mutation of ethane to methanol, and free energy simulations between alanine and serine. The errors for the analytical test cases are all below 0.0007kcal/mol, and the accuracy of the free energy results of ethane to methanol is improved from 0.15 to 0.04kcal/mol. For the alanine to serine case, the phase space overlaps of the unconstrained simulations range between 0.15 and 0.9%. The introduction of constraints increases the overlap up to 2.05%. On average, the overlap increases by 94% relative to the unconstrained value and precision is doubled. CONCLUSIONS: The approach reduces errors arising from constraints by about an order of magnitude. Free energy simulations benefit from the use of constraints through enhanced convergence and higher precision. GENERAL SIGNIFICANCE: The primary utility of this approach is to calculate free energies for systems with disparate energy surfaces and bonded terms, especially in multi-scale molecular mechanics/quantum mechanics simulations. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Blind prediction of distribution in the SAMPL5 challenge with QM based protomer and pK a corrections.

The computation of distribution coefficients between polar and apolar phases requires both an accurate characterization of transfer free energies between phases and proper accounting of ionization and protomerization. We present a protocol for accurately predicting partition coefficients between two immiscible phases, and then apply it to 53 drug-like molecules in the SAMPL5 blind prediction challenge. Our results combine implicit solvent QM calculations with classical MD simulations using the non-Boltzmann Bennett free energy estimator. The OLYP/DZP/SMD method yields predictions that have a small deviation from experiment (RMSD = 2.3 [Formula: see text] D units), relative to other participants in the challenge. Our free energy corrections based on QM protomer and [Formula: see text] calculations increase the correlation between predicted and experimental distribution coefficients, for all methods used. Unfortunately, these corrections are overly hydrophilic, and fail to account for additional effects such as aggregation, water dragging and the presence of polar impurities in the apolar phase. We show that, although expensive, QM-NBB free energy calculations offer an accurate and robust method that is superior to standard MM and QM techniques alone.

Calculating distribution coefficients based on multi-scale free energy simulations: an evaluation of MM and QM/MM explicit solvent simulations of water-cyclohexane transfer in the SAMPL5 challenge.

One of the central aspects of biomolecular recognition is the hydrophobic effect, which is experimentally evaluated by measuring the distribution coefficients of compounds between polar and apolar phases. We use our predictions of the distribution coefficients between water and cyclohexane from the SAMPL5 challenge to estimate the hydrophobicity of different explicit solvent simulation techniques. Based on molecular dynamics trajectories with the CHARMM General Force Field, we compare pure molecular mechanics (MM) with quantum-mechanical (QM) calculations based on QM/MM schemes that treat the solvent at the MM level. We perform QM/MM with both density functional theory (BLYP) and semi-empirical methods (OM1, OM2, OM3, PM3). The calculations also serve to test the sensitivity of partition coefficients to solute polarizability as well as the interplay of the quantum-mechanical region with the fixed-charge molecular mechanics environment. Our results indicate that QM/MM with both BLYP and OM2 outperforms pure MM. However, this observation is limited to a subset of cases where convergence of the free energy can be achieved.

An efficient protocol for obtaining accurate hydration free energies using quantum chemistry and reweighting from molecular dynamics simulations.

The non-Boltzmann Bennett (NBB) free energy estimator method is applied to 21 molecules from the blind subset of the SAMPL4 challenge. When NBB is applied with the SMD implicit solvent model, and the OLYP/DZP level of quantum chemistry, highly accurate hydration free energy calculations are obtained with respect to experiment (RMSD=0.89kcal·mol-1). Other quantum chemical methods are also tested, and the effects of solvent model, density functional, basis set are explored in this benchmarking study, providing a framework for improvements in calculating hydration free energies. We provide a practical guide for using the best QM-NBB protocols that are consistently more accurate than either pure QM or pure MM alone. In situations where high accuracy hydration free energy predictions are needed, the QM-NBB method with SMD implicit solvent should be the first choice of quantum chemists.

Multiple environment single system quantum mechanical/molecular mechanical (MESS-QM/MM) calculations. 1. Estimation of polarization energies.

In combined quantum mechanical/molecular mechanical (QM/MM) free energy calculations, it is often advantageous to have a frozen geometry for the quantum mechanical (QM) region. For such multiple-environment single-system (MESS) cases, two schemes are proposed here for estimating the polarization energy: the first scheme, termed MESS-E, involves a Roothaan step extrapolation of the self-consistent field (SCF) energy; whereas the other scheme, termed MESS-H, employs a Newton-Raphson correction using an approximate inverse electronic Hessian of the QM region (which is constructed only once). Both schemes are extremely efficient, because the expensive Fock updates and SCF iterations in standard QM/MM calculations are completely avoided at each configuration. They produce reasonably accurate QM/MM polarization energies: MESS-E can predict the polarization energy within 0.25 kcal/mol in terms of the mean signed error for two of our test cases, solvated methanol and solvated ß-alanine, using the M06-2X or ωB97X-D functionals; MESS-H can reproduce the polarization energy within 0.2 kcal/mol for these two cases and for the oxyluciferin-luciferase complex, if the approximate inverse electronic Hessians are constructed with sufficient accuracy.

Predicting hydration free energies with a hybrid QM/MM approach: an evaluation of implicit and explicit solvation models in SAMPL4.

The correct representation of solute-water interactions is essential for the accurate simulation of most biological phenomena. Several highly accurate quantum methods are available to deal with solvation by using both implicit and explicit solvents. So far, however, most evaluations of those methods were based on a single conformation, which neglects solute entropy. Here, we present the first test of a novel approach to determine hydration free energies that uses molecular mechanics (MM) to sample phase space and quantum mechanics (QM) to evaluate the potential energies. Free energies are determined by using re-weighting with the Non-Boltzmann Bennett (NBB) method. In this context, the method is referred to as QM-NBB. Based on snapshots from MM sampling and accounting for their correct Boltzmann weight, it is possible to obtain hydration free energies that incorporate the effect of solute entropy. We evaluate the performance of several QM implicit solvent models, as well as explicit solvent QM/MM for the blind subset of the SAMPL4 hydration free energy challenge. While classical free energy simulations with molecular dynamics give root mean square deviations (RMSD) of 2.8 and 2.3 kcal/mol, the hybrid approach yields an improved RMSD of 1.6 kcal/mol. By selecting an appropriate functional and basis set, the RMSD can be reduced to 1 kcal/mol for calculations based on a single conformation. Results for a selected set of challenging molecules imply that this RMSD can be further reduced by using NBB to reweight MM trajectories with the SMD implicit solvent model.

Absolute hydration free energies of blocked amino acids: implications for protein solvation and stability.

Most proteins perform their function in aqueous solution. The interactions with water determine the stability of proteins and the desolvation costs of ligand binding or membrane insertion. However, because of experimental restrictions, absolute solvation free energies of proteins or amino acids are not available. Instead, solvation free energies are estimated based on side chain analog data. This approach implies that the contributions to free energy differences are additive, and it has often been employed for estimating folding or binding free energies. However, it is not clear how much the additivity assumption affects the reliability of the resulting data. Here, we use molecular dynamics-based free energy simulations to calculate absolute hydration free energies for 15 N-acetyl-methylamide amino acids with neutral side chains. By comparing our results with solvation free energies for side chain analogs, we demonstrate that estimates of solvation free energies of full amino acids based on group-additive methods are systematically too negative and completely overestimate the hydrophobicity of glycine. The largest deviation of additive protocols using side chain analog data was 6.7 kcal/mol; on average, the deviation was 4 kcal/mol. We briefly discuss a simple way to alleviate the errors incurred by using side chain analog data and point out the implications of our findings for the field of biophysics and implicit solvent models. To support our results and conclusions, we calculate relative protein stabilities for selected point mutations, yielding a root-mean-square deviation from experimental results of 0.8 kcal/mol.

Investigation of the Impact of Saccharides on the Relative Activity of Trypsin and Catalase after Droplet and Spray Drying.

While using saccharides as stabilizers for therapeutic protein drying is common, the mechanisms underlying the stabilization during drying remain largely unexplored. Herein, we investigated the effect of different saccharides, trehalose dihydrate (TD), dextran (DEX), and hydroxypropyl ß-cyclodextrins (low substitution-HP and high substitution-HPB), on the relative activities of the enzymes trypsin and catalase during miniaturized drying (MD) or spray drying (SD). For trypsin, the presence of saccharides, especially HP, was beneficial, as it significantly improved the enzyme activity following MD. The HPB preserved trypsin's activity during MD and SD. Adding saccharides during MD did not show a notable improvement in catalase activities. Increasing TD was beneficial during the SD of catalase, as indicated by significantly increased activity. Molecular docking and molecular dynamics simulations oftrypsin with HP or HPB revealed the influence of their substitution on the binding affinity for the enzyme. A higher affinity of HP to bind trypsin and itself was observed during simulations. Experimentally, activity reduction was mainly observed during MD, attributable to the higher droplet temperature during MD than during SD. The activities from the experiments and aggregation propensity from molecular modeling helped elucidate the impact of the size of protein and saccharides on preserving the activity during drying.

Concentration-Dependent Inhibition of Mesophilic PETases on Poly(ethylene terephthalate) Can Be Eliminated by Enzyme Engineering.

Enzyme-based depolymerization is a viable approach for recycling of poly(ethylene terephthalate) (PET). PETase from Ideonella sakaiensis (IsPETase) is capable of PET hydrolysis under mild conditions but suffers from concentration-dependent inhibition. In this study, this inhibition is found to be dependent on incubation time, the solution conditions, and PET surface area. Furthermore, this inhibition is evident in other mesophilic PET-degrading enzymes to varying degrees, independent of the level of PET depolymerization activity. The inhibition has no clear structural basis, but moderately thermostable IsPETase variants exhibit reduced inhibition, and the property is completely absent in the highly thermostable HotPETase, previously engineered by directed evolution, which simulations suggest results from reduced flexibility around the active site. This work highlights a limitation in applying natural mesophilic hydrolases for PET hydrolysis and reveals an unexpected positive outcome of engineering these enzymes for enhanced thermostability.

Predicting binding affinities of host-guest systems in the SAMPL3 blind challenge: the performance of relative free energy calculations.

Relative free energy calculations based on molecular dynamics simulations are combined with available experimental binding free energies to predict unknown binding affinities of acyclic Cucurbituril complexes in the blind SAMPL3 competition. The predictions yield root mean square errors between 2.6 and 3.2 kcal/mol for seven host-guest systems. Those deviations are comparable to results for solvation free energies of small organic molecules. However, the standard deviations found in our simulations range from 0.4 to 2.4 kcal/mol, which indicates the need for better sampling. Three different approaches are compared. Bennett's Acceptance Ratio Method and thermodynamic integration based on the trapezoidal rule with 12 λ-points exhibit a root mean square error of 2.6 kcal/mol, while thermodynamic integration with Simpson's rule and 11 λ-points leads to a root mean square error of 3.2 kcal/mol. In terms of absolute median errors, Bennett's Acceptance Ratio Method performs better than thermodynamic integration with the trapezoidal rule (1.7 vs. 2.9 kcal/mol). Simulations of the deprotonated forms of the guest molecules exhibit a poorer correspondence to experimental results with a root mean square error of 5.2 kcal/mol. In addition, a decrease of the buffer concentration by approximately 20 mM in the simulations raises the root mean square error to 3.8 kcal/mol.

Computing eigenvectors of block tridiagonal matrices based on twisted block factorizations.

New methods for computing eigenvectors of symmetric block tridiagonal matrices based on twisted block factorizations are explored. The relation of the block where two twisted factorizations meet to an eigenvector of the block tridiagonal matrix is reviewed. Based on this, several new algorithmic strategies for computing the eigenvector efficiently are motivated and designed. The underlying idea is to determine a good starting vector for an inverse iteration process from the twisted block factorizations such that a good eigenvector approximation can be computed with a single step of inverse iteration. An implementation of the new algorithms is presented and experimental data for runtime behaviour and numerical accuracy based on a wide range of test cases are summarized. Compared with competing state-of-the-art tridiagonalization-based methods, the algorithms proposed here show strong reductions in runtime, especially for very large matrices and/or small bandwidths. The residuals of the computed eigenvectors are in general comparable with state-of-the-art methods. In some cases, especially for strongly clustered eigenvalues, a loss in orthogonality of some eigenvectors is observed. This is not surprising, and future work will focus on investigating ways for improving these cases.