Dynamical Reweighting for Biased Rare Event Simulations.

Dynamical reweighting techniques aim to recover the correct molecular dynamics from a simulation at a modified potential energy surface. They are important for unbiasing enhanced sampling simulations of molecular rare events. Here, we review the theoretical frameworks of dynamical reweighting for modified potentials. Based on an overview of kinetic models with increasing level of detail, we discuss techniques to reweight two-state dynamics, multistate dynamics, and path integrals. We explore the natural link to transition path sampling and how the effect of nonequilibrium forces can be reweighted. We end by providing an outlook on how dynamical reweighting integrates with techniques for optimizing collective variables and with modern potential energy surfaces.

Thermal isomerization rates in retinal analogues using Ab-Initio molecular dynamics.

For a detailed understanding of chemical processes in nature and industry, we need accurate models of chemical reactions in complex environments. While Eyring transition state theory is commonly used for modeling chemical reactions, it is most accurate for small molecules in the gas phase. A wide range of alternative rate theories exist that can better capture reactions involving complex molecules and environmental effects. However, they require that the chemical reaction is sampled by molecular dynamics simulations. This is a formidable challenge since the accessible simulation timescales are many orders of magnitude smaller than typical timescales of chemical reactions. To overcome these limitations, rare event methods involving enhanced molecular dynamics sampling are employed. In this work, thermal isomerization of retinal is studied using tight-binding density functional theory. Results from transition state theory are compared to those obtained from enhanced sampling. Rates obtained from dynamical reweighting using infrequent metadynamics simulations were in close agreement with those from transition state theory. Meanwhile, rates obtained from application of Kramers' rate equation to a sampled free energy profile along a torsional dihedral reaction coordinate were found to be up to three orders of magnitude higher. This discrepancy raises concerns about applying rate methods to one-dimensional reaction coordinates in chemical reactions.

How Chromophore Labels Shape the Structure and Dynamics of a Peptide Hydrogel.

Biocompatible and functionalizable hydrogels have a wide range of (potential) medicinal applications. The hydrogelation process, particularly for systems with very low polymer weight percentages (<1 wt %), remains poorly understood, making it challenging to predict the self-assembly of a given molecular building block into a hydrogel. This severely hinders the rational design of self-assembled hydrogels. In this study, we demonstrate the impact of an N-terminal group on the self-assembly and rheology of the peptide hydrogel hFF03 (hydrogelating, fibril forming peptide 03) using molecular dynamics simulations, oscillatory shear rheology, and circular dichroism spectroscopy. We find that the chromophore and even its specific regioisomers have a significant influence on the microscopic structure and dynamics of the self-assembled fibril, and on the macroscopic mechanical properties. This is because the chromophore influences the possible salt bridges, which form and stabilize the fibril formation. Furthermore, we find that the solvation shell fibrils by itself cannot explain the viscoelasticity of hFF03 hydrogels. Our atomistic model of the hFF03 fibril formation enables a more rational design of these hydrogels. In particular, altering the N-terminal chromophore emerges as a design strategy to tune the mechanic properties of these self-assembled peptide hydrogels.

Prebound State Discovered in the Unbinding Pathway of Fluorinated Variants of the Trypsin-BPTI Complex Using Random Acceleration Molecular Dynamics Simulations.

The serine protease trypsin forms a tightly bound inhibitor complex with the bovine pancreatic trypsin inhibitor (BPTI). The complex is stabilized by the P1 residue Lys15, which interacts with negatively charged amino acids at the bottom of the S1 pocket. Truncating the P1 residue of wildtype BPTI to α-aminobutyric acid (Abu) leaves a complex with moderate inhibitor strength, which is held in place by additional hydrogen bonds at the protein-protein interface. Fluorination of the Abu residue partially restores the inhibitor strength. The mechanism with which fluorination can restore the inhibitor strength is unknown, and accurate computational investigation requires knowledge of the binding and unbinding pathways. The preferred unbinding pathway is likely to be complex, as encounter states have been described before, and unrestrained umbrella sampling simulations of these complexes suggest additional energetic minima. Here, we use random acceleration molecular dynamics to find a new metastable state in the unbinding pathway of Abu-BPTI variants and wildtype BPTI from trypsin, which we call the prebound state. The prebound state and the fully bound state differ by a substantial shift in the position, a slight shift in the orientation of the BPTI variants, and changes in the interaction pattern. Particularly important is the breaking of three hydrogen bonds around Arg17. Fluorination of the P1 residue lowers the energy barrier of the transition between the fully bound state and prebound state and also lowers the energy minimum of the prebound state. While the effect of fluorination is in general difficult to quantify, here, it is in part caused by favorable stabilization of a hydrogen bond between Gln194 and Cys14. The interaction pattern of the prebound state offers insights into the inhibitory mechanism of BPTI and might add valuable information for the design of serine protease inhibitors.

Impact of glycan nature on structure and viscoelastic properties of glycopeptide hydrogels.

Mucus is a complex biological hydrogel that acts as a barrier for almost everything entering or exiting the body. It is therefore of emerging interest for biomedical and pharmaceutical applications. Besides water, the most abundant components are the large and densely glycosylated mucins, glycoproteins of up to 20 MDa and carbohydrate content of up to 80 wt%. Here, we designed and explored a library of glycosylated peptides to deconstruct the complexity of mucus. Using the well-characterized hFF03 coiled-coil system as a hydrogel-forming peptide scaffold, we systematically probed the contribution of single glycans to the secondary structure as well as the formation and viscoelastic properties of the resulting hydrogels. We show that glycan-decoration does not affect α-helix and coiled-coil formation while it alters gel stiffness. By using oscillatory macrorheology, dynamic light scattering microrheology, and fluorescence lifetime-based nanorheology, we characterized the glycopeptide materials over several length scales. Molecular simulations revealed that the glycosylated linker may extend into the solvent, but more frequently interacts with the peptide, thereby likely modifying the stability of the self-assembled fibers. This systematic study highlights the interplay between glycan structure and hydrogel properties and may guide the development of synthetic mucus mimetics.

CommonNNClustering─A Python Package for Generic Common-Nearest-Neighbor Clustering.

Density-based clustering procedures are widely used in a variety of data science applications. Their advantage lies in the capability to find arbitrarily shaped and sized clusters and robustness against outliers. In particular, they proved effective in the analysis of molecular dynamics simulations, where they serve to identify relevant, low-energetic molecular conformations. As such, they can provide a convenient basis for the construction of kinetic (core-set) Markov-state models. Here we present the open-source Python project CommonNNClustering, which provides an easy-to-use and efficient reimplementation of the common-nearest-neighbor (CommonNN) method. The package provides functionalities for hierarchical clustering and an evaluation of the results. We put our emphasis on a generic API design to keep the implementation flexible and open for customization.

Optimizing molecular potential models by imposing kinetic constraints with path reweighting.

Empirical force fields employed in molecular dynamics simulations of complex systems are often optimized to reproduce experimentally determined structural and thermodynamic properties. In contrast, experimental knowledge about the interconversion rates between metastable states in such systems is hardly ever incorporated in a force field due to a lack of an efficient approach. Here, we introduce such a framework based on the relationship between dynamical observables, such as rate constants, and the underlying molecular model parameters using the statistical mechanics of trajectories. Given a prior ensemble of molecular dynamics trajectories produced with imperfect force field parameters, the approach allows for the optimal adaption of these parameters such that the imposed constraint of equally predicted and experimental rate constant is obeyed. To do so, the method combines the continuum path ensemble maximum caliber approach with path reweighting methods for stochastic dynamics. When multiple solutions are found, the method selects automatically the combination that corresponds to the smallest perturbation of the entire path ensemble, as required by the maximum entropy principle. To show the validity of the approach, we illustrate the method on simple test systems undergoing rare event dynamics. Next to simple 2D potentials, we explore particle models representing molecular isomerization reactions and protein-ligand unbinding. Besides optimal interaction parameters, the methodology gives physical insights into what parts of the model are most sensitive to the kinetics. We discuss the generality and broad implications of the methodology.

The molecular basis for the pH-dependent calcium affinity of the pattern recognition receptor langerin.

The C-type lectin receptor langerin plays a vital role in the mammalian defense against invading pathogens. Langerin requires a Ca2+ cofactor, the binding affinity of which is regulated by pH. Thus, Ca2+ is bound when langerin is on the membrane but released when langerin and its pathogen substrate traffic to the acidic endosome, allowing the substrate to be degraded. The change in pH is sensed by protonation of the allosteric pH sensor histidine H294. However, the mechanism by which Ca2+ is released from the buried binding site is not clear. We studied the structural consequences of protonating H294 by molecular dynamics simulations (total simulation time: about 120 µs) and Markov models. We discovered a relay mechanism in which a proton is moved into the vicinity of the Ca2+-binding site without transferring the initial proton from H294. Protonation of H294 unlocks a conformation in which a protonated lysine side chain forms a hydrogen bond with a Ca2+-coordinating aspartic acid. This destabilizes Ca2+ in the binding pocket, which we probed by steered molecular dynamics. After Ca2+ release, the proton is likely transferred to the aspartic acid and stabilized by a dyad with a nearby glutamic acid, triggering a conformational transition and thus preventing Ca2+ rebinding. These results show how pH regulation of a buried orthosteric binding site from a solvent-exposed allosteric pH sensor can be realized by information transfer through a specific chain of conformational arrangements.

A Formylglycine-Peptide for the Site-Directed Identification of Phosphotyrosine-Mimetic Fragments.

Discovery of protein-binding fragments for precisely defined binding sites is an unmet challenge to date. Herein, formylglycine is investigated as a molecular probe for the sensitive detection of fragments binding to a spatially defined protein site . Formylglycine peptide 3 was derived from a phosphotyrosine-containing peptide substrate of protein tyrosine phosphatase PTP1B by replacing the phosphorylated amino acid with the reactive electrophile. Fragment ligation with formylglycine occurred in situ in aqueous physiological buffer. Structures and kinetics were validated by NMR spectroscopy. Screening and hit validation revealed fluorinated and non-fluorinated hit fragments being able to replace the native phosphotyrosine residue. The formylglycine probe identified low-affinity fragments with high spatial resolution as substantiated by molecular modelling. The best fragment hit, 4-amino-phenyl-acetic acid, was converted into a cellularly active, nanomolar inhibitor of the protein tyrosine phosphatase SHP2.

Target Recognition in Tandem WW Domains: Complex Structures for Parallel and Antiparallel Ligand Orientation in h-FBP21 Tandem WW.

Protein-protein interactions often rely on specialized recognition domains, such as WW domains, which bind to specific proline-rich sequences. The specificity of these protein-protein interactions can be increased by tandem repeats, i.e., two WW domains connected by a linker. With a flexible linker, the WW domains can move freely with respect to each other. Additionally, the tandem WW domains can bind in two different orientations to their target sequences. This makes the elucidation of complex structures of tandem WW domains extremely challenging. Here, we identify and characterize two complex structures of the tandem WW domain of human formin-binding protein 21 and a peptide sequence from its natural binding partner, the core-splicing protein SmB/B'. The two structures differ in the ligand orientation and, consequently, also in the relative orientation of the two WW domains. We analyze and probe the interactions in the complexes by molecular simulations and NMR experiments. The workflow to identify the complex structures uses molecular simulations, density-based clustering, and peptide docking. It is designed to systematically generate possible complex structures for repeats of recognition domains. These structures will help us to understand the synergistic and multivalency effects that generate the astonishing versatility and specificity of protein-protein interactions.

Pentafluorophosphato-Phenylalanines: Amphiphilic Phosphotyrosine Mimetics Displaying Fluorine-Specific Protein Interactions.

Phosphotyrosine residues are essential functional switches in health and disease. Thus, phosphotyrosine biomimetics are crucial for the development of chemical tools and drug molecules. We report here the discovery and investigation of pentafluorophosphato amino acids as novel phosphotyrosine biomimetics. A mild acidic pentafluorination protocol was developed and two PF5 -amino acids were prepared and employed in peptide synthesis. Their structures, reactivities, and fluorine-specific interactions were studied by NMR and IR spectroscopy, X-ray diffraction, and in bioactivity assays. The mono-anionic PF5 motif displayed an amphiphilic character binding to hydrophobic surfaces, to water molecules, and to protein-binding sites, exploiting charge and H-F-bonding interactions. The novel motifs bind 25- to 30-fold stronger to the phosphotyrosine binding site of the protein tyrosine phosphatase PTP1B than the best current biomimetics, as rationalized by computational methods, including molecular dynamics simulations.

Iodine-Mediated Tryptathionine Formation Facilitates the Synthesis of Amanitins.

Synthetic methods on the macrocyclization of peptides are of high interest since they facilitate the synthesis of various types of potentially bioactive compounds, e.g. addressing targets like protein-protein-interactions. Herein, we report on an efficient method to construct tryptathionine-cross-links in peptides between the amino acids Trp and Cys. This reaction not only is the basis for the total synthesis of the death cap toxin α-amanitin but also provides rapid access to various new amanitin analogues. This study for the first time presents a systematic compilation of structure-activity relations (SAR) of amatoxins with regard to RNA polymerase II inhibition and cytotoxicity with one amanitin derivative of superior RNAP II inhibition. The present approach paves the way for the synthesis of structurally diverse amatoxins as future payloads for antibody-toxin conjugates in cancer therapy.

Total Synthesis of the Death Cap Toxin Phalloidin: Atropoisomer Selectivity Explained by Molecular-Dynamics Simulations.

Phallotoxins and amatoxins are a group of prominent peptide toxins produced by the death cap mushroom Amanita phalloides. Phalloidin is a bicyclic cyclopeptide with an unusual tryptathionin thioether bridge. It is a potent stabilizer of filamentous actin and in a fluorescently labeled form widely used as a probe for actin binding. Herein, we report the enantioselective synthesis of the key amino acid (2S,4R)-4,5-dihydroxy-leucine as a basis for the first total synthesis of phalloidin, which was accomplished by two different synthesis strategies. Molecular-dynamics simulations provided insights into the conformational flexibility of peptide intermediates of different reaction strategies and showed that this flexibility is critical for the formation of atropoisomers. By simulating the intermediates, rather than the final product, molecular-dynamics simulations will become a decisive tool in orchestrating the sequence of ring formation reactions of complex cyclic peptides.

Single-molecule FRET reveals the energy landscape of the full-length SAM-I riboswitch.

S-adenosyl-L-methionine (SAM) ligand binding induces major structural changes in SAM-I riboswitches, through which gene expression is regulated via transcription termination. Little is known about the conformations and motions governing the function of the full-length Bacillus subtilis yitJ SAM-I riboswitch. Therefore, we have explored its conformational energy landscape as a function of Mg2+ and SAM ligand concentrations using single-molecule Förster resonance energy transfer (smFRET) microscopy and hidden Markov modeling analysis. We resolved four conformational states both in the presence and the absence of SAM and determined their Mg2+-dependent fractional populations and conformational dynamics, including state lifetimes, interconversion rate coefficients and equilibration timescales. Riboswitches with terminator and antiterminator folds coexist, and SAM binding only gradually shifts the populations toward terminator states. We observed a pronounced acceleration of conformational transitions upon SAM binding, which may be crucial for off-switching during the brief decision window before expression of the downstream gene.

Exploring Rigid and Flexible Core Trivalent Sialosides for Influenza Virus Inhibition.

Herein, the chemical synthesis and binding analysis of functionalizable rigid and flexible core trivalent sialosides bearing oligoethylene glycol (OEG) spacers interacting with spike proteins of influenza A virus (IAV) X31 is described. Although the flexible Tris-based trivalent sialosides achieved micromolar binding constants, a trivalent binder based on a rigid adamantane core dominated flexible tripodal compounds with micromolar binding and hemagglutination inhibition constants. Simulation studies indicated increased conformational penalties for long OEG spacers. Using a systematic approach with molecular modeling and simulations as well as biophysical analysis, these findings emphasize on the importance of the scaffold rigidity and the challenges associated with the spacer length optimization.

Multiply Intercalator-Substituted Cu(II) Cyclen Complexes as DNA Condensers and DNA/RNA Synthesis Inhibitors.

Many drugs that are applied in anticancer therapy such as the anthracycline doxorubicin contain DNA-intercalating 9,10-anthraquinone (AQ) moieties. When Cu(II) cyclen complexes were functionalized with up to three (2-anthraquinonyl)methyl substituents, they efficiently inhibited DNA and RNA synthesis resulting in high cytotoxicity (selective for cancer cells) accompanied by DNA condensation/aggregation phenomena. Molecular modeling suggests an unusual bisintercalation mode with only one base pair between the two AQ moieties and the metal complex as a linker. A regioisomer, in which the AQ moieties point in directions unfavorable for such an interaction, had a much weaker biological activity. The ligands alone and corresponding Zn(II) complexes (used as redox inert control compounds) also exhibited lower activity.

Girsanov reweighting for metadynamics simulations.

Metadynamics is a computational method to explore the phase space of a molecular system. Gaussian functions are added along relevant coordinates on the fly during a molecular-dynamics simulation to force the system to escape from minima in the potential energy function. The dynamics in the resulting trajectory are however unphysical and cannot be used directly to estimate dynamical properties of the system. Girsanov reweighting is a recent method used to construct the Markov State Model (MSM) of a system subjected to an external perturbation. With the combination of these two techniques-metadynamics/Girsanov-reweighting-the unphysical dynamics in a metadynamics simulation can be reweighted to obtain the MSM of the unbiased system. We demonstrate the method on a one-dimensional diffusion process, alanine dipeptide, and the hexapeptide Val-Gly-Val-Ala-Pro-Gly (VGVAPG). The results are in excellent agreement with the MSMs obtained from direct unbiased simulations of these systems. We also apply metadynamics/Girsanov-reweighting to a ß-hairpin peptide, whose dynamics is too slow to efficiently explore its phase space by direct simulation.

Interconversion Rates between Conformational States as Rationale for the Membrane Permeability of Cyclosporines.

Cyclic peptides have regained interest as potential inhibitors of challenging targets but have often a low bioavailability. The natural product cyclosporine A (CsA) is the textbook exception. Despite its size and polar backbone, it is able to passively cross membranes. This ability is hypothesized to be due to a conformational change from the low-energy conformation in water to a "congruent" conformation that is populated both in water and inside the membrane. Here, we use a combination of NMR measurements and kinetic models based on molecular dynamics simulations to rationalize the difference in the membrane permeability of cyclosporine E (CsE) and CsA. The structure of CsE differs only in a backbone methylation, but its membrane permeability is one order of magnitude lower. The most striking difference is found in the interconversion rates between the conformational states favored in water and in chloroform, which are up to one order of magnitude slower for CsE compared to CsA.

Intradomain Allosteric Network Modulates Calcium Affinity of the C-Type Lectin Receptor Langerin.

Antigen uptake and processing by innate immune cells is crucial to initiate the immune response. Therein, the endocytic C-type lectin receptors serve as pattern recognition receptors, detecting pathogens by their glycan structures. Herein, we studied the carbohydrate recognition domain of Langerin, a C-type lectin receptor involved in the host defense against viruses such as HIV and influenza as well as bacteria and fungi. Using a combination of nuclear magnetic resonance and molecular dynamics simulations, we unraveled the molecular determinants underlying cargo capture and release encoded in the receptor architecture. Our findings revealed receptor dynamics over several time scales associated with binding and release of the essential cofactor Ca(2+) controlled by the coupled motions of two loops. Applying mutual information theory and site-directed mutagenesis, we identified an allosteric intradomain network that modulates the Ca(2+) affinity depending on the pH, thereby promoting fast ligand release.

Kinetic Models of Cyclosporin A in Polar and Apolar Environments Reveal Multiple Congruent Conformational States.

The membrane permeability of cyclic peptides and peptidomimetics, which are generally larger and more complex than typical drug molecules, is likely strongly influenced by the conformational behavior of these compounds in polar and apolar environments. The size and complexity of peptides often limit their bioavailability, but there are known examples of peptide natural products such as cyclosporin A (CsA) that can cross cell membranes by passive diffusion. CsA is an undecapeptide with seven methylated backbone amides. Its crystal structure shows a "closed" twisted ß-pleated sheet conformation with four intramolecular hydrogen bonds that is also observed in NMR measurements of CsA in chloroform. When binding to its target cyclophilin, on the other hand, CsA adopts an "open" conformation without intramolecular hydrogen bonds. In this study, we attempted to sample the complete conformational space of CsA in chloroform and in water by molecular dynamics simulations in order to better understand its conformational behavior in these two environments and to rationalize the good membrane permeability of CsA observed experimentally. From 10 µs molecular dynamics simulations in each solvent, Markov state models were constructed to characterize the metastable conformational states. The model in chloroform is compared to nuclear Overhauser effect NMR spectroscopy data reported in this study and taken from the literature. The conformational landscapes in the two solvents show significant overlap but also clearly distinct features.