Good Rates From Bad Coordinates: The Exponential Average Time-dependent Rate Approach.

Our ability to calculate rate constants of biochemical processes using molecular dynamics simulations is severely limited by the fact that the time scales for reactions, or changes in conformational state, scale exponentially with the relevant free-energy barrier heights. In this work, we improve upon a recently proposed rate estimator that allows us to predict transition times with molecular dynamics simulations biased to rapidly explore one or several collective variables (CVs). This approach relies on the idea that not all bias goes into promoting transitions, and along with the rate, it estimates a concomitant scale factor for the bias termed the "CV biasing efficiency" γ. First, we demonstrate mathematically that our new formulation allows us to derive the commonly used Infrequent Metadynamics (iMetaD) estimator when using a perfect CV, where γ = 1. After testing it on a model potential, we then study the unfolding behavior of a previously well characterized coarse-grained protein, which is sufficiently complex that we can choose many different CVs to bias, but which is sufficiently simple that we are able to compute the unbiased rate directly. For this system, we demonstrate that predictions from our new Exponential Average Time-Dependent Rate (EATR) estimator converge to the true rate constant more rapidly as a function of bias deposition time than does the previous iMetaD approach, even for bias deposition times that are short. We also show that the γ parameter can serve as a good metric for assessing the quality of the biasing coordinate. We demonstrate that these results hold when applying the methods to an atomistic protein folding example. Finally, we demonstrate that our approach works when combining multiple less-than-optimal bias coordinates, and adapt our method to the related "OPES flooding" approach. Overall, our time-dependent rate approach offers a powerful framework for predicting rate constants from biased simulations.

Microscopic theory, analysis, and interpretation of conductance histograms in molecular junctions.

Molecular electronics break-junction experiments are widely used to investigate fundamental physics and chemistry at the nanoscale. Reproducibility in these experiments relies on measuring conductance on thousands of freshly formed molecular junctions, yielding a broad histogram of conductance events. Experiments typically focus on the most probable conductance, while the information content of the conductance histogram has remained unclear. Here we develop a microscopic theory for the conductance histogram by merging the theory of force-spectroscopy with molecular conductance. The procedure yields analytical equations that accurately fit the conductance histogram of a wide range of molecular junctions and augments the information content that can be extracted from them. Our formulation captures contributions to the conductance dispersion due to conductance changes during the mechanical elongation inherent to the experiments. In turn, the histogram shape is determined by the non-equilibrium stochastic features of junction rupture and formation. The microscopic parameters in the theory capture the junction's electromechanical properties and can be isolated from separate conductance and rupture force (or junction-lifetime) measurements. The predicted behavior can be used to test the range of validity of the theory, understand the conductance histograms, design molecular junction experiments with enhanced resolution and molecular devices with more reproducible conductance properties.

Ensemble Reweighting Using Cryo-EM Particle Images.

Cryo-electron microscopy (cryo-EM) has recently become a leading method for obtaining high-resolution structures of biological macromolecules. However, cryo-EM is limited to biomolecular samples with low conformational heterogeneity, where most conformations can be well-sampled at various projection angles. While cryo-EM provides single-molecule data for heterogeneous molecules, most existing reconstruction tools cannot retrieve the ensemble distribution of possible molecular conformations from these data. To overcome these limitations, we build on a previous Bayesian approach and develop an ensemble refinement framework that estimates the ensemble density from a set of cryo-EM particle images by reweighting a prior conformational ensemble, e.g., from molecular dynamics simulations or structure prediction tools. Our work provides a general approach to recovering the equilibrium probability density of the biomolecule directly in conformational space from single-molecule data. To validate the framework, we study the extraction of state populations and free energies for a simple toy model and from synthetic cryo-EM particle images of a simulated protein that explores multiple folded and unfolded conformations.

Conformational heterogeneity and probability distributions from single-particle cryo-electron microscopy.

Single-particle cryo-electron microscopy (cryo-EM) is a technique that takes projection images of biomolecules frozen at cryogenic temperatures. A major advantage of this technique is its ability to image single biomolecules in heterogeneous conformations. While this poses a challenge for data analysis, recent algorithmic advances have enabled the recovery of heterogeneous conformations from the noisy imaging data. Here, we review methods for the reconstruction and heterogeneity analysis of cryo-EM images, ranging from linear-transformation-based methods to nonlinear deep generative models. We overview the dimensionality-reduction techniques used in heterogeneous 3D reconstruction methods and specify what information each method can infer from the data. Then, we review the methods that use cryo-EM images to estimate probability distributions over conformations in reduced subspaces or predefined by atomistic simulations. We conclude with the ongoing challenges for the cryo-EM community.

Connection between MHC class II binding and aggregation propensity: The antigenic peptide 10 of Paracoccidioides brasiliensis as a benchmark study.

The aggregation of epitopes that are also able to bind major histocompatibility complex (MHC) alleles raises questions around the potential connection between the formation of epitope aggregates and their affinities to MHC receptors. We first performed a general bioinformatic assessment over a public dataset of MHC class II epitopes, finding that higher experimental binding correlates with higher aggregation-propensity predictors. We then focused on the case of P10, an epitope used as a vaccine candidate against Paracoccidioides brasiliensis that aggregates into amyloid fibrils. We used a computational protocol to design variants of the P10 epitope to study the connection between the binding stabilities towards human MHC class II alleles and their aggregation propensities. The binding of the designed variants was tested experimentally, as well as their aggregation capacity. High-affinity MHC class II binders in vitro were more disposed to aggregate forming amyloid fibrils capable of binding Thioflavin T and congo red, while low affinity MHC class II binders remained soluble or formed rare amorphous aggregates. This study shows a possible connection between the aggregation propensity of an epitope and its affinity for the MHC class II cleft.

Omicron mutations increase interdomain interactions and reduce epitope exposure in the SARS-CoV-2 spike.

Omicron BA.1 is a highly infectious variant of SARS-CoV-2 that carries more than thirty mutations on the spike protein in comparison to the Wuhan wild type (WT). Some of the Omicron mutations, located on the receptor-binding domain (RBD), are exposed to the surrounding solvent and are known to help evade immunity. However, the impact of buried mutations on the RBD conformations and on the mechanics of the spike opening is less evident. Here, we use all-atom molecular dynamics (MD) simulations with metadynamics to characterize the thermodynamic RBD-opening ensemble, identifying significant differences between WT and Omicron. Specifically, the Omicron mutations S371L, S373P, and S375F make more RBD interdomain contacts during the spike's opening. Moreover, Omicron takes longer to reach the transition state than WT. It stabilizes up-state conformations with fewer RBD epitopes exposed to the solvent, potentially favoring immune or antibody evasion.

Protocol for iterative optimization of modified peptides bound to protein targets.

Peptides are commonly used as therapeutic agents. However, they suffer from easy degradation and instability. Replacing natural by non-natural amino acids can avoid these problems, and potentially improve the affinity towards the target protein. Here, we present a computational pipeline to optimize peptides based on adding non-natural amino acids while improving their binding affinity. The workflow is an iterative computational evolution algorithm, inspired by the PARCE protocol, that performs single-point mutations on the peptide sequence using modules from the Rosetta framework. The modifications can be guided based on the structural properties or previous knowledge of the biological system. At each mutation step, the affinity to the protein is estimated by sampling the complex conformations and applying a consensus metric using various open protein-ligand scoring functions. The mutations are accepted based on the score differences, allowing for an iterative optimization of the initial peptide. The sampling/scoring scheme was benchmarked with a set of protein-peptide complexes where experimental affinity values have been reported. In addition, a basic application using a known protein-peptide complex is also provided. The structure- and dynamic-based approach allows users to optimize bound peptides, with the option to personalize the code for further applications. The protocol, called mPARCE, is available at: https://github.com/rochoa85/mPARCE/ .

Transition Rates and Efficiency of Collective Variables from Time-Dependent Biased Simulations.

Simulations with adaptive time-dependent bias enable an efficient exploration of the conformational space of a system. However, the dynamic information is altered by the bias. Infrequent metadynamics recovers the transition rate of crossing a barrier, if the collective variables are ideal and there is no bias deposition near the transition state. Unfortunately, these conditions are not always fulfilled. To overcome these limitations, and inspired by single-molecule force spectroscopy, we use Kramers' theory for calculating the barrier-crossing rate when a time-dependent bias is added to the system. We assess the efficiency of collective variables parameter by measuring how efficiently the bias accelerates the transitions. We present approximate analytical expressions of the survival probability, reproducing the barrier-crossing time statistics and enabling the extraction of the unbiased transition rate even for challenging cases. We explore the limits of our method and provide convergence criteria to assess its validity.

Multiple-Allele MHC Class II Epitope Engineering by a Molecular Dynamics-Based Evolution Protocol.

Epitopes that bind simultaneously to all human alleles of Major Histocompatibility Complex class II (MHC II) are considered one of the key factors for the development of improved vaccines and cancer immunotherapies. To engineer MHC II multiple-allele binders, we developed a protocol called PanMHC-PARCE, based on the unsupervised optimization of the epitope sequence by single-point mutations, parallel explicit-solvent molecular dynamics simulations and scoring of the MHC II-epitope complexes. The key idea is accepting mutations that not only improve the affinity but also reduce the affinity gap between the alleles. We applied this methodology to enhance a Plasmodium vivax epitope for multiple-allele binding. In vitro rate-binding assays showed that four engineered peptides were able to bind with improved affinity toward multiple human MHC II alleles. Moreover, we demonstrated that mice immunized with the peptides exhibited interferon-gamma cellular immune response. Overall, the method enables the engineering of peptides with improved binding properties that can be used for the generation of new immunotherapies.

Ab initio metadynamics determination of temperature-dependent free-energy landscape in ultrasmall silver clusters.

Ab initio metadynamics enables the extraction of free-energy landscapes having the accuracy of first-principles electronic structure methods. We introduce an interface between the PLUMED code that computes free-energy landscapes and enhanced-sampling algorithms and the Atomic Simulation Environment (ASE) module, which includes several ab initio electronic structure codes. The interface is validated with a Lennard-Jones cluster free-energy landscape calculation by averaging multiple short metadynamics trajectories. We use this interface and analysis to estimate the free-energy landscape of Ag5 and Ag6 clusters at 10, 100, and 300 K with the radius of gyration and coordination number as collective variables, finding at most tens of meV in error. Relative free-energy differences between the planar and non-planar isomers of both clusters decrease with temperature in agreement with previously proposed stabilization of non-planar isomers. Interestingly, we find that Ag6 is the smallest silver cluster where entropic effects at room temperature boost the non-planar isomer probability to a competing state. The new ASE-PLUMED interface enables simulating nanosystem electronic properties under more realistic temperature-dependent conditions.

Computational Evolution Protocol for Peptide Design.

Computational peptide design is useful for therapeutics, diagnostics, and vaccine development. To select the most promising peptide candidates, the key is describing accurately the peptide-target interactions at the molecular level. We here review a computational peptide design protocol whose key feature is the use of all-atom explicit solvent molecular dynamics for describing the different peptide-target complexes explored during the optimization. We describe the milestones behind the development of this protocol, which is now implemented in an open-source code called PARCE. We provide a basic tutorial to run the code for an antibody fragment design example. Finally, we describe three additional applications of the method to design peptides for different targets, illustrating the broad scope of the proposed approach.

Cardiolipin prevents pore formation in phosphatidylglycerol bacterial membrane models.

Several antimicrobial peptides, including magainin and the human cathelicidin LL-37, act by forming pores in bacterial membranes. Bacteria such as Staphylococcus aureus modify their membrane's cardiolipin composition to resist such types of perturbations that compromise their membrane stability. Here, we used molecular dynamic simulations to quantify the role of cardiolipin on the formation of pores in simple bacterial-like membrane models composed of phosphatidylglycerol and cardiolipin mixtures. Cardiolipin modified the structure and ordering of the lipid bilayer, making it less susceptible to mechanical changes. Accordingly, the free-energy barrier for the formation of a transmembrane pore and its kinetic instability augmented by increasing the cardiolipin concentration. This is attributed to the unfavorable positioning of cardiolipin near the formed pore, due to its small polar head and bulky hydrophobic body. Overall, our study demonstrates how cardiolipin prevents membrane-pore formation and this constitutes a plausible mechanism used by bacteria to act against stress perturbations and, thereby, gain resistance to antimicrobial agents.

Application of ensemble pharmacophore-based virtual screening to the discovery of novel antimitotic tubulin inhibitors.

Tubulin is a well-validated target for herbicides, fungicides, anti-parasitic, and anti-tumor drugs. Many of the non-cancer tubulin drugs bind to its colchicine site but no colchicine-site anticancer drug is available. The colchicine site is composed of three interconnected sub-pockets that fit their ligands and modify others' preference, making the design of molecular hybrids (that bind to more than one sub-pocket) a difficult task. Taking advantage of the more than eighty published X-ray structures of tubulin in complex with ligands bound to the colchicine site, we generated an ensemble of pharmacophore representations that flexibly sample the interactional space between the ligands and target. We searched the ZINC database for scaffolds able to fit several of the subpockets, such as tetrazoles, sulfonamides and diarylmethanes, selected roughly ~8000 compounds with favorable predicted properties. A Flexi-pharma virtual screening, based on ensemble pharmacophore, was performed by two different methodologies. Combining the scaffolds that best fit the ensemble pharmacophore-representation, we designed a new family of ligands, resulting in a novel tubulin modulator. We synthesized tetrazole 5 and tested it as a tubulin inhibitor in vitro. In good agreement with the design principles, it demonstrated micromolar activity against in vitro tubulin polymerization and nanomolar anti-proliferative effect against human epithelioid carcinoma HeLa cells through microtubule disruption, as shown by immunofluorescence confocal microscopy. The integrative methodology succedes in the design of new scaffolds for flexible proteins with structural coupling between pockets, thus expanding the way in which computational methods can be used as significant tools in the drug design process.

A Bayesian approach to extracting free-energy profiles from cryo-electron microscopy experiments.

Cryo-electron microscopy (cryo-EM) extracts single-particle density projections of individual biomolecules. Although cryo-EM is widely used for 3D reconstruction, due to its single-particle nature it has the potential to provide information about a biomolecule's conformational variability and underlying free-energy landscape. However, treating cryo-EM as a single-molecule technique is challenging because of the low signal-to-noise ratio (SNR) in individual particles. In this work, we propose the cryo-BIFE method (cryo-EM Bayesian Inference of Free-Energy profiles), which uses a path collective variable to extract free-energy profiles and their uncertainties from cryo-EM images. We test the framework on several synthetic systems where the imaging parameters and conditions were controlled. We found that for realistic cryo-EM environments and relevant biomolecular systems, it is possible to recover the underlying free energy, with the pose accuracy and SNR as crucial determinants. We then use the method to study the conformational transitions of a calcium-activated channel with real cryo-EM particles. Interestingly, we recover not only the most probable conformation (used to generate a high-resolution reconstruction of the calcium-bound state) but also a metastable state that corresponds to the calcium-unbound conformation. As expected for turnover transitions within the same sample, the activation barriers are on the order of [Formula: see text]. We expect our tool for extracting free-energy profiles from cryo-EM images to enable more complete characterization of the thermodynamic ensemble of biomolecules.

Impact of Structural Observables From Simulations to Predict the Effect of Single-Point Mutations in MHC Class II Peptide Binders.

The prediction of peptide binders to Major Histocompatibility Complex (MHC) class II receptors is of great interest to study autoimmune diseases and for vaccine development. Most approaches predict the affinities using sequence-based models trained on experimental data and multiple alignments from known peptide substrates. However, detecting activity differences caused by single-point mutations is a challenging task. In this work, we used interactions calculated from simulations to build scoring matrices for quickly estimating binding differences by single-point mutations. We modelled a set of 837 peptides bound to an MHC class II allele, and optimized the sampling of the conformations using the Rosetta backrub method by comparing the results to molecular dynamics simulations. From the dynamic trajectories of each complex, we averaged and compared structural observables for each amino acid at each position of the 9°mer peptide core region. With this information, we generated the scoring-matrices to predict the sign of the binding differences. We then compared the performance of the best scoring-matrix to different computational methodologies that range in computational costs. Overall, the prediction of the activity differences caused by single mutated peptides was lower than 60% for all the methods. However, the developed scoring-matrix in combination with existing methods reports an increase in the performance, up to 86% with a scoring method that uses molecular dynamics.

PepFun: Open Source Protocols for Peptide-Related Computational Analysis.

Peptide research has increased during the last years due to their applications as biomarkers, therapeutic alternatives or as antigenic sub-units in vaccines. The implementation of computational resources have facilitated the identification of novel sequences, the prediction of properties, and the modelling of structures. However, there is still a lack of open source protocols that enable their straightforward analysis. Here, we present PepFun, a compilation of bioinformatics and cheminformatics functionalities that are easy to implement and customize for studying peptides at different levels: sequence, structure and their interactions with proteins. PepFun enables calculating multiple characteristics for massive sets of peptide sequences, and obtaining different structural observables derived from protein-peptide complexes. In addition, random or guided library design of peptide sequences can be customized for screening campaigns. The package has been created under the python language based on built-in functions and methods available in the open source projects BioPython and RDKit. We present two tutorials where we tested peptide binders of the MHC class II and the Granzyme B protease.

An automated protocol for modelling peptide substrates to proteases.

BACKGROUND: Proteases are key drivers in many biological processes, in part due to their specificity towards their substrates. However, depending on the family and molecular function, they can also display substrate promiscuity which can also be essential. Databases compiling specificity matrices derived from experimental assays have provided valuable insights into protease substrate recognition. Despite this, there are still gaps in our knowledge of the structural determinants. Here, we compile a set of protease crystal structures with bound peptide-like ligands to create a protocol for modelling substrates bound to protease structures, and for studying observables associated to the binding recognition. RESULTS: As an application, we modelled a subset of protease-peptide complexes for which experimental cleavage data are available to compare with informational entropies obtained from protease-specificity matrices. The modelled complexes were subjected to conformational sampling using the Backrub method in Rosetta, and multiple observables from the simulations were calculated and compared per peptide position. We found that some of the calculated structural observables, such as the relative accessible surface area and the interaction energy, can help characterize a protease's substrate recognition, giving insights for the potential prediction of novel substrates by combining additional approaches. CONCLUSION: Overall, our approach provides a repository of protease structures with annotated data, and an open source computational protocol to reproduce the modelling and dynamic analysis of the protease-peptide complexes.

Validation tests for cryo-EM maps using an independent particle set.

Cryo-electron microscopy (cryo-EM) has revolutionized structural biology by providing 3D density maps of biomolecules at near-atomic resolution. However, map validation is still an open issue. Despite several efforts from the community, it is possible to overfit 3D maps to noisy data. Here, we develop a novel methodology that uses a small independent particle set (not used during the 3D refinement) to validate the maps. The main idea is to monitor how the map probability evolves over the control set during the 3D refinement. The method is complementary to the gold-standard procedure, which generates two reconstructions at each iteration. We low-pass filter the two reconstructions for different frequency cutoffs, and we calculate the probability of each filtered map given the control set. For high-quality maps, the probability should increase as a function of the frequency cutoff and the refinement iteration. We also compute the similarity between the densities of probability distributions of the two reconstructions. As higher frequencies are included, the distributions become more dissimilar. We optimized the BioEM package to perform these calculations, and tested it over systems ranging from quality data to pure noise. Our results show that with our methodology, it possible to discriminate datasets that are constructed from noise particles. We conclude that validation against a control particle set provides a powerful tool to assess the quality of cryo-EM maps.