A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

Structures of ferroportin in complex with its specific inhibitor vamifeport

A central regulatory mechanism of iron homeostasis in humans involves ferroportin (FPN), the sole cellular iron exporter, and the peptide hormone hepcidin, which inhibits Fe²⁺ transport and induces internalization and degradation of FPN. Dysregulation of the FPN/hepcidin axis leads to diverse pathological conditions, and consequently, pharmacological compounds that inhibit FPN-mediated iron transport are of high clinical interest. Here, we describe the cryo-electron microscopy structures of human FPN in complex with synthetic nanobodies and vamifeport (VIT-2763), the first clinical-stage oral FPN inhibitor. Vamifeport competes with hepcidin for FPN binding and is currently in clinical development for β-thalassemia and sickle cell disease. The structures display two distinct conformations of FPN, representing outward-facing and occluded states of the transporter. The vamifeport site is located in the center of the protein, where the overlap with hepcidin interactions underlies the competitive relationship between the two molecules. The introduction of point mutations in the binding pocket of vamifeport reduces its affinity to FPN, emphasizing the relevance of the structural data. Together, our study reveals conformational rearrangements of FPN that are of potential relevance for transport, and it provides initial insight into the pharmacological targeting of this unique iron efflux transporter.

Antibody binding modulates the dynamics of the membrane-bound prion protein

Misfolding of the cellular prion protein (PrP^C) is associated with lethal neurodegeneration. PrP^C consists of a flexible tail (residues 23-123) and a globular domain (residues 124-231) whose C-terminal end is anchored to the cell membrane. The neurotoxic antibody POM1 and the innocuous antibody POM6 recognize the globular domain. Experimental evidence indicates that POM1 binding to PrP^C emulates the influence on PrP^C of the misfolded prion protein (PrP^Sc) while the binding of POM6 has the opposite biological response. Little is known about the potential interactions between flexible tail, globular domain, and the membrane. Here, we used atomistic simulations to investigate how these interactions are modulated by the binding of the Fab fragments of POM1 and POM6 to PrP^C and by interstitial sequence truncations to the flexible tail. The simulations show that the binding of the antibodies restricts the range of orientations of the globular domain with respect to the membrane and decreases the distance between tail and membrane. Five of the six sequence truncations influence only marginally this distance and the contact patterns between tail and globular domain. The only exception is a truncation coupled to a charge inversion mutation of four N-terminal residues, which increases the distance of the flexible tail from the membrane. The interactions of the flexible tail and globular domain are modulated differently by the two antibodies.

Competing interactions give rise to two-state behavior and switch-like transitions in charge-rich intrinsically disordered proteins

The most commonly occurring intrinsically disordered proteins (IDPs) are polyampholytes, which are defined by the duality of low net charge per residue and high fractions of charged residues. Recent experiments have uncovered nuances regarding sequence–ensemble relationships of model polyampholytic IDPs. These include differences in conformational preferences for sequences with lysine vs. arginine and the suggestion that well-mixed sequences form a range of conformations, including globules, conformations with ensemble averages that are reminiscent of ideal chains, or self-avoiding walks. Here, we explain these observations by analyzing results from atomistic simulations. We find that polyampholytic IDPs generally sample two distinct stable states, namely, globules and self-avoiding walks. Globules are favored by electrostatic attractions between oppositely charged residues, whereas self-avoiding walks are favored by favorable free energies of hydration of charged residues. We find sequence-specific temperatures of bistability at which globules and self-avoiding walks can coexist. At these temperatures, ensemble averages over coexisting states give rise to statistics that resemble ideal chains without there being an actual counterbalancing of intrachain and chain-solvent interactions. At equivalent temperatures, arginine-rich sequences tilt the preference toward globular conformations whereas lysine-rich sequences tilt the preference toward self-avoiding walks. We also identify differences between aspartate- and glutamate-containing sequences, whereby the shorter aspartate side chain engenders preferences for metastable, necklace-like conformations. Finally, although segregation of oppositely charged residues within the linear sequence maintains the overall two-state behavior, compact states are highly favored by such systems.

Dynamics of the Histone Acetyltransferase Lysine-Rich Loop in the Catalytic Core of the CREB-Binding Protein

The tight control of transcriptional coactivators is a fundamental aspect of gene expression in cells. The regulation of the CREB-binding protein (CBP) and p300 coactivators, two paralog multidomain proteins, involves an autoinhibitory loop (AIL) of the histone acetyltransferase (HAT) domain. There is experimental evidence for the AIL engaging with the HAT binding site, thus interrupting the acetylation of histone tails or other proteins. Both CBP and p300 contain a domain of about 110 residues (called the bromodomain) that recognizes histone tails with one or more acetylated lysine side chains. Here, we investigate by molecular dynamics simulations whether the AIL of CBP (residues 1556-1618) acetylated at the side chain of Lys1595 can bind to the bromodomain. The structural instability and fast unbinding kinetics of the AIL from the bromodomain pocket suggest that the AIL is not a ligand of the bromodomain on the same protein chain. This is further supported by the absence of strong and persistent contacts at the binding interface. Furthermore, the simulations of unbinding show an initial fast detachment of the acetylated lysine and a slower phase necessary for complete AIL dissociation. We provide further evidence for the instability of the AIL intramolecular binding by comparison with a natural ligand, the histone peptide H3K56ac, which shows higher stability in the pocket.

An ABSINTH-Based Protocol for Predicting Binding Affinities between Proteins and Small Molecules

The core task in computational drug discovery is to accurately predict binding free energies in receptor-ligand systems for large libraries of putative binders. Here, the ABSINTH implicit solvent model and force field are extended to describe small, organic molecules and their interactions with proteins. We show that an automatic pipeline based on partitioning arbitrary molecules into substructures corresponding to model compounds with known free energies of solvation can be combined with the CHARMM general force field into a method that is successful at the two important challenges a scoring function faces in virtual screening work flows: it ranks known binders with correlation values rivaling that of comparable state-of-the-art methods and it enriches true binders in a set of decoys. Our protocol introduces innovative modifications to common virtual screening workflows, notably the use of explicit ions as competitors and the integration over multiple protein and ligand species differing in their protonation states. We demonstrate the value of modifications to both the protocol and ABSINTH itself. We conclude by discussing the limitations of high-throughput implicit methods such as the one proposed here.

High-performance transformation of protein structure representation from internal to Cartesian coordinates

We present a highly parallel algorithm to convert internal coordinates of a polymeric molecule into Cartesian coordinates. Traditionally, converting the structures of polymers (e.g., proteins) from internal to Cartesian coordinates has been performed serially, due to an inherent linear dependency along the polymer chain. We show this dependency can be removed using a tree-based concatenation of coordinate transforms between segments, and then parallelized efficiently on graphics processing units (GPUs). The conversion algorithm is applicable to protein engineering and fitting protein structures to experimental data, and we observe an order of magnitude speedup using parallel processing on a GPU compared to serial execution on a CPU.

Information theoretic measures for quantifying sequence-ensemble relationships of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) contribute to a multitude of functions. De novo design of IDPs should open the door to modulating functions and phenotypes controlled by these systems. Recent design efforts have focused on compositional biases and specific sequence patterns as the design features. Analysis of the impact of these designs on sequence-function relationships indicates that individual sequence/compositional parameters are insufficient for describing sequence-function relationships in IDPs. To remedy this problem, we have developed information theoretic measures for sequence–ensemble relationships (SERs) of IDPs. These measures rely on prior availability of statistically robust conformational ensembles derived from all atom simulations. We show that the measures we have developed are useful for comparing sequence-ensemble relationships even when sequence is poorly conserved. Based on our results, we propose that de novo designs of IDPs, guided by knowledge of their SERs, should provide improved insights into their sequence–ensemble–function relationships.

Model reduction of rigid-body molecular dynamics via generalized multipole potentials

Motivated by the challenges of uncertainty quantification for coarse-grained (CG) molecular dynamics, we investigate the role of perturbation theory in model reduction of classical systems. In particular, we consider the task of coarse-graining rigid bodies in the context of generalized multipole potentials that have controllable levels of accuracy relative to their atomistic counterparts. We show how the multipole framework yields a hierarchy of models that systematically connects a CG "point molecule" approximation to the exact dynamics. We use these results to understand when and how the CG models fail to describe atomistic dynamics at the trajectory level and develop asymptotic error estimates for approximate molecular potential energies. Implications for other model-reduction strategies are also discussed. Key findings of this work are that (i) omitting rotational energy introduces significant error when coarse-graining and (ii) attention to symmetry can improve accuracy of "point-molecule" approximations. Analytical derivations and numerical results support these conclusions. Relevance to nonrigid bodies is also discussed.

q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides

The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.

On the removal of initial state bias from simulation data

Classical atomistic simulations of biomolecules play an increasingly important role in molecular life science. The structure of current computing architectures favors methods that run multiple trajectories at once without requiring extensive communication between them. Many advanced sampling strategies in the field fit this mold. These approaches often rely on an adaptive logic and create ensembles of comparatively short trajectories whose starting points are not distributed according to the correct Boltzmann weights. This type of bias is notoriously difficult to remove, and Markov state models (MSMs) are one of the few strategies available for recovering the correct kinetics and thermodynamics from these ensembles of trajectories. In this contribution, we analyze the performance of MSMs in the thermodynamic reweighting task for a hierarchical set of systems. We show that MSMs can be rigorous tools to recover the correct equilibrium distribution for systems of sufficiently low dimensionality. This is conditional upon not tampering with local flux imbalances found in the data. For a real-world application, we find that a pure likelihood-based inference of the transition matrix produces the best results. The removal of the bias is incomplete, however, and for this system, all tested MSMs are outperformed by an alternative albeit less general approach rooted in the ideas of statistical resampling. We conclude by formulating some recommendations for how to address the reweighting issue in practice.

Improvements to the ABSINTH Force Field for Proteins Based on Experimentally Derived Amino Acid Specific Backbone Conformational Statistics

We present an improved version of the ABSINTH implicit solvation model and force field paradigm (termed ABSINTH-C) by incorporating a grid-based term that bootstraps against experimentally derived and computationally optimized conformational statistics for blocked amino acids. These statistics provide high-resolution descriptions of the intrinsic backbone dihedral angle preferences for all 20 amino acids. The original ABSINTH model generates Ramachandran plots that are too shallow in terms of the basin structures and too permissive in terms of dihedral angle preferences. We bootstrap against the reference optimized landscapes and incorporate CMAP-like residue-specific terms that help us reproduce the intrinsic dihedral angle preferences of individual amino acids. These corrections that lead to ABSINTH-C are achieved by balancing the incorporation of the new residue-specific terms with the accuracies inherent to the original ABSINTH model. We demonstrate the robustness of ABSINTH-C through a series of examples to highlight the preservation of accuracies as well as examples that demonstrate the improvements. Our efforts show how the recent experimentally derived and computationally optimized coil-library landscapes can be used as a touchstone for quantifying errors and making improvements to molecular mechanics force fields.

Disulfide bridge formation influences ligand recognition by the ATAD2 bromodomain

The ATPase family, AAA domain-containing protein 2 (ATAD2) has a C-terminal bromodomain, which functions as a chromatin reader domain recognizing acetylated lysine on the histone tails within the nucleosome. ATAD2 is overexpressed in many cancers and its expression is correlated with poor patient outcomes, making it an attractive therapeutic target and potential biomarker. We solved the crystal structure of the ATAD2 bromodomain and found that it contains a disulfide bridge near the base of the acetyllysine binding pocket (Cys1057-Cys1079). Site-directed mutagenesis revealed that removal of a free C-terminal cysteine (C1101) residue greatly improved the solubility of the ATAD2 bromodomain in vitro. Isothermal titration calorimetry experiments in combination with the Ellman's assay demonstrated that formation of an intramolecular disulfide bridge negatively impacts the ligand binding affinities and alters the thermodynamic parameters of the ATAD2 bromodomain interaction with a histone H4K5ac peptide as well as a small molecule bromodomain ligand. Molecular dynamics simulations indicate that the formation of the disulfide bridge in the ATAD2 bromodomain does not alter the structure of the folded state or flexibility of the acetyllysine binding pocket. However, consideration of this unique structural feature should be taken into account when examining ligand-binding affinity, or in the design of new bromodomain inhibitor compounds that interact with this acetyllysine reader module.

Focused conformational sampling in proteins

A detailed understanding of the conformational dynamics of biological molecules is difficult to obtain by experimental techniques due to resolution limitations in both time and space. Computer simulations avoid these in theory but are often too short to sample rare events reliably. Here we show that the progress index-guided sampling (PIGS) protocol can be used to enhance the sampling of rare events in selected parts of biomolecules without perturbing the remainder of the system. The method is very easy to use as it only requires as essential input a set of several features representing the parts of interest sufficiently. In this feature space, new states are discovered by spontaneous fluctuations alone and in unsupervised fashion. Because there are no energetic biases acting on phase space variables or projections thereof, the trajectories PIGS generates can be analyzed directly in the framework of transition networks. We demonstrate the possibility and usefulness of such focused explorations of biomolecules with two loops that are part of the binding sites of bromodomains, a family of epigenetic "reader" modules. This real-life application uncovers states that are structurally and kinetically far away from the initial crystallographic structures and are also metastable. Representative conformations are intended to be used in future high-throughput virtual screening campaigns.

Precise estimation of transfer free energies for ionic species between similar media

Two-dimensional umbrella sampling is combined with molecular dynamics to calculate correction-free estimates of transfer properties for individual ions.

Hamiltonian Monte Carlo with Constrained Molecular Dynamics as Gibbs Sampling

Compared to fully flexible molecular dynamics, simulations of constrained systems can use larger time steps and focus kinetic energy on soft degrees of freedom. Achieving ergodic sampling from the Boltzmann distribution, however, has proven challenging. Using recent generalizations of the equipartition principle and Fixman potential, here we implement Hamiltonian Monte Carlo based on constrained molecular dynamics as a Gibbs sampling move. By mixing Hamiltonian Monte Carlo based on fully flexible and torsional dynamics, we are able to reproduce free energy landscapes of simple model systems and enhance sampling of macrocycles.

Dynamic microfluidic control of supramolecular peptide self-assembly

The dynamic nature of supramolecular polymers has a key role in their organization. Yet, the manipulation of their dimensions and polarity remains a challenge. Here, the minimalistic diphenylalanine building block was applied to demonstrate control of nano-assemblies growth and shrinkage using microfluidics. To fine-tune differential local environments, peptide nanotubes were confined by micron-scale pillars and subjected to monomer flows of various saturation levels to control assembly and disassembly. The small-volume device allows the rapid adjustment of conditions within the system. A simplified kinetic model was applied to calculate parameters of the growth mechanism. Direct real-time microscopy analysis revealed that different peptide derivatives show unidirectional or bidirectional axial dimension variation. Atomistic simulations show that unidirectional growth is dictated by the differences in the axial ends, as observed in the crystalline order of symmetry. This work lays foundations for the rational control of nano-materials dimensions for applications in biomedicine and material science.

The organization of supramolecular peptide polymers determines their properties; however, controlling their dimensions still remains a problem. Here, Gazit et al. show the spontaneous elongation and shortening of these polymers at an individual nano-assembly level by using a microfluidic platform.