Using Kinetic Network Models To Probe Non-Native Salt-Bridge Effects on α-Helix Folding

Estimation of binding rates and affinities from multiensemble Markov models and ligand decoupling

Accurate and efficient simulation of the thermodynamics and kinetics of protein-ligand interactions is crucial for computational drug discovery. Multiensemble Markov Model (MEMM) estimators can provide estimates of both binding rates and affinities from collections of short trajectories but have not been systematically explored for situations when a ligand is decoupled through scaling of non-bonded interactions. In this work, we compare the performance of two MEMM approaches for estimating ligand binding affinities and rates: (1) the transition-based reweighting analysis method (TRAM) and (2) a Maximum Caliber (MaxCal) based method. As a test system, we construct a small host-guest system where the ligand is a single uncharged Lennard-Jones (LJ) particle, and the receptor is an 11-particle icosahedral pocket made from the same atom type. To realistically mimic a protein-ligand binding system, the LJ ϵ parameter was tuned, and the system was placed in a periodic box with 860 TIP3P water molecules. A benchmark was performed using over 80 µs of unbiased simulation, and an 18-state Markov state model was used to estimate reference binding affinities and rates. We then tested the performance of TRAM and MaxCal when challenged with limited data. Both TRAM and MaxCal approaches perform better than conventional Markov state models, with TRAM showing better convergence and accuracy. We find that subsampling of trajectories to remove time correlation improves the accuracy of both TRAM and MaxCal and that in most cases, only a single biased ensemble to enhance sampled transitions is required to make accurate estimates.

Unprotected peptide macrocyclization and stapling via a fluorine-thiol displacement reaction

We report the discovery of a facile peptide macrocyclization and stapling strategy based on a fluorine thiol displacement reaction (FTDR), which renders a class of peptide analogues with enhanced stability, affinity, cellular uptake, and inhibition of cancer cells. This approach enabled selective modification of the orthogonal fluoroacetamide side chains in unprotected peptides in the presence of intrinsic cysteines. The identified benzenedimethanethiol linker greatly promoted the alpha helicity of a variety of peptide substrates, as corroborated by molecular dynamics simulations. The cellular uptake of benzenedimethanethiol stapled peptides appeared to be universally enhanced compared to the classic ring-closing metathesis (RCM) stapled peptides. Pilot mechanism studies suggested that the uptake of FTDR-stapled peptides may involve multiple endocytosis pathways in a distinct pattern in comparison to peptides stapled by RCM. Consistent with the improved cell permeability, the FTDR-stapled lead Axin and p53 peptide analogues demonstrated enhanced inhibition of cancer cells over the RCM-stapled analogues and the unstapled peptides.

Strategies capable of stapling unprotected peptides in a straightforward, chemoselective, and clean manner, as well as promoting cellular uptake are of great interest. Here the authors report a peptide macrocyclization and stapling strategy which satisfies those criteria, based on a fluorine thiol displacement reaction.

Recent structural evolution of lactam- and imide-functionalized polymers applied in organic field-effect transistors and organic solar cells

Organic semiconductor materials, especially donor-acceptor (D-A) polymers, have been increasingly applied in organic optoelectronic devices, such as organic field-effect transistors (OFETs) and organic solar cells (OSCs). Plenty of high-performance OFETs and OSCs have been achieved based on varieties of structurally modified D-A polymers. As the basic building block of D-A polymers, acceptor moieties have drawn much attention. Among the numerous types, lactam- and imide-functionalized electron-deficient building blocks have been widely investigated. In this review, the structural evolution of lactam- or imide-containing acceptors (for instance, diketopyrrolopyrrole, isoindigo, naphthalene diimide, and perylene diimide) is covered and their representative polymers applied in OFETs and OSCs are also discussed, with a focus on the effect of varied structurally modified acceptor moieties on the physicochemical and photoelectrical properties of polymers. Additionally, this review discusses the current issues that need to be settled down and the further development of new types of acceptors. It is hoped that this review could help design new electron-deficient building blocks, find a more valid method to modify already reported acceptor units, and achieve high-performance semiconductor materials eventually.

Molecular dynamics simulations of an engineered T4 lysozyme exclude helix to sheet transition, and provide insights into long distance, intra-protein switchable motion

An engineered variant of T4 lysozyme serves as a model for studying induced remote conformational changes in a full protein context. The design involves a duplicated surface helix, flanked by two loops, that switches between two different conformations spanning about 20 Å. Molecular dynamics simulations of the engineered protein, up to 1 μs, rule out α-helix to β-sheet transitions within the duplicated helix as suggested by others. These simulations highlight how the use of different force fields can lead to radical differences in the structure of the protein. In addition, Markov state modeling and transition path theory were employed to map a 6.6 μs simulation for possible early intermediate states and to provide insights into the onset of the switching motion. The putative intermediates involve the folding of one helical turn in the C-terminal loop through energy driven, sequential rearrangement of nearby salt bridges around the key residue Arg63. These results provide a first step towards understanding the energetics and dynamics of a rather complicated intra-protein motion.

Exposing the Nucleation Site in α-Helix Folding: A Joint Experimental and Simulation Study

One of the fundamental events in protein folding is α-helix formation, which involves sequential development of a series of helical hydrogen bonds between the backbone C═O group of residues i and the -NH group of residues i + 4. While we now know a great deal about α-helix folding dynamics, a key question that remains to be answered is where the productive helical nucleation event occurs. Statistically, a helical nucleus (or the first helical hydrogen-bond) can form anywhere within the peptide sequence in question; however, the one that leads to productive folding may only form at a preferred location. This consideration is based on the fact that the α-helical structure is inherently asymmetric, due to the specific alignment of the helical hydrogen bonds. While this hypothesis is plausible, validating it is challenging because there is not an experimental observable that can be used to directly pinpoint the location of the productive nucleation process. Therefore, in this study we combine several techniques, including peptide cross-linking, laser-induced temperature-jump infrared spectroscopy, and molecular dynamics simulations, to tackle this challenge. Taken together, our experimental and simulation results support an α-helix folding mechanism wherein the productive nucleus is formed at the N-terminus, which propagates toward the C-terminal end of the peptide to yield the folded structure. In addition, our results show that incorporation of a cross-linker can lead to formation of differently folded conformations, underscoring the need for all-atom simulations to quantitatively assess the proposed cross-linking design.

A Minimum Variance Clustering Approach Produces Robust and Interpretable Coarse-Grained Models

Markov state models (MSMs) are a powerful framework for the analysis of molecular dynamics data sets, such as protein folding simulations, because of their straightforward construction and statistical rigor. The coarse-graining of MSMs into an interpretable number of macrostates is a crucial step for connecting theoretical results with experimental observables. Here we present the minimum variance clustering approach (MVCA) for the coarse-graining of MSMs into macrostate models. The method utilizes agglomerative clustering with Ward's minimum variance objective function, and the similarity of the microstate dynamics is determined using the Jensen-Shannon divergence between the corresponding rows in the MSM transition probability matrix. We first show that MVCA produces intuitive results for a simple tripeptide system and is robust toward long-duration statistical artifacts. MVCA is then applied to two protein folding simulations of the same protein in different force fields to demonstrate that a different number of macrostates is appropriate for each model, revealing a misfolded state present in only one of the simulations. Finally, we show that the same method can be used to analyze a data set containing many MSMs from simulations in different force fields by aggregating them into groups and quantifying their dynamical similarity in the context of force field parameter choices. The minimum variance clustering approach with the Jensen-Shannon divergence provides a powerful tool to group dynamics by similarity, both among model states and among dynamical models themselves.

Mechanisms of Lipid Scrambling by the G Protein-Coupled Receptor Opsin

Several class-A G protein-coupled receptor (GPCR) proteins act as constitutive phospholipid scramblases catalyzing the transbilayer translocation of >10,000 phospholipids per second when reconstituted into synthetic vesicles. To address the molecular mechanism by which these proteins facilitate rapid lipid scrambling, we carried out large-scale ensemble atomistic molecular dynamics simulations of the opsin GPCR. We report that, in the process of scrambling, lipid head groups traverse a dynamically revealed hydrophilic pathway in the region between transmembrane helices 6 and 7 of the protein while their hydrophobic tails remain in the bilayer environment. We present quantitative kinetic models of the translocation process based on Markov State Model analysis. As key residues on the lipid translocation pathway are conserved within the class-A GPCR family, our results illuminate unique aspects of GPCR structure and dynamics while providing a rigorous basis for the design of variants of these proteins with defined scramblase activity.

Bridging Microscopic and Macroscopic Mechanisms of p53-MDM2 Binding with Kinetic Network Models

Under normal cellular conditions, the tumor suppressor protein p53 is kept at low levels in part due to ubiquitination by MDM2, a process initiated by binding of MDM2 to the intrinsically disordered transactivation domain (TAD) of p53. Many experimental and simulation studies suggest that disordered domains such as p53 TAD bind their targets nonspecifically before folding to a tightly associated conformation, but the microscopic details are unclear. Toward a detailed prediction of binding mechanisms, pathways, and rates, we have performed large-scale unbiased all-atom simulations of p53-MDM2 binding. Markov state models (MSMs) constructed from the trajectory data predict p53 TAD binding pathways and on-rates in good agreement with experiment. The MSM reveals that two key bound intermediates, each with a nonnative arrangement of hydrophobic residues in the MDM2 binding cleft, control the overall on-rate. Using microscopic rate information from the MSM, we parameterize a simple four-state kinetic model to 1) determine that induced-fit pathways dominate the binding flux over a large range of concentrations, and 2) predict how modulation of residual p53 helicity affects binding, in good agreement with experiment. These results suggest new ways in which microscopic models of peptide binding, coupled with simple few-state binding flux models, can be used to understand biological function in physiological contexts.

Computational and Experimental Evaluation of Designed β-Cap Hairpins Using Molecular Simulations and Kinetic Network Models

Molecular simulation has been used to model the detailed folding properties of peptides, yet prospective computational peptide design by such approaches remains challenging and nontrivial. To test the accuracy of simulation-based hairpin design, we characterized the folding properties of a series of so-called β-cap hairpin peptides designed to mimic a conserved hairpin of LapD, a bacterial intracellular signaling protein, both experimentally by NMR spectroscopy and computationally by implicit-solvent replica-exchange molecular dynamics using three different AMBER force fields (ff96, ff99sb-ildn, and ff99sb-ildn-NMR). A unique challenge presented by these designs is the presence of both a terminal Trp-Trp capping motif and a conserved GWxQ motif in the hairpin turn required for binding to LapG. Consistent with previous studies, we found AMBER ff96 to be the most accurate when used with the OBC GBSA implicit solvent model, despite its known bias toward β-sheet conformations when used in explicit-solvent simulations. To gain microscopic insight into the folding landscape of the hairpin designs, we additionally performed parallel simulations on the Folding@home distributed computing platform using AMBER ff99sb-ildn-NMR with TIP3P explicit solvent. Markov state models (MSMs) built from trajectory data reveal a number of non-native interactions between Trp and other amino acid side chains, creating potential problems in achieving well-folded hairpin structures in solution.

A Markov State-based Quantitative Kinetic Model of Sodium Release from the Dopamine Transporter

The dopamine transporter (DAT) belongs to the neurotransmitter:sodium symporter (NSS) family of membrane proteins that are responsible for reuptake of neurotransmitters from the synaptic cleft to terminate a neuronal signal and enable subsequent neurotransmitter release from the presynaptic neuron. The release of one sodium ion from the crystallographically determined sodium binding site Na2 had been identified as an initial step in the transport cycle which prepares the transporter for substrate translocation by stabilizing an inward-open conformation. We have constructed Markov State Models (MSMs) from extensive molecular dynamics simulations of human DAT (hDAT) to explore the mechanism of this sodium release. Our results quantify the release process triggered by hydration of the Na2 site that occurs concomitantly with a conformational transition from an outward-facing to an inward-facing state of the transporter. The kinetics of the release process are computed from the MSM, and transition path theory is used to identify the most probable sodium release pathways. An intermediate state is discovered on the sodium release pathway, and the results reveal the importance of various modes of interaction of the N-terminus of hDAT in controlling the pathways of release.

A Maximum-Caliber Approach to Predicting Perturbed Folding Kinetics Due to Mutations

We present a maximum-caliber method for inferring transition rates of a Markov state model (MSM) with perturbed equilibrium populations given estimates of state populations and rates for an unperturbed MSM. It is similar in spirit to previous approaches, but given the inclusion of prior information, it is more robust and simple to implement. We examine its performance in simple biased diffusion models of kinetics and then apply the method to predicting changes in folding rates for several highly nontrivial protein folding systems for which non-native interactions play a significant role, including (1) tryptophan variants of the GB1 hairpin, (2) salt-bridge mutations of the Fs peptide helix, and (3) MSMs built from ultralong folding trajectories of FiP35 and GTT variants of the WW domain. In all cases, the method correctly predicts changes in folding rates, suggesting the wide applicability of maximum-caliber approaches to efficiently predict how mutations perturb protein conformational dynamics.

Markov models of the apo-MDM2 lid region reveal diffuse yet two-state binding dynamics and receptor poses for computational docking

MDM2 is a negative regulator of p53 activity and an important target for cancer therapeutics. The N-terminal lid region of MDM2 modulates interactions with p53 via competition for its binding cleft, exchanging slowly between docked and undocked conformations in the absence of p53. To better understand these dynamics, we constructed Markov State Models (MSMs) from large collections of unbiased simulation trajectories of apo-MDM2, and find strong evidence for diffuse, yet two-state folding and binding of the N-terminal region to the p53 receptor site. The MSM also identifies holo-like receptor conformations highly suitable for computational docking, despite initiating trajectories from closed-cleft receptor structures unsuitable for docking. Fixed-anchor docking studies using a test set of high-affinity small molecules and peptides show simulated receptor ensembles achieve docking successes comparable to cross-docking studies using crystal structures of receptors bound by alternative ligands. For p53, the best-scoring receptor structures have the N-terminal region lid region bound in a helical conformation mimicking the bound structure of p53, suggesting lid region association induces receptor conformations suitable for binding. These results suggest that MD + MSM approaches can sample binding-competent receptor conformations suitable for computational peptidomimetic design, and that inclusion of disordered regions may be essential to capturing the correct receptor dynamics.

Conformational Heterogeneity in the Michaelis Complex of Lactate Dehydrogenase: An Analysis of Vibrational Spectroscopy Using Markov and Hidden Markov Models

Lactate dehydrogenase (LDH) catalyzes the interconversion of pyruvate and lactate. Recent isotope-edited IR spectroscopy suggests that conformational heterogeneity exists within the Michaelis complex of LDH, and this heterogeneity affects the propensity toward the on-enzyme chemical step for each Michaelis substate. By combining molecular dynamics simulations with Markov and hidden Markov models, we obtained a detailed kinetic network of the substates of the Michaelis complex of LDH. The ensemble-average electric fields exerted onto the vibrational probe were calculated to provide a direct comparison with the vibrational spectroscopy. Structural features of the Michaelis substates were also analyzed on atomistic scales. Our work not only clearly demonstrates the conformational heterogeneity in the Michaelis complex of LDH and its coupling to the reactivities of the substates, but it also suggests a methodology to simultaneously resolve kinetics and structures on atomistic scales, which can be directly compared with the vibrational spectroscopy.