Jinzen Ikebe

Enhanced and effective conformational sampling of protein molecular systems for their free energy landscapes

Protein folding and protein–ligand docking have long persisted as important subjects in biophysics. Using multicanonical molecular dynamics (McMD) simulations with realistic expressions, i.e., all-atom protein models and an explicit solvent, free-energy landscapes have been computed for several systems, such as the folding of peptides/proteins composed of a few amino acids up to nearly 60 amino-acid residues, protein–ligand interactions, and coupled folding and binding of intrinsically disordered proteins. Recent progress in conformational sampling and its applications to biophysical systems are reviewed in this report, including descriptions of several outstanding studies. In addition, an algorithm and detailed procedures used for multicanonical sampling are presented along with the methodology of adaptive umbrella sampling. Both methods control the simulation so that low-probability regions along a reaction coordinate are sampled frequently. The reaction coordinate is the potential energy for multicanonical sampling and is a structural identifier for adaptive umbrella sampling. One might imagine that this probability control invariably enhances conformational transitions among distinct stable states, but this study examines the enhanced conformational sampling of a simple system and shows that reasonably well-controlled sampling slows the transitions. This slowing is induced by a rapid change of entropy along the reaction coordinate. We then provide a recipe to speed up the sampling by loosening the rapid change of entropy. Finally, we report all-atom McMD simulation results of various biophysical systems in an explicit solvent.

Theory for trivial trajectory parallelization of multicanonical molecular dynamics and application to a polypeptide in water

Trivial trajectory parallelization of multicanonical molecular dynamics (TTP‐McMD) explores the conformational space of a biological system with multiple short runs of McMD starting from various initial structures. This method simply connects (i.e., trivially parallelizes) the short trajectories and generates a long trajectory. First, we theoretically prove that the simple trajectory connection satisfies a detailed balance automatically. Thus, the resultant long trajectory is regarded as a single multicanonical trajectory. Second, we applied TTP‐McMD to an alanine decapeptide with an all‐atom model in explicit water to compute a free‐energy landscape. The theory imposes two requirements on the multiple trajectories. We have demonstrated that TTP‐McMD naturally satisfies the requirements. The TTP‐McMD produces the free‐energy landscape considerably faster than a single‐run McMD does. We quantitatively showed that the accuracy of the computed landscape increases with increasing the number of multiple runs. Generally, the free‐energy landscape of a large biological system is unknown a priori. The current method is suitable for conformational sampling of such a large system to reduce the waiting time to obtain a canonical ensemble statistically reliable.

Simulation study on the disordered state of an Alzheimer's β amyloid peptide Aβ(12–36) in water consisting of random-structural, β-structural, and helical clusters

The monomeric Alzheimers β amyloid peptide, Aβ, is known to adopt a disordered state in water at room temperature, and a circular dichroism (CD) spectroscopy experiment has provided the secondary‐structure contents for the disordered state: 70% random, 25% β‐structural, and 5% helical. We performed an enhanced conformational sampling (multicanonical molecular dynamics simulation) of a 25‐residue segment (residues 12–36) of Aβ in explicit water and obtained the conformational ensemble over a wide temperature range. The secondary‐structure contents calculated from the conformational ensemble at 300°K reproduced the experimental secondary‐structure contents. The constructed free‐energy landscape at 300°K was not plain but rugged with five clearly distinguishable clusters, and each cluster had its own characteristic tertiary structure: a helix‐structural cluster, two β‐structural clusters, and two random‐structural clusters. This indicates that the contribution from the five individual clusters determines the secondary‐structure contents experimentally measured. The helical cluster had a similarity with a stable helical structure for monomeric Aβ in 2,2,2‐trifluoroethanol (TFE)/water determined by an NMR experiment: The positions of helices in the helical cluster were the same as those in the NMR structure, and the residue–residue contact patterns were also similar with those of the NMR structure. The cluster–cluster separation in the conformational space indicates that free‐energy barriers separate the clusters at 300°K. The two β‐structural clusters were characterized by different strand–strand hydrogen‐bond (H‐bond) patterns, suggesting that the free‐energy barrier between the two clusters is due to the H‐bond rearrangements.

Ab initio simulation of a 57-residue protein in explicit solvent reproduces the native conformation in the lowest free-energy cluster

An enhanced conformational sampling method, multicanonical molecular dynamics (McMD), was applied to the ab intio folding of the 57‐residue first repeat of human glutamyl‐ prolyl‐tRNA synthetase (EPRS‐R1) in explicit solvent. The simulation started from a fully extended structure of EPRS‐R1 and did not utilize prior structural knowledge. A canonical ensemble, which is a conformational ensemble thermodynamically probable at an arbitrary temperature, was constructed by reweighting the sampled structures. Conformational clusters were obtained from the canonical ensemble at 300 K, and the largest cluster (i.e., the lowest free‐energy cluster), which contained 34% of the structures in the ensemble, was characterized by the highest similarity to the NMR structure relative to all alternative clusters. This lowest free‐energy cluster included native‐like structures composed of two anti‐parallel α‐helices. The canonical ensemble at 300 K also showed that a short Gly‐containing segment, which adopts an α‐helix in the native structure, has a tendency to be structurally disordered. Atomic‐level analyses demonstrated clearly that inter‐residue hydrophobic interactions drive the helix formation of the Gly‐containing segment, and that increasing the hydrophobic contacts accompanies exclusion of water molecules from the vicinity of this segment. This study has shown, for the first time, that the free‐energy landscape of a structurally well‐ordered protein of about 60 residues is obtainable with an all atom model in explicit water without prior structural knowledge.

H3 Histone Tail Conformation within the Nucleosome and the Impact of K14 Acetylation Studied Using Enhanced Sampling Simulation

Acetylation of lysine residues in histone tails is associated with gene transcription. Because histone tails are structurally flexible and intrinsically disordered, it is difficult to experimentally determine the tail conformations and the impact of acetylation. In this work, we performed simulations to sample H3 tail conformations with and without acetylation. The results show that irrespective of the presence or absence of the acetylation, the H3 tail remains in contact with the DNA and assumes an α-helix structure in some regions. Acetylation slightly weakened the interaction between the tail and DNA and enhanced α-helix formation, resulting in a more compact tail conformation. We inferred that this compaction induces unwrapping and exposure of the linker DNA, enabling DNA-binding proteins (e.g., transcription factors) to bind to their target sequences. In addition, our simulation also showed that acetylated lysine was more often exposed to the solvent, which is consistent with the fact that acetylation functions as a post-translational modification recognition site marker.

Adaptive lambda square dynamics simulation: an efficient conformational sampling method for biomolecules.

A novel, efficient sampling method for biomolecules is proposed. The partial multicanonical molecular dynamics (McMD) was recently developed as a method that improved generalized ensemble (GE) methods to focus sampling only on a part of a system (GEPS); however, it was not tested well. We found that partial McMD did not work well for polylysine decapeptide and gave significantly worse sampling efficiency than a conventional GE. Herein, we elucidate the fundamental reason for this and propose a novel GEPS, adaptive lambda square dynamics (ALSD), which can resolve the problem faced when using partial McMD. We demonstrate that ALSD greatly increases the sampling efficiency over a conventional GE. We believe that ALSD is an effective method and is applicable to the conformational sampling of larger and more complicated biomolecule systems.

Conformational Ensembles of an Intrinsically Disordered Protein pKID with and without a KIX Domain in Explicit Solvent Investigated by All-Atom Multicanonical Molecular Dynamics

The phosphorylated kinase-inducible activation domain (pKID) adopts a helix–loop–helix structure upon binding to its partner KIX, although it is unstructured in the unbound state. The N-terminal and C-terminal regions of pKID, which adopt helices in the complex, are called, respectively, αA and αB. We performed all-atom multicanonical molecular dynamics simulations of pKID with and without KIX in explicit solvents to generate conformational ensembles. Although the unbound pKID was disordered overall, αA and αB exhibited a nascent helix propensity; the propensity of αA was stronger than that of αB, which agrees with experimental results. In the bound state, the free-energy landscape of αB involved two low free-energy fractions: native-like and non-native fractions. This result suggests that αB folds according to the induced-fit mechanism. The αB-helix direction was well aligned as in the NMR complex structure, although the αA helix exhibited high flexibility. These results also agree quantitatively with experimental observations. We have detected that the αB helix can bind to another site of KIX, to which another protein MLL also binds with the adopting helix. Consequently, MLL can facilitate pKID binding to the pKID-binding site by blocking the MLL-binding site. This also supports experimentally obtained results.

Enhanced sampling simulations to construct free-energy landscape of protein–partner substrate interaction

Molecular dynamics (MD) simulations using all-atom and explicit solvent models provide valuable information on the detailed behavior of protein–partner substrate binding at the atomic level. As the power of computational resources increase, MD simulations are being used more widely and easily. However, it is still difficult to investigate the thermodynamic properties of protein–partner substrate binding and protein folding with conventional MD simulations. Enhanced sampling methods have been developed to sample conformations that reflect equilibrium conditions in a more efficient manner than conventional MD simulations, thereby allowing the construction of accurate free-energy landscapes. In this review, we discuss these enhanced sampling methods using a series of case-by-case examples. In particular, we review enhanced sampling methods conforming to trivial trajectory parallelization, virtual-system coupled multicanonical MD, and adaptive lambda square dynamics. These methods have been recently developed based on the existing method of multicanonical MD simulation. Their applications are reviewed with an emphasis on describing their practical implementation. In our concluding remarks we explore extensions of the enhanced sampling methods that may allow for even more efficient sampling.

Accessibility of the histone H3 tail in the nucleosome for binding of paired readers

Combinatorial polyvalent contacts of histone-binding domains or readers commonly mediate localization and activities of chromatin-associated proteins. A pair of readers, the PHD fingers of the protein CHD4, has been shown to bivalently recognize histone H3 tails. Here we describe a mechanism by which these linked but independent readers bind to the intact nucleosome core particle (NCP). Comprehensive NMR, chemical reactivity, molecular dynamics, and fluorescence analyses point to the critical roles of intra-nucleosomal histone-DNA interactions that reduce the accessibility of H3 tails in NCP, the nucleosomal DNA, and the linker between readers in modulating nucleosome- and/or histone-binding activities of the readers. We show that the second PHD finger of CHD4 initiates recruitment to the nucleosome, however both PHDs are required to alter the NCP dynamics. Our findings reveal a distinctive regulatory mechanism for the association of paired readers with the nucleosome that provides an intricate balance between cooperative and individual activities of the readers.The chromatin remodeller CHD4 contains two PHD finger reader domains that have been shown to bivalently recognize H3 histone tails. Here, the authors describe a mechanism by which the PHD fingers bind to the intact nucleosome core particle, revealing both cooperative and individual interactions.

Conformational requirement on peptides to exert laminin's activities and search for protein segments with laminin's activities

The human laminin α3 chain LG4 module has biological activities of cell adhesion, heparin binding, migration, and neurite outgrowth. The authors had previously identified that the active site of this protein is in residues 1411–1429 (amino‐acid sequence = KNSFMALYLSKGRLVFALG called A3G756) and that a three‐amino‐acid sequence KGR in A3G756 is crucial for exerting the activities. An experiment has shown that a cyclo‐hEF3A peptide (a cyclic analog of A3G756) exhibits stronger activities than a linear‐hEF3A peptide (a linearized peptide of the cyclo‐hEF3A peptide). This experiment implies that adopting a loop conformation may be important for exerting the activities. In this study, the authors first computed the solution structures of the cyclo‐hEF3A and linear‐hEF3A peptides by molecular dynamics simulations. The obtained conformational ensembles consisted of a variety of conformations, which is a usual property of short peptides in solution. The ensembles involved a fraction where the peptide adopted β‐hairpins and KGR was located at the hairpin head. If there are protein segments that adopt β‐hairpins similar to those sampled from the simulation and have the KGR sequence at the hairpin head, these segments may have some activities. Then, the authors searched a database for segments satisfying these requirements and detected six functional segments. Three of them had laminins activity, and the remaining three had activities similar to laminins activities. Analyses on the conformational ensembles of cyclo‐ and linear‐hEF3A peptides suggest that not only the KGR position in the hairpin but also the inter‐strand packing is important for exerting laminins activities.