AMBER-based hybrid force field for conformational sampling of polypeptides

Monitoring Conformation and Protonation States of Glutathione by Raman Optical Activity and Molecular Dynamics

Glutathione (GSH) is a common antioxidant and its biological activity depends on the conformation and protonation state. We used molecular dynamics, Raman and Raman optical activity (ROA) spectroscopies to investigate GSH structural changes in a broad pH range. Factor analysis of the spectra provided protonation constants (2.05, 3.45, 8.62, 9.41) in good agreement with previously published values. Following the analysis, spectra of differently protonated forms were obtained by extrapolation. The complete deprotonation of the thiol group above pH 11 was clearly visible in the spectra; however, many spectral features did not change much with pH. Experimental spectra at various pH values were decomposed into the simulated ones, which allowed us to study the conformer populations and quality of molecular dynamics (MD). According to this combined ROA/MD analysis conformation of the GSH backbone is affected by the pH changes only in a limited way. The combination of ROA with the computations thus has the potential to improve the MD force field and obtain more accurate populations of the conformer species. The methodology can be used for any molecule, but for a more detailed insight better computational techniques are needed in the future.

Conformations and Solvation of Synthetic Polymers in Water by Generalized Born Implicit-Solvent Molecular Dynamics Simulations: Stereoisomers of Poly(acrylic acid) and Poly(methacrylic acid)

We present the GB-OBC model as an approach for implicit-solvent MD simulations of a synthetic macromolecule in water. The model is tested and found to be successful in reproducing the chain dimensions and predicting the free energy of solvation of carboxylic acid vinyl polymers. The influence of stereochemistry and the hydrophobic nature of the polymer was investigated as a function of chain length (20 < N < 600) for poly(acrylic acid) (PAA) and poly(methacrylic acid) (PMA). The dimensionless parameters of the GB-OBC model were parameterized to be applicable to PAA and PMA. Scaling relations for chain dimensions obtained using implicit-solvent MD simulations in this study are in good agreement with those from experiments, theory of solvated chains in good solvents, and all-atom MD simulations in explicit water. Results show that ⟨R_g²⟩/NL² is greater for the atactic chain as compared to the isotactic chain, for PAA as well as PMA. ⟨R_g²⟩/NL² values of chains attain constancy in water for N = 200, with the values being greater for PMA. The PMA chain is conformationally more perturbed than the PAA chain, for both isotactic and atactic stereochemistry. The solvation free energy ΔG_hyd of PAA and PMA in water is negative for all chain lengths (N = 20-600) and becomes more favorable with an increase in molecular weight. The ΔG_hyd values for isotactic and atactic chains are identical at lower values of N but differ slightly for N > 300. Irrespective of the hydrophobic nature of the polymer, the atactic chain is thermodynamically more soluble in water as compared to the isotactic chain. The isotactic chain is less hydrophilic as compared to the atactic chain due to the closer proximity of the COOH groups along the backbone. This implicit solvent method is an effective way to accurately simulate the configurational properties and solvation of synthetic polymers in water.

Quantum chemical studies on hydrogen bonds in helical secondary structures

We present a brief review of our recent computational studies of hydrogen bonds (H-bonds) in helical secondary structures of proteins, α-helix and 3₁₀-helix, using a Negative Fragmentation Approach with density functional theory. We found that the depolarized electronic structures of the carbonyl oxygen of the ith residue and the amide hydrogen of the (i + 4)th residue cause weaker H-bond in an α-helix than in an isolated H-bond. Our calculations showed that the H-bond energies in the 3₁₀-helix were also weaker than those of the isolated H-bonds. In the 3₁₀-helices, the adjacent N-H group at the (i + 1)th residue was closer to the C=O group of the H-bond pair than the adjacent C=O group in the 3₁₀-helices, whereas the adjacent C=O group at the (i + 1)th residue was close to the H-bond acceptor in α-helices. Therefore, the destabilization of the H-bond is attributed to the depolarization caused by the adjacent residue of the helical backbone connecting the H-bond donor and acceptor. The differences in the change in electron density revealed that such depolarizations were caused by the local electronic interactions in their neighborhood inside the helical structure and redistributed the electron density. We also present the improvements in the force field of classical molecular simulation, based on our findings.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12551-022-01034-5.

Thermal Stability Estimation of Single Domain Antibodies Using Molecular Dynamics Simulations

In this chapter, we describe a protocol to estimate the thermal stability of single domain antibodies (sdAbs) using molecular dynamics (MD) simulations. This method measures the Q-value, the fraction of the native contacts, along the trajectory of high-temperature MD simulations starting from the experimental X-ray structure. We show a good correlation between the Q-value and the experimental melting temperature (T_m) in seven sdAbs. Assessing the Q-value on a per-residue level enabled us to identify residues that contribute to the instability and thus demonstrate which residues could be mutated to improve the stability and have later been validated by experiments. Our protocol extends beyond the application on sdAbs, as it is also suitable for other proteins and to determine the interfacial stability between protein and ligand.

Depolarizing Effects in Hydrogen Bond Energy in 310-Helices Revealed by Quantum Chemical Analysis

Hydrogen-bond (H-bond) energies in 3₁₀-helices of short alanine peptides were systematically examined by precise DFT calculations with the negative fragmentation approach (NFA), a modified method based on the molecular tailoring approach. The contribution of each H-bond was evaluated in detail from the 3₁₀-helical conformation of total energies (whole helical model, WH_3-10 model), and the results were compared with the property of H-bond in α-helix from our previous study. The H-bond energies of the WH_3-10 model exhibited tendencies different from those exhibited by the α-helix in that they depended on the helical position of the relevant H-bond pair. H-bond pairs adjacent to the terminal H-bond pairs were observed to be strongly destabilized. The analysis of electronic structures indicated that structural characteristics cause the destabilization of the H-bond in 3₁₀-helices. We also found that the longer the helix length, the more stable the H-bond in the terminal pairs of the WH_3-10 model, suggesting the action of H-bond cooperativity.

Intense chiral signal from α-helical poly-L-alanine observed in low-frequency Raman optical activity

Raman optical activity (ROA) spectral features reliably indicate the structure of peptides and proteins, but the signal is often weak. However, we observed significantly enhanced low-frequency bands for α-helical poly-L-alanine (PLA) in solution. The biggest ROA signal at ∼100 cm^-1 is about 10 times stronger than higher-frequency bands described previously, which facilitates the detection. The low-frequency bands of PLA were compared to those of α-helical proteins. For PLA, density functional simulations well reproduced the experimental spectra and revealed that about 12 alanine residues within two turns of the α-helix generate the strong ROA band. Averaging based on molecular dynamics (MD) provided an even more realistic spectrum compared to the static model. The low-frequency bands could be largely related to a collective motion of the α-helical backbone, partially modulated by the solvent. Helical and intermolecular vibrational coordinates have been introduced and the helical unwinding modes were assigned to the strongest ROA signal at 101-128 cm^-1. Further analysis indicated that the helically arranged amide and methyl groups are important for the strong chiral signal of PLA, while the local chiral centers C_αH contribute in a minor way only. The strong low-frequency ROA can thus provide precious information about the motions of the peptide backbone and facilitate future protein studies.

Enzyme modification using mutation site prediction method for enhancing the regioselectivity of substrate reaction sites

Enzymes with low regioselectivity of substrate reaction sites may produce multiple products from a single substrate. When a target product is produced industrially using these enzymes, the production of non-target products (byproducts) causes adverse effects such as increased processing costs for purification and the amount of raw material. Thus it is required the development of modified enzymes to reduce the amount of byproducts’ production. In this paper, we report a method called mutation site prediction for enhancing the regioselectivity of substrate reaction sites (MSPER). MSPER takes conformational data for docking poses of an enzyme and a substrate as input and automatically generates a ranked list of mutation sites to destabilize docking poses for byproducts while maintaining those for target products in silico. We applied MSPER to the enzyme cytochrome P450 CYP102A1 (BM3) and the two substrates to enhance the regioselectivity for four target products with different reaction sites. The 13 of the total 14 top-ranked mutation sites predicted by MSPER for the four target products succeeded in selectively enhancing the regioselectivity up to 6.4-fold. The results indicate that MSPER can distinguish differences of substrate structures and the reaction sites, and can accurately predict mutation sites to enhance regioselectivity without selection by directed evolution screening.

Generalized-ensemble method study: A helix-mimetic compound inhibits protein-protein interaction by long-range and short-range intermolecular interactions

A heterocyclic compound mS-11 is a helix-mimetic designed to inhibit binding of an intrinsic disordered protein neural restrictive silence factor/repressor element 1 silencing factor (NRSF/REST) to a receptor protein mSin3B. We apply a generalized ensemble method, multi-dimensional virtual-system coupled molecular dynamics developed by ourselves recently, to a system consisting of mS-11 and mSin3B, and obtain a thermally equilibrated distribution, which is comprised of the bound and unbound states extensively. The lowest free-energy position of mS-11 coincides with the NRSF/REST position in the experimentally-determined NRSF/REST-mSin3B complex. Importantly, the molecular orientation of mS-11 is ordering in a wide region around mSin3B. The resultant binding scenario is: When mS-11 is distant from the binding site of mSin3B, mS-11 descends the free-energy slope toward the binding site maintaining the molecular orientation to be advantageous for binding. Then, finally a long and flexible hydrophobic sidechain of mS-11 fits into the binding site, which is the lowest-free-energy complex structure inhibiting NRSF/REST binding to mSin3B.

Difference of binding modes among three ligands to a receptor mSin3B corresponding to their inhibitory activities

A preceding experiment suggested that a compound, which inhibits binding of the REST/NRSF segment to the cleft of a receptor protein mSin3B, can be a potential drug candidate to ameliorate many neuropathies. We have recently developed an enhanced conformational sampling method, genetic-algorithm-guided multi-dimensional virtual-system-coupled canonical molecular dynamics, and in the present study, applied it to three systems consisting of mSin3B and one of three compounds, sertraline, YN3, and acitretin. Other preceding experiments showed that only sertraline inhibits the binding of REST/NRSF to mSin3B. The current simulation study produced the spatial distribution of the compounds around mSin3B, and showed that sertraline and YN3 bound to the cleft of mSin3B with a high propensity, although acitretin did not. Further analyses of the simulation data indicated that only the sertraline-mSin3B complex produced a hydrophobic core similar to that observed in the molecular interface of the REST/NRSF-mSin3B complex: An aromatic ring of sertraline sunk deeply in the mSin3B's cleft forming a hydrophobic core contacting to hydrophobic amino-acid residues located at the bottom of the cleft. The present study proposes a step to design a compound that inhibits competitively the binding of a ligand to its receptor.

Molecular Interaction Mechanism of a 14-3-3 Protein with a Phosphorylated Peptide Elucidated by Enhanced Conformational Sampling

Enhanced conformational sampling, a genetic-algorithm-guided multidimensional virtual-system coupled molecular dynamics, can provide equilibrated conformational distributions of a receptor protein and a flexible ligand at room temperature. The distributions provide not only the most stable but also semistable complex structures and propose a ligand-receptor binding process. This method was applied to a system consisting of a receptor protein, 14-3-3ε, and a flexible peptide, phosphorylated myeloid leukemia factor 1 (pMLF1). The results present comprehensive binding pathways of pMLF1 to 14-3-3ε. We identified four thermodynamically stable clusters of MLF1 on the 14-3-3ε surface and free-energy barriers among some clusters. The most stable cluster includes two high-density spots connected by a narrow corridor. When pMLF1 passes the corridor, a salt-bridge relay (switching) related to the phosphorylated residue of pMLF1 occurs. Conformations in one high-density spot are similar to the experimentally determined complex structure. Three-dimensional distributions of residues in the intermolecular interface rationally explain the binding constant changes resulting from the alanine mutation experiment for the residues. We also performed a simulation of nonphosphorylated peptide and 14-3-3ε, which demonstrated that the complex structure was unstable, suggesting that phosphorylation of the peptide is crucially important for binding to 14-3-3ε.

Free-energy landscape of molecular interactions between endothelin 1 and human endothelin type B receptor: fly-casting mechanism

The free-energy landscape of interaction between a medium-sized peptide, endothelin 1 (ET1), and its receptor, human endothelin type B receptor (hETB), was computed using multidimensional virtual-system coupled molecular dynamics, which controls the system's motions by introducing multiple reaction coordinates. The hETB embedded in lipid bilayer was immersed in explicit solvent. All molecules were expressed as all-atom models. The resultant free-energy landscape had five ranges with decreasing ET1-hETB distance: completely dissociative, outside-gate, gate, binding pocket, and genuine-bound ranges. In the completely dissociative range, no ET1-hETB interaction appeared. In the outside-gate range, an ET1-hETB attractive interaction was the fly-casting mechanism. In the gate range, the ET1 orientational variety decreased rapidly. In the binding pocket range, ET1 was in a narrow pathway with a steep free-energy slope. In the genuine-bound range, ET1 was in a stable free-energy basin. A G-protein-coupled receptor (GPCR) might capture its ligand from a distant place.

Hydrogen bond donors and acceptors are generally depolarized in α-helices as revealed by a molecular tailoring approach

Hydrogen-bond (H-bond) interaction energies in α-helices of short alanine peptides were systematically examined by precise density functional theory calculations, followed by a molecular tailoring approach. The contribution of each H-bond interaction in α-helices was estimated in detail from the entire conformation energies, and the results were compared with those in the minimal H-bond models, in which only H-bond donors and acceptors exist with the capping methyl groups. The former interaction energies were always significantly weaker than the latter energies, when the same geometries of the H-bond donors and acceptors were applied. The chemical origin of this phenomenon was investigated by analyzing the differences among the electronic structures of the local peptide backbones of the α-helices and those of the minimal H-bond models. Consequently, we found that the reduced H-bond energy originated from the depolarizations of both the H-bond donor and acceptor groups, due to the repulsive interactions with the neighboring polar peptide groups in the α-helix backbone. The classical force fields provide similar H-bond energies to those in the minimal H-bond models, which ignore the current depolarization effect, and thus they overestimate the actual H-bond energies in α-helices. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Phosphorylation of an intrinsically disordered region of Ets1 shifts a multi-modal interaction ensemble to an auto-inhibitory state

Multi-modal interactions are frequently observed in intrinsically disordered regions (IDRs) of proteins upon binding to their partners. In many cases, post-translational modifications in IDRs are accompanied by coupled folding and binding. From both molecular simulations and biochemical experiments with mutational studies, we show that the IDR including a Ser rich region (SRR) of the transcription factor Ets1, just before the DNA-binding core domain, undergoes multi-modal interactions when the SRR is not phosphorylated. In the phosphorylated state, the SRR forms a few specific complex structures with the Ets1 core, covering the recognition helix in the core and drastically reducing the DNA binding affinities as the auto-inhibitory state. The binding kinetics of mutated Ets1 indicates that aromatic residues in the SRR can be substituted with other hydrophobic residues for the interactions with the Ets1 core.

Enhanced Sampling of Molecular Dynamics Simulations of a Polyalanine Octapeptide: Effects of the Periodic Boundary Conditions on Peptide Conformation

We investigate the problem of artifacts caused by the periodic boundary conditions (PBC) used in molecular simulation studies. Despite the long history of simulations with PBCs, the existence of measurable artifacts originating from PBCs applied to inherently nonperiodic physical systems remains controversial. Specifically, these artifacts appear as differences between simulations of the same system but with different simulation-cell sizes. Earlier studies have implied that, even in the simple case of a small model peptide in water, sampling inefficiency is a major obstacle to understanding these artifacts. In this study, we have resolved the sampling issue using the replica exchange molecular dynamics (REMD) enhanced-sampling method to explore PBC artifacts. Explicitly solvated zwitterionic polyalanine octapeptides with three different cubic-cells, having dimensions of L = 30, 40, and 50 Å, were investigated to elucidate the differences with 64 replica × 500 ns REMD simulations using the AMBER parm99SB force field. The differences among them were not large overall, and the results for the L = 30 and 40 Å simulations in the conformational free energy landscape were found to be very similar at room temperature. However, a small but statistically significant difference was seen for L = 50 Å. We observed that extended conformations were slightly overstabilized in the smaller systems. The origin of these artifacts is discussed by comparison to an electrostatic calculation method without PBCs.

Molecular dynamics coupled with a virtual system for effective conformational sampling

An enhanced conformational sampling method is proposed: virtual-system coupled canonical molecular dynamics (VcMD). Although VcMD enhances sampling along a reaction coordinate, this method is free from estimation of a canonical distribution function along the reaction coordinate. This method introduces a virtual system that does not necessarily obey a physical law. To enhance sampling the virtual system couples with a molecular system to be studied. Resultant snapshots produce a canonical ensemble. This method was applied to a system consisting of two short peptides in an explicit solvent. Conventional molecular dynamics simulation, which is ten times longer than VcMD, was performed along with adaptive umbrella sampling. Free-energy landscapes computed from the three simulations mutually converged well. The VcMD provided quicker association/dissociation motions of peptides than the conventional molecular dynamics did. The VcMD method is applicable to various complicated systems because of its methodological simplicity. © 2018 Wiley Periodicals, Inc.

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.

Dynamics of the Extended String-Like Interaction of TFIIE with the p62 Subunit of TFIIH

General transcription factor II E (TFIIE) contains an acid-rich region (residues 378-393) in its α-subunit, comprising 13 acidic and two hydrophobic (Phe387 and Val390) residues. Upon binding to the p62 subunit of TFIIH, the acidic region adopts an extended string-like structure on the basic groove of the pleckstrin homology domain (PHD) of p62, and inserts Phe387 and Val390 into two shallow pockets in the groove. Here, we have examined the dynamics of this interaction by NMR and molecular dynamics (MD) simulations. Although alanine substitution of Phe387 and/or Val390 greatly reduced binding to PHD, the binding mode of the mutants was similar to that of the wild-type, as judged by the chemical-shift changes of the PHD. NMR relaxation dispersion profiles of the interaction exhibited large amplitudes for residues in the C-terminal half-string in the acidic region (Phe387, Glu388, Val390, Ala391, and Asp392), indicating a two-site binding mode: one corresponding to the final complex structure, and one to an off-pathway minor complex. To probe the off-pathway complex structure, an atomically detailed free-energy landscape of the binding mode was computed by all-atom multicanonical MD. The most thermodynamically stable cluster corresponded to the final complex structure. One of the next stable clusters was the off-pathway structure cluster, showing the reversed orientation of the C-terminal half-string on the PHD groove, as compared with the final structure. MD calculations elucidated that the C-terminal half-acidic-string forms encounter complexes mainly around the positive groove region with nearly two different orientations of the string, parallel and antiparallel to the final structure. Interestingly, the most encountered complexes exhibit a parallel-like orientation, suggesting that the string has a tendency to bind around the groove in the proper orientation with the aid of Phe387 and/or Val390 to proceed smoothly to the final complex structure.

Variation of free-energy landscape of the p53 C-terminal domain induced by acetylation: Enhanced conformational sampling

The C-terminal domain (CTD) of tumor suppressor protein p53 is an intrinsically disordered region that binds to various partner proteins, where lysine of CTD is acetylated/nonacetylated and histidine neutralized/non-neutralized. Because of the flexibility of the unbound CTD, a free-energy landscape (FEL) is a useful quantity for determining its statistical properties. We conducted enhanced conformational sampling of CTD in the unbound state via virtual system coupled multicanonical molecular dynamics, in which the lysine was acetylated or nonacetylated and histidine was charged or neutralized. The fragments were expressed by an all-atom model and were immersed in an explicit solvent. The acetylation and charge-neutralization varied FEL greatly, which might be convenient to exert a hub property. The acetylation slightly enhanced alpha-helix structures that are more compact than sheet/loop conformations. The charge-neutralization produced hairpins. Additionally, circular dichroism experiments confirmed the computational results. We propose possible binding mechanisms of CTD to partners by investigating FEL. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Elastic properties of dynein motor domain obtained from all-atom molecular dynamics simulations

Dyneins are large microtubule motor proteins that convert ATP energy to mechanical power. High-resolution crystal structures of ADP-bound cytoplasmic dynein have revealed the organization of the motor domain, comprising the AAA(+) ring, the linker, the stalk/strut and the C sequence. Recently, the ADP.vanadate-bound structure, which is similar to the ATP hydrolysis transition state, revealed how the structure of dynein changes upon ATP binding. Although both the ADP- and ATP-bound state structures have been resolved, the dynamic properties at the atomic level remain unclear. In this work, we built two models named 'the ADP model' and 'the ATP model', where ADP and ATP are bound to AAA1 in the AAA(+) ring, respectively, to observe the initial procedure of the structural change from the unprimed to the primed state. We performed 200-ns molecular dynamics simulations for both models and compared their structures and dynamics. The motions of the stalk, consisting of a long coiled coil with a microtubule-binding domain, significantly differed between the two models. The elastic properties of the stalk were analyzed and compared with the experimental results.

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.

Post-translational modification (PTM) of histone tails is an important component of epigenetics. Acetylation of histone tails generally functions to activate gene expression, though the molecular mechanism is not well understood. We used enhanced sampling simulation to examine the impact of acetylation on the structure of the histone H3 tail within the nucleosome. The results suggest acetylation makes the H3 tail conformation more compact and enhances dissociation of nucleosomal DNA from the histone core. Further, the acetylated lysine was more exposed to the solvent, which is consistent with its role as a PTM recognition site marker. These findings increase our understanding of the impact of PTM on nucleosome stability and dynamics and on the higher order structure of chromatin.

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.

Multi-scale ensemble modeling of modular proteins with intrinsically disordered linker regions: application to p53

In eukaryotic proteins, intrinsically disordered regions (IDRs) are ubiquitous and often exist in linker regions that flank the functional domains of modular proteins, regulating their functions. For detailed structural ensemble modeling of IDRs, we propose a multiscale method for IDRs that possess significant long-range order in modular proteins and apply it to the eukaryotic transcription factor p53 as an example. First, we performed all-atom (AA) molecular dynamics (MD) simulations of the explicitly solvated p53 linker region, without experimental restraint terms, finding fractional long-range contacts within the linker. Second, we fed this AA MD ensemble into a coarse-grained (CG) model, finding an optimal set of contact potentials. The optimized CG MD simulations reproduced the contact probability map from the AA MD simulations. Finally, we performed the CG MD simulation of the tetrameric p53 fragments including the core domains, the linker, and the tetramerization domain. Using the obtained ensemble, we theoretically calculated the small angle x-ray scattering (SAXS) profile of this fragment. The obtained SAXS profile agrees well with the experiment. We also found that the long-range contacts in the p53 linker region are required to reproduce the experimental SAXS profile. The developed framework in which we calculate the long-range contact probability map from the AA MD simulation and incorporate it to the CG model can be applied to broad range of IDRs.

Multi-scale modeling of electronic spectra of three aromatic amino acids: importance of conformational averaging and explicit solute-solvent interactions

Electronic transitions in the ultraviolet and visible spectral range can reveal a wealth of information about biomolecular geometry and interactions, such as those involved in protein folding. However, the modeling that provides the necessary link between spectral shapes and the structure is often difficult even for seemingly simple systems. To understand as to how conformational equilibria and solute-solvent interaction influence spectral intensities, we collected absorption (UV-vis), electronic circular dichroism (ECD), and magnetic circular dichroism (MCD) spectra of phenylalanine (Phe), tyrosine (Tyr) and tryptophan (Trp) zwitterions in aqueous solutions, and compared them with quantum-chemical simulations. These aromatic amino acids provide a relatively strong signal in the accessible wavelength range. At the same time, they allow for a relatively accurate modeling. Energies and intensities of spectral bands were reproduced by the time-dependent density functional theory (TD DFT). The solvent was approximated by a continuum as well as clusters containing solvent molecules from the first hydration sphere. The ECD signal was found to be strongly dependent on molecular conformation, and the dependence was much weaker in UV-vis and MCD spectra. All spectral intensities, however, were significantly affected by the solvent approximation; especially for ECD and MCD the usual polarizable continuum solvent model did not yield satisfactory spectral shapes. On the other hand, averaging of the clusters obtained from molecular dynamics simulations provided an unprecedented agreement with the experiment. Proper modeling of the interactions with the environment thus makes the information about the molecular structure, as obtained from the electronic spectra, more accurate and reliable.

Structure of the entire stalk region of the Dynein motor domain

Dyneins are large microtubule-based motor complexes that power a range of cellular processes including the transport of organelles, as well as the beating of cilia and flagella. The motor domain is located within the dynein heavy chain and comprises an N-terminal mechanical linker element, a central ring of six AAA+ modules of which four bind or hydrolyze ATP, and a long stalk extending from the AAA+ring with a microtubule-binding domain (MTBD) at its tip. A crucial mechanism underlying the motile activity of cytoskeletal motor proteins is precise coupling between the ATPase and track-binding activities. In dynein, a stalk region consisting of a long (~15nm) antiparallel coiled coil separates these two activities, which must facilitate communication between them. This communication is mediated by a small degree of helix sliding in the coiled coil. However, no high-resolution structure is available of the entire stalk region including the MTBD. Here, we have reported the structure of the entire stalk region of mouse cytoplasmic dynein in a weak microtubule-binding state, which was determined using X-ray crystallography, and have compared it with the dynein motor domain from Dictyostelium discoideum in a strong microtubule-binding state and with a mouse MTBD with its distal portion of the coiled coil fused to seryl-tRNA synthetase from Thermus thermophilus. Our results strongly support the helix-sliding model based on the complete structure of the dynein stalk with a different form of coiled-coil packing. We also propose a plausible mechanism of helix sliding together with further analysis using molecular dynamics simulations. Our results present the importance of conserved proline residues for an elastic motion of stalk coiled coil and imply the manner of change between high-affinity state and low-affinity state of MTBD.

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.

The intrinsic conformational features of amino acids from a protein coil library and their applications in force field development

The local conformational (φ, ψ, χ) preferences of amino acid residues remain an active research area, which are important for the development of protein force fields. In this perspective article, we first summarize spectroscopic studies of alanine-based short peptides in aqueous solution. While most studies indicate a preference for the P(II) conformation in the unfolded state over α and β conformations, significant variations are also observed. A statistical analysis from various coil libraries of high-resolution protein structures is then summarized, which gives a more coherent view of the local conformational features. The φ, ψ, χ distributions of the 20 amino acids have been obtained from a protein coil library, considering both backbone and side-chain conformational preferences. The intrinsic side-chain χ(1) rotamer preference and χ(1)-dependent Ramachandran plot can be generally understood by combining the interaction of the side-chain Cγ/Oγ atom with two neighboring backbone peptide groups. Current all-atom force fields such as AMBER ff99sb-ILDN, ff03 and OPLS-AA/L do not reproduce these distributions well. A method has been developed by combining the φ, ψ plot of alanine with the influence of side-chain χ(1) rotamers to derive the local conformational features of various amino acids. It has been further applied to improve the OPLS-AA force field. The modified force field (OPLS-AA/C) reproduces experimental (3)J coupling constants for various short peptides quite well. It also better reproduces the temperature-dependence of the helix-coil transition for alanine-based peptides. The new force field can fold a series of peptides and proteins with various secondary structures to their experimental structures. MD simulations of several globular proteins using the improved force field give significantly less deviation (RMSD) to experimental structures. The results indicate that the local conformational features from coil libraries are valuable for the development of balanced protein force fields.

Amino-acid-dependent main-chain torsion-energy terms for protein systems

Many commonly used force fields for protein systems such as AMBER, CHARMM, GROMACS, OPLS, and ECEPP have amino-acid-independent force-field parameters for main-chain torsion-energy terms. Here, we propose a new type of amino-acid-dependent torsion-energy terms in the force fields. As an example, we applied this approach to AMBER ff03 force field and determined new amino-acid-dependent parameters for ψ (N-C(α)-C-N) and ζ (C(β)-C(α)-C-N) angles for each amino acid by using our optimization method, which is one of the knowledge-based approach. In order to test the validity of the new force-field parameters, we then performed folding simulations of α-helical and β-hairpin peptides, using the optimized force field. The results showed that the new force-field parameters gave structures more consistent with the experimental implications than the original AMBER ff03 force field.

A coupled two-dimensional main chain torsional potential for protein dynamics: generation and implementation

Main chain torsions of alanine dipeptide are parameterized into coupled 2-dimensional Fourier expansions based on quantum mechanical (QM) calculations at M06 2X/aug-cc-pvtz//HF/6-31G** level. Solvation effect is considered by employing polarizable continuum model. Utilization of the M06 2X functional leads to precise potential energy surface that is comparable to or even better than MP2 level, but with much less computational demand. Parameterization of the 2D expansions is against the full main chain torsion space instead of just a few low energy conformations. This procedure is similar to that for the development of AMBER03 force field, except unique weighting factor was assigned to all the grid points. To avoid inconsistency between quantum mechanical calculations and molecular modeling, the model peptide is further optimized at molecular mechanics level with main chain dihedral angles fixed before the calculation of the conformational energy on molecular mechanical level at each grid point, during which generalized Born model is employed. Difference in solvation models at quantum mechanics and molecular mechanics levels makes this parameterization procedure less straightforward. All force field parameters other than main chain torsions are taken from existing AMBER force field. With this new main chain torsion terms, we have studied the main chain dihedral distributions of ALA dipeptide and pentapeptide in aqueous solution. The results demonstrate that 2D main chain torsion is effective in delineating the energy variation associated with rotations along main chain dihedrals. This work is an implication for the necessity of more accurate description of main chain torsions in the future development of ab initio force field and it also raises a challenge to the development of quantum mechanical methods, especially the quantum mechanical solvation models.

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.

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, α_A and α_B. 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, α_A and α_B exhibited a nascent helix propensity; the propensity of α_A was stronger than that of α_B, which agrees with experimental results. In the bound state, the free-energy landscape of α_B involved two low free-energy fractions: native-like and non-native fractions. This result suggests that α_B folds according to the induced-fit mechanism. The α_B-helix direction was well aligned as in the NMR complex structure, although the α_A helix exhibited high flexibility. These results also agree quantitatively with experimental observations. We have detected that the α_B 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.

A free-energy landscape for coupled folding and binding of an intrinsically disordered protein in explicit solvent from detailed all-atom computations

The N-terminal repressor domain of neural restrictive silencer factor (NRSF) is an intrinsically disordered protein (IDP) that binds to the paired amphipathic helix (PAH) domain of mSin3. An NMR experiment revealed that the minimal binding unit of NRSF is a 15-residue segment that adopts a helical structure upon binding to a cleft of mSin3. We computed a free-energy landscape of this system by an enhanced conformational sampling method, all-atom multicanonical molecular dynamics. The simulation started from a configuration where the NRSF segment was fully disordered and distant from mSin3 in explicit solvent. In the absence of mSin3, the disordered NRSF segment thermally fluctuated between hairpins, helices, and bent structures. In the presence of mSin3, the segment bound to mSin3 by adopting the structures involved in the isolated state, and non-native and native complexes were formed. The free-energy landscape comprised three superclusters, and free-energy barriers separated the superclusters. The native complex was located at the center of the lowest free-energy cluster. When NRSF landed in the largest supercluster, the generated non-native complex moved on the landscape to fold into the native complex, by increasing the interfacial hydrophobic contacts and the helix content. When NRSF landed in other superclusters, the non-native complex overcame the free-energy barriers between the various segment orientations in the binding cleft of mSin3. Both population-shift and induced-fit (or induced-folding) mechanisms work cooperatively in the coupled folding and binding. The diverse structural adaptability of NRSF may be related to the hub properties of the IDP.

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.

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.