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

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.

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.

Transferable coarse-grained potential for de novo protein folding and design

Protein folding and design are major biophysical problems, the solution of which would lead to important applications especially in medicine. Here we provide evidence of how a novel parametrization of the Caterpillar model may be used for both quantitative protein design and folding. With computer simulations it is shown that, for a large set of real protein structures, the model produces designed sequences with similar physical properties to the corresponding natural occurring sequences. The designed sequences require further experimental testing. For an independent set of proteins, previously used as benchmark, the correct folded structure of both the designed and the natural sequences is also demonstrated. The equilibrium folding properties are characterized by free energy calculations. The resulting free energy profiles not only are consistent among natural and designed proteins, but also show a remarkable precision when the folded structures are compared to the experimentally determined ones. Ultimately, the updated Caterpillar model is unique in the combination of its fundamental three features: its simplicity, its ability to produce natural foldable designed sequences, and its structure prediction precision. It is also remarkable that low frustration sequences can be obtained with such a simple and universal design procedure, and that the folding of natural proteins shows funnelled free energy landscapes without the need of any potentials based on the native structure.

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.

Folding helical proteins in explicit solvent using dihedral-biased tempering

Using a single-trajectory-based tempering method with a high-temperature dihedral bias, we repeatedly folded four helical proteins [α(3)D (PDB ID: 2A3D, 73 residues), α(3)W (1LQ7, 67 residues), Fap1-NR(α) (2KUB, 81 residues) and S-836 (2JUA, 102 residues)] and some of the mutants in explicit solvent within several microseconds. The lowest root-mean-square deviations of backbone atoms from the experimentally determined structures were 1.9, 1.4, 1.0, and 2.1 Å, respectively. Cluster analyses of folding trajectories showed the native conformation usually occupied the most populated cluster. The simulation protocol can be applied to large-scale simulations of other helical proteins on commonly accessible computing platforms.

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.