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.
The hydration structure of human lysozyme was studied with cryogenic X-ray diffraction experiment and molecular dynamics simulations. The crystal structure analysis at a resolution of 1.4 A provided 405 crystal water molecules around the enzyme. In the simulations at 300 K, the crystal structure was immersed in explicit water molecules. We examined correlations between crystal water sites and two physical quantities calculated from the 1-ns simulation trajectories: the solvent density reflecting the time-averaged distribution of water molecules, and the solvent dipole measuring the orientational ordering of water molecules around the enzyme. The local high solvent density sites were consistent with the crystal water sites, and better correlation was observed around surface residues with smaller conformational fluctuations during the simulations. Solvent dipoles around those sites exhibited coherent and persistent ordering, indicating that the hydration water molecules at the crystal water sites were highly oriented through the interactions with hydrophilic residues. Those water molecules restrained the orientational motions of adjoining water molecules and induced a solvent dipole field, which was persistent during the simulations around the enzyme. The coherent ordering was particularly prominent in and around the active site cleft of the enzyme. Because the ordering was significant up to the third to fourth solvent layer region from the enzyme surface, the coherently ordered solvent dipoles likely contributed to the molecular recognition of the enzyme in a long-distance range. The present work may provide a new approach combining computational and the experimental studies to understand protein hydration.
We report a new phenomenon, size-dependent separation of colloidal particles in two-dimensional (2D) convective self-assembly that takes place in a wetting liquid film on a mercury surface [Two-dimensional (2D) convective assembly (Nagayama,K. Phase Transition 1993,45,185)]. During the drying of suspensions of colloidal particles in wetting films, homogeneously mixed particles in the suspensions separated and assembled according to their size. In this size-dependent separation of particles, large particles gathered in the center and were surrounded by small particles. To obtain a better understanding of this new phenomenon, we performed experiments on the convective assembly of particles on a mercury surface using binary mixtures of particles that ranged in size from 144 to 12 nm in diameter. To study the mechanism of this size-dependent separation, we also did computer simulations in which we accounted for two types of assembly forces, lateral capillary force and convective flow, that we have been extensively studying in actual assembly systems. The simulations successfully reproduced a size-dependent separation of particles that was identical to that for the actual assembly systems. From the results of our experiments and simulations, we found that the mechanism that was concluded for the convective assembly also governs the size-dependent separation of particles in the actual assembly systems.
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.
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.
We propose a novel generalized ensemble method, a virtual-system coupled multicanonical molecular dynamics (V-McMD), to enhance conformational sampling of biomolecules expressed by an all-atom model in an explicit solvent. In this method, a virtual system, of which physical quantities can be set arbitrarily, is coupled with the biomolecular system, which is the target to be studied. This method was applied to a system of an Endothelin-1 derivative, KR-CSH-ET1, known to form an antisymmetric homodimer at room temperature. V-McMD was performed starting from a configuration in which two KR-CSH-ET1 molecules were mutually distant in an explicit solvent. The lowest freeenergy state (the most thermally stable state) at room temperature coincides with the experimentally determined native complex structure. This state was separated to other non-native minor clusters by a free-energy barrier, although the barrier disappeared with elevated temperature.
We present a molecular dynamics study of the R-helix formation in a system consisting of a 15-residue poly(L-alanine) and surrounding water molecules. By applying a relatively high temperature, we observed the R-helix formation several times during a 17-ns run, and reversible helix-coil transitions were also observed. The R-helix formations were usually initiated by the -turn structures. A crank-shaft-like motion of the peptide was included in the folding process. In the formed R-helical domains, substantial 3 10 -helix formations were found especially at the termini, as observed by the NMR study. The folding time scale at room temperature estimated from our simulation was found to lie in the range of 100 ns, which is in accord with the time scale of the T-jump experiments. The total energy of the whole system was lower in the R-helix state than in the random-coil state by 20.4 ( 4.8 kcal/mol, which is consistent with the experimental value obtained by calorimetry. This energy decrease in forming the R-helix was mainly caused by the Coulombic energy and the torsional energy.
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