Atomistic detailed free‐energy landscape of intrinsically disordered protein studied by multi‐scale divide‐and‐conquer molecular dynamics simulation

Calcineurin (CaN) is a eukaryotic serine/threonine protein phosphatase activated by both Ca²⁺ and calmodulin (CaM), including intrinsically disordered region (IDR). The region undergoes folding into an α‐helix form in the presence Ca²⁺‐loaded CaM. To sample the ordered structure of the IDR by conventional all atom model (AAM) molecular dynamics (MD) simulation, the IDR and Ca²⁺‐loaded CaM must be simultaneously treated. However, it is time‐consuming task because the coupled folding and binding should include repeated binding and dissociation. Then, in this study, we propose novel multi‐scale divide‐and‐conquer MD (MSDC‐MD), which combines AAM‐MD and coarse‐grained model MD (CGM‐MD). To speed up the conformation sampling, MSDC‐MD simulation first treats the IDR by CGM to sample conformations from wide conformation space; then, multiple AAM‐MD in a limited area is initiated using the resultant CGM conformation, which is reconstructed by homology modeling method. To investigate performance, we sampled the ordered conformation of the IDR using MSDC‐MD; the root‐mean‐square distance (RMSD) with respect to the experimental structure was 2.23 Å.     

Deprotonation of solvated formic acid: Car-Parrinello and metadynamics simulations

The deprotonation of solvated formic acid was investigated theoretically with ab initio simulations. With the Car-Parrinello method, deprotonation and reprotonation by means of a proton wire were observed. The microscopics of these reactions were analyzed, and reveal the key role played by nearby water molecules in catalyzing the reactions. A constrained molecular dynamics calculation was carried out to estimate the dissociation free energy. Deprotonation of formic acid was further investigated with the recently developed metadynamics method using the formic acid oxygen coordination numbers as the collective variables. The determined free-energy landscape gives barriers similar to that obtained with the constrained free-energy calculation.     

Folding of the 25 residue Abeta(12-36) peptide in TFE/water: temperature-dependent transition from a funneled free-energy landscape to a rugged one

The free-energy landscape of the Alzheimer beta-amyloid peptide Abeta(12-36) in a 40% (v/v) 2,2,2-trifluoroethanol (TFE)/water solution was determined by using multicanonical molecular dynamics simulations. Simulations using this enhanced conformational sampling technique were initiated from a random unfolded polypeptide conformation. Our simulations reliably folded the peptide to the experimental NMR structure, which consists of two linked helices. The shape of the free energy landscape for folding was found to be strongly dependent on temperature: Above 325 K, the overall shape was funnel-like, with the bottom of the funnel coinciding exactly with the NMR structure. Below 325 K, on the other hand, the landscape became increasingly rugged, with the emergence of new conformational clusters connected by low free-energy pathways. Finally, our simulations reveal that water and TFE solvate the polypeptide in different ways: The hydrogen bond formation between TFE and Abeta was enhanced with decreasing temperature, while that between water and Abeta was depressed.     

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.     

Modeling the interplay between geometrical and energetic effects in protein folding

A theoretical framework is constructed with the aid of a free-energy functional method that is capable of describing the interplay between geometrical and energetic effects on protein folding. In this paper, we generalize a free-energy functional model based on polymer theory to make it more appropriate for comparison with protein folding simulations and experiments. This generalization is made by introducing cooperativity into the configurational entropy and the internal energy. Modifications to configurational entropy enable the model to account for the loop-loop interactions, a contribution neglected in the original model. Modifications to the internal energy introduce many-body corrections, which are needed to establish quantitative contact to simulations as well as experimental observations. To demonstrate the efficiency of the modified analytical model, we compare our results with C(alpha) structure-based (Go) model simulations of chymotrypsin inhibitor II and the SH3 domain of src.     

Calculation of free-energy differences and potentials of mean force by a multi-energy gap method

A method is proposed to significantly accelerate the convergence of free-energy calculations. It introduces a bias factor in Monte Carlo simulations or, equivalently, a bias force in molecular dynamics simulations. The bias factor targets the energy gap, i.e., the difference in energy function between two states, and is therefore specifically designed for calculating free-energy differences. The goal is to make the probability density of the energy gap as uniform as possible, thus allowing for its accurate determination. An iterative procedure, based on simulations at higher temperatures, is devised to obtain the bias factor. The same method naturally extends to the calculation of potentials of mean force. The generalized coordinate, for which the potential of mean force is to be calculated, now plays the role of the energy gap. Applications to model systems confirm the expected increase in accuracy of calculated free-energy differences and potentials of mean force.     

Kinetic reconstruction of the free-energy landscape

We present a new general method to trace back a lot of valuable information from direct simulations and experiments of activated processes. In particular, it allows the reconstruction of the free-energy landscape for an arbitrary reaction coordinate directly from the out-of-equilibrium dynamics of the process. We demonstrate the power of this concept by its application to a molecular dynamics simulation of nucleation of a Lennard-Jones vapor. The same method can be also applied to Brownian dynamics and stochastic simulations.     

Free-energy landscape of nucleation with an intermediate metastable phase studied using capillarity approximation

Capillarity approximation is used to study the free-energy landscape of nucleation when an intermediate metastable phase exists. The critical nucleus that corresponds to the saddle point of the free-energy landscape as well as the whole free-energy landscape can be studied using this capillarity approximation, and various scenarios of nucleation and growth can be elucidated. In this study, we consider a model in which a stable solid phase nucleates within a metastable vapor phase when an intermediate metastable liquid phase exists. We predict that a composite critical nucleus that consists of a solid core and a liquid wetting layer as well as pure liquid and pure solid critical nuclei can exist depending not only on the supersaturation of the liquid phase relative to that of the vapor phase but also on the wetting behavior of the liquid surrounding the solid. The existence of liquid critical nucleus indicates that the phase transformation from metastable vapor to stable solid occurs via the intermediate metastable liquid phase, which is quite similar to the scenario of nucleation observed in proteins and colloidal systems. By studying the minimum-free-energy path on the free-energy landscape, we can study the evolution of the composition of solid and liquid within nuclei which is not limited to the critical nucleus.     

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.     

Relationship between macroscopic and microscopic models of surfactant adsorption dynamics at fluid interfaces

In a companion preceding paper, we presented an experimental investigation into the adsorption dynamics of a diblock copolymer surfactant to a polymer/polymer interface and found them to be well-described by a microscopic model of diffusion in a potential generated using self-consistent field theory. We compare the predictions of the microscopic approach with a macroscopic (adsorption-diffusion) model and demonstrate the equivalence of the two models when the free-energy well underlying surfactant adsorption is flanked by barriers that are significantly larger than thermal energy (kT). However, when the energy barriers are nonexistent, as is the case for the experimental system of interest, a finite interfacial width must be introduced into the classical model to obtain physically meaningful results (i.e., nonnegative desorption rates). Surprisingly, we find that the predictions of the macroscopic finite interfacial width model with no adjustable parameters are in excellent agreement with experimental data presented in the companion paper even though the latter was obtained with molecular resolution. This agreement provides insight into aspects of the free-energy landscape that determine surfactant transport.     

The thermal stability of lattice-energy minima of 5-fluorouracil: metadynamics as an aid to polymorph prediction

This paper reports a novel methodology for the free-energy minimization of crystal structures exhibiting strong, anisotropic interactions due to hydrogen bonding. The geometry of the thermally expanded cell was calculated by exploiting the dependence of the free-energy derivatives with respect to cell lengths and angles on the average pressure tensor computed in short molecular dynamics simulations. All dynamic simulations were performed with an elaborate anisotropic potential based on a distributed multipole analysis of the isolated molecule charge density. Changes in structure were monitored via simulated X-ray diffraction patterns. The methodology was used to minimize the free energy at ambient conditions of a set of experimental and hypothetical 5-fluorouracil crystal structures, generated in a search for lattice-energy minima with the same model potential. Our results demonstrate that the majority ( approximately 75%) of lattice-energy minima are thermally stable at ambient conditions, and hence, the free-energy (like the lattice-energy) surface is complex and highly undulating. Metadynamics trajectories (Laio, A.; Parrinello, M. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12562) started from the free-energy minima only produced transitions that preserved the hydrogen-bonding motif, and thus, further developments are needed for this method to efficiently explore such free-energy surfaces. The existence of so many free-energy minima, with large barriers for the alteration of the hydrogen-bonding motif, is consistent with the range of motifs observed in crystal structures of 5-fluorouracil and other 5-substituted uracils.     

Amyloid-beta(29-42) dimer formations studied by a multicanonical-multioverlap molecular dynamics simulation

Amyloid-beta peptides are known to form amyloid fibrils and are considered to play an important role in Alzheimer's disease. Amyloid-beta(29-42) is a fragment of the amyloid-beta peptide and also has a tendency to form amyloid fibrils. In order to study the mechanism of amyloidogenesis of this fragment, we applied one of the generalized-ensemble algorithms, the multicanonical-multioverlap algorithm, to amyloid-beta(29-42) dimer in aqueous solution. We obtained a detailed free-energy landscape of the dimer system. From the detailed free-energy landscape, we examined monomer and dimer formations of amyloid-beta(29-42) and deduced dimerization processes, which correspond to seeding processes in the amyloidogenesis of amyloid-beta(29-42).     

基于QuEChERS-HPLC法检测油炸食品中丙烯酰胺的含量

建立了基于QuEChERS(quick,easy,cheap,effective,rugged and safe)-HPLC测定油炸食品中丙烯酰胺含量的方法。 该方法的优势在于：改进的QuEChERS前处理方法中没有引入有机溶剂而直接采用纯水消除样品基底的影响。 研究中,使用纯水超声提取丙烯酰胺,丙基乙二胺(PSA)吸附剂分散净化提取液,乙腈和水(体积比1∶99)作为流动相,水系C18色谱柱分离,208 nm紫外波长条件下检测丙烯酰胺的含量。 结果表明,丙烯酰胺在0.020~0.800 μg/g浓度范围内与出峰面积呈线性关系,相关系数r=0.9994;检测限为0.005 μg/g;加标回收率为83.96%~89.43%,相对标准偏差(RSD)为2.13%~5.87%。 该方法具有操作简单、快速、可靠和灵敏度高等特点,成功应用于方便面等油炸食品中丙烯酰胺含量的测定。     

Study on the Activity of Constrained Geometry Metallocenes

The activities of a several titanium-based constrained geometry metallocenes (CGM) have been examined with respect to their central-metal net charges. A simple method consisting of a combination of the molecular mechanics and the charge equilibration method was adopted here to determine the structure and the net charge. The results obtained indicate that the net charge on the central-metal of the CGM does dominate the activity. A new CGM, (2,6-dipropylphenylamide) dimethyl (tetramethylcyclopentadienyl) silane titanium dichloride, was synthesized and analyzed.     

A random walk through the dynamics of homogeneous vapor-liquid nucleation

A method of calculating rates of homogeneous vapor-liquid nucleation based on Langevin dynamics of a few relevant degrees of freedom on a free-energy surface is proposed. The surface is obtained here from simulation and from a semi empirical expression. The mass and friction coefficients are derived from atomistic umbrella-sampling molecular-dynamics simulations. The calculated nucleation rate agrees with atomistic simulations for one particular state point of the Lennard-Jones fluid. The present method is about four orders of magnitude more computationally efficient than the direct atomistic simulation of the transmission coefficient.     

Free-energy landscape of alcohol driven coacervation transition in aqueous gelatin solutions

Liquid-liquid phase separation of a homogeneous polyampholyte (gelatin) solution into a dense polymer-rich coacervate and the dilute supernatant phase is discussed through free-energy landscape formalism. We have evaluated the free energy and entropy of the system as it undergoes the phenomenon of simple coacervation, driven by the addition of a nonsolvent. Electrophoretic mobility (mu) and turbidity measurements were performed on 0.01% and 0.05% (w/v) aqueous gelatin solutions that were driven towards coacervation by the addition of ethanol. The mobility of the polyampholyte molecules, which was typically mu approximately 0.38+/-0.02 microm/s cm/V in water, gradually reduced for the soluble intermolecular complexes to a plateau value of mu approximately 0.11+/-0.01 microm/s cm/V as the ethanol volume fraction equaled phi(ns) approximately 0.47+/-0.03, which coincided with the first appearance of coacervate droplets (coacervation transition) observed from turbidity measurements, a behavior found to be invariant of gelatin concentration. These results were used as input to the theoretical model to explicitly construct the free-energy landscape for a single gelatin chain and the global system comprising the polymer-rich coacervate and the dilute supernatant phase.     

Free-energy landscape for beta hairpin folding from combined parallel tempering and metadynamics

We develop a new free-energy method, based on the combination of parallel tempering and metadynamics, and apply this method to the calculation of the free-energy landscape of the folding beta hairpin in explicit water. We show that the combined method greatly improves the performance of both parallel tempering and metadynamics. In particular, we are able to sample the high free-energy regions, which are not accessible with conventional parallel tempering. We use our results to calculate the difference in entropy and enthalpy between the folded and the unfolded state and to characterize the most populated configurations in the relevant free-energy basins.