Conserved gatekeeper methionine regulates the binding and access of kinase inhibitors to ATP sites of MAP2K1, 4, and 7: Clues for developing selective inhibitors.

Mitogen-activated protein kinase kinases (MAP2Ks) 1, 4, and 7 are potential targets for treating various diseases. Here, we solved the crystal structures of MAP2K1 and MAP2K4 complexed with covalent inhibitor 5Z-7-oxozeaenol (5Z7O). The elucidated structures showed that 5Z7O was non-covalently bound to the ATP binding site of MAP2K4, while it covalently attached to cysteine at the DFG-1 position of the deep ATP site of MAP2K1. In contrast, we previously showed that 5Z7O covalently binds to MAP2K7 via another cysteine on the solvent-accessible edge of the ATP site. Structural analyses and molecular dynamics calculations indicated that the configuration and mobility of conserved gatekeeper methionine located at the central ATP site regulated the binding and access of 5Z7O to the ATP site of MAP2Ks. These structural features provide clues for developing highly potent and selective inhibitors against MAP2Ks. Abbreviations: ATP, adenosine triphosphate; FDA, Food and Drug Administration; MAP2Ks, mitogen-activated protein kinase kinases; MD, molecular dynamics; NSCLC, non-small cell lung cancer; 5Z7O, 5Z-7-oxozeaenol; PDB, protein data bank; RMSD, root-mean-square deviation.

A cutoff-based method with charge-distribution-data driven pair potentials for efficiently estimating electrostatic interactions in molecular systems.

We introduce a simple cutoff-based method for precise electrostatic energy calculations in the molecular dynamics (MD) simulations of point-particle systems. Our method employs a theoretically derived smooth pair potential function to define electrostatic energy, offering stability and computational efficiency in MD simulations. Instead of imposing specific physical conditions, such as dielectric environments or charge neutrality, we focus on the relationship represented by a single summation formula of charge-weighted pair potentials. This approach allows an accurate energy approximation for each particle, enabling a straightforward error analysis. The resulting particle-dependent pair potential captures the charge distribution information, making it suitable for heterogeneous systems and ensuring an enhanced accuracy through distant information inclusion. Numerical investigations of the Madelung constants of crystalline systems validate the method's accuracy.

Binding and Unbinding Pathways of Peptide Substrates on the SARS-CoV-2 3CL Protease.

Based on many crystal structures of ligand complexes, much study has been devoted to understanding the molecular recognition of SARS-CoV-2 3C-like protease (3CLpro), a potent drug target for COVID-19. In this research, to extend this present static view, we examined the kinetic process of binding/unbinding of an eight-residue substrate peptide to/from 3CLpro by evaluating the path ensemble with the weighted ensemble simulation. The path ensemble showed the mechanism of how a highly flexible peptide folded into the bound form. At the early stage, the dominant motion was the diffusion on the protein surface showing a broad distribution, whose center was led into the cleft of the chymotrypsin fold. We observed a definite sequential formation of the hydrogen bonds at the later stage occurring in the cleft, initiated between Glu166 (3CLpro) and P3_Val (peptide), followed by binding to the oxyanion hole and completed by the sequence-specific recognition at P1_Gln.

Functional dynamics of SARS-CoV-2 3C-like protease as a member of clan PA.

SARS-CoV-2 3C-like protease (3CLpro), a potential therapeutic target for COVID-19, consists of a chymotrypsin fold and a C-terminal α-helical domain (domain III), the latter of which mediates dimerization required for catalytic activation. To gain further understanding of the functional dynamics of SARS-CoV-2 3CLpro, this review extends the scope to the comparative study of many crystal structures of proteases having the chymotrypsin fold (clan PA of the MEROPS database). First, the close correspondence between the zymogen-enzyme transformation in chymotrypsin and the allosteric dimerization activation in SARS-CoV-2 3CLpro is illustrated. Then, it is shown that the 3C-like proteases of family Coronaviridae (the protease family C30), which are closely related to SARS-CoV-2 3CLpro, have the same homodimeric structure and common activation mechanism via domain III mediated dimerization. The survey extended to order Nidovirales reveals that all 3C-like proteases belonging to Nidovirales have domain III, but with various chain lengths, and 3CLpro of family Mesoniviridae (family C107) has the same homodimeric structure as that of C30, even though they have no sequence similarity. As a reference, monomeric 3C proteases belonging to the more distant family Picornaviridae (family C3) lacking domain III are compared with C30, and it is shown that the 3C proteases are rigid enough to maintain their structures in the active state. Supplementary Information: The online version contains supplementary material available at 10.1007/s12551-022-01020-x.

Structures and mechanisms of actin ATP hydrolysis.

The major cytoskeleton protein actin undergoes cyclic transitions between the monomeric G-form and the filamentous F-form, which drive organelle transport and cell motility. This mechanical work is driven by the ATPase activity at the catalytic site in the F-form. For deeper understanding of the actin cellular functions, the reaction mechanism must be elucidated. Here, we show that a single actin molecule is trapped in the F-form by fragmin domain-1 binding and present their crystal structures in the ATP analog-, ADP-Pi-, and ADP-bound forms, at 1.15-Å resolutions. The G-to-F conformational transition shifts the side chains of Gln137 and His161, which relocate four water molecules including W1 (attacking water) and W2 (helping water) to facilitate the hydrolysis. By applying quantum mechanics/molecular mechanics calculations to the structures, we have revealed a consistent and comprehensive reaction path of ATP hydrolysis by the F-form actin. The reaction path consists of four steps: 1) W1 and W2 rotations; 2) PG-O3B bond cleavage; 3) four concomitant events: W1-PO3- formation, OH- and proton cleavage, nucleophilic attack by the OH- against PG, and the abstracted proton transfer; and 4) proton relocation that stabilizes the ADP-Pi-bound F-form actin. The mechanism explains the slow rate of ATP hydrolysis by actin and the irreversibility of the hydrolysis reaction. While the catalytic strategy of actin ATP hydrolysis is essentially the same as those of motor proteins like myosin, the process after the hydrolysis is distinct and discussed in terms of Pi release, F-form destabilization, and global conformational changes.

Molecular basis of ubiquitin-specific protease 8 autoinhibition by the WW-like domain.

Ubiquitin-specific protease 8 (USP8) is a deubiquitinating enzyme involved in multiple membrane trafficking pathways. The enzyme activity is inhibited by binding to 14-3-3 proteins. Mutations in the 14-3-3-binding motif in USP8 are related to Cushing's disease. However, the molecular basis of USP8 activity regulation remains unclear. This study identified amino acids 645-684 of USP8 as an autoinhibitory region, which might interact with the catalytic USP domain, as per the results of pull-down and single-molecule FRET assays performed in this study. In silico modelling indicated that the region forms a WW-like domain structure, plugs the catalytic cleft, and narrows the entrance to the ubiquitin-binding pocket. Furthermore, 14-3-3 inhibited USP8 activity partly by enhancing the interaction between the WW-like and USP domains. These findings provide the molecular basis of USP8 autoinhibition via the WW-like domain. Moreover, they suggest that the release of autoinhibition may underlie Cushing's disease due to USP8 mutations.

Allosteric Regulation of 3CL Protease of SARS-CoV-2 and SARS-CoV Observed in the Crystal Structure Ensemble.

The 3C-like protease (3CLpro) of SARS-CoV-2 is a potential therapeutic target for COVID-19. Importantly, it has an abundance of structural information solved as a complex with various drug candidate compounds. Collecting these crystal structures (83 Protein Data Bank (PDB) entries) together with those of the highly homologous 3CLpro of SARS-CoV (101 PDB entries), we constructed the crystal structure ensemble of 3CLpro to analyze the dynamic regulation of its catalytic function. The structural dynamics of the 3CLpro dimer observed in the ensemble were characterized by the motions of four separate loops (the C-loop, E-loop, H-loop, and Linker) and the C-terminal domain III on the rigid core of the chymotrypsin fold. Among the four moving loops, the C-loop (also known as the oxyanion binding loop) causes the order (active)-disorder (collapsed) transition, which is regulated cooperatively by five hydrogen bonds made with the surrounding residues. The C-loop, E-loop, and Linker constitute the major ligand binding sites, which consist of a limited variety of binding residues including the substrate binding subsites. Ligand binding causes a ligand size dependent conformational change to the E-loop and Linker, which further stabilize the C-loop via the hydrogen bond between the C-loop and E-loop. The T285A mutation from SARS-CoV 3CLpro to SARS-CoV-2 3CLpro significantly closes the interface of the domain III dimer and allosterically stabilizes the active conformation of the C-loop via hydrogen bonds with Ser1 and Gly2; thus, SARS-CoV-2 3CLpro seems to have increased activity relative to that of SARS-CoV 3CLpro.

Multiscale Enhanced Sampling Using Machine Learning.

Multiscale enhanced sampling (MSES) allows for an enhanced sampling of all-atom protein structures by coupling with the accelerated dynamics of the associated coarse-grained (CG) model. In this paper, we propose an MSES extension to replace the CG model with the dynamics on the reduced subspace generated by a machine learning approach, the variational autoencoder (VAE). The molecular dynamic (MD) trajectories of the ribose-binding protein (RBP) in both the closed and open forms were used as the input by extracting the inter-residue distances as the structural features in order to train the VAE model, allowing the encoded latent layer to characterize the difference in the structural dynamics of the closed and open forms. The interpolated data characterizing the RBP structural change in between the closed and open forms were thus efficiently generated in the low-dimensional latent space of the VAE, which was then decoded into the time-series data of the inter-residue distances and was useful for driving the structural sampling at an atomistic resolution via the MSES scheme. The free energy surfaces on the latent space demonstrated the refinement of the generated data that had a single basin into the simulated data containing two closed and open basins, thus illustrating the usefulness of the MD simulation together with the molecular mechanics force field in recovering the correct structural ensemble.

Flexibility and Cell Permeability of Cyclic Ras-Inhibitor Peptides Revealed by the Coupled Nosé-Hoover Equation.

Quantifying the cell permeability of cyclic peptides is crucial for their rational drug design. However, the reasons remain unclear why a minor chemical modification, such as the difference between Ras inhibitors cyclorasin 9A5 and 9A54, can substantially change a peptide's permeability. To address this question, we performed enhanced sampling simulations of these two 11-mer peptides using the coupled Nosé-Hoover equation (cNH) we recently developed. The present cNH simulations realized temperature fluctuations over a wide range (240-600 K) in a dynamic manner, allowing structural samplings that were well validated by nuclear Overhauser effect measurements. The derived structural ensembles were comprehensively analyzed by all-atom structural clustering, mapping the derived clusters onto principal components (PCs) that characterize the cyclic structure, and calculating cluster-dependent geometric and chemical properties. The planar-open conformation was dominant in aqueous solvent, owing to inclusion of the Trp side chain in the main-chain ring, while the compact-closed conformation, which favors cell permeation due to its compactness and high polarity, was also accessible. Conformation-dependent cell permeability was observed in one of the derived PCs, demonstrating that decreased cell permeability in 9A54 is due to the high free energy barrier separating the two conformations. The origin of the change in free energy surface was determined to be loss of flexibility in the modified residues 2-3, resulting from the increased bulkiness of their side chains. The derived molecular mechanism of cell permeability highlights the significance of complete structural dynamics surveys for accelerating drug development with cyclic peptides.

Path Ensembles for Pin1-Catalyzed Cis-Trans Isomerization of a Substrate Calculated by Weighted Ensemble Simulations.

Pin1 enzyme protein recognizes specifically phosphorylated serine/threonine (pSer/pThr) and catalyzes the slow interconversion of the peptidyl-prolyl bond between cis and trans forms. Structural dynamics between the cis and trans forms are essential to reveal the underlying molecular mechanism of the catalysis. In this study, we apply the weighted ensemble (WE) simulation method to obtain comprehensive path ensembles for the Pin1-catalyzed isomerization process. Associated rate constants for both cis-to-trans and trans-to-cis isomerization are calculated to be submicroseconds time scales, which are in good agreement with the calculated free energy landscape where the cis form is slightly less favorable. The committor-like analysis indicates the shift of the transition state toward trans form (at the isomerization angle ω ∼ 110°) compared to the intrinsic position for the isolated substrate (ω ∼ 90°). The calculated structural ensemble clarifies a role of both the dual-histidine motif, His59/His157, and the basic residues, Lys63/Arg68/Arg69, to anchor both sides of the peptidyl-prolyl bond, the aromatic ring in Pro, and the phosphate in pSer, respectively. The rotation of the torsion angle is found to be facilitated by relaying the hydrogen-bond partner of the main-chain oxygen in pSer from Cys113 in the cis form to Arg68 in the trans form, through Ser154 at the transition state, which is really the cause of the shift in the transition state. The role of Ser154 as a driving force of the isomerization is confirmed by additional WE and free energy calculations for S154A mutant where the isomerization takes place slightly slower and the free energy barrier increases through the mutation. The present study shows the usefulness of the WE simulation for substantial path samplings between the reactant and product states, unraveling the molecular mechanism of the enzyme catalysis.

Inter-lobe Motions Allosterically Regulate the Structure and Function of EGFR Kinase.

Protein kinases play important roles in cellular signaling and have been one of the best-studied drug targets. The kinase domain of epidermal growth factor receptor (EGFR) is a receptor tyrosine kinase that has been extensively studied for cancer drug discovery and for understanding the unique activation mechanism by dimerization. Here, we analyzed all available 206 crystal structures of the EGFR kinase and the dynamics observed in molecular simulations to identify how these structures are determined. It was found that the arrangement between the N- and C-terminal lobes plays a key role in regulating the kinase structure by sensitively responding to the intermolecular interactions, or the crystal environment. A whole variety of crystal forms in the database is thus reflected in the broad distribution of the inter-lobe arrangement. The configuration of the catalytically important motifs as well as the bound ATP is closely coupled with the inter-lobe motion. When the intermolecular interactions are those of the activating asymmetric dimer, EGFR kinase takes the open-lobe arrangement that constructs the catalytically active configuration.

Allosteric response to ligand binding: Molecular dynamics study of the N-terminal domains in IP 3 receptor.

Inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) is a huge tetrameric intracellular Ca2+ channel that mediates cytoplasmic Ca2+ signaling. The structural basis of the gating in IP3R has been studied by X-ray crystallography and cryo-electron microscopy, focusing on the domain rearrangements triggered by IP3 binding. Here, we conducted molecular dynamics (MD) simulations of the three N-terminal domains of IP3R responsible for IP3 binding (IBC/SD; two domains of the IP3 binding core, IBCß and IBCα, and suppressor domain, SD) as a model system to study the initial gating stage. The response upon removal of IP3 from the IP3-bound form of IBC/SD was traced in MD trajectories. The two IBC domains showed an immediate response of opening after removal of IP3, and SD showed a simultaneous opening motion indicating a tight dynamic coupling with IBC. However, when IBC remained in a more closed form, the dynamic coupling broke and SD exhibited a more amplified closing motion independently of IBC. This amplified SD motion was caused by the break of connection between SD and IBCß at the hinge region, but was suppressed in the native tetrameric state. The analyses using Motion Tree and the linear response theory clarified that in the open form, SD and IBCα moved collectively relative to IBCß with a response upon IP3 binding within the linear regime, whereas in the closed form, such collectiveness disappeared. These results suggest that the regulation of dynamics via the domain arrangement and multimerization is requisite for large-scale allosteric communication in IP3R gating machinery.

Dynamic recognition and linkage specificity in K63 di-ubiquitin and TAB2 NZF domain complex.

Poly-ubiquitin (poly-Ub) is involved in various cellular processes through the linkage-specific recognition of Ub-binding domains (UBD). In this study, using molecular dynamics (MD) simulation together with an enhanced sampling method, we demonstrated that K63-linked di-Ub recognizes the NZF domain of TAB2, a zinc finger UBD, in an ensemble of highly dynamic structures that form from the weak interactions between UBD and the flexible linker connecting the two Ubs. However, the K63 di-Ub/TAB2 NZF complex showed a much more compact and stable ensemble than the non-native complexes, linear di-Ub/TAB2 NZF and K33 di-Ub/TAB2 NZF, that were modeled from linear di-Ub/HOIL-1L NZF and K33 di-Ub/TRABID NZF1, respectively. We further demonstrated the importance of the length and position of the Ub-Ub linker in the results of MD simulations of K63 di-Ub/TAB2 NZF by changing the Ub linkage from the native K63 to four different non-native linkages, linear, K6, K11, and K48, while maintaining inter-molecular contacts in the native complex. No systems with non-native linkage maintained the native binding configuration. These simulation results provide an atomistic picture of the linkage specific recognition of poly-Ubs leading to the biological functions such as cellular colocalization of various component proteins in the signal transduction pathways.

Conformational change of a biomolecule studied by the weighted ensemble method: Use of the diffusion map method to extract reaction coordinates.

We simulate the nonequilibrium ensemble dynamics of a biomolecule using the weighted ensemble method, which was introduced in molecular dynamics simulations by Huber and Kim and further developed by Zuckerman and co-workers. As the order parameters to characterize its conformational change, we here use the coordinates derived from the diffusion map (DM) method, one of the manifold learning techniques. As a concrete example, we study the kinetic properties of a small peptide, chignolin in explicit water, and calculate the conformational change between the folded and misfolded states in a nonequilibrium way. We find that the transition time scales thus obtained are comparable to those using previously employed hydrogen-bond distances as the order parameters. Since the DM method only uses the 3D Cartesian coordinates of a peptide, this shows that the DM method can extract the important distance information of the peptide without relying on chemical intuition. The time scales are compared well with the previous results using different techniques, non-Markovian analysis and core-set milestoning for a single long trajectory. We also find that the most significant DM coordinate turns out to extract a dihedral angle of glycine, and the previously studied relaxation modes are well correlated with the most significant DM coordinates.

Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques-Searching for Mechanism and Kinetics of Biomolecular Functions.

To understand functions of biomolecules such as proteins, not only structures but their conformational change and kinetics need to be characterized, but its atomistic details are hard to obtain both experimentally and computationally. Here, we review our recent computational studies using novel enhanced sampling techniques for conformational sampling of biomolecules and calculations of their kinetics. For efficiently characterizing the free energy landscape of a biomolecule, we introduce the multiscale enhanced sampling method, which uses a combined system of atomistic and coarse-grained models. Based on the idea of Hamiltonian replica exchange, we can recover the statistical properties of the atomistic model without any biases. We next introduce the string method as a path search method to calculate the minimum free energy pathways along a multidimensional curve in high dimensional space. Finally we introduce novel methods to calculate kinetics of biomolecules based on the ideas of path sampling: one is the Onsager⁻Machlup action method, and the other is the weighted ensemble method. Some applications of the above methods to biomolecular systems are also discussed and illustrated.

Multiscale enhanced sampling of glucokinase: Regulation of the enzymatic reaction via a large scale domain motion.

Enhanced sampling yields a comprehensive structural ensemble or a free energy landscape, which is beyond the capability of a conventional molecular dynamics simulation. Our recently developed multiscale enhanced sampling (MSES) method employs a coarse-grained model coupled with the target physical system for the efficient acceleration of the dynamics. MSES has demonstrated applicability to large protein systems in solution, such as intrinsically disordered proteins and protein-protein and protein-ligand interactions. Here, we applied the MSES simulation to an important drug discovery target, glucokinase (GCK), to elucidate the structural basis of the positive cooperativity of the enzymatic reaction at an atomistic resolution. MSES enabled us to compare two sets of the free energy landscapes of GCK, for the glucose-bound and glucose-unbound forms, and thus demonstrated the drastic change of the free energy surface depending on the glucose concentration. In the glucose-bound form, we found two distinct basins separated by a high energy barrier originating from the domain motion and the folding/unfolding of the α13 helix. By contrast, in the glucose-unbound form, a single flat basin extended to the open and super-open states. These features illustrated the two distinct phases achieving the cooperativity, the fast reaction cycle staying in the closed state at a high glucose concentration and the slow cycle primarily in the open/super-open state at a low concentration. The weighted ensemble simulations revealed the kinetics of the structural changes in GCK with the synergetic use of the MSES results; the rate constant of the transition between the closed state and the open/super-open states, kC/O = 1.1 ms-1, is on the same order as the experimental catalytic rate, kcat = 0.22 ms-1. Finally, we discuss the pharmacological activities of GCK activators (small molecular drugs modulating the GCK activity) in terms of the slight changes in the domain motion, depending on their chemical structures as regulators. The present study demonstrated the capability of the enhanced sampling and the associated kinetic calculations for understanding the atomistic structural dynamics of protein systems in physiological environments.

Energetics and conformational pathways of functional rotation in the multidrug transporter AcrB.

The multidrug transporter AcrB transports a broad range of drugs out of the cell by means of the proton-motive force. The asymmetric crystal structure of trimeric AcrB suggests a functionally rotating mechanism for drug transport. Despite various supportive forms of evidence from biochemical and simulation studies for this mechanism, the link between the functional rotation and proton translocation across the membrane remains elusive. Here, calculating the minimum free energy pathway of the functional rotation for the complete AcrB trimer, we describe the structural and energetic basis behind the coupling between the functional rotation and the proton translocation at atomic resolution. Free energy calculations show that protonation of Asp408 in the transmembrane portion of the drug-bound protomer drives the functional rotation. The conformational pathway identifies vertical shear motions among several transmembrane helices, which regulate alternate access of water in the transmembrane as well as peristaltic motions that pump drugs in the periplasm.

Structure of the Dnmt1 Reader Module Complexed with a Unique Two-Mono-Ubiquitin Mark on Histone H3 Reveals the Basis for DNA Methylation Maintenance.

The proper location and timing of Dnmt1 activation are essential for DNA methylation maintenance. We demonstrate here that Dnmt1 utilizes two-mono-ubiquitylated histone H3 as a unique ubiquitin mark for its recruitment to and activation at DNA methylation sites. The crystal structure of the replication foci targeting sequence (RFTS) of Dnmt1 in complex with H3-K18Ub/23Ub reveals striking differences to the known ubiquitin-recognition structures. The two ubiquitins are simultaneously bound to the RFTS with a combination of canonical hydrophobic and atypical hydrophilic interactions. The C-lobe of RFTS, together with the K23Ub surface, also recognizes the N-terminal tail of H3. The binding of H3-K18Ub/23Ub results in spatial rearrangement of two lobes in the RFTS, suggesting the opening of its active site. Actually, incubation of Dnmt1 with H3-K18Ub/23Ub increases its catalytic activity in vitro. Our results therefore shed light on the essential role of a unique ubiquitin-binding module in DNA methylation maintenance.

Free-Energy Landscape of Protein-Ligand Interactions Coupled with Protein Structural Changes.

Protein-ligand interactions are frequently coupled with protein structural changes. Focusing on the coupling, we present the free-energy surface (FES) of the ligand-binding process for glutamine-binding protein (GlnBP) and its ligand, glutamine, in which glutamine binding accompanies large-scale domain closure. All-atom simulations were performed in explicit solvents by multiscale enhanced sampling (MSES), which adopts a multicopy and multiscale scheme to achieve enhanced sampling of systems with a large number of degrees of freedom. The structural ensemble derived from the MSES simulation yielded the FES of the coupling, described in terms of both the ligand's and protein's degrees of freedom at atomic resolution, and revealed the tight coupling between the two degrees of freedom. The derived FES led to the determination of definite structural states, which suggested the dominant pathways of glutamine binding to GlnBP: first, glutamine migrates via diffusion to form a dominant encounter complex with Arg75 on the large domain of GlnBP, through strong polar interactions. Subsequently, the closing motion of GlnBP occurs to form ligand interactions with the small domain, finally completing the native-specific complex structure. The formation of hydrogen bonds between glutamine and the small domain is considered to be a rate-limiting step, inducing desolvation of the protein-ligand interface to form the specific native complex. The key interactions to attain high specificity for glutamine, the "door keeper" existing between the two domains (Asp10-Lys115) and the "hydrophobic sandwich" formed between the ligand glutamine and Phe13/Phe50, have been successfully mapped on the pathway derived from the FES.

Coupled Nosé-Hoover equations of motion to implement a fluctuating heat-bath temperature.

The Nosé-Hoover (NH) equation provides a universal and powerful computer simulation protocol to realize an equilibrium canonical temperature for a target physical system. Here we demonstrate a general formalism to couple such NH equations. We provide a coupled NH equation that is constructed by coupling the NH equation of a target physical system and the NH equation of a temperature system. Thus, in contrast to the conventional single NH equation, the heat-bath temperature is a dynamical variable. The temperature fluctuations are not ad hoc, but instead are generated by the newly defined temperature system, and the statistical distribution of the temperature is completely described with an arbitrarily given probability function. The current equations of motion thus describe the physical system that develops with a predistributed fluctuating temperature, which allows enhanced sampling of the physical system. Since the total system is governed by a prescribed distribution, the equilibrium of the physical system is also reconstructed by reweighting. We have formulated a scheme for specifically setting the distribution of the dynamical inverse temperature and demonstrate the statistical relationship between the dynamical and physical temperatures. The statistical features, dynamical properties, and sampling abilities of the current method are demonstrated via the distributions, trajectories, dynamical correlations, and free energy landscapes for both a model system and a biomolecular system. These results indicated that the current coupled NH scheme works well.