Introduction of periodic boundary conditions into UNRES force field

In this article, implementation of periodic boundary conditions (PBC) into physics‐based coarse‐grained UNited RESidue (UNRES) force field is presented, which replaces droplet‐like restraints previously used. Droplet‐like restraints are necessary to keep multichain systems together and prevent them from dissolving to infinitely low concentration. As an alternative for droplet‐like restrains cuboid PBCs with imaging of the molecules were introduced. Owing to this modification, artificial forces which arose from restraints keeping a droplet together were eliminated what leads to more realistic trajectories. Due to computational reasons cutoff and smoothing functions were introduced on the long range interactions. The UNRES force field with PBC was tested by performing microcanonical simulations. Moreover, to asses the behavior of the thermostat in PBCs Langevin and Berendsen thermostats were studied. The influence of PBCs on association pattern was compared with droplet‐like restraints on the ββα hetero tetramer 1 protein system. © 2015 Wiley Periodicals, Inc.     

Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.     

Modification and optimization of the united-residue (UNRES) potential energy function for canonical simulations. I. Temperature dependence of the effective energy function and tests of the optimization method with single training proteins

We report the modification and parametrization of the united-residue (UNRES) force field for energy-based protein structure prediction and protein folding simulations. We tested the approach on three training proteins separately: 1E0L (beta), 1GAB (alpha), and 1E0G (alpha + beta). Heretofore, the UNRES force field had been designed and parametrized to locate native-like structures of proteins as global minima of their effective potential energy surfaces, which largely neglected the conformational entropy because decoys composed of only lowest-energy conformations were used to optimize the force field. Recently, we developed a mesoscopic dynamics procedure for UNRES and applied it with success to simulate protein folding pathways. However, the force field turned out to be largely biased toward -helical structures in canonical simulations because the conformational entropy had been neglected in the parametrization. We applied the hierarchical optimization method, developed in our earlier work, to optimize the force field; in this method, the conformational space of a training protein is divided into levels, each corresponding to a certain degree of native-likeness. The levels are ordered according to increasing native-likeness; level 0 corresponds to structures with no native-like elements, and the highest level corresponds to the fully native-like structures. The aim of optimization is to achieve the order of the free energies of levels, decreasing as their native-likeness increases. The procedure is iterative, and decoys of the training protein(s) generated with the energy function parameters of the preceding iteration are used to optimize the force field in a current iteration. We applied the multiplexing replica-exchange molecular dynamics (MREMD) method, recently implemented in UNRES, to generate decoys; with this modification, conformational entropy is taken into account. Moreover, we optimized the free-energy gaps between levels at temperatures corresponding to a predominance of folded or unfolded structures, as well as to structures at the putative folding-transition temperature, changing the sign of the gaps at the transition temperature. This enabled us to obtain force fields characterized by a single peak in the heat capacity at the transition temperature. Furthermore, we introduced temperature dependence to the UNRES force field; this is consistent with the fact that it is a free-energy and not a potential energy function. beta     

Coarse-grained force field: general folding theory

We review the coarse-grained UNited RESidue (UNRES) force field for the simulations of protein structure and dynamics, which is being developed in our laboratory over the last several years. UNRES is a physics-based force field, the prototype of which is defined as a potential of mean force of polypeptide chains in water, where all the degrees of freedom except the coordinates of α-carbon atoms and side-chain centers have been integrated out. We describe the initial implementation of UNRES to protein-structure prediction formulated as a search for the global minimum of the potential-energy function and its subsequent molecular dynamics and extensions of molecular-dynamics implementation, which enabled us to study protein-folding pathways and thermodynamics, as well as to reformulate the protein-structure prediction problem as a search for the conformational ensemble with the lowest free energy at temperatures below the folding-transition temperature. Applications of UNRES to study biological problems are also described.     

Implementations of Nosé-Hoover and Nosé-Poincaré thermostats in mesoscopic dynamic simulations with the united-residue model of a polypeptide chain

Molecular dynamics (MD) simulations generate a canonical ensemble only when integration of the equations of motion is coupled to a thermostat. Three extended phase space thermostats, one version of Nose-Hoover and two versions of Nose-Poincare, are compared with each other and with the Berendsen thermostat and Langevin stochastic dynamics. Implementation of extended phase space thermostats was first tested on a model Lennard-Jones fluid system; subsequently, they were implemented with our physics-based protein united-residue (UNRES) force field MD. The thermostats were also implemented and tested for the multiple-time-step reversible reference system propagator (RESPA). The velocity and temperature distributions were analyzed to confirm that the proper canonical distribution is generated by each simulation. The value of the artificial mass constant, Q, of the thermostat has a large influence on the distribution of the temperatures sampled during UNRES simulations (the velocity distributions were affected only slightly). The numerical stabilities of all three algorithms were compared with each other and with that of microcanonical MD. Both Nose-Poincare thermostats, which are symplectic, were not very stable for both the Lennard-Jones fluid and UNRES MD simulations started from nonequilibrated structures which implies major changes of the potential energy throughout a trajectory. Even though the Nose-Hoover thermostat does not have a canonical symplectic structure, it is the most stable algorithm for UNRES MD simulations. For UNRES with RESPA, the "extended system inside-reference system propagator algorithm" of the RESPA implementation of the Nose-Hoover thermostat was the only stable algorithm, and enabled us to increase the integration time step.     

Implementation of a symplectic multiple-time-step molecular dynamics algorithm, based on the united-residue mesoscopic potential energy function

A symplectic multiple-time-step (MTS) algorithm has been developed for the united-residue (UNRES) force field. In this algorithm, the slow-varying forces (which contain most of the long-range interactions and are, therefore, expensive to compute) are integrated with a larger time step, termed the basic time step, and the fast-varying forces are integrated with a shorter time step, which is an integral fraction of the basic time step. Based on the split operator formalism, the equations of motion were derived. Separation of the fast- and slow-varying forces leads to stable molecular dynamics with longer time steps. The algorithms were tested with the Ala(10) polypeptide chain and two versions of the UNRES force field: the current one in which the energy components accounting for the energetics of side-chain rotamers (U(rot)) can lead to numerically unstable forces and a modified one in which the the present U(rot) was replaced by a numerically stable expression which, at present, is parametrized only for polyalanine chains. With the modified UNRES potential, stable trajectories were obtained even when extending the basic time step to 15 fs and, with the original UNRES potentials, the basic time step is 1 fs. An adaptive multiple-time-step (A-MTS) algorithm is proposed to handle instabilities in the forces; in this method, the number of substeps in the basic time step varies depending on the change of the magnitude of the acceleration. With this algorithm, the basic time step is 1 fs but the number of substeps and, consequently, the computational cost are reduced with respect to the MTS algorithm. The use of the UNRES mesoscopic energy function and the algorithms derived in this work enables one to increase the simulation time period by several orders of magnitude compared to conventional atomic-resolution molecular dynamics approaches and, consequently, such an approach appears applicable to simulating protein-folding pathways, protein functional dynamics in a real molecular environment, and dynamical molecular recognition processes.     

Design and application of basic amino acids displaying enhanced hydrophobicity

Three noncoding basic amino acids, mono-, di-, and trimethyldiaminopropionic acid (mmdap, dmdap, and tmdap), have been synthesized for use in protein design. Covalent modification of a diaminopropionic acid (dap) side chain with an increasing number of methyl moieties results in a family of residues displaying short basic side chains with varying degrees of enhanced hydrophobic character. These residues may be used to introduce charged/polar interactions into the confining hydrophobic interior or interfacial spaces of proteins. As a demonstration of their utility, the ability of these residues to promote interior salt bridge formation at the helix/helix interface of GCN4-p1, a dimeric two-stranded coiled coil, was assessed. Heterodimerization mediated by buried salt bridge formation between a GCN4-based peptide containing either mmdap, dmdap, or tmdap at position 16 and an analogous peptide containing aspartic acid at the same position was studied. Mmdap-derived heterodimers are 0.5 kcal/mol more stable than the corresponding dap-derived heterodimers. This result indicates that the addition of one methyl group to the dap side chain can stabilize the heterodimeric fold. The stabilization can most likely be attributed to a decrease in the desolvation penalty incurred upon folding as well as enhanced van der Waals contacts in the folded state. The addition of three methyl groups to the dap side chain results in heterodimers that are significantly less stable than the corresponding dap-derived heterodimers, suggesting that increased steric bulk is not well accommodated in the interior of this protein. Unexpectedly, the addition of two methyl groups leads to homotrimerization of the dmdap-peptide. The resulting trimer is relatively stable (DeltaG(37)( degrees )(C) degrees = 11.8 kcal/mol) and undergoes cooperative thermal unfolding. The GCN4-p1 system exemplifies how small incremental changes in size and hydrophobicity can alter the folding preferences of a protein. Generally, this versatile suite of residues can be utilized in any protein and offer new options to the protein chemist.     

Introduction of steered molecular dynamics into UNRES coarse‐grained simulations package

In this article, an implementation of steered molecular dynamics (SMD) in coarse‐grain UNited RESidue (UNRES) simulations package is presented. Two variants of SMD have been implemented: with a constant force and a constant velocity. The huge advantage of SMD implementation in the UNRES force field is that it allows to pull with the speed significantly lower than the accessible pulling speed in simulations with all‐atom representation of a system, with respect to a reasonable computational time. Therefore, obtaining pulling speed closer to those which appear in the atomic force spectroscopy is possible. The newly implemented method has been tested for behavior in a microcanonical run to verify the influence of introduction of artificial constrains on keeping total energy of the system. Moreover, as time dependent artificial force was introduced, the thermostat behavior was tested. The new method was also tested via unfolding of the Fn3 domain of human contactin 1 protein and the I27 titin domain. Obtained results were compared with Gø‐like force field, all‐atom force field, and experimental results. © 2017 Wiley Periodicals, Inc.     

Force field parameters for rotation around chi torsion axis in nucleic acids

To raise the accuracy of the force field for nucleic acids, several parameters were elaborated, focusing on the rotation around chi torsion axis. The reliability of molecular dynamics (MD) simulation was significantly increased by improving the torsion parameters at C8--N9--C1'--X (X = H1', C2', O4') in A, G and those at C6--N1--C1'--X in C, T, and U. In this work, we constructed small models representing the chemical structure of A, G, C, T, and U, and estimated energy profile for chi-axis rotation by executing numerous quantum mechanical (QM) calculations. The parameters were derived by discrete Fourier transformation of the calculated QM data. A comparison in energy profile between molecular mechanical (MM) calculation and QM one shows that our presently derived parameters well reproduce the energy surface of QM calculation for all the above torsion terms. Furthermore, our parameters show a good performance in MD simulations of some nucleic acids. Hence, the present refinement of parameters will enable us to perform more accurate simulations for various types of nucleic acids.     

Optimization of parallel implementation of UNRES package for coarse-grained simulations to treat large proteins

We report major algorithmic improvements of the UNRES package for physics-based coarse-grained simulations of proteins. These include (i) introduction of interaction lists to optimize computations, (ii) transforming the inertia matrix to a pentadiagonal form to reduce computing and memory requirements, (iii) removing explicit angles and dihedral angles from energy expressions and recoding the most time-consuming energy/force terms to minimize the number of operations and to improve numerical stability, (iv) using OpenMP to parallelize those sections of the code for which distributed-memory parallelization involves unfavorable computing/communication time ratio, and (v) careful memory management to minimize simultaneous access of distant memory sections. The new code enables us to run molecular dynamics simulations of protein systems with size exceeding 100,000 amino-acid residues, reaching over 1 ns/day (1 μs/day in all-atom timescale) with 24 cores for proteins of this size. Parallel performance of the code and comparison of its performance with that of AMBER, GROMACS and MARTINI 3 is presented.     

A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations

Molecular mechanics models have been applied extensively to study the dynamics of proteins and nucleic acids. Here we report the development of a third-generation point-charge all-atom force field for proteins. Following the earlier approach of Cornell et al., the charge set was obtained by fitting to the electrostatic potentials of dipeptides calculated using B3LYP/cc-pVTZ//HF/6-31G** quantum mechanical methods. The main-chain torsion parameters were obtained by fitting to the energy profiles of Ace-Ala-Nme and Ace-Gly-Nme di-peptides calculated using MP2/cc-pVTZ//HF/6-31G** quantum mechanical methods. All other parameters were taken from the existing AMBER data base. The major departure from previous force fields is that all quantum mechanical calculations were done in the condensed phase with continuum solvent models and an effective dielectric constant of epsilon = 4. We anticipate that this force field parameter set will address certain critical short comings of previous force fields in condensed-phase simulations of proteins. Initial tests on peptides demonstrated a high-degree of similarity between the calculated and the statistically measured Ramanchandran maps for both Ace-Gly-Nme and Ace-Ala-Nme di-peptides. Some highlights of our results include (1) well-preserved balance between the extended and helical region distributions, and (2) favorable type-II poly-proline helical region in agreement with recent experiments. Backward compatibility between the new and Cornell et al. charge sets, as judged by overall agreement between dipole moments, allows a smooth transition to the new force field in the area of ligand-binding calculations. Test simulations on a large set of proteins are also discussed.     

A class of luminescent cyclometalated alkynylgold(III) complexes: synthesis, characterization, and electrochemical, photophysical, and computational studies of [Au(C=N=C)(C triple bond C-R)] (C=N=C = kappa(3)C,N,C bis-cyclometalated 2,6-diphenylpyridyl)

A new class of luminescent cyclometalated alkynylgold(III) complexes, [Au(RC=N(R')=CR)(CCR' ')], i.e., [Au(C=N=C)(C triple bond CR')] (HC=N=CH = 2,6-diphenylpyridine) R' ' = C6H5 1, C6H4-Cl-p 2, C6H4-NO2-p 3, C6H4-OCH3-p 4, C6H4-NH2-p 5, C6H4-C6H13-p 6, C6H13 7, [Au(tBuC=N=CtBu)(C triple bond CC6H5)] 8 (HtBuC=N=CtBuH = 2,6-bis(4-tert-butylphenyl)pyridine), and [Au(C=NTol=C)(CCC6H4-C6H13-p)] 9 (HC=NTol=CH = 2,6-diphenyl-4-p-tolylpyridine), have been synthesized and characterized. The X-ray crystal structures of most of the complexes have also been determined. Electrochemical studies show that, in general, the first oxidation wave is an alkynyl ligand-centered oxidation, while the first reduction couple is ascribed to a ligand-centered reduction of the cyclometalated ligand with the exception of 3 in which the first reduction couple is assigned as an alkynyl ligand-centered reduction. Their electronic absorption and luminescence behaviors have also been investigated. In dichloromethane solution at room temperature, the low-energy absorption bands are assigned as the pi-pi* intraligand (IL) transition of the cyclometalated RC=N(R')=CR ligand with some mixing of a [pi(C triple bond CR') --> pi*(RC=N(R')=CR)] ligand-to-ligand charge transfer (LLCT) character. The low-energy emission bands of all the complexes, with the exception of 5, are ascribed to origins mainly derived from the pi-pi* IL transition of the cyclometalated RC=N(R')=CR ligand. In the case of 5 that contains an electron-rich amino substituent on the alkynyl ligand, the low-energy emission band was found to show an obvious shift to the red. A change in the origin of emission is evident, and the emission of 5 is tentatively ascribed to a [pi(CCC6H4NH2) --> pi*(C=N=C)] LLCT excited-state origin. DFT and TDDFT computational studies have been performed to verify and elucidate the results of the electrochemical and photophysical studies.     

Exploring the parameter space of the coarse‐grained UNRES force field by random search: Selecting a transferable medium‐resolution force field

We explored the energy‐parameter space of our coarse‐grained UNRES force field for large‐scale ab initio simulations of protein folding, to obtain good initial approximations for hierarchical optimization of the force field with new virtual‐bond‐angle bending and side‐chain‐rotamer potentials which we recently introduced to replace the statistical potentials. 100 sets of energy‐term weights were generated randomly, and good sets were selected by carrying out replica‐exchange molecular dynamics simulations of two peptides with a minimal α‐helical and a minimal β‐hairpin fold, respectively: the tryptophan cage (PDB code: 1L2Y) and tryptophan zipper (PDB code: 1LE1). Eight sets of parameters produced native‐like structures of these two peptides. These eight sets were tested on two larger proteins: the engrailed homeodomain (PDB code: 1ENH) and FBP WW domain (PDB code: 1E0L); two sets were found to produce native‐like conformations of these proteins. These two sets were tested further on a larger set of nine proteins with α or α + β structure and found to locate native‐like structures of most of them. These results demonstrate that, in addition to finding reasonable initial starting points for optimization, an extensive search of parameter space is a powerful method to produce a transferable force field. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Molecular dynamics simulation study of gold nanosheet as drug delivery vehicles for anti-HIV-1 aptamers

The adsorption process of three aptamers with gold nanosheet (GNS) as a drug carrier has been investigated with the help of molecular dynamics simulations. The sequencing of the considered aptamers are as (CUUCAUUGUAACUUCUCAUAAUUUCCCGAGGCUUUUACUUUCGGGGUCCU) and (CCGGGUCGUCCCCUACGGGGACUAAAGACUGUGUCCAACCGCCCUCGCCU) for AP1 and AP2, respectively. AP3 is a muted version of AP1 in which nucleotide positions 4, 6, 18, 28 and 39 have C4A, U6G, A18G, G28A, and U39C mutations. At positions 24, and 40, a deletion mutation is seen to eliminate U24 and U40 bases. These aptamers are inhibitors for HIV-1 protease and can be candidates as potential pharmaceutics for treatment of AIDS in the future. The interactions between considered aptamers and GNS have been analyzed in detail with help of structural and energetic properties. These analyses showed that all three aptamers could well adsorb on GNS. Overall, the final results show that the adsorption of AP2 on the GNS is more favorable than other considered ones and consequently GNS can be considered as a device in order to immobilize these aptamers.     

Introduction of a bounded penalty function in contact-assisted simulations of protein structures to omit false restraints

Contact-assisted simulations, the contacts being predicted or determined experimentally, have become very important in the determination of the structures of proteins and other biological macromolecules. In this work, the effect of contact-distance restraints on the simulated structures was investigated with the use of multiplexed replica exchange simulations with the coarse-grained UNRES force field. A modified bounded flat-bottom restraint function that does not generate a gradient when a restraint cannot be satisfied was implemented. Calculations were run with (i) a set of four small proteins, with contact restraints derived from experimental structures, and (ii) selected CASP11 and CASP12 targets, with restraints as used at prediction time. The bounded penalty function largely omitted false contacts, which were usually inconsistent. It was found that at least 20% of correct contacts must be present in the restraint set to improve model quality with respect to unrestrained simulations. © 2019 Wiley Periodicals, Inc.     

Synthesis, photophysics, electrochemistry, theoretical, and transient absorption studies of luminescent copper(I) and silver(I) diynyl complexes. X-ray crystal structures of [Cu3(micro-dppm)3(micro3-eta1-C triple bond CC triple bond CPh)2]PF6 and [Cu3(micro-dppm)3(micro3-eta1-C triple bond CC triple bond CH)2]PF6

A series of soluble trinuclear copper(I) and silver(I) complexes containing bicapped diynyl ligands, [M(3)(micro-dppm)(3)(micro(3)-eta(1)-C triple bond CC triple bond CR)(2)]PF(6) (M = Cu, R = Ph, C(6)H(4)-CH(3)-p, C(6)H(4)-OCH(3)-p, (n)C(6)H(13), H; M = Ag, R = Ph, C(6)H(4)-OCH(3)-p), has been synthesized and their electronic, photophysical, and electrochemical properties studied. The X-ray crystal structures of [Cu(3)(micro-dppm)(3)(micro(3)-eta(1)-C triple bond CC triple bond CPh)(2)]PF(6) and [Cu(3)(micro-dppm)(3)(micro(3)-eta(1)-C triple bond CC triple bond CH)(2)]PF(6) have been determined.