Comparison of thermodynamic integration and Bennett acceptance ratio for calculating relative protein‐ligand binding free energies

The performances of Bennett's acceptance ratio method and thermodynamic integration (TI) for the calculation of free energy differences in protein simulations are compared. For the latter, the standard trapezoidal rule, Simpson's rule, and Clenshaw‐Curtis integration are used as numerical integration methods. We evaluate the influence of the number and definition of intermediate states on the precision, accuracy, and efficiency of the free energy calculations. Our results show that non‐equidistantly spaced intermediate states are in some cases beneficial for the TI methods. Using several combinations of softness parameters and the λ power dependence, it is shown that these benefits are strongly dependent on the shape of the integrand. Although TI is more user‐friendly due to its simplicity, it was found that Bennett's acceptance ratio method is the more efficient method. It is also the least dependent on the choice of the intermediate states, making it more robust than TI. © 2013 Wiley Periodicals, Inc.     

An improved nucleic acid parameter set for the GROMOS force field

Over the past decades, the GROMOS force field for biomolecular simulation has primarily been developed for performing molecular dynamics (MD) simulations of polypeptides and, to a lesser extent, sugars. When applied to DNA, the 43A1 and 45A3 parameter sets of the years 1996 and 2001 produced rather flexible double-helical structures, in which the Watson-Crick hydrogen-bonding content was more limited than expected. To improve on the currently available parameter sets, the nucleotide backbone torsional-angle parameters and the charge distribution of the nucleotide bases are reconsidered based on quantum-chemical data. The new 45A4 parameter set resulting from this refinement appears to perform well in terms of reproducing solution NMR data and canonical hydrogen bonding. The deviation between simulated and experimental observables is now of the same order of magnitude as the uncertainty in the experimental values themselves.     

An improved GROMOS96 force field for aliphatic hydrocarbons in the condensed phase

Over the past 4 years the GROMOS96 force field has been successfully used in biomolecular simulations, for example in peptide folding studies and detailed protein investigations, but no applications to lipid systems have been published yet. Here we provide a detailed investigation of aliphatic liquid systems. For liquids of larger aliphatic chains, n‐heptane and longer, the standard GROMOS96 parameter sets 43A1 and 43A2 yield a too low pressure at the experimental density. Therefore, a reparametrization of the GROMOS96 force field regarding aliphatic carbons was initiated. The new force field parameter set 45A3 shows considerable improvements for n‐alkanes, cyclo‐, iso‐, and neoalkanes and other branched aliphatics. Liquid densities and heat of vaporization are reproduced for almost all of these molecules. Excellent agreement is found with experiment for the free energy of hydration for alkanes. The GROMOS96 45A3 parameter set should, therefore, be suitable for application to lipid aggregates such as membranes and micelles, for mixed systems of aliphatics with or without water, for polymers, and other apolar systems that may interact with different biomolecules. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1205–1218, 2001     

Estimating the temperature dependence of peptide folding entropies and free enthalpies from total energies in molecular dynamics simulations

The temperature dependence of thermodynamic quantities, such as heat capacity, entropy and free enthalpy, may be obtained by using well-known equations that relate these quantities to the enthalpy of the molecular system of interest at a range of temperatures. In turn, the enthalpy of a molecular system can be estimated from molecular dynamics simulations of an appropriate model. To demonstrate this, we have investigated the temperature dependence of the enthalpy, heat capacity, entropy and free enthalpy of a system that consists of a beta-heptapeptide in methanol and have used the statistical mechanics relationships to describe the thermodynamics of the folding/unfolding equilibrium of the peptide. The results illustrate the power of current molecular simulation force fields and techniques in establishing the link between thermodynamic quantities and conformational distributions.     

Simulating the Physiological Phase of Hydrated DPPC Bilayers: The Ester Moiety

Abstract

The charge on the ester oxygen of the sn2 group of the dipalmitoylphosphatidylcholine (DPPC) has a remarkable effect on the square area per lipid in simulations of a hydrated bilayer. This is in contrast to simulations of nonpolar, neutral lipids, where it has been found to have little effect. The charges associated with the GROMOS96 45A3 and 45A4 biomolecular force fields have been previously shown to cause significant membrane shrinkage. We find that the use of larger charges at the ester groups alone (as opposed to on all the polar moieties in the head group) remedies the shrinkage. The source of this effect in DPPC lies in the fact that the charge distribution of this polar group profoundly influences its free energy of hydration and, correspondingly, the water distribution around it. In an attempt to rationally tune the ester parameters, the repulsive Lennard–Jones parameters that represent the van der Waals interaction have been refined to reproduce the experimental density and heat of vaporization, and the charges of the ester groups have been tuned to reproduce the experimental free energies of hydration of a series of alkane esters. The new parameters form part of the GROMOS96 53A5 and 53A6 force fields. However, with the new force‐field parameters, the area per lipid in simulations of hydrated DPPC bilayers lies below that of the physiological liquid‐crystalline phase, the implications of which are discussed.     

Redox Chemistry of Heterobimetallic Polypnictogen Triple-Decker Complexes – Rearrangement,Fragmentation and Transfer

The redox chemistry of the heterobimetallic triple-decker complexes [(Cp*Fe)(Cp′′′Co)(μ,η⁵:η⁴-E₅)] (E=P ( 1 ), As ( 2 ), Cp*=1,2,3,4,5-pentamethyl-cyclopentadienyl, Cp′′′=1,2,4-tri-tertbutyl-cyclopentadienyl) and [(Cp′′′Co)(Cp′′′Ni)(μ,η³:η³-E₃)] (E=P ( 10 ), As ( 11 )) was investigated. Compound 1 and 2 could be oxidized to the monocations 3 and 4 and further to the dications 5 and 6 , while the initially folded cyclo-E₅ ligand planarizes upon oxidation. The reduction leads to an opposite change in the geometry of the middle deck, which is now folded stronger into the direction of the other metal fragment (formation of monoanions 7 and 8 ). For the arsenic compound 8 , a different behavior is found since a fragmentation into an As₆ ( 9 ) and As₃ ligand complex occurs. The Co and Ni triple-decker complexes 10 and 11 can be oxidized initially to the heterometallic monocations 12 and 13 , which are not stable in solution and convert selectively into the homometallic nickel complexes 14 and 15 and the cobalt complexes 16 and 17 . This behavior was further proven by the oxidation of [(Cp′′′Co)(Cp′′Ni)(μ,η³:η²-P₃)] ( 19 , Cp′′=1,3-di-tertbutyl-cyclopentadienyl) comprising two different Cp ligands. The transfer of {Cp^RM} fragments can be suppressed when a {W(CO)₅} unit is coordinated to the P₃ ligand ( 20 ) prior to the oxidation and the mixed cobalt and nickel cation 21 can be isolated. The reduction of 10 and 11 yields the heterometallic monoanions 22 and 23 , where no transfer of the {Cp^RM} fragments is observed.     

Test of a method for sampling the internal degrees of freedom of a flexible solute molecule based on adiabatic decoupling and temperature or force scaling

Simulation of the folding equilibrium of a polypeptide in solution is a computational challenge. Standard molecular dynamics (MD) simulations of such systems cover hundreds of nanoseconds, which is barely sufficient to obtain converged ensemble averages for properties that depend both on folded and unfolded peptide conformations. If one is not interested in dynamical properties of the solute, techniques to enhance the conformational sampling can be used to obtain the equilibrium properties more efficiently. Here the effect on particular equilibrium properties at 298?K of adiabatically decoupling the motion a β-hepta-peptide from the motion of the solvent and subsequently up-scaling its temperature or down-scaling the forces acting on it is investigated. The ensemble averages and rate of convergence are compared to those for standard MD simulations at two different temperatures and a simulation in which the temperature of the solute is increased to 340?K while keeping the solvent at 298?K. Adiabatic decoupling with a solute mass scaling factor s _m ?=?100 and a temperature scaling factor of s _T ?=?1.1 seems to slightly increase the convergence of several properties such as enthalpy of folding, NMR NOE atom–atom distances and ³J-couplings compared to a standard MD simulation at 298?K. Convergence is still slower than that observed at 340?K. The system with a temperature of 340?K for the solute and 298?K for the solvent without scaling of the mass converges fastest. Using a force scaling factor s _V ?=?0.909 perturbs the system too much and leads to a destabilization of the folded structure. The sampling efficiency and possible distortive effects on the configurational distribution of the solute degrees of freedom due to adiabatic decoupling and temperature or force scaling are also analysed for a simpler model, a dichloroethane molecule in water. It appears that an up-scaling of the mass of the solute reduces the sampling more than the subsequent up-scaling of the temperature or down-scaling of the force enhances it. This means that adiabatic decoupling the solute degrees of freedom from the solvent ones followed by an up-scaling of temperature of down-scaling of the forces does not lead to significantly enhanced sampling of the folding equilibrium.     

Nucleotide-binding properties of adenylate kinase from Escherichia coli: A molecular dynamics study in aqueous and vacuum environments

Summary The complex of adenylate kinase with its transition-state inhibitor has been studied by molecular dynamics simulations in water and in vacuum environments with the GROMOS force field over a period of 300 ps. The adenylate kinase, a member of the nucleotide-binding protein family, was exemplarily chosen for the inspection of the nucleotide-binding properties in the active site. The ligand binding and the domain movements have been studied in detail over the simulation period and compared with the crystal structure. Secondary structure transitions and domain closures defined those parts of the structure which are involved in an induced-fit movement of the enzyme. The presence of more stable hydrogen bonds on the substrate side leads to the assumption that substrate binding is more specific than cosubstrate binding. Reliable results were achieved only if water was explicitly included in the simulation.Dedicated to Prof. Dr. J. Seydel on the oceasion of his 65th birthday.     

Influence of Fine Ligand Substitution Modification of the Isocyanidometal Bridge on Metal-to-Metal Charge Transfer Properties in Class II–III Mixed Valence Complexes

The synthesis and characterization of Class II–III mixed valence complexes have been an interesting topic due to their special intermediate behaviour between localized and delocalized mixed valence complexes. To investigate the influence of the isocyanidometal bridge on metal-to-metal charge transfer (MMCT) properties, a family of new isocyanidometal-bridged complexes and their one-electron oxidation products cis-[Cp(dppe)Fe−CN−Ru(L)₂-NC−Fe(dppe)Cp][PF₆]_n (n=2, 3) (Cp=1,3-cyclopentadiene, dppe=1,2-bis(diphenylphosphino)ethane, L=2,2’-bipyridine (bpy, 1[PF₆]_n ), 5,5’-dimethyl-2,2’-bipyridyl (5,5’-dmbpy, 2[PF₆]_n ) and 4,4’-dimethyl-2,2’-bipyridyl (4,4’-dmbpy, 3[PF₆]_n )) have been synthesized and fully characterized. The experimental results suggest that all the one-electron oxidation products may belong to Class II–III mixed valence complexes, supported by TDDFT calculations. With the change of the substituents of the bipyridyl ligand on the Ru centre from H, 5,5’-dimethyl to 4,4’-dimethyl, the energy of MMCT for the one-electron oxidation complexes changes in the order: 1³⁺ < 2³⁺ < 3³⁺ , and that for the two-electron oxidation complexes decreases in the order 1⁴⁺ > 3⁴⁺ > 2⁴⁺ . The potential splitting (ΔE_1/2(2)) between the two terminal Fe centres for N[PF₆]₂ are the largest potential splitting for the cyanido-bridged complexes reported so far. This work shows that the smaller potential difference between the bridging and the terminal metal centres would result in the more delocalized mixed valence complex.