Anomalous surface diffusion of protons on lipid membranes.

The cellular energy machinery depends on the presence and properties of protons at or in the vicinity of lipid membranes. To asses the energetics and mobility of a proton near a membrane, we simulated an excess proton near a solvated DMPC bilayer at 323 K, using a recently developed method to include the Grotthuss proton shuttling mechanism in classical molecular dynamics simulations. We obtained a proton surface affinity of -13.0 ± 0.5 kJ mol(-1). The proton interacted strongly with both lipid headgroup and linker carbonyl oxygens. Furthermore, the surface diffusion of the proton was anomalous, with a subdiffusive regime over the first few nanoseconds, followed by a superdiffusive regime. The time- and distance dependence of the proton surface diffusion coefficient within these regimes may also resolve discrepancies between previously reported diffusion coefficients. Our simulations show that the proton anomalous surface diffusion originates from restricted diffusion in two different surface-bound states, interrupted by the occasional bulk-mediated long-range surface diffusion. Although only a DMPC membrane was considered in this work, we speculate that the restrictive character of the on-surface diffusion is highly sensitive to the specific membrane conditions, which can alter the relative contributions of the surface and bulk pathways to the overall diffusion process. Finally, we discuss the implications of our findings for the energy machinery.

Explicit proton transfer in classical molecular dynamics simulations.

We present Hydrogen Dynamics (HYDYN), a method that allows explicit proton transfer in classical force field molecular dynamics simulations at thermodynamic equilibrium. HYDYN reproduces the characteristic properties of the excess proton in water, from the special pair dance, to the continuous fluctuation between the limiting Eigen and Zundel complexes, and the water reorientation beyond the first solvation layer. Advantages of HYDYN with respect to existing methods are computational efficiency, microscopic reversibility, and easy parameterization for any force field.

Evaluating nonpolarizable nucleic acid force fields: a systematic comparison of the nucleobases hydration free energies and chloroform-to-water partition coefficients.

Nucleic acid force fields have been shown to reproduce structural properties of DNA and RNA very well, but comparative studies with respect to thermodynamic properties are rare. As a test for thermodynamic properties, we have computed hydration free energies and chloroform-to-water partition coefficients of nucleobases using the AMBER-99, AMBER-gaff, CHARMM-27, GROMOS-45a4/53a6 and OPLS-AA force fields. A mutual force field comparison showed a very large spread in the calculated thermodynamic properties, demonstrating that some of the parameter sets require further optimization. The choice of solvent model used in the simulation does not have a significant effect on the results. Comparing the hydration free energies obtained by the various force fields to the adenine and thymine experimental values showed a very large deviation for the GROMOS and AMBER parameter sets. Validation against experimental partition coefficients showed good agreement for the CHARMM-27 parameter set. In view of mutation studies, differences in partition coefficient between two bases were also compared, and good agreement between experiments and calculations was found for the AMBER-99 parameter set. Overall, the CHARMM-27 parameter set performs best with respect to the thermodynamic properties tested here.

Promiscuity of carbonic anhydrase II. Unexpected ester hydrolysis of carbohydrate-based sulfamate inhibitors.

Carbonic anhydrases (CAs) are enzymes whose endogenous reaction is the reversible hydration of CO(2) to give HCO(3)(-) and a proton. CA are also known to exhibit weak and promiscuous esterase activity toward activated esters. Here, we report a series of findings obtained with a set of CA inhibitors that showed quite unexpectedly that the compounds were both inhibitors of CO(2) hydration and substrates for the esterase activity of CA. The compounds comprised a monosaccharide core with the C-6 primary hydroxyl group derivatized as a sulfamate (for CA recognition). The remaining four sugar hydroxyl groups were acylated. Using protein X-ray crystallography, the crystal structures of human CA II in complex with four of the sulfamate inhibitors were obtained. As expected, the four structures displayed the canonical CA protein-sulfamate interactions. Unexpectedly, a free hydroxyl group was observed at the anomeric center (C-1) rather than the parent C-1 acyl group. In addition, this hydroxyl group is observed axial to the carbohydrate ring while in the parent structure it is equatorial. A mechanism is proposed that accounts for this inversion of stereochemistry. For three of the inhibitors, the acyl groups at C-2 or at C-2 and C-3 were also absent with hydroxyl groups observed in their place and retention of stereochemistry. With the use of electrospray ionization-Fourier transform ion cyclotron resonance-mass spectrometry (ESI-FTICR-MS), we observed directly the sequential loss of all four acyl groups from one of the carbohydrate-based sulfamates. For this compound, the inhibitor and substrate binding mode were further analyzed using free energy calculations. These calculations suggested that the parent compound binds almost exclusively as a substrate. To conclude, we have demonstrated that acylated carbohydrate-based sulfamates are simultaneously inhibitor and substrate of human CA II. Our results suggest that, initially, the substrate binding mode dominates, but following hydrolysis, the ligand can also bind as a pure inhibitor thereby competing with the substrate binding mode.

g_membed: Efficient insertion of a membrane protein into an equilibrated lipid bilayer with minimal perturbation.

To efficiently insert a protein into an equilibrated and fully hydrated membrane with minimal membrane perturbation we present a computational tool, called g_membed, which is part of the Gromacs suite of programs. The input consists of an equilibrated membrane system, either flat or curved, and a protein structure in the right position and orientation with respect to the lipid bilayer. g_membed first decreases the width of the protein in the xy-plane and removes all molecules (generally lipids and waters) that overlap with the narrowed protein. Then the protein is grown back to its full size in a short molecular dynamics simulation (typically 1000 steps), thereby pushing the lipids away to optimally accommodate the protein in the membrane. After embedding the protein in the membrane, both the lipid properties and the hydration layer are still close to equilibrium. Thus, only a short equilibration run (less then 1 ns in the cases tested) is required to re-equilibrate the membrane. Its simplicity makes g_membed very practical for use in scripting and high-throughput molecular dynamics simulations.

Reordering hydrogen bonds using hamiltonian replica exchange enhances sampling of conformational changes in biomolecular systems.

Hydrogen bonds play an important role in stabilizing (meta-)stable states in protein folding. Hence, they can potentially be used as a way to bias these states in molecular simulation methods. Previously, Wolf et al. showed that applying repulsive and attractive hydrogen bond biasing potentials in an alternating way significantly accelerates the folding process (Wolf, M. G.; de Leeuw, S. W. Biophys. J. 2008, 94, 3742). As the biasing potentials are only active during a fixed time interval, this alternating scheme does not represent a thermodynamic equilibrium. In this work, we present a Hamiltonian replica exchange molecular dynamics (REMD) scheme that aims to shuffle and reorder hydrogen bonds in the protein backbone. We therefore apply adapted hydrogen bond potentials in a Hamiltonian REMD scheme, which we call hydrogen bond switching (HS). To compare the performance of the HS to a standard REMD method, we performed HS and temperature REMD simulations of a beta-heptapeptide in methanol. Both methods sample the conformational space to a similar extent. As the HS simulation required only five replicas, while the REMD simulation required 20 replicas, the HS method is significantly more efficient. We tested the HS method also on a larger system, 16-residue polyalanine in water. Both of the simulations starting from a completely unfolded and a folded conformation resulted in an ensemble with, apart from the starting structure, similar conformational minima. We can conclude that the HS method provides an efficient way to sample the conformational space of a protein, without requiring knowledge of the folded states beforehand. In addition, these simulations revealed that convergence was hampered by replicas having a preference for specific biasing potentials. As this sorting effect is inherent to any Hamiltonian REMD method, finding a solution will result in an additional increase in the efficiency of Hamiltonian REMD methods in general.

Quantitative prediction of amyloid fibril growth of short peptides from simulations: calculating association constants to dissect side chain importance.

Quantitative prediction of the fibril growth properties of different peptides is conducted with a molecular dynamics approach. Association constants of small peptides used as a model for amyloid formation are calculated, and the results show very good agreement with experiments. Also the free-energy differences associated with two important interactions that characterize fibril growth, namely cross-beta-sheet and lateral interactions, are obtained. These two interactions show different dependencies on the physicochemical properties of the side chains, explaining the variation in fibril morphologies between different peptides.

Rapid free energy calculation of peptide self-assembly by REMD umbrella sampling.

We extend umbrella sampling with replica exchange steps to calculate free energies that are important in the self-assembly of peptides. This leads to a more than 10-fold speed up over conventional umbrella sampling, thereby providing a practical method to calculate these free-energy differences. This approach can also observe first-order phase transitions and pinpoint the location of the concomitant boundary. When conformational changes are involved, this method can handle peptides up to approximately 7 residues, providing a rapid and accurate assessment of the thermodynamic properties of model systems, and can thus be used to answer fundamental questions about peptide self-assembly. When no major conformational changes are involved, we expect the size limit to be equal to that of standard molecular dynamics.

Modeling amyloid fibril formation: a free-energy approach.

Amyloid fibrils are structures consisting of many proteins with a well-defined conformation. The formation of these fibrils has been the subject of intense research, largely due to their connection to several diseases. We focus here on the computational studies and discuss these from a free-energy point of view. The fibrillogenic properties of many proteins can be predicted and understood by taking the relevant free energies into account in an appropriate way. This is because both the equilibrium and the kinetic properties of the protein system depend on its free-energy landscape. Advanced simulation techniques can be used to understand the relationship between the free-energy landscape of a protein and its three-dimensional structure and propensity to form amyloid fibrils. We give an overview of existing simulation techniques that operate at a molecular level of detail and that are capable of generating relevant free-energy values. The free energies obtained with these methods can be inserted into a statistical-mechanical or kinetic framework to predict mean fibril properties on length scales and time scales that are inaccessible by molecular-scale simulation methods.