Predicting proton titration in cationic micelle and bilayer environments

A Guide to the Continuous Constant pH Molecular Dynamics Methods in Amber and CHARMM [Article v1.0]

Like temperature and pressure, solution pH is an important environmental variable in biomolecular simulations. Virtually all proteins depend on pH to maintain their structure and function. In conventional molecular dynamics (MD) simulations of proteins, pH is implicitly accounted for by assigning and fixing protonation states of titratable sidechains. This is a significant limitation, as the assigned protonation states may be wrong and they may change during dynamics. In this tutorial, we guide the reader in learning and using the various continuous constant pH MD methods in Amber and CHARMM packages, which have been applied to predict pK a values and elucidate proton-coupled conformational dynamics of a variety of proteins including enzymes and membrane transporters.

Calculation of apparent pKa values of saturated fatty acids with different lengths in DOPC phospholipid bilayers

We performed all-atom molecular dynamics simulations and calculated free energy profiles and apparent pKa values for neutral and anionic forms of single myristic (C14:0), palmitic (C16:0) and stearic (C18:0) fatty acid embedded in a DOPC bilayer and explicit water solvent. We showed that the neutral forms of the fatty acids are stabilized inside the bilayer by hydrogen bonding of a fatty acid carboxylic group with DOPC phosphate and carbonyl groups. In contrast to the neutral form, the anionic forms of the fatty acids are shifted towards the water-membrane interface and are instead stabilized by hydrogen bonding to interfacial water. By using umbrella sampling simulations, we calculated free energies of stabilization and revealed that the free energy of stabilization inside the bilayer increases with the chain length for both the neutral and deprotonated forms. On the other hand, the free energies of flip-flop of both the neutral and anionic forms are constant upon the prolongation of the fatty acid. Based on the free energy curves, we also calculated apparent fatty acid pKa,app values in the bilayer, which are 7.0, 7.2 and 6.3 for myristic, palmitic and stearic acid and are increased by several pKa units compared to the corresponding pKa values in water. By further analysis of the calculated curves we found that spontaneous protonation of fatty acid anions takes place in the bilayer interior at ca. 1.4 nm from the bilayer center for all studied fatty acids.

Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

pH is a critical parameter for biological and technological systems directly related with electrical charges. It can give rise to peculiar electrostatic phenomena, which also makes them more challenging. Due to the quantum nature of the process, involving the forming and breaking of chemical bonds, quantum methods should ideally by employed. Nevertheless, due to the very large number of ionizable sites, different macromolecular conformations, salt conditions, and all other charged species, the CPU time cost simply becomes prohibitive for computer simulations, making this a quite complex problem. Simplified methods based on Monte Carlo sampling have been devised and will be reviewed here, highlighting the updated state-of-the-art of this field, advantages, and limitations of different theoretical protocols for biomolecular systems (proteins and nucleic acids). Following a historical perspective, the discussion will be associated with the applications to protein interactions with other proteins, polyelectrolytes, and nanoparticles.

All-Atom Continuous Constant pH Molecular Dynamics With Particle Mesh Ewald and Titratable Water

Development of a pH stat to properly control solution pH in biomolecular simulations has been a long-standing goal in the community. Toward this goal recent years have witnessed the emergence of the so-called constant pH molecular dynamics methods. However, the accuracy and generality of these methods have been hampered by the use of implicit-solvent models or truncation-based electrostatic schemes. Here we report the implementation of the particle mesh Ewald (PME) scheme into the all-atom continuous constant pH molecular dynamics (CpHMD) method, enabling CpHMD to be performed with a standard MD engine at a fractional added computational cost. We demonstrate the performance using pH replica-exchange CpHMD simulations with titratable water for a stringent test set of proteins, HP36, BBL, HEWL, and SNase. With the sampling time of 10 ns per replica, most pK_a's are converged, yielding the average absolute and root-mean-square deviations of 0.61 and 0.77, respectively, from experiment. Linear regression of the calculated vs experimental pK_a shifts gives a correlation coefficient of 0.79, a slope of 1, and an intercept near 0. Analysis reveals inadequate sampling of structure relaxation accompanying a protonation-state switch as a major source of the remaining errors, which are reduced as simulation prolongs. These data suggest PME-based CpHMD can be used as a general tool for pH-controlled simulations of macromolecular systems in various environments, enabling atomic insights into pH-dependent phenomena involving not only soluble proteins but also transmembrane proteins, nucleic acids, surfactants, and polysaccharides.

Mechanism of pH-dependent activation of the sodium-proton antiporter NhaA

Escherichia coli NhaA is a prototype sodium-proton antiporter, which has been extensively characterized by X-ray crystallography, biochemical and biophysical experiments. However, the identities of proton carriers and details of pH-regulated mechanism remain controversial. Here we report constant pH molecular dynamics data, which reveal that NhaA activation involves a net charge switch of a pH sensor at the entrance of the cytoplasmic funnel and opening of a hydrophobic gate at the end of the funnel. The latter is triggered by charging of Asp164, the first proton carrier. The second proton carrier Lys300 forms a salt bridge with Asp163 in the inactive state, and releases a proton when a sodium ion binds Asp163. These data reconcile current models and illustrate the power of state-of-the-art molecular dynamics simulations in providing atomic details of proton-coupled transport across membrane which is challenging to elucidate by experimental techniques.

The pH dependence of the activity of Escherichia coli main sodium-proton antiporter NhaA is still not fully understood. Here, the authors use continuous constant pH molecular dynamics simulations to identify NhaA proton carrier residues and elucidate its gating and ion transport processes.