Jana K. Shen

Progress in the prediction of pKa values in proteins

The pKa‐cooperative aims to provide a forum for experimental and theoretical researchers interested in protein pKa values and protein electrostatics in general. The first round of the pKa‐cooperative, which challenged computational labs to carry out blind predictions against pKas experimentally determined in the laboratory of Bertrand Garcia‐Moreno, was completed and results discussed at the Telluride meeting (July 6–10, 2009). This article serves as an introduction to the reports submitted by the blind prediction participants that will be published in a special issue of PROTEINS: Structure, Function and Bioinformatics. Here, we briefly outline existing approaches for pKa calculations, emphasizing methods that were used by the participants in calculating the blind pKa values in the first round of the cooperative. We then point out some of the difficulties encountered by the participating groups in making their blind predictions, and finally try to provide some insights for future developments aimed at improving the accuracy of pKa calculations. Proteins 2011;

Continuous Constant pH Molecular Dynamics in Explicit Solvent with pH-Based Replica Exchange.

A computational tool that offers accurate pKa values and atomically detailed knowledge of protonation-coupled conformational dynamics is valuable for elucidating mechanisms of energy transduction processes in biology, such as enzyme catalysis and electron transfer as well as proton and drug transport. Toward this goal we present a new technique of embedding continuous constant pH molecular dynamics within an explicit-solvent representation. In this technique we make use of the efficiency of the generalized-Born (GB) implicit-solvent model for estimating the free energy of protein solvation while propagating conformational dynamics using the more accurate explicit-solvent model. Also, we employ a pH-based replica exchange scheme to significantly enhance both protonation and conformational state sampling. Benchmark data of five proteins including HP36, NTL9, BBL, HEWL, and SNase yield an average absolute deviation of 0.53 and a root mean squared deviation of 0.74 from experimental data. This level of accuracy is obtained with 1 ns simulations per replica. Detailed analysis reveals that explicit-solvent sampling provides increased accuracy relative to the previous GB-based method by preserving the native structure, providing a more realistic description of conformational flexibility of the hydrophobic cluster, and correctly modeling solvent mediated ion-pair interactions. Thus, we anticipate that the new technique will emerge as a practical tool to capture ionization equilibria while enabling an intimate view of ionization coupled conformational dynamics that is difficult to delineate with experimental techniques alone.

Toward accurate prediction of pKa values for internal protein residues: The importance of conformational relaxation and desolvation energy

Proton uptake or release controls many important biological processes, such as energy transduction, virus replication, and catalysis. Accurate pKa prediction informs about proton pathways, thereby revealing detailed acid‐base mechanisms. Physics‐based methods in the framework of molecular dynamics simulations not only offer pKa predictions but also inform about the physical origins of pKa shifts and provide details of ionization‐induced conformational relaxation and large‐scale transitions. One such method is the recently developed continuous constant pH molecular dynamics (CPHMD) method, which has been shown to be an accurate and robust pKa prediction tool for naturally occurring titratable residues. To further examine the accuracy and limitations of CPHMD, we blindly predicted the pKa values for 87 titratable residues introduced in various hydrophobic regions of staphylococcal nuclease and variants. The predictions gave a root‐mean‐square deviation of 1.69 pK units from experiment, and there were only two pKas with errors greater than 3.5 pK units. Analysis of the conformational fluctuation of titrating side‐chains in the context of the errors of calculated pKa values indicate that explicit treatment of conformational flexibility and the associated dielectric relaxation gives CPHMD a distinct advantage. Analysis of the sources of errors suggests that more accurate pKa predictions can be obtained for the most deeply buried residues by improving the accuracy in calculating desolvation energies. Furthermore, it is found that the generalized Born implicit‐solvent model underlying the current CPHMD implementation slightly distorts the local conformational environment such that the inclusion of an explicit‐solvent representation may offer improvement of accuracy. Proteins 2011.

Charge-leveling and proper treatment of long-range electrostatics in all-atom molecular dynamics at constant pH.

Recent development of constant pH molecular dynamics (CpHMD) methods has offered promise for adding pH-stat in molecular dynamics simulations. However, until now the working pH molecular dynamics (pHMD) implementations are dependent in part or whole on implicit-solvent models. Here we show that proper treatment of long-range electrostatics and maintaining charge neutrality of the system are critical for extending the continuous pHMD framework to the all-atom representation. The former is achieved here by adding forces to titration coordinates due to long-range electrostatics based on the generalized reaction field method, while the latter is made possible by a charge-leveling technique that couples proton titration with simultaneous ionization or neutralization of a co-ion in solution. We test the new method using the pH-replica-exchange CpHMD simulations of a series of aliphatic dicarboxylic acids with varying carbon chain length. The average absolute deviation from the experimental pK(a) values is merely 0.18 units. The results show that accounting for the forces due to extended electrostatics removes the large random noise in propagating titration coordinates, while maintaining charge neutrality of the system improves the accuracy in the calculated electrostatic interaction between ionizable sites. Thus, we believe that the way is paved for realizing pH-controlled all-atom molecular dynamics in the near future.

Thermodynamic Coupling of Protonation and Conformational Equilibria in Proteins: Theory and Simulation

Ionization-coupled conformational phenomena are ubiquitous in biology. However, quantitative characterization of the underlying thermodynamic cycle comprised of protonation and conformational equilibria has remained an elusive goal. Here we use theory and continuous constant pH molecular dynamics (CpHMD) simulations to provide a thermodynamic description for the coupling of proton titration and conformational exchange between two distinct states of a protein. CpHMD simulations with a hybrid-solvent scheme and the pH-based replica-exchange (REX) protocol are applied to obtain the equilibrium constants and atomic details of the ionization-coupled conformational exchange between open and closed states of an engineered mutant of staphylococcal nuclease. Although the coupling of protonation and conformational equilibria is not exact in the simulation, the results are encouraging. They demonstrate that REX-CpHMD simulations can be used to study thermodynamics of ionization-coupled conformational processes--which has not possible using present experimental techniques or traditional simulations based on fixed protonation states.

Self-assembly and bilayer-micelle transition of fatty acids studied by replica-exchange constant pH molecular dynamics.

Recent interest in the development of surfactant-based nanodelivery systems targeting tumor sites has sparked our curiosity in understanding the detailed mechanism of the self-assembly and phase transitions of pH-sensitive surfactants. Toward this goal, we applied a state-of-the-art simulation technique, continuous constant pH molecular dynamics (CpHMD) with the hybrid-solvent scheme and pH-based replica-exchange protocol, to study the de novo self-assembly of 30 and 40 lauric acids, a simple model titratable surfactant. We observed the formation of a gel-state bilayer at low and intermediate pH and a spherical micelle at high pH, with the phase transition starting at 20-30% ionization and being completed at 50%. The degree of cooperativity for the transition increases from the 30-mer to the 40-mer. The calculated apparent or bulk pKa value is 7.0 for the 30-mer and 7.5 for the 40-mer. Congruent with experiment, these data demonstrate that CpHMD is capable of accurately modeling large conformational transitions of surfactant systems while allowing the simultaneous proton titration of constituent molecules. We suggest that CpHMD simulations may become a useful tool in aiding in the design and development of pH-sensitive nanocarriers for a variety of biomedical and technological applications.

Atomistic simulations of pH-dependent self-assembly of micelle and bilayer from fatty acids

Detailed knowledge of the self-assembly and phase behavior of pH-sensitive surfactants has implications in areas such as targeted drug delivery. Here we present a study of the formation of micelle and bilayer from lauric acids using a state-of-the-art simulation technique, continuous constant pH molecular dynamics (CpHMD) with conformational sampling in explicit solvent and the pH-based replica-exchange protocol. We find that at high pH conditions a spherical micelle is formed, while at low pH conditions a bilayer is formed with a considerable degree of interdigitation. The mid-point of the phase transition is in good agreement with experiment. Preliminary investigation also reveals that the effect of counterions and salt screening shifts the transition mid-point and does not change the structure of the surfactant assembly. Based on these data we suggest that CpHMD simulations may be applied to computational design of surfactant-based nano devices in the future.

Simulating pH titration of a single surfactant in ionic and nonionic surfactant micelles.

Calculation of surfactant pK(a)s in micelles is a challenging task using traditional electrostatic methods due to the lack of structural data and information regarding the effective dielectric constant. Here we test the implicit- and hybrid-solvent-based continuous constant pH molecular dynamics (CpHMD) methods for predicting the pK(a) shift of a lauric acid solubilized in three micelles: dodecyl sulfate (DS), dodecyltrimethylammonium (DTA), and dodecyltriethylene glycol ether (DE3). Both types of simulations are able to reproduce the observed positive pK(a) shifts for the anionic DS and nonionic DE3 micelles. However, for the cationic DTA micelle, the implicit-solvent simulation fails to predict the direction of the pK(a) shift, while the hybrid-solvent simulation, where conformational sampling is conducted in explicit solvent, is consistent with experiment, although the specific-ion effects remain to be accurately determined. Comparison between the implicit- and hybrid-solvent data shows that the latter gives a more realistic description of the conformational environment of the titrating probe. Surprisingly, in the DTA micelle, surfactants are only slightly attracted to the laurate ion, which diminishes the magnitude of the electrostatic stabilization, resulting in a positive pK(a) shift that cannot be explained by chemical intuition or other theoretical models. Our data underscores the importance of microscopic models and ionization-coupled conformational dynamics in quantitative prediction of the pK(a) shifts in micelles.

Molecular dynamics simulations of ionic and nonionic surfactant micelles with a generalized born implicit‐solvent model

In recent years, all‐atom and coarse‐grained models have been developed andapplied to simulations of micelles and biological membranes. Here, we explorethe question of whether a combined all‐atom representation of surfactantmolecules and continuum description of solvent based on the generalized Bornmodel can be used to study surfactant micelles. Specifically, we report theparameterization of the GBSW model with a surface‐area dependent nonpolarsolvation energy term for dodecyl sulfate, dodecyl tetramethylammonium, anddodecyl triethyleneglycol ether molecules. In the parameterization procedure,the atomic Born radii were derived from the radial distribution functions ofsolvent charge and refined targeting the potential of mean force of dimerinteractions from explicit‐solvent simulations. The optimized radii were thenapplied in molecular dynamics simulations of the ionic and nonionic micelles.We found that the micelles are stable but more compact and rigid than inexplicit solvent as a consequence of the drastic reduction in solvation andmobility of surfactant monomers within the micelle. Based on these data and ourprevious work, we suggest that in addition to a more accurate description ofthe nonpolar solvation energy, the ruggedness in the short‐range interactionsdue to solvent granularity is a critical feature that needs to be taken intoaccount to accurately model processes such as micelle formation and proteinfolding in implicit solvent. Finally, the explicit‐solvent data presented hereoffers new insights into different conformational behavior of ionic andnonionic micelles which is valuable for understanding hydrophobic assembliesand of interest to the detergent industry.