Accurate, conformation-dependent predictions of solvent effects on protein ionization constants

Abstract

Predicting how aqueous solvent modulates the conformational transitions and influences the pKa values that regulate the biological functions of biomolecules remains an unsolved challenge. To address this problem, we developed FDPB MF, a rotamer repacking method that exhaustively samples side chain conformational space and rigorously calculates multibody protein-solvent interactions. FDPB MF predicts the effects on pKa values of various solvent exposures, large ionic strength variations, strong energetic couplings, structural reorganizations and sequence mutations. The method achieves high accuracy, with root mean square deviations within 0.3 pH unit of the experimental values measured for turkey ovomucoid third domain, hen lysozyme, Bacillus circulans xylanase, and human and Escherichia coli thioredoxins. FDPB MF provides a faithful, quantitative assessment of electrostatic interactions in biological macromolecules.conformational flexibility ͉ electrostatics ͉ pKa prediction ͉ protein modeling B y strongly interacting with charges, the solvent significantly modulates the electrostatic properties of biomolecular systems. Although variations in pH and ionic strength are responsible for physiologically important conformational transitions (1), quantitatively assessing their role in modulating electrostatic energies is particularly challenging (2). Approaches in which solvent is modeled as a continuum polarizable medium while biomolecules are modeled in explicit molecular detail have become widely used in recent years (3, 4). However, no current method combines broad conformational sampling with a rigorous solvation model that can predict quantitatively and efficiently the effects of solvent on protein energetics and conformations.In principle, molecular dynamics and free-energy simulations monitoring protonation events can model accurately the energetic effects of solvation and conformational relaxation of biomolecules. However, despite recent progress, these techniques often fail to converge in a reasonable amount of computer time and therefore do not provide reliable predictions of thermodynamic properties (5, 6).Rotamer repacking methods sample more efficiently and exhaustively the conformational space of biomolecules. However, these methods require the energy function be decomposed into self energies and interaction energies between pairs of residues (7-10). Consequently, repacking methods cannot model the effects of conformational relaxations involving more than two positions at a time. Many important properties of biomolecular surfaces (i.e., their interface with the solvent and the distribution of bulk ions around them) are not pairwise factorable and depend on the simultaneous knowledge of the conformations of all residues. Approximating these effects by relaxing the protein-solvent interface only at the vicinity of solventexposed charged residues does not improve the prediction of pKa values in proteins (11). Current rotamer repacking methods have also difficulties in assessing accurately and reliably the ...

Alchemical free energy simulations for biological complexes: powerful but temperamental …

“…22,77,137 More advanced PB methods, mixing macroscopic continuum and microscopic modeling (e.g., Monte Carlo sampling of sidechain orientations), provide a way forward. 22,136,138,139 We have used extensively a ''PB/LRA'' approach that falls in this class 33,34,77 and is illustrated in Figure 5. To evaluate the preferred protonation state of a particular group, MD simulations are performed with the group in its protonated and deprotonated states (with explicit solvent molecules).…”

A fast and accurate computational approach to protein ionization

“…All of the above has motivated the development of algorithms that couple the treatment of conformational flexibility with the exchange of protons between the acidic and basic groups and the solvent. Examples include meanfield models with side-chain flexibility (You and Bashford 1995;Spassov and Bashford 1999;Barth et al 2007), Monte Carlo sampling (Beroza and Case 1996;Georgescu et al 2002), and advanced protocols for molecular-dynamics simulations (for review, see Mongan and Case 2005). Recently an implementation of replica-exchange method in constant pH dynamics (Khandogin and Brooks III 2006) demonstrated an improvement of the accuracy of this class of models that moves the predictions from first principles to a quantitative level.…”

Adapting Poisson-Boltzmann to the self-consistent mean field theory: Application to protein side-chain modeling

“…We believe that the main difference between the two implementations comes from the fact that we use an analytical expression for the derivatives of the variational free energy of the SCMF method with respect to the weights P (i, j ), while FDPB_MF computes these derivatives numerically. 37 On an Intel Core I7 at 2.66 GHz, the average CPU time required per protein in the DRESS database was 0.3, 0.3, 1.9, 2, 9, and 93 s for SCMF, TREEPACK, OPUS-ROTA, SCWRL4, SCAP, and SCMF-PB, respectively. Clearly, SCMF-PB is slower than the other methods; the time difference, however, is only of one order of magnitude, and SCMF-PB offers an improved level of prediction accuracy for exposed side chains.…”

“…The corresponding FDPB_MF algorithm was found to be slow, its running times varying between 2 and 6 days on a Pentium4, 2.4 GHz CPU. 37 Our implementation of a combined SCMF-PB algorithm is much faster, with computing times in the order of 2 min for predicting the conformations of all side chains of large proteins (370 residues) on a Intel Core I7 at 2.66 GHz with 8 GB of memory. We believe that the main difference between the two implementations comes from the fact that we use an analytical expression for the derivatives of the variational free energy of the SCMF method with respect to the weights P (i, j ), while FDPB_MF computes these derivatives numerically.…”

“…36 Harbury et al expanded upon this approach and developed FDPB_MF, a method that exhaustively samples side-chain conformational space and rigorously calculates multi-body protein-solvent interactions. 37 This method has been used for computing the ionization states of titratable residues in proteins; its implementation, however, is very slow (days of computing time) and limited to predicting the pKas and conformations of only a few residues.…”