Calculation of Protein Ionization Equilibria With Conformational Sampling: pK a of a Model Leucine Zipper, GCN4 and Barnase Alemayehu A. Gorfe, Philippe Ferrara, Amedeo Caflisch, Daniel N. Marti, Hans Rudolf Bosshard, and Ilian Jelesarov * Department of Biochemistry, University of Zurich, Zurich, Switzerland ABSTRACT The use of conformational en- sembles provided by nuclear magnetic resonance (NMR) experiments or generated by molecular dy- namics (MD) simulations has been regarded as a useful approach to account for protein motions in the context of pK a calculations, yet the idea has been tested occasionally. This is the first report of systematic comparison of pK a estimates computed from long multiple MD simulations and NMR en- sembles. As model systems, a synthetic leucine zip- per, the naturally occurring coiled coil GCN4, and barnase were used. A variety of conformational averaging and titration curve-averaging techniques, or combination thereof, was adopted and/or modi- fied to investigate the effect of extensive global conformational sampling on the accuracy of pK a calculations. Clustering of coordinates is proposed as an approach to reduce the vast diversity of MD ensembles to a few structures representative of the average electrostatic properties of the system in solution. Remarkable improvement of the accuracy of pK a predictions was achieved by the use of mul- tiple MD simulations. By using multiple trajectories the absolute error in pK a predictions for the model leucine zipper was reduced to as low as approxi- mately 0.25 pK a units. The validity, advantages, and limitations of explicit conformational sampling by MD, compared with the use of an average structure and a high internal protein dielectric value as means to improve the accuracy of pK a calculations, are discussed. Proteins 2002;46:41– 60. © 2001 Wiley-Liss, Inc. Key words: coiled coil; NMR; molecular dynamics; ensemble; salt bridge; cluster; electro- statics INTRODUCTION Release and uptake of protons are fundamental to a variety of biological processes such as enzymatic catalysis, macromolecular stability, and formation of macromolecu- lar complexes. Determination of the pK a values of protein ionizable groups is key to the understanding of the pH- dependent properties of proteins. Theoretical studies of the ionization behavior of protein charged groups are a vital part of this endeavor. Structure-based predictions of the electrostatic properties of proteins have motivated researchers ever since the beginning of modern structural biology, 1,2 and considerable advances have been made in the last two decades. 3–8 Quantitative computational pre- dictions of pK a values are still problematic in many cases. 6,9 The titration behavior of proteins is governed by the ionization equilibria of their acidic and basic charged groups. The pK a of a group in a folded conformation of a protein can deviate by several pH units from the pK a of a fully solvated model compound because the electrostatic environments experienced by a group in the protein and in solution are very different. Interactions of charged ioniz- able groups with the charged form of other titratable groups (site-site interactions) and with permanent dipoles in the protein (background interactions), as well as the altered interactions with water (Born energy or desolva- tion energy) are the main sources of pK a shifts. 10 The change of the ionization equilibrium of charged groups and the titration behavior of proteins are commonly calculated by the numerical solution of the linearized form of the Poisson Boltzmann (FDPB) equation for a group in a protein relative to an isolated model compound in solu- tion. 4 In the continuum representation, a dielectric bound- ary between the bulk solvent and the protein is defined, usually represented by the solvent accessible surface of the molecule. The solvent is modeled as a continuum of high polarizability, whereas a lower dielectric constant is as- signed to the protein domain, and the protein structure is treated at atomic level. 4–6 The pH-dependent free ener- gies are calculated by Boltzmann summation over all important protonation states in a certain pH interval. As a result, the average degree of protonation of each ionizable group as a function of pH is obtained. This methodology was first applied to titration studies of lysozyme a decade ago 4 and has since been applied to many proteins. 11–13 The Supplementary Material referred to in this section can be found at http://www.interscience.wiley.com/jpages/0887-3585/suppmat/46_1/ v46_1.html Grant sponsor: Bundesamt fu ¨ r Bildung und Wissenschaft; Grant number: 97.0592; Grant sponsor: Swiss National Science Foundation; Grant number: 31.55308.98. *Correspondence to: Ilian Jelesarov, Department of Biochemistry, University of Zurich, Winterthurerstr. 190, CH-8057 Zurich, Switzer- land. E-mail: iljel@bioc.unizh.ch Received 30 March 2001; Accepted 21 August 2001 Published online 00 Month 2001 PROTEINS: Structure, Function, and Genetics 46:41– 60 (2002) © 2001 WILEY-LISS, INC. DOI 10.1002/prot.10027