Theoretical prediction of ionisation properties of proteins

Abstract

This work emphasises on elaboration of improved theoretical and computational methods for determination of protonation/deprotonation equilibria in proteins. It also aims to contribute for a better understanding on atomic level of ionisation properties of proteins and their role in structure-functional relationship. Presented here computations are based on a continuum model of protein-solvent system.

Limitations in the predictive power of current methods for pKa calculations are mostly due to inadequate accounting of the structural flexibility, which is a key element of functional properties of proteins. This problem was approached in two ways. First, by combining calculations of ionisation equilibria with different techniques for generation of ensembles of protein structures alternative conformers in X-ray structures, NMR models, molecular dynamics simulation. Second, the theoretical description of the pKa calculations based on continuum electrostatic model was generalized in order to account explicitly for alternative hydrogen locations on titratable and polar non-titratable groups. This corresponds to an introduction of minor but very important structural flexibility. Such approach not only improves the accuracy of the pKa calculations but also provides detail information that allows, for instance, prediction of pH-dependence of tautomerisation as well as of a reorganisation of H-bond networks. Entropic effects were pointed out.

Irregular (non-sigmoid) titration curves of ionisable groups were analysed theoretically. It was demonstrated that the pKa values, extracted from multiple-step titration curves by means of fitting to a sum of Henderson-Hasselbalch equations, do not describe the ionisation equilibrium correctly, which may lead to irrelevant conclusions for the functional mechanisms. Conditions for appearance of irregular titration were derived analytically.

Continuum model was applied to simulate the non-equilibrium stationary process of steady-state ion flux through protein channels. The Poisson-Nernst-Planck (PNP) equations were modified to account for desolvation of mobile ions in the membrane pore and for effects related to ion sizes. A numerical algorithm was developed for 3D solution of PNP equations, applicable for arbitrary channel geometry and arbitrary protein charge distribution. Basic features of ion transport were illustrated by simulations on model channels. Studied proteins: ribonuclease T1 from the fungus Aspergillus oryzae (RNase T1), alcohol dehydrogenase from Drosophila lebanonensis (DADH), xylanases from Bacillus circulans and Bacillus agaradhaerens, porin Omp32 from the bacterium Delftia acidovorans.

Ionisation properties of individual titratable side chains of RNase T1 were explored in detail both experimentally by NMR spectroscopy and theoretically by pKa calculations. The study revealed a novel interpretation of the observed pH dependence of the chemical shifts of several residues. It was also shown that titration of Asp76 is coupled to dipole reorientation of a bounded water molecule, which suggested an interpretation of presumably contradicting experimental observations.

Theoretical investigations of DADH showed that (i) the protonation/deprotonation transition of the binary complex is related to the coupled ionisation of Tyr151 and Lys155 in the active site and (ii) the pH-dependence of the proton abstraction is correlated with a reorganization of the hydrogen bond network in the active site involving also the O2' ribose hydroxyl group from the co-enzyme, which acts as a switch.

pKa calculations were combined with 1 ns MD simulations based on three different initial structures of xylanase. A tendency of improvement of predicted pKa values was demonstrated, which agrees with the findings of other authors using similar computational protocol. The influence of length of MD simulation and correlations to the initial structure were discussed.