Developing hybrid approaches to predict pK_avalues of ionizable groups

Abstract

Accurate predictions of pKa values of titratable groups require taking into account all relevant processes associated with the ionization/deionization. Frequently, however, the ionization does not involve significant structural changes and the dominating effects are purely electrostatic in origin allowing accurate predictions to be made based on the electrostatic energy difference between ionized and neutral forms alone using a static structure. On another hand, if the change of the charge state is accompanied by a structural reorganization of the target protein, then the relevant conformational changes have to be taken into account in the pKa calculations. Here we report a hybrid approach that first predicts the titratable groups, which ionization is expected to cause conformational changes, termed “problematic” residues, then applies a special protocol on them, while the rest of the pKa’s are predicted with rigid backbone approach as implemented in multi-conformation continuum electrostatics (MCCE) method. The backbone representative conformations for “problematic” groups are generated with either molecular dynamics simulations with charged and uncharged amino acid or with ab-initio local segment modeling. The corresponding ensembles are then used to calculate the pKa of the “problematic” residues and then the results are averaged.

Biomolecular electrostatics and solvation: a computational perspective

“…Significant efforts have been made to accurately measure (Baran et al, 2008; Castañeda et al, 2009; Denisov et al 2004; Fitzkee & García-Moreno E, 2008; Harms et al, 2009; Harms et al, 2008; Isom et al, 2008; Isom et al, 2011; Isom et al, 2010; Karp et al, 2007; Karp et al, 2010) and predict (Alexov et al, 2011; Antosiewicz, 2008; Antosiewicz et al, 1996a; Antosiewicz et al, 1996b; Bashford & Karplus, 1990; Bryce et al, 1998; Carstensen et al, 2011; Flanagan et al, 1981; Georgescu et al, 2002; Karp et al, 2007; Khandogin & Brooks, 2006; Laurents et al, 2003; Li et al, 2002; Li et al, 2004; Li et al, 2005; Mehler & Guarnieri, 1999; Mitra et al, 2011; Nielsen et al, 2011; Nielsen, 2007; Nielsen, 2009; Nielsen & McCammon, 2003; Nielsen & Vriend, 2001; Shan & Mehler, 2011; Tang et al, 2007; Tynan-Connolly & Nielsen, 2006; Wallace & Shen, 2011; Witham et al, 2011) protein titration states to understand the determinants of pK a values for the amino acids in the interior and exterior of proteins. A recent special issue of Proteins (Alexov et al, 2011) provides an excellent review of the state of the art in the area of biomolecular titration state modeling.…”

Structural Reorganization Triggered by Charging of Lys Residues in the Hydrophobic Interior of a Protein

“…In general, the inability of structure-based calculations to reproduce experimentally measured p K a values of internal groups stems from the failure to account correctly for structural reorganization (Karp et al, 2007). Several groups have made recent progress on this important problem (Arthur et al, 2011; Ghosh and Cui, 2008; Gunner et al, 2011; Kamerlin et al, 2009, Kato and Warshel, 2006; Meyer et al, 2011; Song, 2009; Wallace et al, 2011; Williams et al, 2011; Witham et al, 2011;Yoo and Cui, 2008; Zheng et al, 2008). To improve our understanding of determinants of p K a value of internal groups in proteins it is necessary to describe experimentally the character of the reorganization that is triggered by the ionization of internal groups.…”

Continuum Electrostatics Approaches to Calculating pKas and Ems in Proteins

“…The first is the computational expense of running O (2 n ) molecular dynamics simulations to sample the n distinct neutral and ionized charge states. Rational choices can help pick consequential protonation states to sample (Witham et al, 2011; Meyer & Knapp, 2015). The second limitation is the underlying linear response assumption requiring the energy difference between neutral and ionized states is small – which is often not true for the important titration events in protein systems (Di Russo, Marti & Roitberg, 2014).…”

“…Particular improvement was found for methods that increased the response of the protein; e.g. : by using more explicit sampling via continuous-pH molecular dynamics (Wallace et al, 2011), by adding ensembles of structures obtained with MD (Witham et al, 2011), Rosetta (Song, 2011), through increased side-chain conformation sampling (Gunner, Zhu & Klein, 2011), by increasing the effective ε solute to implicitly model more internal water (Meyer et al, 2011), or by using a smoother dielectric boundary (Word & Nicholls, 2011). The errors for calculations with rigid backbones were smaller when crystal structures of the mutants were used rather then when the mutation was made in silico .…”