Some Theoretical and Computational Aspects of the Inclusion of Proton Isomerism in the Protonation Equilibrium of Proteins

Abstract

The present article discusses some aspects concerning the inclusion of proton isomerism in simulations of the global protonation equilibrium of protein molecules. In the context of continuum electrostatic methods, the usual basis for these simulations, this isomerism can be treated as a coexistence of tautomeric forms in equilibrium in a rigid structure; furthermore, it can be formally extended to nontitrable sites with proton isomerism, such as alcohol groups and water molecules. We follow the previously adopted approach of transforming the real system of tautomeric sites into a thermodynamically equivalent one of nontautomeric pseudosites, establishing a proper relation between the two systems. The necessary energetic and entropic modifications of model compound pK a values are also discussed. Additionally, we discuss the new entropy term, named tautomeric entropy, that results from the explicit inclusion of tautomerism in the simulations and how it can be computed together with the occupational entropy. Simulations using tautomerism were done for hen egg white lysozyme (HEWL) using a simple set of tautomers at dihedral energy minima. A very good overall prediction of pK a values was obtained, presumably the best in the literature for HEWL, using a high value for the dielectric constant assigned to the protein region, p . The explicit inclusion of water molecules treated under the extended tautomer formalism further improved the prediction, in contrast with previous works using rigid water molecules. In all calculations performed, the region with p ≈ 20 is shown the to be the optimal one. Some aspects of the somewhat controversial issue of the "proper" p value are also discussed.

Redox-Bohr and Other Cooperativity Effects in the Nine-heme Cytochrome c from Desulfovibrio desulfuricans ATCC 27774

“…The charges, radii, and pK a values for the model compounds were the same as used earlier (42,45,58). The reduction potential used for the heme model was Ϫ249 mV, as calculated by Teixeira et al (45).…”

“…The dielectric constants used were 20 for the protein interior and 80 for the solvent. The dielectric constant applied in CE calculations for the protein region has been a matter of debate (58,(62)(63)(64). In practical terms, this dielectric constant accounts for factors not included explicitly in the continuum model (63,65), particularly the conformational reorganization of the protein upon charge modifications.…”

Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

“…The interplay of so many titratable sites of several ionizable objects will slow down even more the already difficult sampling. The best Krieger et al (2006), Burger andAyers (2011), andOlsson et al (2011) b See Bashford (1997), Baker et al (2001), Anandakrishnan et al (2012), Wang et al (2015), and Sakalli and Knapp (2015) c See Svensson et al (1990), Kesvatera et al (1996Kesvatera et al ( , 1999Kesvatera et al ( , 2001, Teixeira et al (2010), Carnal et al (2015), Barroso da Silva et al (2017a), and Barroso da Silva and MacKernan (2017b) d See Baptista et al (1997, Baptista and Soares (2001), Machuqueiro and Baptista (2007), and Santos et al (2015) e See Lee et al (2004), Shen (2009), Dashti et al (2012), Goh et al (2013a), Chen et al (2013Chen et al ( , 2014Chen et al ( , 2016, Chen and Roux (2015), Socher and Stich (2016), and Donnini et al (2016) f See Tummanapelli and Vasudevan (2015), Kamerlin et al (2009), andLi et al (2002) alternative in this case is the MC titration schemes, particularly the FPTS. From this mesoscopic scheme, other intermediate models can also be derived in order to improve accuracy for specific tasks at higher CPU expenses.…”

Aplicação da equação de Poisson-Boltzmann ao cálculo de propriedades dependentes do pH em proteínas

“…Numa situação ideal, rearranjos estruturais estariam acoplados a mudanças no campo elétrico de modo que interações entre grupos carregados são otimizadas; uma constante dielétrica alta compensa a ausência de flexibilidade estrutural inerente ao modelo. Assim, na ausência de modelos mais detalhados, a constante dielétrica pode ser considerada como um parâmetro ajustável e definido através da comparação entre resultados teóricos e experimentais 25,26 .…”

“…A vantagem deste modelo é a possibilidade de um tratamento fisicamente mais realístico de ambientes dielétricos tão distintos, quanto o interior e a superfície de uma proteína. Mais recentemente, foi proposto que na ausência de modelos mais detalhados para representar a permitividade interna da proteína, a constante dielétrica deveria ser considerada como um parâmetro ajustável, cujo valor deve ser definido através da comparação entre resultados teóri-cos e experimentais e de acordo com o sistema em consideração 25,26 . Indubitavelmente, a restrição mais grave da teoria de PoissonBoltzmann para o cálculo de pK a em biomoléculas é a ausência de flexibilidade conformacional do sistema.…”