Proton binding

For noncompetitive proton binding, the proton coverage degree (fraction of sites that are protonated) is given, following Equation 4.69, as 

the site fraction / becomes a continuous function of the proton-binding parameter K . As mentioned in the preceding discussion, usnaUy a two-peak distribution is assumed for/, one centered about log K,j = 3-5 and the other one about 8-10. As it was discussed in Chapter 4, introduction of the Sips distribution (Equation 4.70) leads to the Langmuir-Freundlich (LF) isotherm  

FIGURE 11.4 Typical Sips and Gauss distribution shapes for protOT binding to h ic substances. The Sips spectrum is given by Equation 11.34, with log = 4, log 2 = 9, Xi = 0.65, X2 = 0.35, = 0.55, and = 0.45 the Gaussian spectrum has the same parameters, 

For comparison, a dual peak Gaussian distribution reads 

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Earlier studies (162) on synthetic iron-sulfur-based clusters showed that protons bind to the bridging sulfur atoms and increase the rate of substitution at the metal atoms. FeMoco exhibits similar behavior, with protonation causing considerable acceleration in the... 

Orttung, WH, Proton Binding and Dipole Moment of Hemoglobin. Refined Calculations, Biochemistry 9, 2394, 1970. 

Table 1. Estimated parameters of proton-binding model...

Simonson T, Carlsson J, Case DA (2004) Proton binding to proteins pKa calculations with explicit and implicit solvent models. J Am Chem Soc 126 4167-4180. 

To illustrate these methods, we consider the main biological problems that have motivated their development. The problems that have received the most attention are the receptor-ligand binding problem [12-16] and the calculation of proton binding affinities (pKa shifts) [17-20], The methods described can also be applied to many related problems, such as redox protein behavior, protein-protein association, protein folding, or membrane insertion. 

Other electrostatic processes studied include proton binding [43] and changing the molecular charge distribution [44], The free energy expansion formula (12.5) was used, including terms up to second order... 

Linear Response Theory Application to Proton Binding and )Ka Shifts... 

We now turn to the problem of proton binding to proteins, an important area for simplified free energy methods. The linear response formalism earlier underlies most of the methods used today. It leads directly to one of the more useful practical methods, the so-called LRA, or linear response approximation method [59], presented here. 

The idea is to do simulations of the system before and after the proton binding i.e., to simulate the reactant and product states. With the assumption of linear response, these provide all the information needed to compute AA. Indeed, the free energy to introduce a fractional charge Aq into the reactant state (0 < A < 1) is a parabolic function of Aq, which can be written ... 

The Choice of Dielectric Constant Proton Binding as a Paradigm... 

The most important model parameter in PBFE and MM/PBSA is the dielectric constant used for the solutes. Most studies have taken an empirical approach, viewing the dielectric constant as an adjustable parameter. While this seems plausible, it is prudent to analyze the physical problem in more detail, because, in some cases, the experimental data can be fit by models that are distinctly unphysical, despite some plausible features. We therefore come back to the simplest possible PBFE calculation the important problem of proton binding, or pKa shifts. We discuss a nonem-pirical model that attempts to avoid parameter fitting and that gives insights into the limitations of simplified continuum electrostatic free energy methods. 

Archontis, G. Simonson, T., Proton binding to proteins a free energy component analysis using a dielectric continuum model, Biophys. J. 2005, 88, 3888-3904... 

Ion-water Proton Binding Times, g, Obtained from IQENS Experiments on Concentrated Aqueous Ionic Solutions at 298 K (26)... 

Y. Niu, L. Sun and R. M. Crooks, Determination of the intrinsic proton binding constants for poly(amidoamine) dendrimers via potentiometric pH titration. Macromolecules 36, 5725—5731 (2003). 

Here, only when the two protons bind to the molecule do we observe a large shift in favor of the trans configuration. 

The oxidation/reduction of redox cofactors in biological systems is often coupled to proton binding/release either at the cofactor itself or at local amino acid residues, which provides the basic mechanochem-ical part of a proton pump such as that foimd in cytochrome c oxidase (95). Despite a thermodynamic cycle that provides that coupling of protonation of amino acids to the reduction process will result in a 60 mV/pH decrease unit in the reduction potential per proton boimd between the pAa values in the Fe(III) and Fe(II) states, the essential pumping of protons in the respiratory complexes has yet to be localized within their three-dimensional structures. 

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