Discrete protonation states methods

The discrete protonation states methods employing implicit solvent models in both MD and MC steps have significantly lower computational cost. Dlugosz and... 

The discrete protonation states methods have been tested in pKa calculations for several small molecules and peptides, including succinic acid [4, 25], acetic acid [93], a heptapeptide derived from ovomucoid third domain [27], and decalysine [61], However, these methods have sofar been tested on only one protein, the hen egg lysozyme [16, 61, 71], While the method using explicit solvent for both MD and MC sampling did not give quantitative agreement with experiment due to convergence difficulty [16], the results using a GB model [71] and the mixed PB/explicit... 

One may consider the relaxation process to proceed in a similar manner to other reactions in electronic excited states (proton transfer, formation of exciplexes), and it may be described as a reaction between two discrete species initial and relaxed.1-7 90 1 In this case two processes proceeding simultaneously should be considered fluorescence emission with the rate constant kF= l/xF, and transition into the relaxed state with the rate constant kR=l/xR (Figure 2.5). The spectrum of the unrelaxed form can be recorded from solid solutions using steady-state methods, but it may be also observed in the presence of the relaxed form if time-resolved spectra are recorded at very short times. The spectrum of the relaxed form can be recorded using steady-state methods in liquid media (where the relaxation is complete) or using time-resolved methods at very long observation times, even as the relaxation proceeds. 

A number of discrete states, differing by the protonation state and the geometry of the protonatable sites, are defined for the chain. Transitions among these states are characterised by rate constants which are taken to be of the TST type, with values evaluated from electrostatic calculations and/or kinetic data. The time course of the state s populations is determined by a set of a large number of coupled differential equations (master equation), which is generally solved with stochastic methods first introduced by Gillepsie. ... 

The method of superposition of configurations is essentially based on the assumption that the basic orbitals form a complete set. The most popular basis used so far in the literature is certainly formed by the hydrogen-like functions, which set contains a discrete and a continuous part. The discrete subset corresponds physically to the bound states of an electron around a proton, whereas the continuous part corresponds to a free electron scattered by a proton, or classically to the elliptic and hyperbolic orbits, respectively, in a central-field problem. 

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