As mentioned in "Theory" section there are many pKa estimates based on different experiments.
On the other hand, one can try to obtain pKa computationally. Here I present example how to optimize pKa in order to obtain more accurate isoelectric point predictions. For that protein dataset(s) with experimentally determined isoelectric points is needed. For proteins there are at least two such: PIP-DB and SWISS-2DPAGE (for more details see "Datasets").

Brute force attack:
Checking all possible combinations is not very tractable as even for 9 variables (charged amino acid pKa) in range of pH of 3 (±1.5 pH of average for given amino acid pKa) with 0.01 precision gives 1.9683 × 10²² possibilities. Far too many to compute.

Basinhopping optimization using truncated Newton algorithm:
This produces suboptimal results in more reasonable time with less than few dozens of iterations with pKa optimized with high precision.

In the nutshell, the basinhopping algorithm is iterative search procedure with each cycle composed of the following features:

• random perturbation of the coordinates
• local minimization
• accept or reject the new coordinates based on the minimized function value of the Metropolis criterion of standard Monte Carlo algorithm

As an initial seed previously published pKa values were used. To limit search space truncated Newton algorithm was used with 2 pH units bounds for pKa variables (e.g. if starting point for Cys pKa was 8.5 the solution was allowed in the interval [6.5, 10.5]).
For more details how those algorithms works go here.

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