# Cysteine titration

We started with getting cysteing $\partial V/\partial \lambda$. Without any force field modifications we managed to get flat distributions


But apparantly inside the protein the cysteine behaviour was sort of sticky. Firtsly, it preffers to stay in the middle a lot, and secondly, the transitions are very rare.


And as you can see, non physicall region is indeed very populated


Thus, we tried to use adaptive barrier, but it didn't solve the issue with the transitions. They are still very rare. But higher barriers don't show the overpopulated non-physical regions (check the $\lambda$-trajectories only before 80 ns, I wrongly implemented barrier checkpointing)


To contine, I calculated the cysteine $\partial V/\partial \lambda$ inside the protein, to estimate the $\Delta$p$K_{\text{a}}$.


The results suggest that the p$K_{\text{a}}$ of cysteine inside the protein is around 7 (experimental value is 5.3). The estimation can be further improved, by taking into account the correct protonation states of other titratable groups and by running longer simulations.

The next thing we tried, was running protein with setting pH and biassing potential of Cys to zero and using new parameters for Cys, obtained inside the protein. In 400 ns, the replicas were inconsestent and the stickiness was obvious, suggesting that there are strong interactions between Cys and the protein environment, which prevents the transition of $\lambda$-coordinate. This might be a general problem, we expect to observe inside the enzyme active site and not only for cysteine. Therefore, we need to seek for a solution.


Some options for now:

- Computing $\partial V/ \partial \lambda$ of a site, while keeping others titratable (so for a specific site $\lambda$ is fixed, for others - not)
- Adding a gaussian noise to the $\lambda$-force from the actal distribution of the force. As we see from calibration runs, the forces have quite large dispersion, and probably keeping this distribution while running constant pH, might provoke additional transitions.
- Running $\lambda$-dynamics at higher temperature
- Anything else?

- Run with LJ of deprotonated case
- Structural details (diff between replicas)
- LJ of oxygen instead of S