Introduction to Constant pH MD

By: Eleftherios Mainas, Ph.D.

outline

• molecular dynamics
• solvent
• monte carlo
• pH thermodynamics
• CpHMD

molecular dynamics

• potential energy

• force

• dynamics: NVE (Newton), NVT (Langevin), NPT (NH)

solvent

monte carlo

• imagine two states, X and Y

• similar to chemical kinetics

• detailed balance

• transition probability

monte carlo

• equal to opposite move

• Boltzmann distribution

• metropolis choice (satisfies condition)

• equivalent to

pH thermodynamics

• Henderson Hasselbach

• is related to Gibbs free energy

pH thermodynamics

• MD people use protonation fraction

• interactions cause deviations

Last note on pH

• protonated fraction in terms of free energy

• by comparing with

• we get

Constant pH Molecular Dynamics (CpHMD)

• md samples configurations under constant protonation states

• we want to sample configurations under constant pH

• also we want titration curve to calculate pKa and Hill coefficient

• hybrid method, leverages monte carlo and classical molecular dynamics

• The key quantity is the free energy of protonation

(Amber
manual
p. 563)

free energy of protonation

• no knowledge of

• need to use reference compound

• thermodynamic cycle

(Vinny's dissertation)

free energy of protonation

• is a state variable, path independent

• AMBER approximation

sampling of protonation states

• within a few lines of algebra

• is precomputed (Biliverdin )

• MC move

• MD/MC will sample entire protonation space, ergodicity

• get as a function of time

• multiple values to get titration curve

questions/observations?