Results in two areas of methodology of free energy simulations are presented: (i) the meaning of free energy components and (ii) the role of bonded (bond and bond angle) terms in free energy ...calculations. In the so-called thermodynamic integration method (TI) an overall free energy difference can be decomposed into contributions according to type and/or origin of the underlying change in interactions. Free energy components obtained in this manner depend on the simulation path, and the origin and extent of this path-dependence are analyzed. The components of a (single) free energy difference resulting from simulations along two (or more) paths differ, but their behavior can be understood and interpreted meaningfully. Furthermore, the utility of studying the alchemical as opposed to the experimental paths in a thermodynamic cycle to calculate a double free energy difference and the relevance of the free energy components obtained for the interpretation of experimental results are demonstrated. A framework for the interpretation of results of free energy simulations based on component analysis is provided. In the second part of this thesis the correct treatment and importance of bonded energy terms in free energy simulations are studied. The proper handling of bond and bond angle terms in free energy simulations is investigated and shown to depend mainly on the choice of a dual vs. a single topology methodology. While there are no difficulties to describe changes in bond and bond angle terms, problems can occur if they are removed or formed in a molecular dynamics simulation. It is demonstrated that formal bond (bond angle) components arise from three physical sources, and vibrational, potential-of-mean-force and Jacobian factor contributions are distinguished. The Jacobian factor term provides a more comprehensive justification of the "moment of inertia correction" or "dynamic stretch free energy" suggested previously. The analysis makes clear when it may be permissible to omit internal energy terms from the free energy formalism, thus addressing the question of self-term contributions from bonded energy terms (contributions arising from changes in the energy function of the part of the system that is mutated).
Recently, we presented a generalisation of the Jarzynski non-equilibrium work
theorem for phase space mappings. The formalism shows that one can determine
free energy differences from approximate ...trajectories obtained from molecular
dynamics simulations in which very large timesteps are used. In this work we
test the method by simulating the force induced unfolding of a deca-alanine
helix in vacuum. The excellent agreement between results obtained with a small,
conservative time step of 0.5 fs and results obtained with a time step of 3.2
fs (i.e., close to the stability limit) indicates that the large time step
approach is practical for such complex biomolecules. We further adapt the
method of Hummer and Szabo for the simulation of single-molecule force
spectroscopy experiments to the large time step method. While trajectories
generated with large steps are approximate and may be unphysical - in the
simulations presented here we observe a violation of the equipartition theorem
- the computed free energies are exact in principle. In terms of efficiency,
the optimum time step for the unfolding simulations lies in the range 1-3 fs.
Recently, we presented a generalisation of the Jarzynski non-equilibrium work theorem for phase space mappings. The formalism shows that one can determine free energy differences from approximate ...trajectories obtained from molecular dynamics simulations in which very large timesteps are used. In this work we test the method by simulating the force induced unfolding of a deca-alanine helix in vacuum. The excellent agreement between results obtained with a small, conservative time step of 0.5 fs and results obtained with a time step of 3.2 fs (i.e., close to the stability limit) indicates that the large time step approach is practical for such complex biomolecules. We further adapt the method of Hummer and Szabo for the simulation of single-molecule force spectroscopy experiments to the large time step method. While trajectories generated with large steps are approximate and may be unphysical - in the simulations presented here we observe a violation of the equipartition theorem - the computed free energies are exact in principle. In terms of efficiency, the optimum time step for the unfolding simulations lies in the range 1-3 fs.
