List of Figures

1. Graph of van der Waals potential with and without switching
2. Graph of electrostatic potential with and without shifting function
3. Graph of electrostatic split between short and long range forces
4. Example of cutoff and pairlist distance uses
5. Graph showing a slice of a ramp potential, showing the effect of mgridforcevoff
6. Graphical representation of a Colvars configuration.
7. Dual topology description for an alchemical simulation. Case example of the mutation of alanine into serine. The lighter color denotes the non-interacting, alternate state.
8. Convergence of an FEP calculation. If the ensembles representative of states $a$ and $b$ are too disparate, equation (67) will not converge (a). If, in sharp contrast, the configurations of state $b$ form a subset of the ensemble of configurations characteristic of state $a$ , the simulation is expected to converge (b). The difficulties reflected in case (a) may be alleviated by the introduction of mutually overlapping intermediate states that connect $a$ to $b$ (c). It should be mentioned that in practice, the kinetic contribution, ${\cal T}({\bf p}_x)$ , is assumed to be identical for state $a$ and state $b$ .
9. Relationship of user-defined $\lambda$ to coupling of electrostatic or vdW interactions to a simulation, given specific values of alchElecLambdaStart or alchVdwLambdaEnd.
10. Sample TI data ( $log(\left <\frac {\partial U}{\partial \lambda }\right >)$ against $\lambda$ ). The blue shaded area shows the integral with fine sampling close to the end point. The red area shows the difference when $\lambda$ values are more sparse. In this example, insufficient sampling before $\lambda$ $\simeq$ 0.1 can result in a large overestimation of the integral. Beyond $\simeq$ 0.2, sparser sampling is justified as dE/d$\lambda$ is not changing quickly.
11. Schematics of the aMD method. When the original potential (thick line) falls below a threshold energy $E$ (dashed line), a boost potential is added. The modified energy profiles (thin lines) have smaller barriers separating adjacent energy basins.
12. Schematic illustration of GaMD. When the threshold energy $E$ is set to the maximum potential ($iE=1$ mode), the system's potential energy surface is smoothened by adding a harmonic boost potential that follows a Gaussian distribution. The coefficient $k_0$ , which falls in the range of $0 - 1.0$ , determines the magnitude of the applied boost potential.
13. The core difference between conventional and constant-pH MD can be illustrated by a simple enzyme $E$ with four protonation states describing the occupancy of two titratable residues, $R_1$ and $R_2$ . A conventional MD simulation handles the states separately (left panel). The relative importance of the states must be known beforehand or computed by other means. Conversely, a constant-pH MD simulation handles the states collectively and actively simulates interconversion (right panel). Determining the relative importance of the states is a direct result of the simulation.
14. The basic constant-pH MD scheme in NAMD is to alternate equilibrium sampling in a fixed protonation state followed by a nonequilibrium MD Monte Carlo move to sample other protonation states. The latter move can be accepted or rejected. If accepted, the simulation continues in the new protonation state. If the move is rejected, sampling continues as if the move were never attempted at all.