Steered Molecular Dynamics

Steered molecular dynamics simulation (SMD) is a technique mimicking the principle of the atomic force microscopy (AFM). In practice, one applies a time dependent mechanical external potential that obliges the system to perform some prescribed motion in a prescribed simulation time. SMD has been widely used to explore the mechanical functions of biomolecules such as ligand receptor binding/unbinding and elasticity of muscle proteins during stretching at the atomic level[145]. The SMD has also been used in the past to approximately estimate the potential of mean force (PMF)^8.1 along a given mechanical coordinate (for example a distance or an angle). The model upon which this technique for estimating the PMF relies was based on the assumption that the driven motion along the reaction coordinate $z$ could be described by an over-damped one-dimensional Langevin equation of the kind

$$\gamma \dot z = -\frac {d \cal W}{dz} + F_{\rm ext}(z,t)+ \xi(t)$$ (8.1)

where $\gamma$ is the friction coefficient, $\cal W$ is the underlying potential of mean force , $F_{\rm ext}(z,t)$ is the external force due the driving potential and $\xi(t)$ is a stochastic force related to the friction through the second fluctuation dissipation theorem. The PMF $W(z)$ can then be determined only if one knows (or can somehow figure it out) the friction coefficient, so as to evaluate the frictional force that discounts the irreversible work done in the driven process. The method also relies on the strong assumption that the friction along $z$ is local in time, i.e. the underlying equilibrium process is Markovian.