Discussion of Other Techniques

Several other techniques are available to compute the PMF. In this section we discuss the steered force molecular dynamics (SMD) [35-37] and the metadynamics of Laio and Parrinello [30-34]. 

In SMD an external force is applied in an attempt to accelerate a chemical process such as unfolding of a protein or dissociation of two molecules. In that respect, it is similar to AFM or optical-tweezers experiments. The applied force is given by  

Metadynamics defines coarse-grained variables which are assumed to be slow coordinates of the system. Those coordinates are similar to the order parameters considered earlier in this chapter. The coarse variables are evolved independently following a steepest-descent equation. In the case of a single variable, Laio and Parrinello [34] use 

The extra term with Gaussian functions helps push the variable away from regions which have already been visited see Fig. 4.7. This enhances the efficiency of the 

The steepest descent (4.48) requires calculation of dA/d . Laio and Parrinello chose to estimate this term by performing short constrained molecular dynamics simulations and computing the potential of mean constraint force (see Carter et al. [45]). 

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Here I will describe first lyotropic liquid crystallinity from the more conventional crystallographic approach, with some discussion of other techniques, including calorimetry, NMR spectroscopy and optical microscopy. Following that, an analysis of topological probes of mesostructure will be given. 

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