J. Valle-Orero, et al., The elastic free energy of a tandem modular protein under force, Biochemical and Biophysical Research Communications (2015), http://dx.doi.org/10.1016/j.bbrc.2015.03.051
The article itself can be found here.
This article presents a model that is used to describe the dynamics of multi-domain protein folding and unfolding. The model is essentially an extension and modification of a model made from Berkovich et al. . The article develops a model that describes the free energy of the protein with respect to its length. This essentially tells us what lengths are correlated with what energies. This curve is created by considering the worm-like chain model modulated by a morse and a gaussian potential (see Equation Set 1).
Equation Set 1:
The different parameters and definition of parameters are given in the supporting information (see supporting information document). These gaussian and morse potentials allow for energy barriers that separate different folded/unfolded states. Now, once we have created a energy landscape describing the protein, we solve a stochastic differential equation, whose domain is actually on the surface of the landscape (see equation 2).
Because this equation depends on the negative of the derivative of the energy landscape it will always tend toward a local minimum, and because of the stochastic term, gamma, that models brownian motion, the equation itself will always tend toward the global minimum of the energy landscape. Due to the energy landscapes force dependency we notice that the minimum energy changes as a function of force (see Figure 1).
This makes intuitive sense, as we expect that applying no force to a protein results in little unfolding, while high force regimes will tend the system to a longer , more unfolded state. The article concludes by discussing the various dependencies on contour length and persistence length, and how they correlate with empirical data (see Figure 2).
 - R. Berkovich, S. Garcia-Manyes, J. Klafter, M. Urbakh, J.M. FernandezHopping around an entropic barrier created by forceBiochem. Biophys. Res. Commun., 403 (2010), pp. 133–137
Supporting Information Document