Free-energy profiles, computation technique

If the interactions between the polymer and the surface and those inside the bulk polymer liquid are known, computer simulations will be well suited to investigate the surface structure and thermodynamics. There are different techniques to measure the surface free energy by computer simulations. One method consists in integrating the difference between the perpendicular and parallel pressure profiles, (2) and P (z)... 

The Sj 2 reaction, X + RY XR + Y", has been simulated with MC equilibrium calculations by Jorgensen and coworkers [81, 82]. The procedure used by these authors involves three steps i) the lowest energy reaction path is determined for the in vacuo system by using ab initio molecular orbital calculations ii) inter-molecular potential functions are obtained to describe the interactions between the substrate and a solvent molecule these potentials depend on the internal structure of the substrate iii) MC simulations are carried out to determine the free energy profile for the reaction in solution. This is a difficult computational task since importance sampling methods are required to explore all the values of the reaction coordinate. A similar technique was used by Madura and Jorgensen [83] in simulating the nucleophilic addition of hydroxide ion to formaldehyde in the gas phase and in aqueous solution. 

Here, we review how the development of SAXS as a structural technique is driven by advances in computer algorithms that allow to reconstruct low-resolution electron density maps ab initio from scattering profiles. In addition, we delineate how these low-resolution models can be used in free energy electrostatics calculations. Finally, we discuss how one can exploit the hierarchical nature of RNA folding by combining the low resolution, global information provided by SAXS with local information on RNA structure, from either experiments or state-of-the-art RNA structure prediction algorithms, to further increase the resolution and quality of models obtained from SAXS. 

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