Asaf Farhi — Page 2

arXiv2013

Temperature Integration: an efficient procedure for calculation of free energy differences

We propose a method, Temperature Integration, which allows an efficient calculation of free energy differences between two systems of interest, with the same degrees of freedom, which may have rough energy landscapes. The method is based on calculating, for each single system, the difference between the values of lnZ at two temperatures, using a Parallel Tempering procedure. If our two systems of interest have the same phase space volume, they have the same values of lnZ at high-T, and we can obtain the free energy difference between them, using the two single-system calculations described above. If the phase space volume of a system is known, our method can be used to calculate its absolute (versus relative) free energy as well. We apply our method and demonstrate its efficiency on a toy model of hard rods on a 1-dimensional ring.

cond-mat.stat-mech↗

arXiv2012

Comparing secondary structures of RNA and calculating the free energy of an interior loop using a novel method for calculating free energy

The thesis consists of two projects. In the first project, we present a software that analyses RNA secondary structures and compares them. The goal of this software is to find the differences between two secondary structures (experimental or predicted) in order to improve or compare algorithms for predicting secondary structures. Then, a comparison between secondary structures predicted by the Vienna package to those found experimentally is presented and cases in which there exists a difference between the prediction and the experimental structure are identified. As the differences originate mainly from faces and hydrogen bonds that are not allowed by the Vienna package, it is suggested that prediction may be improved by integrating them into the software. In the second project we calculate the free energy of an interior loop using Monte-Carlo simulation. We first present a semi-coarse grained model for interior loops of RNA, and the energy model for the different interactions. We then introduce the Monte-Carlo simulations and the method of Parallel Tempering which enables good sampling of configuration space by simulating a system simultaneously at several temperatures. Next we present Thermodynamic Integration, which is a method for calculating free energy differences. Then, We introduce a method that calculates the free energy significantly faster since we need to use only one parameter, $T$. To implement this method, we had to reach a regime in which the partition functions of the two systems are equal, which isn't satisfied for systems that have different entropies in the high temperature limit, so a solution to this problem had to be found. Free energy values calculated for various interior loops are shown, and may, if verified or with a more realistic modelling, be integrated into the Vienna package and supply an alternative to the experiments done.

q-bio.BM↗