# Analysis

## Energetic reweighting of GaMD simulations using PyReweighting

A toolkit of python scripts “PyReweighting” has been developed to facilitate reweighting analysis of aMD and GaMD simulations. PyReweighting implements a list of commonly used reweighting methods, including (1) exponential average that reweights trajectory frames by the Boltzmann factor of the boost potential and then calculates the ensemble average for each bin, (2) Maclaurin series expansion that approximates the exponential Boltzmann factor, and (3) cumulant expansion that expresses the reweighting factor as summation of boost potential cumulants.

Notably, MacLaurin series expansion is equivalent to cumulant expansion on the first order. Cumulant expansion to the 2nd order (“Gaussian approximation”) normally provides the most accurate reweighting results.

Download PyReweighting scripts and tutorial

## Kinetic reweighting of GaMD simulations with Kramers’ Rate Theory

Reweighting of biomolecular kinetics from GaMD simulations can be obtained by applying Kramers rate theory. The curvatures and energy barriers of the reweighted and modified free energy profiles, as well as the apparent diffusion coefficients, are calculated and used in Kramers’ rate equation to determine accelerations of biomolecular kinetics and recover the original biomolecular kinetic rate constants from the GaMD simulations. In addition to “PyReweighting” that facilitates calculations of free energy profiles, a Smoluchowski equation solver coded in C++ (“smol_solver” shared by Prof. Donald Hamelberg) can be used to calculate kinetic rates across PMF free energy barriers as needed to estimate the apparent diffusion coefficients.