# Minimum Free Energy (MFE) Algorithms

Computing the Minimum Free Energy (MFE), i.e. the most stable conformation in thermodynamic equilibrium.

## Zuker’s Algorithm

Our library provides fast dynamic programming Minimum Free Energy (MFE) folding algorithms derived from the decomposition scheme as described by Zuker and Stiegler [1981].

## MFE for circular RNAs

Folding of *circular* RNA sequences is handled as a post-processing step
of the forward recursions. See Hofacker and Stadler [2006] for further details.

## MFE Algorithm API

Predicting the Minimum Free Energy (MFE) and a corresponding (consensus) secondary structure.

In a nutshell we provide two different flavors for MFE prediction:

Global MFE Prediction - to compute the MFE for the entire sequence

Local (sliding window) MFE Prediction - to compute MFEs for each window using a sliding window approach

Each of these flavors, again, provides two implementations to either compute the MFE based on

single RNA (DNA) sequence(s), or

multiple sequences interacting with each other, or

a comparative approach using multiple sequence alignments (MSA).

For the latter, a consensus secondary structure is predicted and our implementations compute an average of free energies for each sequence in the MSA plus an additional covariance pseudo-energy term.

The implementations for Backtracking MFE structures are generally agnostic with respect to whether local or global structure prediction is in place.