Predict the minimum free energy structure of nucleic acids.

seqfold is an implementation of the Zuker, 1981 dynamic programming algorithm, the basis for UNAFold/mfold, with energy functions from SantaLucia, 2004 (DNA) and Turner, 2009 (RNA).

pypy3 -m ensurepip
pypy3 -m pip install seqfold

For a 200bp sequence (on my laptop), pypy3 takes 2.5 seconds versus 15 seconds for CPython.

conda install -c bioconda seqfold

Thank you to @jonas-fuchs for this.

pip install seqfold

from seqfold import fold, dg, dg_cache, dot_bracket

# just returns minimum free energy
dg("GGGAGGTCGTTACATCTGGGTAACACCGGTACTGATCCGGTGACCTCCC", temp = 37.0)  # -13.4

# `fold` returns a list of `seqfold.Struct` from the minimum free energy structure
structs = fold("GGGAGGTCGTTACATCTGGGTAACACCGGTACTGATCCGGTGACCTCCC")
print(sum(s.e for s in structs))  # -13.4, same as dg()
for struct in structs:
    print(struct)  # prints the i, j, ddg, and description of each structure

# `dg_cache` returns a 2D array where each (i,j) combination returns the MFE from i to j inclusive
cache = dg_cache("GGGAGGTCGTTACATCTGGGTAACACCGGTACTGATCCGGTGACCTCCC")

# `dot_bracket` returns a dot_bracket representation of the folding
print(dot_bracket(seq, structs))  # ((((((((.((((......))))..((((.......)))).))))))))

usage: seqfold [-h] [-t FLOAT] [-d] [-r] [--version] SEQ

Predict the minimum free energy (kcal/mol) of a nucleic acid sequence

positional arguments:
  SEQ                   nucleic acid sequence to fold

optional arguments:
  -h, --help            show this help message and exit
  -t FLOAT, --celcius FLOAT
                        temperature in Celsius
  -d, --dot-bracket     write a dot-bracket of the MFE folding to stdout
  -r, --sub-structures  write each substructure of the MFE folding to stdout
  --version             show program's version number and exit

$ seqfold GGGAGGTCGTTACATCTGGGTAACACCGGTACTGATCCGGTGACCTCCC --celcius 32
-15.3

$ seqfold GGGAGGTCGTTACATCTGGGTAACACCGGTACTGATCCGGTGACCTCCC --celcius 32 --dot-bracket --sub-structures
GGGAGGTCGTTACATCTGGGTAACACCGGTACTGATCCGGTGACCTCCC
((((((((.((((......))))..((((.......)))).))))))))
   i    j    ddg  description
   0   48   -1.9  STACK:GG/CC
   1   47   -1.9  STACK:GG/CC
   2   46   -1.4  STACK:GA/CT
   3   45   -1.4  STACK:AG/TC
   4   44   -1.9  STACK:GG/CC
   5   43   -1.6  STACK:GT/CA
   6   42   -1.4  STACK:TC/AG
   7   41   -0.5  BIFURCATION:4n/3h
   9   22   -1.1  STACK:TT/AA
  10   21   -0.7  STACK:TA/AT
  11   20   -1.6  STACK:AC/TG
  12   19    3.0  HAIRPIN:CA/GG
  25   39   -1.9  STACK:CC/GG
  26   38   -2.3  STACK:CG/GC
  27   37   -1.9  STACK:GG/CC
  28   36    3.2  HAIRPIN:GT/CT
-15.3

• The type of nucleic acid, DNA or RNA, is inferred from the input sequence.
• seqfold is case-insensitive with the input sequence.
• The default temperature is 37 degrees Celsius for both the Python and CLI interface.

Secondary structure prediction is used for making PCR primers, designing oligos for MAGE, and tuning RBS expression rates.

While UNAFold and mfold are the most widely used applications for nucleic acid secondary structure prediction, their format and license are restrictive. seqfold is meant to be an open-source, minimalist alternative for predicting minimum free energy secondary structure.

Papers, and how they helped in developing seqfold, are listed below.

Nussinov, Ruth, and Ann B. Jacobson. "Fast algorithm for predicting the secondary structure of single-stranded RNA." Proceedings of the National Academy of Sciences 77.11 (1980): 6309-6313.

Framework for the dynamic programming approach. It has a conceptually helpful "Maximal Matching" example that demonstrates the approach on a simple sequence with only matched or unmatched bp.

Zuker, Michael, and Patrick Stiegler. "Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information." Nucleic acids research 9.1 (1981): 133-148.

The most cited paper in this space. Extends further than Nussinov, 1980 with a nearest neighbor approach to energies and a consideration of each of stack, bulge, internal loop, and hairpin. Their data structure and traceback method are both more intuitive than Nussinov, 1980.

Jaeger, John A., Douglas H. Turner, and Michael Zuker. "Improved predictions of secondary structures for RNA." Proceedings of the National Academy of Sciences 86.20 (1989): 7706-7710.

Zuker and colleagues expand on the 1981 paper to incorporate penalties for multibranched loops and dangling ends.

SantaLucia Jr, John, and Donald Hicks. "The thermodynamics of DNA structural motifs." Annu. Rev. Biophys. Biomol. Struct. 33 (2004): 415-440.

The paper from which almost every DNA energy function in seqfold comes from (with the exception of multibranch loops). Provides neighbor entropies and enthalpies for stacks, mismatching stacks, terminal stacks, and dangling stacks. Ditto for bulges, internal loops, and hairpins.

Turner, Douglas H., and David H. Mathews. "NNDB: the nearest neighbor parameter database for predicting stability of nucleic acid secondary structure." Nucleic acids research 38.suppl_1 (2009): D280-D282.

Source of RNA nearest neighbor change in entropy and enthalpy parameter data. In /data.

Ward, M., Datta, A., Wise, M., & Mathews, D. H. (2017). Advanced multi-loop algorithms for RNA secondary structure prediction reveal that the simplest model is best. Nucleic acids research, 45(14), 8541-8550.

An investigation of energy functions for multibranch loops that validates the simple linear approach employed by Jaeger, 1989 that keeps runtime within O(n³).