Calculate the equilibrium expected value and distribution for each complex popula-

Command:distributions [-ordered] [-maxstates big] [-writestates]

[-sort method] [-quiet] prefix

Description:The executabledistributionscalculates thepartition functionQboxfor aboxcontaining

a small number of strands, given user-definedpopulationsfor each strand species. This is used to calculate theexpected valueandprobability distributionof the population of each species of complex (or ordered com- plex). Partition function information is read from output files generated with the executablecomplexes.

Additional Options:

-ordered

Performs the calculation on ordered complexes rather than complexes. The input is read from the

prefix.ocx(output from the executablecomplexes).

-maxstates big

The maximum number of states of the box to be enumerated (|Λ|, default is 1e7). A segmentation fault will occur if the stack size on your machine is exceeded.

-writestates

Write a (typically large) output file describing properties for all population states of the system.

-sort method

The argumentmethodis one of the following integers.

1: (default) Output is sorted by the expected value of the population of each complex or ordered complex (if-orderedis selected).

2: Output is sorted first by the expected value of the population of each complex and then, if

-orderedis selected, by the expected value of the population of each constituent ordered com-

plex.

3: Output is sorted first by the integer complex identifier and then, if-orderedis selected, by the ordered complex identifier.

4: Output is sorted first by the number of strands in each complex, then by the integersL1 L2 . . . L|Ψ0_| defining the number of each strand type in a given complex (withL1 having the highest prece-

dence, followed byL2, and so on), and finally, if-orderedis selected, by the integer ordered

complex identifier. -quiet

Input: Same as for the executableconcentrations, except the fileprefix.confile is replaced by

prefix.count, which contains the integer population of each of|Ψ0_{|strand species on a separate line.}

The last line of the file contains the volume of the box in liters. This may be entered in scientific notation (e.g.,1.4e-18).

Output:Unless the-quietflag is selected, the following information is written to the screen: • The number of states of the box.

• The free energy of the entire box in units ofkT and in units of kcal. • The wall clock time for the calculation.

The output is written to the files:

• prefix.dist

The content is the same as the input file (with rows sorted according to-sort) with extra columns after the free energy column. The first extra column (for complex or ordered complexj) is the expected value of the populationhmji. Subsequent columns are [pj(0) pj(1) . . . pj(max(m0))]. These represent the probability that complex (or ordered complex)jhas population 0, 1,. . .,max(m0), at equilibrium.

• prefix.states

Generated when-writestatesis selected. Each row corresponds to a population vector,m, for the box. The first column is the probability that the population vector occurs at equilibrium. By default, the remaining entries come in pairs: an integer complex identifier and a nonzero population. If-ordered is selected, the remaining entries come in triples: integer complex and ordered complex identifiers and then a nonzero population. This pattern continues for all complexes (or ordered complexes) with non- zero populations.

Appendix E

Help pages for the NUPACK web

application

E.1

Thermodynamics Input

Nucleic acid type: Select RNA (default) or DNA for strand type. DNA/RNA hybrids are not allowed.

Maximum complex: All complex species up to this size will be considered in the calculation (maximum of 10, default 1). If pseudoknots are allowed, the maximum complex size is 1.

Allow pseudoknots: Include a class of pseudoknots in the calculations. If checked, the maximum complex size is 1 and the nucleic acid type is RNA.

Number of strand species: Select the number of distinct strand species from the pull-down menu (maxi- mum of 10, default 1). If the same sequence is entered twice, it is considered to represent two distinct strand species.

Strand species: For each strand species, enter the name (default “Strand #”) in the left field and the sequence in the right field. Ts or Us are acceptable for both RNA and DNA and will be appropriately converted.

Concentration (if applicable): Enter the initial concentration of the strand species. Use the pull-down menu at right to specify units (defaultµM).

Compute melt: Perform the calculation over a range of temperatures.

Temperature: Enter the temperature (in deg. C). If “Compute melt” is selected, the temperature minimum, increment, and maximum are requested.

Advanced options: Click “Advanced options” to specify additional ordered complexes and select an energy parameter set and dangle treatment.

• Specify additional ordered complexes (if applicable): Enter additional ordered complexes to be included in the calculation (augmenting those automatically specified based on the maximum complex size). Each line of space-separated integers decribes one ordered complex. An example entry for an ordered complex containing one strand each of the first and third strand species and two of the second would be “1 2 3 2”.

• RNA/DNA energy parameters:For RNA, there are two parameter sets, mfold 2.3 (default) and mfold 3.0 (valid only at 37 deg. C). For DNA, the only option is mfold 2.3.

• Dangle treatment:

– None:no dangle energies are considered.

– Some (default): a dangle energy is incorporated for each unpaired base flanking a duplex (a base flanking two duplexes contributes only the minimum of the two possible dangle energies).

– All:a dangle energy is incorporated for each base flanking a duplex regardless of whether it is paired.

Email address: Enter your email address for notification of job completion (required for long jobs).

Reset: Reset all input fields.

Compute time: This order-of-magnitude estimate for the calculation time is updated as the job is specified. Very long calculations are not allowed on the NUPACK server, but source code may be downloaded from the “Downloads” section and used for research purposes on your local machine.

Compute: Start the calculation.