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This is a package for domain-level strand displacement (DSD) system analysis. After installation, you should be able to execute the scripts peppercorn and pilsimulator.

The reaction enumerator Peppercorn reads a file with initially present domain-level complexes, and returns all possible reactions and products. Peppercorn supports arbitrary non-pseudoknotted structures and the following domain-level reactions: bind, open, proximal 3-way and 4-way branch migration, remote 3-way and 4-way branch migration. For more background on reaction semantics we refer to Badelt et al. (2020).

Given a specification of initial species concentrations, the simulation software Pilsimulator can read Peppercorn's output and simulate expected species concentrations over time. Alternatively, you can export the results into SBML format for analysis in your favorite simulator. Note that the reaction rates assume DNA molecules!

For a quick overview of the software, you can also have a look at this talk held at the 26th International Conference on DNA Computing and Molecular Programming (DNA 26).


~$ pip install peppercornenumerator

If you are installing from the git repository, use:

$ python install

Note that support for Python 2.7 was dropped with peppercornenumerator-v1.0. Please consider testing the installation first, e.g. using any of the following commands:

$ python test
$ pytest tests

Quickstart using executable scripts

General workflow

After installation of peppercornenumerator, you must have two excutable scripts, try if they work and look at the options:

$ peppercorn --help
$ pilsimulator --help

Use the executable peppercorn to load the file example.pil and write results to example_enum.pil:

# either using commandline flags
$ peppercorn -o example_enum.pil example.pil
# or read from STDIN and write to STDOUT:
$ cat example.pil | peppercorn > example_enum.pil

Your can simulate the enumerated system using the pilsimulator executable.

$ cat example_enum.pil | pilsimulator --t8 1800 --p0 S1=1e-7 S2=1e-7 C1=1e-9 --atol 1e-10 --rtol 1e-10

Note that default reaction rate constants assume 'M' concentration units, hence we use the same units for specification of initial concentrations (--p0). Due to those small numbers (molar concentrations), we have to specify more sensitive realtive and absolute tolerances for the solver. Check commandline options of peppercorn to change units, e.g. to 'nM', as well as to provide initial concentrations directly in the input file.

Input/Output format

The following input format is recommended. The lengths of all domains are defined first, then all initial complexes are defined in terms of their sequence and secondary structure. For more details on the kernel notation of complexes, see Figure 1 or Section 2 of Badelt et al. (2020).

# <- this is a comment
# Shohei Kotani and William L. Hughes (2017)
# Multi-Arm Junctions for Dynamic DNA Nanotechnology
# Figure 2A: Single-layer catalytic system with three-arm junction substrates.

# Initialize domains (and their complements) and specify their lengths:
length a   = 22  # Domains a and a* with length = 22
length b   = 22
length c   = 22
length t1  = 6   # name = 1 in Figure
length t2  = 6   # name = 2 in Figure
length t3  = 10  # name = 3 in Figure
length T2  = 2

length d1s = 16
length d2  = 6

# Initialize all initial complexes using kernel notation, 
# which combines name, sequence and structure into a single line!
# Always use 5' to 3' direction of sequences.

# The following complex is called C1, has a single strand with 3 unpaired domains:
C1 = t1 c a

# The complex S1 has multiple strands and is connected via paired domains!
# Sequence of S1:  d1s T2 b a t2 + t2* a* c* t1* + c b* 
# Structure of S1:  .  .  ( ( (  +  )  )  (   .  + ) )
S1 = d1s T2 b( a( t2( + ) ) c*( t1* + ) ) 

S2 = t1( c( a( + t2* ) b*( d2 t3 + ) ) )

P1 = t2* a*( c*( t1*( + ) ) )
I1 = d1s T2 b( a t2 + c )
I2 = d1s T2 b( a( t2( + ) ) b*( d2 t3 + ) c*( t1* + ) )

P2 = d1s T2 b( a( t2( + ) ) ) d2 t3
P3 = b( c*( t1* + ) )

R = d1s( d2( + t3* ) )

D = d1s d2
RW = d1s( T2 b( a( t2( + ) ) ) d2( t3( + ) ) )

Let's use reaction condensation for a more compact representation of the reaction network and increase the default maximum complex size to avoid (warnings about) incomplete enumeration.

$ peppercorn -o system-enum.pil --max-complex-size 10 --condensed < system.pil

And then the output file should look something like this. The layout may vary between different Peppercorn versions.

# File generated by peppercorn-v0.9

# Domains (17) 
length a = 22
length b = 22
length c = 22
length d1s = 16
length d2 = 6
length t1 = 6
length T2 = 2
length t2 = 6
length t3 = 10

# Resting complexes (12) 
C1 = t1 c a
D = d1s d2
e52 = t3*( d2*( d1s*( + ) ) + b( c*( t1*( + ) ) a( + t2* ) ) d2 )
e60 = t3*( d2*( d1s*( + ) d2 + b( c*( t1*( + ) ) a( + t2* ) ) ) )
I1 = d1s T2 b( a t2 + c )
P1 = t2* a*( c*( t1*( + ) ) )
P2 = d1s T2 b( a( t2( + ) ) ) d2 t3
P3 = b( c*( t1* + ) )
R = d1s( d2( + t3* ) )
RW = d1s( T2 b( a( t2( + ) ) ) d2( t3( + ) ) )
S1 = d1s T2 b( a( t2( + ) ) c*( t1* + ) )
S2 = t1( c( a( + t2* ) b*( d2 t3 + ) ) )

# Resting macrostates (11) 
macrostate C1 = [C1]
macrostate D = [D]
macrostate e60 = [e60, e52]
macrostate I1 = [I1]
macrostate P1 = [P1]
macrostate P2 = [P2]
macrostate P3 = [P3]
macrostate R = [R]
macrostate RW = [RW]
macrostate S1 = [S1]
macrostate S2 = [S2]

# Condensed reactions (6) 
reaction [condensed      =       466694 /M/s ] e60 + I1 -> P3 + RW + D + C1
reaction [condensed      =      3082.99 /M/s ] I1 + P1 -> S1 + C1
reaction [condensed      =        3e+06 /M/s ] P2 + R -> RW + D
reaction [condensed      =  1.63659e+06 /M/s ] S1 + C1 -> I1 + P1
reaction [condensed      =       466694 /M/s ] S2 + I1 -> P3 + P2 + C1
reaction [condensed      =        3e+06 /M/s ] S2 + R -> e60

Tips & Tricks

  • You can specify concentrations of complexes in the input file, e.g.:

    C1 = t1 c a @initial 10 nM

    The benefit of hard-coding initial concentrations in the input file, is that they do not have to be specified again when simulating the output using the Pilsimulator software.

  • You can name complexes, even though you do not want them initially present. To do that, give them explicitly 0 initial concentration:

    I1 = d1s T2 b( a t2 + c ) @initial 0 nM
  • Every file produced by Peppercorn, can be used as an input to Peppercorn, although some types of input (e.g. macrostate assignments, condensed reactions) may be ignored with a warning. You can use that to specify a reaction with a specific type and rate constant and that reaction will then be part of the enumerated and condensed output of peppercorn. If Peppercorn enumerates an already specified reaction (same type, same complexes), the rate will not be updated.

    reaction [branch-4way    =        1e-10 /s   ] I2 -> P3 + P2

    Of course, all reactants and products must be previously defined complexes. You can use the supported reaction types: open, bind21, bind11, branch-3way, branch-4way ... but not condensed!

  • You can use a short-hand notation for a super sequence that is composed of multiple domains. For example, if a domain k is sometimes split into k1, k2, and k3, e.g. when they are not all bound at the same time, you can define

    sup-sequence k = k1 k2 k3

    and use the domain k as a shorthand for k1 k2 k3 when applicable. Note, that the output will always use the extended format, explicitly listing the most detailed domain composition.

  • You can specify the nucleotide sequence of a domain, and it will remain present in the ouput file. Hower, note that rates (at the moment) only depend on domain length, and not on the nucleotide sequence. Use the keyword sequence to initialize a domain with the nucleotide sequence:

    sequence a = ACGTUGCA : 8

    The digit at the end denotes the length of the domain, it can be omitted, but must not be wrong.

  • Peppercorn supports a range of different input file formats, e.g. the specification language of the Seesaw Compiler. You can use the option --dry-run to translate every valid input into kernel format without enumeration.

    $ cat seesaw_ciruit.ssw | peppercorn --dry-run
  • Consider taking a look at the case studies directory for more examples.


1.1 -- Mayor Python>=3.7 code cleanup and speedups for some core functions.

  • rewrite of all objects to use dsdobjects>=0.8 (an attempt to fix rare segfaults).
  • moved ratemodel related functions to peppercornenumerator/
  • renamed open to open1N in order to avoid name conflicts.
  • default concentration unit for output is now 'nM' throughout the library.
  • updating and extending unittests.
  • some pythonification of old code.
  • removing deprecated code and undocumented experimental features.
  • updated files in case_study directory for compatibility with changes.

1.0.1 -- bugfix for pilsimulator --labels option.

1.0 -- stable release, requires python >= 3.7.


Stefan Badelt, Casey Grun, Karthik V. Sarma, Brian Wolfe, Seung Woo Shin and Erik Winfree.


If you are using this package, plese cite:

  • Stefan Badelt, Casey Grun, Karthik V. Sarma, Seung Woo Shin, Brian Wolfe, and Erik Winfree (2020) "Enumeration, condensation and simulation of pseudoknot-free domain-level DNA strand displacement systems" [Badelt et al. (2020)].
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