biocrnpyler.mechanisms.multi_tx

class biocrnpyler.mechanisms.multi_tx(pol: Species, name: str = 'multi_tx', mechanism_type: str = 'transcription', **kwargs)[source]

Bases: Mechanism

Multi-polymerase transcription with isomerization and occupancy.

A ‘transcription’ mechanism that explicitly models multiple RNA polymerases (RNAPs) binding to a single gene simultaneously, accounting for polymerase spacing, isomerization between open and closed configurations, and competitive binding. This detailed mechanism captures transcriptional queueing and interference effects.

The reaction scheme follows:

\[\begin{split} & {\text{DNA}}\mathord{:}{\text{RNAP}}_n + {\text{RNAP}} \rightleftharpoons {\text{DNA}}\mathord{:}{\text{RNAP}}_{n_c} \rightarrow {\text{DNA}}\mathord{:}{\text{RNAP}}_{n+1} \\ & {\text{DNA}}\mathord{:}{\text{RNAP}}_n \rightarrow {\text{DNA}}\mathord{:}{\text{RNAP}}_0 + n {\text{RNAP}} + n {\text{mRNA}} \\ & {\text{DNA}}\mathord{:}{\text{RNAP}}_{n_c} \rightarrow {\text{DNA}}\mathord{:}{\text{RNAP}}_{0_c} + n {\text{RNAP}} + n {\text{mRNA}} \end{split}\]

where:

$n$ = {0, 1, …, max_occ} is the number of polymerases
max_occ is the physical maximum based on RNAP and DNA dimensions
${\text{DNA}}\mathord{:}{\text{RNAP}}_n$ represents DNA with $n$ open configuration RNAPs
${\text{DNA}}\mathord{:}{\text{RNAP}}_{n_c}$ represents DNA with $n$ open RNAPs and 1 closed RNAP

Parameters:

pol (Species) – RNA polymerase species.
name (str, default 'multi_tx') – Name identifier for this mechanism instance.
mechanism_type (str, default 'transcription') – Type classification of this mechanism.

Attributes:

pol (Species) – The RNA polymerase species.
name (str) – Name of the mechanism instance.
mechanism_type (str) – Type classification (‘transcription’).

See also

Transcription_MM: Simple Michaelis-Menten transcription.
multi_tl: Multi-ribosome translation mechanism.
Mechanism: Base class for all mechanisms.

Notes

This mechanism provides a detailed, spatially-aware model of transcription that captures:

Multiple polymerases on a single gene
Polymerase queueing and spacing constraints
Open/closed conformational states (isomerization)
Coordinated transcript release from multiple polymerases

The model is appropriate for detailed mechanistic studies where:

Polymerase density and spacing matter
Transcriptional queueing affects expression
Multiple concurrent transcription events are important

The mechanism generates many species (2 * max_occ complexes) and reactions (O(max_occ)), so it should be used with caution for computational efficiency.

Required parameters for this mechanism:

‘ktx’ : Transcription/release rate constant
‘kb’ : Forward binding rate for polymerase to DNA
‘ku’ : Reverse unbinding rate for polymerase from DNA
‘k_iso’ : Isomerization rate from closed to open configuration
‘max_occ’ : Maximum polymerase occupancy (integer)

Examples

Model multi-polymerase transcription:

>>> gene = bcp.DNAassembly(
...     name='dna_assembly',
...     promoter='pconst', rbs='RBS_medium', protein='GFP')
>>> rnap = bcp.Species('RNAP')
>>> tx_mechanism = bcp.multi_tx(pol=rnap)
>>> mixture = bcp.Mixture(
...     components=[gene],
...     mechanisms={
...         'transcription': tx_mechanism,
...         'translation': bcp.SimpleTranslation()
...     },
...     parameters={
...         'ktx': 0.05, 'ktl': 0.1, 'kb': 1.0, 'ku': 0.1,
...         'k_iso': 0.5, 'max_occ': 5
...     }
... )
>>> mixture.compile_crn()

For more details, see examples/MultiTX_Demo.ipynb.

Methods

`update_reactions`	Generate reactions for multi-polymerase transcription.
`update_species`	Generate species for multi-polymerase transcription.

update_reactions(dna, transcript, component, part_id, protein=None, **kwargs)[source]

Generate reactions for multi-polymerase transcription.

Creates reactions modeling multiple polymerases binding to DNA, isomerization between configurations, and transcript release with coordination among multiple polymerases.

Parameters:

dna (Species) – The DNA species (gene) being transcribed.
transcript (Species) – The mRNA transcript species produced.
component (Component) – Component containing parameter values. Required for parameter lookup.
part_id (str) – Identifier for parameter lookup. Required to retrieve parameters.
protein (Species, optional) – Protein species (unused, accepted for API consistency).
**kwargs – Additional keyword arguments (unused).

Returns:

List of reactions including:

Polymerase binding reactions (DNA:RNAP$_n$ + RNAP $\rightleftharpoons$ DNA:RNAP$_{n_c}$)
Isomerization reactions (DNA:RNAP$_{n_c}$ $\rightarrow$ $DNA\mathord{:}RNAP$_n$)
Release reactions from open states (DNA:RNAP$_n$ $\rightarrow$ DNA + $n$ RNAP + $n$ mRNA)
Release reactions from closed states (DNA:RNAP$_{n_c}$ $\rightarrow$ DNA:RNAP$_{0_c}$ + $n$ RNAP + $n$ mRNA)
Base binding reaction (DNA + RNAP $\rightleftharpoons$ DNA:RNAP$_{0_c}$)

Return type:

list of Reaction

Notes

The reaction scheme captures:

DNA:RNAP$_n$ + RNAP $\rightleftharpoons$ DNA:RNAP$_{(n+1)_c}$ (rates: ‘kb’, ‘ku’)
DNA:RNAP$_{n_c}$ $\rightarrow$ DNA:RNAP$_n$ (rate: ‘k_iso’)
DNA:RNAP$_n$ $\rightarrow$ DNA + $n$ RNAP + $n$ mRNA (rate: ‘ktx’)
DNA:RNAP$_{n_c}$ $\rightarrow$ DNA:RNAP$_{0_c}$ + $n$ RNAP + $n$ mRNA (rate: ‘ktx’)

Where $n$ ranges from 0 to max_occ-1. The ‘max_occ’ parameter represents the physical maximum occupancy of polymerases on the gene.

update_species(dna, transcript, component, part_id, protein=None, **kwargs)[source]

Generate species for multi-polymerase transcription.

Creates all species and complexes involved in multi-polymerase transcription including DNA with varying numbers of bound polymerases in both open and closed configurations.

Parameters:

dna (Species) – The DNA species (gene) being transcribed.
transcript (Species) – The mRNA transcript species produced.
component (Component) – Component containing parameter values. Required for parameter lookup.
part_id (str) – Identifier for parameter lookup. Required to retrieve ‘max_occ’ parameter.
protein (Species, optional) – Protein species (unused, accepted for API consistency).
**kwargs – Additional keyword arguments (unused).

Returns:

List containing:

DNA:RNAP_n complexes in open configuration (n = 0 to max_occ-1)
DNA:RNAP_n complexes in closed configuration (n = 0 to max_occ-1)
Individual species [polymerase, dna, transcript]

Return type:

list of Species

Notes

For each occupancy level $n$ from 0 to max_occ-1, two complex species are created:

Open configuration: DNA with $n+1$ polymerases, all in open state
Closed configuration: DNA with $n+1$ polymerases (n open, 1 closed)

The ‘max_occ’ parameter determines the maximum number of polymerases that can occupy the gene simultaneously, typically based on physical spacing constraints.