biocrnpyler.mechanisms.Membrane_Signaling_Pathway_MM

class biocrnpyler.mechanisms.Membrane_Signaling_Pathway_MM(name='two_component_membrane_signaling', mechanism_type='membrane_sensor', **kwargs)[source]

Bases: Mechanism

Two-component system membrane sensor with Michaelis-Menten kinetics.

A ‘membrane_sensor’ mechanism that models a two-component system (TCS) for signal transduction across cellular membranes. This mechanism includes signal substrate sensing, membrane sensor protein activation, auto-phosphorylation via ATP, and phosphorylation of response proteins, but does not include downstream reporter circuits.

The mechanism follows a multi-step Michaelis-Menten kinetic scheme with the following reaction pathway:

1. Activation of membrane sensor protein (MSP):

\[ {\text{SP}} + {\text{SigSub}} \rightleftharpoons {\text{SP}}\mathord{:}{\text{SigSub}} \rightarrow {\text{SP}}^* \]

2. Auto-phosphorylation via ATP:

\[ {\text{SP}}^* + n {\text{ATP}} \rightleftharpoons {\text{SP}}^*\mathord{:}n{\text{ATP}} \rightarrow {\text{SP}}^{**}\mathord{:}n{\text{ADP}} \rightarrow {\text{SP}}^{**} + n{\text{ADP}} \]

3. Phosphorylation of response protein (RP):

\[ {\text{SP}}^{**} + {\text{RP}} \rightleftharpoons {\text{SP}}^{**}\mathord{:}{\text{RP}} \rightarrow {\text{SP}}^*\mathord{:}{\text{RP}}^* \rightarrow {\text{SP}}^* + {\text{RP}}^* \]

4. Dephosphorylation of phosphorylated response protein:

\[ {\text{RP}}^* \rightarrow {\text{RP}} + {\text{Pi}} \]

Parameters:

name (str, default 'two_component_membrane_signaling') – Name identifier for this mechanism instance.
mechanism_type (str, default 'membrane_sensor') – Type classification of this mechanism.

Attributes:

name (str) – Name of the mechanism instance.
mechanism_type (str) – Type classification (‘membrane_sensor’).

See also

Mechanism: Base class for all mechanisms.
MichaelisMenten: Enzyme-substrate mechanism with MM kinetics.

Notes

This mechanism models bacterial two-component signaling systems, which are common environmental sensing pathways. The sensor protein spans the membrane and undergoes conformational changes upon binding external signals, leading to autophosphorylation and subsequent phosphotransfer to response proteins that regulate gene expression.

The mechanism requires the membrane sensor protein to have an ATP attribute (membrane_sensor_protein.ATP) that specifies the number of ATP molecules required for autophosphorylation.

Required parameters for this mechanism:

‘kb_sigMS’ : Forward binding rate for signal substrate to membrane sensor protein
‘ku_sigMS’ : Reverse unbinding rate for signal substrate from membrane sensor protein
‘kb_autoPhos’ : Forward binding rate for ATP to activated membrane sensor protein
‘ku_autoPhos’ : Reverse unbinding rate for ATP from activated membrane sensor protein
‘k_hydro’ : ATP hydrolysis rate constant
‘ku_waste’ : Unbinding rate for ADP waste products
‘kb_phosRP’ : Forward binding rate for response protein to phosphorylated membrane sensor
‘ku_phosRP’ : Reverse unbinding rate for response protein from phosphorylated membrane sensor
‘k_phosph’ : Phosphotransfer rate constant to response protein
‘ku_activeRP’ : Unbinding rate for activated response protein
‘ku_dephos’ : Dephosphorylation rate constant for phosphorylated response protein

Examples

Create a two-component signaling system with default parameters:

>>> response = bcp.Protein(name='OmpR')
>>> sensor = bcp.MembraneSensor(
...     membrane_sensor_protein='EnvZ',
...     response_protein=response.species,
...     assigned_substrate='Phosphate',
...     signal_substrate='Osmolarity',
...     ATP=2
... )
>>> mechanism = bcp.Membrane_Signaling_Pathway_MM()
>>> mixture = bcp.Mixture(
...     components=[sensor, response],
...     mechanisms={'membrane_sensor': mechanism},
...     parameters={
...         'kb_sigMS': 1.0, 'ku_sigMS': 0.1,
...         'kb_autoPhos': 1.0, 'ku_autoPhos': 0.1,
...         'k_hydro': 0.5, 'ku_waste': 1.0,
...         'kb_phosRP': 1.0, 'ku_phosRP': 0.1,
...         'k_phosph': 0.5, 'ku_activeRP': 1.0,
...         'ku_dephos': 0.01
...     }
... )
... mixture.compile_crn()

Methods

`update_reactions`	Generate reactions for two-component membrane signaling pathway.
`update_species`	Generate species for two-component membrane signaling pathway.

update_reactions(membrane_sensor_protein, response_protein, assigned_substrate, signal_substrate, product, energy, waste, complex_dict=None, component=None, part_id=None, **kwargs)[source]

Generate reactions for two-component membrane signaling pathway.

Creates all eight reactions comprising the complete signaling cascade from signal detection through response protein activation and dephosphorylation. Reactions follow Michaelis-Menten kinetics with reversible binding steps and irreversible catalytic steps.

Parameters:

membrane_sensor_protein (Species) – The membrane sensor protein that detects the signal. Must have an ATP attribute specifying the number of ATP molecules required for autophosphorylation.
response_protein (Species) – The response protein that receives the phosphate group and becomes activated.
assigned_substrate (Species) – The phosphate substrate (Pi) that is transferred during the signaling cascade.
signal_substrate (Species) – The external signal molecule that activates the membrane sensor protein.
product (Species) – The phosphorylated response protein product (RP*).
energy (Species) – ATP species used for autophosphorylation.
waste (Species) – ADP species produced after ATP hydrolysis.
complex_dict (dict, optional) – Pre-defined dictionary of complex species. If None, complexes are automatically created using the same logic as in update_species.
component (Component) – Component containing parameter values. Required for parameter lookup.
part_id (str) – Identifier for parameter lookup in the component’s parameter database. Required for parameter lookup.
**kwargs – Additional keyword arguments (unused).

Returns:

List of eight reactions representing the complete signaling cascade:

Signal binding (reversible)
ATP binding (reversible)
ATP hydrolysis (irreversible)
ADP release (irreversible)
Response protein binding (reversible)
Phosphotransfer (irreversible)
Activated response protein release (irreversible)
Response protein dephosphorylation (irreversible)

Return type:

list of Reaction

Raises:

AttributeError – If component or part_id is None (required for parameter lookup).

Notes

The reaction scheme follows this pathway:

SP + SigSub \(\rightleftharpoons\) SP:SigSub (rates: ‘kb_sigMS’, ‘ku_sigMS’)
SP:SigSub + nATP \(\rightleftharpoons\) SP:SigSub:nATP (rates: ‘kb_autoPhos’, ‘ku_autoPhos’)
SP:SigSub:nATP \(\rightarrow\) SP:SigSub:Pi:nADP (rate: ‘k_hydro’)
SP:SigSub:Pi:nADP \(\rightarrow\) SP:SigSub:Pi + nADP (rate: ‘ku_waste’)
SP:SigSub:Pi + RP \(\rightleftharpoons\) SP:SigSub:Pi:RP (rates: ‘kb_phosRP’, ‘ku_phosRP’)
SP:SigSub:Pi:RP \(\rightarrow\) SP:SigSub:RP:Pi (rate: ‘k_phosph’)
SP:SigSub:RP:Pi \(\rightarrow\) SP:SigSub + RP:Pi (rate: ‘ku_activeRP’)
RP:Pi \(\rightarrow\) RP + Pi (rate: ‘ku_dephos’)

This method requires both component and part_id parameters to retrieve rate constants from the component’s parameter database.

update_species(membrane_sensor_protein, response_protein, assigned_substrate, signal_substrate, product, energy, waste, complex_dict=None, **kwargs)[source]

Generate species for two-component membrane signaling pathway.

Creates all species involved in the signaling cascade, including the membrane sensor protein, response protein, signal substrate, ATP/ADP energy species, and all intermediate complexes formed during signal transduction and phosphotransfer.

Parameters:

membrane_sensor_protein (Species) – The membrane sensor protein that detects the signal. Must have an ATP attribute specifying the number of ATP molecules required for autophosphorylation.
response_protein (Species) – The response protein that receives the phosphate group and becomes activated.
assigned_substrate (Species) – The phosphate substrate (Pi) that is transferred during the signaling cascade.
signal_substrate (Species) – The external signal molecule that activates the membrane sensor protein.
product (Species) – The phosphorylated response protein product (RP*).
energy (Species) – ATP species used for autophosphorylation.
waste (Species) – ADP species produced after ATP hydrolysis.
complex_dict (dict, optional) – Pre-defined dictionary of complex species with keys ‘Activated_MSP’, ‘ATP:Activated_MSP’, ‘ADP:Activated_MSP:Sub’, ‘Activated_MSP:Sub’, ‘Activated_MSP:Sub:RP’, and ‘Activated_MSP:RP:Sub’. If None, complexes are automatically created.
**kwargs – Additional keyword arguments (unused).

Returns:

List containing individual species and complex array: [membrane_sensor_protein, response_protein, assigned_substrate, signal_substrate, energy, waste, complex_array] where complex_array is a list of all Complex species generated.

Return type:

list

Notes

The method creates six different complex species representing the intermediate states of the signaling cascade:

Activated_MSP : signal_substrate:membrane_sensor_protein
ATP:Activated_MSP : nATP:Activated_MSP
ADP:Activated_MSP:Sub : Activated_MSP:nADP:Pi
Activated_MSP:Sub : Activated_MSP:Pi (phosphorylated sensor)
Activated_MSP:Sub:RP : (Activated_MSP:Pi):response_protein
Activated_MSP:RP:Sub : Activated_MSP:(response_protein:Pi)

The number of ATP/ADP molecules (nATP) is determined by the membrane_sensor_protein.ATP attribute.