ecoli.processes.membrane.membrane_potential

Membrane Potential

MembranePotential calculates membrane potential and the proton motive force by taking into account all of the ions that are permeant through the membrane.

Goldman equation for membrane potential:

\(d_{V} = \frac{RT}{F} * \ln{\frac{\sum_{i}^{n} P_{M^{+}_{i}}[M^{+}_{i}]_{out} + \sum_{j}^{m} P_{A^{-}_{j}}[A^{-}_{j}]_{in}}{\sum_{i}^{n} P_{M^{+}_{i}}[M^{+}_{i}]_{in} + \sum_{j}^{m} P_{A^{-}_{j}}[A^{-}_{j}]_{out} }}\)

  • \(D\): Diffusion constant

  • \(M\) monovalent positive ionic species

  • \(A\) negative ionic species

transmembrane pH difference (currently fixed at -50):

\(d_{pH} = -2.3 * k * T / e\)

  • \(k\): Boltzmann constant

  • \(T\): temperature

proton motive force (PMF):

\(PMF = d_{V} + d_{pH}\)

Note

  • expected d_{V} = -120 mV

  • expected d_{pH} = -50 mV for cells grown at pH 7. (Berg, H. “E. coli in motion”, pg 105)

  • PMF ~170mV at pH 7. ~140mV at pH 7.7 (Berg)

  • E. coli internal pH in range 7.6-7.8 (Berg)

  • (mmol) http://book.bionumbers.org/what-are-the-concentrations-of-different-ions-in-cells/

  • Schultz, Stanley G., and A. K. Solomon. “Cation Transport in Escherichia coli” (1961)

  • Zilberstein, Dan, et al. “Escherichia coli intracellular pH, membrane potential, and cell growth.” Journal of bacteriology 158.1 (1984): 246-252.

  • TODO – add Mg2+, Ca2+

class ecoli.processes.membrane.membrane_potential.MembranePotential(parameters=None)[source]

Bases: Process

Membrane Potential

Ports:

  • internal: holds the concentrations of internal ions

  • external: holds the concentrations of external ions

  • membrane: holds the cross-membrane properties ‘PMF’, ‘d_{V}’, ‘d_{pH}’

defaults: Dict[str, Any]
{   'F': 96485.33212,
    'R': 8.314462618,
    'charge_map': {   'Cl': 'anion',
                      'K': 'cation',
                      'Na': 'cation',
                      'PROTON': 'cation'},
    'e': 1,
    'initial_state': {   'external': {   'Cl': 110,
                                         'K': 5,
                                         'Na': 145,
                                         'PROTON': 0,
                                         'T': 310.15},
                         'internal': {   'Cl': 10,
                                         'K': 300,
                                         'Na': 10,
                                         'PROTON': 0}},
    'k': 1.380649e-23,
    'p_Cl': 0.05,
    'p_K': 1,
    'p_Na': 0.05,
    'p_PROTON': 1,
    'permeability_map': {   'Cl': 'p_Cl',
                            'K': 'p_K',
                            'Na': 'p_Na',
                            'PROTON': 'p_PROTON'}}
name = 'membrane_potential'
next_update(timestep, states)[source]
ports_schema()[source]

declare schema for ports internal, external and membrane.

exception ecoli.processes.membrane.membrane_potential.NoChargeError[source]

Bases: Exception

ecoli.processes.membrane.membrane_potential.main()[source]