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 ionsexternal
: holds the concentrations of external ionsmembrane
: 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'