Transport of charged molecules

This document explains the assumptions about the transport of charged molecules in Maud.

Transport reactions

The driving force of membrane transport is affected by the membrane potential in the form:

\[\Delta G_{transport} = \Delta G_r^0 + RT S log(conc) + n F \psi\]

where \(\Delta G_r^0\) is the standard free reaction energy from formation energies; \(RT\) is the gas constant times the temperature; \(S\) is the stoichiometric matrix; \(F\) is the Faraday constant; \(\psi\) is the membrane potential; and \(n\) is the number of charges being exchanged. Notice how if there is no charge transport, \(n\) is 0 and the driving force expression becomes that of a normal driving force.

\(n\) accounts for both the charge and the directionality. For instance, a reaction that exports 2 protons to the extracellular space in the forward direction would have -2 charge. If a negatively charged molecule like acetate is exported in the forward direction, \(n\) would be 1.

Notice how this does not take into account that the concentration gradient used by the transport is that of the dissociated molecules. Thus, as of now, this expression is only correct for ions whose concentration can be/is expressed in the model only in the charged form; e.g., protons, \(K^+\), \(Na^+\), \(Cl^-\), etc.


A prior of name psi is used in the above equation to account for the membrane potential. This prior is usually negative, around -0.95V and is tied to a particular experiment. The value for the charge is a structural parameter of the reaction and the rest (stoichiometry, concentrations) work as for any other reaction.

The number of transported charges \(n\) can be explicited in the kinetic model TOML file for each reaction as transported_charge (0 by default). For instance:

id = "ATPSm"
name = "ATPase c0"
mechanism = "reversible_modular_rate_law"
water_stoichiometry = 1.0
transported_charge = 3.3
stoichiometry = { adp_c = -1.0, h_e = -3.3, h_c = 3.3, pi_c = -1.0, atp_c = 1.0 }