Membrane transport models with fast and slow reactions: general analytical solution for a single relaxation

Pre-steady-state and steady-state function of the ileal brush border SO4(2-)-OH- exchanger

Rapid-sampling analysis of the detailed time course of 35SO4(2-) uptake under pH-gradient (pHin = 7.5; pHout = 5.5) conditions converged to a model of an initial burstlike pre-steady-state with relaxation to linear steady-state uptake across pig ileal brush border vesicles. A model of low affinity transport (K(m) = 7.7 mM) plus an unsaturable component described the steady-state component of 35SO4(2-) uptake. Steady-state transport was maximal under pH-gradient conditions and sensitive to inhibition by 4,4'-diisothiocyanostilbene-2,2'-disulfonic acid. Significant steady-state 35SO4(2-) transport sensitive to 4,4'-diisothiocyanostilbene-2,2'-disulfonic acid was found under acidic (pHin = pHout = 5.5) and neutral (pHin = pHout = 7.5) pH-equilibrated conditions. Varying conditions from pH gradient to neutral pH equilibrated had no effect on the amplitude of the pre-steady-state burst or on the time constant for relaxation from pre-steady-state to steady-state conditions. However, maximal amplitude was obtained under acidic pH-equilibrated conditions. These results are incorporated into a model for the low affinity ileal brush border SO4(2-)-OH- exchanger whereby, under 0-trans (0 internal substrate concentration) conditions, translocation of inner-facing to outer-facing conformations defines the overall rate-limiting step of the transporter. Provision for slippage of the unloaded carrier could account for 35SO4(2-) transport under acidic pH-equilibrated conditions.

A novel method for the observation of membrane transporter dynamics

A new method is proposed for measuring the dynamic properties of a membrane transporter by means of steady-state fluxes. Any voltage-sensitive transporter will give a flow of substrate in the presence of a steady-state periodic membrane potential. The periodic steady-state flow, averaged over one period, is a flux that can be measured by traditional steady-state techniques, such as the radioactive tracer method. The average flux, solely due to the periodic field, is described by a set of Lorentzian functions that depend on the applied periodic field amplitude and frequency. The normal mode amplitudes and frequencies of these Lorentzians are model-independent parameters of the transport mechanism. Measurement of the average flux as a function of the applied periodic frequency permits determination of system relaxation times as the reciprocals of the midpoints of the Lorentzian curves, which in turn can be used to estimate individual rate constants of specific models. It was found by simulation of a six-state model of the electrogenic Na+/glucose cotransporter, using published estimates of the model rate constants, that the periodic field effects can be large and rich with measurable details that can be used to study the mechanism thoroughly. The new method serves in this case to complement and expand on the information obtainable by means of the voltage clamp method. It was also found by means of simulations of a nonelectrogenic six-state cotransporter model that experimentally measurable effects are expected and that results can be used to distinguished among alternative kinetic models as well as to estimate individual rate constants. The range of dynamic information available with this method is not accessible by voltage clamp or other pre-steady-state methods presently in use.