Current-voltage-time records of ion translocating enzymes

Membrane currents, as non-linear functions of membrane voltage, V, and time, t, can be recorded quickly by triangular V protocols. From the differences, d I(V, t), of these relationships upon addition of a putative substrate of a charge-translocating membrane protein, the I(V, t) relationships of the transporter itself can be determined. These relationships likely comprise a steady-state component, I(a)(V), of the active transporter, and a dynamic component, p(a)(V, t), of its V- and time-dependent activity, p(a). Here, the steady-state component is modeled by a central reaction cycle, which senses a fraction delta(tr) of the total V, whereas 1-delta(tr) can be assigned to an inner and outer pore section with delta(i) and delta(o), respectively (delta(i)+delta(tr)+delta(o) = 1). For the enzymatic cycle, fast binding/debinding is assumed, plus V-sensitive and -insensitive reaction steps which may become rate limiting for charge translocation. At given substrate concentrations, I(a)(V) is defined by eight independent system parameters, including a coefficient for the barrier shape of charge translocation. In ordinary cases, the behavior of p(a)(V, t) can be described by two rate constants (for activation and inactivation) and their respective V-sensitivity coefficients. Here, the effects of the individual system parameters on I(V, t) from triangular V-clamp experiments are investigated systematically. The results are illustrated by panels of typical curve shapes for non-gated and gated transporters to enable a first classification of mechanisms. We demonstrate that all system parameters can be determined fairly well by fitting the model to "experimental" data of known origin. Applicability of the model to channels, pumps and cotransporters is discussed.