The Measuring Device

The electrogenic activity of the transporter (LacY or MelB) gives rise to a current which is directly proportional to the amount of transporters incorporated into proteoliposomes NT and the number of proteoliposomes immobilized on the SSM-electrode N_P. The current generated by the transporters after a step substrate concentration jump I_Model(t) is coupled to the measuring device (Fig. 4A) via the equivalent circuit (Fig. 4B), which distorts I_Model(t) and converts it into I_Circuit(t).

The equivalent circuit is composed of three membranes, each represented by a certain conductivity G and capacitance C (Fig. 4B): the uncovered part of the SSM (G_u and C_u); the proteoliposome membrane (G_p and C_p); and the membrane between the gold electrode and the interior of the proteoliposomes (Gm and Cm). An external

ANALYSIS OF THE TRANSIENT CURRENTS

voltage could be applied through the voltage source (V_Ext). The uncovered parts of the SSM would contribute, if any, to a certain stationary current. As the currents are analyzed with respect of the base line, the equivalent circuit shown in Fig. 4B can be reduced to Fig. 4C (Bamberg et al., 1979; Fendler et al., 1993; Herrmann & Rayfield, 1978).

An external voltage could be applied through the voltage source (VExt). To test the effect of V_Ext on the protein activity, LacY proteoliposomes were allowed to adsorb to the SSM, and the transient currents triggered by 50 mM lactose concentration jumps were investigated in the absence or presence of V_Ext (Fig. 5). The only effect of the external voltage was a small stationary current (not shown on the figure, ~30pA), which can be corrected with the “Offset Nulling” of the amplifier or during data analysis. Neither the magnitude nor the time constant of the transient currents relative to the baseline were affected by the application of an external voltage (Fig.

5). Probably, the external voltage drops mainly in the membrane between the gold electrode and the interior of the proteoliposome and not on the proteoliposome membrane, which implies that G_m << G_p. Furthermore, this experiment also shows one of the present limitations of the SSM-based electrophysiology: the lack of control over the voltage on the proteoliposome membrane.

ANALYSIS OF THE TRANSIENT CURRENTS

Fig. 4. Measuring device and equivalent circuit.

(A) The solid-supported membrane (SSM) is composed of a self-assembled monolayer (SAM) of octadecanethiol and a lipid monolayer of diphytanoyl-phosphatidylcholine (PC). The equivalent circuit consists on three membranes, each represented by a certain conductivity G and capacitance C: the uncovered part of the SSM (Gu and Cu); the proteoliposome membrane (Gp and Cp); and the membrane between the gold electrode and the interior of the proteoliposomes resulting from the adsorption of the proteoliposomes on the surface of the SSM (Gm and Cm). The external voltage source is represented by VExt. The response of the measuring device to the current generated by the transporter after a step substrate concentration jump is represented by ICircuit, and the voltage on the proteoliposome membrane by Vp(t). (B) Equivalent circuit of the measuring device described in (A). (C) As the currents are analyzed with respect to the base line, the equivalent circuit in (B) can be simplified to (C) (Bamberg et al., 1979; Fendler et al., 1993; Herrmann & Rayfield, 1978).

ANALYSIS OF THE TRANSIENT CURRENTS

Fig. 5. Effect of the potential between the electrodes on the activity of LacY.

LacY proteoliposomes absorbed to a SSM were investigated at different external constant voltages VExt. The black trace was recorded in the absence of applied voltage (VExt = 0 mV), while the red trace was obtained in the presence of voltage VExt = - 100 mV and was baseline corrected (~30pA). As shown in the figure, the magnitude the kinetics of the transients are independent of the applied voltage, indicating that the voltage VExt does not drop on the proteoliposome membrane.

The differential equations describing the circuit are (Bamberg et al., 1979; Fendler et al., 1993; Herrmann & Rayfield, 1978):

p

The voltage on the proteoliposome membrane is represented by V_p(t) and k₀ is the reciprocal system time constant. As the current IModel(t) starts after activation of the transporters, which takes place at t = 0, the system of differential equations can be solved using the boundary condition Vp(0) = 0. To better understand the effect of the equivalent circuit, two limiting cases will be considered for the current generated by the transporter after a step substrate concentration jump IModel(t):

3.2.1. Continuous Electrogenic Transport Activity

Here, we will consider that the current I_Model(t) is only due to the continuous electrogenic transport activity of the transporter, and it depends linearly with respect to V_p(t). This limiting case was already considered in the interpretation of the transient currents generated by bR when purple membrane fragments were absorbed to a BLM (Bamberg et al., 1979; Herrmann & Rayfield, 1978). Here, the current generated by the transporter after a step substrate concentration jump I_Model(t) is represented by:

The current generated per transporter IT0 is the product of the charge translocated per turnover and the turnover. V* is a constant which couples I_Model(t) and the

ANALYSIS OF THE TRANSIENT CURRENTS

potential on the proteoliposome membrane V_p(t) in a linear way. As derived in (Bamberg et al., 1979), the response of the measuring device is represented by:

( )

The reciprocal system time constant k₀ was defined in Eq. 2. As shown in Eq. 4, I_Circuit(t) is a transient current that decays with a reciprocal time constant k’₀, which depends on the current generated per transporter I_T0 and the amount of transporters incorporated into proteoliposomes NT (Eq. 7). An increase in NT results in transient currents of higher magnitude and faster decay (Garcia-Celma et al., 2009; Zuber et al., 2005). Furthermore, in this limiting case the measured peak current can be approximated to I(0) (Zuber et al., 2005), which is directly proportional to the turnover (Eq. 4). Consequently, an increase in the turnover results in transients with higher peak currents and faster decay towards the base line (Bamberg et al., 1979; Garcia-Celma et al., 2009).

3.2.2. Initial Charge Displacements

In this limiting case, I_Model(t) is only due to initial charge displacements and no continuous electrogenic transport activity takes place. This initial charge displacement results from one or several electrogenic partial reactions. For simplicity, we will consider that there is only one electrogenic partial reaction although this formalism is easily generalized for an infinite number of electrogenic partial reactions (Fendler et al., 1993). Due to the absence of continuous electrogenic transport, the voltage generated by the electrogenic partial reaction in the proteoliposome membrane can be approximated by zero. Under this assumption, I_Model(t) and I_Circuit(t) are represented by (Borlinghaus et al., 1988; Fahr et al., 1981; Fendler et al., 1993):

(

ANALYSIS OF THE TRANSIENT CURRENTS the time curse of ICircuit(t) is characterized by two exponentials with opposite amplitudes. Importantly, the rate constant of the electrogenic reaction k is, in this case, unaffected by the equivalent circuit (Fendler et al., 1993).

In general, a mixed situation between the two limiting cases is to be expected.

However, it will be shown in sections 5 and 6 that the equations derived above represent a useful benchmark for the analysis of the electrogenic activity of the investigated transporters. Furthermore, these equations allow us to identify the properties that a SSM (and also a BLM) should fulfill to be utilized as capacitive electrodes. As in both limiting cases the initial input current is proportional to α (Eq. 4 and Eq. 8), which has a value between zero (C_m = 0) and one (C_m >> C_p), a situation where C_m >> C_p is desirable. In addition, a low G_m is required to reduce the background noise current, which leads to masking of the signal. As shown by Florin and Gaup (Florin & Gaub, 1993), a SSM presents high specific capacitance and low specific conductance, allowing the use of the SSM as a capacitive electrode.