Supplementary Information for gating charge displacement in voltage-gated ion channels involves limited transmembrane movement
Baron Chanda1, Osei Kwame Asamoah1,2, Rikard Blunck1, Benoit Roux3 and Francisco Bezanilla1,4
a) The Time Course of fluorescence
The FRET between a donor in the channel protein and multiple acceptors in the lipid bilayer can be modeled using standard Forster theory. The experimental situation illustrated in supplementary figure 1 assumes that dipicrylamine molecules (DPA, blue spheres) are randomly distributed on the lipid surface and the proportion of molecules on either surface is governed by a two-state model that is voltage and time dependent. We are interested in the relative quantum yield of the donor q, defined as the ratio of the fluorescence in presence of the acceptors over the fluorescence of donor only,
Eqn. 1
where kF is the intrinsic donor fluorescence rate, knr is the non radiative rate and ki is the rate of transfer from the donor to the acceptor i. According to Förster theory, we can express the rate of transfer as a function of distance and get
Eqn. 2
where R0 is the distance between donor and acceptor for 50% energy transfer. This value is equivalent to 22 Ǻ for the rhodamine-DPA pair, assuming k2=2/3, which is reasonable in view of the multiple orientations for the DPA molecules in the bilayer plane. To evaluate this expression as a function of voltage and time we simulated the distribution of the DPA molecules using a random number generator and a simple two-state model for the movement of the molecules from one plane to the other with parameters that emulate the DPA currents observed experimentally. At the same time, the movement of the donor was implemented as a simple two-state model with kinetics emulating the gating currents of the channel. In a single iteration, the random distribution of N DPA molecules in the initial state (i.e. hyperpolarized) was used to compute q according to eq. 2. A depolarizing pulse was applied and the new position of the donor and the N acceptors were computed as a function of time to obtain all the ri(t). This process was repeated M times and the fluorescence q(t) was obtained as
Eqn .3
Examples of the time course of fluorescence are shown in supplementary figure 2 for several cases of movement of the fluorophore attached to the S4 segment. DPA molecules were excluded in the region of the protein in the external and internal planes of the lipid bilayer which was assumed to be 30 Å thick. The first case shown in supplementary figure 2a corresponds to a donor located 5 A away from the external plane of the bilayer but that moves 15 Ǻ towards the center of the channel upon depolarization (a tilt towards the channel), producing a monotonic change in fluorescence. The second case in supplementary figure 2b corresponds to a fluorophore 5 Å away from the internal plane of the bilayer that remains static during the depolarization, also produces a monotonic fluorescence change but in the opposite direction. The third case shown in supplementary figure 2c is the emulation of the paddle, where the donor moves from 5 Å of the internal plane to 5 Å from the external plane (a total of 20 Å) upon depolarization while it moves 15 Å towards the center of the channel. This case produces the expected transient fluorescence change at the on and off of the pulse. Finally, supplementary figure 2d shows the case where the fluorophore moves from the internal plane of the bilayer to 10 Å away from it while it moves 15 Å closer to the center of the channel. This case would correspond to the extreme case of position 363 with the rhodamine attached to it where the S4 segment is initially almost parallel to the internal plane of the bilayer and becomes perpendicular to the bilayer plane upon depolarization, while the fluorophore always remains below the middle plane of the bilayer. It is apparent that the signal has a large fluorescence transient at the end of the pulse that is not observed in the experimental data.
Supplementary figure 3 shows simulations with the model presented in the paper for positions 363 and 367in the S4 segment. In all cases shown the fluorophores were assumed to be perpendicular to the plane of the membrane and pointing toward the intracellular side. MTSR signals for position 363 is shown in supplementary figure 3a and for 367 is shown in supplementary figure 3b. In both cases the signal is a monotonic fluorescence decrease for a depolarizing pulse, as it is in the experimental case. When ABD is simulated for position 363, the signal becomes an increase in fluorescence during the depolarizing pulse. This is similar to the experimental case, although in the latter the extra increase of fluorescence in the simulation at pulse off is not observed experimentally. This extra increase is eliminated when the ABD is not assumed to be perpendicular to the membrane plane.
b) The transient fluorescence change occurs independent of kinetics and charge
The transient fluorescence change generated by the differential migration of a donor and acceptors of opposite polarity (S4 and DPA) does not require different kinetics of translocation for donor and acceptors. As an extreme case, consider the case of identical kinetics for donor and acceptor. A simulation of the concentration profile of the two species can be obtained by solving the Focker-Planck equation with an energy barrier in the membrane. Supplementary figure 4a shows such simulation for the case of donor (blue) and acceptor (red) at the initial condition of hyperpolarized membrane where most of the donors will be at internal side of the membrane (at –15 A) and the acceptors at the external side (+15 Å). In this case the distance between them is large and there will be little energy transfer therefore the fluorescence will be high. When the membrane potential is reversed, the donors migrate to the outside and the acceptors to the inside and energy transfer will occur. Supplementary figure 4b shows the case where there will be the maximum overlap of donors and acceptors on both sides producing a minimum in the fluorescence. At long times, the distribution of donors and acceptors will be opposite to the initial condition and they will be again separated by the membrane increasing the fluorescence to the initial value (Supplementary figure 4c). Notice that when the membrane potential is repolarized, the same series of events will occur and a transient will be observed again.
The FRET profile remains the same even if both molecules have the same charge and kinetics because of concentration effect. In this case at the start of the pulse the fluorescence will be quenched since both the donor and acceptor are in the same plane. When the voltage pulse is applied the concentration of the donor and acceptor molecules in the same plane reduces as they start to move to the other surface. In other words, same number of molecules has to occupy twice as much area. This would result in a decrease in energy transfer. At long times, both donor and acceptor completely transfer to the other surface which again increases the energy transfer.
c) The positional dependence of FRET signal and their kinetics
Based on various models of voltage gating, we can make testable predictions regarding the trend in FRET signals as we scan down the S4 helix. For instance, if the voltage gating is in accordance with the paddle model then the fluorescence signals from the S4 N-terminus is biphasic whereas those towards the C-terminus are expected to be monophasic. If, on the other hand, the membrane potential causes limited positional change of the voltage sensor, FRET signals from positions on the N and C terminus of the S4 segment are both expected to be monophasic. In this case, as positions are scanned along the S4 the amplitudes of the FRET signals will decrease as we approach residues close to the energy transfer midline. Therefore, these measurements can be used to map the depth of residues in a transmembrane helix relative to the lipid bilayer. Although the determination of this vertical distance requires a quantitative estimate of the donor-acceptor ratio, the distinction between large versus small translocation movement is independent of this ratio and can be clearly determined from the FRET profile.
The movement of the gating charge in the Shaker potassium channel and the intramembrane translocation of the DPA (time constant 700 µs) is completed within 10 ms. Therefore, it is intriguing to observe an additional slow component (time constant of tens of millisecond or slower) of fluorescence change from some positions. This slow change in the fluorescence could be due to slow inactivation, which causes a lateral movement of transmembrane helices changing the DPA-fluorophore distance, and/or excluded volume of DPA around the channel. On the other hand, some of the slow component could also reflect DPA transport across the membrane into the inner cytosolic space. Since DPA is added only to the outer chamber of the cutopen oocyte setup, depolarizing pulses cause a slow transport of DPA into the cytoplasm. Fluorophores near the inner leaflet are more sensitive to this change in internal DPA concentration. Such slow kinetics have also been observed with GFP anchored to the inner leaflet in presence of DPA (unpublished data by Chanda, Blunck and Bezanilla).
d) The voltage-dependent FRET from N-TMR-melittin and DPA pair
In the melittin experiment no transient is observed at the end of the pulse. This lack of a transient at the OFF is expected when the fluorescence recovery is less than 50% because the acceptors and donors will not overlap as much in the internal side. The number of donors that translocate from the external side upon hyperpolarization is only a fraction of the total number of donors. In this case the quenching obtained at the beginning of the pulse will be as effective as the case discussed in b) because DPA translocates much faster than melittin and will completely quench the donor fluorescence. However the recovery of the fluorescence is not complete during the pulse because only a fraction of the donors cross to the internal side. Thus, under these conditions, at the end of the pulse there will be no transient decrease in fluorescence because the acceptors and donors will not overlap as much in the internal side. When the voltage pulse duration is extended in an attempt to facilitate mellitin insertion, the bilayer frequently ruptures-a property consistent with cell lysing activity of melittin.
e) Intrinsic voltage-dependent fluorescence changes from different positions on the Shaker potassium channels.
Voltage-dependent fluorescence changes in the absence of dipicrylamine were measured from different sites after labeling with Sulforhdamine-MTS and ABD-MTS. The positions V349C, V354C and F425C labeled with MTS-sulforhodamine show a small voltage-dependent fluorescence signal when the oocyte membrane is pulsed from –120 to +50 mV (Suppl. Fig. 5). The positions V363C and V367C do not show any voltage-dependent signal when labeled with either with ABD-MTS or sulforhodamine-MTS. With ABD-MTS, the sites V349C, V354C and F425C exhibit little or no evidence of flurorescence labeling. Since ABD fluorescence is extremely solvent dependent, it is quite likely that the fluorescence from these positions is quenched due to high aqueous accessibility.
f) Sequence alignment of Shaker with KvAP.
Supplementary figure 6 shows the alignment used to build the molecular model presented in the paper. The model starts at Shaker residue 215 and ends at Shaker residue 486. Within that sequence all the residues in lower case were deleted.
Figure Legends
Supplementary Figure 1. Schematic depicting the positions of dipicrylamine molecules relative to the S4 helix in the lipid bilayer. The two planes represent the external and internal edges of the lipid bilayer and the cylinder represents the channel protein that has a donor (red sphere) that may move in response to changes in membrane potential. The dipicrylamine molecules are randomly distributed on the lipid plane. Their relative proportion of DPA molecules on the outside with respect to the inside is voltage and time dependent.
Supplementary Figure 2. Simulations of voltage-dependent FRET profile for different versions of gating models. Only one fourth of the channel is shown and it is represented schematically as the blue region with the S4 segment indicated as a cylinder. A) Shows the FRET profile when the S4 segment undergoes a change in tilt [a=5Å and b= 15Å]. B) When the donor molecule is closer to the inner leaflet and the S4 may or may not undergo a tilt [a=5Å]. C) FRET profile when the S4 undergoes a large translocation (Paddle model) with donor molecule attached to N-terminus [a=5Å and a’=25Å]. D) FRET profile when S4 undergoes large translocation with donor molecule towards the middle of the transmembrane segment [a=10Å and b=15Å].
Supplementary Figure 3. Simulations of positions 363 and 367 of S1 using the coordinates of the model presented in the paper. a, MTSR in position 363. b, MTSR in position 367. c, ABD in position 363.