Remarkably, electrophysiologists have long been able to directly observe the behavior of single ion channels [6]. Indeed, despite the great interest currently swirling around single-molecule biophysics, electrophysiologists have been doing single-molecule experiments on ion channels for decades. These
R
¢P
Figure 2.6: Electrophysiology: the patch clamp. Above is a schematic diagram of the patch clamp experiment used to measure channel currents. A membrane patch is created from a cell or vesicle by positioning a micro-pipette next to the membrane and applying suction on the micro-pipette.
The glass pipette forms an extremely tight seal with the membrane allowing current to pass through the membrane channels only. The electrical current, generated by the passage of ions through the channel, is then measured. For MscL, the current is measured as a function of the applied pressure difference over the membrane. The radius of curvature of the membrane is observable. The Laplace law relates the radius of curvature and pressure difference to the membrane tension. (Figure from Ref. [4].)
experiments exploit an experimental technique called patch clamp recording [6]. In this technique, a micro-pipette is pressed against the cell (or vesicle) membrane to form a tight seal. (See Fig.2.3.) This seal is to a good approximation impermeable [6]. The electric current through the membrane patch, corresponding to the passage of ions through the channels, can then be measured as a function of the voltage drop over the membrane.
To study mechanosensitive channels like MscL, the ion current is measured as a function of the pressure difference over the membrane. The radius of curvature of the membrane patch is observable under a microscope. The tension can then be computed using the Laplace law:
α=12P R, (2.5)
whereP is the pressure difference,αis the tension, andRis the radius of curvature of the membrane patch.
A patch clamp recording for a single MscL channel is shown in Fig. 7.3.1. In this experiment,
Figure 2.7: The patch clamp recording from a single MscL channel. The channel gating of the MscL channel is stochastic, fluctuating between states. Panel A shows low time resolution data where the time scale bar is 800 ms. Panel B shows an enlarged interval where the time scale bar is 80 ms.
Panels C and D show smaller intervals still where the time scale bar is respectively 15 and 20 ms.
To analyze the data, it is binned into states based on conductance. Histograms of the data appear to implicate a five state system, but the channel stays predominantly in the open (O) and closed states (C). In this recording, the membrane tension is 12.3 dyn/cm and the probability of the open state is 0.67. (Figure from Ref. [14].)
MscL has been reconstituted into a PC lipid bilayer at low enough MscL concentration that single channels are observed in a typical membrane patch [14]. One important feature to note from the current trace is that the channel inhabits states of well defined conductance. Typically these states can be picked out from a histogram of the channel current. (States correspond to peaks.) Even if the channel were described by two, very well defined conductance states, these peaks would be smeared out by the practical resolution limits of patch clamp experiments. Even in an idealized experiment, there are still fluctuations in the current due to the electrical resistance of the channel (Johnson noise). The fluctuation-dissipation theorem predicts the dependence of Johnson noise on the resistance and bandwidth of the experiment.
For the most part the channel is either in a closed state with negligible conductance or an open state with a fixed conductance. Three additional short-lived sub-states have also been identified with intermediate conductance [14]. We shall assume that these well defined conductance states correspond to well defined channel conformations.
The second important feature of the patch recording is that the channel behavior is stochastic; it fluctuates between conductance states as one would expect for a molecular scale channel undergoing
8 9 10 11 12 13 14 Tension ® (dyn/cm)
{6 {4 {2 0 2 3
¢GOC(kT)
Figure 2.8: The free energy difference between the open and closed states as a function of the membrane tension. The linear dependence on tension suggests that the area difference between the two states is constant. See the discussion in Chapter4. Data from Ref. [14].
thermally-induced transitions. Clearly the language of statistical mechanics will be important to describing the function of the channel. In order to interpret the channel recordings quantitatively, the records are idealized by assigning a channel state as a function of time based upon the instantaneous conductance. (See Fig.7.3.1.) It is typically assumed that the transitions are Markovian (without memory) and are described by a set of first-order rate equations. Channels appear to be well described by this model. The rate constants are then fit to the experimental data. For MscL, the typical transition rates vary from hertz to tens of kilohertz [14].
The relative free energies of the states can be computed from their respective probabilities using the Boltzmann distribution:
∆Gij =−kTlogPi
Pj
, (2.6)
wherePi is the probability of statei and ∆Gij is the free energy difference between states iandj.
The free energy difference between the open and closed states as a function of membrane tension is plotted in Fig.2.3.
We shall discuss this free energy in great detail in the next two chapters. For the moment, let us look at the general behavior of the channel. The opening tension (the tension at which the open and closed probabilities are equal) is 11.8 dynes/cm [14]. Experiments show that the lysis tension for membranes is on order 10 dynes/cm [12]. (This opening tension will depend on the properties of the lipid bilayer.) This high gating tension is one of the motivations for the biological explanation of MscL as an emergency pressure relief valve. Note that the channel is also very sensitive to the pressure. For each dyne/cm drop in the membrane tension, the ratio of the open to the closed probabilities decreases by almost a factor of four. For an emergency relief valve, this tension sensitivity is incredibly important. When the MscL channel opens, the pore is on order thirty angstrom in diameter, implying that many small molecules can escape from the bacteria.
Clearly the MscL channel must open only in emergencies.
The most striking feature of the free energy difference between the open and closed state is that
it depends linearly on the membrane tension. (See Fig.2.3.) This is exactly the tension dependence one would na¨ıvely expect for a two state system if each state had a fixed area under external tension.
The free energy difference between states would then be
∆GOC = ∆G0−α∆AOC, (2.7)
where ∆G0 is constant with respect to the tension and ∆AOC is the area difference between states the open and closed states. Clearly high tension stabilizes the open state with its larger radius. The sensitivity of the channel, the slope of the free energy with respect to tension, is the area difference between states ∆AOC = 6.5 nm2. This measurement of the area change is large for a channel protein.3 This large area change is a consequence of opening a 3 nm pore in channel core and must correspond to a very significant conformational change in the protein.