3.4 Measuring Ensemble Channel Flow
3.4.2 Using Gain-of-Function Mutants
While the experiment, discussed above is relatively simple in concept there are two complications that should be discussed, and for which we have likely found a solution by using mutant forms of MscL that gate at significantly lower tensions. The first issue is that rupture of a bilayer, caused by tension, does not exhibit the same properties as failure in macroscopic materials. In previous sections, we stated that an areal strain greater than ∼ 10% results in membrane rupture, and indeed this is a good upper bound value for the tensile strain of a typical bilayer. Although, unlike a macroscopic material (e.g. latex, steel, etc.), whose tensile strength has a well defined value;
the rupture, and hence rupture tension, of a bilayer is a stochastic process sensitive to thermal fluctuations. More precisely, rupture of a bilayer is caused by the nucleation of membrane holes.
Above a critical size a hole will grow rapidly causing catastrophic failure of membrane integrity [53], similar to the popping of a balloon, where the kinetics of hole nucleation depend on thermal fluctuations and membrane properties.
We can briefly outline this failure mechanism to understand how the rate of failure depends on membrane tension. When a hole is created in a bilayer, the hydrophobic core of the membrane is exposed to water, and lipids will leave their normal positions to partially cover the core. The combined exposure of the hydrophobic core and the deformation of lipids that try to cover the core, cost a certain energy per unit length. This line tension was measured in a series of experiments where giant unilamellar vesicles where electroporated during pipette aspiration, in a manner similar to the experiments discussed here. The line tension was found to beγ '2.5kBT /nm for a typical phosphocholine bilayer (without cholesterol)[165]. If the membrane is subject to a tension τ, the creation of a hole of radiusr will have an elastic free energy
Ghole= 2πrγ−πr2τ. (3.36)
This equation always has a minimum at r= 0, and there is a barrier between this stable state and
a)
b)
c)
d)
e)
0 500 1000 1500
1500 2000 2500 3000
0 500 1000 1500
0.2 0.4 0.6 0.8
0 500 1000 1500101
101.5 102 102.5 103
0.2 0.4 0.6 0.8
2 2.5 3 3.5
4x 10−6
vesicle
micropipette tip
Figure 3.9: Proof of concept by measuring bilayer water permeability. a) Three fluorescent images of an aspirated giant unilamellar vesicle, as water permeates through the bilayer decreasing the enclosed volume. b) Schematic of an aspirated vesicle showing the important shape characteristics and pressures required to calculate volume, area, and tension as a function of vesicle shape. c) Volume of the aspirated vesicle in (a) as a function of time at constant pressure gradientp2 −p3. d) Calculated membrane tension and internal pressure as a function of time as vesicle volume decreases. e) The bilayer permeation coefficient as a function of the calculated membrane tension.
For the approximately linear regime of tension in (d), the permeation coefficient increases slightly, as indicated by the gray ellipse, but has an approximately constant value of 3.5×10−6µm3/pNs.
The average permeation coefficient measured over a number vesicles (n = 16) was 1.9±1.5× 10−6µm3/pNs, in good quantitative agreement with previous measurements [140].
hole nucleation that leads to membrane failure, where the critical size for hole nucleation isrc=γ/τ and the barrier height for the rupture transition is Gbarr=πγ2/τ. We can estimate the maximum tension that can be stably applied to a vesicle by saying that the barrier to hole nucleation must be much greater thankBT, for instanceGbarr∼10kBT, which happens whenτ =πγ2/10kBT. For the value of line tension quoted above, this yields a nominal maximum stable tension of∼2kBT /nm2 which is in line with our previous estimates. The point of this little exercise is to show that membrane failure is actually a stochastic process, whose rate,khole∝e−Gbarr, increases rapidly with τ. Thus if we are forced to subject the bilayer to high membrane tensions, like those estimated in bacteria and measured in vitroto gate the MscL channel, we are already tempting stochastic fate to rupture the membrane. If we can use lower tensions to gate the channel, the chances that the membrane will rupture during an experiment decrease exponentially.
The second issue concerns the requirement that we know the detailed dose-response curve of channel opening. In eqn. 3.1 and borne out in Fig. 3.3, we saw that the gating tension of MscL was ∼2−3kBT /nm2, again close to the expected rupture tension of a membrane. Our analysis of vesicle shape shows that pressures and/or reduction in volume required to achieve this tension are relatively high, and hence to actually relate the volume flux of the channel to the reduction in volume of the vesicle would require detailed knowledge of Po(τ). It is then a bittersweet fact that the dose-response curve changes with lipid type [22] and even shows variability within the same bilayer composition, as shown in Fig.3.3. One way around this complication is to employ a mutant channel whose gating tension is easily achieved, such that past some relatively low value of membrane tension, we can be sure that the probability that any one channel is open is essentially unity. In other words, we seek a mutant form of the channel for which it is easy to force the function Po ' 1 for some value of τ much less than the rupture tension, and hence the detailed nature of the dose-response becomes irrelevant.
Thankfully, mutational studies of MscL have shown that by changing the hydration energy of the channel pore, the free energy of gating related to channel structure, ∆Gprot, can be reduced [34,33]
(or augmented [98]). Specifically, examining the hydrophobicity of residues lining the channel pore that become hydrated upon channel opening, one finds a number of them have a high degree of hydrophobicity, as measured by standard hydropathy [166]. The mutant form of the channel we will use8 has a single point mutation at the 23rd residue from the C-terminus, changing a hydrophobic valine (hydropathy 4.2 [166]) to either of two hydrophilic residues, threonine (hydropathy -0.7 [166]) or aspartic acid (hydropathy -3.5 [166]), at the narrowest point of the channel pore, as shown in Fig.3.10. In practice, the latter mutant opens too easily and hence is generally toxic to the bacteria at expressions levels required for purification of the channel.
Using measured values of the hydration energy of amino acids, in this case free energies of transfer from octanol to water [167], the free energy of transfer of valine is 0.77kBT per molecule,
8Kindly constructed and donated, with a poly-histidine purification tag, for the purposes of this research by S.
Sukharev, University of Maryland.
a) b)
Figure 3.10: Gain of function MscL mutants. a) Top and side view of the V23 point mutation site in the narrowest part of the channel pore as shown by the magenta spheres on each MscL monomer.
In this view, each protein monomer is uniquely colored. b) Top and side view of the V23 point mutation site in the narrowest part of the channel pore as shown by the magenta spheres. In this view, protein residues are colored by hydrophobicity, blue being more hydrophobic than red. We clearly see that the transmembrane helices are generally hydrophobic, as is the conducting pore, hence the reason why this point mutation is effective in changing the protein free energy.
and −0.42kBT and −0.72kBT for threonine and aspartic acid respectively. The channel protein is composed of five identical subunits [11], each carrying the point mutation. Thus within the limitations of this estimate, the hydration of the valines in the pore raises the free energy∼3.9kBT, while hydration of threonine and aspartic acid lower the free energy by∼2.1kBT and ∼3.6kBT respectively. Thus in terms of the change in the change in free energy of gating, from wild type to either of these mutants, we estimate the free energy of the gating transition is lowered by ∼6kBT for the threonine point mutation, and by ∼ 7.5kBT for the aspartic acid mutation. Using our nominal value of the total free energy of gating in the wild type protein of 20kBT, and change of protein area upon gating of 7 nm2we calculate a gating tension of∼2.85kBT /nm2for the wild type protein, again near expected values for membrane rupture. Using our estimates of the reduction in hydration energy of the threonine and aspartic acid point mutants, the gating tensions are reduced to ∼ 1.98kBT /nm2 and ∼ 1.78kBT /nm2, respectively. While this is a naive estimate, it puts the qualitative mechanism of gating tension reduction by pore point mutation on sound theoretical footing. Additionally, using the estimates of membrane hole nucleation, we can estimate the relative decrease in the rate of hole nucleation, and subsequent membrane failure when using the gain of function mutants. Given that the rate of hole nucleation is proportional to the Arrhenius factor e−πγ2/τ, and we now have estimates for the gating tensions in the wild type and mutant channels, the relative decrease in the rate of membrane rupture is given by
kwt
kmut
=eπγ2
“ 1
τmut−τwt1 ”
'20, (3.37)
meaning that the point mutants, on average, extend the life of the experiment by a factor of twenty!
On that high note, let us address one last, less savory experimental reality.