Membranes containing the protein, either native patches or reconstituted proteoliposomes, are adsorbed onto freshly cleaved mica in buffer. The tip is pressed onto the surface so that a terminal segment attaches to it, usually by non-specific adsorption, and the cantilever is then withdrawn at constant speed. Each time a stable structural segment gives way, the force drops and a further length of polypeptide is released, which produces the sawtooth pattern first described for the tandem domains of titin (Rief et al., 1997). The rising flank of each peak is fitted with the worm-like chain model of polymer elasticity (Marko and Siggia, 1995), and the fitted contour length gives the number of amino acids stretched between tip and membrane at that moment.

In bacteriorhodopsin the main peaks correspond to the extraction of transmembrane helices in pairs, with smaller peaks indicating that single helices and loops sometimes unfold separately (Oesterhelt et al., 2000). The same logic has since been applied to other rhodopsins, transporters, channels and receptors, and the positions of the peaks are generally characteristic of the protein (Kedrov et al., 2007). Two features of the trace are therefore available for comparison between lipid conditions: where the peaks fall, which reports on the boundaries of the stable segments, and how high and how frequent they are, which reports on the strength of the interactions that hold each segment in place.

An unfolding force is not a property of the protein alone. It depends on how quickly the load is applied, because thermal fluctuations have more time to carry the system over the barrier when the pulling is slow. Bell (1978) proposed that an applied force lowers an activation barrier in proportion to the distance between the bound state and the transition state, and Evans and Ritchie (1997) showed that the most probable rupture force should then rise linearly with the logarithm of the loading rate. Repeating the experiment at several pulling speeds, known as dynamic force spectroscopy, yields two parameters for each structural segment: the distance to the transition state and the unfolding rate extrapolated to zero force. Later treatments replaced the sharp-barrier assumption with explicit landscape shapes and allow the barrier height to be estimated as well (Dudko et al., 2006).

Equilibrium free energies can also be recovered from repeated non-equilibrium pulls through the work relation of Jarzynski (1997), and a practical reconstruction procedure for pulling experiments was set out by Hummer and Szabo (2001). These analyses matter for the lipid question because a lipid might change a peak height by altering the barrier, by moving the transition state, or by changing the stiffness of the surrounding material, and only measurements across loading rates can separate those possibilities. All of them rest on a calibrated force, and the usual thermal-noise calibration of the cantilever spring constant (Hutter and Bechhoefer, 1993) carries an uncertainty that is not negligible beside the differences expected between lipid conditions.

The oldest of these ideas is hydrophobic matching. In the mattress model of Mouritsen and Bloom (1984), a protein whose hydrophobic span differs from that of the surrounding bilayer forces either the lipids or the protein to deform, at an energetic cost, and Killian (1998) reviewed the experimental consequences for helix tilt, aggregation and activity. For an extraction experiment the prediction is straightforward in direction if not in size: a helix that sits comfortably in its bilayer should be harder to pull out than one that is already strained, and the residues that anchor a helix at the interface may differ between thick and thin membranes.

A second mechanism works through the lateral pressure profile. The interfacial tension at the headgroup region is balanced by repulsive pressure among the chains, and Cantor (1997) pointed out that changing chain unsaturation or adding small amphiphiles redistributes this pressure with depth, which shifts the equilibrium between protein conformations that differ in cross-sectional shape. A third treats the bilayer as an elastic sheet that must bend and compress to meet the protein, so that bilayer stiffness enters the energetics of any conformational change that alters the protein's boundary (Andersen and Koeppe, 2007; Phillips et al., 2009). These continuum effects are non-specific. They should act on every protein in the membrane, though not equally on every segment.

Cholesterol illustrates why general and specific effects are hard to separate. It orders neighbouring acyl chains, thickens fluid bilayers and increases their bending rigidity, all of which are continuum effects, and it also occupies defined grooves on the surface of several proteins. The same duality applies to the annular lipids that exchange rapidly at the protein surface and to the smaller number of lipids bound tightly enough to be retained through purification (Lee, 2004). A change in an unfolding force after cholesterol is added to a membrane therefore does not, taken alone, say which mechanism is responsible. An answer needs comparison with other sterols or with lipids that reproduce the bulk effect without the binding.

Much of what is known comes from membranes that nature supplies in nearly pure form, above all the purple membrane of Halobacterium salinarum, in which bacteriorhodopsin is packed into a two-dimensional lattice with a small complement of archaeal lipids. Work on such samples established that unfolding pathways are reproducible, that they respond to temperature, pH, mutation, ligand binding and oligomeric state, and that each structural segment can be characterised by its own kinetic parameters (Kedrov et al., 2007; Engel and Gaub, 2008). These findings show that SMFS is sensitive enough to detect the kind of change a lipid might cause. They do not isolate the lipid contribution, since in a native patch the lipid composition is fixed and bound up with the crystalline packing of the protein.

Controlling composition requires reconstitution. The clearest example is the study of the human β2-adrenergic receptor by Zocher et al. (2012), who unfolded the receptor from phospholipid liposomes prepared with and without the cholesterol analogue cholesteryl hemisuccinate and applied dynamic force spectroscopy to each structural segment. They reported that the sterol increased the kinetic, energetic and mechanical stability of nearly all segments of the receptor, a result consistent with structural and functional evidence that cholesterol stabilises this class of proteins. The study is valuable because it compares like with like: one protein, one instrument, one analysis, and a single compositional variable.

It also shows the limits of the approach. Reconstitution changes more than the lipid. The density of protein in the membrane, its orientation, its oligomeric state and the residual detergent may all differ between preparations, and each can influence how readily a terminus is picked up and how the molecule unfolds. A cholesterol analogue with a charged headgroup is not cholesterol. And the comparison of two compositions does not establish a dose-response relation or distinguish binding from bulk ordering. Published comparisons of this controlled kind remain few relative to the number of proteins that have been unfolded.

Extraction by the atomic force microscope pulls the polypeptide out of the bilayer along the membrane normal. In terms of the two-stage model of Popot and Engelman (1990), it reverses helix association and helix insertion together, so the measured work includes the cost of transferring hydrophobic segments from lipid to water. Magnetic tweezers allow a different geometry. Min et al. (2015) attached DNA handles to both termini of the rhomboid protease GlpG held in bicelles and applied force laterally, which let the helices separate while remaining in the membrane mimetic. Unfolding occurred at forces low enough for refolding to be observed, and an energy landscape for the second stage of folding could be mapped. The lipid dependence of that second stage is the more relevant quantity for protein stability in a cell, and the review of Neuman and Nagy (2008) sets out how the force range and resolution of the two instruments differ.