NMR spectroscopy and X-ray crystallography are currently the most common techniques capable of determining the structures of biological macromolecules like proteins and nucleic acids at an atomic level of resolution. The atomic force microscope (AFM) is mostly known for its imaging capabilities, but it is also a very sensitive tool for quantitatively measuring forces on a single molecule level.
This capability allows the use of AFM as an alternative technique for the investigation of the structural configuration of macromolecules under native conditions. Measuring forces within and between single molecules provides another approach to the understanding of molecular energy landscapes and chemical reaction kinetics. The AFM can measure individual bonds forming and breaking, rather than being limited to statistical averages over a population.
This report concentrates on the use of the AFM to manipulate single molecules to extract information about the molecular structure or conformation, and intramolecular binding forces. It is also possible to study time dependent phenomena, such as intramolecular dynamics in macromolecules, molecular recognition or protein folding in situ.
Molecular Stretching Experiments
Force spectroscopy is an AFM mode where the tip is moved up and down above a single point on the surface, while the deflection or other cantilever properties are measured. This gives a profile of the forces at different heights above the surface.
In molecular stretching experiments, the tip is usually brought into contact with the surface, the molecules on the substrate are allowed to interact with the tip, and then the cantilever is retracted. This movement is shown schematically in the image series in Figure 1 – towards the sample (the approach) and then away again (the retract). As the cantilever is moved away from the surface, the deflection reflects the forces between the tip and the surface. If a single molecule is held between the tip and the surface, then the deflection of the cantilever gives a measure of the force exerted on the molecule.
In the schematic diagram in Figure 1, a single molecule is shown being stretched between the tip and the substrate. The molecule may have a defined three dimensional folded structure, as for proteins, for example, or it may be a disordered chain, such as many other long polymers. The adhesive interaction between the tip and the molecule usually takes place in the repulsive contact part of the force curve, but the features of interest for the molecular stretching are found in the retract curve.
Figure 1. Schematic diagram of a force spectroscopy experiment where the AFM tip is used to stretch a single molecule
Long chain molecules, such as DNA or dextran, can be stretched between the tip and the sample. The stiffness and persistence length can be seen from the initial stretching of the molecule. Internal molecular transitions can also be studied, such as the melting transition in DNA as the backbone rearranges under higher tension. Molecules with complex 3-dimensional structure, such as many proteins, can be unfolded in a controlled way so that the structural units can be investigated. Titin and bacteriorhodopsin are examples of proteins that have been intensively studied. Membrane proteins can be pulled out of the membrane, and the “popping” out of individual alpha-helices has been seen.
Characteristics of Macromolecules in Solution
Long molecules in solution are rarely rod-like or stiff, and often have a high flexibility along the backbone of the molecule. Even double stranded DNA, which is usually thought of as a "stiff" molecule because of the double-helix structure, is arranged as a random tangle for lengths beyond a few hundred nanometers. This means that there is a large difference between the length of the molecule measured along the chain or backbone (the contour length) and the typical dimensions it occupies in solution (e.g. the radius of gyration or the end-to-end length), which are much smaller.
Figure 2. Schematic diagram of two possible conformations of a long molecule. In A, the molecule is stretched out in an unlikely conformation for a molecule in solution. B shows a more typical conformation, where the molecule is in a disorganised tangle.
The arrangement is represented schematically in Figure 2. In part A, a long molecule is shown in an extended conformation. In part B, a different conformation is shown where the molecule is in a relaxed random tangle that occupies a much smaller lateral dimension than the contour length. There are many more conformations similar to the one shown in B available to the molecule than conformations similar to the one shown in A, and this leads to the difference in entropy or free energy of the different conformations.
There is a cost in free energy to straighten out a molecule from conformation B to A, since the number of available related conformations is reduced. This free energy difference translates to a force that resists the straightening, and acts like an entropic "spring". This is in contrast with the situation on a macroscopic scale, where pulling a flexible string does not require a significant force until it is straight and the actual backbone is stretched.
When long molecules are pulled, a force is required to extend the molecule towards a straight conformation even if the bonds in the backbone are not being stretched.
Two basic models are commonly used for this entropic elasticity, depending whether some chain stiffness is included. In the freely jointed chain (FJC) model, the backbone is modelled as small units connected by completely "free" joints, so that adjacent units can have any angle between them without extra energy cost. The worm-like chain (WLC) model, in contrast, is a continuous filament with chain stiffness built in, and is a better model for molecules such as double-stranded DNA. A persistence length is defined, which represents the length of the chain over which the initial orientation is randomised.
If a force-extension curve is collected, then it can be fitted by one of these models to obtain the length of the molecule being stretched, and the persistence length for the WLC model.
Some specialised molecules, such as proteins, normally have a defined (folded) three-dimensional structure in solution. This structure is the key to their biological function as enzymes or structural units, for example. The polypeptide chain is not a relaxed loose coil, but is folded into a much stiffer structure and held together by many bonds. If the protein is unfolded, by force, chemical or thermal changes, then the free polypeptide chain behaves like a simple linear molecule. The entropic stretching can be seen, as the bonds along the polypeptide backbone are highly flexible. Defined parts of the protein structure, such as alpha-helices or globular domains, can be unfolded sequentially, and the measured "free" length of the molecule based on the stretching curves will increase with each unfolding event. The protein unfolding steps provide information about the normal folded structure and its failure mechanisms.
Xanthan – Simple Molecular Stretching
Xanthan is a bacterial polysaccharide, with a molecular backbone identical to cellulose. The chemical properties of the side groups give the polymer many industrial applications, from food stabilization to oil recovery.
When the Xanthan molecule is stretched between the tip and the surface, the short side groups do not have a significant effect on the elastic properties, and the behaviour is similar to a single (carboxymethylated) cellulose chain. High molecular weight xanthan polymers can have lengths of several microns, and the stretching curves can be used as an example for simple molecular extension. For low forces, the chain is stretched against the entropic spring. At some point, as the end-to-end length approaches the contour length, the elasticity of the backbone elasticity becomes important.
Figure 3 shows the retract curve of a single Xanthan molecule being stretched (in a phosphate buffer solution) using the NanoWizard® AFM. The cantilever deflection has been calibrated using the thermal noise method.
For comparison with the models, the tip-sample distance must also be corrected for the deflection of the cantilever to obtain a real separation value, which is shown here. A larger negative force corresponds to the tip being deflected more towards the surface, and hence a higher extensional force on the molecule.
Figure 3. Force spectroscopy retract curve of a single Xanthan molecule being stretched. A curve for the extended FJC model is also shown for comparison.
A curve from the extended FJC model is also shown in Figure 3 for comparison, calculated using a Kuhn length of 6 nm and a contour length of 1.25 microns. The fit for the simple FJC or WLC model was reasonable for small extensional forces (below around 50pN in this case), but the curves diverged at higher forces. Hence the extended FJC model with the additional segment elasticity was used, to take account of the backbone stretching at higher extensional forces.
In the case of Xanthan, a single long link between the tip and the surface is stretched. Since the molecule is so long, the force to extend it is very small for much of the stretching curve, and the behaviour is dominated by the higher-force stretching where the stretched length is near the contour length. For more complex folded molecules, such as proteins, a series of these stretching events are generally seen as different parts of the structure unfold and are extended.
Bacteriorhodopsin – Extraction and Unfolding
Bacteriorhodopsin is an integral membrane protein from bacterial cells, which generates energy for the cells from light photons. There are 7 transmembrane alpha-helices, with more disorganized peptide loops between them.
When one end of the protein is grasped and pulled, then the alpha-helices are pulled out of the membrane, and they unfold as they are pulled out.
Purple membrane is the natural source for bacteriorhodopsin, and consists of 25% lipids and 75% bacteriorhodopsin. The protein is arranged as trimers in a 2-dimensional crystal structure, which can be imaged using the AFM, as shown in Figure 4 (sample courtesy of D.J. Müller, Technical University, Dresden, Germany. The characteristic trimer shape can be seen in the image. The protein can be imaged using the AFM and then individual proteins selected and pulled using the tip. The tip can be coated specially, and the molecules modified to pick up a particular part of the structure, or the tip can be pressed into the surface to pick up a molecule non-specifically.
Figure 4. AFM height image of purple membrane (cytoplasmic side), taken using JPK NanoWizard® in contact mode in buffer solution (170nm x 100 nm, 1nm height range)
A schematic diagram of the unfolding process is shown in Figure 5. The seven alpha-helices are shown in part A, with the AFM tip picking up one end (note that in the actual protein, the alpha-helices are grouped together in a bundle, not a line). There are many possible unfolding pathways, but the most likely events are that the alphahelices are pulled out in pairs. A progression of three partially unfolded states is shown in part B of Figure 5, with pairs of alpha-helices unfolding as they are extracted from the membrane.
Figure 5. Schematic diagram of bacteriorhodopsin unfolding using the AFM tip. One end of the molecule is picked up by the tip (A), and the alpha-helices are pulled out sequentially in pairs (B).
Figure 6 shows a superposition of 10 bacteriorhodopsin unfolding curves, with the force plotted against the corrected tip-sample separation. There is some adhesion as the tip leaves the surface, followed by three main stretching and unfolding events, corresponding to the three states shown in Figure 5 B. The main peaks are around 20-30nm, 40-50nm and 60-80nm, which agree well with values published in the literature. The cantilever was calibrated using the thermal noise method, and the experiments carried out under buffer (10mM TRIS, 150mM KCl, pH 7.6).
The exact position of the bond failure events varies from curve to curve, which is typical for bonds with energy close to thermal energy at room temperature. The stretching parts of the curves overlay in Figure 6, showing that the same structures are being stretched in each case. Only the actual moment when the stretched bonds break varies from curve to curve. For a bond with energy near the thermal energy, there is some probability of it failing within a certain time, even with no applied force. This corresponds to the normal "off-rate" seen for the binding reaction free in solution. For bonds with energies a little above the thermal energy, which are normally stable, the probability of them failing spontaneously increases as a force is applied.
Figure 6. Unfolding curves of bacteriorhodopsin being pulled out of purple membrane (superposition of 10 retract curves).
One way to think of a stretching event, therefore, is that the bonds are strained until the energy barrier to unfolding is within the thermal range. The actual moment when the bonds suddenly fail depends on a random thermal fluctuation, which takes the molecule over the unfolding energy barrier. The time dependence means that the measured unfolding rate will depend on the loading rate, or the speed with which the tip is pulling the free end of the molecule.
Figure 7. Histogram of the position of the three unfolding peaks (tip sample corrected separation) for a set of 355 bacteriorhodopsin unfolding curves.
Many unfolding curves of bacteriorhodopsin can be collected to give a statistical view of the unfolding events. The molecule may unfold in several ways, so some selection has to be made in the force curves to choose a particular subset. In this case, only curves showing the three main stretching events, such as the examples in Figure 6, were selected. In Figure 7 a histogram is presented, showing the tip-sample separation distribution for the three peaks (data for n = 355 curves). The force curve analysis was partially carried out using the PUNIAS software.
Figure 8. Scatter plot of force against position (tip-sample corrected separation) for the unfolding events shown in Figure 6.
Figure 8 shows a scatter plot of the unfolding force versus the position of the event for the same data set as in Figure 7. The force for the first unfolding event (Peak 1) is significantly higher than for the subsequent events (Peaks 2 and 3). Once the protein structure has been disrupted, then the force required to pull the remaining alpha-helices out of the membrane is reduced. The unfolding curves also show different pathways for the molecule to unfold and pull out of the membrane. From a knowledge of the protein structure and amino acid chain lengths, the extensional curves can be fitted to show clearly which unfolding path is taken in a particular force curve.
Titin is a protein from muscle tissue, which consists of several repeated globular domains. Within the muscle tissue it is responsible for the mechanical properties on a macroscopic scale. The AFM allows the study of the nanomechanical properties of individual titin molecules. As the molecule is stretched, at some point the bonds holding a particular domain together will fail. This particular globular domain then unfolds, leading to a longer contour length for the molecule. With further pulling, this section of linear amino acids is also stretched, and one of the other domains will reach its failure point. This is illustrated schematically in Figure 9.
Figure 9. Schematic diagram of titin stretching, as successive globular domains unfold.
As the protein is pulled, the domains "pop" open sequentially, leading to a characteristic sequence of peaks in the deflection curves. The shape of each successive curved part of the force plot reflects the increased effective length of the molecule as the domains are unfolded.
A typical titin extension force spectroscopy retract curve is shown in Figure 10 (data courtesy of Matthias Amrein, University of Calgary, Canada, obtained using the NanoWizard® AFM on a single Ig8 titin muscle protein). The characteristic titin sequence of unfolding events can be clearly seen. The force increases steadily, as the tension in the molecule increases. Suddenly the force decreases sharply as an Ig domain pops open and the tension is released. The curve of each extending region can be fitted with the FJC or WLC model for the corresponding free amino acid length. The size of the unfolding force for a single domain is in the range of 190-250pN, and the contour length of one domain (peak-to-peak distance) is 28nm.
Figure 10. Force curve of titin stretching, showing sequential unfolding of the globular domains (data courtesy of Matthias Amrein, University of Calgary).
A wide variety of proteins can be stretched and unfolded using the AFM. Two examples have been shown here, one membrane protein and one cytoplasmic protein. This method can be extended to other proteins, to gain information about both the normal protein structure and its failure modes. In the case of bacteriorhodopsin, the protein forms very highly packed structures in the bacterial cell wall, and so is one of the few membrane proteins that can be crystallized for high-resolution structural determination.
This method can be more generally applied, however. For most membrane proteins, the amino acid sequence is much easier to determine than the folded structure, since most membrane proteins are not suitable for crystallization.
Unfolding events measured with the AFM, which show the change in amino acid length as different structural units unfold, can be used with the known sequence to interpret the tertiary structure of membrane proteins. Specific coating of the probe, and modification of the protein to have specific "pick-up" points can lead to pulling the protein at different locations, and hence further information about how the structural units are connected together in the 3-D structure.
Thus AFM is able to give insight into the configuration of a single molecule and allow an independent measurement of molecular properties to refine molecular modelling techniques. AFM can also be combined with single molecule fluorescence techniques such as TIRF or FRET.