Microscopic Interpretation of Atomic Force Microscope Rupture Experiments

That simulation study [49] aimed at a microscopic interpretation of single molecule atomic force microscope (AFM) experiments [50], in which unbinding forces between individual protein-ligand complexes have been measured (Fig. 4, top). In particular we asked, what interatomic interactions cause the experimentally observed unbinding forces.

  

Figure: Typical AFM rupture experiment (top): Receptor molecules are fixed via linker molecules to a surface (left); in the same way, ligand molecules are connected to the AFM cantilever (right). When pulling the cantilever towards the right, the pulling force applied to the ligand can be measured. At the point of rupture of the ligand-receptor complex the measured force abruptly drops to zero so that the rupture force can be measured.
Computer rupture simulation (bottom): In the course of an MD simulation of the ligand-receptor complex at atomic detail the ligand is pulled towards the right with a `computer spring', while the receptor (drawn as a ribbon model) is kept in place. From the elongation of the `spring' the pulling force during the unbinding process is computed, and, thereby, a `force profile' is obtained. The rupture force is interpreted as the maximum of this force.

Both the AFM rupture experiments as well as our simulation studies focussed on the streptavidin-biotin complex as a model system for specific ligand binding. Streptavidin is a particularly well-studied protein and binds its ligand biotin with high affinity and specificity [51]. Whereas previous experiments (see references in Ref. [49]) and simulation studies [52] referred only to bound/unbound states and the associated kinetics, the recent AFM rupture experiments have provided a new and complementary perspective on ligand binding by focussing at atomic details of binding/unbinding pathways: The former were described in terms of binding free energies as thermodynamic quantities, which are independent of the particular reaction pathway; the latter relate to forces, which actually depend on details of the unbinding reaction path and, therefore, can provide new insights into these details.

To enable an atomic interpretation of the AFM experiments, we have developed a molecular dynamics technique to simulate these experiments [49]. From such `force simulations' rupture models at atomic resolution were derived and checked by comparisons of the computed rupture forces with the experimental ones. In order to facilitate such checks, the simulations have been set up to resemble the AFM experiment in as many details as possible (Fig. 4, bottom): the protein-ligand complex was simulated in atomic detail starting from the crystal structure, water solvent was included within the simulation system to account for solvation effects, the protein was held in place by keeping its center of mass fixed (so that internal motions were not hindered), the cantilever was simulated by use of a harmonic `spring potential' and, finally, the simulated cantilever was connected to the particular atom of the ligand, to which in the AFM experiment the linker molecule was connected.

  

Figure: Theory vs. experiment: rupture forces computed from rupture simulations at various time scales (various pulling velocities $v_{\rm cant}$) ranging from one nanosecond ($v_{\rm cant}=0.015\,$Å/ps) to 40 picoseconds ($v_{\rm cant}=0.375\,$Å/ps) (black circles) compare well with the experimental value (open diamond) when extrapolated linearly (dashed line) to the experimental time scale of milliseconds.

However, one significant difference between the AFM experiment and its simulations cannot be avoided at present: Whereas the AFM experiment takes place at a millisecond time scale, our simulations had to be completed within the nanosecond time scale. So, in fact, in the simulation the pulling velocity had to be chosen about six orders of magnitude larger than in the AFM experiment!

In a first attempt to bridge these six orders of magnitude, we performed a series of rupture force simulations using pulling velocities ranging from 0.375 to $0.015\,$Å/ps. As can be seen in Fig. 5, we observed a linear dependency of the computed rupture forces in the velocity range between 0.15 and $0.015\,$Å/ps. This suggests that simple friction dominates the non-equilibrium effects in this regime described by a friction coefficient of $20~{\rm pN~s/m}$. A simple linear extrapolation of the computed rupture forces to the experimental time scale shows agreement between theory and experiment. Clearly, this first step has not yet solved the question how to bridge the six orders of magnitude gap between theory and experiment (cf. also [53]). To answer that question, a better understanding of the physics of rupture experiments using simplified models on the one hand (cf., e.g., Ref. [54]) and, on the other hand, a careful analysis of the atomic processes which cause the velocity dependent rupture forces is necessary.

  

Figure: Force profile obtained from a one nanosecond simulation of streptavidin-biotin rupture showing a series of subsequent force peaks; most of these can be related to the rupture of individual microscopic interactions such as hydrogen bonds (bold dashed lines indicate their time of rupture) or water bridges (thin dashed lines).

One of the results of an MD rupture simulation is the pulling force as a function of time or cantilever position $z_{\rm cant}(t)$, called the force profile. Figure 6 shows an example, derived from an extended 1 ns-simulation, where a pulling velocity of $0.015\,$Å/ps was used. The apparent multitude of force maxima mirrors the complexity of the energy landscape traversed by the biotin on its way out of the binding pocket. The peaks of this force profile can be attributed to the rupture and formation of individual hydrogen bonds and water bridges shown in the snapshots of Fig. 7, which characterize the main steps of the rupture process. The rupture forces in Fig. 5 are the maxima of the corresponding force profiles.

We will not discuss here in detail our atomic model of the unbinding process derived from our simulations and sketched in Fig. 7, but restrict ourselves to two unexpected features. One is that the rupture of the initially very strong hydrogen bonds between the ligand and the residues of the binding pocket (Fig. 7 A) does not entail immediate unbinding. Rather, the complex is stabilized by a transient network of water bridges and other transient hydrogen bonds, which form during the unbinding process (Fig. 7 B and C). Only after subsequent rupture of these hydrogen bonds the maximum force -- the rupture force -- is reached and the biotin rapidly moves out of the entry of the binding pocket (Fig. 7 D). As another feature we observed, towards the end of the unbinding process, a second force maximum, which we attribute to a strong transient hydrogen bond and several water bridges between biotin and the entry of the binding pocket (Fig. 7 E). Crossing of that second barrier, which cannot yet be resolved in the AFM experiment, completes the unbinding process.

In summary, our simulations provided detailed insight into the complex mechanisms of streptavidin-biotin rupture. They attribute the binding force to a network of hydrogen bonds between the ligand and the binding pocket and show that water bridges substantially enhance the stability of the complex. Good agreement with experimental results was obtained. Further `force simulations' of various systems, e.g., an antigen-antibody complex, are in progress.

  

Figure: `Snapshots' of rupture taken (A) at the start of the simulation ($z_{\rm cant}=0$), (B) at $z_{\rm cant}=2.8\,$Å, (C) at $z_{\rm cant}=4.1\,$Å, (D) at $z_{\rm cant}=7.1\,$Å, and (E) at $z_{\rm cant}=10.5\,$Å. The biotin molecule is drawn as a ball-and-stick model within the binding pocket (lines). The bold dashed lines show hydrogen bonds, the dotted lines show selected water bridges.