Although MD simulations are beginning to breach the one microsecond barrier, there is still a long way to go before large-scale conformational changes can be directly observed. In the meantime, there remains a need for techniques that apply external forces to explore conformational changes in a practical amount of time. Here, the focus is on systems where proteins are mechanically pulled to induce unfolding. Such systems have been explored by AFM experiments, which provide detailed force measurements that constitute a rigorous test of the accuracy of any computational force-generating methodology.
In the previous literature, most of the focus has been on constant-velocity AFM pulling experiments, which generate a characteristic saw-tooth force profile over the extension of the protein 
. Sufficiently slow pulling velocities (~10−8
Å/ps) are used to allow accurate closed-loop control. A linear relationship has been observed between the maximum force and the pulling velocity over a range of pulling velocities. More recently, force-clamp AFM experiments have provided an alternative view of the unfolding force profile 
. In force-clamp AFM experiments, constant forces are generated. For certain range of forces, the protein unfolds to a specific end-to-end distance, corresponding to different stages of unfolding. The force-clamp forces provide a different characterization of the unfolding landscape of titin.
Steered MD simulations have been used to explore constant-velocity motions where pulling velocities (1 Å/ps) 108
much faster than the AFM experiments are used to generate sufficient motion within a reasonable timescale (less than a nanosecond). Although Steered MD simulations have reproduced the linear dependency between forces and pulling velocities, the simulated force fluctuations were much larger than expected from the AFM experiments. This has been found using both implicit 
and explicit solvent 
. As such the discrepancy cannot be attributed to hydrogen bonding with explicit solvent. The most likely source is the elasticity of the harmonic springs used to generate the forces in Steered MD.
In contrast, the PUFF methodology generates forces directly without the need of harmonic springs. Although both PUFF and Steered MD simulations are parameterized by a target velocity, the target velocity in PUFF is conceptually different to the target velocity in Steered MD. In Steered MD, once the harmonic spring restraints are set to the target velocity, the instantaneous velocities are allowed to fluctuate wildly, whilst the overall velocity, averaged over a time-scale larger than the response of the harmonic spring, is maintained to a fixed value. In contrast, in a PUFF simulation, it is the instantaneous velocity that is fixed at the beginning of every pulse, which constrains the instantaneous momentum. If the applied momentum is insufficient to break out of a local minimum, then the protein gets trapped.
In PUFF simulations, then, the forces are capped, which can retard the overall motion, whilst in Steered MD, forces can fluctuate wildly, but the overall motion is fixed. Conceptually then, the PUFF simulations are closer to the force-clamp AFM experiments, which measure a range of static forces for different levels of unfolding. Simply by noting whether a PUFF simulation unfolds at the target velocity or at an impeded rate or not all, we can calculate a corresponding range of forces, where the range of forces from PUFF agree well with the force-clamp AFM experiments for titin. As PUFF does not model the kinetics of unfolding at a fixed velocity, it is not expected to model the relationship between force and pulling velocity found in constant-velocity AFM experiments. However, for purposes of comparison with other proteins, we assume that the force measured in constant-velocity AFM experiments falls near the value where the protein unfolds without impedance in the PUFF simulations. As such, the PUFF simulations produce values that agree well with the AFM pulling experiments of e2lip3, and ubiquitin.
Another advantage of PUFF is that the relaxation period after the pulse allows the protein to respond to the applied forces in qualitatively different ways. We can use the trajectories where the I27 domain is trapped to identify unfolding intermediates and reproduce the range of forces that determines the unfolding intermediate. In previous Steered MD simulations, the I27 unfolding intermediate was also identified using constant-force pulling restraints 
. However, such constant-force restraints in Steered MD can only be used to study intermediates at small extensions because for larger motions, it is difficult to rationalize the stability of the constant-force restraints. Instead, constant-velocity restraints must be used for large motions in Steered MD, but they result in highly inaccurate force values 
. In contrast, with PUFF simulations, the same type of constant-momentum simulation can be used to identify both folding intermediates and critical unfolding forces. Given the varied response with the same type of simulation, we can extend PUFF to study protein deformations where there is a differential response of the protein to the applied force. Indeed, we have already been able to generate such differential conformational responses using local rotational forces 
The tradeoff in PUFF is in the overhead of implementing the protocol within standard MD packages. In PUFF, the simulations are performed in pulses outside the MD simulations, which require PYTHON scripts to make calculations between each MD run of the pulses. However, this allows the PUFF technique to be easily ported to other MD packages. As well, it becomes much easier to implement other more complex forces (we are currently exploring domain-domain interactions).
Currently, PUFF is implemented in AMBER using a GB/SA implicit solvent potential. As the implicit potential used in PUFF is able to derive realistic force values, this suggests that the main component of the force barrier are the internal hydrogen bonds. However, the derivation of the complete free-energy profile requires the accurate modeling of kinetics, especially the role of explicit waters. In previous Steered MD studies of the unfolding of titin, it was that found that hydrogen bonding with explicit solvent waters plays a key role in defining the kinetics 
. In particular a reasonable estimate of the unfolding barrier was derived from the first mean passage times. It would thus be useful to extend the PUFF simulations to include explicit solvent. Nevertheless, Steered MD consistently overestimate force fluctuations due to the harmonic springs. To explore other thermodynamic parameters such as the work function, trajectories with better force values will be needed. By removing the dependency on harmonic springs, the adaptive forces of PUFF can generate trajectories with less force fluctuations at faster velocities and shorter simulation times.