Advanced Techniques in MD Simulation: Accelerated MD

Although the basic form of MD simulation has been unchanged over decades, the speed and ac- curacy of these simulations have improved substantially over the past few years(1). A wide range of developments in hardware, software, and methodology aims to maximize MD capabilities to access longer timescales as well as to improve force field accuracy. These methods include the parallelization across general-purpose computer chips(1, 11), developing graphics processing units(12), and special- purpose parallel architectures( such as Anton)(1, 13).

In addition, the long-timescale simulations demands different level of accuracy in force fields; a force field that is sufficient for short-timescale simulations may not work well at longer timescales and, therefore, may need parameter readjustments(1). These adjustments have been carried out for torsion-

al angles in protein backbone and side chain, charge distributions of ionizable amino acid residues as well as different parameters for lipids and small drug-like molecules(1).

On the other end of a wide range spectrum of techniques aimed to make Molecular Dynamics simulation even more efficient are enhanced sampling methods. These methods have been increasingly used in the simulation of events not accessible by conventional MD. Examples of these techniques in- clude targeted molecular dynamics(TMD)(14), Replica Exchange Molecular Dynamics(REMD)(15), um- brella sampling(16), metadynamics(17) and accelerated molecular dynamics (aMD)(18). While the tech- niques based on simple potential modifications such as TMD have provided valuable conformational information, the REMD methods have proven to enhance sampling of the energy landscape(19). How- ever, because of the alteration in the actual kinetics of the systems under study the success of these methods has been empirical rather than rigorous(19). In addition, most of the enhanced-sampling methods need a priori knowledge about the energy landscape of the system. Nevertheless, successful application of enhanced sampling methods can be achieved by considering its specific contexts(19).

Accelerated MD (aMD), the method used in our work, is the enhanced-sampling method with no need for a prior knowledge of the energy landscape of the system. The accelerated MD has been shown to accurately and efficiently explores conformational space with improved sampling(18). The application of aMD simulation in our study provided insightful information on the atomic details of uncatalyzed and CypA-catalyzed peptidyl-prolyl isomerization. The aMD method was proposed by Hamelberg et al.(18), based on the earlier hyperdynamic model(20) which simulates infrequent biomolecular events without any prior knowledge of the energy landscape. In the hyperdynamic method the potential energy surface V(r), is modified by adding a bias potential, ∆V(r), to create an altered potential, V*(r), such that the

potential surfaces near the minima are raised and those near the barriers are left unaffected(18)(Figure 2).

Figure 2 Accelerated molecular dynamics method as represented by normal potential, the biased poten- tial, and the threshold boost energy, E.

Previous suggestions for defining ∆V(r) suffer from different problems such as high computa- tional cost, discontinuity in calculations, low accuracy and the changes in the shape of energy

surface(18). The aMD method, however, suggested a new ∆V(r) in a way that maintain the underlying

shape of the unmodified potential energy surface. In addition, the problem of discontinuity in calcula- tions is removed by smoothly merging the modified potential with the original potential at a threshold ‘‘boost energy’’ value of E(18). The ∆V is therefore defined as:

( ) = ( )

( ( )) (2-2)

Where α is a tuning parameter, that determines how deep the modified potential energy basin would be(18).

Selection of E and α determines how the potential of the system will be altered and how aggres- sively the molecular dynamics will be accelerated. The appropriate choices of E and α are important for

efficient and accurate sampling of the energy landscape. In general, E should be greater than the mini- mum of V(r) near the starting structure. Otherwise, the simulation will always be performed on the true potential that is simply a normal MD simulation. For large molecules with multiple minima very close together, an average potential energy on the true potential can be used as Vmin. Since at low values of E

the modified potential falls below most of the transition state regions with the same probability of

escape as unmodified potentials, the choice of α is not that critical to the overall potential energy landscape. However, at high value of E, the modified potential becomes isoenergetic in most places for

small α, and the molecular system experiences a random walk. Therefore, in order to maintain the basic shape of the potential energy surface at high values of E, and preserve the same potential energy wells

that is present on the unmodified potential surface, α has to be set to a much higher value than zero. The statistics sampled on the biased potential are then corrected to remove the effect of the leading to convergence to the correct canonical probability distribution(18). Normally, the sampled points of a system from an altered Hamiltonian are reused with different statistical weights to evaluate its properties at the original potential(21). A statistical analysis of the precision of reweighting-based simulations such as accelerated MD provided a quantitative method to estimate the number of sampled points required in the crucial step of reweighting of these methods(21). These information and analysis can provide a priori guidance for the strategy of setting up the parameters of advanced simulations be- fore a lengthy one is carried out.

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