Stochastic boundary region

Fig. 6.7 Division into reaction zone and reservoir regions in a simulation using stochastic boundary conditions.

The use of QM-MD as opposed to QM-MM minimization techniques is computationally intensive and thus precluded the use of an ab initio or density functional method for the quantum region. This study was performed with an AMi Hamiltonian, and the first step of the dephosphorylation reaction was studied (see Fig. 4). Because of the important role that phosphorus has in biological systems [62], phosphatase reactions have been studied extensively [63]. From experimental data it is believed that Cys-i2 and Asp-i29 residues are involved in the first step of the dephosphorylation reaction of BPTP [64,65]. Alaliambra et al. [30] included the side chains of the phosphorylated tyrosine, Cys-i2, and Asp-i 29 in the quantum region, with link atoms used at the quantum/classical boundaries. In this study the protein was not truncated and was surrounded with a 24 A radius sphere of water molecules. Stochastic boundary methods were applied [66]. 

An essential feature of the stochastic boundary methods is a partitioning of the many-body system into several regions. The regions are delineated based... 

To characterize structural waters and to follow the dynamics of reactions involving waters, it is necessary to be able to treat in detail the motions of these molecules. A methodology which includes solvents explicitly is required. Both conventional molecular dynamics techniques and the stochastic boundary molecular dynamics approaches can be used. When the region of... 

In many simulations of solute-solvent systems the primary focus is the behaviour of the solute the solvent is of relatively little interest, particularly in regions far from the solute molecule. The use of non-rectangular periodic boundary conditions, stochastic boundaries and solvent shells can all help to reduce the number of solvent molecules required and enable a larger proportion of the computing time to be spent simulating the solute In this section we consider a group of techniques that incorporate the effects of solvent without requiring any explicit specific solvent molecules to be present. 

To overcome problems arising fi-om the finite system size used in MC or MD simulation, boundary conditions are imposed using periodic-stochastic approximations or continuum models. In particular, in stochastic boundary conditions the finite system is not duplicated but a boundary force is applied to interact with atoms of the system. This force is set as to reproduce the solvent regions that have been neglected. Anyway, in general any of the methods used to impose boundary conditions in MC or MD can be used in the QM/MM approach. 

The system may be partitioned as illustrated in Fig. I into three parts a quantum-motif, a classical or molecular mechanics region, and a boundary region. The quantum and classical regions contain the atoms that are explicitly treated in the calculation. The boundary region accounts for the surroundings that are neglected. As such either periodic boundaries or the stochastic boundary method can be used [23, 25]. 

An alternative approach is to employ stochastic boundary conditions where the finite molecular system employed in the simulation is not duplicated, but rather, a boundary force is applied to interact with atoms of the sys-tem. 2-67 Yhe boundary force is chosen to mimic the bulk solvent regions that have been neglected. However, a difficulty with the use of this method is due to the ambiguity associated with the definition and parameterization of the boundary forces. Thus, there is sometimes the impression that the method is not rigorous. Recently, Beglov and Roux provided a formal definition and suggested a useful implementation of the boundary forces. Their results are very promising. 

---