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coordinate. This phenomenon is known as gimbal lock from its disastrous possible<br />

consequences in aircraft control systems.<br />

Both of these issues can be dealt with by specifying rotations using axis/angle rather than<br />

euler angle matrices. This involves rotating about a single axis which can point in any<br />

direction, not just along the x,y, or z axes.[97] We found this less intuitive for the user<br />

and so simply restrict the pitch rotations to less than 90° in either direction.<br />

Optional equilibration<br />

The preceding rotation step invariably results in unphysical bond lengths and angles in<br />

the boundary between L and M, and often in steric clashes between M and the rest of the<br />

protein and/or ligand. If an equilibrated structure free of steric strain is desired, a<br />

Molecular Dynamics equilibration is performed using the GROMACS mdrun program<br />

for 1000-10000 time steps (2-20 ps). We found that the shorter time was sufficient to<br />

relieve the most significant steric strains, and the longer time was sufficient to allow an<br />

exponential decrease in enthalpy to level off (data not shown), indicating a better<br />

equilibrated structure. It was not sufficient time to allow substantial domain motions.<br />

Note that equilibration significantly increased the accuracy of ligand-binding prediction,<br />

so including it is recommended for that application.<br />

247

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