As will be seen from the end of the report on work so far , I have only just begun the investigation of the channel including a hydrated ion. There are many interesting aspects to the interaction between the ion and the channel protein still to be looked at in detail: the perturbation of the structure of the channel by the ion; the mechanism by which the channel discriminates between positive and negative ions; the blocking of the channel in its closed state; the detailed interactions between ion and channel protein at various points along the channel pore; and even the mean passage time of the ion through the channel. By connecting with the experimentally-determined conductivity, the mean passage time would provide an excellent confirmation of the structure of the channel. As was remarked before, the mean first passage time is too long to be simulated directly, but it can be calculated if the the free energy of the ion as a function of its position along the channel is known. I developed some novel techniques for the measurement of free energy as part of my PhD work at Edinburgh , and we expect these to be applicable to this biological system. However, the application of these methods will still be very time-consuming, expecially since the long-range interactions need to be more carefully treated than has been the case, using for example Ewald summation rather than a simple cut-off.
Aside from the work on the acetylcholine receptor, we expect to be able to apply similar techniques to several other ion channels, such as the GABAA receptor (an neuronal anion channel). Here, there is still less structural information, and whether or not the observed conductivity and selectivity can be reproduced may help in the elucidation of the structure.
Much less is known about the parts of ion-channel proteins that do not line the pore directly but instead stablilise the molecule in the membrane, and existing models of protein-membrane interaction do not work well. As a longer-term project, I shall attempt to make some progress on this problem. There are several possible avenues of attack here: the improvement of the model potentials that we use by collaboration with my former colleagues at Edinburgh to use results of ab initio calculations done there; the application of recent advances in the statistical mechanics of membranes and hydrophobic interactions; and the speeding-up of the simulations by the incorporation of multiple-time-step methods and the treatment of long-range interactions by multipole expansions.
I shall also try to adapt a method known as `simulated tempering' to the problem of protein structure refinement. This technique, which I used during my PhD, is related to (and, it seems, rather better than) the `simulated annealing' methods already used in this group as a way of tackling the well-known problem of the inability of simulations to cross potential barriers (in the available simulation time) to find other, more stable structures.