computer modeling in molecular biology.pdf

6.3.5 Relation Between NP and ERT6 Theory of Dansport in Ion Channels 161Traditionally, the ERT and NP approaches take opposite viewpoints in descriptionof ion movements in terms of microscopic events (see Section 6.2) [l]. In fact, undercertain conditions, they can be very similar. Although it is clearly appropriate to expressthe long time transport of Na’ in the 8-helix in terms of a hopping processbetween discrete states, the NP diffusion equation can also provide a meaningfuldescription of the translocation process and a good estimate of the long time transportrate in the present case. In Eq. (6-9) the A,,,-NP involves the effective diffusionconstant, Deff, defined in Eq. (6-11) as a spatial average over the length of thepore. Since the potential of mean force is made of a sequence of identical wells andbarriers, Deff can be approximated as,(6-31)where AW* is the activation free energy, [w(xb)- W(x,)], and W”(xw) and- w,l(xb) are the second derivatives of the potential of mean force at the bottomof the well (x,) and at the top of the barrier (xb), respectively. Under these conditionsA,,-NP is equivalent to A,,-ERT provided the pre-exponential factor istaken as,(6-32)An essential aspect of this approximation, called “high friction limit”, is that inertialdynamical effects are neglected [90], as indicated by the fact that Fp is independentof the mass of the ion.The value of the diffusion constant at the barrier top can be obtained, via theEinstein relation D = k,T/