Phi Value Analysis - Mathematical Definition

Mathematical Definition

The phi value is defined as: \Phi = \frac{(\Delta G^{TS-D}_{W} - \Delta G^{TS-D}_{M})}{(\Delta G^{N-D}_{W} - \Delta G^{N-D}_{M})} = \frac{\Delta\Delta G^{TS-D}}{\Delta\Delta G^{N-D}}

where represents the energy difference between the transition state and the denatured state for the wild-type protein, represents this energy difference for the mutant protein, and the terms represent the energy difference between the native state and the denatured state. Thus, the phi value represents the ratio of the energetic destabilization introduced by the mutation to the transition state versus that introduced to the native folded state.

The phi value should range from 0 to 1. A phi value of 0 implies that the mutation has no effect on the structure of the rate-limiting transition state on the folding pathway, while a phi value of 1 indicates that the degree to which the transition state is destabilized by the mutation is exactly equal to the degree to which the folded state is destabilized. A phi value near 0 suggests that the region surrounding the mutation is relatively unfolded or unstructured in the transition state, while a value near 1 implies that the local structure around the mutation site in the transition state closely resembles the structure in the native state. It is generally the case that conservative substitutions on the surface of a protein yield phi values near 1. When the phi value is intermediate between 0 and 1, the method cannot directly distinguish between the alternative hypotheses that the transition state is partially structured, or that there are two populations of mostly-unfolded and mostly-folded states.

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