For a two-dimensional potential of intersecting parabolic bowls, we ob
tain an analytical approximation for the survival probability in the l
imit that the reactive mode is diffusive and the perpendicular protein
mode frozen. The approximation is used in an automated computer algor
ithm for determining the parameters of the potential. Using this progr
am, we are able to obtain a reasonably good fit to the low- temperatur
e data of CO binding to horse myoglobin. We find, however, that featur
es of the potential such as the saddle-point energy and the effective
barrier, expected to dictate the high-temperature kinetics, are not un
iquely determined for this potential from fitting the low-temperature
data.