  We construct an energy function that describes the crystallographic structure
of spermwhale myoglobin backbone. As a model in our construction, we use the
Protein Data Bank entry 1ABS that has been measured at liquid helium
temperature. Consequently the thermal B-factor fluctuations are very small,
which is an advantage in our construction. The energy function that we utilize
resembles that of the discrete non-linear Schrodinger equation. Likewise, ours
supports solitons as local minimum energy configurations. We describe the 1ABS
backbone in terms of solitons with a precision that deviates from 1ABS by an
average root-mean-square distance, which is less than the experimentally
observed Debye-Waller B-factor fluctuation distance. We then subject the
multisoliton solution to extensive numerical heating and cooling experiments,
over a very wide range of temperatures. We concentrate in particular to
temperatures above 300K and below the theta-point unfolding temperature, which
is around 348K. We confirm that the behavior of the multisoliton is fully
consistent with Anfinsen's principle, up to very high temperatures. We observe
that the structure responds to an increase of temperature consistently in a
very similar manner. This enables us to characterize the onset of thermally
induced conformational changes in terms of three distinct backbone ligand
gates. One of the gates is made of the helix F and the helix E. This is a
pathway that is presumed to have a major role in ligand migration between the
heme and the exterior. The two other gates are chosen similarly, when open they
provide a direct access route for a ligand to reach the heme. We find that out
of the three gates we investigate, the one which is formed by helices B and G
is the most sensitive one to thermally induced conformational changes. Our
approach provides a novel perspective to the important problem of ligand
migration.
