On the role of thermal backbone fluctuations in myoglobin ligand gate dynamics

Abstract

We construct an energy function that describes the crystallographic structure of sperm whale 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 Schrödinger 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 Θ-point unfolding temperature, which is around 348K. We confirm that the behavior of the multisoliton is fully consistent with Anfinsen's thermodynamic 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 rôle 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.

Solution x-ray scattering and structure formation in protein dynamics

“…Thus the free energy E(κ, τ ) can be expanded in the powers of the differences ∆κ i . A detailed analysis which builds on extensive symmetry considerations, in particular on the requirement that the functional form of the energy should remain invariant under local frame rotations, shows [7,8,[25][26][27][28][29][30][31] that in the limit of small variations in ∆κ i the following expansion of the free energy can be used in the case of proteins…”

“…Finally, the last term (V ) includes various long distance two-body interactions such as Coulomb and Lennard-Jones interaction between the residues. In the leading order this contribution can be approximated by a hard ball Pauli repulsion [7,8,[25][26][27][28][29][30][31]; see [32] for more general long range interactions.…”

Gauge fields, strings, solitons, anomalies, and the speed of life

“…At the moment we do not know of an analytical expression of the soliton solution to the equation (67). But we have found [32][33][34] that an excellent approximative solution can be obtained by discretizing the topological soliton (43).…”

“…The fixed point of (68) is clearly a solution of (67). Once the numerically constructed fixed point is available, we calculate the corresponding torsion angles from (66).…”

“…The (red) line is the average of 1.000 simulations, and the surrounding (yellow) shaded area describes the one standard deviation extent of fluctuations. Along the top axis, we have converted the temperature into Kelvin scale, using the renormalization procedure described in [67].…”