Imaging Protein Statistical Substate Occupancy in a Spectrum-Function Phase Space

Hemeprotein ligand rebinding studies reveal varying IR absorbance and rebinding functions across a cryogenic ensemble. Since IR-active vibrations and rebinding barriers couple to structural coordinates, spectral and functional heterogeneity arise from conformational heterogeneity. Modeling rebinding data as a spectrally resolved superposition of first-order rate processes and employing maximum entropy regularization, protein heterogeneity is imaged as an ensemble occupancy of a spectrum-function phase space. Results from myoglobin rebinding carbon monoxide are discussed.

Figure 1

MEM inversion of horse MbCO data. $p=0.1$, $\gamma =2.0{\mathrm{cm}}^{-1}$, $\sigma =0.02{max}_{\nu ,T}\Delta \mathcal{A}(\nu ,T)$, $\mathrm{TEST}\mathrm{\text{threshold}}={10}^{-4}$, $A={10}^{9.2}{\mathrm{s}}^{-1}$. Initial $\mathbf{G}$ and ${\mathbf{G}}^{\prime }$ were uniform and very small.

Figure 2

Spectrum-function association.

Figure 3

Active site with proposed structural coordinate $\alpha$ and electrostatic potential isosurface at $-300(k{T}_0/e)$. Structure data are from PDB code 1dwr [6].

Figure 4

Computed structure-spectrum association. The crystal structure in Fig. 3 corresponds to $\alpha =0$.