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Redox entropy of plastocyanin: Developing a microscopic view of mesoscopic polar solvation
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Image of FIG. 1.
FIG. 1.

Structure of plastocyanin: the active site includes copper ion (green), 2 histidines (blue), methionine (red), and cysteine (orange) residues.

Image of FIG. 2.
FIG. 2.

Distribution of the positive and negative charge on the surface of the protein. The positively and negatively charged residues are shown, respectively, in red and blue. The copper ion is shown in green.

Image of FIG. 3.
FIG. 3.

Diagram of the computational algorithm.

Image of FIG. 4.
FIG. 4.

Separation of real space into regions for the calculation of the Fourier transform of the solute electric field [Eq. (24)]. The Fourier transform is calculated numerically in region 2 and analytically [Eq. (27)] in region 3. The field is set equal to zero within the hard repulsive core of the solute (region 1).

Image of FIG. 5.
FIG. 5.

Longitudinal and transverse polarization structure factors of TIP3P water [Eq. (28)] calculated at different temperatures from MD trajectories. Also shown is the PPSF calculation at .

Image of FIG. 6.
FIG. 6.

Contact of a redox pair with the metal electrode. and show the fluctuating energy gaps for reduction and oxidation electron transfer, respectively. The equilibrium electrochemical potential of the electrode is established when the equilibrium energy gaps are equal for the reduction and oxidation reactions [Eq. (33)]. The Marcus electron transfer parabolas, shown by the dependence of free energy on the energy gap coordinate , are symmetric in this case producing equal oxidation and reduction currents [Eq. (35)].

Image of FIG. 7.
FIG. 7.

Average solute-solvent interaction energy obtained from MD simulations (closed circles), NRFT (diamonds), and DELPHI continuum calculations (vdW cavity, triangles). The closed diamonds refer to the total average energy including the polarization and density components, while the open diamonds denote the polarization component only. The dashed lines represent linear regressions through the points.

Image of FIG. 8.
FIG. 8.

Radial distribution functions between surface residues of PC and oxygens of water. The upper panel shows ionized residues and the lower panel refers to nonpolar residues. The legends in the figure list. aspartic acid (ASP), the probe atom is the oxygen at the first position; lysine (LYS), the probe atom is nitrogen at the position; proline (PRO), the probe atom is the carbon; tyrosine (TYR), with the first carbon as the probe atom.

Image of FIG. 9.
FIG. 9.

Solvation Gibbs energy from MD simulations (closed circles), NRFT calculations (closed diamonds), continuum DELPHI calculation with the standard cavity definition (up triangles), and the cavity surface augmented by the solvent radius (down triangles). The dashed lines are linear regressions through the points.

Image of FIG. 10.
FIG. 10.

Reorganization energy of PC vs temperature calculated from MD simulations (closed circles), from NRFT (diamonds), and from dielectric continuum using solvent-accessible cavity definition (triangles). The dashed lines are linear regressions through the points. The filled diamonds refer to the full NRFT calculation and the open diamonds denote the polarization response only.

Image of FIG. 11.
FIG. 11.

Pair distribution function between oxygen of water and Cu of PC in the reduced (Red) and oxidized (Ox) sates.

Image of FIG. 12.
FIG. 12.

Reorganization energy of charge-transfer transition in -nitroaniline dissolved in SPC/E water. The results are obtained by MD simulations (Ref. 16) (closed circles) and NRFT calculations (diamonds). Closed and open diamonds refer to the full and polarization response, respectively. Triangles denote half of the Stokes shift from MD simulations; in the LRA, . The dielectric constants of SPC/E water at different temperatures, required for the NRFT input, were taken from MD simulations (Ref. 16).

Image of FIG. 13.
FIG. 13.

The distribution of binding energies of water molecules in the first solvation shell of PC(Ox) defined by adding the water diameter to all protein atoms exposed to solution. The binding energy is defined as the total interaction energy of a given water molecule with all atoms of the protein. The inset shows the distribution of distances of charged residues at the protein surface.

Image of FIG. 14.
FIG. 14.

Normalized time self-correlation functions for Cu-water minimum distance, (dotted line), and for the number of particles in the first solvation shell, (solid line). The dashed lines refer to the fits of correlation functions obtained from MD simulations to Eq. (53). The parameters of the fits are listed in the plot.


Generic image for table
Table I.

Atomic partial charges for copper and its four ligands in the reduced (Red) and oxidized (Ox) states of PC.

Generic image for table
Table II.

Temperature-dependent (eV) for PC(Ox). The results are obtained from MD simulations, DELPHI calculations (with vdW and SS cavities), and from NRFT calculations. The calculations were done with three charge distributions of the active site (I–III, see text for description).

Generic image for table
Table III.

Redox thermodynamics of PC (eV).

Generic image for table
Table IV.

Redox solvation free energy and redox entropy in for the Red/Ox states of PC. Also listed are the reorganization energy and reorganization entropy, . All energies are in eV and entropies are in meV/K, .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Redox entropy of plastocyanin: Developing a microscopic view of mesoscopic polar solvation