Electron transfer through proteins

1. Electron transfer through proteins Myeong Lee (02/20/2006)

2. Agenda • Free energy calculations • Hybrid QM/MM approach • Solvent models (effects) • Further issues • Sample systems

3. Redox-active prosthetic groups (coenzymes) • [Fe-S] clusters • Cytochrome c - heme • NAD, FAD • The kinetics of electron transfer between proteins is a sensitive function of their relative redox potentials. • Calculation of redox potential → calculation of the free energy difference between the oxidized and reduced states

4. Free energy calculations • Free energies of molecular systems describe their tendencies to associate and react. • Statistical perturbation • Thermodynamic integration • Accuracy of Hamiltonian (pot. E. function) / sampling problem

5. Hybrid QM/MM approach • Most chemical reactions occur in condensed phase. • Significant electron redistribution during the reaction is often limited to a small number of atoms.

6. QM region - include all those atoms involved in the reaction process. (atoms making bonds or breaking bonds) - atoms are represented as nuclei and electrons. - Born-Oppenheimer approximation • MM region - remaining atoms - represented as atoms - empirical potential energy function

7. System Hamiltonian

8. Frontier bonds in QM/MM methods • In enzyme reaction there are bonds between the QM and MM atoms. • Link atom method • Dummy or link QM atoms(H) are introduced along the broken QM/MM bond. • Link atoms are treated like QM hydrogen atoms. • No interactions between the link atom and MM atoms. • LSCF (Local Self-Consistent Field) approach • Electronic density along the frontier bond is represented as frozen atomic orbital which has a preset geometry and electronic population – not included in SCF procedure

9. Solvent models • Macroscopic continuum model • Treat macromolecule as a single low-dielectric medium with embedded fixed charges, surrounded by a high dielectric medium representing solvent. • PDLD (Protein Diploes Langevin Dipoles) model • Place a cubic grid around the solute atoms • Each grid point within a van der Waals distance from a solute atom is excluded. • The remaining grid points are replaced by point dipoles.

10. Hybrid approach: • Calculate free energies for a solute and a limited number of explicit water molecules • Transfer into bulk solvent and calculate transfer free energy with a continuum model • Explicit water model using MD

11. Solvent effects on protein-protein ET • Until recently water was thought to be a rather poor ET mediator with decay constant of 1.6-1.7 Ǻ-1 compared to proteins (1.0-1.2 Ǻ-1). • Recently many experiments show that a small number of structured water molecules increase the ET rate. • D-to-A electronic coupling <T2DA> shows three regimes. (Science 310 25 2005)

12. Further issues • Proton transfer • Energies (ΔG(m)) of the different protonation states? • Role of different proton transfer pathways? • PDLD • EVB (empirical valence bond) approach • QM/MM methods • Calculation of pKa values

13. Cytochrome c • Small, water-soluble protein, with a single heme group. • ~1000 atoms including protein and heterogen atoms

14. Fe-S proteins