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 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 pK a values

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

14. Fe-S proteins