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Ligand Dynamics in Heme Proteins Ligand Dynamics in Heme Proteins Markus Meuwly Department of Chemistry University of Basel ICERM Workshop 2012 Overview Overview Introduction and Computational Techniques Applications Smoluchowski


  1. Ligand Dynamics in Heme Proteins Ligand Dynamics in Heme Proteins Markus Meuwly Department of Chemistry University of Basel ICERM Workshop 2012

  2. Overview Overview Introduction and Computational Techniques • Applications • Smoluchowski Treatment • Transition Networks • Protein- and Ligand-Motion • Spatial Averaging • Summary • ICERM Workshop 2012

  3. Overview Overview Small ligands play important functional roles in proteins. Heme-proteins (Mb, Hb, Ngb, trHb, etc.) bind ligands such as O 2 , NO, CO with various purposes: • Transport • Removal of NO • Neurotransmission, Vasodilation Fundamental questions: • How do these molecules enter their host proteins • How do they move (cavities) • How do they bind (allostery) ICERM Workshop 2012

  4. Overview Overview The goal is to understand in general terms the processes of ligand dissociation, rebinding, recognition, and discrimination, and to explore ligand entrance and exit pathways in the framework of protein structure and dynamics, using myoglobin as a specific example. Comprehensive studies have been carried out over the time scale from femtoseconds to seconds, under a broad range of experimental conditions such as temperature, pressure, solvent viscosity, and pH, for several species of wild-type myoglobins and for variants of important amino acid residues. [Moffat, Biochem. (2001)] Our experiment shows that the pathway of a small molecule in its trajectory through a protein may be modified by site-directed mutagenesis, and that migration within the protein matrix to the active site involves a limited number of pre-existing cavities identified in the interior space of the protein. [Schlichting, PNAS (2000)] ICERM Workshop 2012

  5. Ligand Dynamics in Heme-Proteins: The Bohr-effect Ligand Dynamics in Heme-Proteins: The Bohr-effect Affinity (binding capacity) of Hb depends on pH and [CO 2 ]. Low pH/high [CO 2 ] leads to reduced O 2 affinity; i.e. regulation R-state: relaxed, 6- coordinated structure, high- O 2 -affinity T-state: tense, 5- coordinated structure, low- O 2 -affinity ICERM Workshop 2012

  6. Ligand Dynamics in Heme-Proteins Ligand Dynamics in Heme-Proteins Time scales for ligand motion “Logic” of ligand migration Comparison with experiment Protein- and ligand-motion ICERM Workshop 2012 Schulten et al., Biophys. J. (2006) Maragliano et al., JACS (2010)

  7. Introduction: Protein Structure and Ligand Diffusion Introduction: Protein Structure and Ligand Diffusion F. Schotte et al., Science 300, 1944 (2003) ICERM Workshop 2012

  8. Introduction: Role of Simulations Introduction: Role of Simulations Understanding of, providing insights into and making predictions about mechanisms at molecular level. MD with improved/modified FFs Relationship between structure, dynamics and spectroscopy? • What do ligands tell us about protein interiors? • ICERM Workshop 2012

  9. Introduction and Computational Techniques Introduction and Computational Techniques  Fluctuating Charge Models  Multipolar Force Fields  Dissociative Force Fields  Morphing Potentials Intermolecular interactions • Solving Smoluchowski Equations on Rough Surfaces Diffusive Dynamics • Transition Networks Chemical Reactions  Reactive MD  Dissociative Force Fields ICERM Workshop 2012

  10. Computational Techniques: Force Fields Computational Techniques: Force Fields Force Field: Atom-based energy expression E tot = E bond + E nonbond Bonded Terms q i   E = ½ k (x-x e ) 2 Bond Energies E = ½ k (  -  e ) 2 Angle Energies x E = V n cos(n  -  e ) 2 Torsion Energies Nonbonded Terms q i q j E ij = q i q j /4  0 r Coulomb E ij = 4  ij (  ij 12 -  ij 6 ) Van der Waals  ij = sqrt(  i  j )  ij =(r ij /  ij )  ij =1/2(  i +  j ) ICERM Workshop 2012

  11. Molecular Simulations Molecular Simulations Given a way to compute the interaction energy V (e.g. force field, quantum, semiempirical) of a system it is then possible to determine physico-chemical properties from a molecular simulation.        F x x   m t V     x t v The result will be a trajectory ; t Using statistical mechanics, numerous experimental observables can be computed: 2 p N 2 K 1  Temperature   i T 3 Nk 3 Nk m  i 1 B B i 1   Specific heat 2 C E V 2 k T NVT B      1   Diffusion coefficient v v D dt 0 t i i 3 0               μ 0 μ Infrared spectrum I dt exp i t t   Accuracy of the intermolecular interactions and the degree of sampling of the configurational space determine the quality of a simulation (and the observables derived from it). ICERM Workshop 2012

  12. Mb: Ligand Rebinding in MbCO (100 ns rebinding) Mb: Ligand Rebinding in MbCO (100 ns rebinding) R/A 10 8 6 4 2 10 5 Xe4(1) 8 DP 0 6 1 –3 Xe4(2) G(kcal/mol) 4 2 Xe4(2) – 5 Xe4(1) DP 4 v/A 2 –2 A A – 10 0 Fe – 2 – 15 – 4 – 6 – 20 10 8 6 X X 4 v/A 2 0 Fe – 2 – 4 – 6 ICERM Workshop 2012 – 13 – 9 – 5 – 1 1 3 5 Banushkina and Meuwly, JCTC, 2, 208 (2005); JPCB, 109, 16911 (2005); JCP (2007) u/A

  13. Solving Smoluchowski Equations on Rough Potentials Smoluchowski simulation of protein folding based on pre-calculated FES. MD simulations of protein G in explicit U solvent. Experimental folding F times: 600 – 700  s 2-30 ms (denaturant dependent) ICERM Workshop 2012 Sheinerman and Brooks, PNAS (1998) Roder et al., Nat. Struc. Biol. (1999)

  14. Solving Smoluchowski Equations on Rough Potentials SE difficult to solve on rough PESs Use of Hierarchical Discrete Approximation: 1 Introduce a hierarchy of grids Having a procedure to solve SEs on rough PESs we can no pre-compute the free energy surface for ligand motion and avoid the long-time scale problem present in explicit sampling. From several independent trajectories this FES can be constructed efficiently. ICERM Workshop 2012 1 Banushkina and Meuwly, JCTC, 2, 218 (2005)

  15. Solving Smoluchowski Equations on Rough Potentials R/A 10 8 6 4 2 10 5 Xe4(1) 8 DP 0 6 1 –3 Xe4(2) G(kcal/mol) 4 2 Xe4(2) – 5 Xe4(1) DP 4 v/A 2 –2 A A – 10 0 Fe – 2 – 15 – 4 – 6 – 20 10 8 6 X X 4 v/A 2 0 Fe – 2 – 4 – 6 – 13 – 9 – 5 – 1 1 3 5 u/A ICERM Workshop 2012

  16. Myoglobin: Smoluchowski Simulations Myoglobin: Smoluchowski Simulations 9.0 t = 0.5 ps 8.0 7.0 6.0 5.0 4.0 3.0 v/Angstrom 2.0 1.0 0.0 – 1.0 – 2.0 – 3.0 – 4.0 – 12 – 10 – 8 – 6 – 4 –2 0 2 4 u/Angstrom ICERM Workshop 2012

  17. Myoglobin: Smoluchowski Simulations Myoglobin: Smoluchowski Simulations 9.0 t = 1.0 ps 8.0 7.0 6.0 5.0 4.0 3.0 v/Angstrom 2.0 1.0 0.0 – 1.0 – 2.0 – 3.0 – 4.0 – 12 – 10 – 8 – 6 – 4 –2 0 2 4 u/Angstrom ICERM Workshop 2012

  18. Myoglobin: Smoluchowski Simulations Myoglobin: Smoluchowski Simulations 9.0 t = 2.5 ps 8.0 7.0 6.0 5.0 4.0 3.0 v/Angstrom 2.0 1.0 0.0 – 1.0 – 2.0 – 3.0 – 4.0 – 12 – 10 – 8 – 6 – 4 –2 0 2 4 u/Angstrom ICERM Workshop 2012

  19. Myoglobin: Smoluchowski Simulations Myoglobin: Smoluchowski Simulations 9.0 t = 5.0 ps 8.0 7.0 6.0 5.0 4.0 3.0 v/Angstrom 2.0 1.0 0.0 – 1.0 – 2.0 – 3.0 – 4.0 – 12 – 10 – 8 – 6 – 4 –2 0 2 4 u/Angstrom ICERM Workshop 2012

  20. Myoglobin: Smoluchowski Simulations Myoglobin: Smoluchowski Simulations 9.0 t = 25.0 ps 8.0 7.0 6.0 5.0 4.0 3.0 v/Angstrom 2.0 1.0 0.0 – 1.0 – 2.0 – 3.0 – 4.0 – 12 – 10 – 8 – 6 – 4 –2 0 2 4 u/Angstrom ICERM Workshop 2012

  21. Myoglobin: Smoluchowski Simulations Myoglobin: Smoluchowski Simulations 9.0 t = 50.0 ps 8.0 7.0 6.0 5.0 4.0 3.0 v/Angstrom 2.0 1.0 0.0 – 1.0 – 2.0 – 3.0 – 4.0 – 12 – 10 – 8 – 6 – 4 –2 0 2 4 u/Angstrom ICERM Workshop 2012

  22. Myoglobin: Smoluchowski Simulations Myoglobin: Smoluchowski Simulations 9.0 t = 100 ps 8.0 7.0 6.0 5.0 4.0 3.0 v/Angstrom 2.0 1.0 0.0 – 1.0 – 2.0 – 3.0 – 4.0 – 12 – 10 – 8 – 6 – 4 –2 0 2 4 u/Angstrom ICERM Workshop 2012

  23. Myoglobin: Smoluchowski Simulations Myoglobin: Smoluchowski Simulations 9.0 t = 250 ps 8.0 7.0 6.0 5.0 4.0 3.0 v/Angstrom 2.0 1.0 0.0 – 1.0 – 2.0 – 3.0 – 4.0 – 12 – 10 – 8 – 6 – 4 –2 0 2 4 u/Angstrom ICERM Workshop 2012

  24. Myoglobin: Smoluchowski Simulations Myoglobin: Smoluchowski Simulations 9.0 t = 500 ps 8.0 7.0 6.0 5.0 4.0 3.0 v/Angstrom 2.0 1.0 0.0 – 1.0 – 2.0 – 3.0 – 4.0 – 12 – 10 – 8 – 6 – 4 –2 0 2 4 u/Angstrom ICERM Workshop 2012

  25. Myoglobin: Smoluchowski Simulations Myoglobin: Smoluchowski Simulations 9.0 t = 1.0 ns 8.0 7.0 6.0 5.0 4.0 3.0 v/Angstrom 2.0 1.0 0.0 – 1.0 – 2.0 – 3.0 – 4.0 – 12 – 10 – 8 – 6 – 4 –2 0 2 4 u/Angstrom ICERM Workshop 2012

  26. Myoglobin: Smoluchowski Simulations Myoglobin: Smoluchowski Simulations 9.0 t = 2.5 ns 8.0 7.0 6.0 5.0 4.0 3.0 v/Angstrom 2.0 1.0 0.0 – 1.0 – 2.0 – 3.0 – 4.0 – 12 – 10 – 8 – 6 – 4 –2 0 2 4 u/Angstrom ICERM Workshop 2012

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