Theoretical/computational study of complex chemistry in biological systems
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1 Theoretical/computational study of complex chemistry in biological systems
2 Preliminary insights into the mechanochemical coupling in myosin with molecular simulations Qiang Cui Department of Chemistry & Theoretical Chemistry Institute University of Wisconsin, Madison IPAM Work shop, May. 2004
3 Rise of the Machines NH2 N N - P - P - P CH2 N H N - ATP H H +H2 ~ -50 kj/mol +H2 NH2 N N - P H H Pi - P - P CH2 N - ADP H N H H Explore mechanisms of bioenergy transduction (bridge static structural data, low-resolution dynamical studies and phenomenological models)
4 Studying energy conversion
5 Why molecular simulations? Bridging structural, dynamical and phenomenological studies Structural studies: do not explicitly provide dynamical information; may not correspond to kinetic state Dynamical/kinetic studies (e.g., single molecule FRET): do not have sufficient spatial resolution Phenomenological theories: some parameters/assumptions difficult to justify; several models seem to work ur long-term goal: evaluate dynamical properties & parameters used in theoretical models in terms of microscopic details ; i.e., jiggling and wiggling of atoms
6 utline Myosin: a classical molecular motor QM/MM studies, molecular dynamics and free energy simulations on the coupling between conformation and ATP hydrolysis (mechanochemical coupling) Initial looks on conformational transitions
7 Myosin: a diverse superfamily
8 Myosin-II: a classical molecular motor Muscle contraction: relative displacements of the thick filaments (myosin) and thin filaments (F-actin) LMM HMM 950 Å +650 Å 75Å 150Å H. E. Huxley: cross-bridge model of contraction (1969)
9 Myosin-II: a classical molecular motor See also: M. A. Geeves, K. C. Holms, Ann. Rev. Biochem. 68, 687 ( 99) R. W. Lymn, E. W. Taylor, Biochem. 10, 4617 ( 71)
10 Mechanochemical cycles in myosin +ATP -A +A M A M ATP M* (ADP Pi) M* A (ADP) + Pi M A + ADP + Pi Utilization of ATP hydrolysis ΔG? Tight coordination among level-arm swing, chemistry and actin binding M* ATP+A M* (ADP Pi)+A M A+ATP M ATP+A K eq <10 Time-scale Mistach (ps-ns vs. µs-ms) M* A (ADP) + Pi ΔG ATP hyd M A + ADP + Pi
11 Key issues in ΔG transduction Conformational transitions Sequence of events (local vs. large-scale swing) Critical residues/interactions Molecular mechanism of ATP hydrolysis Coupling with conformational change; does it really drive conformational change of the motor domain(the Holy Grails )? Chemical details Interaction between actin and myosin Pi/ADP dissociation Competitive binding with ATP
12 Conformational transition in myosin RMS:2.4 Å RMS:20.8 Å Upper 50K Domain Switch-I ATP-binding site ATP/ADP V 4 - Arg 238 1VM (CLSED) Relay helix Actin-binding Interface Ala 183 P-loop Switch-II Glu 459 C-terminal Converter domain 1FMW (PEN) Rayment et al. J. Biol. Chem., 2000, 275, 38494; Biochem , 5405 (Dictyostelium discoideum: amoeba)
13 Simulations of ATP hydrolysis Classical MD simulation Position of key residues/water QM/MM rx path hydrolysis mechanism coupling with conformation Alchemical free energy Include structural fluctuations Component analysis Stochastic boundary simulation
14 Myosin II active site Thr186 Switch I Ser237 Ser236 Wat1 Arg238 Glu264 Asn233 Lys185 Gly182 Closed-state (1VM) P-loop Gly457 Ser181 Glu459 Switch II Rayment et al. J. Biol. Chem., 2000, 275, 38494; Biochem , 5405 (Dictyostelium discoideum: amoeba)
15 Classical MD simulations: the closed state
16 Classical MD simulations: the open state
17 Salt-bridge and water positions Closed-state (ADP V 4 - ; 1VM) Ser 236 Arg 238 Lys 185 Ser 181 Gly 457 Glu 459 Glu 264 pen-state (ATP; 1FMW) G. Li, QC, J. Phys. Chem. B 108, 3342 (2004)
18 pen-state not set up for in-line attack W P γ ATP (Å) 1VM 1FMW W P γ ATP 3β ATP 1VM 1FMW t (ps) t (ps) Appropriate positioning of the attacking water
19 QM/MM analysis of reaction paths Mg 2+ ADP P 3γ R Thr186 Wat696 Asn233 Gly182 2γ Ser236 Path B2 H H H Path A Ser237 Wat695 Mg 2+ Ser236 Lys185 Wat1 Gly457 Ser181 Mg 2+ Ser236 Mg 2+ ADP H ADP H P P H H H TSB1' INTB' Mg 2+ Mg 2+ Ser236 ADP ADP P H H H TSA1 Arg238 AMP P Mg 2+ INTA Ser236 H H P H PA/PB H P H Ser236 H Ser236 H 2γ H rotation (TSA2/TSB2')
20 Ser236 plays a major role ΔE(kcal/mol) 50 kimoto et al. Biophys. J. 81, 2786 (2001) 40 TSB1 Direct water attack 30 (38.8) TSB1' (30.8) INTB (29.0) TSB2 (32.3) TSA2 Ser assisted water attack 20 TSA INTA B3LYP/6-31+G(d,p)/MM //HF/3-21+G/MM 10 Ser236 Arg238 Asn233 Lys185 Wat1 Thermal neutral PA -0.4 CH 2 - Gly182 G. Li, QC, J. Phys. Chem. B 108, 3342 (2004) Ser181 Gly457 PB (-5.1)
21 Conformational control of hydrolysis ΔE(kcal/mol) TSB_FMW 50 [53.6] INTB_FMW [FMW Path B] [45.4] 40 TSB1 Direct water attack 30 (38.8) TSB1' (30.8) INTB (29.0) TSB2 (32.3) TSA2 Ser assisted water attack TSA INTA P_FMW [17.3] B3LYP/6-31+G(d,p)/MM //HF/3-21+G/MM PA -0.4 CH 2 - G. Li, QC, J. Phys. Chem. B 108, 3342 (2004) PB (-5.1)
22 Dual roles of the salt-bridge ATP ADP + Pi 1FMW D454 S236 E264 ΔΔE (kcal/mol) K185 S181 S456 R238 Broken Salt-bridge E459 Resi # Consistent with mutation experiments of nishi et al. PNAS,99, (2002) Might apply to other molecular motor systems such as F1-ATPase, Ca 2+ -ATPase
23 Active site of the R238E/E459R mutant?
![Alchemical free energy simulations ADP-[P 3 - ] + H2 ADP + Pi Mg 2+ Stochastic boundary condition (8061 atoms; 1020 water) 21 λ-windows (0.02, 0.05, 0.1 0.95, 0.](/docs-images/82/84901197/images/24-0.jpg "98) SHAKE hbond, δt=1 fs Each window > 800 ps Charge-scaling protocols for bulk solvation effects Partial charges for P 3 - /Pi fitted from B3LYP-ESP calculations Focus on the difference between")
24 Alchemical free energy simulations ADP-[P 3 - ] + H2 ADP + Pi Mg 2+ Stochastic boundary condition (8061 atoms; 1020 water) 21 λ-windows (0.02, 0.05, , 0.98) SHAKE hbond, δt=1 fs Each window > 800 ps Charge-scaling protocols for bulk solvation effects Partial charges for P 3 - /Pi fitted from B3LYP-ESP calculations Focus on the difference between Closed (1VM) and pen (1FMW) structures
25 Alchemical free energy simulations 500 FMW 222 FMW G/ λ VM ΔG(kcal/mol) VM λ t(ps) [ ] [ ] U Alchemy (X A,X B,X C ;λ) = (1 λ) U AA (X A )+U AC (X A,X C ) +λ U BB (X B )+U BC (X B,X C ) +U CC (X C ) ΔG C AB = 1 dλ G = dλ U Alchemy ( v 1 R ;λ) λ λ 0 0 λ
26 Alchemical free energy simulations ΔΔG(kcal/mol) Closed-state(1VM) favors hydrolysis ΔG(kcal/mol) FMW VM t(ps) t(ps) ΔΔG C,D 1 AB = dλ G C dλ G D λ λ 0 A,B 1 0 A,B ΔG C AB = 1 dλ G = dλ U Alchemy ( v 1 R ;λ) λ λ 0 0 λ
27 Key issues in ΔG transduction Conformational transitions Sequence of events (local vs. large-scale swing) Critical residues/interactions Molecular mechanism of ATP hydrolysis Coupling with conformational change; does it really drive conformational change of the motor domain? (Unlikely?) Chemical details Interaction between actin and myosin Pi/ADP dissociation Competitive binding with ATP
28 Coarse-grained normal modes Coarse graining Direct construction of projected hessian Sparse Matrix diagonalization (Lanczos) Parallel computations Physical intermolecular interactions Tama, F.; Sanejouand, Y. Proteins, 41, 1 (2000) RTB Li, G.; Cui, Q. Biophys. J. 83, 2457 (2002); Biophys. J. 86, 743 (2004) NMA in Chemistry and Biology, Ed. Q. Cui, I. Bahar (CRC Press, 2005)
29 Coarse-grained normal modes 30S ribosome G. Li; Q. Cui, Biophys. J. 83: 2457, 2002; 86: 743, 2004 A. Van Wynsberghe, G. Li, Q. Cui, Biochem. Submitted (RNAP) 3910 residues ~200Å 1 residue per block 9.3 GHz Sparsity: 140
30 Low-ω modes in myosin Q1 Q1
31 Low-ω modes in myosin Q2 Q2
32 RM (a) 0.5 Converter swing and low-frequency modes Residue Number (b) k Σ k I k 2 j=1 I 2 j G. Li, QC, Biophys. J. 86, 743 (2004) Mode number (k) I k = X open X closed X open X closed L k
33 Hinges in low-frequency modes Q112-T117 F482; G680 L27, T28 F692, P693 Q1 Q6
34 Key question: causality? ΔG>0 Bagshaw (2001) Pre-hydrolysis (open) Hydrolyzing (close) Highsmith (1999) Spudich(2000) Hydrolysis - Pi Rebinding Post-hydrolysis (close) Volkman, BF; Lipson, D; Wemmer, D. E. Kern, D. Science, 291, (2001)
35 Brownian motion + Power stroke? Bias -1 Brownian motion M (ADP Pi)+A M* ATP+A M* (ADP Pi)+A Power stroke M A+ATP M ATP+A regulation of ATP hydrolysis K eq <10 Bias -2 M* A (ADP) + Pi ΔG ATP hyd M A + ADP + Pi
36 Further studies are needed Efficient and reliable QM/MM approaches that include fluctuations of the protein environment; other possible hydrolysis pathways Coupling (causal relation) between collective-elastic motions and local changes; critical residues Missing key point: Actin/myosin interaction at atomic resolution Sliding profile; heat, entropy production; fibril function
37 Acknowledgements Cui group: Drs. X. Zhang (PSU), G. Li (Harvard), D. Khoroshun (MPI); Mr. M. Formaneck, D. Riccardi, A. Van Wynsberghe, P. Schaefer, N. Ghosh; Dr. K. Mardis (Chicago S.); Mr. M. Wolfsen; Dr. H. Yu Experimental collaborators: Professor I. Rayment (UW) Discussions: Profs. D. Hackney (CMU), S. Gilbert (Pitt.), Dr. W. Yang, Prof. M. Karplus (ATP para.; Alchemy), Prof. I. nishi Long-time collaborator: Prof. Dr. M. Elstner (Padeborn/Heidelberg) $$ UW Chem. Dept. & Graduate School, ACS-PRF, Research Corp.; NSF-MCB; NSF-CHEM-CAREER; NSF-CHEM-CRC; Alfred P. Sloan Fellowship $$
Mechanochemical Coupling in Myosin: A Theoretical Analysis with Molecular Dynamics and Combined QM/MM Reaction Path Calculations
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