Theoretical/computational study of complex chemistry in biological systems

Theoretical/computational study of complex chemistry in biological systems

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

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)

Studying energy conversion

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

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

Myosin: a diverse superfamily http://www.mrc-lmb.cam.ac.uk/myosin/

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)

Myosin-II: a classical molecular motor http://www.sci.sdsu.edu/movies/actin_myosin_gif.html See also: http://www.scripps.edu/milligan/index.html M. A. Geeves, K. C. Holms, Ann. Rev. Biochem. 68, 687 ( 99) R. W. Lymn, E. W. Taylor, Biochem. 10, 4617 ( 71)

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

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

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. 1996 35, 5405 (Dictyostelium discoideum: amoeba)

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

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. 1996 35, 5405 (Dictyostelium discoideum: amoeba)

Classical MD simulations: the closed state

Classical MD simulations: the open state

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)

pen-state not set up for in-line attack 4.4 4.2 W P γ ATP (Å) 1VM 1FMW 180 170 W P γ ATP 3β ATP 1VM 1FMW 4 160 3.8 150 3.6 3.4 140 130 120 3.2 110 3 0 50 100150 200 250300 350400 450 500 t (ps) 100 0 50 100150 200 250300 350400 450 500 t (ps) Appropriate positioning of the attacking water

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')

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 TSA1 22.9 INTA 21.2 25.9 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)

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 20 10 TSA1 22.9 INTA 21.2 25.9 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)

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, 15339 (2002) Might apply to other molecular motor systems such as F1-ATPase, Ca 2+ -ATPase

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, 0.98) 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

Alchemical free energy simulations 500 FMW 222 FMW G/ λ 400 300 200 100 VM ΔG(kcal/mol) 220 218 216 214 VM 0 212-100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 λ 210 0 500 1000150020002500300035004000 600 800 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

Alchemical free energy simulations ΔΔG(kcal/mol) -7-7.5-8 -8.5-9 Closed-state(1VM) favors hydrolysis ΔG(kcal/mol) 222 220 218 216 214 FMW VM -9.5 212-10 210 0 500 1000150020002500300035004000 600 800 0 500 1000150020002500300035004000 600 800 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

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

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)

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 hrs @1.2 GHz Sparsity: 140

Low-ω modes in myosin Q1 Q1

Low-ω modes in myosin Q2 Q2

RM 00 800 (a) 0.5 Converter swing and low-frequency modes 0 0 100 200 300 400 500 600 700 800 Residue Number 0.7 0.6 (b) k Σ k I k 2 j=1 I 2 j 0.5 0.4 0.3 0.2 90 110 0.1 G. Li, QC, Biophys. J. 86, 743 (2004) 0-10 10 30 50 70 90 110 Mode number (k) I k = X open X closed X open X closed L k

Hinges in low-frequency modes Q112-T117 F482; G680 L27, T28 F692, P693 Q1 Q6

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, 2429-33 (2001)

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

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

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) $$ UW Chem. Dept. & Graduate School, ACS-PRF, Research Corp.; NSF-MCB; NSF-CHEM-CAREER; NSF-CHEM-CRC; Alfred P. Sloan Fellowship $$