Physical Mechanisms of Biological Molecular Motors

1. Physical Mechanisms of Biological Molecular Motors John H. Miller, Jr. Dept. of Physics & Texas Center for Superconductivity University of Houston jhmiller@uh.edu ECRYS-2008 August 24-30, 2008

2. Introduction • Life runs on biological molecular motors. • Most (perhaps all) fall into two categories: • ATP-driven & other nucleoside triphosphate-driven motors • Ion gradient driven motors (F0, flagellar motor, prestin) • Physics is crucial to their understanding. • Other examples of biophysical phenomena: • Ferroelectric transitions in microtubules • CDWs (in cations between actin filaments, on membranes) • Electron transfer in protein complexes • Role of electrostatics in mitotic spindle ECRYS – 2008 jhmiller@uh.edu

3. Phylogenetic tree: Three domains of life. Bacteria Archaea LUCA LUCA = Last Universal Common Ancestor: >3.85 billion years ago. Photosynthesis may have evolved 3.5 – 2.7 billion years ago. Mitochondria evolved from an ancient bacterium in symbiosis w/ a host – a merger that created the 1st eukaryote ~ 2 billion years ago. ECRYS – 2008 jhmiller@uh.edu

4. mitochondrion Bioenergetics: Mechanisms of cell metabolism. • ATP (adenosine triphosphate) = main currency of free energy. • ATP hydrolysis releases energy: ATP + H2O  ADP + Pi . • ATP is produced in the mitochondria of animals and protists. • Energy for ATP production is provided by photosynthesis in the chloroplasts of plants. ECRYS – 2008 jhmiller@uh.edu

5. Frey and Manella, TIBS (2000) Frey et al, BBA (2002) ATP producing enzmes are tightly packed into inner membrane invaginations called “cristae”. Mitochondrial inner membrane is highly convoluted. (Courtesy of P. Petersen, 2007.) ECRYS – 2008 jhmiller@uh.edu

6. ATP ADP + Pi Peter Mitchell H+ Mitochondrial Electron Transport Chain (ETC) NADH NAD+ Inside the matrix Complex I Complex III F1 Complex IV e- F0 O2 ATP Synthase (F0F1) Quinone pool H2O Cytochrome c H+ H+ H+ Complexes I-IV use energy from e-’s donated by NADH to pump protons across membrane. (Courtesy of P. Petersen, 2007. P. Mitchell won 1978 Nobel Prize in Chemistry for chemiosmotic coupling hypothesis.)

7. + + + + + + Dm - - - - - - - F1F0 ATP synthase – The world’s smallest rotary motor ECRYS – 2008 jhmiller@uh.edu

8. Electric field driven torque in F0 Fq Eq rotor stator • Dipole moment of offset half channels • Electric field: acts on ion binding sites of charges ae & –(1-a)e, 0 < a < 1. ECRYS – 2008 jhmiller@uh.edu

9. F0: Scaling between torque & ion motive force Summing the torques (continuum approx.)  scaling law: (consistent with 100% efficiency, setting neDm = 2pt) n = # of rotor ion binding cites: 10 for eukaryotes, 10-14 for bacteria. When F0 couples to F1 via the g-subunit, it must overcome an opposing torque by F1 as g “pries loose” 3 ATP molecules per cycle from F1. At a minimum, W = t· 2p/3 must = DG  0.52 eV to release each ATP molecule from F1 Minimum (critical) Dm for ATP production: ECRYS – 2008 jhmiller@uh.edu

10. Energy landscape of F1 = washboard potential! • Torque measurements w/ magnetic nanorods attached to F1 reveal periodic t vs. gamma stalk rotation angle q. • (Also see O. Panke et al., Biophys. J.81, 1220 (2001).) • Simplified form of opposing torque by F1: (t0 40 pN·nm, t1 20 pN·nm) • Making substitutions: f = 3q, t’ = t – t0, yields Eq. of motion: Just like overdamped oscillator model of CDW. (G. Gruner, A. Zawadowski, P. M. Chaikin, PRL46, 511 (1981)) A. Palanisami, 2008. ECRYS – 2008 jhmiller@uh.edu

11. Ion motive force  Driving torque  Tilts washboard potential V ECRYS – 2008 jhmiller@uh.edu

12. Brownian fluctuations at finite temperatures • Modeled using a Langevin equation: • (See L. Machura et al., PR E73, 031105 (2006).) • x(t) assumed to be Gaussian white noise, <x(t)x(t1)> = d(t-t1). • Convert to Fokker-Planck and then to Smoluchowski eqn. (in overdamped limit) for a distribution function P(f,t). • Can draw upon previous work on resistively shunted Josephson junction (V. Ambegaokar & B. I. Halperin, PRL22, 1364 (1969)). • Compute <df/dt>  ATP production ratevs.t  Dm. ECRYS – 2008 jhmiller@uh.edu

13. ATP production rate vs. Dm Dmonset Dmc Remarkably similar (except for offset) to I-V curve of CDW! ECRYS – 2008 jhmiller@uh.edu

14. What are the implications? • If Dm < Dmonset, ATP production nearly halts. • Unconsciousness (under general anesthesia) • Degeneration of motor neurons (ALS) • Cardiac arrest  death. • But efficiency drops if Dm/Dmc too high. • Excess heat & reactive oxygen species (ROS) production • Overeating, obesity, type-2 diabetes  high Dm, ROS. • Cellular damage, linked to all major age-related diseases. • Aging rate is completely determined by ROS production rate. • Birds have lowest ROS production rates of all animals. • Both Dmc & Dmonset scale inversely with n. • Evolutionary pressure to optimize n & Dmonset (?). ECRYS – 2008 jhmiller@uh.edu

15. Caveats • Washboard potential of F1 is not static. • Fluctuates dynamically as ADP, Pi, and ATP bind & unbind. • f & q don’t increase smoothly with time. • Show stochastic behavior & stepping motion. • Torque of F0 not continuum but likely includes finer grained washboard. • Incommensurability may be favored, i.e. n 3m. ECRYS – 2008 jhmiller@uh.edu

16. Bacterial flagellar motor – Enables bacteria to swim. • Flagellar motor is powerful, generating several thousand pN.nm of torque. • Can reverse direction w/o changing Dm. ECRYS – 2008 jhmiller@uh.edu

17. Proposed model of the flagellar motor Proposed switching mechanism ECRYS – 2008 jhmiller@uh.edu

18. New scaling law due to multiple (Ns) stators model model Fung & Berg, Nature375, 809 (1995) Ryu, Berry, & Berg, Nature403, 444 (2000) ECRYS – 2008 jhmiller@uh.edu

19. Measurement tools: Dielectric spectroscopy Low frequency dielectric response correlates with membrane potential! [Prodan EV, Prodan C, & JHM, Biophys. J. in press]. ECRYS – 2008 jhmiller@uh.edu

20. D odd harmonics correlate with respiratory competence (rho) and rate in yeast. Measurement tools: Nonlinear harmonic response r- strain r+ strain Respiratory-competent (rho+) strain = D273-10B, often used for mitochondrial studies, w/ normal cytochrome content & respiratory activity.  Data shown are means of 3 separate measurements (error bars suppressed for clarity). Respiratory-incompetent (rho-) strain = DS400/A12, isolated from the D273-10B strain.  Appears to lack cytochrome b and cannot undergo normal respiration.  Deficiency confirmed by plating on non-fermentable glycerol media & by oxygen sensor measurements. (Both strains purchased from ATCC.) ECRYS – 2008 jhmiller@uh.edu

21. Future directions • Main focus will be on bioenergetics, metabolism. • ATP synthase – Molecular dynamics studies w/ Margaret Cheung • Develop dielectric spectroscopy as possible probe of mitochondrial membrane potential. • Nonlinear response as probe of enzyme activity • Screening devices for drug discovery • What about magnetic field effects? • …… ECRYS – 2008 jhmiller@uh.edu

22. Acknowledgements • University of Houston • Hans Infante, Vijay Vajrala, James Claycomb, Aki Palanisami, Skip Mercier, Bill Widger, Margaret Cheung, Soniya Yambem • Houston Baptist University • James Claycomb • New Jersey Institute of Technology • Camelia Prodan • Funding sources • NIH, NSF, TcSUH, Welch Foundation, GEAR (UH), IBIS, Texas ARP ECRYS – 2008 jhmiller@uh.edu

23. Thank you! ECRYS – 2008 jhmiller@uh.edu