Physical Mechanisms of Biological Molecular Motors

John H. Miller, Jr.

Dept. of Physics & Texas Center for Superconductivity University of Houston [email protected]

ECRYS-2008 August 24-30, 2008

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 (F 0 , 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 August 24-30, 2008 ECRYS – 2008 [email protected]

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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 1 st eukaryote ~ 2 billion years ago.

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Bioenergetics: Mechanisms of cell metabolism

.

 ATP (adenosine triphosphate) = main currency of free energy.

 ATP hydrolysis releases energy: ATP + H 2 O  ADP + P i .

 ATP is produced in the mitochondria of animals and protists.

 Energy for ATP production is provided by photosynthesis in the chloroplasts of plants.

mitochondrion

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Mitochondrial inner membrane is highly convoluted.

Frey and Manella, TIBS (2000) Frey et al, BBA (2002)

ATP producing enzmes are tightly packed into inner membrane invaginations called “cristae”.

(Courtesy of P. Petersen, 2007.) August 24-30, 2008 ECRYS – 2008 [email protected]

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Mitochondrial Electron Transport Chain (ETC)

NADH NAD + Complex I

Inside the matrix

ADP + P i Complex III Peter Mitchell Complex IV F 1 ATP e H + Quinone pool H + Cytochrome c H + O 2 H 2 O ATP Synthase (F 0 F 1 ) H +

F 0 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 .)

F 1 F 0 ATP synthase – The world’s smallest rotary motor + + + + + + D m - - - - - August 24-30, 2008 ECRYS – 2008 [email protected]

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Electric field driven torque in F

0

F



E

 rotor stator Dipole moment of offset half channels  Electric field: acts on ion binding sites of charges a

e

& –(1 a )

e

, 0 < a < 1.

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E



E

0  

E

0   tan 2  2   1  D m

d

16

r

2 

E

0  tan 2   1  8

F

0

: Scaling between torque & ion motive force

Summing the torques ( continuum approx .)  scaling law: ( consistent with 100% efficiency, setting

ne

D m = 2 p t ) t 

ne

2 p D m

n

= # of rotor ion binding cites: 10 for eukaryotes, 10-14 for bacteria.

When F 0 couples to F 1 torque by F 1 as g via the g -subunit, it must overcome an opposing “pries loose” 3 ATP molecules per cycle from F 1 .

At a minimum,

W

molecule from F 1 = t · 2 p /3 must = D G  0.52 eV to release each ATP  Minimum (critical) D m for ATP production: D m

c

 3 D

G ne

 156 mV if

n

 10.

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Energy landscape of F 1 = washboard potential!

• Torque measurements w/ magnetic nanorods attached to F periodic t vs. gamma stalk rotation angle  .

1 reveal A. Palanisami, 2008.

• • – ( Also see O. Panke et al., Biophys. J. 81 , 1220 (2001).

) Simplified form of opposing torque by F 1 : ( t 0  40 pN ·nm, t 1  20 pN ·nm ) t 0  t 1 sin 3  Making substitutions: f = 3  , t ’ = t – t 0 , yields Eq. of motion: 

d

f

dt

 t '  t 1 sin f Just like overdamped oscillator model of CDW.

( G. Gruner, A. Zawadowski, P. M. Chaikin, PRL 46 , 511 (1981) ) August 24-30, 2008 ECRYS – 2008 [email protected]

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Ion motive force  Driving torque  Tilts washboard potential August 24-30, 2008 ECRYS – 2008 [email protected]

V

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Brownian fluctuations at finite temperatures •  f   t '  t 1 sin f  – (See L. Machura et al., PR E 73 , 031105 (2006).) – x (

t

) assumed to be Gaussian white noise, < x (

t

) x (

t

1 )> =  (

t

-

t

1 ).

2 

kT

x • 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, PRL 22 , 1364 (1969)) .

→ Compute <

d

f

/ dt

>  ATP production rate

vs

.

t  D m .

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ATP production rate vs. D m D m c D m onset Remarkably similar (except for offset) to

I-V

curve of CDW!

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What are the implications?

• If D m < D m onset , ATP production nearly halts.

– Unconsciousness (under general anesthesia) – Degeneration of motor neurons (ALS) – Cardiac arrest  death.

• But efficiency drops if D m/ D m c – Excess heat & reactive oxygen species (ROS) production – Overeating, obesity, type-2 diabetes  high D m , ROS. too high.

– 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 D m c & D m onset scale inversely with

n

.

– Evolutionary pressure to optimize

n

& D m onset (?).

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Caveats

• Washboard potential of F 1 is not static.

– Fluctuates dynamically as ADP, P i , and ATP bind & unbind.

 f &  don’t increase smoothly with time.

– Show stochastic behavior & stepping motion.

• Torque of F 0 not continuum but likely includes finer grained washboard.

– Incommensurability may be favored, i.e.

n

 3

m

.

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15

Bacterial flagellar motor – Enables bacteria to swim.

 Flagellar motor is powerful, generating several thousand pN .

nm of torque.

 Can reverse direction w/o changing D m .

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Proposed model of the flagellar motor August 24-30, 2008 ECRYS – 2008 [email protected]

Proposed switching mechanism 17

New scaling law due to multiple (

N

s ) stators Ryu, Berry, & Berg, Nature 403 , 444 (2000) t 

N

s 2 p

ne

D m .

model Fung & Berg, Nature 375 , 809 (1995) model August 24-30, 2008 ECRYS – 2008 [email protected]

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10 5 Re [  r ] 10 4 10 3 10 2 10 100 Measurement tools: Dielectric spectroscopy

B. Subtilis

10 9 cells/ml 10 7 cells/ml 10 5 cells/ml 10 5 Re [  r ] 10 4 10 3

B. Cereus -

3292 10 9 cells/ml 10 7 cells/ml 10 5 cells/ml 10 3 Frequency (Hz) 10 4 10 5 10 2 10 100 10 3 Frequency (Hz) 10 4 10 5

Low frequency dielectric response correlates with membrane potential!

[ Prodan EV, Prodan C, & JHM,

Biophys. J

. in press ].

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Measurement tools: Nonlinear harmonic response D odd harmonics correlate with respiratory competence (rho) and rate in yeast.

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 .) August 24-30, 2008 ECRYS – 2008 [email protected]

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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? • …… August 24-30, 2008 ECRYS – 2008 [email protected]

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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 August 24-30, 2008 ECRYS – 2008 [email protected]

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Thank you!

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