Physical Mechanisms of Biological Molecular Motors

Physical Mechanisms of Biological Molecular Motors

John H. Miller, Jr.Dept. of Physics & Texas Center for Superconductivity

University of Houston

jhmiller@uh.edu

ECRYS-2008August 24-30, 2008

August 24-30, 2008 ECRYS – 2008jhmiller@uh.edu

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IntroductionIntroduction

• 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

August 24-30, 2008 ECRYS – 2008jhmiller@uh.edu

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Phylogenetic tree: Three domains of life.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.

August 24-30, 2008 ECRYS – 2008jhmiller@uh.edu

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BioenergeticsBioenergetics: Mechanisms of cell metabolism.

mitochondrion

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.

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Mitochondrial inner membrane is highly Mitochondrial inner membrane is highly convoluted.convoluted.

Mitochondrial inner membrane is highly Mitochondrial inner membrane is highly convoluted.convoluted.

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

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

(Courtesy of P. Petersen, 2007.)

Mitochondrial Electron Transport Chain (ETC)Mitochondrial Electron Transport Chain (ETC)Mitochondrial Electron Transport Chain (ETC)Mitochondrial Electron Transport Chain (ETC)

Complex IComplex III

Complex IV

ATP Synthase (F0F1)Cytochrome c

Quinone pool

F1

ADP + Pi

ATP

H+

Peter Mitchell

O2

H2O

H+H+ H+

e-

NADH NAD+

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.)

Inside the matrix

F0

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F1F0 ATP synthase – The world’s smallest rotary motor

+

-

+ + + + +

- - - - - -

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Electric field driven torque in F0

1tan12

tan 20

20

EEE

20 16 rdE

E

F

rotor

stator

Dipole moment of offset half channels

Electric field: acts on ion binding sites of charges e & –(1-)e, 0 < < 1.

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F0: Scaling between torque & ion motive force

Summing the torques (continuum approx.) scaling law:(consistent with 100% efficiency, setting ne = 2)

2

ne

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

When F0 couples to F1 via the -subunit, it must overcome an opposing

torque by F1 as “pries loose” 3 ATP molecules per cycle from F1.

At a minimum, W = · 2/3 must = G 0.52 eV to release each ATP

molecule from F1 Minimum (critical) for ATP production:

10. if mV1563

nne

Gc

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• Torque measurements w/ magnetic nanorods attached to F1 reveal periodic vs. gamma stalk rotation angle .

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

• Simplified form of opposing torque by F1:

(0 40 pN·nm, 1 20 pN·nm)

• Making substitutions: = 3, ’ = – 0, yields Eq. of motion:

Just like overdamped oscillator model of CDW.

(G. Gruner, A. Zawadowski, P. M. Chaikin, PRL 46, 511 (1981))

Energy landscape of FEnergy landscape of F11 = washboard potential! = washboard potential!

A. Palanisami, 2008.

3sin10

sin' 1dt

d

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Ion motive force Driving torque Tilts washboard potential

V

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Brownian fluctuations at finite temperatures

• Modeled using a Langevin equation:

– (See L. Machura et al., PR E 73, 031105 (2006).)

– (t) assumed to be Gaussian white noise, <(t)(t1)> = (t-t1).

• Convert to Fokker-Planck and then to Smoluchowski eqn. (in overdamped limit) for a distribution function P(,t).

• Can draw upon previous work on resistively shunted Josephson junction (V. Ambegaokar & B. I. Halperin, PRL 22, 1364 (1969)).

→ Compute <d/dt> ATP production rate vs. .

tkT 2sin' 1

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ATP production rate vs.

Remarkably similar (except for offset) to I-V curve of CDW!

conset

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What are the implications?

• If < onset, ATP production nearly halts.– Unconsciousness (under general anesthesia)

– Degeneration of motor neurons (ALS)

– Cardiac arrest death.

• But efficiency drops if c too high.– Excess heat & reactive oxygen species (ROS) production

– Overeating, obesity, type-2 diabetes high , 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 c & onset scale inversely with n.– Evolutionary pressure to optimize n & onset (?).

c3 neG

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Caveats

• Washboard potential of F1 is not static.

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

& 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.

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Bacterial flagellar motor – Enables bacteria to swim.Bacterial flagellar motor – Enables bacteria to swim.

Flagellar motor is powerful, generating several thousand pN.nm of torque.

Can reverse direction w/o changing .

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Proposed model of the flagellar motor

Proposed switchingmechanism

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New scaling law due to multiple (Ns) stators

.2s

neN

model

model

Ryu, Berry, & Berg,

Nature 403, 444 (2000)

Fung & Berg,

Nature 375, 809 (1995)

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Measurement toolsMeasurement tools: Dielectric spectroscopy: Dielectric spectroscopy

100 103 104 105

10

103

104

105

Frequency (Hz)

105 cells/ml

107 cells/ml

109 cells/ml

102

B. Subtilis

Re[r ]

B. Cereus - 3292

100 103 104 105

10

103

104

105

102

Frequency (Hz)

105 cells/ml

107 cells/ml

109 cells/ml

Re[r ]

Low frequency dielectric response correlates with membrane potential! [Prodan EV, Prodan C, & JHM, Biophys. J. in press].

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odd harmonics correlate with respiratory competence (rho) and rate in yeast.

Measurement toolsMeasurement tools: Nonlinear harmonic response: Nonlinear harmonic response

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.)

- strain

+ strain

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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 – 2008jhmiller@uh.edu

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AcknowledgementsAcknowledgements

• 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

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Thank you!