# Presentation: 928883

## Rectified Brownian Motion in Subcellular Biology

- Ronald F. Fox
- Mee Choi
- William Mather
- School of Physics
- Georgia Institute of Technology

- R.F. Fox Nanotech 2004

## Slide 2

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## Nanobiology

- Biochemistry
- Molecular biology

- Can we learn mechanisms from nanobiology
- that are applicable to nanotechnology?

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## Rectified Brownian Motion.

- the constructive use of
- thermal energy.
- Such a mechanism
- is called

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## A Few Antecedents

**A. F.** **Huxley**Prog. Biophys. Chem. **7**, 255 (1957)**M.** **Meister**, **S. R.** **Caplan** and **H. C.** **Berg**Biophys. J. **55**, 905 (1989)**R. D.** **Vale** and **F.** **Oosawa**Adv. Biophys. **26**, 97 (1990)

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## Rectified Brownian Movement in Molecular and Cell Biology

- Phys. Rev. E **57**, 2177 (1998)
*Rectified Brownian Motion and Kinesin Motion Along Microtubules*
- Phys. Rev. E **63**, 051901 (2001)
- (with Mee **Choi**)
*Kinesin’s Biased Stepping Mechanism:*
* **Amplification of Neck Linker Zippering*
- Biophysical Journal, **91** 2416-2426 (2006)
- (with William **Mather**)

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## A Minnow

|  | Minnow |
| --- | --- |
| m(gm) | 134 |
| R(cm) | 2 |
| vS (cm/s) | 100 |
| vT (cm/s) | 3 x 10-8 |
| WS (W) | 3.8 x 10-4 |
| WT (W) | 3.4 x 10-23 |

**A Minnow**

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## A Minnow and an E. Coli

|  | Minnow | E. Coli |
| --- | --- | --- |
| m (gm) | 134 | 2 x 10-12 |
| R(cm) | 2 | 5 x 10-5 |
| vS (cm/s) | 100 | 2 x 10-3 |
| vT (cm/s) | 3 x 10-8 | 0.20 |
| WS (W) | 3.8 x 10-4 | 10-17 |
| WT (W) | 3.4 x 10-23 | 10-13 |

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## A Minnow, an E. Coli and Ubiquinone

|  | Minnow | E. Coli | Ubiquinone |
| --- | --- | --- | --- |
| m (gm) | 134 | 2 x 10-12 | 1.4 x 10-21 |
| R (cm) | 2 | 5 x 10-5 | 7.5 x 10-8 |
| vS (cm/s) | 100 | 2 x 10-3 | (0.8) |
| vT (cm/s) | 3 x 10-8 | 0.20 | 9,300 |
| WS (W) | 3.8 x 10-4 | 10-17 | (2.3 x 10-14) |
| WT (W) | 3.4 x 10-23 | 10-13 | 3 x 10-6 |

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## Reynolds Number

|  | Minnow | E. Coli | Ubiquinone |
| --- | --- | --- | --- |
|  |  |  |  |
| Secular | 2 x 104 | 4 x 10-5 | (2.4 x 10-6) |
|  |  |  |  |
| Thermal | 4 x 10-6 | 3 x 10-4 | 1.6 x 10-3 |

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## Biological Energy Couplings

- Photon energy (electron excitation)
- Electron energy (redox reaction)
- Proton energy (pH gradient)
- Phosphate energy (monomer activation)

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## Redox reaction variety

- Pure, 1 electron transfer
- Iron, copper, zinc...
- 1 electron and 1 proton transfer
- FADH2, UQH2,..
- 2 electrons and 1 proton transfer
- NAD+, NADH,..

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## Slide 13

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## Slide 14

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## diffusion for reduced ubiquinone

- boundary layer equation

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## diffusive rate parameter

- reaction rate parameter

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## implications

- Weak linear steady state gradients

- Negligible energy dissipation associated
- with the gradients according to
- non-equilibrium steady state thermodynamics

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## Langevin equation

- Einstein’s
- Relation
- 1905

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## Brownian Work Theorem

- Secular power from secular force

- Stochastic power from Brownian force

- Power expended by drag force

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## Rotary Enzymes

**Lipoamide**
- 1.4 nm long acetyl or succinyl carrier
- pyruvate and -ketoglutarate dehydrogenases
**Biocytin**
- 1.4 nm long CO2 carrier
- pyruvate carboxylase and fatty acid synthetase
**Phosphopantetheine**
- 2.0 nm long thioester carrier
- gramicidin and tyrocidine synthetases
- fatty acid synthetase, polyketide synthetase

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## Slide 21

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## Slide 22

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## Kinesin

- Processivity
- Bias
- Coordination

- A two “headed” motor protein
- that “walks” on microtubules

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## Slide 24

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## Mechanisms

- Direct Chemo-Mechanical Energy Conversion
- “Power Stroke”
- ATP Powered Conformation Change
- Rectified Brownian Motion
-  ATPase Switch
- Heat Powered Conformation Change

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## The trailing head is “thrown forward” 

- The trailing head is “*thrown forward*”
- in a way that is “*akin to a judo *
*expert throwing an opponent with a *
*rearward-to-forward swing of the arm*.”

- [Vale and Milligan, Science **288**, 88 (2000)]

- POWER STROKE

- -sheet boundary
- hydrogen bonds

- ATP powered -sheet closure

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## Slide 27

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**Notes:**
Kinesin movie

## Forces

- Covalent C-C, C-N and C-O bonds
- 4.0 - 4.3 nano-Newtons

- Hydrogen bonds
- ~0.1 - ~50(?) pico-Newtons

- Unbound kinesin head neck linker tensions
- 100 - 200 pico-Newtons

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## Slide 29

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## Slide 30

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## Rectified Brownian Motion

- of binding to the edge of
- the -sheet is only a few kT.

- This is enough energy to cause a significant
- bias for attachment in the forward
- direction, or plus end of the microtubule.

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## Slide 32

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## Slide 33

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## Slide 34

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## Slide 35

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## Slide 36

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## Slide 37

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## Slide 38

| Load (pN) | MFPT (s) |
| --- | --- |
| 0 | 1.7727 x 10-6 |
| 1 | 1.0991 x 10-5 |
| 2 | 1.6465 x 10-4 |
| 3 | 4.0071 x 10-3 |
| 4 | 0.1231 |
| 5 | 4.3005 |
| 6 | 163.1 |
| 7 | 6541 |

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## Slide 39

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## Slide 40

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