14.04 o14 r millane

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DIFFRACTION IMAGING OF THE MYOSIN SUPERLATTICE OF VERTEBRATE MUSCLE

Rick Millane, David Wojtas, Chunhong Yoon* and John Squire+

Department of Electrical and Computer EngineeringUniversity of Canterbury

*Department of Physics, University of Wisconsin - Milwaukee, USA

+Department of Physiology and PharmacologyUniversity of Bristol, Bristol, UK

New Zealand Institute of Physics ConferenceWellington, 17-19 October 2011

Supported in part by the Marsden Fund

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Outline

• Myosin lattice of vertebrate muscle• Electron microscopy and x-ray fibre diffraction• Image analysis• Disordered systems – frustration – statistical physics• X-ray diffraction• Conclusions

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Imaging and diffraction imaging

light

electrons

specimen FT lens image

Microscopy

x-rays

electrons

specimen diffraction pattern

image

Diffraction Imaging

computer

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Myosin lattice

myofibril

sarcomere

Muscle fibre

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Myosin lattice

Simple lattice SuperlatticeRotational disorder

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Electron microscopy and image analysis

Close up

Cross-section of sarcomere

Templateforrotations

Templateforlocations

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Classification of orientations

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Distribution of orientations

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Geometrically frustrated systems

?

A spin system, for example, for which as, a result of lattice topology, the energy of each spin pair cannot be simultaneously minimised.

A very simple classical example is a triangular lattice with antiferromagnetic interactions.

I.e. “unlike’ spins, or states, are energetically preferred.

It is not possible to satisfy the constraints on each elementary plaquette of the lattice.

Leads to a large number of ground states.

This is the triangular Ising antiferromagnet – TIA.

Characterised using spin-pair correlations.

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TIA correlations

Differenttemperatures

Partitioned intotwo sublattices

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Spatial correlations – myosin lattice and TIA

Observed – myosin latticeTIA by Monte Carlo simulation

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Myosin lattice disorder – measured and simulated

Myosin lattice TIA

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X-ray fibre diffraction patterns from muscle

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Fibre diffraction pattern from relaxed frog muscle

Iwamoto et al., Biophys. J., 85, 2492-2506 (2003).

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Measured diffraction data – layer line amplitudes

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Simulation of x-ray diffraction from the myosin array

Develop methods to simulate x-ray diffraction from models of the myosin filament.

Need to incorporate:

The molecular structure and helical symmetry.

The TIA disorder.

Cylindrical averaging.

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Calculated diffraction – ordered crystalline specimen

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Calculated diffraction – completely disordered

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Calculated diffraction – TIA disorder

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Summary

• The superlattice disorder observed in the myosin lattice of higher verebrate muscle is a manifestation of a frustrated system.

• The frustration is due to incompatible preferred interactions between the myosin filaments.

• This may have evolutionary significance for muscle function.

• Direct (electron microscopy) and diffraction (x-ray diffraction) imaging complement each other.

• Effects of disorder can be incorporated into diffraction calculations to allow rigorous analysis of diffraction data.

• Engineers and biophysicists can work productively together and have lots of fun!