the structural basis of the cross-bridge cycle. decorated actin was the first em reconstruction...

The structural basis of the cross-bridge cycle

DECORATED ACTIN

was the first em reconstruction

Moore, Huxley, and DeRosier

1970 J. Mol Biol.

Reconstruction by filtered least squares

P f = g

The classical solution to the equations

P f= g + e

which minimises the sum of squares oferror seTe is

PT P f = PTg

PT P is th enorma l o r Hessia n matrix

The solution is

f = (PTP)-1 PTg

but PTg is the back projection.

Thus the inverse least squares matrix (PTP)-1

provides the analytical filter for turning theback projection into the required density

Projection every 1° (181 projections)

Number of observational equations is

161 x 181=29141

Order of normal matrix 17645.

Problem should be well determined

Oops!!

Crowther, R. A., DeRosier, D. J. and Klug, A. (1972) The reconstruction of a three-dimensional structure from projections and its application to electron microscopy. Proc. Royal Soc. London 317A: 319-40.

Case 2. Projection every 3°, not enough data to invert the normal matrix. How much data is there?

To determine the rank of a positive (semi) definite matrix we determine its eigenvalue spectrum

Decorated actin at 13Å resolving power calculated by filtered least squares

Electron cryo-microscopy (of decorated actin) shows how strong binding of myosin to actin releases nucleotide Holmes, Angert, Kull, Jahn, Schroeder (2003) Nature 425, 423-427

Four sub-domain refinement

The cross-bridge cycle

As revealed by crystallography

Geeves, M.A. & Holmes, K.C. (2005)

The molecular mechanism of muscle contraction

Adv Protein Chem 71, 161-93

Lymn & Taylor, 1971

The myosin motor domain must move the lever arm from pre- to

post- power stroke.

It must bind to actin strongly or weakly

Both functions are controlled by ATP binding and hydrolysis

Crystallography on the motordomain (particularly Dictyostelium Myosin 2) shows two conformations of myosin:

lever UP and lever DOWN

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Fischer et al (2005) PNAS102 6873-8

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Fischer et al (2005) PNAS102 6873-8

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Weak and Strong Binding

Coureux, P. D.Wells, A. L.Menetrey, J.Yengo, C. M.Morris, C. A.Sweeney, H. L.Houdusse, A. (2003)

A structural state of the myosin V motor without bound nucleotide

Nature 425 419-23

Rayment_chicken

Upper/lower 50K fitted

Myo 5

?

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