A Methodology for Deblurring and Recovering Conformational States of Biomolecular Complexes from Single Particle Electron Microscopy

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)

Abstract

In this paper we study two forms of blurring effects that may appear in the reconstruction of 3D Electron Microscopy (EM), specifically in single particle reconstruction from random orientations of large multi-unit biomolecular complexes. We model the blurring effects as being due to independent contributions from: (1) variations in the conformation of the biomolecular complex; and (2) errors accumulated in the reconstruction process. Under the assumption that these effects can be separated and treated independently, we show that the overall blurring effect can be expressed as a special form of a convolution operation of the 3D density with a kernel defined on SE(3), the Lie group of rigid body motions in 3D. We call this form of convolution mixed spatial-motional convolution. We discuss the ill-conditioned nature of the deconvolution needed to deblur the reconstructed 3D density in terms of parameters associated with the unknown probability in SE(3). We provide an algorithm for recovering the conformational information of large multi-unit biomolecular complexes (essentially deblurring) under certain biologically plausible prior structural knowledge about the subunits of the complex in the case the blurring kernel has a special form.

Keywords

Conformational State Projection Direction Conformational Information Biomolecular Complex Blind Deblurring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgements

Research reported in this publication was supported by the National Institute of General Medical Sciences of the National Institutes of Health under award number R01GM113240.

References

  1. 1.
    Arsigny, V., Pennec, X., Ayache, N.: Bi-invariant means in Lie groups. application to left-invariant polyaffine transformations (2006)Google Scholar
  2. 2.
    Chirikjian, G.S.: Stochastic Models, Information Theory, and Lie Groups. Springer, Boston (2012)CrossRefMATHGoogle Scholar
  3. 3.
    Feigin, L., Svergun, D.I., Taylor, G.W.: Structure Analysis by Small-angle X-ray and Neutron Scattering. Springer, Berlin (1987)CrossRefGoogle Scholar
  4. 4.
    Frank, J.: Three-dimensional electron microscopy of macromolecular assemblies: Visualization of biological molecules in their native (2006)Google Scholar
  5. 5.
    Frank, J.: Story in a sample-the potential (and limitations) of cryo-electron microscopy applied to molecular machines. Biopolymers 99(11), 832–836 (2013)CrossRefGoogle Scholar
  6. 6.
    Hirsch, M., Schölkopf, B., Habeck, M.: A blind deconvolution approach for improving the resolution of cryo-EM density maps. J. Comput. Biol. 18(3), 335–346 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Kishchenko, G.P., Leith, A.: Spherical deconvolution improves quality of single particle reconstruction. J. Struct. Biol. 187(1), 84–92 (2014)CrossRefGoogle Scholar
  8. 8.
    Park, W., Chirikjian, G.S.: An assembly automation approach to alignment of noncircular projections in electron microscopy. IEEE Trans. Autom. Sci. Eng. 11(3), 668–679 (2014)CrossRefGoogle Scholar
  9. 9.
    Park, W., Midgett, C.R., Madden, D.R., Chirikjian, G.S.: A stochastic kinematic model of class averaging in single-particle electron microscopy. Int. J. Rob. Res. 30(6), 730–754 (2011)CrossRefGoogle Scholar
  10. 10.
    Pennec, X., Arsigny, V.: Exponential barycenters of the canonical cartan connection and invariant means on Lie groups. In: Nielsen, F., Bhatia, R. (eds.) Matrix Information Geometry, pp. 123–166. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  11. 11.
    Scheres, S.H., Gao, H., Valle, M., Herman, G.T., Eggermont, P.P., Frank, J., Carazo, J.-M.: Disentangling conformational states of macromolecules in 3D-EM through likelihood optimization. Nature Methods 4(1), 27–29 (2007)CrossRefGoogle Scholar
  12. 12.
    van Heel, M., Gowen, B., Matadeen, R., Orlova, E.V., Finn, R., Pape, T., Cohen, D., Stark, H., Schmidt, R., Schatz, M., et al.: Single-particle electron cryo-microscopy: towards atomic resolution. Q. Rev. Biophys. 33(04), 307–369 (2000)CrossRefGoogle Scholar
  13. 13.
    Wang, Y., Chirikjian, G.S.: Error propagation on the Euclidean group with applications to manipulator kinematics. IEEE Trans. Robot. 22(4), 591–602 (2006)CrossRefGoogle Scholar
  14. 14.
    Zhao, Z., Singer, A.: Rotationally invariant image representation for viewing direction classification in cryo-EM. Journal of structural biology 186(1), 153–166 (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Johns Hopkins UniversityBaltimoreUSA

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