Elastic Image Registration To Fully Explore Macromolecular Dynamics By Electron Microscopy Qiyu Jin 1, Carlos Oscar Sanchez Sorzano 2, Isabelle Callebaut 1, Florence Tama 3, and Slavica Jonic 1 1 IMPMC, Sorbonne Universités - CNRS UMR 7590, UPMC Univ Paris 6, MNHN, IRD UMR 206, Paris, France. 2 Biocomputing Unit, Centro Nacional de Biotecnología – CSIC, Madrid, Spain. 3 RIKEN, Advanced Institute for Computational Sciences, Kobe, Hyogo, , Japan.

Normal mode analysis (NMA) High frequenciesLow frequencies Dynamics is described as a linear combination of independent harmonic oscillators 2 Mode 28Mode 80Mode 107 Tomato Bushy Stunt Virus (TBSV) Deformation (displacement) amplitude : N atoms, 3N coordinates : Initial structure Modes : Frequency :

Eigenvalues problem Hessian: 2 nd derivative of the potential Eigenvector = normal mode Eigenvalue = frequency^2 Size of the system (3Nx3N) Harmonic dynamics of the potential energy function around a minimum energy conformation 3 Elastic Network Model : Atoms connected via elastic springs Computation of normal modes

Cowpea chlorotic mottle virus (CCMV) Tama et al., 2002, JMB 318 TBSV Flexible fitting: Flexible 3D-to-3D alignment of two different conformations Study of conformational changes for unveiling biological functions: Use of normal modes to explore different conformations A B C

5 TBSV experiments: pseudo-atomic structure as reference Flexible 2D-to-3D alignment Hybrid Electron Microscopy Normal Mode Analysis (HEMNMA) Structure 22: , 2014

6 Normal modes are used within a flexible 2D-to-3D alignment of images with a reference EM or atomic structure Hybrid approach Possible movements of unknown amplitudes are determined by NMA Movements computed by NMA are verified experimentally by determining their amplitudes through image analysis (flexible 2D-to-3D alignment) HEMNMA allows identifying intermediate conformations and continuous conformational changes of complexes in the sample Each particle image may represent a unique conformation Image classification and 3D reconstruction are not mandatory but can be done after image analysis HEMNMA highlights

7 TBSV experiments: atomic structure as reference 24%23%11%19%23% RMSD=2.1 nm JEOL JEM 2100F, ultra high-resolution pole piece (Cs=0.5 mm) 4000 images analyzed with combined modes 28, 80 and 107

8 Normal Mode Analysis and Flexible Alignment modules HEMNMA integral graphical interface and protocol J Struct Biol, Sep 27, 2014 xmipp.cnb.csic.es

9 Advanced Results Analysis module

10 HEMNMA: Combination of single-particle electron microscopy, normal mode analysis, and image analysis Elastic registration of images with a reference high- or low-resolution structure Full dynamics (distribution of conformations) Modeling of transition pathways Continuous conformational changes User-friendly integral graphical interface in Xmipp Access to other Xmipp methods for single-particle analysis Study of TBSV conformational changes – work in progress Analysis of larger number of images to better quantify the dynamics at atomic level Conclusions and Further work

11 Thank you

12 Iterative 3D-to-2D elastic registration