Lecture 8 Methods for determination of 3D volumes from 2D experimental data 15th November 2022 Jiri Novacek Content - principles - electron tomography - single particle analysis - common lines - random conical tilt Revision - 2D projections of an 3D object (handedness) - high noise level (low sensitivity) - convolution with microscope point spread functions Revision - 2D projections of an 3D object (handedness) - high noise level (low sensitivity) - convolution with microscope point spread functions Revision - 2D projections of an 3D object (handedness) - high noise level (low sensitivity) - convolution with microscope point spread functions Revision n=1 n=2 n=8 n=16 n=64 n=256 - 2D projections of an 3D object - high noise level (low sensitivity) - convolution with microscope point spread functions Revision n=1 n=2 n=8 n=16 n=64 n=256 - 2D projections of an 3D object - high noise level (low sensitivity) - convolution with microscope point spread functions 3D reconstruction 1. Different orientations 2. Known orientations 3. Many particles 4. CTF parameters 3D reconstruction Two general ways for 3D reconstruction: - Real space - Fourier space We are going to reconstruct a 2D object from 1D projections. The principle is the similar to, but simpler than, reconstructing a 3D object from 2D projections. 3D reconstruction Real space reconstruction 3D reconstruction Real space reconstruction 3D reconstruction Real space reconstruction 3D reconstruction - reconstruction is the inversion of projection 3D reconstruction - reconstruction is the inversion of projection 3D reconstruction - reconstruction is the inversion of projection 3D reconstruction - reconstruction is the inversion of projection 3D reconstruction The reconstruction does not agree well with the projections Potential solution: Simultaneous Iterative Reconstruction Technique Original Reconstructed 3D reconstruction - simultaneous iterative reconstruction technique Compute re-projections of your model. Compare the re-projections to your experimental data. There will be differences. Weight the differences by a fudge factor, λ. Adjust the model by the difference weighted by λ. Repeat 3D reconstruction - simultaneous iterative reconstruction technique 3D reconstruction Fourier space reconstruction Projection theorem Central section theorem 3D reconstruction Fourier space reconstruction Projection theorem Central section theorem 3D reconstruction Converting from polar to Cartesian coordinates 3D reconstruction 3D reconstruction 1. Different orientations 2. Known orientations 3. Many particles 4. CTF parameters 3D reconstruction Tomography Tomography We know orientations... We have different view... Tomography We are destroying the sample as we image itWe are destroying the sample as we image it Tomography Accumulated beam damage If number of views is limited → image distorsions Tomography Accumulated beam damage If number of views is limited → image distorsions If we have many identical molecules and if we can determine their orientations, we can use one exposure per molecule and use the images in the reconstruction → single particle analysis Single particle analysis Unlike the tomography data, we do not know how the orientations between individual images are related → reference based alignment Single particle analysis Unlike the tomography data, we do not know how the orientations between individual images are related → reference based alignment Single particle analysis Projection of the reference at the defined angular step Single particle analysis Projection of the reference at the defined angular step Single particle analysis Projection of the reference at the defined angular step Single particle analysis Projection of the reference at the defined angular step Single particle analysis Projection of the reference at the defined angular step Single particle analysis Projection of the reference at the defined angular step Single particle analysis Projection of the reference at the defined angular step Single particle analysis Projection of the reference at the defined angular step Single particle analysis Projection of the reference at the defined angular step Single particle analysis 1. Compare the experimental images to all of the reference projections 2. Fing the reference projection with whicch the experimental images match the best 3. Assign the Euler angles of that reference to the experimental image Single particle analysis 4. Calculate a new reference 5. Project the new reference 6. Repeat from 1 Common lines Angular Reconstruction Common lines Angular Reconstruction Random conical tilt Random conical tilt Random conical tilt Random conical tilt Random conical tilt Random conical tilt Random conical tilt - we cannot tilt the stage to 90 deg → “missing cone” Random conical tilt - filling the missing cone