Low-dose phase retrieval of biological specimens using cryo-electron ptychography

Cryo-electron microscopy is an essential tool for high-resolution structural studies of biological systems. This method relies on the use of phase contrast imaging at high defocus to improve information transfer at low spatial frequencies at the expense of higher spatial frequencies. Here we demonstrate that electron ptychography can recover the phase of the specimen with continuous information transfer across a wide range of the spatial frequency spectrum, with improved transfer at lower spatial frequencies, and as such is more efficient for phase recovery than conventional phase contrast imaging. We further show that the method can be used to study frozen-hydrated specimens of rotavirus double-layered particles and HIV-1 virus-like particles under low-dose conditions (5.7 e/Å2) and heterogeneous objects in an Adenovirus-infected cell over large fields of view (1.14 × 1.14 μm), thus making it suitable for studies of many biologically important structures.


Room temperature ptychographyof an Adenovirus-infected cell embedded in resin
Datasets from an Adenovirus infected cell (Fig. 4a, Supplementary Fig. 8a

Electron ptychography illumination optics
A schematic of the illumination optics for the electron ptychography experiments on the JEOL ARM300CF compared to normal STEM operation is shown in Supplementary Fig. 11. A pencil beam with small convergence semi-angle was formed using the pre-sample optics of the microscope ( Supplementary Fig. 11b). To fine-tune the convergence semi-angle of the probe at the specimen plane, the CL2 cross-over position was adjusted by strengthening the CL2 lens whilst weakening the CL3 lens.
All round transfer lenses in the probe corrector were turned off. In contrast conventional STEM uses a large convergence semi-angle ( ) compared to that used in this work ( p for a pencil beam). CL1, CL2 and CL3 represent the condenser lens system, while SD (small dodecapole), TLS, TLR, TLL (transfer lenses) and LD (long dodecapole) are the optical elements in the probe-corrector which are unused and not necessary for this ptychographic optical configuration. The pre-specimen condenser mini-lens system (CMT and CM) and the objective lens pre-field are also shown.

Cryo-EM preparation of rotavirus double layered particles (DLPs)
Rotavirus DLPs (strain SA11) were prepared as previously described 3

Preparation of TEM grids of Adenovirus-infected cells embedded in resin
Human Adenovirus type 5 (Ad5) was inoculated on human embryo kidney cells 293 were collected on 300 mesh Quantifoil holey carbon EM grids. Finally, the TEM grids were air-dried.

Ptychographic reconstruction
The easiest way to measure the CTF is to compare power spectra of a measured phase image of an object against that of the known object. Specifically, CTFPty, the phase CTF for ptychographic reconstruction can be evaluated as: where FT represents a Fourier transform.  Fig. 2o) was calculated using Eq. 1.
For the experiments reported, diffraction patterns were recorded in an electron counting detector at low dose. Hence, the main experimental detector noise can be considered as Poisson distributed shot noise, modelled as follows.
Assuming independent measurements , at the i-th pixel on the detector in the n-th illumination of electron probe, the probability that the entire ptychographic data set I is collected is 4 : where , is the expected number of events for the i-th pixel in the n-th illumination.
Adding Poisson distributed shot noise, the detected intensity , at i-th pixel in the n-  Fig. 2a and Supplementary Fig.   2o) was similarly calculated using from Eq. 1.
Without noise in the ptychographic dataset, the phase CTFs can extend to the Nyquist frequency for each convergence semi-angle considered in the calculations, indicating that ptychographic reconstruction uses signal up to the maximum collection angle of the detector, even when the signal is low. However, when noise was introduced the S/N in the dark field region is too low to allow any signal beyond the bright field disc to be reconstructed, limiting the ultimate resolution. As a consequence, the high frequency bound of the noise limited CTFPty lies at the twice the convergence semi-angle as shown in Fig. 2a and Supplementary Fig. 2o.
Therefore, for the experiments as reported here, the level of the S/N ratio at the detector plane within the collection angle used to record the data can impose a lower resolution limit and specifically in the weak phase approximation, the resolution for iterative ptychography is limited to twice the convergence semi-angle of the probe used.

Supplementary Note 4: Fourier ring correlation
To evaluate the resolution (the high spatial frequency bound) of a ptychographic reconstruction, Fourier ring correlation (FRC) 10,11 was used, which measures the degree of correlation between two images at different spatial frequencies. The full dataset (126 × 126 diffraction patterns) recorded from an Adenovirus particle shown in Supplementary Fig. 3a was split into two independent datasets (63 × 63 diffraction patterns) as illustrated in Supplementary Fig. 3f, for ptychographic reconstruction. The FRC was then calculated from the complex function of these two reconstructions as a function of spatial frequency. To quantify the resolution from the FRC, a threshold criterion of ½-bit was chosen 11 . However, since the independent reconstructions use half the number of electrons and a reduced probe overlap 12 , the independent, separate reconstructions are of lower quality than that from the full dataset. Hence, this method provides a conservative estimate of the resolution in the ptychographic reconstruction.

Room Temperature TEM of Adenovirus particles embedded in resin
Conventional phase contrast TEM images of Adenovirus particles (Figs. 2d-f and Supplementary Figs. 5a-e were acquired using a JEOL ARM 300CF operated at 80 kV. The Adenovirus particle was imaged across a range of defoci from -0.32 μm to -25 μm, with a fixed spherical aberration coefficient of 2.24 μm. A pixel size of 0.74 nm and a dose of 180 e/Å 2 were used to record the data, similar to those used in the ptychographic reconstruction shown in Fig. 2c (0.74 nm and 146 e/Å 2 ).

Cryo TEM of DLPs
Movies of rotavirus DLPs in vitrified ice were acquired on a Titan Krios using a Falcon III detector in linear mode with a total exposure of 35 e/Å 2 distributed over 29 motioncorrected fractions.

Evaluation of the dataset redundancy
For ptychographic reconstruction, the quantity σpty 13 can be used to estimate the degree of redundancy of a ptychographic dataset as: where J represents the total number of pixels in the diffraction patterns used for reconstruction. Using Setting (1)
For the datasets of the Adenovirus with different convergence semi angles of 1.37 mrad ( Supplementary Fig. 3a), 4.68 mrad (Supplementary Fig. 3b) and 10 mrad 32 ( Supplementary Fig. 3c respectively. For the micrometer dataset of Adenovirus infected cell shown in (Fig. 4a), the overlap ratio is 77 % and the redundancy is 191 with the central 194 × 194 pixels in the diffraction pattern used for reconstruction. All probe and object functions shown were obtained after 300 iterations of the ePIE algorithm. The estimated and reconstructed probe functions used for Setting (4) in Supplementary Table 4 are given in Supplementary Fig. 13.