Supplementary Information for

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1 Supplementary Information for Unsupervised single-particle deep classification via statistical manifold learning Jiayi Wu 1,2, Yongbei Ma 2, Charles Condgon 3, Bevin Brett 3, Shuobing Chen 1,2, Qi Ouyang 1,5, Youdong Mao 1,2,4 * 1 State Key Laboratory for Mesoscopic Physics, Institute of Condense Matter Physics, School of Physics, Peking University, Beijing , China. 2 Intel Parallel Computing Center for Structural Biology, Dana-Farber Cancer Institute, Boston, MA 02215, USA. 3 Software and Services Group, Intel Corporation, Santa Clara, CA 95052, USA. 4 Department of Microbiology and Immunobiology, Harvard Medical School, Boston, MA 02115, USA. 5 Center for Quantitative Biology, Peking-Tsinghua Center for Life Sciences, Peking University, Beijing, China *Correspondence should be addressed to Y.M. Tel: Fax: address: youdong_mao@dfci.harvard.edu 1

2 Supplementary Figure 1. Typical results of unsupervised classification for three cryo-em experimental datasets by ROME. a, A typical cryo-em micrograph of the inflammasome. 2

3 White boxes mark the particles picked from the micrograph and contributed to the dataset used in testing our SML algorithm implemented in ROME. b, Typical reference-free SML-based classification following MAP-based image alignment 2D class averages of the 10-fold, 11-fold, 12-fold inflammasome complex. c, A typical cryo-em micrograph of the proteasome among the analyzed dataset. We boxed half of the holoenzyme, including half of the CP, in complex with a complete RP, named RP-CP subcomplex (white box). d, Typical reference-free SML-based classification following MAP-based image alignment 2D class averages of the RP-CP subcomplex. e, A typical cryo-em micrograph of the human RP proteasome among the analyzed dataset. We boxed all particles, including free RP complex and RP-CP subcomplex, whose box center is focused on that of RP (white box). f, Typical reference-free SML-based classification following MAP-based image alignment 2D class averages of the RP complex. 3

4 Supplementary Figure 2. Comparison of unsupervised classification on inflammasome dataset by SML and MAP. 17,103 inflammasome particles are classified into 300 referencefree classes. Only classes whose particle numbers were larger than 9 were exhibited. a, Unsupervised classification with SML in ROME. Among 300 classes, 49 classes have shown the 4

5 various views of inflammasome complexes of different symmetry. b, Unsupervised classification with MAP in RELION. 28 classes also exhibited views of inflammasome complexes in different symmetry. The MAP in RELION generated considerably less amount of distinct classes than did the SML in ROME, indicating that SML is more efficient in distinguishing structural differences. 5

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7 Supplementary Figure 3. Deep classification on the RP dataset by ROME. 117,471 RP complex particles were used to do 2D classification based on ROME into 1,000 classes. All particles were aligned by MAP and then partitioned by SML. 858 class averages were not blank. These classes exhibit different views of RP complex. Supplementary Figure 4. Comparison of deeper unsupervised classification between 7

8 ROME and other approaches. a, 2D classification for 50 classes based on ROME. The red box exhibits the side view projection of 10-fold inflammasome complex, whose length is smaller than others. The green box exhibits the incomplete inflammasome complex particles. b, 2D classification for 50 classes based on RELION. The major class exhibits the side view projections of 11-fold inflammasome complex, whereas all of the rest classes present junk. c, Unsupervised K-means clustering for 50 classes in SPIDER. The red box exhibits the side view projection of 10-fold inflammasome complex, whose length is smaller than others. However, the green box indicates the misalignment of translation and in-plane rotation, as well as misclassification of misaligned particle images. 8