Extended Data Table 1. Cryo-EM data collection, refinement and validation statistics.

	#1 INO80core (EMD-4264) (PDB 6FHS)	#2 INO80core+nuc (EMD-4277) (PDB 6FML)	#3 INO80 Grappler A (EMD-4278)	#4 INO80 Grappler B (EMD-4280)
Data collection and processing
Camera	Gatan K2	Gatan K2	Gatan K2	Gatan K2
Voltage (kV)	300	300	300	300
Electron exposure (e–/Å2)	59.6	59.6	59.6	59.6
Defocus range (µm)	1.3-3.5	1.3-3.5	1.3-3.5	1.3-3.5
Pixel size (Å)	1.06	1.06	1.06	1.06
Symmetry imposed	Cl	Cl	Cl	Cl
Initial particle images (no.)	251692	251692	251692	251692
Final particle images (no.)	144278	33937	16287	17263
Map resolution (Å)	3.75	4.34	4.68	4.62
0.143 FSC threshold
Map sharpening B-factor (Å2)	-142	-114	-124	-136
Refinement
Initial model used (PDB code)	models for refinement were build de novo or based on 4WW4 (Rvbl/2) and lNWK (actin)	models for refinement were build on 6FHS (INO80core) and 4r8p (nucleosome)
Model resolution (Å)	3.82	4.47
0.5 FSC threshold
Model resolution range (Å)	360.4 - 3.7	360.4 – 4.3
Map sharpening B factor (Å2)	-142	-114
Model composition
Non-hydrogen atoms	27184	43462
Protein and DNA residues	3481	5114
Ligands	7	7
B factors (Å2)
Protein and DNA	59.6	112.9
Ligand	54.3	80.29
R.m.s. deviations
Bond lengths (Å)	0.008	0.010
Bond angles (°)	0.93	1.203
Validation
MolProbity score	1.7	1.68
Clashscore	4.8	4.75
Poor rotamers (%)	0.1	0.13
Ramachandran plot
Favored (%)	92.8	93.3
Allowed (%)	7.2	6.6
Disallowed (%)	0.0	0.1