Protein space groups

Protein structures being restricted to non-mirror and non-inversion symmetry operations, the number of possible space groups are reduced to the 65 non-enantiogenic space groups.

Crystal system (65)	Number	Point Group	Space Groups
TRICLINIC (1)	1	$C_1$	$P1$
MONOCLINIC (3)	3	$C_2$	$P2$, $P2_1$,$C2$
ORTHORHOMBIC(9)	9	$D_2$	$P222$, $P222_1$, $P2_12_12$, $P2_12_12_1$, $C222_1$, $C222$, $F222$, $I222$, $I2_12_12_1$
TETRAGONAL (16)	6	$C_4$	$P4$, $P4_1$, $P4_2$, $P4_3$, $I4$, $I4_1$
	10	$D_4$	$P422$, $P42_12$, $P4_122$, $P4_12_12$, $P4_222$, $P4_22_12$, $P4_322$, $P4_32_12$, $I422$, $I4_122$
TRIGONAL (11)	4	$C_3$	$P3$, $P3_1$, $P3_2$, $R3$
	7	$D_3$	$P312$, $P321$, $P3_112$, $P3_121$, $P3_212$, $P3_221$, $R32$
HEXAGONAL (12)	6	$C_6$	$P6$, $P6_1$, $P6_5$, $P6_2$, $P6_4$, $P6_3$
	6	$D_6$	$P622$, $P6_122$, $P6_522$, $P6_222$, $P6_422$, $P6_322$
CUBIC (13)	5	$T$	$P23$, $F23$, $I23$, $P2_13$, $I2_13$
	8	$O$	$P432$, $P4_232$, $F432$, $F4_132$, $I432$, $P4_332$, $P4_132$, $I4_132$

An entropic model indicates that space groups $P2_1$ and $P2_12_12_1$ are the least restrictive to packing explaining there abundance.

Laue groups

Patterson symmetry is the Laue class (or group) plus allowed centring.

2D

Laue class	Patterson symmetry	plane groups	count
2	p2	p1,p2	2
2mm	p2mm	p1m1,p1g1,p2mm,p2gg,p2gm	5
	c2mm	c1m1,c2mm	2
4	p4	p4	1
4mm	p4mm	p4mm,p4gm	2
6	p6	p3,p6	2
6mm	p6mm	p3m1,p31m,p6mm	3

3D

Links

Python

• crystals python library

Structures

• Berkeley database
• Space group
• Point groups
• Crystal structures periodic table

Other

• web material Bfactor.
• 65 protein non-enantiogenic space groups.
• proteopedia

MicroED

• wiki
• google scholar