HMM_1_1_0: with only one match state to model any residue pair.

HMM_1_1_1: with 2 match states. One match state models residue pairs in core blocks, the other match state models residue pairs in unaligned (structurally divergent) regions.

HMM_1_3_1: with 4 match states. Residue pairs in core blocks are modeled by 3 match states corresponding to three secondary structure types (helix, strand, and coil). Residue pairs in unaligned regions are modeled by 1 match state. 

HMM_3_1_1: with 4 match states. Residue pairs in core blocks are modeled by 3 match states corresponding to three categories of relative sidechain solvent accessibility (<11.2, 11.2~51.7, and >51.7). Residue pairs in unaligned regions are modeled by 1 match state.

HMM_3_3_1: with 10 match states. Residue pairs in core blocks are modeled by 9 match states corresponding to combinations of three secondary structure types and three solvent accessibility categories. Residue pairs in unaligned regions are modeled by 1 match state.

Here are diagrams about HMM_1_1_0, HMM_1_1_1 and HMM_1_3_0.

Running time order: HMM_1_1_0 < HMM_1_1_1 < HMM_1_3_1 ≈ HMM_3_1_1 < HMM_3_3_1

Alignment quality generally in the order: HMM_1_1_0 < HMM_1_1_1 < HMM_3_1_1 < HMM_1_3_1 ≈ HMM_3_3_1

HMM_1_3_1 is the default since it balances running time and alignment quality. The two best performing HMMs (HMM_1_3_1 and HMM_3_3_1) give on average slightly better results (several percent) than ProbCons (version 1.1), MAFFT (version 5.667) and MUSCLE (version 3.52) on several multiple alignment testing datasets (Pei and Grishin, submitted).