D-QUARK ('Distance-assisted QUARK') is an ab initio (also known as template-free modeling, FM) approach for protein structure prediction (Figure 1). D-QUARK consists of 4 consecutive steps: (1) residue-residue distance and orientation prediction by DeepPotential using DeepMSA2 multiple sequence alignments; (2) distance- and orientation-guided L-BFGS fragment generation; (3) fragment assembly REMC simulation guided by a composite force field coupling deep-learning restraints with the QUARK-based knowledge-based potential; and (4) clustering by SPICKER and refinement by ModRefiner/FG-MD for final model generation. In the following figure, the lower left inset depicts the geometric definition of dihedral angles Ω and Θ as well as the angle Φ for orientation prediction between residue i (black) and residue j (grey), where Ω is symmetric (Ω_ij=Ω_ji) while Θ and Φ are asymmetric (Θ_ij≠Θ_ji and Φ_ij≠Φ_ji).

Figure 1. The D-QUARK pipeline for distance-based ab initio structure prediction.

Model quality estimation.

Estimated TM-score:

The estimated TM-score (eTM) of D-QUARK final models are derived from three parameters:
• C, the number of decoys in the largest SPICKER cluster divided by total number of decoy;
• TM(init), the TM-score between the model and an initial model constructed by L-BFGS; and
• TM(model1), the TM-score between the model and Model 1.
The formulas for calculating the eTM is model specific:

Model	Equation for eTM
Model 1:	eTM = 0.15469977*C + 0.46708873*TM(init) + 0.13485522
Model 2:	eTM = 0.40079969*TM(init) + 0.31421774*TM(model1)
Model 3:	eTM = 0.41521800*TM(init) + 0.30207216*TM(model1)
Model 4:	eTM = 0.36814485*TM(init) + 0.33152681*TM(model1)
Model 5:	eTM = 0.37219591*TM(init) + 0.33126615*TM(model1)

Estimated RMSD:


The estimated RMSD (eRM) of D-QUARK final models are derived from three parameters:

• C, the number of decoys in the largest SPICKER cluster divided by total number of decoy;
• RM(init), the RMSD between the model and an initial model constructed by L-BFGS; and
• RM(model1), the RMSD between the model and Model 1.
The formulas for calculating the eRM is model specific:

Model	Equation for eRM
Model 1:	eRM = -5.60731603*C + 0.24886347*RM(init) + 9.77186191
Model 2:	eRM = -3.81879814*C + 0.20247168*RM(init) + 0.29088287*RM(model1) + 8.54458740
Model 3:	eRM = -4.19182847*C + 0.14743717*RM(init) + 0.26417156*RM(model1) + 9.13669855
Model 4:	eRM = -3.13746601*C + 0.14056058*RM(init) + 0.41393724*RM(model1) + 8.20942740
Model 5:	eRM = -4.04812605*C + 0.17108867*RM(init) + 0.26174424*RM(model1) + 9.08764688