SlowGuess/NeurIPS_2023_OCR huggingface dataset:
$^{5}$ https://zdock.umassmed.edu  
 $^{6}$ https://cluspro.org  
 $^{7}$ http://hdock.phys.hust.edu.cn  
 $^{8}$ (MIT license) https://github.com/octavian-ganea/equidock_public  
 $^{9}$ (Apache-2.0 license) https://github.com/aqlaboratory/openfold  
 $^{10}$ (MIT license) https://github.com/pylelab/USalign  
 $^{11}$ (GPL-3.0 license) https://github.com/bjornwallner/DockQ  
 $^{12}$ https://ftp.uniprot.org/pub/databases/uniprot/current_release/knowledgebase/idmapping
13The sym_id is used to distinguish chains with the same sequence. For example, we consider a complex comprising five chains  $\{A,B,B,C,C\}$ , where  $A,B$ , and  $C$  represent three unique chains. The corresponding sym_ids for each chain would be  $\{1,1,2,1,2\}$ , respectively.
(5) The mean deletion value of size  $[N_{cls}, N_{res}, 1]$  is computed as  $\frac{2}{\pi}\arctan \frac{\bar{c}}{3}$ , where  $\bar{c}$  represents the average number of deletions to all residues on the left of each position.
Structure-modal Input For the structure modality, we extract angle features  $F^{ang} \in \mathbb{R}^{N_{res} \times 57}$  and pair features  $F^p \in \mathbb{R}^{N_{res} \times N_{res} \times 88}$  from the rigid protein structures. These features capture important structure-modal information and are used as input for our docking model. Specifically,
- The angle feature  $F^{ang} \in \mathbb{R}^{N_{res} \times 57}$  comprises three components. (1) The one-hot representation of the amino acid types with a size of  $[N_{res}, 22]$ , including 20 amino acids, one unknown type, and one gap or missing residue. (2) The angle representations of size  $[N_{res}, 28]$  use sine and cosine to encode three backbone torsion angles, four side-chain torsion angles, and alternative torsion angles with  $180^{\circ}$  rotation symmetry for each local frame of residue. (3) The angle indicator with size  $[N_{res}, 7]$  indicates the presence or absence of torsion angles.
- The pair feature  $F^p \in \mathbb{R}^{N_{res} \times N_{res} \times 88}$  comprises five components. (1) The histogram feature of size  $[N_{res}, N_{res}, 39]$  represents the discretized distances between C $\beta$  atoms. In the case of glycine, which lacks C $\beta$  atoms, C $\alpha$  is used instead. The distances are discretized into 38 bins of equal width ranging from 3.25 to 50.75 Å, with an additional bin accounting for larger distances. (2) The residue type feature of size  $[N_{res}, N_{res}, 44]$  is derived from expanding one-hot representations of residue types with dimensions of  $[N_{res}, 1, 22]$  and  $[N_{res}, 22, 1]$ . (3) The backbone feature of size  $[N_{res}, N_{res}, 3]$  is obtained by constructing the unit vector of the local frame through the Gram-Schmidt process based on the original N-C $\alpha$ -C coordinates. (4) The residue indicator with size  $[N_{res}, N_{res}, 1]$  is expanded from the indicator of residue existence. (5) The pair indicator of size  $[N_{res}, N_{res}, 1]$  indicates whether the pair is masked.
MSA Mask Policy Reflecting on Section 3.1, we design a masked MSA loss to supervise the learning of evolution representations and the integration of cross-modal information. Specifically, we randomly mask each position in an MSA cluster center with a  $15\%$  probability. Each masked token is replaced according to the following policies:
-  $70\%$  probability of substitution with a special token  $\star$
-  $10\%$  probability of substitution with a randomly selected amino acid from a uniform distribution
-  $10\%$  probability of substitution with an amino acid sampled from the MSA profile that corresponds to the position
-  $10\%$  probability of no substitution
Hyperparameter Settings We initialize specific parameters of the cross-modal transformer with the checkpoint of Multimer and implement bi-level optimization using TorchOpt $^{14}$  library. The crop size is set to 412, and the batch size is set to 1. The coefficients in Equation (13) are  $\lambda_{1} = 0.2$ ,  $\lambda_{2} = 2.0$ , and  $\lambda_{3} = 10.0$ . For optimization, we employ the Adam optimizer with a learning rate of  $10^{-4}$  and integrate learning rate warmup, gradually increasing the learning rate from 0 to  $10^{-4}$  within the first 100 steps. The exponential moving average (EMA) strategy applies a decay rate of  $\beta = 0.999$  and undergoes updates every 200 steps. The environment where we run all experiments is:
- Operating system: Linux version 5.13.0-30-generic
- CPU information: AMD EPYC 7742 64-Core Processor
- GPU information: NVIDIA A100-SXM4-80GB
Effects of Noisy Structures Classical software relies on score functions derived from statistics in the protein data bank. This dependency renders them susceptible to noise. When using folding algorithms to predict unbounded proteins, the performance of these software can degrade significantly. To validate this intuition, we conduct a docking performance analysis on the DB5.5 dataset using ground truth and predicted structures from folding models as unbounded structures, respectively. As shown in Table 6, these results illustrate that although HDOCK performs exceptionally well with
$^{14}$ Apache-2.0 license) https://github.com/metaopt/torchopt
Table 6: Impacts of noisy structures on the docking performance of classical software and BiDock. (bold: best; underline: runner-up)
Ground Truth	Predicted Structure
RMSD ↓	TM-score ↑	DockQ ↑	RMSD ↓	TM-score ↑	DockQ ↑
ZDOCK	11.830±5.227	0.738±0.120	0.095±0.130	12.491±6.294	0.689±0.114	0.084±0.113
ClusPro	11.486±7.993	0.780±0.133	0.204±0.256	14.135±8.153	0.702±0.118	0.118±0.192
HDOCK	3.464±7.394	0.935±0.144	0.815±0.364	11.328±8.073	0.742±0.167	0.314±0.390
BiDock	6.173±8.825	0.892±0.156	0.648±0.432	7.280±8.117	0.847±0.158	0.564±0.369
ground truth, minor noise in predicted structures leads to a substantial decline in its performance. On the contrary, BiDock consistently generates acceptable predictions regardless of the input type, showcasing its robustness to noise. In real-world applications, reliance on the availability of ground truth structures is impractical. The ability of BiDock to maintain high prediction quality when confronted with noisy structures makes it an invaluable tool.