Towards Predicting Equilibrium Distributions for Molecular Systems with Deep Learning

Advances in deep learning have greatly improved structure prediction of molecules. However, many macroscopic observations that are important for real-world applications are not functions of a single molecular structure, but rather determined from the equilibrium distribution of structures. Traditional methods for obtaining these distributions, such as molecular dynamics simulation, are computationally expensive and often intractable. In this paper, we introduce a novel deep learning framework, called Distributional Graphormer (DiG), in an attempt to predict the equilibrium distribution of molecular systems. Inspired by the annealing process in thermodynamics, DiG employs deep neural networks to transform a simple distribution towards the equilibrium distribution, conditioned on a descriptor of a molecular system, such as a chemical graph or a protein sequence. This framework enables efficient generation of diverse conformations and provides estimations of state densities. We demonstrate the performance of DiG on several molecular tasks, including protein conformation sampling, ligand structure sampling, catalyst-adsorbate sampling, and property-guided structure generation. DiG presents a significant advancement in methodology for statistically understanding molecular systems, opening up new research opportunities in molecular science.

Exploring evolution-based & -free protein language models as protein function predictors

Large-scale Protein Language Models (PLMs) have improved performance in protein prediction tasks, ranging from 3D structure prediction to various function predictions. In particular, AlphaFold, a ground-breaking AI system, could potentially reshape structural biology. However, the utility of the PLM module in AlphaFold, Evoformer, has not been explored beyond structure prediction. In this paper, we investigate the representation ability of three popular PLMs: ESM-1b (single sequence), MSA-Transformer (multiple sequence alignment) and Evoformer (structural), with a special focus on Evoformer. Specifically, we aim to answer the following key questions: (i) Does the Evoformer trained as part of AlphaFold produce representations amenable to predicting protein function? (ii) If yes, can Evoformer replace ESM-1b and MSA-Transformer? (iii) How much do these PLMs rely on evolution-related protein data? In this regard, are they complementary to each other? We compare these models by empirical study along with new insights and conclusions. Finally, we release code and datasets for reproducibility.

Pre-training Co-evolutionary Protein Representation via A Pairwise Masked Language Model

Understanding protein sequences is vital and urgent for biology, healthcare, and medicine. Labeling approaches are expensive yet time-consuming, while the amount of unlabeled data is increasing quite faster than that of the labeled data due to low-cost, high-throughput sequencing methods. In order to extract knowledge from these unlabeled data, representation learning is of significant value for protein-related tasks and has great potential for helping us learn more about protein functions and structures. The key problem in the protein sequence representation learning is to capture the co-evolutionary information reflected by the inter-residue co-variation in the sequences. Instead of leveraging multiple sequence alignment as is usually done, we propose a novel method to capture this information directly by pre-training via a dedicated language model, i.e., Pairwise Masked Language Model (PMLM). In a conventional masked language model, the masked tokens are modeled by conditioning on the unmasked tokens only, but processed independently to each other. However, our proposed PMLM takes the dependency among masked tokens into consideration, i.e., the probability of a token pair is not equal to the product of the probability of the two tokens. By applying this model, the pre-trained encoder is able to generate a better representation for protein sequences. Our result shows that the proposed method can effectively capture the inter-residue correlations and improves the performance of contact prediction by up to 9% compared to the MLM baseline under the same setting. The proposed model also significantly outperforms the MSA baseline by more than 7% on the TAPE contact prediction benchmark when pre-trained on a subset of the sequence database which the MSA is generated from, revealing the potential of the sequence pre-training method to surpass MSA based methods in general.

Seq-SetNet: Exploring Sequence Sets for Inferring Structures

Sequence set is a widely-used type of data source in a large variety of fields. A typical example is protein structure prediction, which takes an multiple sequence alignment (MSA) as input and aims to infer structural information from it. Almost all of the existing approaches exploit MSAs in an indirect fashion, i.e., they transform MSAs into position-specific scoring matrices (PSSM) that represent the distribution of amino acid types at each column. PSSM could capture column-wise characteristics of MSA, however, the column-wise characteristics embedded in each individual component sequence were nearly totally neglected. The drawback of PSSM is rooted in the fact that an MSA is essentially an unordered sequence set rather than a matrix. Specifically, the interchange of any two sequences will not affect the whole MSA. In contrast, the pixels in an image essentially form a matrix since any two rows of pixels cannot be interchanged. Therefore, the traditional deep neural networks designed for image processing cannot be directly applied on sequence sets. Here, we proposed a novel deep neural network framework (called Seq-SetNet) for sequence set processing. By employing a {\it symmetric function} module to integrate features calculated from preceding layers, Seq-SetNet are immune to the order of sequences in the input MSA. This advantage enables us to directly and fully exploit MSAs by considering each component protein individually. We evaluated Seq-SetNet by using it to extract structural information from MSA for protein secondary structure prediction. Experimental results on popular benchmark sets suggests that Seq-SetNet outperforms the state-of-the-art approaches by 3.6% in precision. These results clearly suggest the advantages of Seq-SetNet in sequence set processing and it can be readily used in a wide range of fields, say natural language processing.

Predicting protein inter-residue contacts using composite likelihood maximization and deep learning

Accurate prediction of inter-residue contacts of a protein is important to calcu- lating its tertiary structure. Analysis of co-evolutionary events among residues has been proved effective to inferring inter-residue contacts. The Markov ran- dom field (MRF) technique, although being widely used for contact prediction, suffers from the following dilemma: the actual likelihood function of MRF is accurate but time-consuming to calculate, in contrast, approximations to the actual likelihood, say pseudo-likelihood, are efficient to calculate but inaccu- rate. Thus, how to achieve both accuracy and efficiency simultaneously remains a challenge. In this study, we present such an approach (called clmDCA) for contact prediction. Unlike plmDCA using pseudo-likelihood, i.e., the product of conditional probability of individual residues, our approach uses composite- likelihood, i.e., the product of conditional probability of all residue pairs. Com- posite likelihood has been theoretically proved as a better approximation to the actual likelihood function than pseudo-likelihood. Meanwhile, composite likelihood is still efficient to maximize, thus ensuring the efficiency of clmDCA. We present comprehensive experiments on popular benchmark datasets, includ- ing PSICOV dataset and CASP-11 dataset, to show that: i) clmDCA alone outperforms the existing MRF-based approaches in prediction accuracy. ii) When equipped with deep learning technique for refinement, the prediction ac- curacy of clmDCA was further significantly improved, suggesting the suitability of clmDCA for subsequent refinement procedure. We further present successful application of the predicted contacts to accurately build tertiary structures for proteins in the PSICOV dataset. Accessibility: The software clmDCA and a server are publicly accessible through http://protein.ict.ac.cn/clmDCA/.