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Abstract MotivationComputational methods for compound–protein affinity and contact (CPAC) prediction aim at facilitating rational drug discovery by simultaneous prediction of the strength and the pattern of compound–protein interactions. Although the desired outputs are highly structure-dependent, the lack of protein structures often makes structure-free methods rely on protein sequence inputs alone. The scarcity of compound–protein pairs with affinity and contact labels further limits the accuracy and the generalizability of CPAC models. ResultsTo overcome the aforementioned challenges of structure naivety and labeled-data scarcity, we introduce cross-modality and self-supervised learning, respectively, for structure-aware and task-relevant protein embedding. Specifically, protein data are available in both modalities of 1D amino-acid sequences and predicted 2D contact maps that are separately embedded with recurrent and graph neural networks, respectively, as well as jointly embedded with two cross-modality schemes. Furthermore, both protein modalities are pre-trained under various self-supervised learning strategies, by leveraging massive amount of unlabeled protein data. Our results indicate that individual protein modalities differ in their strengths of predicting affinities or contacts. Proper cross-modality protein embedding combined with self-supervised learning improves model generalizability when predicting both affinities and contacts for unseen proteins. Availability and implementationData and source codes are available at https://github.com/Shen-Lab/CPAC. Supplementary informationSupplementary data are available at Bioinformatics online. 

Abstract We present the results for CAPRI Round 54, the 5th joint CASP‐CAPRI protein assembly prediction challenge. The Round offered 37 targets, including 14 homodimers, 3 homo‐trimers, 13 heterodimers including 3 antibody–antigen complexes, and 7 large assemblies. On average ~70 CASP and CAPRI predictor groups, including more than 20 automatics servers, submitted models for each target. A total of 21 941 models submitted by these groups and by 15 CAPRI scorer groups were evaluated using the CAPRI model quality measures and the DockQ score consolidating these measures. The prediction performance was quantified by a weighted score based on the number of models of acceptable quality or higher submitted by each group among their five best models. Results show substantial progress achieved across a significant fraction of the 60+ participating groups. High‐quality models were produced for about 40% of the targets compared to 8% two years earlier. This remarkable improvement is due to the wide use of the AlphaFold2 and AlphaFold2‐Multimer software and the confidence metrics they provide. Notably, expanded sampling of candidate solutions by manipulating these deep learning inference engines, enriching multiple sequence alignments, or integration of advanced modeling tools, enabled top performing groups to exceed the performance of a standard AlphaFold2‐Multimer version used as a yard stick. This notwithstanding, performance remained poor for complexes with antibodies and nanobodies, where evolutionary relationships between the binding partners are lacking, and for complexes featuring conformational flexibility, clearly indicating that the prediction of protein complexes remains a challenging problem. 

Modeling population dynamics is a fundamental problem with broad scientific applications. Motivated by real-world applications including biosystems with diverse populations, we consider a class of population dynamics modeling with two technical challenges: (i) dynamics to learn for individual particles are heterogeneous and (ii) available data to learn from are not time-series (i.e, each individual’s state trajectory over time) but cross-sectional (i.e, the whole population’s aggregated states without individuals matched over time). To address the challenges, we introduce a novel computational framework dubbed correlational Lagrangian Schrödinger bridge (CLSB) that builds on optimal transport to “bridge" cross-sectional data distributions. In contrast to prior methods regularizing all individuals’ transport “costs” and then applying them to the population homogeneously, CLSB directly regularizes population cost allowing for population heterogeneity and potentially improving model generalizability. Specifically our contributions include (1) a novel population perspective of the transport cost and a new class of population regularizers capturing the temporal variations in multivariate relations, with the tractable formulation derived, (2) three domain-informed instantiations of population regularizers on covariance, and (3) integration of population regularizers into data-driven generative models as constrained optimization and an approximate numerical solution, with further extension to conditional generative models. Empirically, we demonstrate the superiority of CLSB in single-cell sequencing data analyses (including cell differentiation and drug-conditioned cell responses) and opinion depolarization. 

This paper considers the problem of offline optimization, where the objective function is unknown except for a collection of “offline" data examples. While recent years have seen a flurry of work on applying various machine learning techniques to the offline optimization problem, the majority of these works focused on learning a surrogate of the unknown objective function and then applying existing optimization algorithms. While the idea of modeling the unknown objective function is intuitive and appealing, from the learning point of view it also makes it very difficult to tune the objective of the learner according to the objective of optimization. Instead of learning and then optimizing the unknown objective function, in this paper we take on a less intuitive but more direct view that optimization can be thought of as a process of sampling from a generative model. To learn an effective generative model from the offline data examples, we consider the standard technique of “re-weighting", and our main technical contribution is a probably approximately correct (PAC) lower bound on the natural optimization objective, which allows us to jointly learn a weight function and a score-based generative model from a surrogate loss function. The robustly competitive performance of the proposed approach is demonstrated via empirical studies using the standard offline optimization benchmarks. 

Proteins, often represented as multi-modal data of 1D sequences and 2D/3D structures, provide a motivating example for the communities of machine learning and computational biology to advance multi-modal representation learning. Protein language models over sequences and geometric deep learning over structures learn excellent single-modality representations for downstream tasks. It is thus desirable to fuse the single-modality models for better representation learning, but it remains an open question on how to fuse them effectively into multi-modal representation learning with a modest computational cost yet significant downstream performance gain. To answer the question, we propose to make use of separately pretrained single-modality models, integrate them in parallel connections, and continuously pretrain them end-to-end under the framework of multimodal contrastive learning. The technical challenge is to construct views for both intra- and inter-modality contrasts while addressing the heterogeneity of various modalities, particularly various levels of semantic robustness. We address the challenge by using domain knowledge of protein homology to inform the design of positive views, specifically protein classifications of families (based on similarities in sequences) and superfamilies (based on similarities in structures). We also assess the use of such views compared to, together with, and composed to other positive views such as identity and cropping. Extensive experiments on enzyme classification and protein function prediction benchmarks demonstrate the potential of domain-informed view construction and combination in multi-modal contrastive learning 

Generating 3D graphs of symmetry-group equivariance is of intriguing potential in broad applications from machine vision to molecular discovery. Emerging approaches adopt diffusion generative models (DGMs) with proper re-engineering to capture 3D graph distributions. In this paper, we raise an orthogonal and fundamental question of in what (latent) space we should diffuse 3D graphs. ❶ We motivate the study with theoretical analysis showing that the performance bound of 3D graph diffusion can be improved in a latent space versus the original space, provided that the latent space is of (i) low dimensionality yet (ii) high quality (i.e., low reconstruction error) and DGMs have (iii) symmetry preservation as an inductive bias. ❷ Guided by the theoretical guidelines, we propose to perform 3D graph diffusion in a low-dimensional latent space, which is learned through cascaded 2D–3D graph autoencoders for low-error reconstruction and symmetry-group invariance. The overall pipeline is dubbed latent 3D graph diffusion. ❸ Motivated by applications in molecular discovery, we further extend latent 3D graph diffusion to conditional generation given SE(3)-invariant attributes or equivariant 3D objects. ❹ We also demonstrate empirically that out-of-distribution conditional generation can be further improved by regularizing the latent space via graph self-supervised learning. We validate through comprehensive experiments that our method generates 3D molecules of higher validity / drug-likeliness and comparable or better conformations / energetics, while being an order of magnitude faster in training. Codes are released at https://github.com/Shen-Lab/LDM-3DG. 

Transfer learning on graphs drawn from varied distributions (domains) is in great demand across many applications. Emerging methods attempt to learn domain-invariant representations using graph neural networks (GNNs), yet the empirical performances vary and the theoretical foundation is limited. This paper aims at designing theory-grounded algorithms for graph domain adaptation (GDA). (i) As the first attempt, we derive a model-based GDA bound closely related to two GNN spectral properties: spectral smoothness (SS) and maximum frequency response (MFR). This is achieved by cross-pollinating between the OT-based (optimal transport) DA and graph filter theories. (ii) Inspired by the theoretical results, we propose algorithms regularizing spectral properties of SS and MFR to improve GNN transferability. We further extend the GDA theory into the more challenging scenario of conditional shift, where spectral regularization still applies. (iii) More importantly, our analyses of the theory reveal which regularization would improve performance of what transfer learning scenario, (iv) with numerical agreement with extensive real-world experiments: SS and MFR regularizations bring more benefits to the scenarios of node transfer and link transfer, respectively. In a nutshell, our study paves the way toward explicitly constructing and training GNNs that can capture more transferable representations across graph domains. Codes are released at https://github.com/Shen-Lab/GDA-SpecReg.