A Variational Graph Partitioning Approach to Modeling Protein Liquid-liquid Phase Separation

Abstract

Protein Liquid-Liquid Phase Separation (LLPS) plays an essential role in cellular processes and is known to be associated with various diseases. However, our understanding of this enigmatic phenomena remains limited. In this work, we propose a graph-neural-network(GNN)-based interpretable machine learning approach to study the intricate nature of protein structure-function relationships associated with LLPS. For many protein properties of interest, information relevant to the property is expected to be confined to local domains. For LLPS proteins, the presence of intrinsically disordered regions (IDR)s in the molecule is arguably the most important information; an adaptive GNN model which preferentially shares information within such units and avoids mixing in information from other parts of the molecule may thus enhance the prediction of LLPS proteins. To allow for the accentuation of domain restricted information, we propose a novel graph-based model with the ability to partition each protein graph into task-dependent subgraphs. Such a model is designed not only to achieve better predictive performance but also to be highly interpretable, and thus have the ability to suggest novel biological insights. In addition to achieving state-of-the-art results on the prediction of LLPS proteins from protein structure for both regulator and scaffold proteins, we examine the properties of the graph partitions identified by our model, showing these to be consistent with the annotated IDRs believed to be largely responsible for LLPS. Moreover, our method is designed in a generic way such that it can be applied to other graph-based predictive tasks with minimal adaption.

Predicting Spatially Resolved Gene Expression via Tissue Morphology using Adaptive Spatial GNNs

“…6 can be shown to improve the value of F (i.e. the inverse loss) in expectation (as shown in [3,11]); hence:…”

“…asGNN begins by extracting image features from image patches over capturing spots arranged in an 8-connected spatial graph with an encoder. Adaptive graph refinement is then applied, as introduced in [3]; for each meta-epoch, asGNN samples N s sets of parameters for a linear Meta-feature transformation, that projects the image features to a set of meta-features for each spot, and graph refinement is performed by applying Affinity Propagation (AP) clustering to the meta-features to sparsify the input graph. We use a GTN as the backbone model in asGNN, and train the ensemble of GTNs with image features on the sparsified spatial graphs to predict the gene expression separately.…”

“…6 can be shown to improve the value of F (i.e. the inverse loss) in expectation (as shown in [3, 11]); hence: where Q t = 𝒩 (.| μ t , σ t ) is the variational distribution over W 0 at meta-epoch t , and 𝔼[.] is the expectation operator.…”

“…Spatial gene expression prediction performance comparison of state-of-the-art models ST-Net and HisToGene, basic GTN models with full (8-connected) spatial adjacency graphs, GTN model with sparsified spatial graph by AP clustering (AP-GTN), and the asGNN model, using both morphological and convolutional features from HoVerNet and DenseNet-121 as image features respectively, and performing both holdout and external validation on two data cohorts consisting of 68 and 32 breast cancer tissue sections separately. The basic GTN and AP-GTN models are as outlined in [3]. The best performance in terms of mean square error (MSE) and Pearson correlation coefficient (PCC) are underlined in each column of the table (See complete results in Table S1).…”

“…To overcome the aforementioned issues, we propose an adaptive spatial Graph Neural Network (asGNN) for spatial gene expression prediction, which builds on the smoothing based GNN (SBGNN) framework of [3]. The SBGNN framework was developed to predict liquid-liquid phase separation from 3D molecular graphs, by using graph structure to adaptively refine molecular graphs to remove task irrelevant edges to help perform graph classification.…”