bioRxiv2020
Cancer is a disease of aberrant cellular signaling and tumor-specific aberrations in signaling systems determine the aggressiveness of a cancer and response to therapy. Identifying such abnormal signaling pathways causing a patients cancer would enable more patient-specific and effective treatments. We interpret the cellular signaling system as a causal graphical model, where it is known that genomic alterations cause changes in the functions of signaling proteins, and the propagation of signals among proteins eventually leads to changed gene expression. To represent such a system, we developed a deep learning model, referred to as a redundant input neural network (RINN), with a redundant input architecture and an L1 regularized objective function to find causal relationships between input, latent, and output variables--when it is known a priori that input variables cause output variables. We hypothesize that training RINN on cancer omics data will enable us to map the functional impacts of genomic alterations to latent variables in a deep learning model, allowing us to discover the hierarchical causal relationships between variables perturbed by different genomic alterations. Importantly, the direct connections between all input and all latent variables in RINN make the latent variables partially interpretable, as they can be easily mapped to input space. We show that gene expression can be predicted from genomic alterations with reasonable accuracy when measured as the area under ROC curves (AUROCs). We also show that RINN is able to discover the shared functional impact of genomic alterations that perturb a common cancer signaling pathway, especially relationships in the PI3K, Nrf2, and TGF{beta} pathways, including some causal relationships. However, despite high regularization, the learned causal relationships were somewhat too dense to be easily and directly interpretable as causal graphs. We suggest promising future directions for RINN, including differential regularization, autoencoder pretrained representations, and constrained evolutionary strategies. Author summaryA modified deep learning model (RINN with L1 regularization) can be used to capture cancer signaling pathway relationships within its hidden variables and weights. We found that genomic alterations impacting the same known cancer pathway had interactions with a similar set of RINN latent variables. Having genomic alterations (input variables) directly connected to all latent variables in the RINN model allowed us to label the latent variables with a set of genomic alterations, making the latent variables partially interpretable. With this labeling, we were able to visualize RINNs as causal graphs and capture at least some of the causal relationships in known cancer signaling pathways. However, the graphs learned by RINN were somewhat too dense (despite large amounts of regularization) to compare directly to known cancer signaling pathways. We also found that differential expression can be predicted from genomic alterations by a RINN with reasonably high AUROCs, especially considering the very high dimensionality of the prediction task relative to the number of input variables and instances in the dataset. These are encouraging results for the future of deep learning models trained on cancer genomic data.