NCAE: data-driven representations using a deep network-coherent DNA methylation autoencoder identify robust disease and risk factor signatures.

Precision medicine relies on the identification of robust disease and risk factor signatures from omics data. However, current knowledge-driven approaches may overlook novel or unexpected phenomena due to the inherent biases in biological knowledge. In this study, we present a data-driven signature discovery workflow for DNA methylation analysis utilizing network-coherent autoencoders (NCAEs) with biologically relevant latent embeddings. First, we explored the architecture space of autoencoders trained on a large-scale pan-tissue compendium (n = 75 272) of human epigenome-wide association studies. We observed the emergence of co-localized patterns in the deep autoencoder latent space representations that corresponded to biological network modules. We determined the NCAE configuration with the strongest co-localization and centrality signals in the human protein interactome. Leveraging the NCAE embeddings, we then trained interpretable deep neural networks for risk factor (aging, smoking) and disease (systemic lupus erythematosus) prediction and classification tasks. Remarkably, our NCAE embedding-based models outperformed existing predictors, revealing novel DNA methylation signatures enriched in gene sets and pathways associated with the studied condition in each case. Our data-driven biomarker discovery workflow provides a generally applicable pipeline to capture relevant risk factor and disease information. By surpassing the limitations of knowledge-driven methods, our approach enhances the understanding of complex epigenetic processes, facilitating the development of more effective diagnostic and therapeutic strategies.

Deriving disease modules from the compressed transcriptional space embedded in a deep autoencoder.

Disease modules in molecular interaction maps have been useful for characterizing diseases. Yet biological networks, that commonly define such modules are incomplete and biased toward some well-studied disease genes. Here we ask whether disease-relevant modules of genes can be discovered without prior knowledge of a biological network, instead training a deep autoencoder from large transcriptional data. We hypothesize that modules could be discovered within the autoencoder representations. We find a statistically significant enrichment of genome-wide association studies (GWAS) relevant genes in the last layer, and to a successively lesser degree in the middle and first layers respectively. In contrast, we find an opposite gradient where a modular protein-protein interaction signal is strongest in the first layer, but then vanishing smoothly deeper in the network. We conclude that a data-driven discovery approach is sufficient to discover groups of disease-related genes.

Optimized evolution of networks for principal eigenvector localization.

Network science is increasingly being developed to get new insights about behavior and properties of complex systems represented in terms of nodes and interactions. One useful approach is investigating the localization properties of eigenvectors having diverse applications including disease-spreading phenomena in underlying networks. In this work, we evolve an initial random network with an edge rewiring optimization technique considering the inverse participation ratio as a fitness function. The evolution process yields a network having a localized principal eigenvector. We analyze various properties of the optimized networks and those obtained at the intermediate stage. Our investigations reveal the existence of a few special structural features of such optimized networks, for instance, the presence of a set of edges which are necessary for localization, and rewiring only one of them leads to complete delocalization of the principal eigenvector. Furthermore, we report that principal eigenvector localization is not a consequence of changes in a single network property and, preferably, requires the collective influence of various distinct structural as well as spectral features.

Optimization of synchronizability in multiplex networks by rewiring one layer.

The mathematical framework of multiplex networks has been increasingly realized as a more suitable framework for modeling real-world complex systems. In this work, we investigate the optimization of synchronizability in multiplex networks by evolving only one layer while keeping other layers fixed. Our main finding is to show the conditions under which the efficiency of convergence to the most optimal structure is almost as good as the case where both layers are rewired during an optimization process. In particular, interlayer coupling strength responsible for the integration between the layers turns out to be a crucial factor governing the efficiency of optimization even for the cases when the layer going through the evolution has nodes interacting much more weakly than those in the fixed layer. Additionally, we investigate the dependency of synchronizability on the rewiring probability which governs the network structure from a regular lattice to the random networks. The efficiency of the optimization process preceding evolution driven by the optimization process is maximum when the fixed layer has regular architecture, whereas the optimized network is more synchronizable for the fixed layer having the rewiring probability lying between the small-world transition and the random structure.

Evolution of correlated multiplexity through stability maximization.

Investigating the relation between various structural patterns found in real-world networks and the stability of underlying systems is crucial to understand the importance and evolutionary origin of such patterns. We evolve multiplex networks, comprising antisymmetric couplings in one layer depicting predator-prey relationship and symmetric couplings in the other depicting mutualistic (or competitive) relationship, based on stability maximization through the largest eigenvalue of the corresponding adjacency matrices. We find that there is an emergence of the correlated multiplexity between the mirror nodes as the evolution progresses. Importantly, evolved values of the correlated multiplexity exhibit a dependence on the interlayer coupling strength. Additionally, the interlayer coupling strength governs the evolution of the disassortativity property in the individual layers. We provide analytical understanding to these findings by considering starlike networks representing both the layers. The framework discussed here is useful for understanding principles governing the stability as well as the importance of various patterns in the underlying networks of real-world systems ranging from the brain to ecology which consist of multiple types of interaction behavior.

Interplay of mutation and disassortativity.

Despite disassortativity being commonly observed in many biological networks, our current understanding of its evolutionary origin is inadequate. Motivated by the occurrence of mutations during an evolutionary time span that results in changes in the behavior of interactions, we demonstrate that if we maximize the stability of the underlying system, the genetic algorithm leads to the evolution of a disassortative structure. The mutation probability governs the degree of saturation of the disassortativity coefficient, and this reveals the origin of the wide range of disassortativity values found in real systems. We analytically verify these results for star networks, and by considering various values for the antisymmetric couplings, we find a regime in which scale-free networks are more stable than the corresponding random networks.

Emergence of clustering: role of inhibition.

Though biological and artificial complex systems having inhibitory connections exhibit a high degree of clustering in their interaction pattern, the evolutionary origin of clustering in such systems remains a challenging problem. Using genetic algorithm we demonstrate that inhibition is required in the evolution of clique structure from primary random architecture, in which the fitness function is assigned based on the largest eigenvalue. Further, the distribution of triads over nodes of the network evolved from mixed connections reveals a negative correlation with its degree providing insight into origin of this trend observed in real networks.

Extreme-value statistics of brain networks: importance of balanced condition.

Despite the key role played by inhibitory-excitatory couplings in the functioning of brain networks, the impact of a balanced condition on the stability properties of underlying networks remains largely unknown. We investigate properties of the largest eigenvalues of networks having such couplings, and find that they follow completely different statistics when in the balanced situation. Based on numerical simulations, we demonstrate that the transition from Weibull to Fréchet via the Gumbel distribution can be controlled by the variance of the column sum of the adjacency matrix, which depends monotonically on the denseness of the underlying network. As a balanced condition is imposed, the largest real part of the eigenvalue emulates a transition to the generalized extreme-value statistics, independent of the inhibitory connection probability. Furthermore, the transition to the Weibull statistics and the small-world transition occur at the same rewiring probability, reflecting a more stable system.

Classification of HIV-1 sequences using profile Hidden Markov Models.

Accurate classification of HIV-1 subtypes is essential for studying the dynamic spatial distribution pattern of HIV-1 subtypes and also for developing effective methods of treatment that can be targeted to attack specific subtypes. We propose a classification method based on profile Hidden Markov Model that can accurately identify an unknown strain. We show that a standard method that relies on the construction of a positive training set only, to capture unique features associated with a particular subtype, can accurately classify sequences belonging to all subtypes except B and D. We point out the drawbacks of the standard method; namely, an arbitrary choice of threshold to distinguish between true positives and true negatives, and the inability to discriminate between closely related subtypes. We then propose an improved classification method based on construction of a positive as well as a negative training set to improve discriminating ability between closely related subtypes like B and D. Finally, we show how the improved method can be used to accurately determine the subtype composition of Common Recombinant Forms of the virus that are made up of two or more subtypes. Our method provides a simple and highly accurate alternative to other classification methods and will be useful in accurately annotating newly sequenced HIV-1 strains.