Reconstructing gene regulatory networks of biological function using differential equations of multilayer perceptrons

Abstract

Background Building biological networks with a certain function is a challenge in systems biology. For the functionality of small (less than ten nodes) biological networks, most methods are implemented by exhausting all possible network topological spaces. This exhaustive approach is difficult to scale to large-scale biological networks. And regulatory relationships are complex and often nonlinear or non-monotonic, which makes inference using linear models challenging. Results In this paper, we propose a multi-layer perceptron-based differential equation method, which operates by training a fully connected neural network (NN) to simulate the transcription rate of genes in traditional differential equations. We verify whether the regulatory network constructed by the NN method can continue to achieve the expected biological function by verifying the degree of overlap between the regulatory network discovered by NN and the regulatory network constructed by the Hill function. And we validate our approach by adapting to noise signals, regulator knockout, and constructing large-scale gene regulatory networks using link-knockout techniques. We apply a real dataset (the mesoderm inducer Xenopus Brachyury expression) to construct the core topology of the gene regulatory network and find that Xbra is only strongly expressed at moderate levels of activin signaling. Conclusion We have demonstrated from the results that this method has the ability to identify the underlying network topology and functional mechanisms, and can also be applied to larger and more complex gene network topologies.

Biologically informed NeuralODEs for genome-wide regulatory dynamics

“…The trained neural network block thus encodes the ODEs governing the dynamics of gene expression, and hence encodes the underlying vector field and GRN. An important advantage of incorporating an ODE solver is that we can predict expression-changes for arbitrarily long time intervals without relying on predefined Euler discretizations, as is required by many other methods [4,12,18]. We further augmented this framework by allowing users to include prior knowledge of gene regulation in a flexible way, which acts as a domain-knowledge-informed regularizer or soft constraint of the NeuralODE [24] (Figure 1).…”

“…In the process of learning transitions between PHOENIX 3 consecutive time points, these "one-step" methods implicitly learn the local derivative (often referred to as "RNA velocity" [16]) dx dt | x=xt m , as an intermediary to estimating f . One significant issue with these approaches is scalability, and studying meaningfully large dynamical systems (ideally those describing the entire genome) has been too costly in terms of runtime and performance loss [4,6,17,18]. This leads to potential issues with generalizability as regulatory processes operate genome-wide and even small perturbations can have wide-ranging regulatory effects.…”

Biologically informed NeuralODEs for genome-wide regulatory dynamics

“…The trained neural network block thus encodes the ODEs governing the dynamics of gene expression and hence encodes the underlying vector field and GRN. An important advantage of incorporating an ODE solver is that we can predict expression changes for arbitrarily long time intervals without relying on predefined Euler discretizations, as is required by many other methods [4, 12, 18]. We further augmented this framework by allowing users to include prior knowledge of gene regulation in a flexible way, which acts as a domain-knowledge-informed regularizer or soft constraint of the NeuralODE [24] ( Figure 1 ).…”

“…In the process of learning transitions between consecutive time points, these “one-step” methods implicitly learn the local derivative (in the context of single cell sequencing often referred to as “RNA velocity” [16]) , as an intermediary to estimating f . One significant issue with these approaches is scalability, and studying meaningfully large dynamical systems (ideally those describing the entire genome) has so far been hindered by a large performance loss and missing interpretability [4, 6, 17, 18]. This leads to potential issues with generalizability as regulatory processes operate genome-wide and even small perturbations can have wide-ranging regulatory effects.…”

Application of multivariate time-series model for high performance computing (HPC) fault prediction

“…In recent years, owing to the increasing demand for high-performance computing (HPC) as well as the scale-up supercomputers and intelligent computing systems, the reliability of large-scale computing systems has been investigated extensively [ 1 – 4 ]. The system operation is complex, and failures occur frequently which are difficult to detect, locate, diagnose, analyze, and debug [ 1 , 5 , 6 ].…”