Inferring structural and dynamical properties of gene networks from data with deep learning

Abstract

The reconstruction of gene regulatory networks (GRNs) from data is vital in systems biology. Although different approaches have been proposed to infer causality from data, some challenges remain, such as how to accurately infer the direction and type of interactions, how to deal with complex network involving multiple feedbacks, as well as how to infer causality between variables from real-world data, especially single cell data. Here, we tackle these problems by deep neural networks (DNNs). The underlying regulatory network for different systems (gene regulations, ecology, diseases, development) can be successfully reconstructed from trained DNN models. We show that DNN is superior to existing approaches including Boolean network, Random Forest and partial cross mapping for network inference. Further, by interrogating the ensemble DNN model trained from single cell data from dynamical system perspective, we are able to unravel complex cell fate dynamics during preimplantation development. We also propose a data-driven approach to quantify the energy landscape for gene regulatory systems, by combining DNN with the partial self-consistent mean field approximation (PSCA) approach. We anticipate the proposed method can be applied to other fields to decipher the underlying dynamical mechanisms of systems from data.

Revealing neural dynamical structure of C. elegans with deep learning

“…To reveal how the transition patterns rise from the dynamical structure, we focus on the transition area, where an attractor is positioned, and two limit cycles intersect ( Figure 4 D). This attractor shapes steady-state probabilities with a Gaussian distribution, 17 , 32 creating a potential basin in the landscape. Simultaneously, limit cycles offer potential escape routes.…”

“…We first estimate the diffusion coefficient D , i.e., the half of using the MLE: W hen the system is a multistable system with only attractors, previous works 17 , 27 , 28 , 32 , 48 have shown that can be formulated as a combination of Gaussian distributions: and the mean and covariance of each Gaussian distribution can be calculated by the convergent values from the ODEs, where the matrix A is the Jacobi of F, i.e., . When it comes to the periodic oscillation systems with limit cycles, we need to introduce a new method for calculating landscape.…”

“…When applying the original Guassian-like approaches 17 to periodic oscillatory systems, we face a challenge where the covariance matrix may diverge to infinity. Hence, a novel and efficient method is required for computing the landscape of such periodic oscillatory systems.…”

“…We assume that in the steady state, there exists a local neighborhood where the flux (including Gaussian noise) entering or leaving maintains a balance at any point on the boundary of this neighborhood. As a result, the correlation matrix of the low-rank part (excluding the direction of ) can be obtained through a similar procedure as original approaches 17 , 32 by excluding the direction of from the matrix. Let’s denote as the unit vector in the tangent direction, and as a orthonormal basis.…”

“… 12 , 13 , 14 , 15 , 16 The utility of deep learning becomes particularly evident when dealing with the complexities arising from high-dimensional data and complex forms of dynamic forces. Inspired by previous studies on deep-learning neural networks (DNN) and neural dynamics modeling, 17 , 18 , 19 we seek to perform DNN to reconstruct the neural network of C. elegans . Kato et al.…”