[Paper Review] Toward deciphering developmental patterning with deep neural network.

Jingxiang Shen, Feng Liu+1 more|arXiv (Cornell University)|Jul 23, 2018

Gene Regulatory Network Analysis56 references3 citations

TL;DR

This paper proposes a deep neural network (DNN)-enhanced differential equation model to decode complex developmental patterning in *Drosophila* gap genes. By replacing the traditional fixed-form synthesis term with a DNN, the model achieves perfect fitting to wild-type and mutant patterns and generates accurate predictions, while also enabling interpretable mapping to a simplified regulatory network consistent with biological knowledge.

ABSTRACT

Abstract Dynamics of complex biological systems is driven by intricate networks, the current knowledge of which are often incomplete. The traditional systems biology modeling usually implements an ad hoc fixed set of differential equations with predefined function forms. Such an approach often suffers from overfitting or underfitting and thus inadequate predictive power, especially when dealing with systems of high complexity. This problem could be overcome by deep neuron network (DNN). Choosing pattern formation of the gap genes in Drosophila early embryogenesis as an example, we established a differential equation model whose synthesis term is expressed as a DNN. The model yields perfect fitting and impressively accurate predictions on mutant patterns. We further mapped the trained DNN into a simplified conventional regulation network, which is consistent with the existing body of knowledge. The DNN model could lay a foundation of “in-silico-embryo”, which can regenerate a great variety of interesting phenomena, and on which one can perform all kinds of perturbations to discover underlying mechanisms. This approach can be readily applied to a variety of complex biological systems.

Motivation & Objective

• To overcome the limitations of traditional systems biology models that rely on fixed, predefined differential equation forms.
• To improve predictive power in modeling high-complexity biological systems prone to overfitting or underfitting.
• To develop a data-driven yet interpretable model for *Drosophila* early embryogenesis gap gene dynamics.
• To map the trained DNN into a simplified regulatory network that aligns with existing biological knowledge.
• To establish a foundation for an 'in-silico-embryo' capable of simulating diverse developmental perturbations.

Proposed method

• Formulating a differential equation model where the synthesis term of gap gene expression is parameterized by a deep neural network (DNN).
• Training the DNN on wild-type and mutant gap gene expression data to learn the underlying regulatory dynamics.
• Using backpropagation and gradient descent to optimize the DNN parameters for fitting observed spatial expression patterns.
• Applying interpretability techniques to map the trained DNN into a simplified, conventional gene regulatory network.
• Validating the model’s predictive power by simulating mutant phenotypes not used during training.
• Ensuring consistency of the derived regulatory network with known biological interactions and regulatory logic.

Experimental results

Research questions

• RQ1 Can a DNN-based model outperform traditional fixed-form differential equation models in capturing complex developmental patterning?
• RQ2 To what extent can a DNN-embedded model predict mutant gap gene patterns not seen during training?
• RQ3 Can the trained DNN be meaningfully interpreted as a biologically plausible gene regulatory network?
• RQ4 Does the model enable the creation of a predictive in-silico embryo for systems-level developmental studies?
• RQ5 How does the DNN model handle high-dimensional, nonlinear regulatory interactions in early embryogenesis?

Key findings

• The DNN-enhanced model achieved perfect fitting to wild-type gap gene expression patterns across multiple time points.
• The model demonstrated impressively accurate predictions on experimentally observed mutant patterns, including those not used in training.
• The trained DNN could be successfully mapped into a simplified regulatory network that aligns with the established biological knowledge of gap gene interactions.
• The resulting model supports the feasibility of building an 'in-silico-embryo' capable of simulating diverse developmental perturbations.
• The approach provides a generalizable framework applicable to other complex biological systems beyond *Drosophila* embryogenesis.
• The model's predictive accuracy and interpretability suggest a significant advance over conventional systems biology modeling approaches.