Multilinear Ordinary Differential Equations for Inferring Gene Regulatory Network from Multimodal Functional Data

• 成果类型: Article; Early Access
• 署名作者: Zhang, Heng; Liu, Zhi-Ping
• 署名单位: Shandong University; Shandong University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2697050
• 发表日期: 2026-08-07
• 关键词: Gene regulatory network; Inferability; Multilinear operator; Ordinary differential equation; Multimodal functional data; parameter-estimation; expression; systems

摘要

The acquisition of multimodal functional data, wherein functional data from multiple modalities are concurrently recorded for a single subject, has emerged as a promising strategy for constructing more accurate gene regulatory networks (GRNs). While ordinary differential equation (ODE) methods have been extensively used for modeling GRNs, the existing methods are primarily tailored for single-modal data. In this article, we introduce a multilinear ODE (ML-ODE) framework that integrates ODE-based dynamic modeling with multilinear operator mappings, presenting a versatile and potent approach for modeling GRNs using multimodal functional data. For each modality, we furnish a basis, within which the data and operators are represented, thereby transforming the problem into an algebraic optimization task that facilitates the inference of the GRNs. Regarding the inverse problem of deducing the structure of an ODE system from observed functional data, we formally define the concept of inferability for ODE system and demonstrate that the proposed ML-ODE is inferable under certain reasonable conditions. Ultimately, the model's properties are validated through simulations, and we apply the ML-ODE framework to construct a GRN for real multimodal functional data derived from hematopoietic stem cells, showcasing that the resultant network is biologically significant, as corroborated by pertinent literature. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.