A Novel Hybrid Logic-ODE Modeling Approach to Overcome Knowledge Gaps

Abstract

Mathematical modeling allows using different formalisms to describe, investigate, and understand biological processes. However, despite the advent of high-throughput experimental techniques, quantitative information is still a challenge when looking for data to calibrate model parameters. Furthermore, quantitative formalisms must cope with stiffness and tractability problems, more so if used to describe multicellular systems. On the other hand, qualitative models may lack the proper granularity to describe the underlying kinetic processes. We propose a hybrid modeling approach that integrates ordinary differential equations and logical formalism to describe distinct biological layers and their communication. We focused on a multicellular system as a case study by applying the hybrid formalism to the well-known Delta-Notch signaling pathway. We used a differential equation model to describe the intracellular pathways while the cell–cell interactions were defined by logic rules. The hybrid approach herein employed allows us to combine the pros of different modeling techniques by overcoming the lack of quantitative information with a qualitative description that discretizes activation and inhibition processes, thus avoiding complexity.

Logic-Based Modeling of Inflammatory Macrophage Crosstalk with Glomerular Endothelial Cells in Diabetic Kidney Disease

“…We were interested in predicting continuous signaling dynamics with limited data and mechanistic details. Previously, a hybrid modeling method has utilized the benefits of an ODE model to explain pathway interactions, while a qualitative logic-based model was used to define cell-cell interactions within a tissue environment (34). We applied a modeling technique that combines continuous dynamic ODE models with qualitative LBMs (30), which is termed a logic-based ordinary differential equations (LBODEs) model.…”

Hybrid modelling of biological systems: current progress and future prospects

“…Selvaggio et al [ 79 ] proposed an HBO method for hierarchical models with different abstraction levels, in which they use ODEs to represent the bottom layer in a fine-grained manner and Boolean logic to represent the regulative interactions of higher layers in a coarse-grained fashion. They also applied their approach to simulating the pattern development of the Delta-Notch pathway.…”

“…Compared with [ 77 ], the approaches of both [ 78 ] and [ 79 ] do not require recasting to a common description of ODEs and thus re-parameterization. These approaches are a good attempt to combine the pros of different modelling formalisms by overcoming the lack of quantitative information with a qualitative description that models activation and inhibition processes.…”