Prospects for Declarative Mathematical Modeling of Complex Biological Systems

TL;DR

This paper explores the use of declarative modeling languages with formal semantics for complex biological systems, enabling advanced analysis, model reduction, and multiscale integration to better understand developmental processes.

Contribution

It introduces a formal operator algebra semantics for declarative biological models, along with semantics-preserving transformations and a hierarchical organization framework.

Findings

Defined semantics for reaction-like dynamics in declarative models

Developed semantics-preserving model reduction methods

Outlined a meta-hierarchy for organizing declarative models

Abstract

Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation program, in a general-purpose programming language. Examples of such computations on models include model analysis, relatively general-purpose model-reduction maps, and the initial phases of model implementation, all of which should preserve or approximate the mathematical semantics of a complex biological model. The potential advantages are particularly relevant in the case of developmental modeling, wherein complex spatial structures exhibit dynamics at molecular, cellular, and organogenic levels to relate genotype to multicellular phenotype. Multiscale modeling can benefit from both the expressive power of declarative modeling languages and the application of model reduction methods to link models across scale. Based on previous work, here we define declarative modeling of complex biological systems by defining the operator algebra semantics of an increasingly powerful series of declarative modeling languages including reaction-like dynamics of parameterized and extended objects; we define semantics-preserving implementation and semantics-approximating model reduction transformations; and we outline a "meta-hierarchy" for organizing declarative models and the mathematical methods that can fruitfully manipulate them.