# Frame-based mathematical models – a tool for the study of molecular genetic systems

## TL;DR

This paper explores frame-based mathematical models for studying molecular genetic systems, showing how small biological units can be combined to create complex models.

## Contribution

The paper introduces a method for generating frame-based models using domain-specific languages and graphical standards.

## Key findings

- Frame-based models can be used to identify new behaviors by adding a single gene.
- The repressilator model demonstrates how reactant concentrations can control model behavior.
- The approach allows for modeling biological systems at multiple levels, from cells to communities.

## Abstract

This paper reviews existing approaches for reconstructing frame-based mathematical models of molecular genetic systems from the level of genetic synthesis to models of metabolic networks. A frame-based mathematical model is a model in which the following terms are specified: formal structure, type of mathematical model for a particular biochemical process, reactants and their roles. Typically, such models are generated automatically on the basis of description of biological processes in terms of domain-specific languages. For molecular genetic systems, these languages use constructions familiar to a wide range of biologists in the form of a list of biochemical reactions. They rely on the concepts of elementary subsystems, where complex models are assembled from small block units (“frames”). In this paper, we have shown an example with the generation of a classical repressilator model consisting of three genes that mutually inhibit each other’s synthesis. We have given it in three different versions of the graphic standard, its characteristic mathematical interpretation and variants of its numerical calculation. We have shown that even at the level of frame models it is possible to identify qualitatively new behaviour of the model through the introduction of just one gene into the model structure. This change provides a way to control the modes of behaviour of the model through changing the concentrations of reactants. The frame-based approach opens the way to generate models of cells, tissues, organs, organisms and communities through frame-based model generation tools that specify structure, roles of modelled reactants using domain-specific languages and graphical methods of model specification.