Agent-based modeling of morphogenetic systems: Advantages and challenges

Abstract

The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction–diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.

A sense of place, many times over ‐ pattern formation and evolution of repetitive morphological structures

“…Pattern formation is an essential feature of multicellular organism development, and variations in patterning mechanisms are thought to contribute substantially to morphological diversification. Consequently, pattern formation has fascinated scientists for centuries and, owing to its amenability to abstraction, has stimulated collaborations between experimental and theoretical biologists . Formation of periodic patterns, in particular, has attracted mathematicians and computational modelers alike .…”

“…Consequently, pattern formation has fascinated scientists for centuries and, owing to its amenability to abstraction, has stimulated collaborations between experimental and theoretical biologists. [14][15][16] Formation of periodic patterns, in particular, has attracted mathematicians and computational modelers alike. 17 Two of the most prominent conceptual frameworks in the field of pattern formation are certainly Wolpert's theory on positional information, and Alan Turing's "reaction-diffusion"-based mechanisms.…”

Impact of force function formulations on the numerical simulation of centre-based models

“…An extensive review of cell-based models for general tissue mechanics can be found in [7]. Additionally, there are several reviews dealing with prominent applications areas, such as tumour growth [16,17] and morphogenetic problems [18,19,20]. In [21] the authors compare five cell-based frameworks (cellular automata, cellular potts, CBM OS and Voronoi variants and vertex models) with respect to four common biological problems: cell sorting, monoclonal conversion, lateral inihibition and morphogen-dependent proliferation.…”

Is evolution predictable? Quantitative genetics under complex genotype‐phenotype maps

“…; Glen et al. ). These models give rise to different morphologies because they start from different initial conditions and include different networks of interactions between genes.…”

“…Most mathematical models of development are based on similar interactions between gene products and cell behaviors (Oster and Alberch 1982;Raspopovic et al 2014;Osterfield et al 2017;Hirashima et al 2017;Glen et al 2019). These models give rise to different morphologies because they start from different initial conditions and include different networks of interactions between genes.…”