A multiscale computational framework for the development of spines in molluscan shells

Abstract

From mathematical models of growth to computer simulations of pigmentation, the study of shell formation has given rise to an abundant number of models, working at various scales. Yet, attempts to combine those models have remained sparse, due to the challenge of combining categorically different approaches. In this paper, we propose a framework to streamline the process of combining the molecular and tissue scales of shell formation. We choose these levels as a proxy to link the genotype level, which is better described by molecular models, and the phenotype level, which is better described by tissue-level mechanics. We also show how to connect observations on shell populations to the approach, resulting in collections of molecular parameters that may be associated with different populations of real shell specimens. The approach is as follows: we use a Quality-Diversity algorithm, a type of black-box optimization algorithm, to explore the range of concentration profiles emerging as solutions of a molecular model, and that define growth patterns for the mechanical model. At the same time, the mechanical model is simulated over a wide range of growth patterns, resulting in a variety of spine shapes. While time-consuming, these steps only need to be performed once and then function as look-up tables. Actual pictures of shell spines can then be matched against the list of existing spine shapes, yielding a potential growth pattern which, in turn, gives us matching molecular parameters. The framework is modular, such that models can be easily swapped without changing the overall working of the method. As a demonstration of the approach, we solve specific molecular and mechanical models, adapted from available theoretical studies on molluscan shells, and apply the multiscale framework to evaluate the characteristics of spines from three distinct populations of Turbo sazae. Author summaryConnecting genotype to phenotype is a fundamental goal in developmental biology. While many studies examine this link in model organisms for which gene regulatory networks are well known, for non-model organisms, different techniques are required, and multiscale computational modeling offers a promising direction. In this paper, we develop a framework linking molecular-scale interactions to tissue-level growth and mechanics to organism-level characteristics in order to investigate spine formation in T. sazae, a species of mollusc that displays remarkable phenotypic plasticity in spine form. Our analysis uncovers a subtle but statistically significant difference in spine form between shell specimens collected from three different localities in Japan. Moreover, by tracing the difference in form through parametric differences in the multiscale framework, we provide mechanistic insight as to how environmental differences may translate to a change in form. The methodology we present may readily be extended to more detailed modeling of this system, and the conceptual framework is amenable for multiscale analysis in other systems.