The physical basis of mollusk shell chiral coiling

Possible roles of Wnt in the shell growth of the pond snail Lymnaea stagnalis

Although the mechanisms of molluscan shell growth have been studied using mathematical models, little is known about the molecular basis underpinning shell morphogenesis. Here, we performed Wnt activation experiments to elucidate the potential roles of Wnt signaling in the shell growth of Lymnaea stagnalis. In general, we observed following three types of shell malformations in both dose- and developmental stage-dependent manners: (i) cap-shaped shell, (ii) cap-shaped shell with hydropic soft tissues, and (iii) compressed shell with a smaller number of coiling. We analyzed the morphologies of these malformed shells using the growing tube model, revealing that the compressed malformations show significantly larger values for T (torsion), with no significant changes in the values for the remaining parameters E (expansion) and C (curvature). We also found that cap-shaped malformations have significantly larger values for E, suggesting that the effects of BIO on shell formation may change during growth. Since the changes in T and/or E parameter values can greatly alter the shell morphologies from a planispiral or a cap-shaped one to various three-dimensional helices, changes in shell developmental processes possibly controlled by Wnt signaling may account for at least a part of the evolution of diverse shell forms in molluscs.

Assembly of short amphiphilic peptoids into nanohelices with controllable supramolecular chirality

A long-standing challenge in bioinspired materials is to design and synthesize synthetic materials that mimic the sophisticated structures and functions of natural biomaterials, such as helical protein assemblies that are important in biological systems. Herein, we report the formation of a series of nanohelices from a type of well-developed protein-mimetics called peptoids. We demonstrate that nanohelix structures and supramolecular chirality can be well-controlled through the side-chain chemistry. Specifically, the ionic effects on peptoids from varying the polar side-chain groups result in the formation of either single helical fiber or hierarchically stacked helical bundles. We also demonstrate that the supramolecular chirality of assembled peptoid helices can be controlled by modifying assembling peptoids with a single chiral amino acid side chain. Computational simulations and theoretical modeling predict that minimizing exposure of hydrophobic domains within a twisted helical form presents the most thermodynamically favorable packing of these amphiphilic peptoids and suggests a key role for both polar and hydrophobic domains on nanohelix formation. Our findings establish a platform to design and synthesize chiral functional materials using sequence-defined synthetic polymers.

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

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.

Theoretical study of time-resolved photoelectron circular dichroism in the photodissociation of a chiral molecule

Photoelectron circular dichroism (PECD), the forward-backward asymmetry of the photoelectron angular distribution when ionizing randomly oriented chiral molecules with circularly polarized light, is an established method to investigate chiral properties of molecules in their electronic ground state. Here, we develop a computational strategy for predicting time-resolved PECD (TRPECD) of chemical reactions and demonstrate the method on the photodissociation of 1-iodo-2-methylbutane. Our approach combines multi-configurational quantum-chemical calculations of the relevant potential-energy surfaces of the neutral and singly ionized molecule with ab initio molecular-dynamics (AIMD) calculations. The PECD parameters along the AIMD trajectories are calculated with the aid of electron-molecule scattering calculations based on the Schwinger variational principle implemented in ePolyScat. Our calculations have been performed for two probe wavelengths (133 and 160 nm) accessible through low-order harmonic generation in gases. Our results show that the TRPECD is a highly sensitive probe of photochemical reaction dynamics. Most interestingly, the TRPECD is found to change sign multiple times along the photodissociation coordinate, in agreement with recent experiments on CHBrFI [Svoboda et al., "Femtosecond photoelectron circular dichroism of chemical reactions," Sci. Adv. 8, eabq2811 (2022)]. The computational protocol introduced in the present work is general and readily applicable to other chiral photochemical processes.

Biological light-weight materials: The endoskeletons of cephalopod mollusks

Structural biological hard tissues fulfill diverse tasks: protection, defence, locomotion, structural support, reinforcement, buoyancy. The cephalopod mollusk Spirula spirula has a planspiral, endogastrically coiled, chambered, endoskeleton consisting of the main elements: shell-wall, septum, adapical-ridge, siphuncular-tube. The cephalopod mollusk Sepia officinalis has an oval, flattened, layered-cellular endoskeleton, formed of the main elements: dorsal-shield, wall/pillar, septum, siphuncular-zone. Both endoskeletons are light-weight buoyancy devices that enable transit through marine environments: vertical (S. spirula), horizontal (S. officinalis). Each skeletal element of the phragmocones has a specific morphology, component structure and organization. The conjunction of the different structural and compositional characteristics renders the evolved nature of the endoskeletons and facilitates for Spirula frequent migration from deep to shallow water and for Sepia coverage over large horizontal distances, without damage of the buoyancy device. Based on Electron-Backscatter-Diffraction (EBSD) measurements and TEM, FE-SEM, laser-confocal-microscopy imaging we highlight for each skeletal element of the endoskeleton its specific mineral/biopolymer hybrid nature and constituent arrangement. We demonstrate that a variety of crystal morphologies and biopolymer assemblies are needed for enabling the endoskeleton to act as a buoyancy device. We show that all organic components of the endoskeletons have the structure of cholesteric-liquid-crystals and indicate which feature of the skeletal element yields the necessary mechanical property to enable the endoskeleton to fulfill its function. We juxtapose structural, microstructural, texture characteristics and benefits of coiled and planar endoskeletons and discuss how morphometry tunes structural biomaterial function. Both mollusks use their endoskeleton for buoyancy regulation, live and move, however, in distinct marine environments.

Fractal-like geometry as an evolutionary response to predation?

Fractal-like, intricate morphologies are known to exhibit beneficial mechanical behavior in various engineering and technological domains. The evolution of fractal-like, internal walls of ammonoid cephalopod shells represent one of the most clear evolutionary trends toward complexity in biology, but the driver behind their iterative evolution has remained unanswered since the first hypotheses introduced in the early 1800s. We show a clear correlation between the fractal-like morphology and structural stability. Using linear and nonlinear computational mechanical simulations, we demonstrate that the increase in the complexity of septal geometry leads to a substantial increase in the mechanical stability of the entire shell. We hypothesize that the observed tendency is a driving force toward the evolution of the higher complexity of ammonoid septa, providing the animals with superior structural support and protection against predation. Resolving the adaptational value of this unique trait is vital to fully comprehend the intricate evolutionary trends between morphology, ecological shifts, and mass extinctions through Earth's history.

A Mathematical Model for Mollusc Shells Based on Parametric Surfaces and the Construction of Theoretical Morphospaces

In this study, we propose a mathematical model based on parametric surfaces for the shell morphology of the phylum Mollusca. Since David Raup’s pioneering works, many mathematical models have been proposed for different contexts to describe general shell morphology; however, there has been a gap in the practicality of models that allow the estimation of their parameter values in real specimens. Our model collects ideas from previous pioneering studies; it rests on the equation of the logarithmic spiral, uses a fixed coordinate system (coiling axis), and defines the position of the generating curve with a local moving system using the Frenet frame. However, it improves upon previous models by applying apex formation, rotations, and substantially different parameter definitions. Furthermore, the most conspicuous improvement is the development of a simple and standardized methodology to obtain the six theoretical parameters from shell images from different mollusc classes and to generate useful theoretical morphospaces. The model was applied to reproduce the shape of real mollusc-shell specimens from Gasteropoda, Cephaloda and Bivalvia, which represent important classes in geological time. We propose a specific methodology to obtain the parameters in four morphological groups: helicoidal, planispiral, conic, and valve-like shells, thereby demonstrating that the model offers an adequate representation of real shells. Finally, possible improvements to the model are discussed along with further work. Based on the above considerations, the capacity of the model to allow the construction of theoretical morphospaces, the methodology to estimate parameters and from the comparison between several existing models for shells, we believe that our model can contribute to future research on the development, diversity and evolutionary processes that generated the diversity in mollusc shells.