Turing Instability-Driven Biofabrication of Branching Tissue Structures: A Dynamic Simulation and Analysis Based on the Reaction⁻Diffusion Mechanism †

Mechanism of branching morphogenesis inspired by diatom silica formation

The silica-based cell walls of diatoms are prime examples of genetically controlled, species-specific mineral architectures. The physical principles underlying morphogenesis of their hierarchically structured silica patterns are not understood, yet such insight could indicate novel routes toward synthesizing functional inorganic materials. Recent advances in imaging nascent diatom silica allow rationalizing possible mechanisms of their pattern formation. Here, we combine theory and experiments on the model diatom Thalassiosira pseudonana to put forward a minimal model of branched rib patterns-a fundamental feature of the silica cell wall. We quantitatively recapitulate the time course of rib pattern morphogenesis by accounting for silica biochemistry with autocatalytic formation of diffusible silica precursors followed by conversion into solid silica. We propose that silica deposition releases an inhibitor that slows down up-stream precursor conversion, thereby implementing a self-replicating reaction-diffusion system different from a classical Turing mechanism. The proposed mechanism highlights the role of geometrical cues for guided self-organization, rationalizing the instructive role for the single initial pattern seed known as the primary silicification site. The mechanism of branching morphogenesis that we characterize here is possibly generic and may apply also in other biological systems.

Instability mechanisms of repelling peak solutions in a multi-variable activator-inhibitor system

We study the linear stability properties of spatially localized single- and multi-peak states generated in a subcritical Turing bifurcation in the Meinhardt model of branching. In one spatial dimension, these states are organized in a foliated snaking structure owing to peak-peak repulsion but are shown to be all linearly unstable, with the number of unstable modes increasing with the number of peaks present. Despite this, in two spatial dimensions, direct numerical simulations reveal the presence of stable single- and multi-spot states whose properties depend on the repulsion from nearby spots as well as the shape of the domain and the boundary conditions imposed thereon. Front propagation is shown to trigger the growth of new spots while destabilizing others. The results indicate that multi-variable models may support new types of behavior that are absent from typical two-variable models.

A review of regulated self-organizing approaches for tissue regeneration

Tissue and organ regeneration is the dynamic process by which a population of cells rearranges into a specific form with specific functions. Traditional tissue regeneration utilizes tissue grafting, cell implantation, and structured scaffolds to achieve clinical efficacy. However, tissue grafting methods face a shortage of donor tissue, while cell implantation may involve leakage of the implanted cells without a supportive 3D matrix. Cell migration, proliferation, and differentiation in structured scaffolds may disorganize and frustrate the artificially pre-designed structures, and sometimes involve immunogenic reactions. To overcome this limitation, the self-organizing properties and innate regenerative capability of tissue/organism formation in the absence of guidance by structured scaffolds has been investigated. This review emphasizes the growing subfield of the regulated self-organizing approach for neotissue formation and describes advances in the subfield using diverse, cutting-edge, inter-disciplinarity technologies. We cohesively summarize the directed self-organization of cells in the micro-engineered cell-ECM system and 3D/4D cell printing. Mathematical modeling of cellular self-organization is also discussed for providing rational guidance to intractable problems in tissue regeneration. It is envisioned that future self-organization approaches integrating biomathematics, micro-nano engineering, and gene circuits developed from synthetic biology will continue to work in concert with self-organizing morphogenesis to enhance rational control during self-organizing in tissue and organ regeneration.

The nonlinear initiation of side-branching by activator-inhibitor-substrate (Turing) morphogenesis

An understanding of the underlying mechanism of side-branching is paramount in controlling and/or therapeutically treating mammalian organs, such as lungs, kidneys, and glands. Motivated by an activator-inhibitor-substrate approach that is conjectured to dominate the initiation of side-branching in a pulmonary vascular pattern, I demonstrate a distinct transverse front instability in which new fingers grow out of an oscillatory breakup dynamics at the front line without any typical length scale. These two features are attributed to unstable peak solutions in 1D that subcritically emanate from Turing bifurcation and that exhibit repulsive interactions. The results are based on a bifurcation analysis and numerical simulations and provide a potential strategy toward also developing a framework of side-branching for other biological systems, such as plant roots and cellular protrusions.

Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach

We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework. It is proposed that some of these processes satisfy an optimal transport of informational entropy condition. This optimality condition allows us to derive an equation of the Monge–Ampère type for the information flow that accounts for the branching structure of neurons via the linearization of this equation. Based on this fact, we discuss a version of Murray’s law in this context.