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

Abstract

Four-dimensional (4D) biofabrication techniques aim to dynamically produce and control three-dimensional (3D) biological structures that would transform their shapes or functionalities with time, when a stimulus is imposed or cell post-printing self-assembly occurs. The evolution of 3D branching patterns via self-assembly of cells is critical for the 4D biofabrication of artificial organs or tissues with branched geometry. However, it is still unclear how the formation and evolution of these branching patterns are biologically encoded. Here, we study the biofabrication of lung branching structures utilizing a simulation model based on Turing instability that raises a dynamic reaction–diffusion (RD) process of the biomolecules and cells. The simulation model incorporates partial differential equations of four variables, describing the tempo-spatial distribution of the variables in 3D over time. The simulation results present the formation and evolution process of 3D branching patterns over time and also interpret both the behaviors of side-branching and tip-splitting as the stalk grows and the fabrication style under an external concentration gradient of morphogen, through 3D visualization. This provides a theoretical framework for rationally guiding the 4D biofabrication of lung airway grafts via cellular self-organization, which would potentially reduce the complexity of future experimental research and number of trials.

The control of lung branching morphogenesis

“…The potential of Turing mechanisms to explain lung branching morphogenesis was recognised early on, and several other Turing mechanisms have been proposed to explain lung branching morphogenesis (Guo et al, 2014;Meinhardt, 1976;Warburton et al, 2003;Xu et al, 2017;Zhu and Yang, 2018). Together, these mathematical studies demonstrate that important hallmarks of branching morphogenesis can be recapitulated by Turing mechanisms.…”

Mechanism of branching morphogenesis inspired by diatom silica formation

“…Our minimal model is conceptually simpler than a class of reaction-diffusion models proposed previously to address branching morphogenesis [56]- [58] as it comprises a linear reaction chain with autocatalytic enhancement and a single negative feedback loop through the inhibitor. The model obeys mass balance, and makes explicit how transient dynamics builds solid-like structures.…”

Is order creation through disorder in additive manufacturing possible?

“…Micro-engineering approaches for the construction of functional tissues are being developed with a better understanding of morphogenetic processes and in the ability to direct them in vitro without being able to build robust organs. Numerous challenges remain to associate micro-engineering, morphogenesis and cellular self-organization (Martin et al, 2019;Zhu & Yang, 2018).…”

“…Turing structures corresponding to spatially periodic variations in the concentrations of chemical species could be localized by localized energy inputs and/or by molecular diffusions in an artificially bounded space (Szalai et al, 2012). Apart from a 3D bio-manufacturing process (Zhu & Yang, 2018), we found only a limited number of scientific references for the exploitation of this idea of realizing "pixelized" polymers with specific properties.…”