Turing pattern design principles and their robustness

Turing patterns have morphed from mathematical curiosities into highly desirable targets for synthetic biology. For a long time, their biological significance was sometimes disputed but there is now ample evidence for their involvement in processes ranging from skin pigmentation to digit and limb formation. While their role in developmental biology is now firmly established, their synthetic design has so far proved challenging. Here, we review recent large-scale mathematical analyses that have attempted to narrow down potential design principles. We consider different aspects of robustness of these models and outline why this perspective will be helpful in the search for synthetic Turing-patterning systems. We conclude by considering robustness in the context of developmental modelling more generally. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Interfacial Adsorption of Monoclonal Antibody COE-3 at the Solid/Water Interface

Spectroscopic ellipsometry (SE) and neutron reflection (NR) data for the adsorption of a monoclonal antibody (mAb, termed COE-3, pI 8.44) at the bare SiO₂/water interface are compared here to the simulations based on Derjaguin-Landau-Verwey-Overbeek theory. COE-3 adsorption was characterized by an initial rapid increase in the surface-adsorbed amount (Γ) followed by a plateau. Only the initial rate of the increase in Γ was strongly correlated with the bulk concentration (0.002-0.2 mg/mL), with Γ at the plateau being about 2.2 mg/m² (pH 5.5). Simulations captured COE-3 adsorption at equilibrium most accurately, the point at which the outgoing flux of molecules within the adsorbed plane matched the adsorption flux. Increasing the buffer pH from 5.5 to 9 increased Γ at equilibrium to ∼3 mg/m² (0.02 mg/mL COE-3), revealing a dominant role for lateral repulsion between adsorbed mAb molecules. In contrast, increasing the buffer ionic strength (pH 6) reduced Γ, which was captured by simulations accounting for electrostatic screening by ions, in addition to mAb/SiO₂ attractive forces and lateral repulsion. NR data at the same bulk concentrations corroborated the SE data, albeit with slightly higher Γ due to longer adsorption times for data acquisition; for example, at pH 9, Γ was 3.6 mg/m² (0.02 mg/mL COE-3), equivalent to a relatively high volume fraction of 0.5. An adsorbed monolayer with a thickness of 50-52 Å was consistently determined by NR, corresponding to the short axial lengths of fragment antigen-binding and fragment crystallization and implying minimal structural perturbation. Thus, the simulations enabled a mechanistic interpretation of the experimental data of mAb adsorption at the SiO₂/water interface.

The design principles of discrete turing patterning systems

The formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic parameters, raising the question of how they may be adopted and realised in naturally evolved systems. The vast majority of mathematical studies of Turing patterns have used continuous models specified in terms of partial differential equations. Here, we complement this work by studying Turing patterns using discrete cellular automata models. We perform a large-scale study on all possible two-species networks and find the same Turing pattern producing networks as in the continuous framework. In contrast to continuous models, however, we find these Turing pattern topologies to be substantially more robust to changes in the parameters of the model. We also find that diffusion-driven instabilities are substantially weaker predictors for Turing patterns in our discrete modelling framework in comparison to the continuous case, in the sense that the presence of an instability does not guarantee a pattern emerging in simulations. We show that a more refined criterion constitutes a stronger predictor. The similarity of the results for the two modelling frameworks suggests a deeper underlying principle of Turing mechanisms in nature. Together with the larger robustness in the discrete case this suggests that Turing patterns may be more robust than previously thought.