Mechanism of branching morphogenesis inspired by diatom silica formation

Abstract

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.

Keywords: biomineralization; branching morphogenesis; diatom; silica patterning.

Fig. 1.

Diatom cell wall morphogenesis. (A) Schematic of the cell wall (Left) and scanning electron microscopy (SEM) image (Right) of T. pseudonana, highlighting valves (red) and girdle bands (blue). (B, Top) TEM images of valve SDVs showing nascent silica rib networks. The putative outline of the SDV membrane is indicated in purple. (B, Bottom) Schematic showing a diatom cell in cross-section shortly after cytokinesis, highlighting the expanding valve SDVs (purple) in each daughter protoplast (red: valve, blue: girdle bands, yellow: cytoplasm, olive: nucleus; all other organelles are omitted for clarity).

Fig. 2.

Minimal model of rib pattern morphogenesis. (A) Proposed reaction scheme, comprising silica precursor ($S^{\ast }·I$), intermediate ($S^{\ast \ast }·I$), and solidified silica ($S$). Inside the SDV, a constant precursor concentration is converted into solid silica, thereby releasing an inhibitor ($I$) that slows down precursor conversion. (B) Putative biochemical model of silica deposition in the SDV. Polyamine-based inhibitor molecules (gray) form a protective shell around a silicic acid molecule (blue) together constituting the precursor $S^{\ast }·I$, which is incapable of condensation outside the SDV. In the acidic pH of the SDV, the affinity between inhibitor and silicic acid is reduced, thereby exposing some of the silanol groups of the silicic acid. The silicic acid of the precursor then undergoes condensation reactions with the poly-silicic acid of the pre-existing intermediate $S^{\ast \ast }·I$ (magenta). As the condensation reactions proceed toward insoluble silica $S$ (red), more silanol groups disappear, eventually setting free the inhibitor $I$. The rising concentration of free inhibitor molecules would lead to an increasing inhibition of silicic acid condensation by reversible binding of inhibitor molecules to precursor or intermediate, thereby reducing their reactivity. (C) Simulated rib patterns using Eq. 1 (blue), together with the pseudotime course of nascent rib networks from skeletonized TEM images representing subsequent stages of valve development (red). (D) Spacing between neighboring ribs in experimentally observed rib patterns (red, n = 38 valves) pooled over different developmental stages, and in simulated patterns (blue). The mean spacing was used to calibrate unit length in simulations. (E) Diameter of the central annulus observed in experiments (red, n = 23) and simulations (blue). The annulus diameter was used to scale initial conditions in simulations (gray arrow). (F) Number of initial stems of the central annulus in experiments (red, n = 23) and simulations (blue). (G) Number of rib branches $N_b$ (stem branching points excluded) as a function of valve radius $r$ for experimentally observed patterns (red), simulated patterns (blue), as well as the prediction from a simple geometric law (black).

Fig. 3.

Mechanism of rib branching. (A) Simulated time series of a branching rib pattern (showing normalized concentration of solid $S$, see color map), together with region-of-interest (ROI). (B) Normalized concentration profiles of precursor ($S^{\ast }·I$, blue), intermediate ($S^{\ast \ast }·I$, magenta), solid silica ($S$, red), and inhibitor ($I$, black) across the line-scans indicated in gray in the ROIs in panel A. Arrowheads of corresponding color highlight changes in concentration profiles. (C) Control of rib branching by externally imposed inhibitor concentration. Left: “artificial” ribs consisting of imposed inhibitor profiles (gray) at a distance equal to the typical inter-rib spacing from a propagating rib suppress branching of this rib. Right: Increasing the lateral distance of the “artificial” ribs immediately triggers branching of the propagating rib.

Fig. 4.

Modeling other valve silica patterns. (A, Left) TEM image of an aberrant nascent T. pseudonana valve containing two PSSs (red dots). (A, Right) simulated rib patterns in a valve using these two PSS as initial condition. The mean nematic direction for both patterns is shown for comparison below on the Bottom Right of each image (for reference see color wheel on the Top Right). The same parameters as for normal valves shown in Fig. 2 were used. (B) Silica rib pattern in the nascent valve of the pennate diatom A. sibiricum (27) (Left), and simulated pattern using an elongated PSS with a nonsmooth boundary (Right). (C) Silica pattern in the nascent valve of the centric diatom C. cryptica (26) (Left), and simulated pattern using a dynamic switch of parameters (Right).