Molecular assembly indices of mineral heteropolyanions: some abiotic molecules are as complex as large biomolecules

Abstract

Molecular assembly indices, which measure the number of unique sequential steps theoretically required to construct a three-dimensional molecule from its constituent atomic bonds, have been proposed as potential biosignatures. A central hypothesis of assembly theory is that any molecule with an assembly index ≥15 found in significant local concentrations represents an unambiguous sign of life. We show that abiotic molecule-like heteropolyanions, which assemble in aqueous solution as precursors to some mineral crystals, range in molecular assembly indices from 2 for H₂CO₃ or Si(OH)₄ groups to as large as 21 for the most complex known molecule-like subunits in the rare minerals ewingite and ilmajokite. Therefore, values of molecular assembly indices ≥15 do not represent unambiguous biosignatures.

Keywords: Titan; assembly theory; heteropolyanion; mineral evolution; molecular complexity.

Figure 1.

The crystal structure of the tourmaline group mineral fluor-uvite [14] projected approximately parallel to the c axis (a) and the (Mg₃B₃Si₆O₃₆)³³⁻ island (b). In fluor-uvite: X = Ca, Y = Mg, Z = Al, T = Si.

Figure 2.

The ‘exact’ MA index assembly pathway for the fluor-uvite cluster shown in figure 1b: the basic element of the silicate ring (a); three basic elements that include dimeric silicate unit (b), MgO bond (c) and BO₃ triangle (d); the linkage of the three basic elements shown in (b) into a complex unit (e); the resulting fluor-uvite island centred by additional anion (f; the outlines of the subunits shown in (e) are indicated by the dashed lines). The value of MA index is written below each structure.

Figure 3.

(a) The eudialyte [Na₁₅Ca₆Fe₃Zr₃Si(Si₂₅O₇₃)(O,OH,H₂O)₃(Cl,OH)₂] structure [22] features sodium atoms (yellow spheres), Ca polyhedra (orange), Fe polyhedra (grey), Zr octahedra (dark blue), Si–Nb polyhedra (light blue), Si tetrahedra (red), and Cl atoms (green spheres). Hydrogen atoms are not shown. (b) Eudialyte incorporates at least two different molecule-like sub-assemblies. One example, shown here, includes an edge-sharing six-member ring of calcium octahedra (in orange), with three-member (Si₃O₉) rings (red) above and below and six additional (Si₃O₁₀) three-tetrahedron segments around the periphery to form a [Ca₆(Si₃O₉)₂(Si₃O₁₀)₆]³⁰⁻ cluster. We also focus on the strongly bonded sandwich-like subunit of (ZrO₆) octahedra between two (Si₉O₂₇) rings [(Si₉O₂₇)₂(ZrO₄)₆]⁶⁰⁻, as represented by adjacent red and dark blue polyhedra in (a). (From Johnson & Grice [22], used with permission from the Canadian Journal of Mineralogy and Petrology.)

Figure 4.

(a) The [(As³⁺V^4+,5+₁₂As⁵⁺₆)O₅₁] heteropolyanionic cluster found in several mineral species is a strongly bonded subunit of a more extensive structure. Arsenic polyhedra are shown in red, while vanadium polyhedra are shown in orange [24]. (b) The crystal structure of vanarsite [NaCa₁₂(As³⁺V⁴⁺₂V⁵⁺₁₀As⁵⁺₆O₅₁)₂·78H₂O] reveals weakly bonded interstitial regions with Na–O, Ca–O, and hydrogen bonding between polyanionic clusters [24]. Sodium and calcium atoms are shown in blue; larger and smaller white spheres represent oxygen and hydrogen atoms, respectively. (From Kampf et al. [24], used with permission from the Canadian Journal of Mineralogy and Petrology.)

Figure 5.

Polyhedral representation of the [CuCa₂U⁶⁺₄O₁₂(CO₃)₁₂]¹⁸⁻ polyoxometalate subunit, which is a central feature of the complex structure of paddlewheelite [MgCa₅Cu₂(UO₂)₄(CO₃)₁₂(H₂O)₃₃]. After Olds et al. [19].

Figure 6.

Portions of the complex ewingite structure [Mg₈Ca₈(UO₂)₂₄(CO₃)₃₀O₄(OH)₁₂(H₂O)₁₃₈], showing polyhedral clusters (from [20]). (a,b) Polyhedral representations of the uranyl carbonate cage in two different orientations. (c) Both polyhedral and ball-and-stick representations of the ‘fundamental building unit’ FBU-1, with (d) FBU-2 and (e) FBU-3. Uranyl pentagonal and hexagonal bipyramids are yellow, carbonate triangles are black. Uranium, carbon, and oxygen atoms are shown as yellow, black, and red spheres, respectively. Not shown in this figure are numerous connecting Mg and Ca polyhedra, as well as (OH) groups.

Figure 7.

The complex structure of ilmajokite [Na₁₁KBaCe₂Ti₁₂Si_37.5O₉₄(OH)₃₀·29H₂O] (adapted from [28]) incorporates trigonal prismatic titanosilicate clusters of composition [Ce(Ti₂SiO₁₂)₃(Si₁₇O₃₁)], which is possibly the most complex known molecule-like subunit thus far observed in minerals. Titanium octahedra (blue) and silicon tetrahedra (yellow) form a cage-like structure around a central cerium atom (green sphere). Note that this cluster model does not include numerous apical OH⁻ (i.e. silanol) groups on silicate tetrahedra.