Segmentation and Oxygen Diffusion in the Ediacaran Dickinsonia: an Applied Analysis
Total Page:16
File Type:pdf, Size:1020Kb
Journal and Proceedings of the Royal Society of New South Wales, vol. 147, nos. 453 & 454, pp. 107-120. ISSN 0035-9173/14/020107-14 Segmentation and Oxygen Diffusion in the Ediacaran Dickinsonia: an Applied Analysis Brett Gooden1 1Wellington Caves Fossil Studies Centre, 89 Caves Road, Wellington, NSW 2820, Australia E-mail: [email protected] Abstract Many Ediacarans are constructed of multiple parallel segments. Two forms of segment were analysed in the present study, a cylindrical and cuboidal form. The theoretical surface area to volume (A/V) ratio of a structure composed of cylindrical segments is twice that of one composed of cuboidal segments of the same thickness. In this analysis the Ediacaran Dickinsonia was assumed to be a bottom-dwelling marine animal. Individual A/V ratios were calculated for 60 fossil specimens of Dickinsonia of known thickness and diameter assuming either a structure composed of tapering cylinders (conical frusta) or tapering cuboids (square frusta). With increasing body diameter a lower limit of the A/V ratio was approached in both structural forms at a body diameter of approximately 50 millimetres. The segments were assumed to contain solid connective tissue. The theoretical oxygen concentration gradient due to simple diffusion into both forms was calculated and the effect of a collagenous segmental wall on these gradients was determined. The cylindrical form with a collagenous wall was found to be viable within the constraints of this analysis but not the cuboidal form. The findings support the hypothesis that Dickinsonia could have obtained adequate oxygenation by simple diffusion with cylindrical but not cuboidal segments. Keywords Dickinsonia, Ediacarans, segmentation, oxygen diffusion. Introduction The characteristic surface feature of many In 1964 Berkner and Marshall hypothesised species of Ediacaran is a repeated parallel that the trigger for the emergence of segmentation. In 1989 Seilacher suggested metazoans was the appearance of oxygen in that a wide range of Ediacarans including the atmosphere. Since then the estimated Pteridinium and Dickinsonia had a common oxygen content of the Precambrian structural form composed of parallel atmosphere has progressively increased chambers underlying the defining surface (Butterfield, 2009; Canfield, 2007; Shields- segmentation (Figs. 1, 2 and 3). He Zhou, 2011), which raises once more the represented these chambers as essentially vexed question of the relationship between cuboidal in shape. Grazhdankin (2002) the structure and the mode of oxygen drew these chambers as purely box-like or delivery in the Ediacaran biota (Raff, 1970; cuboidal in form with square cross section. Runnegar, 1982). 107 JOURNAL AND PROCEEDINGS OF THE ROYAL SOCIETY OF NEW SOUTH WALES Gooden – Oxygen Diffusion in the Ediacaran Dickinsonia (2009) modelled Pteridinium on the basis of a cuboidal structure in order to analyse the A/V ratio. However illustrative material presented by Jenkins (1992) raised the possibility that the segments in Pteridinium may have been more cylindrical than cuboidal in shape and recent photographic evidence lends further support to this concept (Elliott, 2011). Figure 3: Schematic diagram of Dickinsonia lying on the biomat covering the ocean floor (dark grey shaded area) showing a section through a tapering cylindrical segment and diffusion paths LM of thickness 1.6 mm adjacent to the periphery and NP Figure 1: Fossil of Dickinsonia. Scale in centimetres of thickness 0.8 mm adjacent to the midline. (South Australian Museum, specimen No. P49355). Recently Retallack (2012) has suggested that some Ediacarans including Pteridinium and Dickinsonia were terrestrial organisms similar to lichens. Though the matter is clearly contentious, it would appear that the generally held view at the present time is that the Ediacarans were marine organisms (Switek, 2012) and for the purposes of the present palaeo-physiological analysis the author has assumed that to be the case. The first objective of the present study was to analyse theoretically the A/V ratio of two Figure 2: Fossil of Pteridinium. Scale in hypothetical structural forms, one centimetres (specimen by courtesy of Dr Jim Gehling, composed of purely cylindrical segments South Australian Museum). and the other of purely cuboidal segments. These ratios were then applied to data from The surface area to volume (A/V) ratio is actual fossil specimens of Dickinsonia in critical for the survival of marine organisms which the profile thickness and diameter that are dependent solely on the diffusion of were known. In this way the A/V ratio of oxygen from a watery environment through each specimen could be calculated for either their surface and into their living tissue a purely cylindrical or cuboidal form of (Krogh, 1941; Alexander, 1971). Laflamme segmentation and compared. Finally. the 108 JOURNAL AND PROCEEDINGS OF THE ROYAL SOCIETY OF NEW SOUTH WALES Gooden – Oxygen Diffusion in the Ediacaran Dickinsonia theoretical oxygen concentration gradient in segment exposed to the external cylindrical and cuboidal segments was environment, Vcub is the volume of the calculated and considered in relation to the segment and x is half the length of a side of possible viability of each structural form. the square cross section (Fig. 5). Methods Factors affecting the A/V ratio Ratio of diametrical length to arc length Consider a section composed of n Figure 5: Cylindrical and cuboidal segments. semicircular arcs, then Lateral view. Shaded area indicates surface in contact with external watery environment. l a/l d = n. π. r/ n.2. r = π/2 (1) A/V ratio of a cylindrical segment where la is the total arc length of the section, ld is the total diametrical length of the Consider a hypothetical cylindrical segment section and r is the radius of an arc (Fig. 4). of the length L. Rearranging Eq. 1 la = ld . π/2. 2 Acyl/Vcyl = π 2x L/π x L = 2/x (3) Therefore rolling a section of n arcs flat increases its diametrical length by a factor of where Acyl is the surface area of the 1.57 times (see Fig. 8B). cylindrical segment exposed to the external environment, Vcyl is the volume of the cylindrical segment and x is the radius of the cylinder (Fig. 5). A/V ratio of a hypothetical Dickinsonia constructed of tapering cuboidal segments Figure 4: Portion of a section of n semicircular arcs of radius r. The arc length is π/r and the diametrical length is 2r, hence the ratio of the arc length to the diametrical length is π/2. Figure 6A: Tapering cylindrical (conical frustum) and tapering cuboidal (square frustum) segments. A/V ratio of a cuboidal segment With reference to points A and B, see Fig. 11 and Consider a hypothetical cuboidal segment 12. with square cross section and length L. 2 2 ADtcub/VDtcub = 2 π R /π R 2x = 1/x (4) 2 Acub/Vcub = 4 x L/4 x L = 1/x (2) where ADtcub is the surface area of a tapering where Acub is the surface area (upper plus cuboidal segment (square frustum), (upper lower surfaces only) of the cuboidal plus lower surfaces only) exposed to water, 109 JOURNAL AND PROCEEDINGS OF THE ROYAL SOCIETY OF NEW SOUTH WALES Gooden – Oxygen Diffusion in the Ediacaran Dickinsonia VDtcub is the volume of the segment, R = beginning to the end of the diffusion half the mean overall diameter of the distance ∂x. Dickinsonia and x = half the mean thickness of the Dickinsonia (Fig. 6A and B). The maximum diffusion distance for oxygen in a cuboidal segment of connective tissue s = C02DCT / MCT (Warburg, 1923; Alexander, 1971) (7) where s = half the thickness in millimetres (mm) of a viable cuboidal segment of connective tissue in which oxygen diffuses Figure 6B: Portion of the cross section of a from both upper and lower surfaces, Co = hypothetical Dickinsonia constructed of either the difference in oxygen concentration, cylindrical or cuboidal segments. expressed as a fraction of one atmosphere, from either surface of the segment to half A/V ratio of a hypothetical Dickinsonia its thickness where the oxygen constructed of tapering cylindrical segments concentration falls to zero, DCT = the 2 2 ADtcyl/VDtcyl = (π R) / (π R) x/2 = 2/x (5) diffusion coefficient of oxygen in connective tissue in millilitres (ml) of where ADtcyl is the surface area of tapering oxygen diffusing per cubic centimetre of cylindrical segment (conical frustum) surface area per minute at a pressure exposed to water and VDtcyl is the volume of gradient of one atmosphere per centimetre -4 the segment. R and x as in (4) (Fig. 6A and of tissue thickness (= 0.11 x 10 ), MCT = B). the rate of oxygen consumption of connective tissue in ml of oxygen per gram Note: This hypothetical calculation assumes of tissue per minute (=1/600). that there is no loss in surface area of a cylindrical segment at the junctions between The maximum diffusion distance for oxygen segments (see Discussion). in a cylindrical segment of connective tissue = Factors affecting the rate of diffusion r C0 4DCT / MCT of oxygen (Fenn, 1927; Alexander, 1971) (8) Fick's first law where r = maximum radius of a viable ∂v/∂t = A. D. ∂c/∂x (Prosser, 1961) (6) cylinder of connective tissue in mm, Co = the difference in the oxygen concentration, where ∂v/∂t = volume of oxygen ∂v that expressed as a fraction of one atmosphere, diffuses in time ∂t, A = the area of the from the surface of the cylindrical segment surface across which the oxygen diffuses to its central axis where the oxygen into the tissue , D = the diffusion concentration falls to zero. DCT and MCT as coefficient of oxygen in the tissue, ∂x = the in (7). distance the oxygen diffuses into the tissue and ∂c = the concentration gradient of oxygen in the tissue, that is, the difference in the oxygen concentration from the 110 JOURNAL AND PROCEEDINGS OF THE ROYAL SOCIETY OF NEW SOUTH WALES Gooden – Oxygen Diffusion in the Ediacaran Dickinsonia Source of data for the analysis of connective tissue.