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Nonlinear Variation in Simulated Complex Pattern Development
J. theor. Biol. (1998) 192, 73–79
Nonlinear Variation in Simulated Complex Pattern Development A R. H Department of Earth Sciences, University of Wales Cardiff, P.O. Box 914, Cardiff CF1 3YE, Wales, U.K. (Received on 2 October 1997, Accepted in revised form on 10 December 1997)
Simulated spore walls manufactured from colloidal polystyrene latex, cyclohexane and water demonstrate a range of structure comparable with that occurring within the walls of Selaginella megaspores. Initial investigation of the relationship between the initiation parameters of the self-assembling simulation and its ultimate structure imply a nonlinear relationship. It is suggested that such self-assembly processes result in structure that cannot be directly mapped onto an equivalent genetic coding and that phylogenetic analyses based on self-assembled structure may differ in its conclusions from that based on DNA sequences. 7 1998 Academic Press Limited
Introduction In recent years, consideration of the processes of organismal structural development has occasionally focused on mathematical and simple physical simulations (e.g. Kauffman, 1991, 1993; Walsh & Mann, 1995; Mann & Ozin, 1996; Davis et al., 1997; Ne´de´lec et al., 1997), rather than concentrating wholly upon the traditional examination of biological development in vivo. Self-assembly of components within biological systems forms part of this new concept. However, self-assembled systems commonly rely on a complex set of interactions between components and, as such, they exhibit chaotic behaviour (Gleick, 1988) which may limit prediction. This discussion examines one particular system exhibiting a long fossil history of self-assembly and assesses the likely impact of morphology attractors and their complex boundaries upon the diversity of structure, with implications for modern and fossil species delineation. Spores and pollen [e.g. Fig. 1(a,b)] provide an excellent subject for the study of microscopic morphological change through time as the material from which they are formed (sporopollenin) is resistant to decay in acidic and anaerobic conditions. 0022–5193/98/090073 + 07 $25.00/0/jt970610
Sporopollenin thus retains patterning both on the spore surface and within the spore wall for as much as 400 million years (Taylor, 1995, 1996; Wellman et al., 1998). It is sporopollenin and spore wall structure that illustrate the significance of chaotic and fractal effects in relation to concepts of morphological variation, pattern production and character distribution. The exact chemical structure of sporopollenin (SP) is not known (van Bergen et al., 1995) although something of its composition has been established [it contains only C, H, and O (in empirical proportions of 90, 142 and 36, respectively, for Lilium henryi) Shaw, 1971]. This lack of knowledge results from the same properties that lead to its longevity as a fossil, namely a resistance to disassembly into identifiable (and consistent) fragments. A number of experiments involving saponification (Herminghaus et al., 1988; Schulze Osthoff & Wiermann, 1987; Wehling et al., 1989) have yielded p-coumaric acid indicating an aromatic (phenolic) component. Other analyses (Guilford et al., 1988; Hemsley et al., 1993, 1996a) have demonstrated the presence of chains of saturated carbon, indicating aliphatic, probably fatty acid components. Despite these apparently different interpretations of constituents, there is little doubt 7 1998 Academic Press Limited
74
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F. 1. (a) Pollen of Ipomoea leari and (b) megaspore of Selaginella myosurus demonstrate reticulate patterns with spines and ridges typical of the intricate surface structures of spores and pollen. Internally, the wall of S. myosurus (c) is complex, consisting of an inner layer (1) of random units, (2) a layer of close-packed particles and (3) ridges composed of convoluted laminae. Scale bars (a) 12 mm, (b) 100 mm, (c) 2 mm.
that SP is quite consistent in terms of its basic composition amongst the major groups of plants, and would appear to have been so since its first appearance (Hemsley et al., 1993, 1996a). None the less, variations do seem to occur, and these are chiefly in the proportion of aromatic to aliphatic components. We appear to have therefore, a co-polymer of phenolic and fatty acid units which are most likely present as monomer(s) within the sporangium during spore/pollen wall development.
Simulation of Natural Structure Surface patterning and complex internal structure, as illustrated in Fig. 1, do not appear immediately in the fossil record and many of the earliest spores lack distinguishing features (i.e. are laevigate, Richardson, 1996). The basic unit of SP construction appears to be a laminar micelle (Rowley & Southworth, 1967; Blackmore & Barnes, 1987; Rowley, 1990) which may itself participate in wall construction, or perhaps just
provide a method of transport for SP monomer and aliphatic components. The processes by which laminae are organised to produce complex structures are unclear, but such laminae are within colloidal dimensions, and as such, they may interact in often unexpected ways (Collinson et al., 1993). By analogy, it is probable that both assembly of such laminae, and their organisation into the basis of wall patterning are at least in part self-assembling (e.g. van Blaaderen et al., 1997). The frequency with which certain pattern types arise, i.e. reticulate networks of polygons, support the view that some of this patterning is based on ‘‘non-biological’’ principles of close-packing and space-filling (Scott, 1994). The reliance of the basis of pattern formation on self-organising properties of the components of the system might also have restricted the permitted variation in the molecular structure of SP reflected in some analytical studies (Hemsley et al., 1996a), and may support the view that SP has retained a more primitive composition than other polyphenolics such as lignin. Recent studies of megaspore development in the club moss genus Selaginella have provided an insight into further aspects of self-organisation and assembly in the production of complex pattern. Within this genus the wall structure is composed of variations in the packing system of small particles, generally each around 0.25 mm (Taylor, 1991a). Surprisingly, evidence is available of such particles forming the walls of related megaspores from the late Carboniferous, Triassic, Cretaceous and Tertiary (Kempf, 1971; Hueber, 1982; Taylor & Taylor, 1988; Hemsley, 1992). Particles first appear within the sporangia at around 0.01 mm (Taylor, 1991b) and in some cases already occur in their final arrangement. Growth of particles is rapid and associated with the development of adjacent structures. Filaments of mucopolysaccharide/glycoprotein surround the developing particles (Morbelli & Rowley, 1993) and it is the interaction between these, the particles, and the hydrophilic/hydrophobic reactions within the sporangium that appear to result in the relatively complex wall structure found in these megaspores (Hemsley et al., 1994, 1997). Such interactions are colloidal in nature and may be simulated using a colloidal suspension of tiny polystyrene particles (a latex) (Hemsley et al., 1996b, 1997). These mimic SP in composition and might be expected to show similar colloidal behaviour (Lin et al., 1989). Changes in wall structure are associated with changes in the composition of the construction mixture during development and it is of interest that such chemical changes (which are probably gradual and minor) can result in dramatic changes in ultimate structure,
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a chaotic effect [see organisations 1, 2 and 3 in Fig. 1(c)]. Since it is possible to simulate the Selaginella megaspore wall construction system in vitro (Hemsley et al., 1996b), it is also possible to assess variation in resulting structure on the basis of variation in the initial components. It would seem, as a result of initial observations (Fig. 2), that gradual change in components is not related to a similar gradual change in resulting structure. Instead, the structure produced exhibits stability punctuated by rapid change. Such experiments require further verification since an accurate picture can only result from the detailed examination of the entire spectrum, often involving the variation of up to five different components, even in the simplest models. None the less, this is an interesting (but perhaps predictable) result. Nonlinear Variation in Construction Processes Clearly in vivo, the initial set up of a self-organising system is governed (at least in part) by the genetic code, translation of which gives rise to proteins which regulate the chemistry of the organism. The interplay of genetic input and self-organising systems is poorly understood. However, one aspect is clear; it is highly likely that there are many basic self-organising and self-assembling aspects to biological construction since these represent a potential energy saving (apparently catalysing the development of complexity). It must be advantageous to incorporate as many such systems as possible providing the criteria for their initiation are not too stringent. These systems would run subject to minor environmental fluctuation beyond the control of the organism (those that did not, rapidly becoming eliminated by extinction). Like individual enzymes, once incorporated into a biological process, self-organising systems would become both essential and relatively unalterable. It is probable that the basic structures common to spore and pollen wall construction (e.g. laminae, spines, muri, polygons) comply with these criteria and arose early in the history of SP wall self-assembly. In relation to the genetics of the organism there are further parallels between self-organising systems and enzymes. As with the simulations of spore walls, small changes in genetic coding (e.g. a base pair switch) may have no significant effect (perhaps by coding for the same amino acid) or the change may be massive (a different protein folding pattern causing a change in the operation of the enzyme). This big change/no change texture occurs in the simulations of Selaginella megaspore wall construction. Take, for example, a simple situation in which
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F. 2. Simulated wall components constructed from polystyrene latex by self-assembly [following the method detailed by Hemsley et al. (1996b) and utilizing 80 ml of styrene alone] yield (a) regular close-packed particles and (b) bubble-like cavities. Using 50 ml of styrene and 50 ml of cyclohexane, irregular particles merging to produce strings (c) and regular, but loosely-packed particles (d) can be produced. Under certain conditions (50 ml styrene and 100 ml cyclohexane), cyclohexane droplets act as nuclei upon which, artificial ‘‘walls’’ form, complete with surface patterning [(e) and (f)]. Scale bars (a) 1.5 mm, (b) 20 mm, (c) 5 mm, (d) 3 mm, (e) 5 mm, (f) 10 mm.
Concentration of monomer
wall structure is determined by concentration of styrene and cyclohexane (in the plant, these would be SP monomer and lipid) all in a water base. Different arrangements of polystyrene particles occur depending upon the conditions at the initiation of polymerisation. In the example shown in Fig. 3, compositions and conditions represented by a and a' are different. They result from slightly different genetic codings but despite this, they both give rise to the same ultimate structure (they are within the same domain of the diagram). Examples b and b' may have much more similar genetic codings (they may differ only in a single base pair and thus produce similar concentrations of components) but because this gives rise to initiation points either side of a domain boundary, the resulting structure is different, possibly very different (strings vs. laminae). Examples c and c', although probably closer to each other (genetically) than a and a', may be considered to exhibit the greatest difference in morphological expression since these are separated by two domain boundaries. Each domain may be thought of as the field of effect of an attractor toward which any system with a composition within the boundary is drawn. Significantly, it may not matter for any subsequent stage of development from where within the field of effect of an attractor, the original composition was positioned since what matters is how the new components interact to initiate the next stage of development. It is abundantly clear from this illustration, that assessment of phylogeny based on comparison of the genetic code would differ somewhat from any assessment of relationships (for example) based on morphology and ultrastructure of the spore wall. Close–packed particles
Strings °
b
d
Random a particles °
°
a'
°
Laminae °
100% water
b'
°
c
°
d'
c'
°
100% lipid/90% water
F. 3. Hypothetical representation of a set of morphological domains defined by monomer concentration and proportion of lipid. Each domain contains a morphology attractor which defines structure regardless of the exact composition, providing this lies within its boundary. Letters a to d and a' to d' represent specific concentrations of components. The dotted line d to d' shows a pathway of changing concentration by which an exine such as that shown in Fig. 1(c) might be constructed.
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Consider the likely outcome of such analyses on b, b', c and c'. There are further complications in that composition will usually change as wall development occurs [consider dots from d to d' and compare with Fig. 1(c), development is from bottom to top]. In addition, any in vivo self-assembly system such as this is reliant upon second hand manipulation by proteins/enzymes which have already been through a similar structural compartmentalisation based on similar variability constraints. Conclusions Mechanisms such as that proposed above can be viewed as a series of developmental categorisations, each stage in the process effectively changing the variation that can be exhibited from uniform to increasingly bunched. Thus at each stage, large amounts of potential variation are eliminated from the range of possible outcomes by simple physical and chemical processes. In essence, at each stage of development, chaotic attractors act as ‘‘noise reduction’’ systems, allowing progression to completion of a consistent functioning structure despite differences in initial information/components. Equally, small differences may send development down a totally different series of attractors which also result in a structure, but one rather different to the original. Dichotomies of this form seem likely to give development a robust appearance (Goodwin et al., 1993; Kauffman, 1993; Goodwin, 1994) with associated severe breakdowns of functionality (structure). As a further consideration, although the genetic component is transferred from generation to generation, we know that the genetic code is not alone enough to assemble an organism or probably any of its parts. Some of the system of decoding and assembly is transferred as well. Each genetic code is adapted to its own compliment of attractors and assembly mechanisms and if genetic compliment is not compatible with these, the resulting organism (if viable) will not be the same (Cohen, 1995). In other words, putting genetic code A through self-assembly and attractor series B does not result in organism A, or for that matter, B. Self-assembly mechanisms governed by attractors would clearly have an effect in reiterating similar patterns in a wide range of plant spores and pollen, particularly if the fundamental mechanisms were incorporated early in their evolutionary history. However, this should not necessarily be interpreted as leading to an absence of characteristic pattern with its resulting systematic benefits. Reticulate patterns are widespread, and many spore/pollen types express
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these to some degree. Commonly, they show subtle differences which may often be sufficient to delimit species. Such subtleties result from some stage(s) within wall development exhibiting a more analogue spectrum of variation, one that is free from the activity of attractors. Which stage this is/are is probably dependant upon plant group. In Selaginella, four principle wall structure groups have been recognised (Minaki, 1984; Kovach, 1994) which might imply four different attractor sequences. Variation shown by individual species within these groups appears to result from the amount of SP available to construct the wall (not necessarily related to monomer concentration at the initiation of polymerisation) and this may be a significant analogue input. It is likely that the limited variability exhibited by SP, both now and in the past, the frequency with which similar patterns occur in differing groups of plants, the widespread occurrence of laminae during wall development and the distribution of variation of wall structure within groups are all facets of a largely self-assembling mechanism mediated by chaotic attractors controlling the potential structural variation which may be exhibited. These operate at different levels in development, the most fundamental being that which ensures the initial composition of the monomer/precursor and its immediate environment within the sporangium. The history of SP is one of incorporation of various self-organising processes, autopolymerisation (probably now enzymatic), accumulation, and arrangement of polymer units into structure. It also becomes apparent that if we are to utilise spore and pollen wall structure in the reconstruction of phylogenetic lineages and relationships of extinct plants, it is necessary to understand the relationships between SP chemistry, development and structure in order to refer back to likely genetic relationships in any confident way. Despite these reservations, some progress can be made. Within Selaginella, sufficient is now known with regard to the chemistry of wall development to argue, on the basis of fossil structure, in favour of particular sporangial compositions in extinct species. This provides the potential for the comparative grouping of species of living and extinct Selaginella on the basis of similarity of spore developmental mechanism with that based on morphology. As Fig. 3 illustrates, this at least permits some estimation of phylogenetic relationship (i.e. following d to d', spores with laminate walls are more similar to those with walls composed of close packed particles than they are to those made of random particles). It may soon be possible to apply this reasoning to other spore
groups in which the understanding of similar variation would contribute considerably to their systematics. Self-assembly and self-organising systems are often difficult to isolate and are even more so in the fossil record. However, as here, the process may be extrapolated from the final result and similar examples may be more widespread than we are at present aware. I thank the Royal Society for a University Research Fellowship. I also thank M. E. Collinson, B. Vincent, and P. C. Griffiths for many useful discussions and J. Crawley and V. Williams for photographic assistance.
REFERENCES B, P. F., C, M. E., B, D. E. G., L, J. W., S, A. C., E, R. P. & F, P. (1995). Resistant biomacromolecules in the fossil record. Acta Bot. Neerlandica 44, 319–342. B, A., R, R. & W, P. (1997). Template directed colloidal crystallisation. Nature 385, 321–324. B, S. & B, S. H. (1987). Embryophyte spore walls: origin, development and homologies. Cladistics 3, 185–195. C, J. (1995). Who do we blame for what we are. In: How things are (Brockman, J. & Matson, K., eds) pp. 51–60. London: Widenfield & Nicholson. C, M. E., H, A. R. & T, W. A. (1993). Sporopollenin exhibiting colloidal organization in spore walls. Grana (Suppl.), 1, 31–39. D, S. A., B, S. L., M, N. H. & M, S. (1997). Bacterial templating of ordered macrostructures in silica and silica-surfactant mesophases. Nature 385, 420–423. G, J. (1988). Chaos. Making a New Science. London: Heinemann. 325 pp. G, B. C. (1994). Generative explanations of plant form. In: Shape and Form in Plants and Fungi (Ingram, D. S. & Hudson, A., eds) pp. 3–16. London: Academic Press. G, B. C., K, S. & M, J. D. (1993). Is morphogenesis an intrinsically robust process. J. theor. Biol. 163, 135–144. G, W. J., S, D. M., L, J. & O, S. J. (1988). High resolution solid state 13C NMR. Investigation of sporopollenin from different plant classes. Plant Physiol. 86, 134–136. H, A. R. (1992). Evolution of exine ultrastructure in Palaeozoic lycopod megaspores. Courier Forsch. Senckenberg 147, 93–107. H, A. R., B, P. J., C, W. G. & S, A. C. (1993). The composition of sporopollenin and its use in living and fossil plant systematics. Grana (Suppl.), 1, 2–11. H, A. R., S, A. C., B, P. J. & C, W. G. (1996a). Studies of fossil and modern spore wall biomacromolecules using 13C solid state NMR. Ann. Botany 78, 83–94. H, A. R., J, P. D., C, M. E. & V, B. (1996b). Experimental modelling of exine self-assembly. Bot. J. Linnean Soc. 121, 177–187. H, A. R., G, P. C., V, B. & C, M. E. (1997). Advances in the understanding of complex pattern formation in spore and pollen walls. In: Plant Biomechanics (Jeronimidis, G. & Vincent, J. F. V. eds), pp. 97–103. Reading: Centre for Biomimetics, University of Reading. H, A. R., C, M. E., K, W. L., V, B. & W, T. (1994). The role of self-assembly in biological systems: evidence from iridescent colloidal sporopollenin in
Selaginella megaspore walls. Phil. Trans. R. Soc. Lond. B 345, 163–173. H, S., G, S., A, S. & W, R. (1988). The occurrence of phenols as degradation products of natural sporopollenin—a comparison with ‘‘synthetic sporopollenin’’. Z. Naturforsch. 43c, 491–500. H, F. M. (1982). Megaspores and a polynomorph from the Lower Potomac Group in Virginia. Smithsonian Contr. Palaeobiol. 49, 1–69. K, S. A. (1991). Antichaos and adaptation. Sci. Am. 265, 64–70. K, S. A. (1993). The Origins of Order. Oxford: Oxford University Press. K, E. K. (1971). Electron microscopy of Mesozoic megaspores from Denmark. Grana 11, 151–163. K, W. L. (1994). A review of Mesozoic megaspore ultrastructure in: Ultrastructure of Fossil Spores and Pollen (Kurmann, M. H. & Doyle, J. A. eds) pp. 23–37. Kew, London: Royal Botanic Gardens. L, M. Y., L, H. M., W, D. A., B, R. C., K, R. & M, P. (1989). Universality in colloidal aggregation. Nature 339, 360–362. M, S. & O, G. A. (1996). Synthesis of inorganic materials with complex form. Nature 382, 313–318. M, M. (1984). Macrospore morphology and taxonomy of Selaginella. Pollen Spores 26, 421–480. M, M. A. & R, J. R. (1993). Megaspore development in Selaginella. 1—‘‘Wicks’’, their presence, ultrastructure, and presumed function. Sexual Plant Reproduction 6, 98–107. N´´, F. J., S, T., M, A. C. & L, S. (1997). Self-organization of microtubules and motors. Nature 389, 305–308. R, J. B. (1996). Lower and Middle Palaeozoic records of terrestrial palynomorphs. In: Palynology: Principles and Applications, Vol. II (Jansonius, J. & McGregor, D. C., eds), pp. 555–574. American Association of Stratigraphic Palynologists Foundation. R, J. R. (1990). The fundamental structure of the pollen exine. Plant Systematics Evol. 5 (Suppl.), 13–29.
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R, J. R. & S, D. (1967). Deposition of sporopollenin on lamellae of unit membrane dimensions. Nature 18, 703–704. S O, K. & W, R. (1987). Phenols as integrated compounds of sporopollenin from Pinus pollen. J. Plant Physiol. 131, 5–15. S, R. J. (1994). Pollen exine—the sporopollenin enigma and the physics of pattern. In: Molecular and Cellular Aspects of Plant Reproduction (Scott, R. J. & Stead, M. A. eds), pp. 49–81. Cambridge: Cambridge University Press. S, G. (1971). The chemistry of sporopollenin. In: Sporopollenin (Brooks, J., Grant, P. R., Muir, M., van Gizel, P. & Shaw, G. eds), pp. 305–348. London: Academic Press. T, W. A. (1991a). Megaspore wall ultrastructure in Selaginella. Pollen Spores 31, 251–288. T, W. A. (1991b). Ultrastructural analysis of sporoderm development in megaspores of Selaginella galeotti (Lycophyta). Plant Systematics Evol. 174, 171–182. T, W. A. (1995). Ultrastructure of Tetrahedraletes medinensis (Strother and Traverse) Wellman and Richardson, from the Upper Ordovician of sourthern Ohio. Rev. Palaeobot. Palynol. 85, 183–187. T, W. A. (1996). Ultrastructure of Lower Paleozoic dyads from southern Ohio. Rev. Palaeobot. Palynol. 92, 269–279. T, W. A. & T, T. N. (1988). Ultrastructural analysis of selected Cretaceous megaspores from Argentina. J. Micropalaeontology 7, 73–87. W, D. & M, S. (1995). Fabrication of hollow porous shells of calcium carbonate from self-organizing media. Nature 377, 320–323. W, K., N, C., B, J. J., W, M. T. M. & W, R. (1989). p-coumaric acid—a monomer in the sporopollenin skeleton. Planta 179, 376–380. W, C. H., E, D. & A, L. (1998). Ultrastructure of laevigate hilate cryptospores in sporangia and spore masses from the Upper Silurian and Lower Devonian of the Welsh Borderland. Phil. Trans. R. Soc. Lond. B.
Nonlinear Variation in Simulated Complex Pattern Development A R. H Department of Earth Sciences, University of Wales Cardiff, P.O. Box 914, Cardiff CF1 3YE, Wales, U.K. (Received on 2 October 1997, Accepted in revised form on 10 December 1997)
Simulated spore walls manufactured from colloidal polystyrene latex, cyclohexane and water demonstrate a range of structure comparable with that occurring within the walls of Selaginella megaspores. Initial investigation of the relationship between the initiation parameters of the self-assembling simulation and its ultimate structure imply a nonlinear relationship. It is suggested that such self-assembly processes result in structure that cannot be directly mapped onto an equivalent genetic coding and that phylogenetic analyses based on self-assembled structure may differ in its conclusions from that based on DNA sequences. 7 1998 Academic Press Limited
Introduction In recent years, consideration of the processes of organismal structural development has occasionally focused on mathematical and simple physical simulations (e.g. Kauffman, 1991, 1993; Walsh & Mann, 1995; Mann & Ozin, 1996; Davis et al., 1997; Ne´de´lec et al., 1997), rather than concentrating wholly upon the traditional examination of biological development in vivo. Self-assembly of components within biological systems forms part of this new concept. However, self-assembled systems commonly rely on a complex set of interactions between components and, as such, they exhibit chaotic behaviour (Gleick, 1988) which may limit prediction. This discussion examines one particular system exhibiting a long fossil history of self-assembly and assesses the likely impact of morphology attractors and their complex boundaries upon the diversity of structure, with implications for modern and fossil species delineation. Spores and pollen [e.g. Fig. 1(a,b)] provide an excellent subject for the study of microscopic morphological change through time as the material from which they are formed (sporopollenin) is resistant to decay in acidic and anaerobic conditions. 0022–5193/98/090073 + 07 $25.00/0/jt970610
Sporopollenin thus retains patterning both on the spore surface and within the spore wall for as much as 400 million years (Taylor, 1995, 1996; Wellman et al., 1998). It is sporopollenin and spore wall structure that illustrate the significance of chaotic and fractal effects in relation to concepts of morphological variation, pattern production and character distribution. The exact chemical structure of sporopollenin (SP) is not known (van Bergen et al., 1995) although something of its composition has been established [it contains only C, H, and O (in empirical proportions of 90, 142 and 36, respectively, for Lilium henryi) Shaw, 1971]. This lack of knowledge results from the same properties that lead to its longevity as a fossil, namely a resistance to disassembly into identifiable (and consistent) fragments. A number of experiments involving saponification (Herminghaus et al., 1988; Schulze Osthoff & Wiermann, 1987; Wehling et al., 1989) have yielded p-coumaric acid indicating an aromatic (phenolic) component. Other analyses (Guilford et al., 1988; Hemsley et al., 1993, 1996a) have demonstrated the presence of chains of saturated carbon, indicating aliphatic, probably fatty acid components. Despite these apparently different interpretations of constituents, there is little doubt 7 1998 Academic Press Limited
74
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F. 1. (a) Pollen of Ipomoea leari and (b) megaspore of Selaginella myosurus demonstrate reticulate patterns with spines and ridges typical of the intricate surface structures of spores and pollen. Internally, the wall of S. myosurus (c) is complex, consisting of an inner layer (1) of random units, (2) a layer of close-packed particles and (3) ridges composed of convoluted laminae. Scale bars (a) 12 mm, (b) 100 mm, (c) 2 mm.
that SP is quite consistent in terms of its basic composition amongst the major groups of plants, and would appear to have been so since its first appearance (Hemsley et al., 1993, 1996a). None the less, variations do seem to occur, and these are chiefly in the proportion of aromatic to aliphatic components. We appear to have therefore, a co-polymer of phenolic and fatty acid units which are most likely present as monomer(s) within the sporangium during spore/pollen wall development.
Simulation of Natural Structure Surface patterning and complex internal structure, as illustrated in Fig. 1, do not appear immediately in the fossil record and many of the earliest spores lack distinguishing features (i.e. are laevigate, Richardson, 1996). The basic unit of SP construction appears to be a laminar micelle (Rowley & Southworth, 1967; Blackmore & Barnes, 1987; Rowley, 1990) which may itself participate in wall construction, or perhaps just
provide a method of transport for SP monomer and aliphatic components. The processes by which laminae are organised to produce complex structures are unclear, but such laminae are within colloidal dimensions, and as such, they may interact in often unexpected ways (Collinson et al., 1993). By analogy, it is probable that both assembly of such laminae, and their organisation into the basis of wall patterning are at least in part self-assembling (e.g. van Blaaderen et al., 1997). The frequency with which certain pattern types arise, i.e. reticulate networks of polygons, support the view that some of this patterning is based on ‘‘non-biological’’ principles of close-packing and space-filling (Scott, 1994). The reliance of the basis of pattern formation on self-organising properties of the components of the system might also have restricted the permitted variation in the molecular structure of SP reflected in some analytical studies (Hemsley et al., 1996a), and may support the view that SP has retained a more primitive composition than other polyphenolics such as lignin. Recent studies of megaspore development in the club moss genus Selaginella have provided an insight into further aspects of self-organisation and assembly in the production of complex pattern. Within this genus the wall structure is composed of variations in the packing system of small particles, generally each around 0.25 mm (Taylor, 1991a). Surprisingly, evidence is available of such particles forming the walls of related megaspores from the late Carboniferous, Triassic, Cretaceous and Tertiary (Kempf, 1971; Hueber, 1982; Taylor & Taylor, 1988; Hemsley, 1992). Particles first appear within the sporangia at around 0.01 mm (Taylor, 1991b) and in some cases already occur in their final arrangement. Growth of particles is rapid and associated with the development of adjacent structures. Filaments of mucopolysaccharide/glycoprotein surround the developing particles (Morbelli & Rowley, 1993) and it is the interaction between these, the particles, and the hydrophilic/hydrophobic reactions within the sporangium that appear to result in the relatively complex wall structure found in these megaspores (Hemsley et al., 1994, 1997). Such interactions are colloidal in nature and may be simulated using a colloidal suspension of tiny polystyrene particles (a latex) (Hemsley et al., 1996b, 1997). These mimic SP in composition and might be expected to show similar colloidal behaviour (Lin et al., 1989). Changes in wall structure are associated with changes in the composition of the construction mixture during development and it is of interest that such chemical changes (which are probably gradual and minor) can result in dramatic changes in ultimate structure,
75
a chaotic effect [see organisations 1, 2 and 3 in Fig. 1(c)]. Since it is possible to simulate the Selaginella megaspore wall construction system in vitro (Hemsley et al., 1996b), it is also possible to assess variation in resulting structure on the basis of variation in the initial components. It would seem, as a result of initial observations (Fig. 2), that gradual change in components is not related to a similar gradual change in resulting structure. Instead, the structure produced exhibits stability punctuated by rapid change. Such experiments require further verification since an accurate picture can only result from the detailed examination of the entire spectrum, often involving the variation of up to five different components, even in the simplest models. None the less, this is an interesting (but perhaps predictable) result. Nonlinear Variation in Construction Processes Clearly in vivo, the initial set up of a self-organising system is governed (at least in part) by the genetic code, translation of which gives rise to proteins which regulate the chemistry of the organism. The interplay of genetic input and self-organising systems is poorly understood. However, one aspect is clear; it is highly likely that there are many basic self-organising and self-assembling aspects to biological construction since these represent a potential energy saving (apparently catalysing the development of complexity). It must be advantageous to incorporate as many such systems as possible providing the criteria for their initiation are not too stringent. These systems would run subject to minor environmental fluctuation beyond the control of the organism (those that did not, rapidly becoming eliminated by extinction). Like individual enzymes, once incorporated into a biological process, self-organising systems would become both essential and relatively unalterable. It is probable that the basic structures common to spore and pollen wall construction (e.g. laminae, spines, muri, polygons) comply with these criteria and arose early in the history of SP wall self-assembly. In relation to the genetics of the organism there are further parallels between self-organising systems and enzymes. As with the simulations of spore walls, small changes in genetic coding (e.g. a base pair switch) may have no significant effect (perhaps by coding for the same amino acid) or the change may be massive (a different protein folding pattern causing a change in the operation of the enzyme). This big change/no change texture occurs in the simulations of Selaginella megaspore wall construction. Take, for example, a simple situation in which
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F. 2. Simulated wall components constructed from polystyrene latex by self-assembly [following the method detailed by Hemsley et al. (1996b) and utilizing 80 ml of styrene alone] yield (a) regular close-packed particles and (b) bubble-like cavities. Using 50 ml of styrene and 50 ml of cyclohexane, irregular particles merging to produce strings (c) and regular, but loosely-packed particles (d) can be produced. Under certain conditions (50 ml styrene and 100 ml cyclohexane), cyclohexane droplets act as nuclei upon which, artificial ‘‘walls’’ form, complete with surface patterning [(e) and (f)]. Scale bars (a) 1.5 mm, (b) 20 mm, (c) 5 mm, (d) 3 mm, (e) 5 mm, (f) 10 mm.
Concentration of monomer
wall structure is determined by concentration of styrene and cyclohexane (in the plant, these would be SP monomer and lipid) all in a water base. Different arrangements of polystyrene particles occur depending upon the conditions at the initiation of polymerisation. In the example shown in Fig. 3, compositions and conditions represented by a and a' are different. They result from slightly different genetic codings but despite this, they both give rise to the same ultimate structure (they are within the same domain of the diagram). Examples b and b' may have much more similar genetic codings (they may differ only in a single base pair and thus produce similar concentrations of components) but because this gives rise to initiation points either side of a domain boundary, the resulting structure is different, possibly very different (strings vs. laminae). Examples c and c', although probably closer to each other (genetically) than a and a', may be considered to exhibit the greatest difference in morphological expression since these are separated by two domain boundaries. Each domain may be thought of as the field of effect of an attractor toward which any system with a composition within the boundary is drawn. Significantly, it may not matter for any subsequent stage of development from where within the field of effect of an attractor, the original composition was positioned since what matters is how the new components interact to initiate the next stage of development. It is abundantly clear from this illustration, that assessment of phylogeny based on comparison of the genetic code would differ somewhat from any assessment of relationships (for example) based on morphology and ultrastructure of the spore wall. Close–packed particles
Strings °
b
d
Random a particles °
°
a'
°
Laminae °
100% water
b'
°
c
°
d'
c'
°
100% lipid/90% water
F. 3. Hypothetical representation of a set of morphological domains defined by monomer concentration and proportion of lipid. Each domain contains a morphology attractor which defines structure regardless of the exact composition, providing this lies within its boundary. Letters a to d and a' to d' represent specific concentrations of components. The dotted line d to d' shows a pathway of changing concentration by which an exine such as that shown in Fig. 1(c) might be constructed.
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Consider the likely outcome of such analyses on b, b', c and c'. There are further complications in that composition will usually change as wall development occurs [consider dots from d to d' and compare with Fig. 1(c), development is from bottom to top]. In addition, any in vivo self-assembly system such as this is reliant upon second hand manipulation by proteins/enzymes which have already been through a similar structural compartmentalisation based on similar variability constraints. Conclusions Mechanisms such as that proposed above can be viewed as a series of developmental categorisations, each stage in the process effectively changing the variation that can be exhibited from uniform to increasingly bunched. Thus at each stage, large amounts of potential variation are eliminated from the range of possible outcomes by simple physical and chemical processes. In essence, at each stage of development, chaotic attractors act as ‘‘noise reduction’’ systems, allowing progression to completion of a consistent functioning structure despite differences in initial information/components. Equally, small differences may send development down a totally different series of attractors which also result in a structure, but one rather different to the original. Dichotomies of this form seem likely to give development a robust appearance (Goodwin et al., 1993; Kauffman, 1993; Goodwin, 1994) with associated severe breakdowns of functionality (structure). As a further consideration, although the genetic component is transferred from generation to generation, we know that the genetic code is not alone enough to assemble an organism or probably any of its parts. Some of the system of decoding and assembly is transferred as well. Each genetic code is adapted to its own compliment of attractors and assembly mechanisms and if genetic compliment is not compatible with these, the resulting organism (if viable) will not be the same (Cohen, 1995). In other words, putting genetic code A through self-assembly and attractor series B does not result in organism A, or for that matter, B. Self-assembly mechanisms governed by attractors would clearly have an effect in reiterating similar patterns in a wide range of plant spores and pollen, particularly if the fundamental mechanisms were incorporated early in their evolutionary history. However, this should not necessarily be interpreted as leading to an absence of characteristic pattern with its resulting systematic benefits. Reticulate patterns are widespread, and many spore/pollen types express
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these to some degree. Commonly, they show subtle differences which may often be sufficient to delimit species. Such subtleties result from some stage(s) within wall development exhibiting a more analogue spectrum of variation, one that is free from the activity of attractors. Which stage this is/are is probably dependant upon plant group. In Selaginella, four principle wall structure groups have been recognised (Minaki, 1984; Kovach, 1994) which might imply four different attractor sequences. Variation shown by individual species within these groups appears to result from the amount of SP available to construct the wall (not necessarily related to monomer concentration at the initiation of polymerisation) and this may be a significant analogue input. It is likely that the limited variability exhibited by SP, both now and in the past, the frequency with which similar patterns occur in differing groups of plants, the widespread occurrence of laminae during wall development and the distribution of variation of wall structure within groups are all facets of a largely self-assembling mechanism mediated by chaotic attractors controlling the potential structural variation which may be exhibited. These operate at different levels in development, the most fundamental being that which ensures the initial composition of the monomer/precursor and its immediate environment within the sporangium. The history of SP is one of incorporation of various self-organising processes, autopolymerisation (probably now enzymatic), accumulation, and arrangement of polymer units into structure. It also becomes apparent that if we are to utilise spore and pollen wall structure in the reconstruction of phylogenetic lineages and relationships of extinct plants, it is necessary to understand the relationships between SP chemistry, development and structure in order to refer back to likely genetic relationships in any confident way. Despite these reservations, some progress can be made. Within Selaginella, sufficient is now known with regard to the chemistry of wall development to argue, on the basis of fossil structure, in favour of particular sporangial compositions in extinct species. This provides the potential for the comparative grouping of species of living and extinct Selaginella on the basis of similarity of spore developmental mechanism with that based on morphology. As Fig. 3 illustrates, this at least permits some estimation of phylogenetic relationship (i.e. following d to d', spores with laminate walls are more similar to those with walls composed of close packed particles than they are to those made of random particles). It may soon be possible to apply this reasoning to other spore
groups in which the understanding of similar variation would contribute considerably to their systematics. Self-assembly and self-organising systems are often difficult to isolate and are even more so in the fossil record. However, as here, the process may be extrapolated from the final result and similar examples may be more widespread than we are at present aware. I thank the Royal Society for a University Research Fellowship. I also thank M. E. Collinson, B. Vincent, and P. C. Griffiths for many useful discussions and J. Crawley and V. Williams for photographic assistance.
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