A Natural O-Ring Optimizes the Dispersal of Fungal Spores
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A natural O-ring optimizes the dispersal of fungal spores Joerg A. Fritz1, Agnese Seminara1,3, Marcus Roper4, Anne Pringle2 rsif.royalsocietypublishing.org and Michael P. Brenner1 1School of Engineering and Applied Sciences, Kavli Institute for Bionano Science and Technology, and 2Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA 3CNRS – Laboratoire de physique de la matie`re condense´e, UMR 7336, Parc Valrose, 06108 Nice, France 4Department of Mathematics, University of California, Los Angeles 90095, CA, USA Research The forcibly ejected spores of ascomycete fungi must penetrate several milli- Cite this article: Fritz JA, Seminara A, Roper metres of nearly still air surrounding sporocarps to reach dispersive airflows, M, Pringle A, Brenner MP. 2013 A natural and escape is facilitated when a spore is launched with large velocity. To O-ring optimizes the dispersal of fungal spores. launch, the spores of thousands of species are ejected through an apical ring, a small elastic pore. The startling diversity of apical ring and spore J R Soc Interface 10: 20130187. shapes and dimensions make them favoured characters for both species http://dx.doi.org/10.1098/rsif.2013.0187 descriptions and the subsequent inference of relationships among species. However, the physical constraints shaping this diversity and the adaptive benefits of specific morphologies are not understood. Here, we develop an elastohydrodynamic theory of the spore’s ejection through the apical ring Received: 26 February 2013 and demonstrate that to avoid enormous energy losses during spore ejection, Accepted: 28 May 2013 the four principal morphological dimensions of spore and apical ring must cluster within a nonlinear one-dimensional subspace. We test this prediction using morphological data for 45 fungal species from two different classes and 18 families. Our sampling encompasses multiple loss and gain events and potentially independent origins of this spore ejection mechanism. Subject Areas: Although the individual dimensions of the spore and apical ring are only biomechanics, biophysics, biomathematics weakly correlated with each other, they collapse into the predicted subspace with high accuracy. The launch velocity appears to be within 2 per cent of Keywords: the optimum for over 90 per cent of all forcibly ejected species. Although spore dispersal, fungi, morphological diversity, the morphological diversity of apical rings and spores appears startlingly fluid dynamics, elastohydrodynamics, diverse, a simple principle can be used to organize it. optimization 1. Introduction Author for correspondence: Spore dispersal is the primary determining factor for the range and distribution Joerg A. Fritz of fungi in nature. The importance of understanding this process in detail has been highlighted in recent years by an unprecedented number of fungal dis- e-mail: [email protected] eases, which have caused some of the most severe die-offs and extinctions ever witnessed in wild species [1] and are increasingly considered a worldwide threat to food security [2]. An effective control of these emerging diseases is possible only if we can understand and control how they propagate. The defining feature of the largest fungal phylum, Ascomycota, is the ascus, a fluid-filled sac from which spores are ejected. Ejection is powered by a build-up of osmotic pressure [3], which forces spores through a ring or hole at the tip of the ascus, after a critical pressure is reached [4]. Ascus and spore morphologies are highly variable and have been an essential element of species descriptions for more than 200 years [5,6]. Since spores are the primary agents of dispersal, these morphologies also play a critical role in the ascomycete life cycle: most fungi grow on highly heterogeneous landscapes, and to persist a fungus must move between disjoint patches of habitat [7], thus effective dispersal is critical Electronic supplementary material is available to the fitness of an individual. at http://dx.doi.org/10.1098/rsif.2013.0187 or To reach dispersive air currents, spores must be launched with enough speed to cross the stagnant air layer around the fungus, the fluid mechanical via http://rsif.royalsocietypublishing.org. boundary layer. Although typical boundary layer thicknesses are around 1 mm [8], a spore’s small size (approx. 10 mm) causes rapid deceleration after & 2013 The Author(s) Published by the Royal Society. All rights reserved. (a)(b)(c)(d d)(e) 2 h0 U rsif.royalsocietypublishing.org J R Soc Interface 10: 20130187 b l spore ring x L W h(x) Figure 1. The spore shooting apparatus. (a) Sporocarps on the stalk of a plant. (b) Flask-shaped sporocarp, containing five asci. (c) Upper part of an ascus with a mature spore close to the apical ring, which is still sealed. The length L and width W of the spore and the dimensions of the apical ring (‘, b, d) are indicated. (d) Spore moving at velocity U and deforming the apical ring at launch. A lubricating layer of fluid separates the spore from the ring. (e) The region where the spore first deforms the ring. Here, x measures the distance from the point where the spore starts to compress the ring; the gap thickness h varies with x and asymptotes to a constant value h0 at x . l as described in the text. Dashed line denotes dry contact deformation. launch, meaning that it must be launched at very high vectors, we test whether genetics are a constraint on mor- velocity even to travel a very small distance, and the likeli- phology. In fact, these species have very different apical hood of effective dispersal is directly correlated to the ring and spore shapes, suggesting natural selection is the thickness of boundary layer that the spore is able to cross [9]. force maintaining collapse into the one-dimensional subspace The critical role of the apical ring in spore dispersal caused for species with functional apical rings. speculation about whether the diverse morphologies of the spore ejection apparatus are tunedtoalloweffectivedispersal. Buller [10] proposed a relationship between the dimensions of the apical ring and the size of the spore, ostensibly to prevent 2. Results spores from tumbling during flight. Ingold [7] thought spores would be shaped to maximize the force used by apical rings to 2.1. Fluid mechanics of spore and apical ring coupling push on them. But, surprisingly, the individual geometric dimen- Figure 1 shows a representative context in which spore ejec- sions of apical rings and spores critical to these hypotheses are tion occurs. The sporocarps of a fungus are scattered on a either very weakly or not correlated. host (e.g. the stalk of a plant, figure 1a). These structures Here, we resolve this discrepancy by demonstrating a are produced by the fungus with the sole purpose of dis- strikingly tight coupling between the size of the spore and persing the spores. Within each sporocarp, there can be a nonlinear function of multiple dimensions of the apical hundreds of asci, each generally containing eight spores ring. The relationship is suggested by physical constraints (figure 1b). When the spores in an ascus are mature, osmo- on spore ejection: the requirement to efficiently convert the lytes are produced, leading to water influx into the highly potential energy stored in the ascus to kinetic energy of the elastic ascus, resulting in a significant increase in volume spore. The apical ring is an elastic seal, and distorts signifi- and pressure [4]. When the osmotic pressure p0 inside an cantly when the spore, which is lubricated by a thin fluid ascus is sufficiently high, the spores are singly ejected into layer, passes through it. The basic physical principles govern- the surrounding air. ing this kind of process were discovered 50 years ago, in the The speed U at which a spore is launched depends criti- study of elastomeric seals and O-rings used to control fluid cally on energy losses during ejection. If the osmotic flow in engines, pipes and other engineering applications pressure were entirely converted to kinetic energy, the [11]. By adapting these theories to the fluid mechanics of spore would be ejected at an ideal velocity spore ejection, we demonstrate that although there are at 2p0 least five independent dimensions to the morphological Uideal ; 2:1 ¼ sffiffiffiffiffiffiffirs ð Þ diversity of spores and apical rings, the need to minimize energy losses during ejection restricts spore and ascus where rs is the density of the spore and p0 is the overpressure morphologies to a one-dimensional subspace, where the in the ascus. dimensions of a spore and its apical ring are tightly coupled. However, the ideal launch velocity is necessarily degraded We test this theory using published electron micrographs by both friction and fluid loss as the spore moves through the of apical rings and spores [12–19] and a recently published apical ring (figure 1c,d). The apical ring consists of an elastic ascomycete phylogeny [20], which identifies two potentially material with thickness b and height ‘. The size of the opening independent groups of species with spores singly ejected of the apical ring before the spore starts to pass through it, d, is through apical rings. Quantitative descriptions of spores and much smaller than the width W of the spore. During the ejec- apical rings at a high resolution are available for 45 species, tion of the spore, the apical ring is strongly deformed, and with dimensions of the spore and apical ring characters varying there is a thin layer of fluid with viscosity m and density r, over one order of magnitude. Nonetheless, the observed vari- separating the apical ring from the spore. ation is confined to the predicted one-dimensional subspace Energy losses arise from two different processes occurring with surprising accuracy: energy losses are held within 2 in this lubricating fluid layer of thickness h0: first, there is fric- per cent of the theoretical optimum.