A mechanistic explanation of the transition to simple multicellularity in fungi.

Development of multicellularity was one of the major transitions in evolution and occurred independently multiple times in algae, plants, animals, and fungi. However recent comparative genome analyses suggest that fungi followed a different route to other eukaryotic lineages. To understand the driving forces behind the transition from unicellular fungi to hyphal forms of growth, we develop a comparative model of osmotrophic resource acquisition. This predicts that whenever the local resource is immobile, hard-to-digest, and nutrient poor, hyphal osmotrophs outcompete motile or autolytic unicellular osmotrophs. This hyphal advantage arises because transporting nutrients via a contiguous cytoplasm enables continued exploitation of remaining resources after local depletion of essential nutrients, and more efficient use of costly exoenzymes. The model provides a mechanistic explanation for the origins of multicellular hyphal organisms, and explains why fungi, rather than unicellular bacteria, evolved to dominate decay of recalcitrant, nutrient poor substrates such as leaf litter or wood.

Quantitation of ER Structure and Function.

The plant endoplasmic reticulum forms a network of tubules connected by three-way junctions or sheet-like cisternae. Although the network is three-dimensional, in many plant cells, it is constrained to a thin volume sandwiched between the vacuole and plasma membrane, effectively restricting it to a 2-D planar network. The structure of the network, and the morphology of the tubules and cisternae can be automatically extracted following intensity-independent edge-enhancement and various segmentation techniques to give an initial pixel-based skeleton, which is then converted to a graph representation. Collectively, this approach yields a wealth of quantitative metrics for ER structure and can be used to describe the effects of pharmacological treatments or genetic manipulation. The software is publicly available.

The Mycelium as a Network.

The characteristic growth pattern of fungal mycelia as an interconnected network has a major impact on how cellular events operating on a micron scale affect colony behavior at an ecological scale. Network structure is intimately linked to flows of resources across the network that in turn modify the network architecture itself. This complex interplay shapes the incredibly plastic behavior of fungi and allows them to cope with patchy, ephemeral resources, competition, damage, and predation in a manner completely different from multicellular plants or animals. Here, we try to link network structure with impact on resource movement at different scales of organization to understand the benefits and challenges of organisms that grow as connected networks. This inevitably involves an interdisciplinary approach whereby mathematical modeling helps to provide a bridge between information gleaned by traditional cell and molecular techniques or biophysical approaches at a hyphal level, with observations of colony dynamics and behavior at an ecological level.

Energetic Constraints on Fungal Growth.

Saprotrophic fungi are obliged to spend energy on growth, reproduction, and substrate digestion. To understand the trade-offs involved, we developed a model that, for any given growth rate, identifies the strategy that maximizes the fraction of energy that could possibly be spent on reproduction. Our model's predictions of growth rates and bioconversion efficiencies are consistent with empirical findings, and it predicts the optimal investment in reproduction, resource acquisition, and biomass recycling for a given environment and timescale of reproduction. Thus, if the timescale of reproduction is long compared to the time required for the fungus to double in size, the model suggests that the total energy available for reproduction is maximal when a very small fraction of the energy budget is spent on reproduction. The model also suggests that fungi growing on substrates with a high concentration of low-molecular-weight compounds will not benefit from recycling: they should be able to grow more rapidly and allocate more energy to reproduction without recycling. In contrast, recycling offers considerable benefits to fungi growing on recalcitrant substrates, where the individual hyphae are not crowded and the time taken to consume resource is significantly longer than the fungus doubling time.

Advection, diffusion, and delivery over a network.

Many biological, geophysical, and technological systems involve the transport of a resource over a network. In this paper, we present an efficient method for calculating the exact quantity of the resource in each part of an arbitrary network, where the resource is lost or delivered out of the network at a given rate, while being subject to advection and diffusion. The key conceptual step is to partition the resource into material that does or does not reach a node over a given time step. As an example application, we consider resource allocation within fungal networks, and analyze the spatial distribution of the resource that emerges as such networks grow over time. Fungal growth involves the expansion of fluid filled vessels, and such growth necessarily involves the movement of fluid. We develop a model of delivery in growing fungal networks, and find good empirical agreement between our model and experimental data gathered using radio-labeled tracers. Our results lead us to suggest that in foraging fungi, growth-induced mass flow is sufficient to account for long-distance transport, if the system is well insulated. We conclude that active transport mechanisms may only be required at the very end of the transport pathway, near the growing tips.

Mathematical modelling of fungal growth and function.

This contribution is based on the six presentations given at the Special Interest Group meeting on Mathematical modelling of fungal growth and function held during IMC9. The topics covered aspects of fungal growth ranging across several orders of magnitude of spatial and temporal scales from the bio-mechanics of spore ejection, vesicle trafficking and hyphal tip growth to the form and function of mycelial networks. Each contribution demonstrated an interdisciplinary approach to questions at specific scales. Collectively, they represented a significant advance in the multi-scale understanding of fungal biology.

Growth-induced mass flows in fungal networks.

Cord-forming fungi form extensive networks that continuously adapt to maintain an efficient transport system. As osmotically driven water uptake is often distal from the tips, and aqueous fluids are incompressible, we propose that growth induces mass flows across the mycelium, whether or not there are intrahyphal concentration gradients. We imaged the temporal evolution of networks formed by Phanerochaete velutina, and at each stage calculated the unique set of currents that account for the observed changes in cord volume, while minimizing the work required to overcome viscous drag. Predicted speeds were in reasonable agreement with experimental data, and the pressure gradients needed to produce these flows are small. Furthermore, cords that were predicted to carry fast-moving or large currents were significantly more likely to increase in size than cords with slow-moving or small currents. The incompressibility of the fluids within fungi means there is a rapid global response to local fluid movements. Hence velocity of fluid flow is a local signal that conveys quasi-global information about the role of a cord within the mycelium. We suggest that fluid incompressibility and the coupling of growth and mass flow are critical physical features that enable the development of efficient, adaptive biological transport networks.