The Neighbour-Sensing mathematical model of hyphal growth is a set of interactive computer models that simulate the way

fungi A fungus ( : fungi or funguses) is any member of the group of eukaryotic organisms that includes microorganisms such as yeasts and molds, as well as the more familiar mushrooms. These organisms are classified as a kingdom, separately fr ...

hyphae grow in three-dimensional space. The three-dimensional simulation is an experimental tool which can be used to study the

morphogenesis Morphogenesis (from the Greek ''morphê'' shape and ''genesis'' creation, literally "the generation of form") is the biological process that causes a cell, tissue or organism to develop its shape. It is one of three fundamental aspects of deve ...

of fungal hyphal networks. The modelling process starts from the proposition that each

hypha A hypha (; ) is a long, branching, filamentous structure of a fungus, oomycete, or actinobacterium. In most fungi, hyphae are the main mode of vegetative growth, and are collectively called a mycelium. Structure A hypha consists of one or ...

in the fungal

mycelium Mycelium (plural mycelia) is a root-like structure of a fungus consisting of a mass of branching, thread-like hyphae. Fungal colonies composed of mycelium are found in and on soil and many other substrates. A typical single spore germinates ...

generates a certain abstract field that (like known physical fields) decreases with increasing distance. Both scalar and vector fields are included in the models. The field(s) and its (their) gradient(s) are used to inform the algorithm that calculates the likelihood of branching, the angle of branching and the growth direction of each hyphal tip in the simulated mycelium. The growth vector is being informed of its surroundings so, effectively, the virtual hyphal tip is sensing the neighbouring mycelium. This is why we call it the Neighbour-Sensing model. Cross-walls in living hyphae are formed only at right angles to the long axis of the hypha. A daughter hyphal apex can only arise if a branch is initiated. So, for the fungi, hyphal branch formation is the equivalent of cell division in animals, plants and protists. The position of origin of a branch, and its direction and rate of growth are the main formative events in the development of fungal tissues and organs. Consequently, by simulating the mathematics of the control of hyphal growth and branching the Neighbour-Sensing model provides the user with a way of experimenting with features that may regulate hyphal growth patterns during morphogenesis to arrive at suggestions that could be tested with live fungi. The model was proposed by Audrius Meškauskas and David Moore in 2004 and developed using the

supercomputing A supercomputer is a computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second ( FLOPS) instead of million instruction ...

facilities of the

University of Manchester The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The university owns and operates majo ...

. The key idea of this model is that all parts of the fungal mycelium have identical field generation systems, field sensing mechanisms and growth direction altering algorithms. Under properly chosen model parameters it is possible to observe the transformation of the initial unordered mycelium structure into various forms, some of them being very like natural fungal fruit bodies and other complex structures. In one of the simplest examples, it is assumed that the hyphal tips try to keep a 45 degree orientation with relation to the Earth’s gravity vector field, and also generate some kind of scalar field that the growing tips try to avoid. This combination of parameters leads to development of hollow conical structures, similar to the fruit bodies of some primitive fungi. In another example, the hypha generates a vector field parallel to the hyphal axis, and the tips tend to turn parallel to that field. After more tips turn in the same direction, their hyphae form a stronger directional field. In this way, it is possible to observe spontaneous orientation of growing hypha in a single direction, which simulates the strands, cords and rhizomorphs produced by many species of fungi in nature. The parameters under which the model operates can be changed during its execution. This allows a greater variety of structures to be formed (including mushroom - like shapes) and may be supposed to simulate cases where the growth strategy depends on an internal biological clock. The Neighbour-Sensing model explains how various fungal structures may arise because of the ‘crowd behaviour’ of the community of hyphal tips that make up the mycelium.

Literature

* Meškauskas A, Fricker M.D, Moore D (2004). Simulating colonial growth of fungi with the Neighbour-Sensing model of hyphal growth. ''Mycological research'', 108, 1241-1256
pdf
* Meškauskas, A., McNulty, Moore, D. (2004). Concerted regulation of tropisms in all hyphal tips is sufficient to generate most fungal structures. ''Mycological research'', 108, 341-353
pdf
* Money NP. (2004) Theoretical biology: mushrooms in cyberspace. ''Nature'', 431(7004):32
link
* Davidson A.F, Boswell G.P., Fischer M.W.F, Heaton L., Hofstadler D, Roper M. (2011). ''IMA Fungus''. 2(1): 33–37
NCBI link

Additional links

Further details are available from these websites

(primary) an

(mirror). The programs, with extensive documentation, are distributed as freeware by both these sites.

Notes

Developmental biology Mycology Theoretical computer science Crowds