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Review

Modelling hyphal networks

Graeme P. BOSWELLa, Fordyce A. DAVIDSONb,*aDepartment of Computing and Mathematics, University of Glamorgan, Pontypridd, CF37 1DL, UKbDivision of Mathematics, University of Dundee, Perth Road Dundee, DD1 4HN, UK

a r t i c l e i n f o

Article history:

Received 15 June 2011

Accepted 3 February 2012

Keywords:

Anastomosis

Cellular automata

Lattice-free model

Mathematical model

Mycelium

Translocation

* Corresponding author.E-mail addresses: gpboswel@glam.ac.uk (

1749-4613/$ e see front matter ª 2012 The Bdoi:10.1016/j.fbr.2012.02.002

a b s t r a c t

The indeterminate growth habit of fungal mycelial can produce massive organisms span-

ning kilometres, whereas the hypha, the modular building block of these structures, is

only a fewmicrons in diameter. The qualitative and quantitative relationship between these

scales is difficult to establishusing experimentalmethods alone anda largenumber ofmath-

ematical models have been constructed to assist in the investigation of themulti-scale form

and function of filamentous fungi. Many suchmodels operate at the colony-scale, represent-

ing the hyphal network as either a regular lattice or as a geometrically-unconstrained struc-

ture that changes according to aminimal set of specified rules focussed on the fundamental

processes responsible for growth and function. In this reviewwediscuss thehistorical devel-

opment and recent applications of such models and suggest some future directions.

ª 2012 The British Mycological Society. Published by Elsevier Ltd. All rights reserved.

1. Introduction organisms (one clone of Armillaria gallica covers over 15 hect-

Recent advances in genomics and the reactive development of

“systems biology” have driven many aspects of biological

research in a direction heavily weighted towards computa-

tional, quantitative and predictive analysis. Mathematical

modelling is a key part in this development and it is unsur-

prising that it has played a significant role in expanding our

understanding of the growth and function of the fungalmyce-

lium. An excellent and extensive review of the applications of

mathematical modelling to fungal growth, conducted up to

the mid-1990s, can be found in Prosser (Prosser et al., 1995).

General modelling advances since that date are summarized

in Davidson (2007) and Davidson et al. (2011).

One of the main problems that faces modellers is the

choice of scale. In the study of fungal mycelia, the question

of scale is expressed in an extreme manner. The indetermi-

nate growth habit of the mycelium can produce massive

G. P. Boswell), fdavidsonritish Mycological Societ

ares of forest (Smith et al., 1992)), whilst the modular building

block of these structures, the fungal hypha, is only a few

microns in diameter. To model the interaction of such

extremes of scale seems an almost overwhelming task. Not

too surprisingly then, most developments in modelling myce-

lial fungi have been made by focussing on selected scales.

At the macro-scale, the interaction of fungi with the envi-

ronment forms the main focus. Variables in such models

represent densities (or numbers) and the interaction of these

densities is usuallymodelled via systems of ordinary or partial

differential equations. Examples include the modelling of

carbon cycling in the environment (Lamour et al., 2000), fungal

crop pathogens (Parnell et al., 2008) and biocontrol (Jeger et al.,

2009; Cunniffe and Gilligan, 2009; Stevens and Rizzo, 2008).

At the other extreme of scale, much modelling work has

focussed on hyphal tips where two main hypotheses have

developed in parallel over recent decades. The steady-state

@maths.dundee.ac.uk (F. A. Davidson).y. Published by Elsevier Ltd. All rights reserved.

Modelling hyphal networks 31

(SS) theory of Sietsma andWessels, 1994 proposed that plastic

wall material is continually deposited at the hyphal apex and

cross-linked into a more rigid form over time. The vesicle

supply centre (VSC) hypothesis (Bartnicki-Garcia et al., 1995;

Bartnicki-Garcia et al., 2001) predicts that the Spitzenk€orper,

or equivalent structure, acts as a distribution point for vesicles

containing cell wall synthesizingmaterials. Turgor pressure is

also assumed to play some role in driving tip growth (Regalado

et al., 1997; Bartnicki-Garcia and Oslewacz, 2002). A detailed

and extensive account of the development of the various theo-

ries regarding hyphal tip growth are given in Bartnicki-Garcia

and Oslewacz (2002), Goriely and Tabor (2003a, b). More

recently, Tindemans et al. (2006) modelled important details

of the diffusive transfer of the vesicles from the Spitzenk€orper

to the hyphal wall and their subsequent fusion with the cell

membrane. Thematuration process resulting in the stiffening

of themembrane ismodelled by Eggen et al. (2011). Goriely and

Tabor (2008) provide an excellent overview of tip modelling to

that date.

The focus of this review is at the intermediate or “single

colony” scale where modelling approaches generally fall into

two categories. One strategy is to assume that the mycelium

is a continuum, the properties of which can be viewed in

some sense as an average of the individual components

(much like in the modelling of fluid dynamics, for example).

Such models have their roots in earlier work of Edelstein and

co-workers (see Edelstein, 1982; Edelstein and Segel, 1983;

Edelstein-Keshet and Ermentrout, 1989). The models devel-

oped and analysed in e.g. Regalado et al. (1996) and Davidson

(1998), and references therein, and more recently by L�opez

and Jensen (2002), Boswell et al. (2002); Boswell et al. (2003a, b)

and Falconer et al. (2006) all fall into this category. In these

studies, systems of equations (non-linear partial differential

equations) are derived that represent the (implicit or explicit)

interaction of fungal biomass and at least one growth-

limiting substrate (e.g. a carbon source) aswell as other factors

(e.g. toxins). Such an approach is ideal when modelling dense

mycelia, for example growth in Petri dishes or on the surfaces

of solid substrates such as foodstuffs, plant surfaces and

building materials. This modelling strategy has, for example,

allowed the studyof biomassdistributionwithin themycelium

in homogeneous and heterogeneous conditions, translocation

in a variety of habitat configurations as well as certain func-

tional consequences of fungal growth including acid produc-

tion. The models developed by Boswell et al. (2002); Boswell

et al. (2003a, b), Boswell (2008) are the distillation of much of

the modelling work conducted over the previous 10 years.

A second category of colony-scalemodel is based on a discrete

modelling approach, in which individual hyphae are identi-

fied. It is this second approach, which explicitly details the

development of the hyphal network, that will form the focus

of the remainder of our review.

2. Modelling of hyphal networks

Historical context

Discrete models for the development of hyphal networks

generally take the form of computer-generated simulations

(e.g. Regalado et al., 1996; Prosser and Trinci, 1979; Soddell

et al., 1994; Me�skauskas et al., 2004a, b) and are often derived

from statistical properties of the experimental system under

investigation. Some of these models (e.g. Prosser and Trinci,

1979) yield statistical properties close to those of real mycelia,

whilst others (e.g. Me�skauskas et al., 2004a) produce images

almost indistinguishable from real fungi and are therefore

very appealing. Significant advances can be made using these

types of model, for example in the testing of hypotheses con-

cerning basic growth architecture. In particular the models

developed by Me�skauskas et al. (which were developed into

a user-interactive experimental system) can consider

different species growing in 3-dimensional space and within

a variety of nutrient distributions. It must be noted, however,

that in this modelling category there is the tendency to use

non-mechanistic rules to generate hyphal tip extension and

branching, i.e. the underlying mechanisms for growth are

not modelled directly and are instead replaced by abstract

branching and growth rules. Consequently, difficulties arise

in attempting to make and test hypotheses concerning

changes in growth dynamics and mycelial function in

response to external factors. Moreover, because of this

abstraction, it is difficult to choose parameter values in any

a priori meaningful way. Furthermore, because of computa-

tional difficulties, it is only very recently that the two key

processes of anastomosis and translocation, have been incor-

porated (see Boswell et al., 2007). These processes are crucial to

mycelial development in general and in particular to growth

in heterogeneous environments.

This class of discrete models can be further divided into

two important subgroups: lattice-based and lattice-free

models. Essentially, the former assumes that the mycelial

network is constrained to a predetermined grid or lattice.

The latter allows the network to be free of a priori constraints,

although this freely developing network has to be mapped

onto a discrete grid for computational purposes at some point

in the calculations. Both approaches have advantages and

disadvantages. Clearly the former restricts the topology of

the network, whilst the latter can be computationally expen-

sive. We now outline the structure and development of these

two approaches in turn.

Lattice-based models

A well-established and computationally efficient approach to

modelling filamentous fungi has been to use a regular lattice

as the basis for the mycelial network. Such models are essen-

tially forms of cellular automata (CA) and are typically discrete

in time, space and state. By formulating a series of carefully

selected stochastic rules applied at the local level, the status

of each element in the lattice changes over regular time steps

representing the growth and development of the fungal

network.

An early CA model was devised by Ermentrout and

Edelstein-Keshet (1993) in which a regular grid comprising

square cells was used to represent the growth environment.

Despite exceptionally simple growth rules covering only the

processes of tip growth, branching and anastomosis, a variety

of networks were created that captured the fractal-like struc-

ture of filamentous fungi implicating, at least in uniform

32 G. P. Boswell, F. A. Davidson

growth conditions, the fundamental processes of tip forma-

tion and movement in mycelial growth (Fig. 1). Indeed, the

model derived by Ermentrout and Edelstein-Keshet (1993)

provided the template for numerous other lattice-based

models that describing the growth, and later function, of

fungal mycelia.

An entirely different approach was adopted by L�opez and

Jensen (2002). Building on a previousmodel used to investigate

the changing morphology of colony peripheries (L�opez and

Jensen, 1998) L�opez and Jensen constructed a stochasticmodel

in which a hypothetical inhibitingwastematerial produced by

the fungus itself diffused and affected the ability of the fungus

to grow elsewhere. While no explicit hyphal network was

simulated in their model, predictions were made on the

morphology of the growth fronts of simulated mycelia in

response to different nutrient concentrations (that were

assumed uniform and constant through the simulation) and

different sensitivities to the inhibitory substance. These

predictions were consistent with experimental observations

reported in Matsuura and Miyazima (1992); Matsuura and

Miyazima (1993).

Smith et al. (2011) adopted a novel approach by construct-

ing a network automata (NA) in which connections in network

(rather than states of “cells” in a CA) were updated at each

time step. Such an approach was shown to be particularly

suited to the situation where the creation of connections in

the network was coupled to a dynamic process occurring

Fig. 1 e Output from the lattice-based mycelial network

model of Ermentrout and Edelstein-Keshet (1993). Image

reproduced with permission.

upon the network. Nutrient translocation in fungal mycelia

was used as a good example. While the resultant network

structure did not represent a mycelium, the concentration of

the internalized nutrients was shown to have the same distri-

butions as radioactively-labelled amino acid within Phanero-

chaete velutina.

A closely related approach had been previously developed

in Boswell et al. (2007). This hybrid mathematical model repre-

sented a growth-promoting substrate (a carbon source) as

a continuous variable and the biomass network as a discrete

structure. The explicit inclusion of internal and external

substrate allowed for the modelling of the fundamental rela-

tionship between nutrient availability and hyphal tip growth.

This enabled, for the first time, simulation of the growth of

hyphal networks in response to heterogeneous environments.

Moreover, this model was able to predict a functional conse-

quence of such growth, namely the acidification of the

surrounding environment. Finally, another advantage of this

method was that it used parameter values and rules for

growth and metabolism drawn directly from the calibrated

and tested continuum model developed by Boswell et al.

(2003b).

The simulated network developed according to stochastic

rules calibrated for the fungus Rhizoctonia solani in which tip

extension and branching were related to internally located

substrate, which itself was translocated, by both passive diffu-

sion and activemetabolically-driven processes. As amodel tip

movedbetweenneighbouringnodes ona triangular lattice, the

edge connecting thesenodes becamean active hypha involved

in the uptake of substrate and its subsequent translocation

through the network, much like the NA framework later

proposed by Smith et al. (2011). The model was applied to

a series of planar environments representing uniform condi-

tions, nutritionally heterogeneous conditions and soil slices

that exhibited both nutritional and structural heterogeneities.

It was shown that substrate translocation and the physical

environment significantly influenced the structure of the

networks produced and the extent of zones of acidification

that preceded the leading edge of the biomass network (Fig. 2).

A three-dimensional version of this model was subse-

quently developed by Boswell (2008) to simulate the formation

of mycelia in soil-like systems using a face-centred cubic

lattice. A related approach used to model the growth of aerial

hyphae has been recently adopted by Coradin et al. (2011) to

further understand the role of filamentous fungi in solid state

fermentation processes (Nopharatana et al., 1998).

Irrespective of the processes represented in lattice-based

models (and indeed the lattice structure), the regular geom-

etry imposes certain limitations on the network constructed.

Computationally, a regular geometry has numerous advan-

tages (compared to an irregular geometry) principally because

there are a finite number of orientations adopted by lengths of

biomass and hence a finite number of rules governing the

development of the biomass structures. While the use of

regular geometries may be suitable for certain applications,

in other instances, e.g. the representation of mycelial growth

in response to various tropisms (Gooday and Carlile, 1975;

Fomina et al., 2000), such a regular geometry may fail to suffi-

ciently capture the complex behaviour exhibited. Therefore,

models that represent mycelial networks using non-regular

Fig. 2 e Simulations from the calibrated model of Boswell et al., (2007). A two-dimensional representation of non-saturated

soils where a water film surrounds soil particles (denoted by black cells) with air-filled gaps elsewhere (open cells). The

network is represented by solid lines. The predicted pH of the environment is shown over regular time intervals (dark red

indicates regions with low pH).

Modelling hyphal networks 33

geometries (i.e. are lattice-independent) have been developed

alongside lattice-based models.

Lattice-free models

Although strictly not an mathematical model for the develop-

ment of fungal mycelia, the first attempt to develop a lattice-

free model for networks was conducted by Cohen (1967). He

developed a generic model of branching networks in two

spatial dimensions and considered filamentous fungi as one

such application. While this computer simulation produced

images highly reminiscent of certain fungal mycelia, it did

not relate the rules of the network’s development to available

nutrients and therefore its predictive ability was limited.

None-the-less, despite these important limitations, this pio-

neering approach created a template upon which a series of

improved and revised lattice-free mathematical models

were developed.

In a pain of papers Yang et al. (1992a, b) developed a hybrid

model that generated an explicit network representing the

growth of both filamentous fungi and mycelial bacteria. Their

model had a similar form to that developed by Cohen, 1967

except it had a mechanistic underpinning. Principally, the

rules governing branching and hyphal tip extension were

dependent on an internally located and self-produced mate-

rial that was transported by diffusion through the developing

network.

In a series of papers Stack et al. (1987); Knudsen et al. (1991,

2006) developed and calibrated an individual-based computer

simulation that described the three-dimensional growth of

a biological control fungus in soils. Their models were again

based on that of Cohen (1967) where the fungal mycelium

was represented by a series of connected straight line

segments where each segment contained information about

its position, orientation, connectivity and relative nutrient

status.

Fig. 3 e Examples of networks produced using the neighbour-sensing model of Me�skauskas et al. (2004b). (Images obtained

from the online simulation at http://www.world-of-fungi.org/Models/mycelia_3D/index.html.)

34 G. P. Boswell, F. A. Davidson

A related approach to modelling the development in

three dimensions was adopted by Me�skauskas et al. (2004a,

b) that described a neighbour-sensing mathematical model

for hyphal growth (Fig. 3). The fungal network was again

Fig. 4 e Biomass networks developing from a continually-reple

model of Carver and Boswell (2008). Figures (a)e(d) correspond

increase in the diffusive translocation component.

represented by a collection of line segments but unlike in

previous models, a variety of tropisms were considered

including negative autotropism (measured with respect to

the density of other line segments), galvanotropism (based

nished nutrient source. Simulations produced using the

to networks generated where the only difference is an

Modelling hyphal networks 35

on self-generated electric fields that either align or diverge

adjacent hyphae) and gravitropism (with growth either

following or opposing the gravitational field).

The first lattice-free model to incorporate the key property

of anastomosis was developed by Carver and Boswell (2008).

Their approach essentially combined the planar model of

Cohen (1967) with the nutrient reallocation techniques of

Yang et al. (1992b) and checked for the crossing of line

segments at each stage of the simulation. During a regular

time step, each tip could extend a fixed distance with a proba-

bility that increased with the substrate concentration in the

corresponding line segment (similar to Boswell et al., 2007)

and in a direction normally-distributed from its previous

orientation. The simulated interconnected networks closely

resembled genuine mycelia and the morphological effects of

increasing the rate of nutrient translocation resulted in

increasingly dense biomass structures at the colony periphery

(Fig. 4). While this model was only partially calibrated

for R. solani and applied to a highly specific experimental

system corresponding to outgrowth from a nutrient source,

it provided the basis for further mathematical models capable

of simulating fungal growth and function in more complex

environments.

Boswell andHopkins (2008) andHopkins and Boswell (2012)

extended the work of Carver and Boswell (2008) to allow for

the simulation of planar growth in arbitrary nutritional condi-

tions. Similar to the lattice-basedmodel of Boswell et al. (2007),

a generic substrate was assumed to exist in two forms: (i) free

in the external environment where it could diffuse and (ii)

contained within the biomass network where it was translo-

cated and used to fuel tip extension. An important advance

made by Hopkins and Boswell (2012) over earlier lattice-free

models was the manner in which the orientation of hyphae

Fig. 5 e Mycelial growth from a nutrient source into

a nutrient-replete environment. Simulation using themodel

of Hopkins and Boswell (2012). The thick line segments in

the biomass network contain greater concentrations of

internal substrate than the thin line segments suggesting

the emergence of fungal cords from the nutrient source.

weremodelled. Previously, model tips were typically assumed

to change direction according to a random variable drawn

from a normal distribution and, therefore, statistical proper-

ties obtained from experimental data were used to calibrate

the reorientation process, meaning the predictive aspects of

the models were limited to situations resembling the calibra-

tion experiment. To overcome this limitation, Hopkins and

Boswell (2012) utilized a (biased) circular random walk to

model tip orientation and related this to the corresponding

FokkerePlanck partial differential equation (which describes

statistical properties of the random walk). When simulated

in heterogeneous conditions, the model predicted the emer-

gence of pathways in the biomass network radiating out

from substrate sources that contained significantly more

internal substrate than other model hyphae in the structure

(Fig. 5). Such a feature is consistent with the emergence of

fungal cords (Boddy, 1993, 1999) and noticeably did not require

any “global” input. Instead, these pathways arose through an

initially stochastic but then self-reinforcing locally-applied

process, a concept independently suggested in a recent

modelling investigation by Heaton et al. (2010) who used

scanned images of fungal colonies and related the internal

flow of material to that of currents in electric circuits.

A variety of lattice-free approaches have been developed

over the last couple of decades, each offering differing degrees

of flexibility and applicability. Almost all such models have

relied on a mixture of deterministic and stochastic elements.

The modelling complexity and computation costs associated

with such models have often forced compromises and

possibly important biological features have been simplified

or even omitted. The challenge formodellers is to find amean-

ingful balance between biological function and mathematical

computability.

3. Current approaches and applications

It is well-established that certain fungi can be used as agents in

bioremediation (Sayer et al., 1995; Gadd, 2001), but recent inves-

tigations have shown they can also be used as conduits to

significantly speed up the dispersal of other micro-organisms,

capable of biorestoration, through soil systems (Kohlmeier

et al., 2005; Banitz et al., 2011). In order tomake best use of fungi

in such settings, it is essential to first predict the growth

dynamics of hyphal networks and then study how these can

be advantageously manipulated. To this end, the model in

Hopkins andBoswell (2012) has recently beenadapted (Hopkins

and Boswell, unpublished) in the following manner.

The model is being applied to consider the problem of

a pollutant diffusing in an essentially planar environment

(e.g. shallow soil) (Fig. 6). Consistent with experimental obser-

vations and previously successful modelling approaches,

model tips are assumed to reorientate themselves away

from both existing biomass (Hickey et al., 2002) and, indepen-

dently, the pollutant (Fomina et al., 2000), with the latter at

a rate dependent on the pollutant concentration and level of

an internal substrate, si. Thus, the biomass resilience to the

effects of the pollutant is increased with nutrient availability

(Gadd et al., 2001; Fomina et al., 2003).

Fig. 6 e Network structure after 2 d growth in the presence of a pollutant under three different configurations of an external

substrate. Simulations produced using the model of Hopkins and Boswell (2012). The initial pollutant concentration is

confined to the circular region and the locations of the external substrate are represented by the square blocks that are either

located (a) at the site of inoculation, (b) at the inoculation site and at edge of the diffusing pollutant, and (c) at the inoculation

site and at the pollutant source. The mean position of the edge of the network (dotted line) and the position of where the

network density first exceeded unity (solid line, representing the “functional” part of the network (Hopkins and Boswell,

2012)) were calculated from three replicates over the duration of the simulation along a rectangular strip between the

inoculation site and pollutant source where (d)e(f) correspond to the configurations in (a)e(c) respectively.

36 G. P. Boswell, F. A. Davidson

At discrete time steps, each model tip is assumed to reor-

ientate itself according to a preferred direction of growth

depending on the pollutant and biomass densities. Local

gradients dictate the direction of least biomass and

pollutant, generating a preferential direction of growth qc

and qp respectively (see Hopkins and Boswell, 2012, for

details). The bias of reorientation of a model tip of alignment

q is given by

mðqÞ ¼ �dpðsiÞ sin�q� qp

�� dc sinðq� qcÞ

where dpðsiÞ ¼ g1pð1� si=ðg2 þ siÞÞ and dc are the relative reor-

ientation rates in response to differences in the current and

preferred growth alignment and g1, g2, dc are constants. (If

qp ¼ qc then this is the preferred direction of growth. If

qc s qp the model tip essentially seeks a compromise in the

growth orientation between the different tropisms. In both

instances, stochastic variations about the preferred direction

are also included.) The reorientation process itself is simu-

lated by a biased randomwalk obtained fromaFokkerePlanck

equation that relates statistical properties of the tip reorien-

tation process to external stimuli (see Hopkins and Boswell,

2012; Plank and Sleeman 2004, for full details). Once the

new orientation is determined, provided there is sufficient

internal substrate, the model tip advances a fixed distance

and if there is a collision with an existing line segment it

undergoes fusion (representing anastomosis in the network).

A new line segment is then generated between the old and

updated position of the model tip. The production of new

model tips, corresponding to subapical branching, is included

and since turgor pressure has been implicated in branching

(Gow and Gadd, 1995; Riquelme and Bartnicki-Garcia, 2004)

it is assumed the branching rate is zero if si is less than a crit-

ical value and otherwise increases proportionally with si.

Internal substrate is updated, representing growth costs, by

the uptake of new resources and by translocation, which

comprises both diffusive directed components (towards the

nearest tip) (see Hopkins and Boswell, 2012, for details on

the implementation of this process).

The growth domain represents a polluted environment

prior to the introduction of fungal biomass. To investigate

the effects of the augmentation of nutrients, three configura-

tions have been considered:

Modelling hyphal networks 37

1. single block at “inoculation” site (Fig. 6a),

2. two blocks, first at “inoculation” site and second between

“inoculation” site and pollutant source (Fig. 6b),

3. two blocks, first at “inoculation” site and second at the

pollutant source (Fig. 6c).

The total amount of augmented external substrate is taken

to be equal in all instances (its concentration is halved when

divided between two substrate blocks). The model was simu-

latedwith three replicates for each configuration over a period

of time representative of 2 d and the biomass density along

a rectangular strip between the site of inoculation and the

pollutant centre was calculated.

In all configurations, the biomass initially expanded

outward in a radially-symmetric manner. After this transient

feature, line segments extending away from the pollutant

continued to extend and branch but those line segments

initially extending towards the pollutant source typically expe-

rienced a sharp reorientation due to the presence of the

diffusing pollutant (Fig. 6a, c). However, when the external

substrate was divided evenly between the site of inoculation

and midway between that and the centre of the pollutant

concentration, the resultant increased level of internal

substrate within the biomass, caused increased branching

and tips resilience to the pollutant (e.g. Fig. 6b). By locating

where the leading edge of the biomass density first exceeded

a critical value (representing the extent of the “functionally”

capablemycelium (Hopkins andBoswell, 2012)) itwas observed

that the simulated network extended closer to the pollutant

source when external substrate was available at the pollutant

edge than when it was distributed elsewhere (Fig. 6d, e, f).

These simulations suggest that the extent of mycelial

growth can be advantageously manipulated when subjected

to toxic conditions. Crucially, themodel predicts that a simple,

uniform addition of extra nutrients would not be sufficient to

promote a change in mycelial extent; instead the location of

the extra nutrients relative to the pollutant is fundamentally

important. These and related predictions may assist further

refinements in the application of fungi in bioremediation.

4. Future challenges

The delivery of wall buildingmaterials to the tip,movement of

organelles over large distances at high speed and nuclearmix-

ing are all facets of mature networks that invite further inves-

tigation. At the other end of the development cycle, early germ

tube growth and anastomosis is only now beginning to be

understood (Roca et al., 2010). We suggest that a major chal-

lenge for fungal biology is to link this increasing body of infor-

mation at the micro-scale to the large scale form and function

of hyphal networks.

The increasingly quantitative nature of experimental data

regarding tip growth, cytoplasmic flow, nutrient transport

and the imaging of network architecture will undoubtedly

underpin the development of new models that are genuinely

predictive. The authors predict that mathematical models of

the type discussed here, where the dynamic formation and

function of the mycelium is explicitly captured, could play

a significant role in linking information across scales.

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