modelling hyphal networks - divisionmathematical modelling to fungal growth, conducted up to the...
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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: [email protected] (
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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