EXPERIMENTAL MODELS OF MORPHOGENESIS

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EXPERIMENTAL MODELS OF MORPHOGENESIS
David Moore Audrius Meškauskas School of
Biological Sciences, The University of
Manchester, Manchester M13 9PT, U.K.
1. There is no reason why the rules which
govern morphogenesis should not be established.
From the rules and a few dimensions, times and
rate values a mathematical expression to describe
the morphogenetic process could emerge. Computer
models could be derived from that to simulate the
whole process. Nice idea! But where do you start?
Start simple. Making a stem bend in response to a
tropic stimulus is a suitably simple experimental
approach. YOU can choose when to apply the
stimulus, it is easily replicated and reaction
and response times can be measured readily. Also,
the response itself can be measured so the
quantitative demands of mathematical modelling
can be satisfied.
2. We have used the gravitropic reactions of
mushroom fruit bodies to study control of
morphogenesis because being the right way up is
crucial to a mushroom. Changing orientation is a
non-invasive stimulus. Weve coupled video
observation and image analysis to get detailed
descriptions of the kinetics. Weve made and used
clinostats to vary exposure to gravity, and weve
combined a variety of microscopic observation
techniques to make quantitative observations.
6. The model we have now describes the shapes
assumed by real stems of Coprinus cinereus.
Bending rate is determined by the balance between
signals from detectors of the direction of
gravity (a function of the angle of the stem) and
for curvature compensation (a function of the
local amount of bending). In a straight stem
displaced to the horizontal the gravitropic
signal is maximal and curvature compensation
signal is zero. As the stem bends the gravitropic
signal weakens (as the angle of displacement of
the perception system lessens) but the bending
enhances the curvature compensation signal.
3. The first step is to summarize these
observations and experiments into a flow chart
(as shown at left). This concentrates attention
on critical features and, in a non-mathematical
way, produces a formalized description which is a
good starting point for mathematical analysis.
The video sequence in the background shows (top)
a culture placed on its side at 1637h. The
weight of the cap makes the Coprinus cinereus
fruit body swing downwards, but by 1919h it has
bent upwards at 45o. Sadly, one second later the
connection with the mycelium breaks and the fruit
body swings round so the cap points downwards.
But it doesnt give up! By 2037 its back to the
horizontal by 2210 its almost upright, and by
2258 the cap is fully expanded and releasing
spores.
7. In our local curvature distribution model,
therefore, straightening is determined by local
curvature, independently of the spatial
orientation of that part of the stem.
4. Next, a scheme needs to be constructed which
lends itself to mathematical expression whilst
still keeping a firm footing in cell physiology.
The basic assumptions of ours are that change in
the angle of the apex occurs as a result of four
consecutive stages (i) the physical change which
occurs when the subject is disoriented (this is
called susception) (ii) conversion of the
physical change into a physiological change (this
is called perception) (iii) transmission of the
physiological signal to the competent tissue
(called transduction) (iv) the differential
regulation of growth which causes the bend and
change in apex angle (called response). We used
this scheme to estimate and calculate numerical
values for the various parameters of a combined
equation that could generate apex angle kinetics
which imitated the reaction of mushroom stems
quite well.
The gravitational imperative ...
8. This model is predictive and successfully
describes the gravitropic reaction of stems
treated with metabolic inhibitors, confirming its
credibility and indicating plausible links
between the equations and real physiology.
9. Where do we go from here? Its a predictive
model, so we need to make predictions and test
them. We need to develop the maths into three
spatial dimensions and to cope with hyphal
communities. Most importantly, we need to
convince somebody to fund the project!
5. This imitational model dealt with change in
apex angle only. Observations of real stems show
a complex distribution of bending and
straightening. Almost 90 of the initial
curvature is reversed by subsequent straightening
(we call it curvature compensation). A
realistic model of gravitropic bending would
describe the process in space as well as in time.
This is where imitation ends and simulation
begins.
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Key references

• Stockus, A. Moore, D. (1996). Comparison of
  plant and fungal gravitropic responses using
  imitational modelling. Plant, Cell Environment
  19, 787-800.
• Moore, D. Stockus, A. (1998). Comparing plant
  and fungal gravitropism using imitational models
  based on reiterative computation. Advances in
  Space Research 21 (8/9), 1179-1182.
• Meškauskas, A., Moore, D. Novak Frazer, L.
  (1998). Mathematical modelling of morphogenesis
  in fungi spatial organization of the gravitropic
  response in the mushroom stem of Coprinus
  cinereus. New Phytologist 140, 111-123.
• Meškauskas, A., Novak Frazer, L. Moore, D.
  (1999). Mathematical modelling of morphogenesis
  in fungi a key role for curvature compensation
  (autotropism) in the local curvature
  distribution model. New Phytologist 143, 387-399.
• Meškauskas, A., Jurkoniene, S. Moore, D.
  (1999). Spatial organisation of the gravitropic
  response in plants applicability of the revised
  local curvature distribution model to Triticum
  aestivum coleoptiles. New Phytologist 143,
  401-407.

Acknowledgements
We thank the British Mycological Society and
Federation of European Microbiological Societies
for award of FEMS short term Fellowships to the
late Alvidas Sto?kus and to Audrius Meškauskas
which enabled this research to be initiated. A
Royal Society NATO Research Fellowship to AM
supported the consolidation and further
development of the work to the stage described
here.