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similar to the ventral one. If the ventrally expressed DIV is lost, the ventral petal shortens,
entering what is interpreted as the 'ground state' of being a basic petal with no special rules
applied. 85
Based on the idea that the genes mentioned above are required for polarizing activities
that emerge from dorsal and ventral domains to control how other cells grow d that they
effectively orientate the mathematical transformations the cells achieve d the computer
model for growth-driven flower development can be run with these mutations simulated
as loss of polarizing activity from the dorsal or ventral sides. The result is the formation of
model flowers that have broadly the same defects as real mutants. 85 The power of the model
to 'predict' the effects of the mutations strengthens its claim to accurately summarize the
basic developmental processes ('predict' is in inverted commas because in reality the mutant
phenotypes were known first).
Another way of using models is to set up 'organ rudiments' in a computer and then apply
different types of transformation programmes, to see which produce interesting outcomes
('interesting' usually means being very similar to a real mature petal or leaf, but sometimes it
can mean having the form of a 'missing link' or some other shape that is plausible but not
observed in nature). Sometimes, more than one transformation system can be successful,
a fact that may carry interesting evolutionary implications (see Chapter 28). Detailed study
of the living system, informed by predictions of themodels, can then be used to discover which
system most closely approximates real life. An example is provided by leaf growth in
Arabidopsis thaliana. The model begins with an organ rudiment that is organized around two
polarizing influences that operate at right angles to one another. These polarizing influences
(which may be, for example, gradients in the concentration of a signalling molecule) control
the extent of growth along their axes, setting the main direction of growth of a cell and also
howmuch it bothers to grow at all. Inmodels, there are two ways in which a leaf patternmight
be achieved. 86 One way retains the initial direction of polarizing influences and proceeds by
cells showing a complex, location-dependent response to their values. The other way allows
the axes of polarization themselves to distort with the growth of the tissue and allows the cells
to grow in response to them according to comparatively simple rules ( Figure 22.16 ).
Observation of the directions of growth of marked cells in real A. thaliana leaf rudiments
produces data that agree much more closely with the model in which polarizing axes are dis-
torted by growth. 85 The distortion of the axes of polarization that organize growth in
response to growth itself may be considered to be a type of feedback, in which axes of polar-
ization control growth and the results of growth realign (bend) axes of polarization. In terms
of biology, this type of model for growth has the advantage of simplicity: all cells respond in
a similar and simple way to their local conditions. In terms of analysis and prediction, it
involves researchers in detailed modelling because, especially when three-dimensional
systems are involved, understanding in detail how growth will bend axes to change growth
to bend axes more is beyond the intuition of most people.
One feature of morphogenetic feedback systems like this is that a modest change in param-
eters (for example, the ratio of along-to-across expansion in a cell experiencing a given signal)
can create a very different final morphology. This may be very important in understanding
the evolution of plants and also of animals (the biology of which would still include these
considerations, albeit with additional complications). This topic will be considered in
Chapter 28.
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