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AMER. ZOOL., 22:91-104 (1982)
The Relation Between Scale and the Completeness of Pattern
in Vertebrate Embryogenesis: Models and Experiments 1
JONATHAN COOKE
The National Institute for Medical Research,
Mill Hill, London, NW7 1AA, United Kingdom
SYNOPSIS. The distinctive features of the theory of positional information for pattern
formation are described, as applied to early vertebrate development. The results that
follow two experimental challenges to the pattern control mechanism in the amphibian
gastrula and neurula are presented, together with a discussion of the problems they
present for most models that have been proposed for the generation of positional signal
gradients. An alternative model which is related to the positional information idea, but
which departs significantly from it in explaining the proportioning of patterns, is given
in outline. Finally, differences between the behaviour of the antero-posterior patterning
system of the chick limb-bud and that of the gastrular axial pattern are described and the
concept is introduced that features of the limb pattern, namely its repetitive elements,
may require the introduction of a growth control system to regulate tissue size in the
rudiment in relation to the forming pattern.
INTRODUCTION
This chapter is concerned with the control mechanism whereby a complete set of
developmental tendencies, or determinations, becomes distributed in characteristically proportioned zones across the available space within a sheet of tissue in the
early embryo. The particular tissue sheet
in question is the roughly cylindrical, essentially monolayered amphibian mesodermal mantle at gastrula and neurula
stages, and the pattern is the medial-to-lateral (dorsal-to-ventral) sequence of axial
structures in the body pattern. By early
tailbud stages this has achieved division
into four discrete and recognisable parts,
due to patterning processes that are probably completed during gastrulation and
neurulation (Holtfreter and Hamburger,
1955; Forman and Slack, 1980). Axial pattern in the remaining, ectodermal and endodermal cell layers is basically coordinated with that of the mesoderm during
organogenesis because information is
transferred from the latter in processes
coming under the heading of "induction."
The true pattern formation that occurs
within the plane of the mesoderm at early
stages is thus, in vertebrates, the ultimate
site for control of the whole body plan.
1
From the Symposium on Principles and Problems
of Pattern Formation in Animals presented at the An-
nual Meeting of the American Society of Zoologists,
27-30 December 1980, at Seattle, Washington.
91
In many types of embryo, development
of a qualitatively complete pattern of morphogenesis can occur across whatever material remains, following much removal,
addition or rearrangement of material
within the early uncommited cell population. Since individual cell migration, leading to change of neighbour relationships,
occurs very little during the crucial period
of spatial organisation, the developmental
tendencies of cells or their descendants
must be modifiable according to the relative positions which they sense themselves
to occupy within the whole, in order that
normal pattern be achieved despite such
disturbances. This requires us to postulate
a signalling system, operating to coordinate on a wide scale the determinations
achieved by cells. In each embryonic system studied there is characteristically an
"organiser" region or group of cells (Spemann and Mangold, 1924) whose own fate
as part of the pattern is pre-determined
from earlier stages, but which acts as a
boundary or reference region when grafted elsewhere, so that the fates of surrounding tissue become organised into a
typical edition of the pattern of the embryo concerned, but centred upon the organiser.
Observations of this type have received
renewed interest in the last fifteen years
because of a few theoretical contributions,
that have re-formulated the basic problem
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JONATHAN COOKE
of pattern in terms which make contemporary biologists in reasonable numbers
able to focus on it after a considerable
eclipse period. Pre-eminent among these
is Lewis Wolpert's concept of positional information (1969, 1971) which builds a precise theory of how pattern might be
achieved, growing out of much older but
vaguer ideas concerning "physiological
gradients" or dominance hierarchies in developing systems (Child, 1941). A decade
ago, the otherwise complete surveys of organismic and molecular biology that constituted zoology courses at several major
British universities failed completely to
confront the problem of the harmony of
form that is reliably achieved during early
development in each species, and there is
no doubt that we owe the recent improvement in this situation largely to the energy
and clarity of the positional information
formulation. It remains, nevertheless, a
stimulating conjecture rather than an established mechanism, as applied to the initial generation of pattern. I shall outline
what I perceive as the salient or diagnostic
features of the theory as applied to early
embryos, since it is through these that one
would hope to approach an experimental
test of its adequacy by manipulations and
observations on actual systems. I thus draw
up a list of critical experimental questions
we should like to ask embryos in the light
of the theory. I shall then describe some
quantitative observations on regulation of
the amphibian medio-lateral axial pattern,
and explain the difficulties they offer to
strictly positional information-based models
for the control mechanism. An alternative
model, sharing features with positional information theory but also departing crucially from some of its tenets, is then outlined. Finally I shall compare the behaviour
of this primary vertebrate pattern with
that observed in the antero-posterior dimension of pattern formation for a vertebrate limb-bud, a secondary and later-developing field within the body plan as a
whole (see also Summerbell and Honig,
1982). In some ways, the chick limb pattern seems to fit the needs of positional
information theory more closely than does
the primary axial pattern, leading to the
speculation that the need to specify two
basic aspects of biological patterns independently might underlie variations in the
control system.
The demands on a positional
information system
Before the complexity of morphogenetic movements obscures them, two features
are exhibited in the large-scale patterns
determined under natural and experimental conditions in the tissue-sheets of embryos. They show overall polarity, in that
the pattern parts or zones of the various
differentiations always occur in a particular sequence centred around or proceeding from the element deriving from the
organiser region. They also follow the rule
of continuity, in that pattern parts are never
missed out from within the normal sequence, although they may be omitted
from one end if regulation does not occur
or if two incomplete sequences of opposite
polarity are joined due to the presence of
two organisers in one experimental embryo. These features are illustrated for
formation of the medio-lateral pattern of
the amphibian in Figure la. The application of the idea of positional information
to this is shown in Figure lb. Normal pattern, and its regulation despite early disturbances, is achieved because a signalling
system operates through the entire field to
ensure that some cellular variable, whose
local value sets the cells' state to determine
which particular pattern part shall develop, becomes distributed in a gradient profile with absolute "boundary" levels at the
extremes of pattern and a particular, monotonically graded distribution (i.e., a single
slope) in between. Boundary characteristics are pre-set by localisation in the egg
structure, or are achieved early on in development due to symmetry-breaking processes (e.g., Gierer and Meinhardt, 1972)
to give regions having organiser status.
These then behave autonomously if grafted, as they set up gradients in surrounding
tissues to re-organise their development.
This accounts nicely for the properties of
polarity and continuity in the final patterns, but note that the achievement of
normal pattern is crucially dependent on
SCALE AND VERTEBRATE PATTERN FORMATION
93
(a) chemical and physical limits upon the
ability to obtain a normal-shaped and complete gradient occupying the whole system
regardless of the extent of tissue available, and
(b) the "interpretation" machinery of the
cells whereby they utilise particular bands
or zones of signal level in order reliably to
choose between however many alternative
pathways of development are available to
them.
It is important to distinguish between,
on the one hand, the abstract idea or formalism of the positional information gradient which seems to flow naturally from
the empirical observations of pattern polarity and continuity and the organiser
phenomenon, and on the other hand particular mechanistic hypotheses (models) as
to what the positional signal and the intercommunication system really are. Such
models may or may not postulate a literal FIG. 1. a. Schematic transverse sections of a midgradient in concentration of a signal mol- gastrula and a tailbud stage amphibian embryo, midecule (morphogen), organised by diffu- way along the antero-posterior axis. Density of stipsion. Any cell state variable which obeys pling, graded in the gastrular mesodermal cylinder
which is essentially one cell thick, represents
the laws of continuous, monotonic varia- (M)
graded development tendences which ultimately betion between "boundary" value settings come fixed as differentiating pattern parts, notocould fit the bill (e.g., Goodwin and Cohen, chord (N), somite (S), pro-nephros (PN) and lateral
1969). In practice, however, the diffusion plate (LP). These have undergone their initial differand concentration gradient has been most entiations, including a dorsal convergence or piling
of cells, by the time of the second diagram when
used in detailed models applied to partic- up
pattern is assayed by cell counting. E = ectoderm and
ular systems (Wolpert et al., 1974; Sum- induced neural tube. End. = yolky endoderm or gut
merbell and Tickle, 1977), while Crick anlage. b. Profile of a graded distribution in a cellular
(1970) offered plausibility calculations to variable (e.g., concentration of a morphogen) representing the normal size and proportions of the meshow that diffusion transfer of substances dio-lateral
mesodermal pattern. The four thicknesses
of reasonable molecular weight is consis- of baseline represent the extents of the pattern zones
tent with the timespans (—a few hours) in tissue at their first determination, while arrowand extents (—around 1 mm) across which heads on the ordinate denote threshold signal values
significant gradients must be set up and that might determine the boundaries between them.
Use for reference when examining the results of exremain in order to encompass the phe- periments
as represented in Figure 3. The profile is
nomena of biological pattern formation. drawn concavely nonlinear simply because most conModels invoking autocatalytic processes crete models for gradient control (e.g., diffusion from
which produce a particular state of cellular a source) produce such a profile, but only a monoactivation locally, but also lead to longer- tonic nature to the gradient is necessary to the posirange diffusive fields of an inhibitor of tional information theory.
their own activity (—reaction/diffusion
processes), and others postulating pre-dif- struction of morphogen at separate sites
ferentiated morphogen sources with uni- are postulated, then two sites having comform destruction elsewhere, have been plementary organiser or "boundary" propused to simulate gradient formation and erties should be expected in each system.
match the data from various developing When we remember that on the positional
systems (Meinhardt, 1978; Herth and information paradigm the production of
Sander, 1973).
a complete and proportioned pattern deIf localised synthesis and localised de- pends upon the prior existence (—if only
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JONATHAN COOKE
d
3.5% = N = b.0%
40%= S = 4
,11%=PN=1
b
FIG. 2. a. The removal of blastomeres by pricking with a hot needle at morula/early blastula stages, followed
by healing under pressure of the vitelline membrane to give a small, morphologically intact blastula and
gastrula. There is a short delay, after which development proceeds at normal speed through the periods of
pattern determination and expression without any intervening rise in the rate of cell multiplication, b. Normal
and experimentally small embryos at tailbud stages (Fig. la) used to assay pattern proportions by cell counting.
Frames mark the anterior and posterior limits between which pattern was assayed, since head and tailbud
each represent morphologically complex situations that involve a small percentage of the total cells present.
There is independent evidence for size-independence of pattern in the head-to-tail dimension, c. The operation transplanting an early gastrula dorsal lip (organiser) graft to the ventral marginal zone of a late blastula
host. The control (sham) operation involves no positional disparity, as one organiser region is replaced with
SCALE AND VERTEBRATE PATTERN FORMATION
95
transiently) of a complete and normal gra- plete the process of specification, and in
dient profile in the signal, then each set of evolution have acquired mechanisms to asprocesses that has been postulated places sure them of this?
its own constraints on the actual performance that would be expected on the part Experiments on the amphibian pattern
of the regulatory system as studied experUsing histological techniques, a stanimentally. It is to be hoped that detailed dard estimate can be made of the numbers
information on the performance features of cells in the mesodermal pattern parts of
of models can be derived from the litera- the amphibian embryo shortly after the
ture on them, but at least it is evident that completion of pattern specification at
concrete hypotheses, rather than the ab- young tailbud stages. The medio-lateral
stract notion of positional information, pattern proportions (i.e., those seen in acgive the whole idea its power as a scientific curate transverse section) have been astheory because they render it most chal- sayed between two set levels in the long
lenging to experimentalists.
axis (see Fig. 2b) for normal individuals in
I would regard the following empirical two species, the anuran Xenopus laevis and
questions about actual pattern-forming the urodele Ambystoma mexicanum, and for
systems in embryos as of prime importance their sibling embryos where the process of
pattern specification had been challenged
for assessing adequacy of models.
1) How precise is the maintenance of the experimentally by creating two different
proportions between pattern parts, in sets of abnormal conditions.
terms of the relative space or cell numbers
In the first test, so many presumptively
devoted to them, under development at ventral cells (—those furthest from the
different overall sizes, or when two organ- pre-determined dorsal organiser region)
iser regions have been situated in one nor- had been removed at the blastula stage,
mal-sized field so as to partition its terri- that the system was faced with specifying
tory into two patterns?
pattern across an abnormally small though
2) Is there evidence for two active geometrically normal mesoderm cell sheet
"boundary regions" or organisers main- in the gastrula and neurula (Fig. 2a, b).
taining complementary ends of the pat- Morphologically normal small gastrulae
tern, or is one, "the" organiser, sufficient with as little as 20% of the usual mesoto control and proportion each edition of dermal cell population can be produced,
provided that the future dorsal lip region
the pattern.
3) Does a supernumerary organiser is left in the embryo. In cell lineage terms,
when implanted to an abnormal site within only cells whose normal fates would have
the embryo, interact with the original one been to contribute their descendents to the
to influence the scale of the pattern parts dorsal two of the four pattern parts recontrolled by it, as well as setting up a new main. In the second test, embryos have
been provided at late blastula stage with an
pattern centred upon itself?
4) Is there a system at early stages which extra organiser by grafting a second dorsal
seems to control the schedule of cell divi- blastoporal lip, from a donor early gastrusion in the tissue in relation to require- la, into the ventral marginal zone. Under
ments of the pattern-controlling system; these conditions the small donor cell group
i.e., do any biological systems behave as if organises some third of the total mesothey require a set amount of tissue to com- derm into a new axis of pattern, having
another one, resulting in normal morphogenesis, d. Transverse sectional appearance of tailbud embryos as
in Figure la, but after the sham operation and the ventral organiser graft. Again without any measurable
increase in the schedule of cell division since operation, the experimental mesoderm has become determined
as two small axial patterns, each remarkably complete in its organisation. The total porportion of cells devoted
to each pattern part within doubly organised embryos closely approaches that normal for the species, as
ventral pattern is only slightly under-represented. Labelling as in Figure la.
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JONATHAN COOKE
full cellular continuity in the mesodermal
cylinder with that centred on the original
dorsal midline (Fig. 2c, d).
Elements of the pattern are notochord
(dorsal midline)—some 3.5% of the cells,
followed by paired somite-producing
zones—40% of cells, paired pronephrosproducing zones—8-12% of cells, and the
remaining lateral plate and blood-producing mesoderm containing some 45—50% of
the cells laterally and ventrally. The determination of pattern occurs according to a
generally medio-lateral time sequence,
normally over a period of some 24 hr (very
variable according to species and temperature) and across some 1 mm or 70 cell
diameters in the dimension we are considering. Earlier cell cycle studies (Cooke,
1979a, b) have indicated that cell numbers
increase only modestly by division over this
period (undergoing an average of perhaps
1.5 cycles) and have shown no feedback
effect upon the schedule of cell divisions
from processes that are modifying the
fates of cells during regulation after surgical manipulations (see question 4 in previous section). Thus newly determined
patterns in initially small embryos have the
proportionately reduced cell populations
expected in view of the material removed,
while patterns with two dorsal midlines in
single embryos consist of the same number
of cells in toto as the singly organised ones
in normal sibling embryos at identical developmental stages. These situations continue across stages when the proportions
of patterns are assessed in this work, but
whether there is ever compensatory growth
to "normalise" the tissue within each body
pattern is a quite separate problem in organismic biology. Does the completeness
of pattern ultimately control tissue mass in
the differentiated, growing body, as opposed to possible effects of cell number
upon the completeness of pattern in the
embryo? We do not know the answer.
ure 3. Proportions in the patterns of normal individuals have appreciable variability—some 20% relative variation in
notochord and pronephros, centred on absolute values of 3.5 and 10% of the mesoderm respectively, and some 10% relative
variation for the larger elements, somite
and lateral plate. Although the Ambystoma
mesoderm contains more than five times
as many cells as the Xenopus at these stages,
their proportions for the four pattern elements are indistinguishable. Small embryos showing down to little more than
one third the usual cell number in transverse section also achieve medio-lateral
proportions that are comparable with normal siblings. Present observations suggest
that pronephros is more variable in proportion than normal, in very small embryos, and that perhaps relatively more tissue than normal is devoted to lateral
plate—the reverse of what might be expected in view of the ventral material originally removed. After organiser grafting,
the total proportional numbers of cells devoted to each pattern part within the whole
embryo, regardless of position, are normal
or only slightly overbalanced in the direction of dorsal structures, even though pattern elements are distributed as two normal series, joined ventrally. Since the
slightly smaller of the two patterns, that
centred round the new organiser, makes
one think of a steeper more local gradient,
it would be expected on most models for
gradient control. This is because the graft,
implanted at the onset of gastrulation, has
had relatively restricted opportunity for
interaction with adjoining tissue in comparison to the embryo's endogenous organiser. The striking feature observed in
these double patterns, however, is that
presence of the new organiser in the embryo has scaled down significantly the cell
numbers incorporated into the dorsal pattern elements formed around the host's
original organiser. What does this observation, particularly, suggest about the dynamics of pattern determination?
The striking responses of the regulatory
mechanism to the experimental challenges
are described by the percentage figures for
pattern accompanying the diagrams of
One of the simpler diffusion-based
Figure 2, and by the use of a standard gra- models for gradients carrying positional
dient profile to symbolise or represent the information seems to be ruled out for this
proportions and scales of patterns in Fig- system. This is the supposition that the or-
SCALE AND VERTEBRATE PATTERN FORMATION
ganiser region is a source maintaining a set
(boundary) concentration, while cells
everywhere else in the system are sinks
that destroy the morphogen either at a
constant rate or at a rate varying simply
with the flux of morphogen experienced.
Since the field as a whole is the sink, ability
to produce complete gradients and hence
whole patterns will be sharply dependent
on tissue size in relation to the number of
organising regions. We would expect failure to restore presumptive ventral parts of
patterns following their removal from early embryos (Fig. 3a, version 1) or even
"flooding out" to lose specification of more
pattern than that corresponding to removed tissue (3a, version 2). In double
dorsal, normal-sized mesoderms, similarly,
a range of results between versions 1 and
2 of Figure 3b would be expected, due to
loss of gradient values specifying more
ventral elements and to flooding out.
Diffusion gradients could be maintained
in complete form, independently of tissue
scale, if concentrations were pinned to
boundary levels at localised, chemodifferentiated sources and sink regions. The
present operations, on this assumption,
will have removed one boundary in one
case and replaced it by an active boundary
of the opposite character in the other case,
so that a system would be required with
the inherent dynamics to reinstate either
source or sink characteristics at appropriate localities following their removal from
the system. Furthermore, "upper" and
"lower" boundary cells would be expected
to manifest complementary organiser
properties when used as grafts, due to active modification of the gradient landscape
in neighbouring tissue. In fact, only the
dorsal lip region gives evidence of organiser properties, for the dorsal midline of
pattern, in the primary vertebrate field.
The animal-vegetal pattern of the echinoderm blastula (not homologous anatomically with the medio-lateral gastrula pattern) is to my knowledge the only system
showing any phenomenological indication
of utilising two absolute boundaries (Horstadius, 1973).
The reaction diffusion class of model
(Gierer and Meinhardt, 1972; Meinhardt,
97
FIG. 3. a. Representation of pattern in terms of gradients profile to scale with Figure lb, but in an experimentally small embryo. Versions 1 and 2 represent results expected from certain simple diffusion
models (see text) using the organiser as a fixed source
concentration and all other cells as sink. Loss of ventral pattern and even expansion of the remaining
pattern parts is expected in small embryos. Version
3 represents the actual results, b. Representation as
in Figure la, but after grafting a second organiser
ventrally into the blastula (see text). Versions 1 and
2, again involving loss of ventral pattern and expansion of dorsal, represent what would be expected on
the simplest models for positional gradients, whereas
version 3 represents the observed behaviour.
Certain sophisticated gradient mechanisms might
be capable of achieving the regulation required by
version 3, but an alternative hypothesis (see text)
would relieve the gradient of the need for accurate
regulation of its profile in relation to scale and the
number of organisers.
1978; Meinhardt and Gierer, 1980) includes systems which in contrast to those
just mentioned, show a certain ability to
adapt the profile and scale of a morphogen
gradient to the available tissue extent. The
precise way in which this is achieved may
be derived from the above publications
(see also Papageorgiou, 1980). Essentially,
there may be a steepening of the morphogen profile following a simulation of size
reduction in the system, or in systems start-
98
JONATHAN COOKE
ing from the condition of possessing too
many activated morphogen peaks in relation to their size. This property fits qualitatively with the observations described
here, and has been used successfully in
quantitative simulations of the Hydra head/
body pattern (Bode and Bode, 1980;
MacWilliams, 1982). The hydra pattern,
however, as studied by these authors, requires only one sharp boundary between
choices made by cells, situated relatively
near one end of the system. A gradient
profile with a steep local peak at the "upper" end, thus only carrying information
utilisable by cells near one end of the system, could suffice, and is indeed the type
of profile which reaction/diffusion kinetics
can most easily size-regulate {i.e., they reduce the size and extent of a terminal
"peak" in proportion to the overall extent
of a system). But the sort of profile with
which we must deal, if we are to account
in this way for patterns such as the vertebrate mediolateral one, contains significantly graded information with precision
of slope, at positions far from the boundary. Consider the pronephros, which is (a)
centred almost on the 50% point of the
system in terms of tissue extent from the
organiser, and (b) situated at the right
places, and significantly size-regulated in
small and doubled patterns. The stringency of the demands that this would place
upon a regulating signal gradient can be
appreciated from scanning the diagrams
of Figure 3, and it must be considered
doubtful whether most of the model mechanisms that have been explored could rise
to this challenge without being extremely
parameter-sensitive and therefore improbable. Meinhardt and Gierer (1980) however discuss other classes of model whose
performances might prove relevant.
Another possible response when faced
with behaviour such as that here described
in a pattern-forming system, is to consider
that it constitutes a prima facie case against
the adequacy of a strictly positional information-based theory, whose criteria were
given in the previous section. We are then
led to examine other theories, and I present here the outline of one which departs
from the positional information idea and
looks in part to the work of Rose (e.g.,
Rose, 1967). The model involves a wavefront organised by a gradient, and a set of
logically interconnected, alternative cell
states.
Let us suppose that the organiser does
act as a boundary region controlling a gradient of "morphogen" or some physiological variable in surrounding tissue, but that
such a gradient is neither particularly stable in profile over time, nor strictly regulated in profile against scale. All it imparts,
in fact, is a reliable, coherent polarity or
direction to the time-sequence with which
development occurs across the tissue. This
is because the level in the gradient acts to
set the rate at which embryonic mesoderm
cells move towards determination (—considered as a point in developmental progression) but does not itself specify which
determinative choices they are going to
make. There is much evidence that mechanisms in early development can operate
to set the time-schedule with which cells
pass through developmental sequences, in
intimately graded ways. The result, when
we consider the spatio-temporal pattern of
the later cellular events that concern us
(—in this case the onset of determination
or differentiation per se), is a wavefront
with respect to the event, sweeping across
the tissue in a direction determined by the
location of the organiser at its origin. It is
as if a population of alarm clocks had been
lined up at an earlier time, each one set to
ring at a unit interval later than the previous one. The rings will occur as what has
been called a kinematic wave. Evidence for
the biological occurrence of such organisation has come from experiments explanting small pieces of gastrulae, and
from work on the pattern of somites in the
longitudinal body dimension (Cooke and
Zeeman, 1976; Pearson and Elsdale,
1979). This supposition at once relieves
the cell interaction system that sets up the
gradient of all demands upon its regulatory powers. It could be quite simple. All
that is required is that in any gastrula possessing an organiser, a wavefront with respect to cell maturation sweeps coherently
down the medio-lateral dimension of pattern from the dorsal midline, while in a
SCALE AND VERTEBRATE PATTERN FORMATION
gastrula possessing two organisers, two
wavefronts originate from the respective
midlines to converge, both setting out and
travelling across approximately the same
developmental time (—we have seen that
patterns around recently implanted organisers tend to be smaller, possibly because
more recently produced gradients are local and steep, or wavefronts begin a little
later).
Switching attention to the intracellular
machinery governing the determined
state, let us suppose that possible determined states are arranged in a logical sequence as follows. Once activated by the
physiological effect due to presence of the
organiser, cells progress automatically towards state A (notochord) unless the experience of above-threshold concentrations of an inhibitor specific to A diverts
them at an early stage of their progression,
whereupon they switch towards state B
(somite) until and unless a new inhibitor
specific to B builds up enough to divert
them again, and so on through pronephros (C) to lateral plate (D). Let us further
suppose that an early biosynthetic product
within cells, of the entry to each determined or differentiating state, is the specific inhibitor of access to that state by less
mature cells. We assume these inhibitors
to be so diffusible that their concentration
builds up widely in the tissue sheet, within
a short time relative to the progress of the
slow wavefront of determination. We then
see that as the wavefront progresses the
determination produced will change, to
give the successive zones of different
character corresponding to each pattern
element. Each inhibitor, synthesized in
increasing amounts as more cells progressively enter the state that produces
it, has only the available tissue as a diffusive sink, so that its rate of build-up in concentration acts in effect as a size-sensor of
the system as a whole. The smaller the
field, the more rapidly will entry to each
successive state become prohibited to further cells, which will thereby be switched
towards development of the next determined state leading to global build-up of
the next inhibitor. As the wavefront of development progresses, the width of the
99
zone occupied by each determined state
may be adapted to the size of the whole
tissue, in a way that is formally equivalent
to the operation of a temporal series of
regulating reaction-diffusion systems, each
specifying one boundary. If the inhibitors
are sufficiently diffusible, relative to the
developmental rate, for inhibitor contributed from two similar developing zones to
be summated in the territory between
them, we have an explanation for the crucial result in Figure 3b, version 3, that the
presence of an extra organiser scales down
the pattern parts controlled by the original
one as well as leading to a new pattern of
its own. In its most general form this might
be termed a serial switch model rather than
a serial inhibition model, since by symmetry, the logical sequence of cell states might
be implemented by a series of positive, diffusible activators for succeeding states (i.e.,
A —» B) as opposed to self-inhibition by
each state.
Certain details of the results (Cooke, in
preparation) such as a lesser degree of size
regulation by the earliest-determined notochord, correspond to weak predictions
of the model. A strong prediction, which
has not yet been tested, concerns the effect
of large pieces of already-determined somite or pronephric zone, transplanted
from older gastrulae to the ventral region
of younger, undetermined hosts. Specific
suppressant effects upon the size of homologous elements in the host pattern
should be observed. On the positional information theory only the organiser itself,
implanted from a young donor, should be
able to cause such effects, and they must
be accompanied by a whole new pattern
sequence in ventral opposition to the host
sequence. The serial switch model also relieves cellular interpretative mechanisms
of the demands generally imposed by the
positional information concept, in that
each interpretative "decision" is essentially
binary, the final multiplicity being achieved
because of cellular history (i.e., in a combinatorial fashion), rather than by exact
perception of many levels of a continuous
positional variable. We lack information
that makes us confident that cells could
accomplish the latter task.
100
JONATHAN COOKE
The chick limb antero-posterior pattern
growth on normal schedule
Vf'
FIG. 4. Model which best fits the current data relating limb pattern specification to early growth control.
Pattern-controlling and growth-promoting signals in
the system are seen as distinct entities, only loosely
correlated in profile, though both organised from the
ZPA at the posterior edge of the field. The process
of setting up a complete gradient and founding all
the digit rudiments is one that intrinsically occupies
a particular space, perhaps because a pre-pattern as
well as a simple "diffusion" gradient system is involved. On this view, anterior graft of a new ZPA, as
well as causing mirror duplication of pattern, leads
initially to "flooding out" of pattern corresponding to
digit 2. Widespread enhanced growth due to the extra ZPA however allows both pattern specification systems to be once again complete by stages of determination. The first three levels of the diagram
represent the normal situation, and the two timepoints within the first, say, 24 hr after an anterior
ZPA graft. The bottom line gives the proportions
(—the scale is by then much greater, and irrelevant)
in the later limb cross-section. Ordinate is the signal
value for each location, abscissa the anterior (left) to
posterior (right) tissue extent at each stage. Profile of
pattern-determining signal,
. Profile of a signal
influencing the cell cylce,
. Levels of signal
associated with particular digits, but with cell fate still
undetermined, 2, 3, 4. Tissue determined as or actually forming particular digits, (5 © ©. Note that
growth is greatest for more posterior elements in the
pattern.
The vertebrate limb-bud is an example
of a secondary field, in that the limb pattern is regulated as a whole, but has derived its location in the body and its overall
orientation from the primary embryonic
field during axial patterning. Subject to
the lively argumentation that attended the
limb presentations at this symposium, an
organiser region for the antero-posterior
pattern dimension, which is initially expressed in the skeleton and skin, can be
defined at the posterior edge of the undifferentiated chick wingbud. This appears to
control pattern according to a gradient
formalism such as in the case of the primary medio-lateral pattern just discussed,
although the system is complicated by the
rapid growth that is undergone while pattern is actually being determined. Transplantation of this "zone of polarising activity" as a graft to the anterior border of a
bud at stages around 19 (Hamburger and
Hamilton, 1951) results with high reliability in the ultimate formation of a wing
digit and forearm pattern mirror-imaged
around the normal anterior border.
When presenting their model for "Pattern formation in epimorphic fields,"
French et al. (1976) suggested that development in all seconary fields might be
found to show an intimate relationship between growth control and the control of
pattern, whereas primary pattern formation in fact shows no such inter-relationship or dependency. A shape change that
includes a widening has been noted as an
early accompaniment of successful pattern
duplication in limb buds following ZPA
grafting. Summerbell and 1 therefore decided to look in detail at the cell cycle in
host wingbud mesenchyme during the 17
hr following the anterior graft of a (normally posterior) ZPA mesenchymal region
that results in symmetric double pattern
formation. Anterior-to-anterior grafting,
with little or no positional disparity, served
as a control for any effect of operation per
se upon thymidine uptake; this turns out
to be localised and transitory at most.
The results have been presented in de-
SCALE AND VERTEBRATE PATTERN FORMATION
tail elsewhere (Cooke and Summerbell,
1980; see also Summerbell and Honig,
1982). Though very striking, they are not
consistent either with the idea that the new
pattern is produced by intercalation in tissue specifically grown at the host/graft
junction, or with the idea of a cell cycle
schedule in wingbud mesenchyme that is
independent of pattern specification, as in
primary fields. Between 9 and 17 hr after
a positional disparity has been imposed by
the anterior graft, a cell cycle response that
will in due course increase the rate of
growth has been instigated in the tissue of
more than half the bud, and often extending to parts of the original posterior border. The response is certainly concentrated in the anterior half, which fits with the
finding (Honig, in preparation) that the
anterior duplicated limb structure, although it usually ends up equal to the normal structure in size, is derived from an
initially small (25%) sector of the original
bud width. But even tissue that is undoubtedly to contribute to the posterior limb
pattern, of normal polarity, experiences
significant stimulation of the cell cycle just
after anterior ZPA grafting.
We believe that by the time the duplicated, mirror symmetrical digit pattern in
these limbs is actually being laid down, the
width of tissue in the handplate will have
approached a doubling relative to what it
would normally be. Determination of pattern probably only occurs when the tissue
has expanded throughout, and the growth
schedule is once again receding towards
that normal for the stage concerned. The
signalling mechanism whereby this is
achieved remains to be elucidated, but it
seems most likely that each ZPA is a source
for some growth control agent as well as
a specifically pattern-specifying signal, and
that the growth stimulation "diffuses"
much more rapidly than does the signal
respecifying pattern around that source if
it is placed ectopically as a graft. This model (Fig. 4) contrasts with the idea of a tight
linkage between position values in pattern
formation and the control of growth, as in
epimorphic intercalation of pattern (French
elal., 1976).
101
French flags, repeating patterns
and pre-patterns
The above observations on the behaviour of the limb bud are particularly interesting because we already have evidence,
from primary embryonic pattern formation such as that described earlier, that biological machinery exists for the control of
pattern in a way that is independent of
spatial scale over a considerable range.
Why then, when we come to the setting up
of a pattern like that of the limb, do we see
behaviour which seems to indicate that the
mechanism requires a certain amount of
tissue in order to specify completely, and
has acquired additional features to make
sure that tissue mass indeed coincides with
the number of pattern elements to be laid
down? Feedback mechanisms that adapt
the final sizes of growing limbs to their
hosts must exist, after all, so that by analogy with the primary body pattern's behaviour, we might expect twin, complete
but miniature limb patterns to be founded
in one normal-sized bud after ZPA grafting, with each structure perhaps going on
to grow up to normal size over a period
when, in any case, an enormous amount of
growth occurs.
In conclusion, I should like to speculate,
and to suggest there may be a difference,
in principle, between the tasks of specifying on the one hand a "French Flag" pattern of stripes or zones (Wolpert, 1969),
each showing a unique cellular activity as
in the medio-lateral body pattern, and on
the other hand a pattern exhibiting repetitions of an obviously similar group of cellular activities, such as we see across the
vertebrate limb rudiment. Both pattern
types are fundamental to animal form. In
repeating patterns, successive collections
of cells undertake the same, obviously homologous or similar set of activities, then
differentiations, while cells in between do
something different or else simply aggregate towards the centres of the developing
structures. The deepest problem is to get
the number of centres correct, while superimposed on this is a gradation in
unique properties—the "little finger-to-
102
JONATHAN COOKE
thumb" character in the present case, that
exhibits the phenomenology of organiser
boundaries, polarity and continuity in response to experiments on the embryo and
so draws the mind towards the idea of the
positional information gradient. The available gradation between boundaries is expressed primitively in five repetitions of
the structure in the tetrapod hand, whereas bird hands express it in three (—the rudiment for a fourth is laid down but lost
embryonically). In French Flag patterns
only the unique series of features behaving
according to gradient phenomenology is
seen, and it is fundamental to them. Populations of cells embark on unique programmes of activity and differentiation,
showing almost no homology with those
elsewhere in the system, according to their
positions relative to the boundaries of pattern.
The concept of "pre-patterns," together
with a family of models as to how these
might be set up during early development
(see Turing, 1952; Gierer and Meinhardt,
1972) was evolved in attempts to explain
the control of certain types of repetitive
pattern in morphogenesis, where number
of structures is kept constant within the
species. The skeletal pattern of the limb
rudiment is a good example of such repetitiveness in two dimensions. By a prepattern, we mean a spatial distribution in
concentration of unknown "morphogens"
or some quantifiable cell state as in the positional information idea, but this time the
distribution is in some important way isomorphic with the pattern that can finally be
seen to develop as a result of the (hypothetical) pre-pattern. Thus if we could
view the undifferentiated tissue through
some appropriate microscope or spectroscope, we should recognise the form of the
pattern already in the landscape of the
spatial variable that was to control cellular
activity. The task of pre-pattern machinery
is to control by cell biosynthetic interaction
and diffusion the non-monotonic distribution {i.e., a particular number of peaks
separated by troughs or valleys) of morphogen in order to control the pattern
produced. This notion contrasts sharply
with positional information in the expla-
nation of morphologically repetitive patterns, in that the latter postulates a very
simple, monotonic distribution of signal
and, necessarily, a complex set of cellular perceptions and responses to this,
rather than a complex signal distribution
and a simple, on-off cellular response (see
MacWilliams and Papageorgiou, 1978, for
further discussion).
One effect of the more recent ascendancy of positional information theory, indeed one of its assertions, is that the concept of pre-patterns is largely unnecessary
and redundant. To air a difference in
viewpoint which, I imagine, will not be resolved until it is replaced by real knowledge of cells and the apparatus at their
disposal, I find it implausible to imagine
that the pattern of, say, the wrist and hand
cartilage condensations could initially be
produced only by cellular interpretation of
one or two variables, simply graded between boundaries. The mapping function
from the spatial variables onto cellular activity would seem to present too complex
a task to intracellular interpretative machinery. Each element of such a pattern is
obviously comparable with others in terms
of cell activity and differentiation, even
though they may go on to exhibit nonequivalence in subsequent development
(Summerbell and Lewis, 1975) so that a
positional grid system is also indicated.
Thus it seems to me more parsimonious to
assume that a set of spatially distributed,
locally equivalent situations of the pre-pattern type is being responded to in parallel
with a range of unique readings for some
other variable to give the graded properties.
It is intriguing to note that all models
for generating pre-patterns thus far described and explored by simulation, have
at most a very limited capacity to adjust the
spatial "wavelength" at which they specify
pattern units, to differences in overall field
size (though see Papageorgiou, 1980). Prepattern models are essentially reaction-diffusion gradient models (see earlier discussion) with the effective inhibitor range adjusted downwards to allow development of
multiple activation peaks. Each set of biosynthetic and diffusion parameters pro-
SCALE AND VERTEBRATE PATTERN FORMATION
grammed into such models gives rise to
peaks separated by a particular "chemical
wavelength" which it is hard, in principle,
to have adjusted according to the tissue
size that individual embryos of a species
might have available. In practical, and especially biological, terms this means that
the number of elements produced in repetitive patterns set up by pre-patterns
would be a function of the extent of tissue
available at the time. Quantitatively and
qualitatively normal pattern would tend
strongly to require normal size initially.
The intimate control relationship between
growth schedule and pattern specification,
displayed in the limb field but absent from
the primary mediolateral pattern, could
thus have evolved in response to requirements of the system that sets up the repetitive class of pattern that is involved in
the secondary field.
103
French, V., P. J. Bryant, and S.V. Bryant. 1976. Pattern regulation in epimorphic fields. Science
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