Growth and morphogenesis at the vegetative shoot apex of ...

Journal of Experimental Botany, Vol. 54, No. 387, pp. 1585±1595, June 2003
DOI: 10.1093/jxb/erg166
RESEARCH PAPER
Growth and morphogenesis at the vegetative shoot apex
of Anagallis arvensis L.
Dorota Kwiatkowska 1,3 and Jacques Dumais 2
1 Institute of Plant Biology, Wrocøaw University, Kanonia 6/8, 50±328 Wrocøaw, Poland
2 Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of
Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Received 29 October 2002; Accepted 5 March 2003
Abstract
A non-destructive replica method and a 3-D reconstruction
algorithm are used to analyse the geometry
and expansion of the shoot apex surface. Surface
expansion in the central zone of the apex is slow and
nearly isotropic while surface expansion in the peripheral
zone is more intense and more anisotropic.
Within the peripheral zone, the expansion rate, expansion
anisotropy, and the direction of maximal expansion
vary according to the age of adjacent leaf
primordia. For each plastochron, this pattern of
expansion is rotated around the apex by the
Fibonacci angle. Early leaf primordium development
is divided into four stages: bulging, lateral expansion,
separation, and bending. These stages differ in their
geometry and expansion pattern. At the bulging
stage, the site of primordium initiation shows an
intensi®ed expansion that is nearly isotropic. The following
stages develop sharp meridional gradients of
expansion rates and anisotropy. The adaxial primordium
boundary inferred from the surface curvature is
shifting until the separation stage, when a crease
develops between the primordium and the apex dome.
The cells forming the crease, i.e. the future leaf axil,
expand along the axil and contract across it. Thus
they are arrested in this unique position.
Key words: Shoot apical meristem, strain anisotropy, strain
rates, surface curvature, surface expansion.
Introduction
Primary shoot structures originate from the shoot apical
meristem, and all the cells of the shoot are derived from
3 To whom correspondence should be addressed. Fax: +48 71 375 41 18. e-mail: dorotak@biol.uni.wroc.pl
Journal of Experimental Botany, Vol. 54, No. 387, ã Society for Experimental Biology 2003; all rights reserved
putative stem cells located at the top of the apex dome.
Growth at the shoot apex is unique among plant meristems
because it integrates two fundamental processes: the selfperpetuation
of the apex dome and the initiation of lateral
organs. Self-perpetuation requires the maintenance of
meristem size despite the continuous ¯ow of cells through
the meristem. The initiation of lateral organs depends on
the speci®cation of groups of cells and their gradual
separation from the meristem proper. The superposition of
these two processes at the shoot apex leads to a complex,
yet predictable, sequence of shapes. The complexity of
meristem morphogenesis combined with the technical
dif®culties involved in observing the meristem explain
why a detailed analysis of shoot apex morphogenesis has
yet to be performed (Erickson, 1976; Silk, 1984).
Some signi®cant features of shoot apex morphogenesis
are nevertheless known. As a rule, all cells in the meristem
are dividing (Clowes, 1959, 1961). However, the expansion
and division rates of these cells vary over the apex
volume. In the case of vegetative apices, growth is less
intensive at the distal portion of the dome (the central
zone) and more intensive at the periphery (the peripheral
zone), especially where lateral organs are initiated
(Romberger et al., 1993; Laufs et al., 1998a; Lyndon,
1998). The expansion of the shoot apical meristem is
therefore inhomogeneous. Moreover, cells do not expand
at the same rate in all directions. Instead, many cells show
a main axis of extension while little extension is observed
in the perpendicular direction (HernaÂndez et al., 1991;
Tiwari and Green, 1991). Meristem expansion is therefore
anisotropic.
Little is known about the quantitative aspect of
meristem morphogenesis beyond the general trends mentioned
above. Perhaps the most fundamental reason why a
detailed analysis of meristem morphogenesis is necessary
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1586 Kwiatkowska and Dumais
is that a particular sequence of shapes can result from a
wide range of growth patterns at the cell level (Hejnowicz
and Nakielski, 1979; Nakielski, 1982, 1987). The only way
to address the role of individual cells in morphogenesis is
to quantify their contribution directly. Such quantitative
data about meristem morphogenesis would be an important
addition to the molecular knowledge of this process. They
would help us to understand how known cytohistological
zones (Clowes, 1961; Romberger et al., 1993) and gene
expression domains (Bowman and Eshed, 2000; Brand
et al., 2001; Traas and Doonan, 2001) are maintained, even
if the cells that compose these zones and domains are
continually changing. In particular, quantitative data on the
rate of cell migration from one expression domain to the
next would indicate how quickly cells need to acquire new
`identities'.
With these applications in mind, what would constitute
an adequate quantitative description of morphogenesis at
the shoot apical meristem? Ideally, morphogenesis should
be described in 3-D and with high spatial and temporal
resolution. The two fundamental variables for any quantitative
analysis of morphogenesis are the surface curvature
and the surface strain rates. Curvature is a measure of
the local geometry of the surface, while the strain rates
measure its relative rate of expansion. If surface curvature
and strain rates are to be compared with gene expression
data, cellular resolution of these variables is needed since
the transition between gene expression domains can occur
over one cell length. Morphogenesis at the shoot apical
meristem repeats itself at a regular time interval, the
plastochron, corresponding to the time required for the
initiation of successive leaves or groups of leaves at
the apex (Erickson and Michelini, 1957). While, for the
root meristem, a description of geometry at one instant is
suf®cient to apprehend the entire morphogenetic process
(Silk et al., 1989), for the shoot apical meristem the
description must span the whole plastochron. Therefore,
protocols to investigate morphogenesis at the shoot apex
must be able to resolve morphogenesis within a plastochron,
which, in apices producing relatively large leaf
primordia, usually lasts for a couple of days (Dale and
Milthorpe, 1983; Lyndon, 1998).
This paper presents an analysis of surface expansion at
the shoot apical meristem. The protocol uses a noninvasive
replica method (Williams and Green, 1988) and a
new computational approach that includes 3-D reconstruction
of the meristem surface (Dumais and Kwiatkowska,
2002). This protocol allows the quanti®cation of the
geometry and expansion of the apex with relatively high
temporal and spatial resolution. The data collected are used
to address two fundamental questions concerning morphogenesis
at the shoot apex: (i) what is the surface
expansion pattern leading to the self-perpetuation of the
apical dome; and (ii) what is the surface expansion pattern
leading to partitioning of new leaf primordia from the
meristem proper. The investigation is performed on
vegetative shoots of Anagallis arvensis L. (Primulaceae)
exhibiting spiral Fibonacci phyllotaxis.
Materials and methods
Plant material
Four shoot apices of A. arvensis were used in this investigation. With
this material, meristem morphogenesis could be followed over seven
plastochrons. Two apices (the ®rst and the second apex) came from a
plant collected on the Stanford University campus and kept in a
growth chamber under a 16/8 h day/night cycle, a 15 W m ±2
illumination, and a temperature of 20±21 °C (Dumais and
Kwiatkowska, 2002). These conditions were non-inductive despite
the fact that A. arvensis is a long day plant (Brulfert et al., 1985),
presumably because the light spectrum did not include the inductive
wavelengths. The other two apices (including the third apex
presented here) originated from a clone derived by means of
vegetative propagation from a wild plant growing in the Sudety Mts.,
Poland (the same clone as used by Kwiatkowska, 1997). These
plants were kept at a temperature ranging from 18±24 °C, in short
days (10/14 h day/night) to prevent ¯owering, with an illumination
of 9 W m ±2 .
Data collection and analysis
A non-destructive replica method (Williams and Green, 1988; Green
et al., 1991; HernaÂndez et al., 1991) was used to obtain a
developmental sequence for each apex. To expose the meristem
surface, thin threads were glued to the tip of the young leaves
overarching the meristem so that these leaves could be temporarily
pulled away. The leaves were returned to their original position once
the replica was completed. Replicas were made at 12±24 h time
intervals and examined with scanning electron microscopy (Philips
SEM505 and LEO435VP).
Computer tools developed earlier (Dumais and Kwiatkowska,
2002) were used to collect and analyse the morphogenetic data. The
cell vertices, i.e. the points where three cells come into contact, were
used as surface markers. For each member of a developmental
sequence, two scanning electron micrographs were taken, one tilted
by 10° with respect to the other. The x±y position of vertices was
collected manually from one of the images, while for the other image
the vertex locations were found with an area matching protocol.
Since the two images offer slightly different perspectives of the same
structure, the distances between vertices differed in these images.
This shift in the x±y position of vertices was used to determine the
elevation (the z position) of the vertices.
The curvature of the meristem surface was computed from the
reconstructed meristem. A quadratic surface was ®rst ®tted to the
vertices of a given cell and its contacting neighbours. The local
curvature could then be computed from the coef®cients of this
quadratic surface. The computation of strain rates requires the
identi®cation of corresponding vertices on consecutive replicas of
the growing meristem. This was done with a clonal analysis in which
cells and their progeny were identi®ed in consecutive images, like
the exemplary cells highlighted in Fig. 1A±E. The strain rates at a
given vertex were then computed from the deformation of the
triangle de®ned by the three vertices in direct contact with that
vertex. The overall strain rates for the cell were computed as the
weighted sum of the strain rates at the cell's vertices. A graphical
user interface and computer programs written in Matlab (The
Mathworks, Natick, MA, USA) can be downloaded at: http://
culex.biol.uni.wroc.pl/instbot/dorotak.
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Results
Similarity of the developmental sequences con®rms
the validity of quantitative data
Although the manipulations of the meristem required to
make replicas do not involve any wounding, they could
nevertheless disrupt morphogenesis. Inspection of the
material collected indicates that the geometry of the
meristem has not been affected. For example, casts of
apices at the same plastochron stage are strikingly similar.
This is true whether replicas from the same apex, further
referred to as members of the same developmental
sequence (e.g. Fig. 1A, E), or from different apices (e.g.
Figs 1A, 2C) are compared. The meristem manipulations
could also have slowed down the rate of growth, which
would lead to a longer plastochron. Such an effect on
growth was indeed observed in some sequences excluded
from this investigation. An increase in the length of the
plastochron can also be seen in the sequence published in
Fig. 5 of Green et al. (1991). A careful comparison of the
observed plastochron is therefore in order. The estimated
plastochrons for the sequences presented in this paper fall
between 40 h and 45 h, irrespective of the origin of the
plant material and the growth conditions. The material
presented is therefore consistent at that level. Precise
measurements of the plastochron were also published by
other authors (Ballard and Grant Lipp, 1964; Brulfert et al.,
1985), for decussate vegetative shoots of A. arvensis kept
in the growth conditions similar to the plants used here.
Again, this plastochron is consistent with the measured
plastochrons for decussate shoots from which replicas
were made (results not shown). The plastochron for shoots
with decussate phyllotaxis is more than twice as long as
shoots with spiral phyllotaxis, but not surprisingly since in
decussate phyllotaxis two leaf primordia are initiated
simultaneously. Therefore, half rather than the whole
plastochron characteristic for decussate shoots should be
compared with that of spiral ones (Rutishauser, 1998).
Variables describing the geometry and expansion of
the shoot apex surface
The geometrical analysis yields the principal curvatures
and the Gaussian curvature for each cell on the reconstructed
meristem surface. It should be emphasized that the
curvature values reported do not refer to individual outer
walls of the cells but rather to the curvature of the smooth
surface de®ning the overall geometry of the meristem. The
principal curvatures are the extreme curvature values,
attained on a surface along principal curvature directions.
In plots of the meristem curvature (the second column in
Figs 1±3), the principal curvature directions for each cell
are illustrated by the two arms of a cross. The length of
these arms is proportional to the curvature in their
direction. If in the arm direction the surface is convex,
the cross arm appears in black; if the surface is concave,
Growth of the shoot apex surface 1587
the arm is red. The Gaussian curvature is the product of the
principal curvatures and shows how much a surface differs
from being ¯at. If a surface is ¯at or can be ¯attened
without any tears or folds, its Gaussian curvature is zero. A
concave or convex surface that tears when ¯attened, for
example, a hemisphere, has a positive Gaussian curvature.
A surface shaped like a saddle, which will form folds, if
¯attened, has a negative Gaussian curvature. In curvature
plots, the Gaussian curvature is indicated by the colour
assigned to each cell (Figs 1±3). The warmer the colour,
the higher is the curvature.
The growth analysis yields the principal strain rates ( : e1
and : e2) and directions, areal strain rate, and strain rate
anisotropy. The strain rates are the relative rates of
extension (Erickson, 1966, 1976; Hejnowicz and
Romberger, 1984; Silk, 1984; Goodall and Green, 1986;
Dumais and Kwiatkowska, 2002). If surface expansion is
anisotropic, these rates assessed in different directions are
not the same. There are two unique mutually orthogonal
directions on the surface, in which strain rates attain
extremal, minimal and maximal, values. These directions
are the principal strain rate directions. The extremal values
are called principal strain rates. The crosses plotted for
each cell in the third column in Figs 1±3 indicate the
principal strain rate directions. The length of cross arms is
proportional to the corresponding principal strain rate.
Positive strain rates (extension) are indicated with black
cross arms, negative strain rates (contraction) are in red.
The principal strain rate directions used in the present paper
are the same as directions pointed by the `strain crosses'
introduced by Goodall and Green (1986), and theoretically
de®ned principal directions of growth (Hejnowicz and
Romberger, 1984). The areal strain rate is computed as the
sum of the principal strain rates and is indicated in the
strain rate plots by the cell colour. The warmer the colour,
the higher is the areal strain rate. The strain rate anisotropy,
given by the equation ( : :
e1 e2†=… : e1 ‡ : e2), shows how much
the two principal strain rates differ from each other.
Geometry and growth of the apical dome are not
uniform and change during the plastochron
The apical dome is always in contact with three leaf
primordia of various ages. The Gaussian curvature of the
central zone of the dome is positive but close to zero
(the second column in Figs 1, 2). The curvature of the
peripheral zone depends on the plastochron stage and the
age of the contacting leaf primordium. At the beginning of
the plastochron, a new leaf primordium becomes discernible
within the peripheral zone as a region where the
Gaussian curvature is locally higher and minimal and
maximal curvatures are very similar (e.g. P1 in Fig. 2F).
Leaf initiation sites become apparent before any signs of
bulging can be seen on scanning electron micrographs of
the apex surface (compare P1 in micrograph in Fig. 2C
with the curvature plot in Fig. 2F). During the second half
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1588 Kwiatkowska and Dumais
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of the plastochron, a narrow band, one to three cells wide,
becomes visible within the peripheral zone along the
recently initiated primordium (e.g. along P3 in Fig. 1G).
Growth of the shoot apex surface 1589
These cells are curved almost exclusively in the direction
of the primordium margin. Thus a typical cross of principal
curvatures is reduced to a latitudinal line segment. At the
Fig. 2. Scanning electron micrographs (A±C), curvature (D±F), and strain rate plots (G±H) for the second apex. Labelling as in Fig. 1. This
sequence covers 36 h, which is slightly less than one plastochron. Primordia are initiated in a counter-clockwise order. The sequence begins
during the ®rst half of the plastochron.
Fig. 1. Scanning electron micrographs (A±E), curvature plots (F±J), and strain rate plots (K±N) for the developmental sequence of the ®rst shoot
apex. The time at which the replica was made is given in the lower right corner of each micrograph. Leaf primordia are numbered from the youngest
primordium observed in the sequence to the oldest. Each primordium is labelled as soon as it becomes discernible as a region of locally elevated
Gaussian curvature. Cells included in the analysis are outlined in black on the micrographs. An exemplary cell and its progeny are outlined in red in
all the sequence members. The colour map for the curvature plots represents the Gaussian curvature measured for a cell and its adjacent neighbours.
Note that all the measurements were made in 3-D but are here presented as 2-D projections for clarity. The Gaussian curvature on the scale bar is
given in 10 ±4 mm ±2 . The orientation and length of the cross arms indicate the direction and magnitude of the principal curvatures, respectively. The
arm appears in red if the surface in its direction bends upward (concave). Areal strain rates and strain rate crosses are plotted for each cell on the
plot of cell outlines as they appeared at the beginning of the considered time interval. The colour map represents the areal strain rate measured in
units of 10 ±2 h ±1 . Cross arms are oriented along principal strain rate directions; their length is proportional to the corresponding principal strain rates.
The arms appear in red if negative strain rate, i.e. contraction, took place in their direction. Regions that will give rise to a leaf primordium during
the following time interval are outlined in black. Additional lines are added along the primordium margin to delineate the future leaf axil. The
sequence covers 83 h, which is about two plastochrons, and starts during the ®rst half of the plastochron. The second plastochron begins at the third
sequence member. Primordia are formed in a clockwise order. Two of them, P1 and P0, are initiated within the time of observation.
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1590 Kwiatkowska and Dumais
Fig. 3. Developmental sequence of a primordium formed on the ¯anks of the third shoot apex. Scanning electron micrographs (A±D), curvature
(E±H), and strain rate (I±K) plots are labelled as in Fig. 1. The sequence covers 70 h, starting from the lateral expansion stage of P1 up to the
bending stage. Slightly less than the ®rst two plastochrons of the primordium development can be followed.
same time a part of the peripheral zone where the next
primordium will be initiated attains a slightly higher
curvature (e.g. the upper right portion of the dome in
Fig. 2E). During the following plastochron the cells
forming the band of zero Gaussian curvature give rise to
the primordium axil (compare cells located along the P3
margin in Fig. 2D, E). In the present paper the term axil
cells is referring to cells, which have the most negative
meridional curvature of all the cells located near the
primordium margin. In the curvature plots they have the
longest red arms, such as the cells on the margin of
primordium P3 in Fig. 2F. The parts of the peripheral zone
contacting the axil (e.g. at the contact with P4 in Fig. 1F
and G) are usually saddle-shaped: convex along the dome
circumference (black cross arms), and slightly concave
along its meridian (red cross arms). Between the regions
contacting leaf primordia, the peripheral zone cells are
curved predominantly in the meridional direction (between
P2 and P3 in Fig. 1H).
The expansion of the apex dome surface is non-uniform
and generally anisotropic (the third column in Fig. 1 and
2). In terms of surface expansion, the central zone and the
peripheral zone merge into each other gradually. Areal
strain rates are the lowest and strain is nearly isotropic in
the central zone, while in the peripheral zone both strain
anisotropy and areal strain rates are generally higher.
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Fig. 4. Leaf primordia delineated on plots of cell outlines of the last
sequence member in which a given primordium was observed. The
lines of various colours are primordium boundaries as recognized in
consecutive members of the sequence. Corresponding member
numbers are: red line ± member 1; blue ± 2; green ± 3; black ± 4;
orange ± 5. Primordia labels are the same as in the micrographs of the
sequences. (A) P1 and P2 of the ®rst apex (refer to Fig. 1) plotted on
cell outlines of member 5 of the ®rst developmental sequence. No
crease has yet been formed on P1 margins and its delineation is not
stable. The boundary of P2 is stable starting from member 4 (black
line), where shifts occur only on the axil sides. (B) Outlines of
primordia P2 and P3 shown on member 3 of the sequence for the
second apex (refer to Fig. 2). The boundary of P3 is stable starting
from member 2 (blue line). P2 has not yet been delineated from the
meristem by a crease. (C) Outlines of primordium P1 shown on
member 4 of the third sequence (refer to Fig. 3). The boundary of P1
is unstable in members 1±2 (red and blue lines), and become stable
when the crease appears in member 2.
However, expansion of the peripheral zone is not uniform.
It is slow and not strongly anisotropic in the region
adjacent to the recently formed primordium (e.g. the cells
adjacent to P2 in Fig. 1L±M), where maximum strain rates
Growth of the shoot apex surface 1591
are latitudinal, i.e. in the direction parallel to the
primordium margin. The above-mentioned band of cells
having nearly zero Gaussian curvature gives rise to the leaf
axil expanding along the primordium margin (latitudinally)
and contracting across it (meridionally, like the cells
along P3 in Fig. 1L). The expansion of the formed axil
cells is similar (like cells of the axil of P3 in Fig. 1M or P3
in Fig. 2H). The area of these cells is almost not changing,
or slightly diminishing. Where the dome ¯anks are
rebuilding at the contact with the primordium axil (for
example, adjacent to the axil of P3 in Fig. 1M), areal strain
rates and anisotropy are high. There the maximal strain
rate is in the meridional direction. This direction is
perpendicular to the maximal strain rate direction of the
adjacent axil cells. The region contacting the axil is the
fastest growing portion of the peripheral zone during
the ®rst half of the plastochron (Fig. 1M). In the second
half of the plastochron, an additional region of increased
areal strain rate appears at the initiation site of the next
primordium. This region covers a portion of the peripheral
zone larger than is actually contributing to the formation of
a new primordium (e.g. around P1 in Fig. 1L). When the
next plastochron begins, the cycle is repeated but rotated
by the Fibonacci angle around the apex, e.g. by about
137.5° clockwise between members of the ®rst sequence
shown in Fig. 1K and M.
Emerging leaf primordia show increasing gradients of
curvature and strain rate
Four developmental stages can be distinguished in the
course of the primordium formation covered in this study.
These are: (i) the bulging stage; (ii) the lateral expansion
stage; (iii) the separation stage; and (iv) the bending stage.
The ®rst two stages cover about one plastochron. The third
one lasts nearly half of a plastochron; whereas the fourth
one extends beyond the period covered in this study.
Primordium P2 from the ®rst sequence (Fig. 1) and
primordium P1 from the third one (Fig. 3) can illustrate all
the stages. In the ®rst stage, the leaf buttress is
characterized by locally elevated Gaussian curvature (P2
in Fig. 1F±H). The buttress surface is expanding with high
areal strain rates and nearly isotropically (P2 in Fig. 1K,
L). The region of increased expansion sometimes covers
more than the surface of the emerging primordium (e.g. P2
in Fig. 1L). During the second stage, the buttress attains an
oval shape (P2 in Fig. 1I; P1 in Fig. 3E). Cells on the
primordium surface expand mostly latitudinally, while
some contraction may take place in the meridional
direction (P2 in Fig. 1M). The cell area, however, is still
increasing since the latitudinal expansion exceeds the
meridional contraction. During the third stage (P2 in
Fig. 1J; P1 in Fig. 3F), the buttress becomes separated from
the dome by the axil. At the same time, the primordium
surface expands similarly to the preceding stage. Finally in
the fourth stage (P1 in Fig. 3G, H), a ¯attened primordium
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1592 Kwiatkowska and Dumais
is formed with an adaxial surface of negative Gaussian
curvature and an upper portion of high positive curvature.
The adaxial surface is concave meridionally and convex
latitudinally. At this stage the primordium starts to
overarch the apex (like P1 in Fig. 3G, H). The fourth
stage is characterized by differential growth. The expansion
of the upper leaf portion where the Gaussian curvature
becomes relatively high is intensive and not strongly
anisotropic (for example, the outermost cells of P1 in
Fig. 3J, K). The adaxial surface of the primordium bends
towards the dome. Its cells expand relatively slowly and
with high strain rate anisotropy (see remaining cells of the
above-mentioned primordium). Some meridional contraction
is observed on the adaxial side of the primordium,
while the maximal strain rate direction is parallel to the
leaf axil.
Leaf primordium boundaries inferred from the surface
curvature are unstable with respect to cells during early
leaf development, i.e. during the bulging and lateral
expansion stages. The boundaries are shifting during these
two stages by one or two rows of cells. Both an
incorporation of new cells into the primordium (e.g. P1
in Fig. 4A) and, less often, a reduction of the primordium
area can take place (P2 in Fig. 4A). Starting from the third
developmental stage, the displacements of the primordium
boundaries are signi®cantly reduced. This corresponds to
the time when the leaf axil is formed between the apical
dome and the leaf primordium. Subsequently, shifting of
the primordium boundaries is restricted to the lateral sides
of the primordium (right side of P1 in Fig. 4C), where the
Gaussian curvature is negative but closer to zero than in
the middle of the axil. Sometimes, starting from the
separation stage, the boundaries do not move at all (P3 in
Fig. 4B).
Discussion
A non-invasive replica method and a 3-D reconstruction
algorithm were used to quantify the geometry and surface
expansion of the shoot apex of A. arvensis. The results
were analysed in the light of two fundamental processes
occurring at the shoot apex: the self-perpetuation of the
apical dome and the formation of leaf primordia. The
observed changes in the geometry and expansion of a leaf
primordium surface were characteristic enough to differentiate
early leaf development into distinct stages. These
stages could be regarded as representative for the early
development of dicot leaves, of which the leaf of A.
arvensis is a typical example.
Self-perpetuation of the vegetative shoot apical dome
The overall pattern of expansion in the shoot apex is
characterized by a gradual increase in the rate of expansion
and expansion anisotropy as one goes from the central
zone to the peripheral zone. These observations are in
agreement with earlier studies of shoot apex growth
(Newman, 1956; Soma and Ball, 1963; Hussey, 1971;
Green et al., 1991; Lyndon, 1998; Laufs et al., 1998a).
This particular pattern of expansion, however, is not
unique in its ability to maintain the size and dome-like
shape of the shoot apical meristem (Hejnowicz and
Nakielski, 1979; Nakielski, 1987). Opposite gradients of
expansion were observed on the dome of tip-growing cells
(Hejnowicz et al., 1977; Shaw et al., 2000) and there is no
geometrical reason why a similar expansion pattern would
not work in the shoot apical meristem. A possible
biological explanation for the slow growth of the central
zone is that it helps the plant preserve the genetic material
of reproductive cells which will originate from this region
(Hejnowicz and Nakielski, 1979; Klekowski, 1988). If the
rate of expansion is low, the cells will divide less
frequently thus reducing the likelihood that replication
errors will occur. An alternative explanation is that the
high rate of growth in the peripheral zone results from the
rapid initiation of lateral organs. This explanation is
incomplete since in the pin1 mutant of A. thaliana the
in¯orescence apex does not initiate lateral organs and yet
the mitotic index remains relatively high in the peripheral
zone (Vernoux et al., 2000).
The peripheral zone is differentiated into regions whose
distribution is related to the youngest three leaf primordia.
Similar sectors, comprising the peripheral zone of the
shoot apex of Clethra barbinervis Sieb. et Zucc. exhibiting
spiral phyllotaxis, were reported by Hara (1971) who
determined them based on the anticlinal cell walls pattern.
In the apex of A. arvensis, the geometry and growth of
these sectors were shown to depend on the age of the
adjacent leaf primordium. The sectors differ in their
Gaussian curvature and in their expansion rates and
anisotropy. Even the direction of maximal strain rate in
adjacent sectors may be entirely different. The site of leaf
primordium initiation is characterized by locally intensi-
®ed growth. Interestingly, the region of high strain rate
also includes cells that will not contribute to the new
primordium. For each plastochron, the growth pattern is
rotated around the apex by a ®xed angle (the Fibonacci
angle). The temporal and spatial complexity of the dome
expansion is a consequence of the fact that the continuous
initiation of leaf primordia in a regular but asymmetric
pattern is superimposed on the self-perpetuation of the
dome.
Formation of the leaf axilÐpartitioning of the shoot
apex
The leaf axil is unique among the different regions of the
meristem, both in its geometry and growth. The meridional
gradients of curvature, areal strain rate, and strain rate
anisotropy are especially sharp across this region. The
expansion observed in the leaf axil is similar to the
expansion observed during the formation of the radial
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creases between stamens in A. arvensis ¯owers
(HernaÂndez et al., 1991), and also the creases delimiting
organs in adventitious shoots of Graptopetalum paraguayense
E. Walther (Tiwari and Green, 1991). The
expansion of the future axil cells is very slow, and takes
place only along the axil as observed also by Green et al.
(1991). Thus, the cells forming the axil are arrested in this
particular position. This observation may explain why
Soma and Ball (1963), as well as Hussey (1971), noted that
some of the markers applied to the apex surface were not
moving out of the young leaf axils. Another consequence
of such a pattern of cell expansion is that its appearance on
the adaxial margins of a leaf primordium signi®cantly
reduces the displacement of the primordium boundary, i.e.
it partitions the shoot apex surface into the dome and new
leaf primordium.
Early development of the leaf primordium
In this study, the course of leaf primordium formation is
divided into four stages. These stages cover the ®rst
(`organogenesis') stage and a part of the second (`early
growth of the primordium') stage of leaf development
de®ned by Sylvester et al. (1996). Distinct changes in
primordium geometry and growth allow the ®rst, `organogenesis'
stage to be resolved. It comprises the bulging,
the lateral expansion, and the separation stages of the
present paper, while the bending stage is at the beginning
of the stage of `early growth'. During the bulging stage,
growth of the primordium is relatively intensive and
isotropic. The cytoplasm of cells comprising the primordium
at this stage, visible in longitudinal sections of the
apex, stains more intensely than the cytoplasm of other
meristem cells (Fontaine, 1972). The intense staining is
another manifestation of the high meristematic activity of
these cells. By contrast with the bulging stage, lateral
expansion of the primordium surface relies on relatively
low areal strain rates, but high strain rate anisotropy. Later,
during primordium development, sharp meridional gradients
of strain rates and anisotropy appear, and the
primordium surface becomes differentiated into regions
of various expansion and geometry.
The control of areal strain rates and strain rate
anisotropy
One important conclusion from this work is that morphogenesis
at the shoot apex depends on sharp gradients of
areal strain rates as well as on anisotropy of strain rates.
One should therefore ask how these gradients and
anisotropy are created and maintained at the cell and
molecular levels.
Areal strain rate is scalar, that is, any given point of the
meristem surface has a single areal strain rate value. Its
level could be directly regulated by a scalar factor, such as
the concentration of gene products or growth regulators
(Hejnowicz and Romberger, 1984). In the apical dome, the
Growth of the shoot apex surface 1593
distribution of such factors can be regulated by genes
whose expression is speci®c to the peripheral or central
zone (Nishimura et al., 1999; Zondlo and Irish, 1999).
Some of these genes, such as CLAVATA and MGOUN, are
known to regulate the size of these meristem zones (Laufs
et al., 1998a, b; Traas and Doonan, 2001). The primordium
initiation site, in turn, shows an elevated expression of the
expansin gene (Reinhardt et al., 1998). Also, exogenous
application of expansin to the apex surface can induce leaflike
outgrowths (Fleming et al., 1999), while local
induction of expansin expression can induce the entire
process of leaf formation (Pien et al., 2001). The
intensi®ed areal strain rate observed at leaf initiation
may result from a local loosening of cell walls on the apex
surface by secreted expansin proteins (Fleming et al.,
1999).
Future axil cells presumably also express speci®c genes,
although the exact spatial and temporal relationships
between gene expression domains and future axil cells
remain unknown. The expression domains of CUP-
SHAPED COTYLEDON in Arabidopsis thaliana (L.)
Heynh. (Aida et al., 1999; Brand et al., 2001; Traas and
Doonan, 2001), NO APICAL MERISTEM in Petunia sp.
hybrids (Souer et al., 1996), and various OSH genes in
Oryza sativa L. (Sentoku et al., 1999) are correlated
with primordium boundaries. The CUP-SHAPED
COTYLEDON2 gene is thought to act as a local growth
suppressor (Traas and Doonan, 2001). Theoretically, a
crease can be formed by locally lowering the areal strain
(Todd, 1986). Therefore, some of the above-mentioned
genes may be directly involved in the control of axil
formation by locally inhibiting cell expansion.
Unlike areal strain rates, the strain rate anisotropy must
be regulated by factors of a similar, anisotropic nature
(Hejnowicz and Romberger, 1984). The signi®cance of
anisotropic factors in morphogenesis is supported by the
fact that dividing plant cells seem to `perceive' stress or
growth anisotropy existing in their environment (Miller,
1980; Hejnowicz, 1984; Lintilhac and Vesecky, 1984;
Lynch and Lintilhac, 1997). Neither the concentration of
gene products (scalars), nor the concentration gradients of
such gene products (vectors) are anisotropic factors. The
latter have only a single direction de®ned together with a
corresponding scalar value. By contrast, cellular structures
such as the cytoskeleton or the cell wall often show
anisotropy. A connection between cytoskeletal arrangement,
cell wall reinforcement, and anisotropic cell expansion
has been shown (see for example Selker and Green,
1984; Tomos et al., 1989; Green, 1992; Bichet et al.,
2001). In the case of cell walls, a non-random alignment of
cellulose micro®brils results in differences in mechanical
properties of walls along different directions. Cell walls
are mechanically reinforced in the direction of cellulose
alignment. Since the outer walls of tunica cells in the shoot
apical meristem are the thickest of all the meristem cell
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1594 Kwiatkowska and Dumais
walls, the reinforcement of these particular walls is a good
candidate for the direct control of the apex surface growth
(Green, 1986; Green and Selker, 1991). Combining the
study of cell wall mechanics with quantitative data on the
morphogenesis at the shoot apical meristem may help to
understand how meristem growth is controlled.
Acknowledgements
The authors thank Dr Zygmunt Hejnowicz (Silesian University,
Poland) for critical reading of the manuscript and Drs Zo®a Czarna
and Krystyna Heller (Electron Microscopy Laboratory, Wrocøaw
University of Agricultural Sciences, Poland) for help in preparing
some of the scanning electron micrographs used in this work. Part of
this research was ®nanced by a research grant No. 3P04C 015 22
from the Polish Committee for Scienti®c Research to DK and a NSF
grant to the late Paul Green. DK acknowledges additional support
from the Fulbright Foundation while visiting Stanford University.
JD acknowledges support from the Center for Computational
Genetics and Biological Modeling (Stanford University).
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