Annals of Botany 88: 1141-1152, 2001
doi:10.1006/anbo.2001.1397, available online at http://www.idealibrary.com on IDEKL
The Natural Philosophy of Plant Form: Cellular Autoreproduction as a Component of a
Structural Explanation of Plant Form
P. W. BARLOW*t, H. B. LUCKJ and J. LUCK§
\IACR-Long Ashton, Long Ashton Research Station, Department of Agricultural Sciences, University of Bristol, Long
Ashton, Bristol, BS41 9AF, UK, %Val d'Arenc, 83330 Le Beausset, France and §CNRS ERS 6100, Faculte des
Sciences et Techniques de Saint-Jerome, 13397 Marseille, France
Received: 2 May 2000
Returned for revision: 25 June 2000 Accepted: 25 January 2001
A map-L-system is described which simulates the development of the two-dimensional patterns of cell walls
displayed at the surfaces of shoot apices of Psilolum nudum. The simulation of these cellular patterns commences
with the division of a triangular cell and continues until a complete set of ten different cells, including new
triangular cells, is formed amongst the descendants of each merophyte. The triangular cells generated by means of
this division pathway, PI, are, in their three-dimensional aspect, four-sided apical cells. In the plant, they have the
potentiality to support the development of a shoot apex. The generation of new triangular cells by pathway PI
therefore seems to be a precondition for the branching of the shoot. Observed variations upon the cellular pattern
developed by pathway PI have also been analysed. Two of these variant pathways, P2 and P3, suggest the types of
controls which are required to bring about all three (P1-P3) patterns of cells. These controls may involve the
participation of the plant cytoskeleton and may also require an influence from the apical cell itself. The triangular
shoot apical cells of Psilolum are autoreproductive cells: that is, at each division, one of the daughters is a new
triangular cell, the other daughter has some other shape. This example of triangular cell autoreproduction and selfmaintenance and its relation to organogenesis is discussed in light of the views on reproduction and selfmaintenance expressed by Agnes Arber (1950) in her book The natural philosophy of plant form (Cambridge:
Cambridge University Press).
© 2001 Annals of Botany Company
Key words: Agnes Arber, apical cell, cell division patterns, computer simulation, cytoskeleton, L-systems, Living
Systems Theory, meristems, Psilotum, shoot apex, stem cell.
THE HOLISTIC VISION OF AGNES ARBER
connectedness that is inherent to living entities. Seemingly,
she was ready to include within the orbit of this connectedUpon opening The natural philosophy of plant form, we find
ness parameters belonging to different levels of plant
that Agnes Arber (1950) quickly reaches to the heart of plant
organization—from the aforesaid macroscopic 'outward
morphology. On page 2, she writes 'it is the business of
form' to the microscopic 'internal anatomical and nuclear
morphology to connect into a coherent whole all that may
structure'. We might conjecture that Arber's philosophy
be held to belong to the intrinsic nature of a living being'.
embraced holism (Smuts, 1926) and that she would have
And concerning morphology, Arber realizes that this science
been only a small step away from an acceptance of Systems
need not limit itself to external features: it should not only
Science (e.g. von Bertalanffy, 1968) whose aim is the
embrace 'the outward form seen by the artist and systemintegration of processes across many levels of biological
atist', but it also 'should invoke the analytic detail of
organization.
anatomical and nuclear structure seen by the microscopist'.
A systems' approach to plant life was already in place in
From these statements, and indeed from the rest of her
survey of plant morphology in The natural philosophy of the botanical literature when Arber wrote The natural
plant form, it is clear that Agnes Arber possessed a vision of philosophy of plant form. It had been presented by G.
plants that was as broad as it was profound. Moreover, from Haberlandt in his book Physiologisches Pflanzenanatomie,
her study of botanical history, she could trace the trains an English edition of which was published in 1914
of reasoning that had led to the mid-20th century con- (Haberlandt, 1884, 1914), and was carried forward into
cepts of plant morphology from their beginnings two the 1950s by text-books such as Lehrbuch der allgemeinen
millenia before1. Arber was also clearly persuaded of the Botanik by H. von Guttenberg (1956). Around this time, a
similar 'Living Systems Theory' was proposed by Miller
(1965).
The tenets of this theory seem, however, to have had
• For correspondence. Fax +44 (0)1275 394007, e-mail peter,
their origins in the contemporaneously burgeoning fields of
barlow^bbsrc.ac.uk
1
Nowadays, with the benefit of a long historical perspective, some cybernetics and information theory (e.g. Ashby, 1956), and
of the ideas of the early morphologists seem distinctly peculiar.
they focus not so much on the natural world at large, but on
Perhaps they bear out Karl Popper's argument that 'we do not know,
Man, especially his physiology, psychology and social
we can only guess, and our guesses are guided by the unscientific, the
constructions. Not unexpectedly, Miller, in propounding
metaphysical faith in regularities' (Popper, 1968).
0305-7364/01/121141 + 12 S35.00/00
S, 2001 Annals of Botany Company
Barlow et al.—Cellular Autoreproduction and Plant Form
1142
his theory, largely ignored plant life. It has been possible,
however, to repair this omission and develop Miller's
conception of Living Systems in terms of the plant world
(Barlow, 1987, 1993, 1999). This reappraisal appears to be
quite successful, not least because in many respects it
reaches, quite independently, many of the same conclusions
that were formulated by Haberlandt decades earlier.
Briefly, the recasting of Living Systems Theory in terms
of plant life (Barlow, 1987, 1999) proposes that the living
plant system is organized into an hierarchical set of'levels'.
In this respect, the scheme is no different to Miller's original
proposition. The span of the levels is from the cellular (LI)
to the community (L5). A property of the Living Systems'
hierarchy is its self-similarity: not only does each level (L/j)
emerge from the one below (Ln-1) but, importantly, it also
shares with it a similar organizational structure. According
to Miller's analysis, each of the eight levels which he was
able to identify in the human system is supported by a
similar set of 20 sub-systems (sl-s20) (Miller and Miller,
1990), each sub-system being identified by its 'main feature',
i.e. 'reproducer', 'boundary', 'timer', etc. The sub-systems
are split into three sub-sets, sl-s2, s3-sl0 and si 1—s20,
which process matter, energy and information, respectively.
In Plant Living Systems Theory, the homologous levels
seem to contain fewer sub-systems, the 'missing' subsystems (sl5-sl7) being those which deal with information
processing (Barlow, 1999), but it may be that these subsystems have yet to be identified.
The sub-system si, designated 'Reproducer,' reunites us
with Arber's The natural philosophy of plant form for, in
Chapter 6, she reminds us of the significance of reproduction. For her, reproduction is intimately associated with selfmaintenance which, in turn, is a fundamental characteristic
of all living things—this being an idea that dates back to the
Stoics of Ancient Greece. Arber also recalls (pp. 77-78) that
the Dutch philosopher, Benedictus de Spinoza (1632-1677)
referred to this thesis of self-maintenance in the following
words: 'The effort by which each thing endeavours to
preserve in its own being is nothing but the actual essence of
the thing itself. Thus, the very 'essence' of life lies in both
self-maintenance and reproduction. Where in plants can
these 'essential' properties be found?
CELLULAR
AUTOREPRODUCTION
Within each level of the plant hierarchy there is a
'Reproducer' sub-system, si (Barlow, 1999). At the level
of the organism (L3), the metamer (or phytomer) is
responsible for this sub-system function (i.e. for vegetative
reproduction), whereas at the level of the organ (L2) it is the
meristem that corresponds with the Reproducer. If the
Reproducer could be more closely defined at this level, it
might help to uncover the basic unit of self-maintenance
and hence illuminate Spinoza's 'essence of the thing'. Each
plant meristem is made up of two parts, one which is
permanent and the other which is disposable, this latter
part being periodically removed beyond the boundary of
the meristem. (This is mirrored at the organism level, L3, by
the immortal germ line and the disposable soma, as
conceptualized by the zoologist, August Weismann.) The
permanent portion of the root meristem corresponds to the
cytogenerative centre (Clowes, 1954), and the impermanent
portion to the proximal and distal meristems (Torrey and
Feldman, 1977).
In terms of the cells which construct meristems, the only
cells possessing a self-maintaining, reproductive property
are initial cells or stem cells (Barlow, 1997), and these are
located within the cytogenerative centre. A defining
characteristic of a stem cell is that following a mitotic
division, at least one of its two daughters (a cell designated
p) divides again. The other daughter (designated q) may or
may not divide. If the q cell does divide, it will do so a
limited number of times, thus contributing to the impermanent portion of the meristem, before it is subsumed into
the mature corpus of the organ (see Luck et al., 1997).
Therefore, the stem cell, p, is a unit of self-maintenance and
reproduction. To be relevant to the self-maintenance and
reproduction of an organ, the descendants (q) of the stem
cell should have access to information for the generation of
an organ to which they (the q cells) and the stem cell (p) are
an integral part. In the case of either a root or a shoot, the
meristematic q descendants of the respective p cells must
contain the properties of 'rootiness' or 'shootiness' in order
to accomplish organogenesis. One means of realizing this is
if the p cell itself is intrinsically imbued with the relevant
organogenetic properties and these are handed on to its
descendant q cells. If true, then the stem cell, p, is truly the
bearer of the organ 'essence' in the sense that it is the
ultimate repository of information for reproduction and
self-maintenance, not only of itself, but for the complete
organ. Maybe a gene such as RAC (described in tobacco)
provides the key to 'rootiness' since mutant rac plants
cannot form adventitious roots even though the necessary
cell divisions occur (Lund et al., 1996).
The concept of the 'histogen' helps clarify further the
property of self-maintenance. A long history of observations on meristems shows that not only do they produce
new cells, they also constantly generate new tissue. Whereas
all the cells of an organ are derived from the stem cells, its
tissues are derived from histogens which we consider to be
comprised of q cells or their immediate descendants.
However, because of the descendance of q cells from
autoreproductive stem cells (p cells), these p cells must also
be the proximate source of tissues. Nowhere is the colocation of cytogenesis and histogenesis more evident than
in the structural initials of apical meristems, and especially
in the distinctive apical cells of cryptogams (Barlow, 1994).
These special cells not only conserve their own being but are
also the source of cells for organogenesis. Agnes Arber
would probably have supported this view since she implies
that 'persistence of being', besides providing continuity in
time, also denotes an endeavour to actualize potentialities.
This is exactly the aforementioned two-fold aspect of the
apical cell, for here, on the one hand, there is selfmaintenance (autoreproduction) and, on the other hand,
cell reproduction. The progressive unfolding of organ and
tissue development is carried out by the cellular descendants, or merophytes, of the apical cell.
Barlow et al.—Cellular Autoreproduction and Plant Form
A U T O R E P R O D U C I N G APICAL CELLS
Apical cells have two remarkable properties.
Asymmetric divisions. The two daughter cells of a
division, p and q, are different. The p cell is autoreproductive and retains the shape and properties of the parent cell.
The q cell and its descendants have limited division
potential and they eventually differentiate as tissues.
Rotating divisions. In the case where the apical cell is
triangular (as seen in surface view), the plane of cell division
is usually angled 120° from that of the preceding division.
Successive divisions take place in either a clockwise or
counterclockwise sense. The three sides of the triangular
cell mark the edges of its wall facets and reflect the fact that
in three dimensions, the cell is actually a four-sided
tetrahedron. In shoots, the facet which faces the exterior
of the organ never passes in its entirety into q daughter
cells, whereas the three facets which face the interior do so.
In roots, all four facets pass into a q daughter cell, and
hence the apical cell is located beneath the surface of the
organ, covered by root cap tissue.
The difference between the behaviour of the apical cell in
shoots and roots gives a clue to how the plane of division
may be regulated. To see this, it is necessary to revisit their
origin during embryogeny (e.g. Vladesco, 1935). The apical
cell of both the root and the shoot arises by the division of
cells which face the exterior of the embryo. In the case of the
shoot apical cell, the outward-facing facet makes no contact
with any other cell, whereas in the case of the root apical cell
there is contact between the outward-facing facet and an
external layer of cells. This contact may play a role in
determining the direction of nuclear and cell division in such
a way that the outward-facing facet becomes one of the walls
of a q daughter cell. The other daughter, the p apical cell,
becomes progressively more internal, though its outwardfacing walls retain contact with its sister q cells.
The above proposal may apply to embryos with
exoscopic polarity where the apical pole of the zygote
faces the archegonium (e.g. Equisetum spp.) (Foster and
Gifford, 1959). Whether it also applies to embryos which
are endoscopic in origin, where the apical pole is embedded
in gametophyte tissue, is uncertain. The general question
remains, however, whether cell-cell interactions, of either a
physical or a chemical nature, play a role in determining the
plane of division of any given cell (Lintilhac, 1987; Lynch
and Lintilhac, 1997). The alternative is that the division
plane is independent of neighbouring cells and is, therefore,
inherent to each cell capable of division. Both these
questions arise in analyses of cellular autoreproduction in
the shoot apex of Pteridophytes with apical cells.
S I M U L A T I O N OF CELL D I V I S I O N
PATHWAYS IN THE SHOOT APEX O F
PSILOTUM
NUDUM
Self-reproducing cell wall patterns can be simulated by
means of map-L-systems (Lindenmayer and Rozenberg,
1979; Luck et al., 1988), these being extensions into two
1143
dimensions of the earlier L-systems developed by Lindenmayer (Lindenmayer, 1968). Generally, L-systems are
algorithms that reproduce recurrent events during development. Previous analyses (Luck et al., 1988; Barlow et al.,
2000) of the two-dimensional cell wall patterns seen on the
surface of shoots of Pteridophytes revealed that these
patterns could be simulated exactly by means of a doublewall map L-system (dwMOL-system) (Luck and Luck, 1981).
A feature of L-systems is that the current state of a
constructional element (e.g. a cell) determines its future
state. This new state is acquired after the elapse of a period
of time (timestep). A number representing a state is
attached to each cell wall or wall segment of the cellular
array. At each successive timestep, /, another state is
substituted for the pre-existing state. The sequence of state
substitutions is specified by a deterministic algorithm. Each
timestep corresponds to a cell division. The algorithm also
conveys instructions as to where a new division wall should
be inserted; it thus includes a division rule. By allowing the
division rule to act upon a single cell with an initial set of
wall labels (co0), a regular pattern of cell walls quickly builds
up. Although there is no theoretical limit to the number of
state substitutions that can be made, or the number of
timesteps available, rather few are usually needed to reach a
pattern of walls which starts to be repeated with further
simulation. That L-system simulation of cell patterns
should be so successful implies that each cell which is
involved in pattern formation contains some element with
sufficient information to specify its continuing development.
Commencing with the cell wall patterns of the shoot
apices of Psilotum nudum, which were illustrated by
Takiguchi et al. (1997), it was found that one dwMOLsystem called S 5 5 gives an exact representation of these
patterns (Barlow et al., 2000). The cell pattern thus
simulated corresponds to the outcome of one of the two
most frequent pathways of cell division, PI, found by
Takiguchi et al. (1997). Commencing with a triangular, ptype apical cell, system S5.5 generates a set of ten different
cells which are descendants of the <?-type daughter cell, or
merophyte (Fig. 1). Each cell within the set can be identified
with a letter and a number (Barlow et al., 2000). The
original triangular cell, a3, always maintains itself; it is an
autoreproductive, or self-maintaining, stem cell.
The complete set of ten cells requires / — 5 timesteps for
its production. At the fourth step (/' = 4) a new a3 cell is
created from one of the cellular descendants within the
oldest (fourth) merophyte (Figs IE and 2A). This new
apical cell then repeats the aforementioned sequence of
divisions, producing another set of ten cells that now
includes a second-generation, autoreproductive triangular
a3 cell.
The triangular cell emits a four-sided daughter merophyte, bA\, at each of its three sides in turn. As a
consequence, the sequence of daughter merophytes (old
to young) seems to lie on a spiral which winds towards the
triangular cell (Fig. 1). The spiral may be either clockwise
or counterclockwise, its sense being reversed around each
successive generation of triangular cells: that is, if the spiral
of merophytes winding towards the new, first-generation
1144
Barlow et al.—Cellular Autoreproduction and Plant Form
1145
Barlow et al.—Cellular Autoreproduction and Plant Form
apical cell is clockwise, then the spiral which winds towards
the antecedent, parental triangular cell is counterclockwise.
Another frequent division pathway at the Psilotum apex
is designated P2 (Takiguchi et al., 1997). It arrives at a
similar pattern of cells, except for the arrangement of walls
in the immediate vicinity of the triangular cell, 63 (Fig. 2B).
A third, less frequent pathway is P3. It gives a cellular
pattern quite different from the other two pathways, PI and
P2 (Fig. 2C). No new triangular a3 or b3 cells are created in
the merophytes, and there are other features of the wall
placements in the merophytes that are different from those
found in the other pathways. Although in pathway P3 these
differences seem to predict the failure of new triangular cell
production, there is nothing to suggest that the division
process itself is abnormal; it is only the orientations of the
new walls which are at variance with those found in
pathway PI.
If the conditions which determine each of the pathways
PI, P2 and P3 could be revealed, then deeper insights might
be gained of the rules which govern cellular patterns in both
the Psilotum apex and in multicellular systems generally.
Moreover, which cellular pathway is adopted within an apex
might have a consequence for organ branching. At issue,
therefore, is the fundamental question of what significance
cell shape and cell production have for organogenesis itself.
For example, whenever and wherever a triangular cell is
produced on the Psilotum apex, can it be presumed to
possess the potential for shoot organogenesis? And are cells
a3 and b3 similar in this respect, even though each cell has
different types of neighbouring cells? If, in both cases, the
answers are affirmative, then the regular production of
successive generations of triangular cells via pathways PI
and P2 could potentially lead to a regular branching of the
shoot. Conversely, when new triangular cells are not
generated, as in pathway P3, the question is whether this is
associated with a total loss of branching and new organ
production? In his investigation of young shoots of Psilotum
mulurn, Bierhorst (1954) found that no more than four
generations of dichotomies occurred, even though, after the
final branching, the shoots continued to grow. One may ask,
therefore, whether the early dichotomies of the shoot apex
are the result of pathways PI and P2, and whether these are
superceded by a pathway such as P3 which does not support
branching.
Psilotum apex; pathways P2 and P3 are variants of PI. As a
prelude to an hypothesis concerning how P2 and P3 might
arise, details are now given of the map-L-system representation of pathway PI. The following division rule, Al,
which is the algorithmic representation of system S5.5 is
applied:
1
2
3
4
5
-> 4-5/67
8
->
9
->
-> 0/,2
3
->
6 -> 5/ 6 7.
7
-f
9
8 - > 0/.2
9
- •
3
0 ->
4
(Al)
In its initial state (co0), at step / = 0, the map is represented
by a cell with three walls consisting of five segments in total
(Fig. 1A). The wall segments of this triangular cell are
numbered 1. 23. fL5, in clockwise fashion. The underlining
indicates that a wall is comprised of two or more segments,
each of which is given a label. The points (.) simply indicate
the separateness of walls and wall segments, even though
contiguous segments may compose one wall, as denoted by
the underlining. It is not necessarily whole walls, but
segments, which are the items operated upon by this and
similar algorithms. When the cell divides, a new division
wall is formed. The slash (/) in Al indicates the division wall
attachment node; the subscript of the slash (e.g. /, and /6)
indicates the label (1 or 6) which is to be taken by the new
division wall.
Because the triangular cell has three neighbouring cells, a
corresponding double-wall notation (expressed in the
language of the dwMOL-system) can also be used. This
notation incorporates all the wall segments of the triangular
cell as well as those of its neighbouring cells: | (for the
division wall), ^ or j ^ (the two double wall segments are
the same), and j | for the two other walls.
This double-wall labelling indicates the labels which are
held by walls and segments on their two opposite sides. The
notation pertains to all the cells generated by algorithm Al.
The working-out of the system from algorithm Al is shown
in Fig. 1A-F.
DIVISION PATHWAY C O N T R O L :
AN HYPOTHESIS
Map-L-systems and cellular biology
An autoreproductive cell division algorithm
As shown by Takiguchi el al. (1997), pathway PI is the
principal one associated with the cellular patterning of the
The algorithm Al specifies the wall pattern derived from
map-L-system S5.5. But the wall patterns of living plant cells
are dependent upon cytokinesis which, in turn, is dependant upon the placement of a transient pre-prophase band
F I G . 1. From an initial map (A), five successive maps (B-F) are derived according to map-L-system S5.5 and division rule A l . At each timestep, i,
the cells divide in synchrony and all walls are re-labelled. A set often different cells is produced over the course of / = 5 timesteps. As shown in the
inset, each of the ten cells is defined according to the number of its neighbouring cells (superscript numeral) and its order number (subscript
numeral); the arrows indicate the state change at each timestep. Cell a3 is a self-reproducing triangular cell whose daughter merophyte is
designated 6 4 ,. A new, first-generation triangular cell, b3, is generated in the merophyte at step i = 3 (D). After / = 5 timesteps (F), there are 36
cells, eight of which are triangular cells (the initial a3 cell, three other a3 cells and four b3 cells). Within each cell in A-D there is a sketch of the
nucleus (O) and the phragmoplast (broken line across the nucleus). The nucleus is joined by arcs (broken lines) to the angles (*) of certain wall
segments (0.6, 6.7, 5.1 or 1.2, where the points correspond to the angles; at the next cell generation these sites are renumbered 4.5, 8.9, 3.4, 7.8,
respectively). The phragmoplast is shown in the orientation which the new division wall will adopt after cytokinesis. New division walls are
coloured red, and are labelled j . The series of successively younger merophytes lies on a clockwise spiral which winds towards the initial triangular
a3 cell.
1146
Barlow et al.—Cellular Autoreprocluction and Plant Form
B
D
F I G . 2. Schemes showing four pathways of development (P1-P4) at the shoot apex of Psilotum nudum. A, Pathway PI conforms to map-L-system
S5.5. Successively produced merophytes are numbered 1-4. A new triangular cell is marked </; it corresponds to cell b3. B and C, In comparison
with pathway PI, pathways P2 and P3 have variant divisions in the fourth and second merophytes, respectively, counting from the triangular cell
(a 3 ). D, The earliest variant division of P4 affects the triangular cell itself, other divisions follow pathway P3.
(PPB) of microtubules (reviewed in Davies et al., 1996). The
wall site formerly occupied by the PPB, the microtubules of
which dispersed during mitosis, secures the new cell plate
within the mother cell wall, thereby giving rise to two
daughter cells. In points 1-3 and 5-7 below, we propose a
cytological scheme which, when integrated with the map-Lsystem S5.5, forms a basis for pathway PI. The scheme also
indicates the adjustments to its elements (see point 4) that
are necessary to derive pathways P2 and P3.
(1) The PPB is guided to its location at the mother cell
periphery by microtubules which radiate from two
opposite poles (N and S) of the nucleus. Hence, the
position of the N and S poles at the stage of interphase
immediately prior to PPB formation determines where
the PPB will be located.
(2) The final orientation of the N and S nuclear poles is
related to the states of the cell walls facing these poles.
The new division wall forms initially from a phragmoplast and cell plate whose plane is perpendicular to that
of the N - S axis.
(3) The PPB site at the cell periphery contains cytoskeletal
material which persists after the PPB microtubules have
disappeared at mitosis and which actively assists the
positioning of the new division wall.
cell in the third merophyte from the apical cell (see Fig. 2B);
in P3 the critical cell is b4i in the first merophyte from the
apical cell (see Fig. 2C). In both cases, the new division wall
forms in a 'default' position which conforms to the classical
division rules that the new wall is of minimal surface and is
placed so as to effect equal volumes of the two daughter cells
(see Korn and Spalding, 1973).
A more extreme pathway, P4, involves divisions of the
triangular apical cell in which the successive reorientations
of the cell plate do not follow the usual sequence (Figs 2D
and 3). This pathway is said to be seen at later stages of
shoot development (see Fig. 18 in Takiguchi et al., 1997).
Disorientation of the division pattern in pathway P4 could
Point 2 was shown (Barlow et al., 2000) to be an acceptable
condition for the development of pathway PI, as traced out
from algorithm A1. However, to account for pathways P2
and P3, a modification is introduced so that:
(4) If the influence of the wall states on nuclear orientation
is removed immediately prior to PPB formation, then
the nucleus is free to adopt some other orientation.
As a consequence of this last-mentioned point, a PPB could
form in a novel position, though by chance it would
sometimes also be in the usual position according to point
2. If the PPB were in a novel position, however, then the
division wall would be inserted in an orientation which,
though perpendicular to the N - S nuclear axis, would be
uncharacteristic of pathway PI.
The two pathways P2 and P3 differ from each other
according to which cell shows the critical reorientation of
the nucleus as a result of the putative absence of the
influence upon which nuclear orientation usually relies. In
the case of pathway P2, the critical cell is the triangular b3
F I G . 3. Tracing of an apex of Psilotum nudum. Successive merophytes,
recognizable on the apical surface, are numbered 1-5. Merophytes
surrounding the apical cell (A) have divided in accordance with
pathway P3. The clockwise rotational sequence of apical cell division
has been maintained until the last division whereupon the cellular
system entered pathway P4, as shown by the position of merophyte 1
(cf Fig. 2D). Consequently, the apical cell may continue growing and
dividing in such a way that its triangular outline is lost. Redrawn from
Fig. 18 in Takiguchi el al. (1997).
Barlow et al.—Cellular Autoreproduction and Plant Form
result in the apical cell eventually growing and dividing in
such a way that its triangular outline is lost and five-sided
cellular descendants take its place, as was illustrated by
Hagemann (1980).
The proposed relationship between nuclear orientation
and wall state (Barlow et al., 2000) can now be refined
further with additional points 5 and 6 relating to postdivision behaviour. If implemented in a cellular context,
these points would set up preconditions for all the observed
wall orientations.
(5) The cytoskeletal material which persists at the former
site of the PPB is bisected by the new division wall.
Hence, in the two daughter cells of the division, this
material resides at the edges formed by the new wall
junction. We suggest that these new edge sites and their
contents are critical for the location of N and S poles of
the nucleus.
(6) There are two such edge sites belonging to each newly
divided cell. In the two-dimensional representation of
the cells, and in the notation of algorithm Al, these sites
are 0.6, 6.7, 1.2 and 5.1; at the next cell generation these
sites are renumbered 4.5, 8.9, 7.8 and 3.4, respectively.
In each case, the sites are sought out by the N and
S poles of the interphase nucleus (perhaps by means of
cytoskeletal fibres or filaments). The nucleus then
adopts an orientation which determines the plane of
the subsequent cytokinesis (see point 2). Although the
cytoskeletal material is maintained at the edges long
enough to orient the nucleus, there might be situations
where this does not occur, as mentioned in point 4.
Intriguingly, an osmiophilic substance was found at the
edges of cells in the root meristem of Azolla pinnata by
Gunning et al. (1978). Its identity is unknown, but it has
some connection with the microtubular component of the
cytoskeleton.
It is evident from studying the pattern of walls that,
although a system for wall placement based on nuclear and
phragmoplast position could in many circumstances be
sufficient to generate a deterministic pattern, it cannot alone
account for markedly unequal cell divisions. In pathway PI,
for example, both the first and second divisions are unequal
within each newly formed merophyte, i.e. the divisions of
cells b4{ and b43 (Fig. 1). Therefore, it is necessary to
propose a final point:
(7) Prior to division of a mother cell, only certain walls or
portions of walls are conditioned to receive the cell plate
and, hence, to accept the new division wall into the
overall pattern of walls.
Usually, this last point (which is implicit in algorithm Al
and which supplements point 3 above) acts in conjunction
with the system for nuclear orientation (point 6). Together,
they exactly specify the positioning of the division wall.
Occasionally, however, this combination of rules does not
operate and nuclear orientation seems to become the sole
determinant of the division plane. When cells b3 and b\ fail
to develop their usual cell-plate reception sites, pathways P2
and P3, respectively, are initiated.
1147
What the variant pathways reveal about division control at
the apex
The three pathways, P2, P3 and P4, may be evidence of a
loss, during the course of plant development, of the strict
control over cell division at the apex which is normally
manifested in pathway PI, the sequence of this developmental breakdown being PI —> P2 —> P3 —> P4. Notice
that pathways P2 and P3 (Fig. 2B and C) indicate a loss of
control in cells which are progressively closer to the apical
cell. Pathway P4 involves the apical cell itself (Fig. 2D),
with the surrounding merophytes dividing in accordance
with pathway P3 (Fig. 3). The feature which indicates the
entry of the cellular complex into P4 is that the most recent
division in the apical cell does not conform to that expected
of successive 120° rotations of its division plane. In pathway
P3, however, the apical cell does divide with the characteristic rotational sequence (Fig. 2C). Seen in another way, it is
as though, in pathway PI, the apical cell, a3, is able to exert
an influence over the divisions which occur in all those
merophytes with which it shares a border (merophytes 1-3)
and a little way beyond (into merophyte 4). Should this
influence diminish, the neighbouring merophytes might
then behave more independently of cell a3 and cells would
become free to form default division patterns. Eventually,
with the extinction of influence from cell a3, there could be a
loss of controlled division orientation, not only in the
neighbouring merophytes (as occurs in pathway P3) but
also in cell a3 itself. This is proposed to account for pathway
P4.
The loss of control over the cell patterning and the final
acquisition of pathway P4 do not, however, preclude further
cell divisions. These continue and follow a pathway in which
no triangular cell is involved. This type of cell is obliterated
by differential cell wall growth and, after further divisions,
its place is occupied by four- or five-sided cells. Occasionally, however, a new triangular cell can be regenerated
within such a cell group (Hagemann, 1980). This cell may
then continue dividing, acquire organogenetic capability
and, later in development, be responsible for the emergence
of a new shoot branch. Thus, under some circumstances, the
outcome of pathways P4 and P3 could lead to the return to
pathway PI.
The same situation applies in apices of higher plants. For
example, in maize roots, sets of formative divisions create
all the cell files of the root. Then the files move into the
proliferative zone of the proximal meristem and follow
other division pathways (see Luck et al., 1997). Nevertheless, within pericycle tissue there is the potential for the
recreation of sets of autoreproductive stem cells whose
descendants form lateral root primordia and thence new
roots (see Barlow et al., 2001).
The belief that there must be other controls over the
placement of the new wall in addition to the simple control
which, as mentioned above, utilizes the orientation of the
nucleus and mitotic apparatus, accounted for the introduction of point 7 above. But, so far, the states of the cell walls
have not been considered as determinants of wall positioning. Of particular interest are the deviations from the pattern
of walls in merophytes which had commenced development
1148
Barlow et al.—Cellular Autoreproduction and Plant Form
B
0
F I G . 4. Tracings of cellular patterns within the fifth merophyte from the apical cell in three shoot apices of Psiloium nudum. A and B, Apices have
been participating in cell division pathway PI. In A, the merophyte has developed over i = 4 timesteps; in B, an additional timestep has occurred
(/ = 5 timesteps). In both cases, new, first-generation 6 3 triangular cells have appeared ( • ) , as predicted by the division rules of map-L-system S5.5
and algorithm A l . Cells which have been formed by divisions not in accordance with this algorithm are marked (*). They signal entry of the
cellular system into a passive division pathway. In B, the triangular b} cell (•) shows evidence of having divided according to pathway PI. C, The
apex is participating in pathway P3 and no triangular cells have been produced. However, the apical cell (a3, not shown) persists and divides in a
rotational sequence. Cell patterns A - C are redrawn from Figs 21, 23 and 24, respectively, in Takiguchi et al. (1997).
new site
F I G . 5. Cell patterns at the apex of Psiloium nudum. Walls and wall segments are numbered in conformity with algorithm Al. New division walls
are drawn as unbroken grey lines. A, A triangular cell (a3) and its first descendant merophyte (the reference merophyte at the upper right-hand
side) have both divided. B and C, At the next two steps, the reference merophyte is, respectively, the third and fourth merophyte from the apical
cell. C, The division of the right-hand pair of cells (seen in B) has placed one end of a division wall ( | ) on what was wall 2 of the mother cell
(labelled 'new site'), but which is now the wall labelled 8. This does not accord with algorithm Al. No new triangular cell has been formed, as
expected from A1, because wall 4 of the mother cell was not used as an attachment site for the division wall. The other attachment wall, wall 1 of
the mother cell, has been used, as expected. Expected positions of division walls are indicated by broken grey lines in B and C; actual positions of
new division walls are indicated by solid grey lines and the label 'new site'. In these figures, O represents the mitotic nucleus and an arc (
) links
the nucleus to an attachment site (*). The nucleus, together with its pair of arcs and attachment sites, are indicated as they would be prior to the
division of the mother cell. It is proposed that by means of its arcs, the nucleus is oriented so that its opposite N and S poles face towards these
sites (see A). The new division wall has a propensity to form in a plane perpendicular to the N - S nuclear axis. Where this occurs, the nucleus is
indicated by O. The attachment sites are in the angles formed by a new division wall and the wall of the former mother cell, (see Fig. 1 and the
text). It seems that the failure to use correct division wall acceptance sites coincides with the non-utilization of algorithm Al in the fourth
merophyte shown in C. In this case (and also in B), where the division plane is incorrect, the nucleus is shown as a •**>. The cell patterns are
derived from Fig. 21 in Takiguchi et al. (1997).
within the context of pathway PI. As shown in Fig. 4, there
are wall positions and cell patterns within the fifth
merophyte that do not appear to conform to those
generated by algorithm Al (cf. Fig. 1). But we cannot be
certain of this unless we assign numbers to the walls of the
cell, apply the algorithm, and see whether the apparently
variant patterns still develop (Figs 5-7). To this end,
consider the most right-hand merophyte shown in Fig. 5.
When this merophyte was the first from the apical cell, it
commenced development with wall labels 6. 7. S3J). 0. At the
next step (Fig. 5A), when this reference merophyte is now
the second merophyte from the apical cell, the walls of the
two cells are labelled 1.23.4. 5 and 6. 7J3. 9. 0. After a
further step (Fig. 5B), in which the reference merophyte is
now the third merophyte from the apical cell, the wall which
at the previous step was formerly labelled 4 has been
Barlow et al.—Cellular Autoreproduction and Plant Form
1149
F I G . 6. Development of cell patterns at the apex of Psilotum midum. The symbolic conventions are as in Fig. 5. A, Divisions have occurred in
accordance with algorithm Al. B, A misplaced division wall occurs in the fourth merophyte from the apical cell (arrow). The correct position is
indicated by the broken grey line. C, At the next timestep, pathway P2 commences in the third merophyte from the apical cell. The triangular cell,
A3 (marked with • in B), has divided, but has not used the correct attachment walls for the new division wall (the correct placement of the division
wall is indicated by the broken grey line). The analogous cell in the merophyte produced one generation earlier (marked by • • in A) did make use
of the correct attachment walls, however, and it therefore continued along pathway PI. The P2 pathway is assumed to arise by default and is
associated with the absence of arcs and attachment sites. Other deviations from pathway PI (indicated by •<•) occur in the fifth merophyte from
the apical cell. These cells are shown at the bottom right-hand side of the fifth merophyte in C. As anticipated, the correct new division wall is
indicated by the broken line; the actual wall is indicated by the solid line, attaching at a site marked by an arrow. The cell patterns are derived from
Fig. 23 in Takiguchi et al. (1997).
F I G . 7. Development of cell patterns at the apex of Psilotum nudum according to pathway P3. The conventions are as in Fig. 5. Only the divisions
within the triangular cell conform to map-L-system S5.5 and algorithm Al. A, A misplaced division wall has been inserted in the second merophyte
from the apical cell (solid grey line; the expected wall position is shown by a broken grey line) and has resulted in the wide offsetting of the two
division walls in this tetrad (see also B). The areas of daughter cells in this merophyte are more equal than unequal, as would be expected if
pathway PI were followed. The relative areas of the cells are in accordance with Hofmeister's division rule. B and C, Pathway P3 continues with
divisions which do not conform to algorithm Al. One division wall remains unlabelled (arrow) as the relabelling rule does not specify what labels
it should carry. The cell patterns are derived from Fig. 24 in Takiguchi et al. (1997).
replaced by label 0/,2. The new division wall with label 1 is
inserted asymmetrically along this former wall 4, the wall
segment 0 being much shorter than segment 2. This creates a
larger daughter with walls 1. 2. 3. 4^5 and a smaller daughter
with walls 6. 7. 8J). 0. It is, perhaps, a consequence of this
inequality of cell size that, in the biological system, the larger
daughter does not divide in an orientation that conforms to
the expected outcome of algorithm Al. Instead of a
triangular cell being formed in the larger cell (cf. Fig. ID)
by utilization of wall 4 as an attachment site for a division
wall, the new wall goes to that pre-existing wall which is
labelled 2. This results in the production of a five-sided cell
with walls 1.8.9. 0.2.3. 4.5. At this step, the relabelling of
the wall segments that were 4^5 produces segments 0.2.3
(Fig. 5C), but without the expected new division wall, 1,
being inserted into it (see also Fig. 4A). At this point, the
wall relabelling sequence associated with algorithm Al no
longer holds.
Although commencing correctly (Fig. 6A), a similar
variation in wall positioning occurs in the fourth merophyte
from the apical cell shown in Fig. 6B (see also Fig. 4B). A
triangular cell with walls 1. 2_J. 4L5 forms as one of the cells
within a tetrad of cells (Fig. 6B, arrowed), but the new
division wall, 1, seems misplaced in its attachment to what
was wall 4 in the mother cell (see Fig. 6A). The pattern in
these cells (Fig. 6B) begins to deviate from that expected of
pathway PI (cf. Fig. IE). At this stage of apical development, it is possible to observe that pathway P2 is
1150
Barlow et al.—Cellular Autoreproduction and Plant Form
commencing in the third merophyte from the apical cell.
The triangular cell, b3 (marked with • in Fig. 6B) divides,
but the new division wall (solid line) fails to find the correct
attachment walls. (The correct placement of the new
division wall would have been that indicated by the grey
broken line in Fig. 6C.) Thus, from a cell with walls
numbered 6. 7J5. 9 ^ (Fig. 6B) there arise two daughter cells
with wall numberings 6. 8. 9.0.2. 3 and 1. 4. 5 J (Fig. 6C).
Although pairings of the walls of neighbouring cells (i.e. the
double-wall labellings) are correct, the numberings of walls
in the cells are incorrect according to those prescribed by
algorithm Al. The homologous b3 in the merophyte
produced one timestep earlier cell (marked • • in Fig. 6A)
did, however, make use of the correct attachment walls, and
thus continued along pathway PI. It is not possible to say
why, in the biological system, one cell continued in pathway
PI whereas another cell, apparently identical, switched to
pathway P2.
Pathway P3 is characterized by an absence of asymmetric
cell divisions and, in particular, by the lack of new
triangular cells (Fig. 4C). The pathway commences with
the equal division of the first merophyte generated by the
apical cell to give daughter cells 1. 23_. 4. 5 and 6. 18. 9. 0
(Fig. 7A). Further divisions (Fig. 7B and C), presumed here
to be default-type divisions that accord with the aforementioned division rules, create at the next timestep a tetrad of
cells, one pair of daughters bearing wall labels 9. 0_2. 3 and
3. 4.5.7. 8, and another pair bearing labels 6. 4. 5.7.8. 9.0
and 1. 2. 3. 4 (Fig. 7B). The cells have unexpected wall
labels; the wall pairings (double-wall labellings) and the
division wall attachment sites are also incorrect. In this
pathway, as in pathways PI and P2, the apical cell
maintains its rotational division (Fig. 2C). It seems as
though the divisions within the merophytes undergoing
pathway P3 are controlled in a way that differs from those
which follow either pathway PI or P2. What is striking is
that the offsetting segments of older walls between two
division walls [a-segments in Barlow el al. (2000)] are
relatively long and are uncharacteristically used as attachment sites for new division walls. The unusual offsetting
pattern may be responsible for the subsequent variant
divisions and cell wall patterns.
When merophytes follow pathway PI, it seems that the
sites for division wall attachment (on walls with labels 1, 4,
6 and 8) are 'active' sites in that they actively influence the
division plane. If such active wall sites are not correctly
established, then deviations from the cell patterns expected
of pathway PI will occur. Whatever their wall states, cells
are driven to divide by the processes of the mitotic cycle. If
the wall states conform to those of algorithm Al, then the
division pattern expected of pathway PI will emerge, but if
they do not conform, then a default division system is called
into play. Probably, the default system is constantly
available to all cells, but is usually subordinated to
instructions pertaining to some other, more active system.
The triangular cell might be actively directing the division
process in the surrounding merophytes and thus ensures
that the patterns of wall growth and cytoskeletal activity
enable the division rules that accord with map-L-system
S5.5. The PI pathway which is held to be induced by the
triangular cell is thus an 'active' division pathway.
Active and passive division pathways
Consideration of all the division pathways in the Psilotum
apex leads to a more general proposal that there are 'active'
pathways, or division systems, driven by formative algorithms modelled by Al, and 'passive' (default) division
systems driven by proliferative algorithms in which default
division rules (Korn and Spalding, 1973) apply. In the
Psilotum apex, pathway PI is an active pathway, whereas
pathway P4 and all divisions in pathway P3 except those
concerning the triangular cell, are passive division systems.
There must be a stage in the development of the
merophytes when the active pathway PI and its formative
algorithm Al no longer regulate the division plane. At this
point, a passive pathway takes over. That this must be so is
evident from the non-appearance, in the apices described by
Takiguchi et al. (1997), of second-generation triangular
cells (a3 or A3) in the fifth or sixth merophytes (compare
Figs 1 F and 4A); such cells should emerge as the outcome
of the continued application of algorithm A1. Divisions can
be found in these merophytes but their orientations do not
conform with those expected (Fig. 4A and B). These nonconforming divisions co-exist with others which do conform to algorithm Al. It seems as though the influence of
the original triangular cell, a3, ceases at a certain distance
from this cell (Fig. 5C), and algorithm Al no longer
applies. It is possible that the influence of the apical cell on
divisions in its neighbouring merophytes is mediated by the
permeability of the plasmodesmatal channels on their
common walls (van Bel and Oparka, 1995; Cooke et al.,
1996). Intriguingly, it is in the fifth merophyte with its nonconforming cells that the new apical cells, a3 and b3, become
active in generating their own sets of merophytes. An
absence of influence from the parental apical cell might be
necessary to avoid a conflict with the influence issuing from
the new, descendant apical cells. At the same time, the fact
that the cells in the fifth merophyte are now dividing
according to a passive pathway means that no new
triangular cells of the second generation (a3) can be
produced. The implementation of the passive pathway
could thus set a limitation on the branching of the shoot.
From the foregoing application of an L-system and the
corresponding simulation of cell patterns, it might be
presumed that within the actual apex, the triangular cells a3
and b3 are (a) self-maintaining, (b) influence the orientation
of cell division within the merophytes derived from them
and, hence, (c) maintain the active pathway PI. A consequence of pathway PI, and especially its continuation in
cells beneath the epidermis (recall that, strictly speaking, PI
and the other pathways apply only to the surface layer of
cells), is that it gives rise to the cell files which contribute to
the structure of the organ and also to successive generations
of organ branches via the creation of new triangular cells.
Thus, pathway PI leads not only to the self-maintenance of
cell a3 but also to reproduction at the organ level with the
self-maintenance of a shoot branching system.
Barlow et al.—Cellular Autoreproduction and Plant Form
Loss of organogenetic capacity is presumed to be associated with loss of the triangular cell. Conversely, wherever
there is a triangular cell, there may be the potentiality for
organogenesis. Whatever the orientation of a new division
wall within such a cell, a new triangular cell is always recreated. Thus, its shape alone, if coupled with binary cell
division, is sufficient to ensure its self-maintenance. Threesided cells can also arise in four- or five-sided cells by
oblique and unequal divisions, and in this way the
autoreproductive and organogenetic properties could be
regained (cf. Hagemann, 1980). But evidently the triangular
shape alone is not a sufficient condition to give rise to the
active division pathway PI, since, as we have seen, the
passive pathway, P3, also exists and maintains an autoreproductive «3 triangular cell.
The key to maintaining the PI pathway must be through
the ability of cell a3 to activate its own cell walls and cytoplasm, and those of the neighbouring cells, and bring them
to a state in which the cell-biological processes that support
system S5 5 can apply. This situation can also be interpreted
from the viewpoint of Living Systems Theory. At the
cellular level, the reproducer sub-system may require the cooperation of a number of other sub-systems for an active
division pathway to be pursued, whereas if fewer subsystems participate then a passive pathway may be followed.
For example, the transition from an active to a passive
pathway may involve the deactivation of informationprocessing sub-systems in the merophytes that are neighbours to cell «3.
It may be that cell a3 has the ability to synthesize a
diffusible morphogen, though why such a property should
be associated with a triangular shape is a potent question
for future research. It seems that within the triangular a3
cell resides the 'essence' of the Psiloium plant. However,
Agnes Arber's usage of the word 'essence' is in keeping
with her inclination for metaphysical ideas (Arber, 1950).
We would propose that the triangular shape of the a3 cell is
an indication that its activity is empowered with the
essential preconditions for autoreproduction and organ
maintenance.
ACKNOWLEDGEMENTS
IACR receives grant-aided support from the Biotechnology
and Biological Sciences Research Council of the United
Kingdom. Thanks are also extended to the referees and to
Dr Bruce Kirchoff, all of whom made valuable comments
and suggestions concerning the manuscript.
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