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INDEHISCENT, abbreviated IND, is an Arabidopsis thaliana regulatory gene whose encoded transcription factor helps specify the fruit tissues required for opening and seed dispersal. The gene name and its protein product are related uses of the name; an INDEHISCENT mutant is an altered organism, not a separate anatomical layer. A 2004 study identified IND and its role in patterning dispersal-related fruit cell types.^[ref]

The distinction between growth and identity is experimentally useful. The 2004 work showed that the action of FRUITFULL included preventing misplaced IND activity, rather than simply acting as a direct fruit-elongation switch.^[ref] A malformed short fruit can therefore reflect a change in tissue identity rather than failure of a generic growth process.

A 2016 study compared normal fruits with INDEHISCENT mutants and found an early defect in the cell divisions that form the dehiscence zone. It connected the factor to auxin transport and response during early development.^[ref] Together these experiments motivate a regulatory explanation: local gene expression changes developmental signals, those signals influence cell behaviour, and the resulting tissue arrangement makes a separation layer possible.

Researcher studying stem cells and aging. Cheng and collaborators linked centrosome misorientation with reduced stem-cell division, providing a cellular mechanism through which tissue maintenance can change with age.^[ref]

A developmental biologist who tracked epidermal cells in living tissue, testing how local differentiation and cell loss influence compensatory cell division.^[ref]

Kasper van Gelderen investigates how developmental signals shape plants. He coauthored a 2016 study of INDEHISCENT, auxin response and formation of the separation layer in Arabidopsis thaliana fruits. Comparing normal and altered fruits connected a regulatory gene with the local cell divisions that establish a controlled opening site.^[ref]

The study distinguished early tissue specification from later fruit dehiscence. Altering auxin transport during early stages prevented the normal developmental outcome, showing why the time of a perturbation matters as well as its location.^[ref] A signal that has one role while a tissue is forming need not have the same role when the mature tissue opens.

Institutional research profile: www.uu.nl/en/organisation/working-at-the-faculty-of-science/kasper-van-gelderen .

Researcher in chromosome segregation and chromatin organization. Nasmyth’s laboratory investigated how cohesin holds sister DNA molecules together and how related molecular complexes organize loops, connecting molecular topology with accurate cell division.^[ref]

A lamin is a type of intermediate filament protein forming part of the nuclear lamina, a network associated with the inner surface of the nuclear envelope. Lamins contribute to nuclear shape and mechanical organization and interact with components connecting the envelope to chromatin. They differ from laminin, an extracellular-matrix protein, despite the similar names. ^[ref]

Regulated assembly is useful during cell division. Phosphorylation of lamins helps promote lamina disassembly as the nuclear envelope breaks down in open mitosis; subsequent reassembly supports daughter nuclei. Thus a structural protein can form a load-bearing network while retaining a chemically regulated route for dismantling it.

Matrix growth and plate-advection balance relates newly supplied nail material to movement and changing geometry of the nail plate. The nail matrix contains the growth-producing region, whereas the mature nail plate is transported material.^[ref] Measured advance is consequently a material-flow observation, not a direct count of cell divisions.

For an original one-dimensional conservation of mass model, define line density $m(x,t)=\rho (x,t)A(x,t)$, where $A$ is plate cross-sectional area, $\rho$ its density and $v$ its advance speed. A local production rate $s(x,t)$ per unit length gives the continuity equationIf the chosen downstream segment has negligible production or loss, $s=0$. At steady state its mass flux $mv$ is constant. Uniform density then makes the volume flux $Q=Av$ constant, recovering the simple width-times-thickness model.

For stipulated $Q=0.30\mathrm{m}{\mathrm{m}}^3/day$, cross-sectional areas of 3 and $2\mathrm{m}{\mathrm{m}}^2$ require speeds 0.10 and 0.15 mm/day. Equal production can therefore accompany unequal advance when geometry changes. Conversely, equal speeds do not establish equal production without knowing area and density.

For a fixed segment $[a,b]$, integrating the continuity equation givesIf inflow exceeds outflow, material accumulates rather than vanishing from the accounting. Growth, hydration-related geometry change and clipping must be assigned to appropriate terms before interpreting an apparent imbalance.

The nail-marking study measured displacement over known time intervals in 22 young adults.^[ref] Extending that design with repeated width and thickness measurements would test a nail-plate storage balance, rather than assuming steady geometry. Inferring a mitotic rate would require further information about cell size and conversion into mature material.

Researcher studying asymmetric cell division. Inaba and collaborators investigated how the polarity protein Baz positions the centrosome in the male Drosophila germline, connecting intracellular organization with the orientation of a stem-cell division.^[ref]

MOS7 is a nuclear-pore-associated protein of Arabidopsis thaliana required for normal reproductive cell division. Although the nuclear pore complex is familiar as a transport gateway, some of its components also have roles during mitosis, when nuclear organization is extensively rebuilt.

Guen Tae Park and colleagues examined a loss-of-function MOS7 mutant. Developing pollen showed disorganized microtubules, defective spindle apparatus formation and abnormal division; female reproductive development and embryonic development were also affected. A transgene carrying functional MOS7 rescued the reproductive defects, making the attribution to the disrupted gene stronger than a comparison of unrelated abnormal and normal plants.^[ref] The experiments establish a requirement for MOS7, while leaving details of its molecular action on the division machinery open.

The quantities $n_i(\tau ,t)$ are cell-cycle age densities: $n_i(\tau ,t)d\tau$ counts biological cells whose time since entering phase $i$ lies in $[\tau ,\tau +d\tau ]$. Here $\tau$ is time spent in the current phase, rather than time since birth. In this two-stage approximation to the cell cycle, a biological cell passes from G1 phase to G2 phase, then completes cell division and produces two daughters entering G1 phase.

The time derivative measures change at fixed phase age. The age derivative transports biological cells towards larger $\tau$ at unit speed, because $d\tau /dt=1$. Thus each equation is an age-structured population equation. The nonnegative hazard function ${\Gamma }_i(\tau )$ means that, conditional on still being in phase $i$ at age $\tau$, the probability of leaving during the next $dt$ is ${\Gamma }_i(\tau )dt+o(dt)$. Its product with $n_i$ is the loss from that phase-age class; it is not an additional death term.

The boundary condition at $\tau =0$ specifies the incoming flux. Every G1 phase exit contributes one entrant to G2 phase, whereas every G2 phase exit contributes two entrants to G1 phase. The initial conditions specify the phase-age composition at $t=0$. Consequently integration over phase age gives the useful population balanceEach completed cell division increases the total number of biological cells by one.

Nineteenth-century embryology transformed knowledge of reproduction from an account of fluids and visible growth into an increasingly cellular account of fertilization and biological development. It did not end with a complete mechanism of heredity. The century must be treated as a changing sequence: what was established by the 1890s cannot be attributed without qualification to an investigator in 1800. The key changes concerned the material contributions of the parents, the origin of embryonic structures and the evidential power of observation versus intervention.

An early problem was identifying the mammalian ovum. A large ovarian follicle is not itself the ovum, and failure to distinguish the two could confuse the material starting point of biological development. In 1827 Karl Ernst von Baer described the mammalian ovum, notably from the dog, in De ovi mammalium et hominis genesi by Karl Ernst von Baer. Dissection located the relevant structures; optical microscopy distinguished the small ovum within the follicle. The evidence was therefore a combination of anatomical placement and magnified appearance. The work's title must not be taken as proof that he directly observed every corresponding stage in human reproduction.^[ref]

This mattered to the contest between preformationism and epigenesis. If the embryo were already a tiny formed individual, growth would chiefly enlarge structures already present. Successive observations of incubated eggs instead showed structures appearing and differentiating over time. Serially examining embryos at different stages made an ordered developmental account possible; it did not normally follow the same opaque mammalian embryo continuously from beginning to end. Nor did rejection of a miniature adult settle every question about invisible inherited organization. An investigator could accept the visible emergence of structures yet propose pre-existing determinants below the resolving power of the optical microscope.^[ref]

During the century, cell theory and improved techniques made cell division a central explanatory object. Lenses, illumination, thin sections, fixation and staining helped observers distinguish cell nuclei, chromosomes and patterns of division. These were achievements of preparation as well as magnification: a preparation could preserve a fleeting structure but also distort it. Comparing preparations and checking fixed material against living specimens were therefore important safeguards. By the late century, a developmental sequence could be described as successive divisions and rearrangements of cells, rather than the spontaneous appearance of a fully organized body from undifferentiated fluid.^[ref]

Fertilization became a particularly revealing test. External fertilization in transparent marine eggs allowed investigators to mix sperm and unfertilized ova at a known time and watch the sequence under an optical microscope. Oscar Hertwig's sea-urchin investigations in the 1870s connected sperm entry with the appearance and union of the male and female nuclear contributions before the first cleavage division. His later The Cell by Oscar Hertwig presents these events as central to the process. Separating eggs from sperm, observing them before mixing, and comparing the sequence after mixing could distinguish fertilization from ordinary changes in an ageing egg. Serial nuclear observations supplied evidence about what entered and what happened next, not merely a correlation between mating and later offspring.^[ref]

Nevertheless, fusion of parental nuclear material did not reveal the modern molecular mechanism of heredity. Chromosomes supplied observable structures whose behavior could be compared across cell divisions, and the contributions of the two gametes could be investigated. This is different from knowing that DNA encodes information in a particular nucleotide sequence, or knowing how that information directs development. Even the apparent continuity or disappearance of a cell nucleus during division was a historically difficult observational problem. The distinction between a visible structure and the theoretical function assigned to it is essential.^[ref]

The final decades added experimental embryology. In 1888 Wilhelm Roux injured one of the first two blastomeres of a frog embryo with a heated needle; partial development of the survivor appeared to support a mosaic theory of development, in which early divisions distribute distinct developmental capacities. In 1891 Hans Driesch separated early sea-urchin blastomeres by shaking and found that an isolated blastomere could form a small complete larva. That showed a regulatory capacity inconsistent with an exclusively rigid allocation of half the future organism to each of the first two cells.^[ref]

The comparison requires care: killing a cell and leaving it attached is not the same intervention as removing it, and a frog is not a sea urchin. The results therefore did not establish that all embryos develop identically or that every early cell can make an entire organism. They did establish that a normal developmental fate cannot automatically be equated with an irreversible developmental capacity. Hans Driesch's later commitment to vitalism was one interpretation of this capacity, not something a complete larva logically proved. His 1908 retrospective account is valuable participant evidence, but it is later than the nineteenth-century trials it describes.^[ref]

By the century's end, investigators had strong evidence for the cellular starting points of sexual reproduction, parental nuclear participation in fertilization and active organization during biological development. They knew these things through dissection, prepared and living microscopic observations, comparison of stages, and increasingly discriminating interventions. Their continuing uncertainty about heredity and developmental organization was productive: it concerned mechanisms that their best observations had made more precisely questionable, rather than a simple absence of facts.

Mutual support is a major component of evolution, but its universal superiority to competition is neither a well-defined nor an established empirical claim. cooperation and conflict often explain different levels of the same biological system. The productive question is how support remains advantageous and stable when individuals or genetic elements can gain by contributing less, and how its ecological effects compare with the costs of competition in a specified setting.

In Mutual Aid: A Factor of Evolution by Peter Kropotkin, Peter Kropotkin emphasized animal associations and cooperative benefits that an exclusively combative picture of nature overlooks. ^[ref] This is a historically important corrective, not a controlled survey assigning a universal effect size to helping. Its descriptive examples generate hypotheses about survival and reproduction. They cannot establish how common cooperation is after correcting for which taxa, environments and conspicuous associations were observed. A claim about the entire organic world also exceeds a collection concerned principally with selected animal and human examples.

Definitions matter. mutualism supplies benefits to both participants, whereas evolutionary altruism imposes a direct fitness cost on an actor while benefiting another. cooperation can be mutually beneficial and require no sacrifice at all. Moreover, a short-term feeding cost can be part of a relationship that ultimately increases the donor's own lifetime reproductive success. The biological categories depend on the stated comparison and timescale, not on whether an action appears generous. Conversely, physical aggression is not required for competition: individuals can reduce one another's reproduction by consuming the same limiting resource without meeting.

Some support is explained by immediate complementary returns. Group defence or joint foraging can be individually advantageous when combined actions achieve something inaccessible alone. Field work on groupers and giant moray eels documented recruitment and nonrandom associations during hunting, consistent with gains from their complementary ways of accessing prey. ^[ref] The evidence concerns a particular interspecific association; it does not imply that all joint hunting is reciprocal altruism. To estimate the benefit rigorously, compare prey availability, effort, detection and success with and without the partner, accounting for selective association in especially profitable locations. Shared location alone would be weaker evidence than coordinated recruitment and complementary actions.

Support among relatives can evolve even when its actor pays a direct cost. In a simplified marginal accounting, let $C$ be the actor's loss, $B$ a recipient's gain, and $r$ the appropriate genetic association between them. An altruistic change is favoured when:inclusive fitness theory makes clear why effects on other individuals can influence selection on an actor. ^[ref] The coefficients and effects require specification: relatedness is not simply physical proximity, benefits must be measured in relevant reproductive units, and local demographic competition can change their net value. The expression is not a licence to label every action benefiting relatives adaptive without measuring costs and alternatives.

Experiments with siderophore production in Pseudomonas aeruginosa show why both association and competition matter. Manipulating relatedness and the scale of competition changed the success of cooperative production. ^[ref] High relatedness can make benefits to neighbours genetically valuable, but the same neighbours may compete for the same limited opportunities. Under sufficiently local competition, one relative's gain can replace another's rather than increase their collective contribution to future populations. Experimental mixing, replicated populations and controls for iron availability and bacterial growth help identify these mechanisms. The mere observation that producers grow better together than nonproducers would leave the evolutionary competition between the types unresolved.

Support among unrelated individuals has additional routes. by-product mutualism can supply immediate returns; partner fidelity feedback makes a persistent partner's improved condition beneficial to the actor; partner choice can redirect future opportunities toward good partners. Conditional withdrawal of benefits can limit exploitation. These mechanisms do not require all participants to value the group's success independently of their own reproduction. Their presence also does not eliminate evolutionary conflict over how the joint benefit is divided. A mutualism can remain beneficial to both participants while each favours a different exchange rate.

Even highly integrated societies contain competition over reproduction. In honeybees, workers can produce male eggs, and experiments showed discrimination against worker-laid eggs, supporting worker policing. ^[ref] Relatedness under multiple mating can contribute to the incentive to suppress worker reproduction, while effects on colony productivity also require consideration. The observed collective organization is therefore maintained partly by controlling opportunities for individual reproduction. Egg transfer experiments, controls for egg age and handling, and tests of recognition cues distinguish policing from generalized removal of damaged eggs. A peaceful-looking colony need not be free of conflict, and aggressive enforcement can help maintain collective functioning.

The same logic extends to integration across biological levels. A multicellular organism depends on coordinated cell activities, but somatic evolution can favour cell lineages that undermine organismal reproduction. A single-cell bottleneck, regulation of cell division and restrictions on reproductive lineages can reduce such conflicts. These are candidate mechanisms for alignment, not evidence that every part of the organism has always had identical interests. Major evolutionary transitions are important partly because cooperation becomes stable enough to form new reproductive units; suppression of lower-level competition can be part of that success rather than its conceptual opposite.

multilevel selection provides another accounting of these processes. Groups with more contributors can produce more descendants while noncontributors increase within mixed groups. Whether contribution spreads depends on the strength of both effects and on how groups form and reproduce. Simply demonstrating that a group performs well does not show that its costly contributing trait resists invasion. In appropriate models, inclusive-fitness and multilevel descriptions can track the same underlying change from different partitions, so changing vocabulary alone does not supply a different biological mechanism.

Assessing relative importance requires an explicit metric. One might compare effects on population persistence, individual lifetime reproduction, biomass production or the rate of a major transition. Those answers need not agree. A short interval of severe competition can determine the outcome despite long periods of cooperation; alternatively, cooperative defence can be essential during a rare environmental crisis. Support within a group can also improve that group's capacity to compete with others, transferring rather than eliminating antagonism. Neither the proportion of observations that look peaceful nor the number of visibly aggressive events measures total selective importance.

The defensible conclusion is that mutual support is pervasive and often indispensable, while evolutionary competition and conflict help explain when that support evolves, how it is regulated and where it breaks down. Mechanistic and comparative tests support this joint account more strongly than a universal ranking of support over struggle.

cell specification and morphogenesis can form a reciprocal causal loop: cell identity changes force production and tissue material properties, while the resulting geometry and loading alter signalling and differentiation. A molecular programme need not first assign every identity and then leave mechanics merely to implement a predetermined shape. Conversely, correlation between a new shape and a new marker does not establish that mechanical input instructed the fate. Developing intestine, avian skin and lung illustrate distinct mechanisms and experimental tests.

Cells generate forces through actomyosin contractility, transmit them through cell adhesion and the extracellular matrix, and respond through mechanotransduction. Changes in cell number, volume, polarity and matrix composition modify the mechanical problem. A deformed tissue can change ligand distribution, receptor exposure or intracellular signalling without any change in a ligand's production rate. One must therefore distinguish force generation, transmission and sensing. A contractility inhibitor can disrupt all three as well as cell division, so an abnormal organ alone is not a mechanistic explanation.

In the embryonic chick intestine, differentiation of surrounding smooth muscle changes the constraints on epithelial growth. Successive muscle layers restrict expansion in different directions, helping a growing epithelial–mesenchymal composite form ridges, zigzags and eventually villi through buckling. Muscle perturbations and artificial confinement support a causal role for physical boundary conditions rather than a purely epithelial prepattern. ^[ref] Here an initial differentiation event supplies a mechanical constraint that changes tissue shape. Equivalent external confinement is especially informative because it can replace a mechanical function without restoring all molecular products of the missing muscle.

The new geometry then feeds back into regional cell-state regulation. Epithelial Sonic hedgehog signals become concentrated beneath the curved villus tips, promoting mesenchymal BMP signalling; the resulting signals restrict the stem-cell-associated proliferative programme away from those tips. ^[ref] Thus spatially patterned signalling can arise from deformation of a source that was initially more uniform. The result concerns localization of a developmental stem-cell programme, not proof that every cell has irreversibly acquired one terminal identity. Comparing curved and flattened explants, measuring ligand production as well as local pathway activity, and changing pathway activity downstream of deformation distinguish altered geometry from a change in total ligand supply.

This chick mechanism should not be imposed unchanged on mouse intestine. Mesenchymal patterning and surface deformation have different temporal relationships in different species. The reusable principle is a feedback between differentiated supporting tissue, physical geometry and local signalling; the exact sequence is an empirical question. A useful control compares developmental stage and viability, since a tissue that has simply stopped developing may lack both folds and differentiation markers without either being the direct cause of the other.

Avian skin supplies a different route from mechanics to identity. Contractile dermal cells aggregate beneath the epidermis, mechanically compressing it. Experiments linked this dermal self-organization to activation of epidermal beta-catenin and initiation of the feather-follicle programme. Altering contractility or tissue mechanical conditions changed aggregate formation and pattern. ^[ref] This makes the feather placode an emergent epithelial–mesenchymal structure rather than requiring a complete molecular placode map to exist before any cell movement.

The important distinction is between beta-catenin's junctional and transcriptional roles. Redistribution of an adhesion-associated protein alone is not evidence for a fate change; nuclear activity and appropriate target expression, followed by placode development, provide a stronger chain. To test ordering, one can alter dermal force production while preserving epidermal viability, apply controlled compression, and perturb the epithelial response separately. Restoration of placode gene activity by a downstream intervention would place that activity after mechanical input, but would not necessarily rescue normal spacing. Molecular identity and periodic geometry are related outputs that can be experimentally separated.

In the developing lung, differences in how epithelial cells experience a common physical input help generate different differentiated states. live-cell imaging and perturbations showed that forces associated with fetal breathing movements and fluid displacement contribute to type I alveolar cell differentiation. A subset of progenitors protrudes toward mesenchyme through FGF10–FGFR2-dependent signalling; enrichment of apical myosin in those cells resists flattening and supports type II alveolar cell fate. ^[ref] Thus a local biochemical signal changes the cell's mechanical response, while loading helps determine whether it becomes thin and extended or retains the alternative morphology and differentiation programme.

A decisive lung experiment must therefore vary force and growth-factor signalling independently. If a receptor perturbation changes fate, it could act through competence, proliferation, survival or the physical protection from flattening. Cell tracking and early marker measurements distinguish transformation of an existing progenitor from selective loss of one population. Controlled loading, matched fluid and culture conditions, measurement of cell shape, and restoration of the relevant contractile response can separate these alternatives. Flattening alone is not a sufficient endpoint: the molecular and functional differentiation of the two alveolar classes must also be assessed.

These systems demonstrate three forms of coupling: differentiation changes a tissue constraint, geometry reorganizes an extracellular signal, and local signalling tunes a cell's response to a physical force. They need not all use the same sensor or transcription factor. Nor does mechanics replace biochemical information: the same deformation can elicit different responses in cells with different developmental competence. A fate programme can also alter adhesion or matrix properties and thereby change the mechanical input experienced by neighbouring cells, closing a mechanochemical feedback loop.

The strongest general strategy combines time-resolved live-cell imaging, fate or lineage reporters, a physical measurement and an independently targeted perturbation. Initial recoil after laser ablation reports load relative to resistance rather than an absolute force without a material model; substrate deformation and pressure measurements likewise need calibrated assumptions. Acute and tissue-restricted perturbations, sham procedures, independent genetic alleles and appropriate rescue help avoid generalized damage as the explanation. Fate and form are coupled through specific causal chains, but identifying a mechanically instructive step requires measuring both the physical intermediate and the resulting change in developmental state.

Researcher in cell division. Steigemann and collaborators investigated an Aurora-B-dependent abscission checkpoint that protects against tetraploidy, connecting chromosome segregation with completion of cellular separation.^[ref]

Researcher in cell cycle control. Russell coauthored experiments showing inhibitory phosphorylation of Cdc2 by human Wee1, connecting kinase action with regulation of cell division.^[ref]

A pome is a fleshy accessory fruit developing from an inferior ovary, with an enlarged hypanthium surrounding the central fruit tissues. An apple is a familiar example. Much of its edible flesh comes from tissue around the ovary, whereas the central core corresponds to the developed ovary. Thus the fleshy part of a pome cannot simply be identified with the pericarp, the wall derived from the ovary.^[ref]

To see the distinction, cut an apple lengthwise through its stalk and centre: locate the seeds, the enclosing core and the surrounding flesh. The fruit integrates structures with different developmental origins.

In a 2008 study, Bart J. Janssen and colleagues sampled developing apple fruits at eight times and used a DNA microarray representing roughly 13000 genes. They identified coordinated gene expression patterns associated with early cell division, later growth and starch accumulation, and ripening. The experiment illustrates how the anatomy of a pome motivates a molecular question: how are growth and maturation of its different tissues coordinated?^[ref]

Authors include Philipp J. Keller.

Science 322, pp. 1065–1069. Multiview live imaging and nuclear tracking establish early cell divisions and movements.

The retroviral life cycle includes entry, RNA-to-DNA copying by reverse transcriptase, a DNA intermediate and gene expression followed by particle production. Integration as a provirus can make the genetic change persistent across cell divisions.

A separation layer is a specialized layer of cells at a controlled opening site in a plant. In the Arabidopsis thaliana fruit, the separation layer lies at the margin between the valves and central replum, within the dehiscence zone. Loss of adhesion between its cells allows the valves to detach during fruit dehiscence. The adjacent layer reinforced with lignin has a different mechanical role; the separation layer is not the whole dehiscence zone.^[ref]

A useful developmental experiment compares normal fruits with mutants of the INDEHISCENT regulatory gene. A 2016 study found an early defect in the cell divisions that normally establish the dehiscence zone, alongside altered auxin response. Tissue-targeted changes in auxin transport also prevented normal opening.^[ref] The experiment connects local cell identity and hormone response to a later mechanical outcome.

Timing matters. An early auxin response and a later local auxin minimum describe different developmental stages, not contradictory recipes for one unchanging tissue. Similarly, an accidental tear can release seeds without establishing that a normal separation layer formed. Comparing local anatomy, developmental stage and the eventual opening site distinguishes a specified release layer from simple damage.

Y. L. Ruan is the first-listed author of a 2001 study of how a single cotton fiber cell elongates. The work connected changing permeability of the plasmodesma connections at the fiber base with sucrose transport, potassium transport, turgor pressure and the wall-loosening protein expansin. A cotton fiber is an illuminating growth model because a conspicuous length increase occurs within one cell, rather than being explained by repeated cell division.^[ref]

Using confocal microscopy, the researchers followed a fluorescent tracer that could pass through open plasmodesma connections but not freely across the cell membrane. Tracer entry changed during development and later returned, demonstrating reversible connectivity rather than permanent separation. Measurements of transporter expression and turgor pressure helped connect this change with growth. The tracer experiment measures permeability, while the other measurements test the proposed relationship between solute supply, pressure and cell wall expansion.^[ref]