Plant patterning, known as phyllotaxis, brings together multiple independent fields of inquiry: mathematics, physics, botany, genetics, communication theory, and even philosophy: Why should brainless plants produce spirals that follow the Golden Ratio? The last times we looked at this question in some detail, we found mechanistic answers unsatisfactory. Periodic structures can be explained, but why do they use the Fibonacci Series? Why do we find them beautiful?
A new open-access paper in Current Biology provides some of the best detail on this question in recent times. Cris Kuhlemeyer from the University of Bern has sliced and diced the cells at shoot tips, looking for clues. He identified specific plant hormones and proteins involved in development of shoot primordia, the locations where new leaves or flowers will grow. Moreover, he is fully aware of the history of the question.
Leaves and flowers are arranged in regular patterns around the stem of a plant, a phenomenon known as phyllotaxis. Different arrangements occur, such as distichous, decussate or spiral (Figure 1). Most prevalent in nature are spirals in which the average divergence angles between successive organs are close to 137.5°, the so-called ‘golden angle’. It is this exact number that has given phyllotaxis its special flavor as a quantitative developmental problem, and over the centuries, it has enjoyed the attention of scientists far beyond botany. In the 1830s mathematicians described the spirals as they related to the Fibonacci numbers, and in the 1860s improved microscopes made it possible for botanists to observe the initiation of leaf and flower primordia in a diversity of plants. This descriptive work led to the conclusion that new organ primordia form in the first available space between existing primordia, a conclusion still valid today. But how does it work? [Emphasis added.]
In his Primer, Kuhlemeyer tackles the question from several angles. He considers answers from the perspective of mechanics. He looks at the interactions of plant hormones, such as auxin and its transporters, the PIN family of proteins. He delves into communication and network theory, examining whether feedback loops can explain the patterns. From the view of evolution, he asks whether the patterns are adaptive in some way. Do any of these perspectives yield the “Aha!” moment?
In his experimental work, Kuhlemeyer has examined the tip of a growing stem, called the apical meristem, in great detail. There’s nothing about the meristem that suggests a Golden Ratio spiral will emerge.
The lateral organs have their origin in the shoot apical meristem, a simple dome-shaped structure at the very tip of the stem (Figure 2A). This meristem is usually defined as the tissue above the youngest lateral organ primordium, a leaf or a flower. So defined, the meristem is about 1/10th of a millimeter in diameter and consists of a few hundred cells that together weigh no more than 2 micrograms. This tiny organ generates all the stems, leaves and flowers of the adult plant. And it keeps doing so over the lifespan of the plant — for a few weeks in Arabidopsis, for year after year in long-lived species.
The shoot apical meristem has been the object of intense study from when it was first viewed under a microscope in 1759. Meristem cells are small and, when viewed under a light microscope, they look more or less the same; at best, subtle anatomical differences can be observed between them. There are no asymmetric cell divisions. The internal cells tend to divide with randomly oriented division planes, whereas the cells in the surface layer (the protoderm) divide perpendicular to the surface and, as a result, the protoderm maintains its identity as a single-cell layer that eventually forms the epidermis of the leaf. Cell division is also non-synchronous: even neighboring cells can differ in cell-cycle length by as much as a factor of four.
Of special interest in the meristem are four cells at the tip, called apical initials. “Analysis of clonal sectors and, more recently, direct in vivo imaging,” he says, “demonstrate that these apical initials have a high probability of maintaining their position, whereas their descendants are displaced from the center.” And yet the surrounding cells do not differentiate either. “Only after further divisions do cells acquire the option to differentiate into the cell types of the central axis and lateral organs,” he observes. A group of cells around them, in the “central zone” devoid of leaf primordia, express a hormone called CLV3. Here, we start to see some differentiation:
Approximately 20 cells at the tip of the meristem express a small peptide, CLV3, which moves to the cells below to repress the homeobox gene WUSCHEL (WUS). WUS in turn induces the expression of CLV3. The negative feedback loop between the two proteins stabilizes the sizes of the CLV3 and WUS domains. In analogy with animal nomenclature, the CLV3-expressing cells are now often called ‘stem cells’.
Of interest to design theorists, the apical cells avoid the effects of mutations in the way they divide. This allows some trees to survive thousands of years:
Despite this lack of cellular structure, geometry imposes order…. In the classical literature apical and subapical cells are together referred to as the central zone, whereas cells below the central zone are defined as the peripheral zone. Their stable position at the tip of the meristem provides the apical initials with a special attribute that determines how new mutations are propagated (Figure 2C). Together with early sequestration of axillary meristems, this allows trees to live for thousands of years without suffering mutational meltdown.
Figure 2C shows what happens to mutations. They tend to propagate downward, affecting small sectors of the stem but not the apical cells themselves. As a result,
a mutation in a subapical initial…will be rapidly displaced from the meristem and affect only a narrow and short section of the shoot. Due to early sequestration of axillary meristems, in a tree with 1,000 branches there will be only ∼60 cell divisions between the embryonic meristem and the meristems in the terminal branches.
The fewer the cell divisions, the fewer the mutations. That’s how a giant sequoia avoids mutational meltdown. Fascinating!
He said that geometry imposes order. But does order impose geometry? What about that Golden Ratio?
Cells in the central zone of the meristem divide but do not differentiate. Once in the peripheral zone, they have the option to enter a pathway of organ formation. Cells become bigger and grow faster than their neighbors, with the result that a bump forms on the flank of the meristem. In 2000 we demonstrated that tomato meristems placed on inhibitors of polar auxin transport grow vigorously but fail completely to induce new leaves (Figure 3A). This highly specific ‘phenotype’ can be reversed by the application of a minuscule droplet of auxin to the peripheral zone. Moreover, the position of the droplet determines the position of the leaf and the auxin concentration in the droplet determines the number of cells recruited into the leaf primordium. From these experiments we concluded that actively transported auxin is the instructive signal that determines both the induction and the positioning of lateral organs.
It sounds like Kuhlemeyer has found a strong lead, like a bloodhound on a scent. Further experiments showed that the PIN1 protein, a transporter for auxin, gives it direction:
The PIN1 proteins are oriented within the plasma membrane in a coordinated fashion, in such a way that they will transport auxin towards young and incipient primordia and deplete it from the surrounding tissue (Figure 3B).Therefore, patterning is not through an inhibitor emanating from the young leaves, but the opposite: through redistribution of an activator — auxin — that is present in the meristem itself.
We’re getting warmer. Auxin and its transporter, PIN1, regulate each other in a cycle. We see a timing mechanism emerge below those undifferentiated cells in the central zone:
The combined experimental results suggest models in which an autoregulatory loop between auxin and subcellular PIN localization creates auxin maxima. The auxin–PIN1 interaction can be envisaged to function as a pattern generator, conceptually similar to the circadian clock (Figure 3C). Like the circadian oscillator, it generates outputs, responds to inputs and is subject to feedback regulation. Inputs are the enzymes and regulatory proteins involved in the synthesis of auxin and PINs, but can also be factors that indirectly affect phyllotaxis, such as meristem size, light or metabolism. Outputs are the lateral organs and all the steps in between: transcription factors, wall-loosening enzymes, and mechanical stresses.
In fact, another protein, a cytokinin, stabilizes the angle at which a new primordium emerges. “This suggests a mechanism in which inhibition of cytokinin signaling prevents premature outgrowth of correctly patterned incipient primordia.”
Let’s take stock of what we’ve learned. From an undifferentiated beginning, cells at the tip express a peptide that migrates to cells outside the central zone, preserving the “stemness” of the apical cells. The peptides repress a homeobox gene in the lower cells, allowing more peptide to be expressed. This initiates a bump, or primordium, where a new leaf will appear. PIN1 directs auxin to these incipient primordia, while cytokinin stabilizes the angle. In addition, he explains, the flow of auxin insures that vascular bundles in the bump will connect with those in the stem.
So do we now have a Golden Ratio? No. Nothing in the above explains why these primordia arrange themselves in a spiral.
Phyllotaxis is an inherently quantitative problem. But how can a small molecule in concert with its transporter induce organ formation at angles of 137°? Early computational models posited an inhibitor that is produced by pre-existing primordia and diffuses into the meristem. When the inhibitor decays with time and distance, patterns are produced. Such ‘pre-auxin’ models are simple and robust and, by varying parameters, they can reproduce all major phyllotactic patterns. Integrating the recent pharmacological and genetic data makes models biologically more plausible but, unfortunately, also more complex and less robust. This is even more of a challenge when models are implemented on geometrically realistic templates, with cells that grow and divide as in a real-life meristem.
And yet, he goes on to say, the computational models cannot discriminate between auxin-based or biophysical models. So far it is impossible to measure auxin concentrations accurately enough to solve this “inherently quantitative problem.” He laments, “We need more experimental data rather than more computational models.”
Kuhleman briefly looks at evolution. “It is not altogether clear what the adaptive function of the different phyllotactic patterns is,” he says. Do they maximize sunlight? Do they prevent unequal bending? Do they limit the access for pathogens? “Perhaps the rather unsatisfactory default explanation is,” he quips, “that regular patterning is simply an emergent property of the molecular mechanism of lateral organ initiation.” In short, he finds none of the proposals satisfactory. They appear to be the usual Darwinian narrative gloss applied after the fact, without explaining how the patterns emerge in DNA coding. He speaks later of “Our lack of understanding of the selective advantage of the various phyllotactic patterns,” hoping it can be remedied with more research (i.e., promissory notes).
Kuhleman’s paper ends with a series of questions, showing that evolutionary biologists really know very little about phyllotaxis. “Experimental evidence and computational modeling strongly suggest that phyllotactic patterning works through a positive feedback loop between auxin and its transporter,” he boasts from his own experimental work, but none of that explains the origin of the feedback loops, the origin of auxin, the origin of the transporter, the origin of the genes that build these machines, or why any of those factors should follow the Golden Ratio.
Could mechanics have perhaps been a crude ancestral mechanism that predated auxin-dependent patterning? What about phyllotactic patterns in flowers? Phyllotaxis reaches its greatest diversity in the flower, where it is obviously related to different reproductive strategies. How do regulatory mechanisms of phyllotaxis interact with the extremely well-studied floral organ identity determinants? It is not that we have run out of basic questions to be asked in model plants; instead, there is a world of diversity waiting to be explored.
He’s clearly reaching at this point. How can “mechanics” be an ancestral “mechanism”? If you can answer that play on words, how would auxin know to take it over later? Remember, all this had to come about by natural selection working on random mutations. Flowers don’t have “reproductive strategies,” because they have no brains. We fail to see how phyllotaxis is “obviously related” to reproductive strategies, when many plants do fine without Fibonacci spirals.
So that’s it. We looked for a really detailed answer to Golden Ratio patterns in plants, and were left with only more questions. By admitting new complexities, Kuhleman even indicates that answers now are more elusive than they used to be. Darwin-of-the-gaps is a bad strategy for scientific explanation when the gap has been getting wider for centuries. There is a cause we know that can generate patterns that are both precise and beautiful. There is a cause that can pre-program genetic software to control the interactions of elements that generate the patterns. That cause is, naturally, intelligence.