On the scaling of the skeletal system

By Tomer Stern, the skeletal development laboratory of Prof. Elazar Zelzer, Department of Molecular Genetics, Weizmann Institute of Science, Israel.

Proper shape-size relation is essential for the function of all organs and organisms. Thus, one of the key challenges shared by developing organs is the adjustment of physical dimensions to the massively growing body, known as scaling. There are two basic modes of scaling: isometric, in which the physical proportions are maintained throughout growth, and allometric, in which the proportions undergo changes. A well-known example for the latter is the change in relative size of the human head from early infancy to adulthood. Despite the fundamental importance of this phenomenon, our understanding of the mechanisms underlying scaling is surprisingly limited.

The question

In a Walt Disney cartoon, bones are typically depicted as smooth cylinders with a round joint popping at each end. However, it only takes a quick glance at a 3D micro-CT image of a bone to realize how complex and unique the morphology of each bone is. Much of this complexity is due to the existence of various asymmetrical protrusions located at specific positions along the bone, which allow the attachment of muscles and the formation of complex joint structures. As such, the specific position of these protrusions directly dictates the ability of the organism to control the movement of the bone while chasing prey or escaping from predators, as well as the mechanical efficiency of movement. Thus, any inaccuracy in the positioning of protrusions during development is likely to significantly compromise motility. Interestingly, although the average bone elongates by more than 5 times during development, its protrusions constantly remain in the same relative positions, to say, long bones scale isometrically. However, since bones are rigid organs that elongate only from their ends, the question is: How is the relative position of each protrusion between the two ends maintained during growth?

The answer

Our starting point for addressing this question was a prevalent hypothesis proposed more than 60 years ago. In an iconic work, Nigel Bateman¹ argued that bone protrusions continuously drift along the bone, as they are destroyed and rebuilt by bone-absorbing and bone-depositing cells. As this hypothesis offered a straightforward mechanism for regulation of the longitudinal position of protrusions, we saw it as an elegant way to explain how long bones scale isometrically. Filled with scientifically inappropriate optimism, we were on the direct track to solving our enigma!

To do so, we generated a massive database of 200 three-dimensional micro-CT images of long bones, ranging from early developmental stages to adulthood. Then, to allow proper comparison between the morphologies of all bones, we developed an automated computer algorithm that accurately aligns all imaged bones to one another. Lastly, we documented the exact physical position of each protrusion in each bone at each time point. Under these settings, any change in the position of a protrusion over time would indicate that it has undergone drift, as predicted by Bateman’s hypothesis. Yet, to our surprise, most protrusions drifted very little if at all. Rather, bone shape was maintained by a completely different mechanism.

The right answer

As mentioned, the rigid bones elongate solely from their ends. The driving force behind elongation is a thin layer of cartilage called the growth plate, which is composed of chondrocytes that undergo a well-defined differentiation program resulting in their replacement by ossified tissue. Without prior knowledge, it would be reasonable to assume that the rate at which each growth plate lengthens the bone is the same at both ends. However, the interesting fact is that each of the hundreds of growth plates in our body has a unique growth rate. The first indications for this variability have been provided almost 300 year ago. However, the developmental rationale behind it and the biological code that determines the specific activity rate of each growth plate have remained open key questions in the field of skeletal biology.

Our finding that the relative positions of protrusions are kept throughout development without drifting has led us to hypothesize that the balance between the rates of growth at the two bone ends may be the mechanism that underlies isometric scaling. This may happen if when a protrusion is much closer to one end of the bone, that end will grow more slowly, while the opposite end will grow more quickly. In this manner, no matter how much the bone increases in size, the protrusion will always maintain its relative location. Such a growth ratio-based mechanism would render drifting unnecessary. To test this hypothesis, we constructed a mathematical model for the relation between the balance of the growth rates and the relative position of protrusions. When we fed the model with real growth data, it predicted the positions of non-drifting protrusions and the rate at which drifting protrusions moved with striking accuracy, thus providing strong support to our hypothesis. Lastly, through additional mathematical analyses, we showed that the newly discovered mechanism also minimizes the total drift activity of each bone during development. As the mineral deposition and absorption that occur during drift are assumed to be highly energy consuming, this finding suggests that the mechanism we have discovered follows the energetically optimal path for achieving the challenging goal of isometric scaling of developing bones.

For the full article: “Isometric scaling in developing bones is achieved by an optimal epiphyseal growth balance” ², and for a synopsis of the article: “Make no bones about it: Long bones scale isometrically” ³.

1. Bateman, N. Bone growth: a study of the grey-lethal and microphthalmic mutants of the mouse. J Anat 88, 212-262 (1954).
2. Stern, T. et al. Isometric Scaling in Developing Long Bones Is Achieved by an Optimal Epiphyseal Growth Balance. PLoS Biol 13, e1002212, doi:10.1371/journal.pbio.1002212 (2015).
3. Sedwick, C. Make No Bones about It: Long Bones Scale Isometrically. PLoS Biol 13, e1002211 (2015).

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