Critical waves and the length problem of biology

Abstract

It is pointed out that the mystery of how biological systems measure their lengths vanishes away if one premises that they have discovered a way to generate linear waves analogous to compressional sound. These can be used to detect length at either large or small scales using echo timing and fringe counting. It is shown that suitable linear chemical potential waves can, in fact, be manufactured by tuning to criticality conventional reaction-diffusion with a small number substance. Min oscillations in Escherichia coli are cited as precedent resonant length measurement using chemical potential waves analogous to laser detection. Mitotic structures in eukaryotes are identified as candidates for such an effect at higher frequency. The engineering principle is shown to be very general and functionally the same as that used by hearing organs.growth and form | waves | laser amplifier | MinDE | mitosis I t is not known how living things measure their lengths. This is true notwithstanding the immense progress made over the past 30 y in understanding morphogen gradients in embryogenesis (1-6). The problem is captured nicely by the confusion over regulation of the bicoid profile in Drosophila (7-11), but it is also reflected in the notorious instability, hysteresis, and lack of scalability of traditional static reaction-diffusion (12, 13). No one knows why cells are the size they are (14), why plants and animals are the size they are (15), how organs grow maintaining their proportions (16), and how some animal bodies regenerate lost limbs (17). On the matter of length determination, per se, very little progress has been made beyond Thompson's 1917 treatise on biological form (18).Length has a special place in biology by virtue of being a primitive quantity with units. It is not possible for living things to size themselves properly without having developed the skill of measuring these quantities as numbers and relating these numbers to each other mathematically. They require meter sticks to do this. They must fabricate these meter sticks using diffusion and motors, because they are the only biochemical elements that involve length. The relationships of these meter sticks to each other and to the lengths they measure must be precise and described by equations. This is because precise mathematical relationships among lengths are what size and shape are.In this paper I point out that the difficulty of accounting for length relationships of parts of organisms with equations disappears instantly if the organism is premised to have discovered a way to emulate elementary physical law. In particular, one simple invention is sufficient to facilitate the measurement and construction of body plans of any shape and size one might wish in a way that is both plastic and scalable: the conversion of diffusive motion into linear waves using engines. The concept is general because all motion in the presence of disorder, including motion of cytoskeletal components, becomes diffusive at long time and length scales by virtue of evolving into a...

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