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Critical waves and the length problem of biology

Significance This paper invokes physical principles to answer the question of why pure reaction–diffusion ideas do not produce a satisfactory explanation of biological growth and form. Two ideas have been missing. One is that oscillation is necessary to achieve the necessary design stability and plasticity. The other is that the system must be tuned to criticality to stabilize the propagation velocity, thus enabling clocks to function as meter sticks. The larger significance is twofold: First, a fundamental piece of the machinery of life is probably invisible to present-day biochemical methods because they are too slow. Second, the simplicity of growth and form identified a century ago by D'Arcy Thompson is probably a symptom of biological engineering strategies, not primitive law. 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.