A functional analysis of myotomal muscle-fibre reorientation in developing zebrafish Danio rerio

The fast muscle fibres in the anterior trunk of teleost fish are primarily responsible for large amplitude undulatory swimming motions. Previous theoretical studies suggested that the near-helical arrangement of these fibres results in a (fairly) uniform distribution of fibre strain and work output during swimming. However, the underlying simplifications of these studies precluded unequivocal support for this hypothesis. We studied the fast muscle-fibre reorientation and the concomitant myotomal strain variance in a body segment near the anus during larval and juvenile development in the zebrafish. From 2 to 4 days post fertilization (d.p.f.), the measured angles between the muscle fibres and the longitudinal axis of the zebrafish were small. Yet, onset of a near-helical muscle-fibre arrangement was recognized. Juveniles of 51 d.p.f. have larger mean fibre angles and already possess the near-helical pattern of adult teleosts. We present a model that computes the distribution of the strain along the muscle fibres from measured muscle-fibre orientations, body curvature and prescribed tissue deformations. We selected the most extreme body curvatures, which only occur during fast starts and turning manoeuvres. Using the model, we identified the (non-linear) tissue deformations that yield the least variance in the muscle-fibre strain. We show that simple beam theory cannot reliably predict the strain distribution: it results in very small strains and negligible work output of the most medial fibres. In our model, we avoided these functional limitations by adding a shear deformation to the simple beam deformation. At 2 d.p.f., the predicted variance in the muscle-fibre strain for the shear deformation optimized for strain uniformity is fairly small, due to the small variation in the fibre distances to the medial plane that is caused by the relatively large spinal cord and notochord. The predicted minimal strain variance increases sharply from 2 d.p.f. to 3 d.p.f., remains relatively large at 4 d.p.f., but decreases again considerably at 15 and 39 d.p.f. The 51 d.p.f. stage exhibits the smallest variance in the fibre strains (for the identified optimal deformation), in spite of the widely varying muscle-fibre distances to the medial plane. The non-linear nature of the body deformations with the least strain variance implies an interesting optimization constraint: the juvenile muscle-fibre arrangement results in small predicted spatial strain variations at large-amplitude body curvatures, at the (modest) expense of a large coefficient of variation for small curvatures. We conclude that larval fish rapidly change their muscle-fibre orientations (probably in response to mechanical signals). Within the theoretically examined plausible range of deformations, the closest correspondence to a uniform strain field was found for the juvenile stage.