Our results show for two species of squids that substantial gradients of circumferential strain and strain rate exist across the mantle wall. Although we do not yet understand the implication of gradients for locomotor performance of squids, such large gradients of strain and strain rate have implications for circular muscle performance. A gradient of strain (figures c
) probably results in the circular muscle fibres near the inner and outer surfaces of the mantle operating over different ranges of sarcomere length and, therefore, potentially producing different levels of force during the same mantle contraction. Because the work produced by a muscle depends on the product of force and the change in length of the fibre (e.g. Josephson 1999
), the unit work output may vary transmurally, particularly during the high circumferential strains of rapid jetting. Furthermore, the circular muscle fibres near the inner surface of the mantle experienced strain rates from 0.2 to 0.9 lengths s−1
higher than those near the outer surface during vigorous jets (b
). These differences are large relative to the maximum unloaded shortening velocity of the circular fibres (5.1 lengths s−1
; Thompson et al. 2008
) and suggest that fibres near the inner surface experience lower loads for a given mantle contraction.
Gradients of strain require the circular fibres near the inner lumen surface of the mantle to generate force over an especially wide range of lengths (+25% to −42%; a
). Such performance requirements are unusual among muscles that generate power for locomotion (Burkholder & Lieber 2001
), although the pectoralis fibres of pigeons come close in their operating length range (+15% to −27%; Soman et al. 2005
). The body wall musculature of most soft-bodied invertebrates, including squid, is composed of obliquely striated fibres. The factors favouring the ubiquity of oblique striation are unknown, but experimental evidence from the obliquely striated fibres of leeches (Miller 1975
) shows that such fibres can generate force over an impressive range of lengths. If the obliquely striated fibres of squids can similarly generate force over a wide range of lengths, then gradients of strain may have been a selective pressure favouring the evolution of oblique striation in the circular fibres.
It is often assumed that there are no regional differences in fibre strain within a striated muscle, though recent work on vertebrates has shown this assumption to be false (e.g. Huijing 1985
; Pappas et al. 2002
; Ahn et al. 2003
; Higham et al. 2008
). Our finding that fibres at different locations within the same muscular organ experience very different strain and strain rates also contradicts this long-standing assumption. Furthermore, the mantle (indeed, the muscular organs and body walls of all soft-bodied invertebrates) is distinctive in that it lacks the aponeuroses or myotendinous junctions that are important contributors to non-uniform strain in vertebrate striated muscles.
It is interesting to note that studies of hollow cylindrical muscular organs in vertebrates, such as the mammalian heart and arteries, have not reported transmural gradients of muscle fibre strain. A gradient of strain is not observed in the left ventricle of mammals, for example, because relatively few muscle fibres within the thick myocardium simply wrap around the circumference of the ventricle. Rather, adjacent groups of fibres vary in their orientation as a function of position in the thickness of the ventricle wall (Anderson et al. 2009
; Smerup et al. 2009
). This architecture virtually eliminates transmural gradients of strain and also permits the fibres to operate over a relatively small range of sarcomere lengths, while still ejecting most of the fluid from the ventricle chamber (e.g. MacGowan et al. 1997
). By contrast, fibre orientation appears uniform among the striated circular muscles of invertebrate body walls (e.g. Trueman 1975
), and gradients of strain and strain rate in circular muscle layers may therefore be universal among soft-bodied invertebrates.