Characteristic differences in modulation of stomatogastric musculature by a neuropeptide in three species of Cancer crabs

Abstract

Stomatogastric musculature from crabs in the genus Cancer provides a system in which modulatory roles of peptides from the FLRFamide family can be compared. The anterior cardiac plexus (ACP) is a neuroendocrine release site within the Cancer stomatogastric nervous system that is structurally identical in C. borealis, C. productus, and C. magister but that appears to contain FLRFamide-like peptide(s) only in C. productus. We measured the effect of TNRNFLRFamide on nerve-evoked contractions of muscles that were nearby, an intermediate distance, or far from the ACP. We found the spatial pattern of FLRFamidergic modulation of muscles in C. productus to be qualitatively different than in C. borealis or C. magister. In C. productus, muscles proximal to the ACP were more responsive than distal muscles. In C. borealis, FLRFamidergic response was less dependent on muscle location. These results suggest that functionally different roles of FLRFamides in modulating stomatogastric muscle movements may have evolved in different Cancer species.

Appendix

Let n(x, y, t) be the time-varying concentration of FLRFamide in saline confined to an infinite plane. Assume its evolution is described by the two-dimensional diffusion equation $\frac{\partial n}{\partial t} = D\nabla^{2} n$, where D is the diffusion constant, and that n(x, y, 0) = n ₀ δ(x)δ(y)—initially all peptide is confined at the origin. The solution to this equation has azimuthal symmetry and is most simply expressed using polar coordinates:

$$ n(r,t) = \frac{{n_{0} }}{4\pi Dt}{\text{e}}^{{ - \frac{{r^{2} }}{4Dt}}} $$

(1)

The time at which the concentration at r = R is maximum can be obtained by solving $\frac{{\partial n\left( {R,t} \right)}}{\partial t} = 0.$ The resulting condition is 4Dt = R ². This result can be substituted back into Eq. 1 to eliminate t and to yield the maximum concentration at r = R:

$$ n_{\max } \left( R \right) = \frac{{n_{0} }}{{\pi R^{2} }}{\text{e}}^{ - 1} $$

(2)

which varies as the inverse square of the distance from the origin.