Comparing the orthogonal and homotopy functor calculi

Goodwillie’s homotopy functor calculus constructs a Taylor tower of approximations toF , often a functor from spaces to spaces. Weiss’s orthogonal calculus provides a Taylortower for functors from vector spaces to spaces. In particular, there is a Weiss towerassociated to the functor V ÞÑ FpSVq, where SVis the one-point compactification of V .In this paper, we give a comparison of these two towers and show that when F isanalytic the towers agree up to weak equivalence. We include two main applications, oneof which gives as a corollary the convergence of the Weiss Taylor tower of BO. We alsolift the homotopy level tower comparison to a commutative diagram of Quillen functors,relating model categories for Goodwillie calculus and model categories for the orthogonal calculus.

Mucosal modulation of contractility in bladder strips from normal and overactive rat models and the effect of botulinum toxin A on overactive bladder strips

AIMS: To investigate the local, regulatory role of the mucosa on bladder strip contractility from normal and overactive bladders and to examine the effect of botulinum toxin A (BoNT-A).

METHODS: Bladder strips from spontaneously hyperactive rat (SHR) or normal rats (Sprague Dawley, SD) were dissected for myography as intact or mucosa-free preparations. Spontaneous, neurogenic and agonist-evoked contractions were investigated. SHR strips were incubated in BoNT-A (3 h) to assess effects on contractility.

RESULTS: Spontaneous contraction amplitude, force-integral or frequency were not significantly different in SHR mucosa-free strips compared with intacts. In contrast, spontaneous contraction amplitude and force-integral were smaller in SD mucosa-free strips than in intacts; frequency was not affected by the mucosa. Frequency of spontaneous contractions in SHR strips was significantly greater than in SD strips. Neurogenic contractions in mucosa-free SHR and SD strips at higher frequencies were smaller than in intact strips. The mucosa did not affect carbachol-evoked contractions in intact versus mucosa-free strips from SHR or SD bladders. BoNT-A reduced spontaneous contractions in SHR intact strips; this trend was also observed in mucosa-free strips but was not significant. Neurogenic and carbachol-evoked contractions were reduced by BoNT-A in mucosa-free but not intact strips. Depolarisation-induced contractions were smaller in BoNT-A-treated mucosa-free strips.

CONCLUSIONS: The mucosal layer positively modulates spontaneous contractions in strips from normal SD but not overactive SHR bladder strips. The novel finding of BoNT-A reduction of contractions in SHR mucosa-free strips indicates actions on the detrusor, independent of its classical action on neuronal SNARE complexes.