I don't really understand what you're after, it'd be great if you could expand a little bit; anyway, some pointers to the use of profunctors in related matters (possibly you already know about all this things):

## Hughes' arrows

This is what I think is more related to your question; *arrows* (these are not 1-cells/morphisms! (well, they are, see below)) are a generalization of (strong = enriched) monads as they're used in functional programming; the paper introducing them is

Hughes - *Generalising monads to arrows* - Science of computer programming :: (website)

Now, arrows correspond to strong monads in $\mathbf{Prof}$; (something like) this was first published in

Heunen, Jacobs - *Arrows, like Monads, are Monoids* - Electronic Notes in Theoretical Computer Science :: (pdf)

and a more precise account together with some generalizations is given in

Asada - *Arrows are strong monads* - Proceedings of the third ACM SIGPLAN workshop on Mathematically structured functional programming :: (pdf)

## semantics of concurrency

I guess this started with

Joyal, Nielsen, Winskel - *Bisimulation from open maps* - Logic in Computer Science :: (pdf)

where, viewing processes as presheaves, it is shown that in a lot of situations, bisimulations between processes can be defined in terms of spans of open maps between them (open here essentially the same as Joyal-Moerdijk); two processes are then bisimilar if there's a span of *surjective* open maps between them. This includes bisimilarity for synchronization trees, labelled transition systems, event structures, etc.

The connection with profunctors was first (I think) identified in

Cattani, Winskel - *Profunctors, open maps and bisimulation* - Mathematical Structures in Computer Science :: (pdf)

Where it is shown that profunctors (viewed as cocontinuous functors between presheaf categories) preserve open maps, and are thus a good notion of higher-order process: a profunctor $F \colon A \nrightarrow B$ maps $A$-processes to $B$-processes, an bisimulations to bisimulations. When viewing profunctors as higher-order processes, the structure of $\mathbf{Prof}$ (compact-closed, and thus traced, etc) starts to play a key role, and things start to look more like Abramsky geometry of interaction stuff and/or Walters (bi)categories with feedback etc: see for example

Hildebrandt, Panangaden, Winskel - *Relational semantics of non-deterministic dataflow* - CONCUR'98 Concurrency Theory :: (pdf)

This (presheaf categories - open maps - profunctors) setting has been somewhat generalized (modulo size issues) to work with a dense lax-idempotent 2-monad $T$ in $\mathbf{Cat}$, which in the presheaves and profunctors case would be (would it exist) the free-cocompletion 2-monad: one defines a notion of open map for a morphism in $TC$, and morphisms in the Kleisli 2-category $Alg_T$ preserve open maps.