  Probabilistic inference provides a language for describing how organisms may
learn from and adapt to their environment. The computations needed to implement
probabilistic inference often require specific representations, akin to having
the suitable data structures for implementing certain algorithms in computer
programming. Yet it is unclear how such representations can be instantiated in
the stochastic, parallel-running biochemical machinery found in cells (such as
single-celled organisms). Here, we show how representations for supporting
inference in Markov models can be embodied in cellular circuits, by combining a
concentration-dependent scheme for encoding probabilities with a mechanism for
directional counting. We show how the logic of protein production and
degradation constrains the computation we set out to implement. We argue that
this process by which an abstract computation is shaped by its biochemical
realization strikes a compromise between "rationalistic" information-processing
perspectives and alternative approaches that emphasize embodiment.
