Event triggered signalling codecs for molecular estimation

Low molecule numbers and intrinsically noisy, coupled stochastic chemical reactions are common in cell biology. For such environments, [12] showed that the accuracy with which molecular populations can be estimated and controlled can be bounded from below by regarding molecular coupling as an information transfer across a finite capacity Poisson channel. In conjunction with a diffusion approximation for the target species, this leads to a clear distortion bound for arbitrary signal-target molecular coupling. For static signal-target coupling, sharp, biologically relevant bounds result, which appear to still hold for the original discrete system. However, when arbitrary non-linear, dynamic coupling is allowed, [13] showed that event-triggered codecs can be constructed that are capable of outperforming the general diffusion bound, both for estimation and control. This paper extends the estimation results from [13] to various molecular signalling topologies and integer encoders. It is found that the bound can be outperformed across all serial and parallel networks by a M|M|1 queue type codec, which is likely optimal for a single stage, over a small parameter regime. Outside this regime queueing delay leads to increasingly worse estimation. The application of integer coding variants in an attempt to improve stability and increase the regime of good performance is largely fruitless, thus indicating that even the simplest non-trivial estimation problem cannot be solved with intuitively sensible codecs.