  A method of data assimilation (DA) is employed to estimate
electrophysiological parameters of neurons simultaneously with their synaptic
connectivity in a small model biological network. The DA procedure is cast as
an optimization, with a cost function consisting of both a measurement error
and a model error term. An iterative reweighting of these terms permits a
systematic method to identify the lowest minimum, within a local region of
state space, on the surface of a non-convex cost function. In the model, two
sets of parameter values are associated with two particular functional modes of
network activity: simultaneous firing of all neurons, and a pattern-generating
mode wherein the neurons burst in sequence. The DA procedure is able to recover
these modes if: i) the stimulating electrical currents have chaotic waveforms,
and ii) the measurements consist of the membrane voltages of all neurons in the
circuit. Further, this method is able to prune a model of unnecessarily high
dimensionality to a representation that contains the maximum dimensionality
required to reproduce the provided measurements. This paper offers a
proof-of-concept that DA has the potential to inform laboratory designs for
estimating properties in small and isolatable functional circuits.
