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Hybrid circuits that connect living and model neurons allow studying neural dynamics to assess the role of specific cells and synapses in emergent phenomena of neural computation (Reyes-Sanchez et al. 2020). In this work, we deal with the automatic adaptation and mapping of parameters in hybrid circuits and, in particular, those that yield dynamical invariants. Such invariants take the form of robust relationships between the intervals that build robust sequences arising from the cell interactions and have been recently unveiled in well-known CPGs (Elices et al. 2019). In our methodology, we input biological time series with a characteristic temporal structure of spiking-bursting dynamics to different model neurons with monodirectional and bidirectional synapses implemented with dynamic clamp. To illustrate the protocol, we searched for dynamical invariants established between a living pyloric CPG cell and a Komendantov-Kononenko model neuron connected through a graded synapse model. The biological recordings were preprocessed to automatically adapt the corresponding time and amplitude scales to those of the synapse and neuron models employed. Our automatic experimental protocol then mapped the neuron and synapse parameters that yielded a predefined dynamical invariant. By using parallel computing, this approach readily achieved a full characterization of the parameter space that resulted in the predefined target dynamics. To search for dynamical invariants in real-time bidirectional connections, we also developed a genetic search that found valid set of parameters to reproduce the target dynamical invariant in a few iterations. We illustrated this methodology in the study of the coordination generated by the dynamical invariants to balance flexibility and robustness in neural rhythms. Our results demonstrate that maps showing the presence of dynamical invariants can be built in a few minutes for monodirectional hybrid circuits and that the genetic algorithm can readily find dynamical invariants in bidirectional connections between living and model neurons. The proposed strategy can be generalized for any hybrid circuit and can also be used in the design of hybrots, i.e., robots whose locomotion is controlled by living neural circuits with feedback from the sensor robots.

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