Nonlinear Dynamics of Neural Circuits

  • Joseph Taylor

Student thesis: Doctoral ThesisPhD


This thesis describes the development of a data assimilation methodology for building single-neuron conductance models. Data assimilation seeks to determine unmeasured states and parameters of experimental systems from observable macro- scopic quantities. Here, we attempt to estimate parameters governing unobserved ionic transport at the molecular level from observed membrane voltage recordings. We implement a variational assimilation method that uses constrained nonlinear optimization to synchronize the output of neuron models to observed time series data.
When using real-world data, measurement noise and model error can impede the identification of the optimal parameter solution. We present a regularization method that improves convergence towards this optimal solution when data are imperfect and the model is unknown, and derive the conditions under which this optimal solution is obtainable. This method is then applied to the construction of hardware neuron models comprising equations of intracellular currents embodied in analog solid-state electronics. We successfully transfer the complete dynamics of hippocampal and respiratory neurons into silicon devices which are found to respond nearly identically to their biological counterparts under a wide range of current stimulation protocols.
These solid-state models are used to construct inhibitory neural circuits, and the dependence of network dynamics on synaptic parameters in these circuits is quantitatively characterised. The single-neuron parameter estimation developed in the first part of the thesis is finally extended to the construction of inhibitory neuronal networks. To overcome the challenges associated with optimizing a whole- network model, we develop a novel phase reduction approach that allows each neuron in the network to be optimized individually. This work further expands the applicability of variational assimilation to complex neuronal systems.
Date of Award2 Dec 2020
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorAlain Nogaret (Supervisor) & Richard James (Supervisor)

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