Synaptic plasticity is a crucial neuronal mechanism for learning and memory. It allows synapses to change their strength over time. This dissertation focuses on a particular form of synaptic plasticity called synaptic scaling, a homeostatic mechanism that preserves relative synaptic strengths in an activity-dependent manner. Synaptic scaling is fundamental for neuronal stability, regulating other plasticity mechanisms like Hebbian plasticity or long-term potentiation (LTP).

The aims of this dissertation are to explore the implications of synaptic scaling (and other forms of plasticity, such as structural plasticity) on the overall behavior of neurons. This is done using system-theoretic tools and feedback control. We first formulate a biophysical closed loop model of synaptic scaling. We then study how synaptic scaling affect neurons’ behavior in both abstract and reconstructed morphologies. This study reveals important tradeoffs between robustness, convergence rate, and accuracy of scaling.

We first look at synaptic scaling as a “global control action” whose main role is to guarantee a steady level of neural activity. We then consider activity-dependent degradation as a “local control action” whose role is to assist the neuron in fine-tuning different desirable spatial concentration profiles. We show that, in extreme scenarios, it can promote a level of competition between synapses that has a destabilizing effect on the overall behavior. At the methodological level, we use compartmental modeling and we focus on the in- teraction between feedback and transport, in linear and nonlinear settings. Using classical system-theoretic tools like Bode and Nyquist analysis and singular perturbation arguments, and more recent tools like contraction and dominance theory, we derive parameter ranges under which synaptic scaling is stable and well-behaved (slow regulation), stable and oscilla- tory (aggressive regulation), and unstable (pathological regulation). We also study the system robustness against static and dynamics uncertainties.

Finally, to understand how different plasticity mechanisms simultaneously affect the neuron behavior, we study synaptic scaling in the presence of activity-dependent growth (mimicking a structural plasticity mechanism). This is a third layer of control action shaping the neuron morphology. We find that activity-dependent growth improves the neuron’s performance when synaptic scaling is insufficient.