Synaptic scaling is a homeostatic normalization mechanism that preserves relative synaptic strengths by adjusting them with a common factor. This multiplicative change is believed to be critical, since synaptic strengths are involved in learning and memory retention. Further, this homeostatic process is thought to be crucial for neuronal stability, playing a stabilizing role in otherwise runaway Hebbian plasticity [1-3]. Synaptic scaling requires a mechanism to sense total neuron activity and globally adjust synapses to achieve some activity set-point [4]. This process is relatively slow, which places limits on its ability to stabilize network activity [5]. Here we show that this slow response is inevitable in realistic neuronal morphologies. Furthermore, we reveal that global scaling can in fact be a source of instability unless responsiveness or scaling accuracy are sacrificed." "A neuron with tens of thousands of synapses must regulate its own excitability to compensate for changes in input. The time requirement for global feedback can introduce critical phase lags in a neuron’s response to perturbation. The severity of phase lag increases with neuron size. Further, a more expansive morphology worsens cell responsiveness and scaling accuracy, especially in distal regions of the neuron. Local pools of reserve receptors improve efficiency, potentiation, and scaling, but this comes at a cost. Trafficking large quantities of receptors requires time, exacerbating the phase lag and instability. Local homeostatic feedback mitigates instability, but this too comes at the cost of reducing scaling accuracy." "Realization of the phase lag instability requires a unified model of synaptic scaling, regulation, and transport. We present such a model with global and local feedback in realistic neuron morphologies (Fig. 1). This combined model shows that neurons face a tradeoff between stability, accuracy, and efficiency. Global feedback is required for synaptic scaling but favors either system stability or efficiency. Large receptor pools improve scaling accuracy in large morphologies but worsen both stability and efficiency. Local feedback improves the stability-efficiency tradeoff at the cost of scaling accuracy. This project introduces unexplored constraints on neuron size, morphology, and synaptic scaling that are weakened by an interplay between global and local feedback.

Plasticity shapes the brain during development, and mechanisms of plasticity continue into adulthood to enable learning and memory. Nearly all brain functions are influenced by past events, reinforcing the view that the confluence of plasticity and computation in the same circuit elements is a core component of biological intelligence. My laboratory studies plasticity in the cerebral cortex during development, and plasticity during behaviour that is manifest as cortical dynamics. I will describe how cortical plasticity is implemented by learning rules that involve not only Hebbian changes and synaptic scaling but also dendritic renormalization. By using advanced techniques such as optical measurements of single-synapse function and structure in identified neurons in awake behaving mice, we have recently demonstrated locally coordinated plasticity in dendrites whereby specific synapses are strengthened and adjacent synapses with complementary features are weakened. Together, these changes cooperatively implement functional plasticity in neurons. Such plasticity relies on the dynamics of activity-dependent molecules within and between synapses. Alongside, it is increasingly clear that risk genes associated with neurodevelopmental disorders disproportionately target molecules of plasticity. Deficits in renormalization contribute fundamentally to dysfunctional neuronal circuits and computations, and may be a unifying mechanistic feature of these disorders.