Necessity of the sleep–wake cycle for synaptic homeostasis: system-level analysis of plasticity in the corticothalamic system

Neural field theory is used to study the system-level effects of plasticity in the corticothalamic system, where arousal states are represented parametrically by the connection strengths of the system, among other physiologically based parameters. It is found that the plasticity dynamics have no fixed points or closed cycles in the parameter space of the connection strengths, but parameter subregions exist where flows have opposite signs. Remarkably, these subregions coincide with previously identified regions that correspond to wake and slow-wave sleep, thus demonstrating state dependence of the sign of synaptic modification. We then show that a closed cycle in the parameter space is possible when the plasticity dynamics are driven by the ascending arousal system, which cycles the brain between sleep and wake to complete a closed loop that includes arcs through the opposite-flow subregions. Thus, it is concluded that both wake and sleep are necessary, and together are able to stabilize connection weights in the brain over the daily cycle, thereby providing quantitative realization of the synaptic homeostasis hypothesis.