Abstract
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.
Highlights
Sleep has been argued to induce the reorganization of neuronal structure, leading to reinforcement of learning and memory consolidation, but the mechanisms are poorly understood [1,2,3,4]
Plasticity dynamics are governed by equation (2.14), where the rate of change of the connection strengths depends on the spectral features of the system at any given moment
We evaluate equation (2.14) at the parameter values representative of the traditional arousal stages given in table 2, which correspond to seven points in XYZ space
Summary
Sleep has been argued to induce the reorganization of neuronal structure, leading to reinforcement of learning and memory consolidation, but the mechanisms are poorly understood [1,2,3,4]. Plasticity in NFT can be written as a generalized learning rule that preserves the relative timings of input and output activity, allowing the representation of both correlation-dependent plasticity (CDP) and STDP dynamics [11,21] In this formulation, the average plasticity responses depend upon temporal correlations between presynaptic inputs and postsynaptic responses. Spectral analysis of plasticity applied to a population of excitatory neurons with external input and feedback has revealed the strong role of system-level resonances in plasticity, including the reversal of the plasticity sign at different frequencies (transitions from LTD to LTP and vice versa) [11] These results provide a starting point for a quantitative description of synaptic homeostasis via sleep and wake, as they demonstrate that the sign of plasticity can change between arousal states, as the shape of the power spectrum changes [11]. We show that it is possible to achieve synaptic homeostasis by accounting for the sleep –wake 3 cycle, which moves the brain parametrically between states of opposite flow (sign of synaptic modification), thereby stabilizing the system
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