Diniz Behn Cecilia G, Booth Victoria
Dept. of Mathematics, Univ. of Michigan, Ann Arbor, MI 48109, USA.
J Neurophysiol. 2010 Apr;103(4):1937-53. doi: 10.1152/jn.00795.2009. Epub 2010 Jan 27.
This study presents a novel mathematical modeling framework that is uniquely suited to investigating the structure and dynamics of the sleep-wake regulatory network in the brain stem and hypothalamus. It is based on a population firing rate model formalism that is modified to explicitly include concentration levels of neurotransmitters released to postsynaptic populations. Using this framework, interactions among primary brain stem and hypothalamic neuronal nuclei involved in rat sleep-wake regulation are modeled. The model network captures realistic rat polyphasic sleep-wake behavior consisting of wake, rapid eye movement (REM) sleep, and non-REM (NREM) sleep states. Network dynamics include a cyclic pattern of NREM sleep, REM sleep, and wake states that is disrupted by simulated variability of neurotransmitter release and external noise to the network. Explicit modeling of neurotransmitter concentrations allows for simulations of microinjections of neurotransmitter agonists and antagonists into a key wake-promoting population, the locus coeruleus (LC). Effects of these simulated microinjections on sleep-wake states are tracked and compared with experimental observations. Agonist/antagonist pairs, which are presumed to have opposing effects on LC activity, do not generally induce opposing effects on sleep-wake patterning because of multiple mechanisms for LC activation in the network. Also, different agents, which are presumed to have parallel effects on LC activity, do not induce parallel effects on sleep-wake patterning because of differences in the state dependence or independence of agonist and antagonist action. These simulation results highlight the utility of formal mathematical modeling for constraining conceptual models of the sleep-wake regulatory network.
本研究提出了一种新颖的数学建模框架，该框架特别适用于研究脑干和下丘脑睡眠-觉醒调节网络的结构和动态。它基于一种群体发放率模型形式，经过修改以明确纳入释放到突触后群体的神经递质浓度水平。利用这个框架，对参与大鼠睡眠-觉醒调节的原发性脑干和下丘脑神经元核之间的相互作用进行建模。该模型网络捕捉了由觉醒、快速眼动（REM）睡眠和非快速眼动（NREM）睡眠状态组成的真实大鼠多相睡眠-觉醒行为。网络动态包括NREM睡眠、REM睡眠和觉醒状态的循环模式，这种模式会因神经递质释放的模拟变异性和网络的外部噪声而受到干扰。对神经递质浓度的明确建模允许模拟将神经递质激动剂和拮抗剂微量注射到一个关键的促觉醒群体——蓝斑（LC）中。追踪这些模拟微量注射对睡眠-觉醒状态的影响，并与实验观察结果进行比较。由于网络中LC激活存在多种机制，被认为对LC活动有相反作用的激动剂/拮抗剂对，通常不会对睡眠-觉醒模式产生相反作用。此外，由于激动剂和拮抗剂作用的状态依赖性或独立性存在差异，被认为对LC活动有平行作用的不同药物，不会对睡眠-觉醒模式产生平行作用。这些模拟结果突出了形式化数学建模在约束睡眠-觉醒调节网络概念模型方面的实用性。
