Recent experimental results have identified brainstem and hypothalamic neuronal populations whose neurotransmitter-mediated interactions are proposed to compose a regulatory network for the control of sleep and wake transitions. While there is wide support for the contribution and interactions of specific wake-promoting and sleep-promoting neuronal populations in this network, by contrast, there has been much debate about the network components involved in the regulation of rapid-eye movement (REM) sleep. This project analyzes how the structure of competing proposed sleep-wake regulatory networks determines sleep-wake behavior and dynamics of behavioral state transitions. The researchers have developed a novel firing rate model formalism explicitly including neurotransmitter dynamics that is uniquely suited to model dynamics of the sleep-wake regulatory network. Using a reduction of this formalism, models of the current competing proposed structures for the subnetwork governing REM sleep generation are analyzed to determine intrinsic dynamics dictated by the network structure, and the dependence of those dynamics on subnetwork components. Additionally, state transition dynamics in competing proposed network structures for regulation of wake and sleep states are investigated. Maintaining the reduced model formalism, the focus is on determining the mechanisms by which the competing network structures generate key features of human sleep patterning that will be characterized from experimental sleep recordings. Dynamics of competing model networks, using the full model formalism including stochastic components, are fit to the fine temporal architecture of sleep-wake patterning recorded in multiple species, including rodent, feline, and human, with focus on investigating common dynamic features of sleep-wake patterning and variability in sleep-wake regulatory mechanisms across species. The researchers collaborate with three leading experimental sleep scientists who provide sleep recordings and consultation on the proposed projects.

In mammals, states of waking and sleep are actively controlled by populations of neurons located in the brainstem and hypothalamus. Currently, in experimental sleep science, the interactions of these populations, mediated by primary neurotransmitters, are believed to form a regulatory network for the control of sleep and wake transitions. While there is wide support for the contribution and interactions of specific wake-promoting and sleep-promoting neuronal populations in this network, by contrast, there has been much debate about the network components involved in the regulation of rapid-eye movement (REM) sleep. Experimental investigation of the sleep-wake regulatory is limited by the fact that the outcome measurement, namely sleep-wake patterning, only exists in the intact animal. The experimental techniques available to probe the neuronal regulatory mechanisms are limited to those that can be conducted in vivo without disrupting sleep, or post-mortem studies that can identify anatomy of synaptic projections between populations but not their time-varying interactions that underlie sleep-wake transitions. This project uses mathematical modeling as an investigative tool to bridge the gaps left by these limitations in experimental studies. The modeling studies address the physiologically compelling and currently debated question of the structure of the mammalian sleep-wake regulatory network. Numerous experimental groups have proposed schematics of network structures and provided hypothetical descriptions of how network interactions drive behavioral state transitions. However, static conceptual models lack the ability to replicate time dynamics of transitions between sleep-wake states or to determine dynamic interactions inherent to network structure. Construction and analysis of mathematical models of these proposed networks identifies the dynamic interactions of constituent populations and neurotransmitters, and provides quantitative understanding of how network dynamics generate the fine temporal architecture of sleep-wake patterning. Model solutions are compared to experimental recordings of rodent, feline and human sleep to determine mechanisms contributing to the differences in sleep-wake patterning observed in these multiple species. Results of the modeling studies identify limitations of each of the proposed network structures in accounting for various characteristics of sleep-wake regulation and will generate predictions suggesting how experimental approaches can refine our knowledge of the physiological network structure.

Project Report

The field of sleep research has a strong tradition of using mathematical models to frame understanding and explore conceptual hypotheses regarding the mechanisms of sleep-wake regulation. Recent experimental results have identified numerous brainstem and hypothalamic neuronal populations whose neurotransmitter-mediated interactions compose a regulatory network that is proposed to control sleep and wake transitions. Detailed experimental investigation of this distributed sleep-wake regulatory network is limited by the fact that its output, namely sleep-wake patterning, only exists in the intact animal. No reduced experimental preparation, such as brain slice, in situ preparation or culture of disassociated cells, which could permit close study of the time-varying activity of neuronal interactions within the network has been identified to exhibit any characteristics of the sleep or waking state. As such, the experimental techniques available to probe the sleep-wake network are limited to those that can be conducted in vivo without disrupting sleep, or post-mortem studies that can identify anatomy but not dynamic interactions. Mathematical modeling can contribute to overcoming these experimental limitations by providing a framework in which related hypotheses gained from different experimental studies can be combined consistently and comprehensively to investigate the entire sleep-wake network system. The funded projects developed a new generation of math models based on the recently identified neuroanatomy of sleep-wake regulation that sleep researchers can use to formalize and interpret experimental results going forward. The funded projects specifically addressed the scientifically compelling and currently debated question of the structure of the mammalian sleep-wake regulatory network. Our construction and analysis of mathematical models of proposed conceptual networks identified the dynamic interactions of constituent populations and neurotransmitters, and provided quantitative understanding of how network dynamics generated sleep-wake behavior observed in rats and humans. Neuroanatomy indicated that the periodic dynamics of sleep-wake and circadian behavior may be regulated by a network of coupled subsystems that can be modeled by equations for limit cycle oscillators or using discontinuous equations capable of generating hysteresis loop dynamics. Thus, mathematically, the grant projects contributed analysis techniques and results to understand solutions of systems of continuous limit cycle oscillators coupled to discontinuous hysteresis loop oscillators. The funded projects directly contributed to the understanding of the physiological basis of sleep in the following ways: (1) our analysis of REM/NREM cycling in reciprocal interaction and mutual inhibition networks was the first direct comparison of behaviors dictated by these two leading hypotheses for REM sleep regulation; (2) our human sleep-wake regulation model predicted a unifying physiological mechanism to account for interindividual differences in internally desynchronized sleep-wake behavior; and (3) our mutual inhibition sleep-wake regulatory network model predicted specific synaptic pathways between state promoting populations that generated the fine temporal architecture of rat sleep-wake behavior. These results were transferable to sleep physiology in the form of experimentally-testable predictions and disseminated in journals with experimental readerships and at meetings of experimental societies. The grant provided funding for the training and development in interdisciplinary research in mathematics and biology to 1 postdoctoral fellow and 3 undergraduate students participating in summer REU projects at the University of Michigan. Grant projects also provided interdisciplinary training in mathematics and biology research to a master’s graduate student and 5 undergraduate students at the University of Michigan, Gettysburg College and Colorado School of Mines.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
1121361
Program Officer
Mary Ann Horn
Project Start
Project End
Budget Start
2011-10-01
Budget End
2014-09-30
Support Year
Fiscal Year
2011
Total Cost
$299,998
Indirect Cost
Name
University of Michigan Ann Arbor
Department
Type
DUNS #
City
Ann Arbor
State
MI
Country
United States
Zip Code
48109