Research
My research applies multiscale mathematical modeling to investigate key research questions in metabolism, sleep, and circadian rhythms. Specifically, I model key dynamics in whole-body metabolism including changes in glucose, glycerol, and insulin; sleep and circadian (~24 h) neurophysiology; and the diverse interactions among these systems.
Dysregulation of metabolism and/or sleep has dramatic implications for human health, and the complex ways in which these systems interact, both on a mechanistic and on a behavioral level, are just beginning to be understood. My research in mathematical and computational neuroscience focuses on understanding neurophysiologic mechanisms for sleep/wake regulation and my work in whole-body glucose-insulin dynamics focuses on insulin resistance in adolescents.
Mathematically, my research contributes to the development of novel techniques to understand high-dimensional multiscale systems of differential equations; analyze connections between structure and dynamics of general networks; and investigate dynamics at the interface of deterministic and stochastic behavior. In addition, I leverage my expertise in neuroscience and biological development to develop methods in network analysis (with biological and quantum computing applications) and biologically-inspired machine learning.
During the course of my graduate training in the Department of Mathematics and the Center for BioDynamics at Boston University, my postdoctoral training in the Division of Sleep Medicine at Harvard Medical School and the Department of Mathematics at the University of Michigan, and my faculty appointments, I have developed a strong, externally-funded research program in applied math with vital connections to experimentalists and clinicians.
I lead the AMS Math Biology Research Group.
A complete list of my publications can be found on my Google Scholar page.
Diniz Behn Research Group
My research group currently includes
- PhD student Shelby Stowe
- PhD student Justin Garrish
- PhD student Michael Ivanitskiy
- MS student Brandon Barton
- MS student Sydney Medina
- Undergraduate Armelle Duston
- Undergraduate Mason Kugler
- Undergraduate Addison Olstad
See the Research Group page for more details.
Current research
Multiple time scales in sleep-wake modeling
Sleep-wake behavior is produced by the interaction of many processes occurring on a range of spatial and temporal scales: individual neurons spiking on a millisecond time scale coordinate their activity to promote states of wake and sleep that are modulated by processes, such as the approximately 24-hour circadian drive, that act on time scales of days. Mathematical modeling provides a key tool for integrating anatomic and physiologic data across these scales to probe the dynamic interactions of these elements. Current and ongoing work in this area involves the application of reduction of dimension and fast-slow techniques to identify mechanisms of state transition; establishing numerical criteria to compare and contrast the existence and robustness of REM/non-REM cycling produced by different putative REM-generating network structures; computing 1-D piecewise continuous maps that capture key elements of sleep/wake regulatory dynamics; and integrating molecular and electrophysiological models to investigate modulation and signaling of the circadian clock<. Projects include work in both human and nonhuman animal models.
Applying mathematical modeling to protocol design and interpretation of circadian data
Experimental investigation of the human circadian system is very resource-intensive, and it is challenging to optimize experimental protocols in the lab. In recent work, we have been applying mathematical models of the circadian clock to optimize protocol design and to provide insights into the role of inter-individual differences in data collection and interpretation. Recent work has focused on interactions between the circadian system and melatonin, a naturally-occurring hormone and circadian marker that is increasingly being used as a supplement in children and adults.
Glucose-insulin dynamics and tissue-specific insulin resistance
In recent years, my research program has increasingly addressed questions of whole-body metabolism. From a physiological perspective, the common role of the hypothalamus provides a unified substrate for sleep/circadian and metabolic investigation. However, my current research considers metabolism in contexts outside, as well as inside, the brain. My collaborators are pioneering novel experimental protocols involving multiple stable isotope tracers to provide less-invasive techniques to assess tissue-specific insulin resistance (IR) in at-risk adolescent populations. We also seek to combine these measures of IR with characterization of sleep and circadian measures including obstructive sleep apnea indices and melatonin secretion profiles. My research in this area focuses on developing the novel mathematical tools that are necessary for optimal mining and interpretation of these complex data sets while considering the unique features of adolescent metabolism and the role of sex as a biological variable.
Orexin/hypocretin neurons and their role in stabilizing sleep-wake behavior
In normal sleep-wake behavior, the neuropeptide orexin (also known as hypocretin) helps to stabilize transitions between wake and sleep, and dysregulation of orexin is associated with the sleep disorder narcolepsy. Since the state instability that characterizes narcolepsy reflects an alteration of the network dynamics producing sleep-wake behavior, mathematical approaches aimed at understanding the stability of the network provide vital complementary techniques to traditional sleep research. In previous work I have developed higher-order statistical and signal-processing techniques to analyze the altered dynamics of sleep-wake behavior in mice with disrupted orexinergic systems; modeled the action of orexin at the network level; and described a Hodgkin-Huxley-type model orexin neuron. Recent work has analyzed the role of progressive orexin cell loss in a novel rodent model of narcolepsy and characterization of narcolepsy in children. Orexin neurons are also glucose-sensing and, therefore, they are ideally situated to integrate information between sleep-wake and metabolic systems.
Stochastic and deterministic contributions to the fine architecture of sleep-wake behavior
The fine architecture of sleep-wake behavior reflects the underlying deterministic and stochastic processes that produce it and provides an important constraint for models seeking to represent this system. Systematic analysis of the effects of different kinds of noise on resulting dynamics has provided insights into the interaction between deterministic and stochastic elements of the system and revealed some fundamental asymmetries in the network dynamics producing states of wake and sleep. Current work includes assessing the relative contributions of stochastic and deterministic elements to fundamental features of sleep-wake behavior and development of novel methodologies for fitting noisy models. This work also includes comparative analyses across different mammalian species and involves collaborations with several labs investigating sleep in mice, rats, cats, degus, and humans.
NETWORK SCIENCE AND BIOLOGICALLY-INSPIRED MACHINE LEARNING
Although artificial neural networks (ANNs) differ from biological neural networks in many ways, I am interested in ways in which we can leverage understanding of biological neural networks to improve training, efficiency, and interpretability of ANNs. Current work focuses on implementing different learning states, analogous to behavioral states of wake, rapid eye movement (REM) sleep, and non-REM sleep, to improve a network’s performance on out-of-distribution tasks. In addition, in collaboration with colleagues in Physics, I am investigating key properties of complex-valued complex networks and the application of these networks to better understand quantum states.