John H. Abel

Functional network inference of the suprachiasmatic nucleus.

Significance In mammals, circadian rhythms are controlled by a network of neurons in the brain. The structure of this network dictates organism-wide behavior and adaptation to the environment. We used a neurotoxin to desynchronize this circadian network and then used tools from information theory to determine which cells communicate to establish synchronization. Our results show that this functional network consists of two densely-connected cores, surrounded by sparsely connected shell regions. These findings represent the first time, to our knowledge, that this network has been examined at single cell resolution and show that the importance of these core network regions is independent of light input. In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within a neuronal network to generate precise system-wide circadian rhythms. Although the intracellular genetic oscillator and intercellular biochemical coupling mechanisms have been examined previously, the network topology driving synchronization of the SCN has not been elucidated. This network has been particularly challenging to probe, due to its oscillatory components and slow coupling timescale. In this work, we investigated the SCN network at a single-cell resolution through a chemically induced desynchronization. We then inferred functional connections in the SCN by applying the maximal information coefficient statistic to bioluminescence reporter data from individual neurons while they resynchronized their circadian cycling. Our results demonstrate that the functional network of circadian cells associated with resynchronization has small-world characteristics, with a node degree distribution that is exponential. We show that hubs of this small-world network are preferentially located in the central SCN, with sparsely connected shells surrounding these cores. Finally, we used two computational models of circadian neurons to validate our predictions of network structure.

Porosity-Tuned Chitosan–Polyacrylamide Hydrogel Microspheres for Improved Protein Conjugation

We report a robust method to manufacture polyacrylamide-based functional hydrogel microspheres with readily tunable macroporous structures by utilizing a simple micromolding-based technique. Specifically, surface tension-induced droplet formation of aqueous solutions of chitosan and acrylamide in 2D-shaped micromolds followed by photoinduced polymerization leads to monodisperse microspheres. Pore sizes of the microspheres can be readily tuned by simple addition of inert long-chain poly(ethylene glycol) porogen at low content in the prepolymer solution. The as-prepared chitosan-polyacrylamide microspheres exhibit chemical functionality through chitosans primary amines, rapid protein conjugation with selective tetrazine-trans-cyclooctene reaction, and nonfouling property. Combined with the potential to create anisotropic network structures, we envision that our simple fabrication-conjugation method would offer a potent route to manufacture a variety of biofunctionalized hydrogel microentities.

Amplitude Metrics for Cellular Circadian Bioluminescence Reporters

Bioluminescence rhythms from cellular reporters have become the most common method used to quantify oscillations in circadian gene expression. These experimental systems can reveal phase and amplitude change resulting from circadian disturbances, and can be used in conjunction with mathematical models to lend further insight into the mechanistic basis of clock amplitude regulation. However, bioluminescence experiments track the mean output from thousands of noisy, uncoupled oscillators, obscuring the direct effect of a given stimulus on the genetic regulatory network. In many cases, it is unclear whether changes in amplitude are due to individual changes in gene expression level or to a change in coherence of the population. Although such systems can be modeled using explicit stochastic simulations, these models are computationally cumbersome and limit analytical insight into the mechanisms of amplitude change. We therefore develop theoretical and computational tools to approximate the mean expression level in large populations of noninteracting oscillators, and further define computationally efficient amplitude response calculations to describe phase-dependent amplitude change. At the single-cell level, a mechanistic nonlinear ordinary differential equation model is used to calculate the transient response of each cell to a perturbation, whereas population-level dynamics are captured by coupling this detailed model to a phase density function. Our analysis reveals that amplitude changes mediated at either the individual-cell or the population level can be distinguished in tissue-level bioluminescence data without the need for single-cell measurements. We demonstrate the effectiveness of the method by modeling experimental bioluminescence profiles of light-sensitive fibroblasts, reconciling the conclusions of two seemingly contradictory studies. This modeling framework allows a direct comparison between in vitro bioluminescence experiments and in silico ordinary differential equation models, and will lead to a better quantitative understanding of the factors that affect clock amplitude.

Ontogeny of Circadian Rhythms and Synchrony in the Suprachiasmatic Nucleus

In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus coordinates daily rhythms including sleep–wake, hormone release, and gene expression. The cells of the SCN must synchronize to each other to drive these circadian rhythms in the rest of the body. The ontogeny of circadian cycling and intercellular coupling in the SCN remains poorly understood. Recent in vitro studies have recorded circadian rhythms from the whole embryonic SCN. Here, we tracked the onset and precision of rhythms in PERIOD2 (PER2), a clock protein, within the SCN isolated from embryonic and postnatal mice of undetermined sex. We found that a few SCN cells developed circadian periodicity in PER2 by 14.5 d after mating (E14.5) with no evidence for daily cycling on E13.5. On E15.5, the fraction of competent oscillators increased dramatically corresponding with stabilization of their circadian periods. The cells of the SCN harvested at E15.5 expressed sustained, synchronous daily rhythms. By postnatal day 2 (P2), SCN oscillators displayed the daily, dorsal-ventral phase wave in clock gene expression typical of the adult SCN. Strikingly, vasoactive intestinal polypeptide (VIP), a neuropeptide critical for synchrony in the adult SCN, and its receptor, VPAC2R, reached detectable levels after birth and after the onset of circadian synchrony. Antagonists of GABA or VIP signaling or action potentials did not disrupt circadian synchrony in the E15.5 SCN. We conclude that endogenous daily rhythms in the fetal SCN begin with few noisy oscillators on E14.5, followed by widespread oscillations that rapidly synchronize on E15.5 by an unknown mechanism. SIGNIFICANCE STATEMENT We recorded the onset of PER2 circadian oscillations during embryonic development in the mouse SCN. When isolated at E13.5, the anlagen of the SCN expresses high, arrhythmic PER2. In contrast, a few cells show noisy circadian rhythms in the isolated E14.5 SCN and most show reliable, self-sustained, synchronized rhythms in the E15.5 SCN. Strikingly, this synchrony at E15.5 appears before expression of VIP or its receptor and persists in the presence of blockers of VIP, GABA or neuronal firing. Finally, the dorsal-ventral phase wave of PER2 typical of the adult SCN appears ∼P2, indicating that multiple signals may mediate circadian synchrony during the ontogeny of the SCN.

Shape-Encoded Chitosan-Polyacrylamide Hybrid Hydrogel Microparticles with Controlled Macroporous Structures via Replica Molding for Programmable Biomacromolecular Conjugation.

Polymeric hydrogel microparticle-based suspension arrays with shape-based encoding offer powerful alternatives to planar and bead-based arrays toward high throughput biosensing and medical diagnostics. We report a simple and robust micromolding technique for polyacrylamide- (PAAm-) based biopolymeric-synthetic hybrid microparticles with controlled 2D shapes containing a potent aminopolysaccharide chitosan as an efficient conjugation handle uniformly incorporated in PAAm matrix. A postfabrication conjugation approach utilizing amine-reactive chemistries on the chitosan shows stable incorporation and retained chemical reactivity of chitosan, readily tunable macroporous structures via simple addition of low content long-chain PEG porogens for improved conjugation capacity and kinetics, and one-pot biomacromolecular assembly via bioorthogonal click reactions with minimal nonspecific binding. We believe that the integrated fabrication-conjugation approach reported here could offer promising routes to programmable manufacture of hydrogel microparticle-based biomacromolecular conjugation and biofunctionalization platforms for a large range of applications.

A systems theoretic approach to analysis and control of mammalian circadian dynamics

The mammalian circadian clock is a complex multi-scale, multivariable biological control system. In the past two decades, methods from systems engineering have led to numerous insights into the architecture and functionality of this system. In this review, we examine the mammalian circadian system through a process systems lens. We present a mathematical framework for examining the cellular circadian oscillator, and show recent extensions for understanding population-scale dynamics. We provide an overview of the routes by which the circadian system can be systemically manipulated, and present in silico proof of concept results for phase resetting of the clock via model predictive control.

A Coupled Stochastic Model Explains Differences in Cry Knockout Behavior

In the mammalian suprachiasmatic nucleus (SCN), a population of noisy cell-autonomous oscillators synchronizes to generate robust circadian rhythms at the organism level. Within these cells, two isoforms of Cryptochrome, <italic>Cry1</italic> and <italic>Cry2</italic>, participate in a negative feedback loop driving oscillation. Previous work has shown that single, dissociated SCN neurons respond differently to <italic>Cry1</italic> and <italic>Cry2</italic> knockouts. These differences have led to speculation that CRY1 and CRY2 may play different functional roles in the oscillator. To address this proposition, we have developed a new coupled, stochastic model focused on the <italic>Period</italic> (<italic>Per</italic>) and <italic>Cry</italic> feedback loop, and incorporating intercellular coupling via vasoactive intestinal peptide. We show that single dissociated <italic>Cry1</italic> knockouts display partially rhythmic behavior. Additionally, intrinsic molecular noise and differences in relative abundance, rather than differing functions, are sufficient to explain the range of rhythmicity encountered in <italic>Cry</italic> knockouts in the SCN. The results further highlight the essential role of stochastic behavior in understanding and accurately modeling the circadian network.

GillesPy: A Python Package for Stochastic Model Building and Simulation

GillesPy is an open-source Python package for model construction and simulation of stochastic biochemical systems. GillesPy consists of a Python framework for model building and an interface to the StochKit2 suite of efficient simulation algorithms based on the Gillespie stochastic simulation algorithms. To enable intuitive model construction and seamless integration into the scientific Python stack, we present an easy-to-understand action-oriented programming interface. Here, we describe the components of this package and provide a detailed example relevant to the computational biology community.

Controlling Biological Time: Nonlinear Model Predictive Control for Populations of Circadian Oscillators

In mammals, circadian regulation of gene expression is accomplished within each cell through a transcriptional oscillator commonly modeled by a limit cycle. There has been recent interest in regulating this oscillator by delivering doses of pharmaceuticals or light in a systematic manner. Generally, controller design for circadian manipulation has been formulated by considering the dynamics of a single oscillator representing the average dynamics of the population. We illustrate in this paper that such an approximation can result in desynchronization of circadian oscillators even if the mean dynamics attain desired behavior, due to the range of dynamic responses elicited among oscillators in a population with nonidentical phases. To address this issue, we present herein nonlinear MPC for control of phase and synchrony within a population of uncoupled circadian oscillators, by explicitly predicting the evolution of the phase probability density function. We then demonstrate in silico phase shifting of an example oscillator population while maintaining a high degree of synchrony. The MPC strategy formulated herein is a step toward a detailed, systems approach integrating population effects, pharmacokinetics and pharmacodynamics, and interactions between different oscillator populations.