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Theta and gamma rhythms and their cross-frequency coupling play critical roles in perception, attention, learning, and memory. Available data suggest that forebrain acetylcholine (ACh) signaling promotes theta-gamma coupling, although the mechanism has not been identified. Recent evidence suggests that cholinergic signaling is both temporally and spatially constrained, in contrast to the traditional notion of slow, spatially homogeneous, and diffuse neuromodulation. Here, we find that spatially constrained cholinergic stimulation can generate theta-modulated gamma rhythms. Using biophysically-based excitatory-inhibitory (E-I) neural network models, we simulate the effects of ACh on neural excitability by varying the conductance of a muscarinic receptor-regulated K + current. In E-I networks with local excitatory connectivity and global inhibitory connectivity, we demonstrate that theta-gamma-coupled firing patterns emerge in ACh modulated network regions. Stable gamma-modulated firing arises within regions with high ACh signaling, while theta or mixed theta-gamma activity occurs at the peripheries of these regions. High gamma activity also alternates between different high-ACh regions, at theta frequency. Our results are the first to indicate a causal role for spatially heterogenous ACh signaling in the emergence of localized theta-gamma rhythmicity. Our findings also provide novel insights into mechanisms by which ACh signaling supports the brain region-specific attentional processing of sensory information. 

Abstract We study the impact of light on the mammalian circadian system using the theory of phase response curves. Using a recently developed ansatz we derive a low-dimensional macroscopic model for the core circadian clock in mammals. Significantly, the variables and parameters in our model have physiological interpretations and may be compared with experimental results. We focus on the effect of four key factors which help shape the mammalian phase response to light: heterogeneity in the population of oscillators, the structure of the typical light phase response curve, the fraction of oscillators which receive direct light input and changes in the coupling strengths associated with seasonal day-lengths. We find these factors can explain several experimental results and provide insight into the processing of light information in the mammalian circadian system. In particular, we find that the sensitivity of the circadian system to light may be modulated by changes in the relative coupling forces between the light sensing and non-sensing populations. Finally, we show how seasonal day-length, after-effects to light entrainment and seasonal variations in light sensitivity in the mammalian circadian clock are interrelated. 

Mathematical models have a long and influential history in the study of human circadian rhythms. Accurate predictive models for the human circadian light response have been used to study the impact of a host of light exposures on the circadian system. However, generally, these models do not account for the physiological basis of these rhythms. We illustrate a new paradigm for deriving models of the human circadian light response. Beginning from a high-dimensional model of the circadian neural network, we systematically derive low-dimensional models using an approach motivated by experimental measurements of circadian neurons. This systematic reduction allows for the variables and parameters of the derived model to be interpreted in a physiological context. We fit and validate the resulting models to a library of experimental measurements. Finally, we compare model predictions for experimental measurements of light levels and discuss the differences between our model’s predictions and previous models. Our modeling paradigm allows for the integration of experimental measurements across the single-cell, tissue, and behavioral scales, thereby enabling the development of accurate low-dimensional models for human circadian rhythms.