Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations - similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system’s role in fractal regulation.

Striatal oscillatory activity is associated with movement, reward, and decision-making, and observed in several interacting frequency bands. Local field potential recordings in rodent striatum show dopamine-and reward-dependent transitions between two states: a "spontaneous" state involving β (*15-30 Hz) and low γ (*40-60 Hz), and a state involving θ (*4-8 Hz) and high γ (*60-100 Hz) in response to dopaminergic agonism and reward. The mechanisms underlying these rhythmic dynamics, their interactions, and their functional consequences are not well understood. In this paper, we propose a biophysical model of striatal microcircuits that comprehensively describes the generation and interaction of these rhythms, as well as their modulation by dopamine. Building on previous modeling and experimental work suggesting that striatal projection neurons (SPNs) are capable of generating β oscillations, we show that networks of striatal fast-spiking interneurons (FSIs) are capable of generating δ/θ (ie, 2 to 6 Hz) and γ rhythms. Under simulated low dopaminergic tone our model FSI network produces low γ band oscillations, while under high dopaminergic tone the FSI network produces high γ band activity nested within a δ/θ oscillation. SPN networks produce β rhythms in both conditions, but under high dopaminergic tone, this β oscillation is interrupted by δ/θ-periodic bursts of γ-frequency FSI inhibition. Thus, in the high dopamine state, packets of FSI γ and SPN β alternate at a δ/θ timescale. In addition to a mechanistic explanation for previously observed rhythmic interactions and transitions, our model suggests a hypothesis as to how the relationship between dopamine and rhythmicity impacts motor function. We hypothesize that high dopamine-induced periodic FSI γ-rhythmic inhibition enables switching between β-rhythmic SPN cell assemblies representing the currently active motor program, and thus that dopamine facilitates movement in part by allowing for rapid, periodic shifts in motor program execution.

DynaSim is an open-source MATLAB/GNU Octave toolbox for rapid prototyping of neural models and batch simulation management. It is designed to speed up and simplify the process of generating, sharing, and exploring network models of neurons with one or more compartments. Models can be specified by equations directly (similar to XPP or the Brian simulator) or by lists of predefined or custom model components. The higher-level specification supports arbitrarily complex population models and networks of interconnected populations. DynaSim also includes a large set of features that simplify exploring model dynamics over parameter spaces, running simulations in parallel using both multicore processors and high-performance computer clusters, and analyzing and plotting large numbers of simulated data sets in parallel. It also includes a graphical user interface (DynaSim GUI) that supports full functionality without requiring user programming. The software has been implemented in MATLAB to enable advanced neural modeling using MATLAB, given its popularity and a growing interest in modeling neural systems. The design of DynaSim incorporates a novel schema for model specification to facilitate future interoperability with other specifications (e.g., NeuroML, SBML), simulators (e.g., NEURON, Brian, NEST), and web-based applications (e.g., Geppetto) outside MATLAB. DynaSim is freely available at http://dynasimtoolbox.org. This tool promises to reduce barriers for investigating dynamics in large neural models, facilitate collaborative modeling, and complement other tools being developed in the neuroinformatics community.

In recent years, schizophrenia research has focused on inhibitory interneuron dysfunction at the level of neurobiology, and on cognitive impairments at the psychological level. Reviewing both experimental and computational findings, we show how the temporal structure of the activity of neuronal populations, exemplified by brain rhythms, can begin to bridge these levels of complexity. Oscillations in neuronal activity tie the pathophysiology of schizophrenia to alterations in local processing and large-scale coordination, and these alterations in turn can lead to the cognitive and perceptual disturbances observed in schizophrenia.