Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons : comparison and implementation

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models.Characterizing the dynamics of biophysically modeled, large neuronal networks usually involves extensive numerical simulations. As an alternative to this expensive procedure we propose efficient models that describe the network activity in terms of a few ordinary differential equations. These systems are simple to solve and allow for convenient investigations of asynchronous, oscillatory or chaotic network states because linear stability analyses and powerful related methods are readily applicable. We build upon two research lines on which substantial efforts have been exerted in the last two decades: (i) the development of single neuron models of reduced complexity that can accurately reproduce a large repertoire of observed neuronal behavior, and (ii) different approaches to approximate the Fokker-Planck equation that represents the collective dynamics of large neuronal networks. We combine these advances and extend recent approximation methods of the latter kind to obtain spike rate models that surprisingly well reproduce the macroscopic dynamics of the underlying neuronal network. At the same time the microscopic properties are retained through the single neuron model parameters. To enable a fast adoption we have released an efficient Python implementation as open source software under a free license

Towards a bionic neural link for implantable prosthetics

Published versio

Global and local fMRI signals driven by neurons defined optogenetically by type and wiring

Despite a rapidly-growing scientific and clinical brain imaging literature based on functional magnetic resonance imaging (fMRI) using blood oxygenation level-dependent (BOLD) signals, it remains controversial whether BOLD signals in a particular region can be caused by activation of local excitatory neurons. This difficult question is central to the interpretation and utility of BOLD, with major significance for fMRI studies in basic research and clinical applications. Using a novel integrated technology unifying optogenetic control of inputs with high-field fMRI signal readouts, we show here that specific stimulation of local CaMKIIα-expressing excitatory neurons, either in the neocortex or thalamus, elicits positive BOLD signals at the stimulus location with classical kinetics. We also show that optogenetic fMRI (ofMRI) allows visualization of the causal effects of specific cell types defined not only by genetic identity and cell body location, but also by axonal projection target. Finally, we show that ofMRI within the living and intact mammalian brain reveals BOLD signals in downstream targets distant from the stimulus, indicating that this approach can be used to map the global effects of controlling a local cell population. In this respect, unlike both conventional fMRI studies based on correlations and fMRI with electrical stimulation that will also directly drive afferent and nearby axons, this ofMRI approach provides causal information about the global circuits recruited by defined local neuronal activity patterns. Together these findings provide an empirical foundation for the widely-used fMRI BOLD signal, and the features of ofMRI define a potent tool that may be suitable for functional circuit analysis as well as global phenotyping of dysfunctional circuitry

Criteria on Balance, Stability, and Excitability in Cortical Networks for Constraining Computational Models

During ongoing and Up state activity, cortical circuits manifest a set of dynamical features that are conserved across these states. The present work systematizes these phenomena by three notions: excitability, the ability to sustain activity without external input; balance, precise coordination of excitatory and inhibitory neuronal inputs; and stability, maintenance of activity at a steady level. Slice preparations exhibiting Up states demonstrate that balanced activity can be maintained by small local circuits. While computational models of cortical circuits have included different combinations of excitability, balance, and stability, they have done so without a systematic quantitative comparison with experimental data. Our study provides quantitative criteria for this purpose, by analyzing in-vitro and in-vivo neuronal activity and characterizing the dynamics on the neuronal and population levels. The criteria are defined with a tolerance that allows for differences between experiments, yet are sufficient to capture commonalities between persistently depolarized cortical network states and to help validate computational models of cortex. As test cases for the derived set of criteria, we analyze three widely used models of cortical circuits and find that each model possesses some of the experimentally observed features, but none satisfies all criteria simultaneously, showing that the criteria are able to identify weak spots in computational models. The criteria described here form a starting point for the systematic validation of cortical neuronal network models, which will help improve the reliability of future models, and render them better building blocks for larger models of the brain

Electrophysiological evidence for tinnitus in the central nucleus of the inferior colliculus

In previous work, little attention has been paid to the differences between neural responses to a sound exposure that did or did not produce a tinnitus percept. Here, neurons in rat central nucleus of the inferior colliculus were studied in noise-exposed rats characterized for the presence of a tonal tinnitus percept using a gap inhibition acoustic startle response paradigm. Recordings were done in three groups of animals: unexposed, exposed with tinnitus, and exposed without tinnitus. Presumably the neural correlates of tinnitus can be isolated from the effects of sound exposure in this way. A single electrode recording method was utilized to isolate and record from single units with monaural free field stimulation of the ear contralateral to the inferior colliculus. There is a loss of inhibition in tinnitus positive animals, specifically a loss of narrowly tuned type I units in the regions of threshold shift. This is accompanied by an edge effect, hyperactivity flanked by hypoactivity in the frequency regions affected by the sound exposure, and highly regularly firing units in the hyperactive region

Spike rate dynamics of coupled adaptive model neurons

Non UBCUnreviewedAuthor affiliation: Technical University of BerlinFacult