Detecting single-cell stimulation in a large network of integrate-and-fire neurons

A novel non-invasive brain stimulation technique: "Temporally interfering electrical stimulation"

For decades, neuromodulation technology has demonstrated tremendous potential in the treatment of neuropsychiatric disorders. However, challenges such as being less intrusive, more concentrated, using less energy, and better public acceptance, must be considered. Several novel and optimized methods are thus urgently desiderated to overcome these barriers. In specific, temporally interfering (TI) electrical stimulation was pioneered in 2017, which used a low-frequency envelope waveform, generated by the superposition of two high-frequency sinusoidal currents of slightly different frequency, to stimulate specific targets inside the brain. TI electrical stimulation holds the advantages of both spatial targeting and non-invasive character. The ability to activate deep pathogenic targets without surgery is intriguing, and it is expected to be employed to treat some neurological or psychiatric disorders. Recently, efforts have been undertaken to investigate the stimulation qualities and translation application of TI electrical stimulation via computational modeling and animal experiments. This review detailed the most recent scientific developments in the field of TI electrical stimulation, with the goal of serving as a reference for future research.

Information transmission in recurrent networks: Consequences of network noise for synchronous and asynchronous signal encoding

Information about natural time-dependent stimuli encoded by the sensory periphery or communication between cortical networks may span a large frequency range or be localized to a smaller frequency band. Biological systems have been shown to multiplex such disparate broadband and narrow-band signals and then discriminate them in later populations by employing either an integration (low-pass) or coincidence detection (bandpass) encoding strategy. Analytical expressions have been developed for both encoding methods in feedforward populations of uncoupled neurons and confirm that the integration of a population's output low-pass filters the information, whereas synchronous output encodes less information overall and retains signal information in a selected frequency band. The present study extends the theory to recurrent networks and shows that recurrence may sharpen the synchronous bandpass filter. The frequency of the pass band is significantly influenced by the synaptic strengths, especially for inhibition-dominated networks. Synchronous information transfer is also increased when network models take into account heterogeneity that arises from the stochastic distribution of the synaptic weights.

Critical current for giant Fano factor in neural models with bistable firing dynamics and implications for signal transmission

Bistability in the firing rate is a prominent feature in different types of neurons as well as in neural networks. We show that for a constant input below a critical value, such bistability can lead to a giant spike-count diffusion. We study the transmission of a periodic signal and demonstrate that close to the critical bias current, the signal-to-noise ratio suffers a sharp increase, an effect that can be traced back to the giant diffusion and large Fano factor.

A network model of the barrel cortex combined with a differentiator detector reproduces features of the behavioral response to single-neuron stimulation

The stimulation of a single neuron in the rat somatosensory cortex can elicit a behavioral response. The probability of a behavioral response does not depend appreciably on the duration or intensity of a constant stimulation, whereas the response probability increases significantly upon injection of an irregular current. Biological mechanisms that can potentially suppress a constant input signal are present in the dynamics of both neurons and synapses and seem ideal candidates to explain these experimental findings. Here, we study a large network of integrate-and-fire neurons with several salient features of neuronal populations in the rat barrel cortex. The model includes cellular spike-frequency adaptation, experimentally constrained numbers and types of chemical synapses endowed with short-term plasticity, and gap junctions. Numerical simulations of this model indicate that cellular and synaptic adaptation mechanisms alone may not suffice to account for the experimental results if the local network activity is read out by an integrator. However, a circuit that approximates a differentiator can detect the single-cell stimulation with a reliability that barely depends on the length or intensity of the stimulus, but that increases when an irregular signal is used. This finding is in accordance with the experimental results obtained for the stimulation of a regularly-spiking excitatory cell.

It is widely assumed that only a large group of neurons can encode a stimulus or control behavior. This tenet of neuroscience has been challenged by experiments in which stimulating a single cortical neuron has had a measurable effect on an animal’s behavior. Recently, theoretical studies have explored how a single-neuron stimulation could be detected in a large recurrent network. However, these studies missed essential biological mechanisms of cortical networks and are unable to explain more recent experiments in the barrel cortex. Here, to describe the stimulated brain area, we propose and study a network model endowed with many important biological features of the barrel cortex. Importantly, we also investigate different readout mechanisms, i.e. ways in which the stimulation effects can propagate to other brain areas. We show that a readout network which tracks rapid variations in the local network activity is in agreement with the experiments. Our model demonstrates a possible mechanism for how the stimulation of a single neuron translates into a signal at the population level, which is taken as a proxy of the animal’s response. Our results illustrate the power of spiking neural networks to properly describe the effects of a single neuron’s activity.

How many neurons are sufficient for perception of cortical activity?

Many theories of brain function propose that activity in sparse subsets of neurons underlies perception and action. To place a lower bound on the amount of neural activity that can be perceived, we used an all-optical approach to drive behaviour with targeted two-photon optogenetic activation of small ensembles of L2/3 pyramidal neurons in mouse barrel cortex while simultaneously recording local network activity with two-photon calcium imaging. By precisely titrating the number of neurons stimulated, we demonstrate that the lower bound for perception of cortical activity is ~14 pyramidal neurons. We find a steep sigmoidal relationship between the number of activated neurons and behaviour, saturating at only ~37 neurons, and show this relationship can shift with learning. Furthermore, activation of ensembles is balanced by inhibition of neighbouring neurons. This surprising perceptual sensitivity in the face of potent network suppression supports the sparse coding hypothesis, and suggests that cortical perception balances a trade-off between minimizing the impact of noise while efficiently detecting relevant signals.

Receiver operating characteristic curves for a simple stochastic process that carries a static signal

The detection of a weak signal in the presence of noise is an important problem that is often studied in terms of the receiver operating characteristic (ROC) curve, in which the probability of correct detection is plotted against the probability for a false positive. This kind of analysis is typically applied to the situation in which signal and noise are stochastic variables; the detection problem emerges, however, also often in a context in which both signal and noise are stochastic processes and the (correct or false) detection is said to take place when the process crosses a threshold in a given time window. Here we consider the problem for a combination of a static signal which has to be detected against a dynamic noise process, the well-known Ornstein-Uhlenbeck process. We give exact (but difficult to evaluate) quadrature expressions for the detection rates for false positives and correct detections, investigate systematically a simple sampling approximation suggested earlier, compare to an approximation by Stratonovich for the limit of high threshold, and briefly explore the case of multiplicative signal; all theoretical results are compared to extensive numerical simulations of the corresponding Langevin equation. Our results demonstrate that the sampling approximation provides a reasonable description of the ROC curve for this system, and it clarifies limit cases for the ROC curve.