Phase diagrams and dynamics of a computationally efficient map-based neuron model

Optimal input reverberation and homeostatic self-organization toward the edge of synchronization

Transient or partial synchronization can be used to do computations, although a fully synchronized network is sometimes related to the onset of epileptic seizures. Here, we propose a homeostatic mechanism that is capable of maintaining a neuronal network at the edge of a synchronization transition, thereby avoiding the harmful consequences of a fully synchronized network. We model neurons by maps since they are dynamically richer than integrate-and-fire models and more computationally efficient than conductance-based approaches. We first describe the synchronization phase transition of a dense network of neurons with different tonic spiking frequencies coupled by gap junctions. We show that at the transition critical point, inputs optimally reverberate through the network activity through transient synchronization. Then, we introduce a local homeostatic dynamic in the synaptic coupling and show that it produces a robust self-organization toward the edge of this phase transition. We discuss the potential biological consequences of this self-organization process, such as its relation to the Brain Criticality hypothesis, its input processing capacity, and how its malfunction could lead to pathological synchronization and the onset of seizure-like activity.

Adaptive spike threshold dynamics associated with sparse spiking of hilar mossy cells are captured by a simple model

Hilar mossy cells (hMCs) in the dentate gyrus (DG) receive inputs from DG granule cells (GCs), CA3 pyramidal cells and inhibitory interneurons, and provide feedback input to GCs. Behavioural and in vivo recording experiments implicate hMCs in pattern separation, navigation and spatial learning. Our experiments link hMC intrinsic excitability to their synaptically evoked in vivo spiking outputs. We performed electrophysiological recordings from DG neurons and found that hMCs displayed an adaptative spike threshold that increased both in proportion to the intensity of injected currents, and in response to spiking itself, returning to baseline over a long time scale, thereby instantaneously limiting their firing rate responses. The hMC activity is additionally limited by a prominent medium after-hyperpolarizing potential (AHP) generated by small conductance K+ channels. We hypothesize that these intrinsic hMC properties are responsible for their low in vivo firing rates. Our findings extend previous studies that compare hMCs, CA3 pyramidal cells and hilar inhibitory cells and provide novel quantitative data that contrast the intrinsic properties of these cell types. We developed a phenomenological exponential integrate-and-fire model that closely reproduces the hMC adaptive threshold nonlinearities with respect to their threshold dependence on input current intensity, evoked spike latency and long-lasting spike-induced increase in spike threshold. Our robust and computationally efficient model is amenable to incorporation into large network models of the DG that will deepen our understanding of the neural bases of pattern separation, spatial navigation and learning. KEY POINTS: Previous studies have shown that hilar mossy cells (hMCs) are implicated in pattern separation and the formation of spatial memory, but how their intrinsic properties relate to their in vivo spiking patterns is still unknown. Here we show that the hMCs display electrophysiological properties that distinguish them from the other hilar cell types including a highly adaptive spike threshold that decays slowly. The spike-dependent increase in threshold combined with an after-hyperpolarizing potential mediated by a slow K+ conductance is hypothesized to be responsible for the low-firing rate of the hMC observed in vivo. The hMC's features are well captured by a modified stochastic exponential integrate-and-fire model that has the unique feature of a threshold intrinsically dependant on both the stimulus intensity and the spiking history. This computational model will allow future work to study how the hMCs can contribute to spatial memory formation and navigation.

Large-scale biophysically detailed model of somatosensory thalamocortical circuits in NetPyNE

The primary somatosensory cortex (S1) of mammals is critically important in the perception of touch and related sensorimotor behaviors. In 2015, the Blue Brain Project (BBP) developed a groundbreaking rat S1 microcircuit simulation with over 31,000 neurons with 207 morpho-electrical neuron types, and 37 million synapses, incorporating anatomical and physiological information from a wide range of experimental studies. We have implemented this highly detailed and complex S1 model in NetPyNE, using the data available in the Neocortical Microcircuit Collaboration Portal. NetPyNE provides a Python high-level interface to NEURON and allows defining complicated multiscale models using an intuitive declarative standardized language. It also facilitates running parallel simulations, automates the optimization and exploration of parameters using supercomputers, and provides a wide range of built-in analysis functions. This will make the S1 model more accessible and simpler to scale, modify and extend in order to explore research questions or interconnect to other existing models. Despite some implementation differences, the NetPyNE model preserved the original cell morphologies, electrophysiological responses and spatial distribution for all 207 cell types; and the connectivity properties of all 1941 pathways, including synaptic dynamics and short-term plasticity (STP). The NetPyNE S1 simulations produced reasonable physiological firing rates and activity patterns across all populations. When STP was included, the network generated a 1 Hz oscillation comparable to the original model in vitro-like state. By then reducing the extracellular calcium concentration, the model reproduced the original S1 in vivo-like states with asynchronous activity. These results validate the original study using a new modeling tool. Simulated local field potentials (LFPs) exhibited realistic oscillatory patterns and features, including distance- and frequency-dependent attenuation. The model was extended by adding thalamic circuits, including 6 distinct thalamic populations with intrathalamic, thalamocortical (TC) and corticothalamic connectivity derived from experimental data. The thalamic model reproduced single known cell and circuit-level dynamics, including burst and tonic firing modes and oscillatory patterns, providing a more realistic input to cortex and enabling study of TC interactions. Overall, our work provides a widely accessible, data-driven and biophysically-detailed model of the somatosensory TC circuits that can be employed as a community tool for researchers to study neural dynamics, function and disease.

Ephaptic entrainment in hybrid neuronal model

In recent decades, there has been a growing interest in the impact of electric fields generated in the brain. Transmembrane ionic currents originate electric fields in the extracellular space and are capable of affecting nearby neurons, a phenomenon called ephaptic neuronal communication. In the present work, the Quadratic Integrated-and-Fire model (QIF-E) underwent an adjustment/improvement to include the ephaptic entrainment behavior between neurons and electric fields. Indeed, the aim of our study is to validate the QIF-E model, which is a model to estimate the influence of electric fields on neurons. For this purpose, we evaluated whether the main properties observed in an experiment by Anastassiou et al. (Nat Neurosci 14:217-223, 2011), which analyzed the effect of an electric field on cortical pyramidal neurons, are reproduced with the QIF-E model. In this way, the analysis tools are employed according to the neuronal activity regime: (i) for the subthreshold regime, the circular statistic is used to describe the phase differences between the input stimulus signal (electrode) and the modeled membrane response; (ii) in the suprathreshold regime, the Population Vector and the Spike Field Coherence are used to estimate phase preferences and the entrainment intensity between the input stimulus and Action Potentials. The results observed are (i) in the subthreshold regime the values of the phase differences change with distinct frequencies of the input stimulus; (ii) in the supra-threshold regime the preferential phase of Action Potentials changes for different frequencies. In addition, we explore other parameters of the model, such as noise and membrane characteristic-time, in order to understand different types of neurons and extracellular environment related to ephaptic communication. Such results are consistent with results observed in empirical experiments based on ephaptic phenomenon. In addition, the QIF-E model allows further studies on the physiological importance of ephaptic communication in the brain, and its simplicity may open a door to simulate the ephaptic response in neuronal networks and assess the impact of ephaptic communication in such scenarios.