Homogenization theory and neural field models

Neurons in the brain form thousands of connections, or synapses, with one another, allowing signals to pass from one cell to the next. To activate a neuron, a high enough activating signal or ‘action potential’ must be reached. However, the accepted view of signal transmission assumes that the great majority of synapses are too weak to activate neurons. This means that often simultaneous inputs from many neurons are required to trigger a single neuron’s activation. However, such coordination is likely unreliable as neurons can react differently to the same stimulus depending on the circumstances. An alternative way of transmitting signals has been reported in turtle brains, where impulses from a single neuron can trigger activity across a network of connections. Furthermore, these responses are reliably repeatable, activating the same neurons in the same order. Riquelme et al. set out to understand the mechanism that underlies this type of neuron activation using a mathematical model based on data from the turtle brain. These data showed that the neural network in the turtle’s brain had many weak synapses but also a few, rare, strong synapses. Simulating this neural network showed that those rare, strong synapses promote the signal’s reliability by providing a consistent route for the signal to travel through the network. The numerous weak synapses, on the other hand, have a regulatory role in providing flexibility to how the activation spreads. This combination of strong and weak connections produces a system that can reliably promote or stop the signal flow depending on the context. Riquelme et al.’s work describes a potential mechanism for how signals might travel reliably through neural networks in the brain, based on data from turtles. Experimental work will need to address whether strong connections play a similar role in other animal species, including humans. In the future, these results may be used as the basis to design new systems for artificial intelligence, building on the success of neural networks.

Ca2+/calmodulin-dependent protein kinase II (CaMKII) is a key enzyme in long-term plasticity in many neurons, including in the nociceptive circuitry of the spinal dorsal horn. However, although the role of CaMKII heterooligomers in neuronal plasticity is isoform-dependent, the distribution and co-localization of CaMKII isoforms in the dorsal horn have not been comprehensively investigated. Here, quantitative immunofluorescence analysis was used to examine the distribution of the two major neuronal CaMKII isoforms, α and β, in laminae I–III of the rat dorsal horn, with reference to inhibitory interneurons and neuronal populations defined by expression of parvalbumin, calretinin, and calbindin D28k. Unexpectedly, all or nearly all inhibitory and excitatory neurons showed both CaMKIIα and CaMKIIβ immunoreactivity, although at highly variable levels. Lamina III neurons showed less CaMKIIα immunoreactivity than laminae I–II neurons. Whereas CaMKIIα immunoreactivity was found at nearly similar levels in inhibitory and excitatory neurons, CaMKIIβ generally showed considerably lower immunoreactivity in inhibitory neurons. Distinct populations of inhibitory calretinin neurons and excitatory parvalbumin neurons exhibited high CaMKIIα-to-CaMKIIβ immunoreactivity ratios. CaMKIIα and CaMKIIβ immunoreactivity showed positive correlation at GluA2+ puncta in pepsin-treated tissue. These results suggest that, unlike the forebrain, the dorsal horn is characterized by similar expression of CaMKIIα in excitatory and inhibitory neurons, whereas CaMKIIβ is less expressed in inhibitory neurons. Moreover, CaMKII isoform expression varies considerably within and between neuronal populations defined by laminar location, calcium-binding protein expression, and transmitter phenotype, suggesting differences in CaMKII function both between and within neuronal populations in the superficial dorsal horn.

The firing patterns of neuronal populations often exhibit emergent collective oscillations, which can display substantial regularity even though the dynamics of individual elements is very stochastic. One of the many phenomena that is often studied in this context is coherence resonance, where additional noise leads to improved regularity of spiking activity in neurons. In this work, we investigate how the coherence resonance phenomenon manifests itself in populations of excitatory and inhibitory neurons. In our simulations, we use the coupled FitzHugh-Nagumo oscillators in the excitable regime and in the presence of neuronal noise. Formally, our model is based on the concept of a two-layered network, where one layer contains inhibitory neurons, the other excitatory neurons, and the interlayer connections represent heterotypic interactions. The neuronal activity is simulated in realistic coupling schemes in which neurons within each layer are connected with undirected connections, whereas neurons of different types are connected with directed interlayer connections. In this setting, we investigate how different neurophysiological determinants affect the coherence resonance. Specifically, we focus on the proportion of inhibitory neurons, the proportion of excitatory interlayer axons, and the architecture of interlayer connections between inhibitory and excitatory neurons. Our results reveal that the regularity of simulated neural activity can be increased by a stronger damping of the excitatory layer. This can be accomplished with a higher proportion of inhibitory neurons, a higher fraction of inhibitory interlayer axons, a stronger coupling between inhibitory axons, or by a heterogeneous configuration of interlayer connections. Our approach of modeling multilayered neuronal networks in combination with stochastic dynamics offers a novel perspective on how the neural architecture can affect neural information processing and provide possible applications in designing networks of artificial neural circuits to optimize their function via noise-induced phenomena.

Balanced networks are a frequently employed basic model for neuronal networks in the mammalian neocortex. Large numbers of excitatory and inhibitory neurons are recurrently connected so that the numerous positive and negative inputs that each neuron receives cancel out on average. Neuronal firing is therefore driven by fluctuations in the input and resembles the irregular and asynchronous activity observed in cortical in vivo data. Recently, the balanced network model has been extended to accommodate clusters of strongly interconnected excitatory neurons in order to explain persistent activity in working memory-related tasks. This clustered topology introduces multistability and winnerless competition between attractors and can capture the high trial-to-trial variability and its reduction during stimulation that has been found experimentally. In this prospect article, we review the mean field description of balanced networks of binary neurons and apply the theory to clustered networks. We show that the stable fixed points of networks with clustered excitatory connectivity tend quickly towards firing rate saturation, which is generally inconsistent with experimental data. To remedy this shortcoming, we then present a novel perspective on networks with locally balanced clusters of both excitatory and inhibitory neuron populations. This approach allows for true multistability and moderate firing rates in activated clusters over a wide range of parameters. Our findings are supported by mean field theory and numerical network simulations. Finally, we discuss possible applications of the concept of joint excitatory and inhibitory clustering in future cortical network modelling studies.

Computational analyses of in-vivo cerebral activity show that gamma oscillations in the olfactory cortex originate from local feedback inhibition following each sniff and serve to segregate competing odor representations through a winner-take-all process, providing an optimal window to decode odor.

Oscillations are ubiquitous features of brain dynamics that undergo task-related changes in synchrony, power, and frequency. The impact of those changes on target networks is poorly understood. In this work, we used a biophysically detailed model of prefrontal cortex (PFC) to explore the effects of varying the spike rate, synchrony, and waveform of strong oscillatory inputs on the behavior of cortical networks driven by them. Interacting populations of excitatory and inhibitory neurons with strong feedback inhibition are inhibition-based network oscillators that exhibit resonance (i.e., larger responses to preferred input frequencies). We quantified network responses in terms of mean firing rates and the population frequency of network oscillation; and characterized their behavior in terms of the natural response to asynchronous input and the resonant response to oscillatory inputs. We show that strong feedback inhibition causes the PFC to generate internal (natural) oscillations in the beta/gamma frequency range (>15 Hz) and to maximize principal cell spiking in response to external oscillations at slightly higher frequencies. Importantly, we found that the fastest oscillation frequency that can be relayed by the network maximizes local inhibition and is equal to a frequency even higher than that which maximizes the firing rate of excitatory cells; we call this phenomenon population frequency resonance. This form of resonance is shown to determine the optimal driving frequency for suppressing responses to asynchronous activity. Lastly, we demonstrate that the natural and resonant frequencies can be tuned by changes in neuronal excitability, the duration of feedback inhibition, and dynamic properties of the input. Our results predict that PFC networks are tuned for generating and selectively responding to beta- and gamma-rhythmic signals due to the natural and resonant properties of inhibition-based oscillators. They also suggest strategies for optimizing transcranial stimulation and using oscillatory networks in neuromorphic engineering. Author Summary The prefrontal cortex (PFC) flexibly encodes task-relevant representations and outputs biases to mediate higher cognitive functions. The relevant neural ensembles undergo task-related changes in oscillatory dynamics at beta- and gamma frequencies. Using a computational model of the PFC network, we show that strong feedback inhibition causes the PFC to generate internal oscillations and to prefer external oscillations at similar frequencies. The precise frequencies that are generated and preferred can be flexibly tuned by varying the synchrony and strength of input network activity, the level of background excitation, and neuromodulation of intrinsic ion currents. We also show that the peak output frequency in response to external oscillations, which depends on the synchrony and strength of the input as well as the strong inhibitory feedback, is faster than the internally generated frequency, and that this difference enables exclusive response to oscillatory inputs. These properties enable changes in oscillatory dynamics to govern the selective processing and gating of task-relevant signals in service of cognitive control.

A layered continual population model of primary visual cortex has been constructed, which reproduces a set of experimental data, including postsynaptic responses of single neurons on extracellular electric stimulation and spatially distributed activity patterns in response to visual stimulation. In the model, synaptically interacting excitatory and inhibitory neuronal populations are described by a conductance-based refractory density approach. Populations of two-compartment excitatory and inhibitory neurons in cortical layers 2/3 and 4 are distributed in the 2-d cortical space and connected by AMPA, NMDA and GABA type synapses. The external connections are pinwheel-like, according to the orientation of a stimulus. Intracortical connections are isotropic local and patchy between neurons with similar orientations. The model proposes better temporal resolution and more detailed elaboration than conventional mean-field models. In comparison to large network simulations, it excludes a posteriori statistical data manipulation and provides better computational efficiency and minimal parametrization.

Dynamics of an interconnected population of excitatory and inhibitory spiking neurons wandering around a Bogdanov-Takens (BT) bifurcation point can generate the observed scale-free avalanches at the population level and the highly variable spike patterns of individual neurons. These characteristics match experimental findings for spontaneous intrinsic activity in the brain. In this paper, we address the mechanisms causing the system to get and remain near this BT point. We propose an effective stochastic neural field model which captures the dynamics of the mean-field model. We show how the network tunes itself through local long-term synaptic plasticity by STDP and short-term synaptic depression to be close to this bifurcation point. The mesoscopic model that we derive matches the directed percolation model at the absorbing state phase transition.

Genetically identified neurons in avian auditory pallium mirror core principles of their mammalian counterparts

Neural population coding and auditory temporal pattern analysis

Requirement of keratan sulfate proteoglycan phosphacan with a specific sulfation pattern for critical period plasticity in the visual cortex

Simply complex - the structure of the cerebellar neuronal lineage.

In this work, I overview some novel results concerning the theoretical calculation of a non‐equilibrium potential function for a biologically motivated model of a neural network. Such model displays competition between different populations of excitatory and inhibitory neurons, which is known to originate synchronous dynamics, fast activity oscillations, and other nontrivial behavior in more sophisticated models of neural media.

To assess temporal associations in spike activity between pairs of neurons in the primary motor cortex (MI) related to different behaviors, we compared the incidence of coincident spiking activity of task-related (TR) and non-task-related (NTR) neurons during a skilled motor task and sitting quietly in adult cats (Felis domestica). Chronically implanted microwires were used to record spike activity of MI neurons in four animals (two male and two female) trained to perform a skilled reaching task or sit quietly. Neurons were identified as TR if spike activity was modulated during the task (and NTR if not). Based on spike characteristics, they were also classified as either regular-spiking (RS, putatively excitatory) or fast-spiking (FS, putatively inhibitory) neurons. Temporal associations in the activities of simultaneously recorded neurons were evaluated using shuffle-corrected cross-correlograms. Pairs of NTR and TR neurons showed associations in their firing patterns over wide areas of MI (representing forelimb and hindlimb movements) during quiet sitting, more commonly involving RS neurons. During skilled task performance, however, significantly coincident firing was seen almost exclusively between TR neurons in a smaller part of MI (representing forelimb movements), involving mainly FS neurons. The findings of this study show evidence for widespread interactions in MI when the animal sits quietly, which changes to a more specific and restricted pattern of interactions during task performance. Different populations of excitatory and inhibitory neurons appear to be synchronized during skilled movement and quiet sitting.

A neuron carries out its functions in networks receiving contacts from roughly 104 presynaptic neurons. Such a dense connectivity profile for a single neuron may give rise to enormous complex neuronal topologies, which might be very difficult to understand the underlying mechanisms of neurological functions and diseases. Extensive experimental data from neuroanatomical studies have uncovered that neural networks include some recurring topologies of microcircuits, known as network motifs which serve as characteristic building blocks of complex networks [1,2]. Therefore, it is widely assumed that a clear explanation on dynamical and functional features of these network motifs can be considered as the first step to understand large networks. Following this motivation, in this study, we investigate the Vibrational Resonance (VR) phenomenon in a triple-neuron feed-forward-loop (FFL) which is one of the most significant brain network motifs, shown in Figure ​Figure1.1. VR is a physical phenomenon found in nonlinear systems where a weak signal can be detected and processed by the system with the assistance of another high frequency signal. It is very similar to the well-known stochastic resonance phenomenon, where the role of noise is replaced in VR by a high frequency signal. In recent years, there exists a growing interest in applications of VR to neuroscience because two frequency signals are pervasive in neural systems, i.e. bursting neurons exhibit two widely different time scales, simultaneous arrival of vocal signals having distinct frequencies to auditory neurons. Due to the significance of its potential in neural signal processing, the VR phenomenon has already been studied with computational models of neurons and their networks [3,4]. However, a population of excitatory and inhibitory neurons has not been considered, yet. Here, we study the VR dynamics depending on whether the neurons in the FFL motifs are excitatory or inhibitory considering eight possible structural configurations of the considered microcircuit (Table ​(Table1).1). Such an approach provides us to test the functional influences of structural configuration on VR dynamics in neural populations. Figure 1 Schematic illustration of the considered feed-forward-loop motif. LF and HF refers to low and high frequency signals, respectively. Neuron 1 and 3 is considered as input and output neurons, respectively. Table 1 Eight possible FFL types. We found that the weak signal transmission in the network via the VR mechanism is possible depending on both the coupling strength between neurons and the network structure. For instance, when a weak coupling strength is present between connected neurons, weak signal injected to the input neuron can be transmitted to the output with only T8-FFL motif. In this case, signal transmission is impossible for other types of network motifs. For intermediate coupling strengths, signal transmission performance is high for all motifs and motif type does not change very much VR dynamics. Finally, for strong coupling strengths, the best VR performance is obtained with T1-FFL motif where all the neurons in the network are excitatory. We also clarify the mechanisms that underlies the differences in performance of network motifs.