Frontiers in Computational Neuroscience

Equilibrium propagation (EP) is a biologically plausible alternative to backpropagation that has demonstrated competitive performance across a range of machine learning tasks. Recent work has extended EP to spiking neural networks (SNNs), leveraging leaky integrate-and-fire (LIF) neurons and spike-based plasticity rules to improve biological realism while maintaining strong performance. In this work, we propose an EP-based SNN framework that combines LIF neural dynamics with a predictive learning rule, replacing conventional spike-timing-dependent plasticity (STDP) with a learning rule more directly aligned with predictive coding principles. We evaluate the proposed model on multiple image classification benchmarks, including MNIST, KMNIST, and Fashion-MNIST, and compare its performance with a BP-trained LIF SNN baseline. Our results show that the proposed EP-based LIF model (EP+LIF) achieves competitive accuracy across datasets, with performance approaching that of the BP-trained counterpart (BP+LIF) while relying on a biologically motivated local learning rule. In addition, analysis of hidden-layer spiking activity reveals that EP+LIF produces more persistent hidden-state activity, whereas BP+LIF yields sparser spiking representations. These results demonstrate that predictive learning can support effective EP-based training in LIF spiking networks, while also highlighting differences in activity patterns that motivate future work on activity regulation and sparse spiking dynamics.

Wave recurrent neural networks (wRNNs) are biologically inspired recurrent architectures that use traveling-wave dynamics to support sequence learning and memory. However, their input-to-hidden pathway remains relatively simple compared with biological neurons, where dendrites perform nonlinear input integration. In this study, we introduce the Dendritic Wave Recurrent Neural Network (DWRNN), which augments the input pathway of the wRNN with nonlinear basal dendritic branches while preserving the original recurrent wave dynamics. We evaluate DW-RNN on a simple copy task, sequential MNIST (sMNIST), permuted sequential MNIST (psMNIST), and noisy sequential CIFAR-10 (nsCIFAR-10). On the copy task, DW-RNN shows learning behavior comparable to the standard wRNN, suggesting that dendritic input integration does not disrupt the recurrent wave-based memory mechanism. On the three sequential image-classification benchmarks, DW-RNN outperforms the standard wRNN, improving accuracy from 97.27 {+/-} 0.15% to 97.82 {+/-} 0.12% on sMNIST, from 96.74 {+/-} 0.17% to 96.92 {+/-} 0.10% on psMNIST, and from 54.30 {+/-} 0.79% to 55.65 {+/-} 0.55% on nsCIFAR-10. In addition to improving mean accuracy, DW-RNN exhibits lower across-seed variability on all three classification benchmarks, suggesting that dendritic input integration may improve the stability of wRNN training. Hidden-activity visualizations further show that DW-RNN preserves the characteristic traveling-wave patterns of the original wRNN. These results suggest that dendritic computation and traveling-wave recurrent dynamics provide complementary mechanisms for biologically inspired sequence learning.

The organizational principles of natural neural networks could inspire the new architecture design of artificial neural networks (ANNs). Analysis of single-neuron connectomes of mouse brains revealed distinct profiles of three-node connectivity motifs in various cortical areas and hippocampal formation. A connectome-informed neural network algorithm ("CINA") was developed to incorporate natural connectivity motifs into ANN algorithms represented by recurrent neural network (RNN) and transformer-based large language model (LLM). We found that incorporation of the average profile of cortical motifs improved the RNNs performance in noise-resistant categorization and motor learning benchmark tasks, as compared with RNNs with random connectivity. Notably, incorporating cortex-specific motifs further elevated the RNNs performance in tasks related to the cortical function, and this effect was enhanced by artificially increasing the bias in the motif profile. Similar experimental results were verified on an LLM using Motif-Transformer for natural language question answering and brain-signal decoding tasks. Graph-theoretic analyses showed that incorporating natural motifs drove the emergence of modular and small-world properties in ANNs. Together, we demonstrated not only connectome-inspired optimization of ANN architecture but also functional significance of specific motif profiles in various cortices.

Categorisation is often treated as a form of compression: a high-dimensional stimulus space is reduced to a smaller set of behaviourally or cognitively useful classes. However, compression alone does not determine whether a category map is useful. The present manuscript develops an information-theoretic framework for evaluating categorisation in terms of both category complexity and target-relevant information preservation. Across a set of synthetic demonstrations, alternative category maps over the same stimulus space are shown to preserve different target variables, including identity, action, nuisance, and hierarchical category structure. The framework is then extended to learned visual representations by analysing layer-derived category maps from a pretrained ResNet-50 network applied to CIFAR-10 images. Two scenarios are compared: a clean-only object run and a pooled nuisance run containing clean, blurred, pixelated, and noise-perturbed images. The results show that category maps can have substantial entropy while preserving information about a variable that is not aligned with the specified target, and that the value of a categorisation depends on the target variable to be preserved. The manuscript argues that categorisation should therefore be evaluated not only by compression or separability, but by the information retained about a specified cognitive, behavioural, or computational target.

Cerebellar neural circuit dynamics rely on a rich repertoire of synaptic and excitability mechanisms, which are thought to determine network computation in physiological and pathological conditions. In this work, we develop and validate a biologically-grounded spiking neural network of the cerebellar cortex, embedding key mechanisms of cellular excitability and synaptic transmission, and assess their impact on signal processing. Neuronal input-output functions, short-term synaptic plasticity, receptor-specific kinetics, and NMDA channel voltage-dependent gating were calibrated against detailed multicompartmental models through automatic tuning procedures. Incorporating these realistic biological properties allowed the network model to simulate key features observed in recordings from acute cerebellar slices. The neuronal discharge and local field potentials elicited by mossy fiber stimulation faithfully reproduced the natural patterns with millisecond precision. Then, selective receptor switch-off revealed the contribution of NMDA, GABA, and AMPA receptors to the frequency-dependent input-output function of the granular layer and Purkinje cells, linking previous empirical findings to specific synaptic mechanisms. This model combines high computational performance with biological realism and offers a computationally efficient framework to investigate neurophysiological phenomena and the neural correlates of behavior in large-scale long-lasting simulations, such as those needed to address the neural underpinnings of learning and of cerebellar pathologies.

Dopaminergic signalling is central to value learning and decision making. It has been observed that multiple pathways with different patterns of connectivity project to midbrain dopaminergic neurons, some involving direct excitatory projections while others involve disinhibition. However, the respective contributions of these patterns to dopamine control, and their computational and functional advantages remain unclear. In the current work we simulate and evaluate two fully spiking neural models of dopaminergic control, based either solely on disinhibition, or solely on direct inhibitory and excitatory projections. We compare these models in terms of their engineering properties, their resulting spiking profiles, and their ability to successfully acquire representations of expected value in a 3-armed bandit task. We find that both models are able to operate at an asynchronous-irregular firing regime, but that the firing profile of the direct integration model is less resilient to disruption and more sensitive to incoming signals. In addition, the disinhibition model performs better in the learning task. We conclude that while the direct model is more parsimonious, disinhibition-based control remains advantageous in the operational context. Our results have implications for the study of decision-making brain circuits as well as for the design of brain-inspired systems.

Stabilizing synaptic plasticity together with the neurons activity has remained a central challenge in theoretical neuroscience since the introduction of Hebbian learning principles. Classical Hebbian learning rules typically lead to unbounded synaptic growth, motivating the development of stabilization mechanisms such as normalization methods, BCM-type learning, synaptic scaling and others. While these approaches can prevent divergence, they can also exhibit different limitations e.g. resulting in too-sparse synaptic configurations or leading to poor scalability with increasing network size. A recently introduced meta-plasticity mechanism, termed annealed linear learning (ALL), dynamically reduces the learning rate as neuronal output increases, thereby preserving stable and interpretable fixed-point behavior of the output. However, the original formulation leads to an irreversible decay of the learning rate, preventing adaptation to changing environmental conditions. To address this, in the present study, we balance learning rate reduction at large outputs with recovery at small outputs and in addition introduce forgetting that gradually reduces synaptic weights. These extensions allow the system to discard outdated representations and adapt to novel input conditions. Analytical investigations demonstrate that the favorable output fixed-point properties of the original ALL framework are preserved under the extended rule. Furthermore, simulations with an artificial agent show that the proposed mechanism enables robust and fast re-learning and adaptation in changing environments.

Human object recognition is robust to challenging conditions, such as when ones view of an object is fragmented due to an occluding foreground object. In comparison, deep neural networks (DNNs) are typically more susceptible to occlusion, suggesting that human vision relies on distinct mechanisms. Here, we investigated the role of visual diet in the emergence of these mechanisms by asking whether human-like robustness might arise in DNNs when trained with image datasets that better reflect the properties of occlusion in natural vision. We trained convolutional and transformer DNNs to classify clear images only, images augmented with artificial occluders (i.e., geometric shapes) or natural occluders (objects segmented from photographs). We then evaluated DNN occlusion robustness and compared their performance profiles with 30 human participants. We found that DNNs trained with artificial occluders remained vulnerable to natural occlusion and exhibited less human-like performance than those trained with natural occlusion. Our findings suggest that human robustness to visual occlusion arises from learning to disentangle natural objects from each other rather than simply learning to recognize objects from partial views. They also imply that commonly used forms of artificial occlusion are unsuitable for the evaluation or promotion of robustness to real-world occlusion in DNNs.

Robotic motor control built on liquid neural networks and related continuous-time models, such as LTC and CfC, is typically trained offline via backpropagation through time and lacks an explicit mechanism for recalibrating online as plant dynamics change. We ask whether a frozen CfC core, whose liquid state spans a fixed continuous-time basis, can support cerebellar-style online adaptation by adapting only its linear readout with a climbing-fiber-like error signal. In a planar two-link reaching simulation with a velocity-dependent curl force field, we adapt the readout online with a feedback-error-learning (FEL) signal under a least-mean-squares (LMS) rule, leaving the core untouched. The frozen-core readout-only controller re-straightens curl-perturbed reaches and, upon field removal, produces a mirror-image after-effect, a behavioral signature consistent with internal-model learning, which a feedback-only controller does not produce. The result generalizes from a dense CfC to a sparse Neural-Circuit-Policy (NCP) wiring when the recurrent state, rather than the projected motor output, is used as the readout basis; it is robust to force-field strength and direction; and a recursive-least-squares variant adapts faster but de-adapts slowly because its covariance collapses, a rigidity that a covariance-reset safe-forgetting rule removes. Within the explored two-link planar simulation range, we did not find a readout-only failure case that required adapting the frozen core in the tested conditions. In this simulation study, adapting only the readout therefore provides a biologically inspired, low-cost online error-adaptation layer for offline-trained continuous-time controllers.

Background / Introduction: Biologically inspired spiking neural networks can model adaptive behavior, but learning multiple goals is difficult because synaptic updates for different targets can interfere. We tested whether multi-timescale plasticity and context-specific credit assignment could improve continual multi-goal learning in a spiking navigation system inspired by entorhinal-hippocampal circuitry. Methods: We developed a closed-loop spiking model containing grid-like, place-like, target-related, association, and motor-output populations. An agent navigated in a two-dimensional environment with randomized starting locations and learned through reward-modulated spike-timing dependent plasticity (STDP/RL) and a novel evidence-gated plasticity (EGP) framework. EGP accumulates candidate synaptic modifications, evaluates them using reward evidence, and consolidates only changes that improve performance. A target-context variant maintained separate proposal stores and reward evaluation for each target. Results: STDP/RL learned and retained a single-target navigation policy, but multi-target training produced substantial interference, including attraction to incorrect targets after learning. Across 10 connectivity seeds, target-context EGP achieved higher late-stage reward than global EGP, improved weakest-target performance, and increased the fraction of targets achieving positive reward. In a longer continual-learning simulation, reward increased for all targets, TEST-phase performance increasingly exceeded TRAIN-phase performance, and proposal magnitudes grew over learning. Dwell-time confusion analyses showed that target-context EGP reduced wrong-target attraction and improved target selectivity relative to multi-target STDP/RL. Conclusions: These results demonstrate that spiking navigation circuits can learn goal-directed behavior using local plasticity, but robust multi-goal learning benefits from context-specific evidence-based consolidation. Target-context EGP provides a biologically motivated mechanism for reducing interference during continual reinforcement learning in spiking neural networks.

Animals must often navigate environments where feedback about progress toward a goal is sparse or delayed, requiring internal representations of space and memory of prior experience. The hippocampal-entorhinal system is believed to support this capability through distributed spatial representations that guide goal-directed behavior. However, many computational models of these circuits focus primarily on reproducing neural dynamics rather than demonstrating how such representations support learning on navigation tasks. We present a biologically inspired spiking neuronal network (SNN) model that combines grid-cell-derived spatial representations, {Delta}Q-modulated Hebbian plasticity, and context-dependent modulation to support navigation under sparse reward conditions. Grid Cell populations generate distributed spatial codes that are transformed by an Association Cell population into more spatially selective internal representations. Learning is driven by changes in Q-values ({Delta}Q) computed from a goal-conditioned Q-table, allowing local synaptic plasticity to incorporate information about long-term navigation outcomes. For environments containing multiple navigation objectives, a Context Cell population provides task-dependent modulation that enables a shared network architecture to support distinct navigation policies. Across two complementary maze environments, the model demonstrates three core capabilities: generation of distinct spatial representations, learning of efficient navigation policies under sparse and delayed reward, and support for multiple navigation objectives within a shared environment. The results further show that contextual modulation introduces subtle task-dependent variations into a largely shared population representation, allowing identical spatial locations to support different navigation behaviors. These findings demonstrate that biologically inspired spatial representations, value-guided plasticity, and contextual modulation can jointly support flexible navigation in spiking neuronal networks, providing a bridge between mechanistic neural circuit models and functional reinforcement learning.

The awake brain is known to display asynchronous (AS) states during periods of attention and arousal, but the responsiveness properties of such states remain unclear. Here, we investigate this question using computational models of spiking networks of excitatory and inhibitory neurons, mimicking recurrently-connected networks in layer 2/3 of the cerebral cortex. The networks can generate a continuum of AS states, but with different responsiveness characteristics. By using a mean-field model to infer the dynamic properties of the system, we find that there are two families of AS states, which we call "underdamped" (UD) and "overdamped" (OD). Responsiveness is maximised at the transition between OD and UD states, which identifies a "working point" that may present advantageous computational properties.

We present a novel astro-neural-field population model with application to migraine-related cortical spreading depolarization. The model is composed of four spatio-temporal state variables: excitatory and inhibitory membrane potentials, astrocytic potassium uptake recruitment, and extracellular potassium concentration. Extending a previous neural field model, we incorporate activity-dependent astrocytic potassium clearance via a nonlinear term coupled to astrocyte dynamics. The astrocyte transfer function, like its neural counterpart, exhibits three regimes governed by extracellular potassium, capturing its effect on clearance. This yields a more comprehensive framework, better fits experimental data, and provides new insights into the mechanisms of cortical spreading depolarization.

Tracking dynamic moving objects in the external world is ethologically important for many organisms. Recent experiments have examined neural dynamics supporting such behaviors by employing visually-guided pursuit in freely moving rodents, yet computational principles underlying this cognitive process are not well understood. To address this, we developed a recurrent neural network model for examining the predictive behaviors and computations that emerge during pursuit. We demonstrate that the model generates internal predictions of the targets future locations, with anticipatory behaviors increasing with exposure to stereotyped trajectories of the target. These internal predictions can be used by the model to pursue a target in a complex environment, and the models emergent strategy is aligned with behavior when tested in rodents. In investigating the computations that underlie the models ability to perform predictive pursuit, we found units sensitive to the position of the target relative to the artificial agent, a representation analogous to egocentric target neurons observed in animals performing pursuit tasks. Ablating these units significantly reduced model performance, establishing a causal role of this functional response type in efficient pursuit. Given the complexity of the task and agent behavior, we hypothesized that RNN models may use high-dimensional neural codes to support predictive pursuit. To test this, we trained models of varying rank and found that anticipatory behavior emerged only when the rank was sufficiently high, despite strong pursuit performance in lower rank models. All RNNs encoded the egocentric location of the target, whereas allocentric self and target locations emerged only in high-dimensional networks. Overall, our results suggest that, unlike commonly studied vision, motor, or memory tasks, predictive pursuit emerges in high-dimensional networks with sufficient resources.

Computational models of brain structures impacted by Parkinsons disease are useful for exploring potential therapies. We use the Hindmarsh-Rose neuronal model to simulate synchronized activity in the subthalamic nucleus, capturing key features of the pathological rhythms observed in Parkinsons disease using a relatively small network of 100 neurons. Our model incorporates unidirectional excitatory chemical synapses whose strengths evolve according to a spike-timing-dependent plasticity (STDP) rule. To account for inputs from unmodelled neurons, both uniformly distributed white noise and Poisson noise were explored. White noise produced a single stable state of synchronized neuronal activity whereas Poisson noise resulted in two stable states, one synchronized and one desynchronized. We applied coordinated reset stimulation with a rapidly varying sequence (RVS CR) to examine its ability to reduce neuronal synchrony. The neuronal population was divided into subpopulations representing distinct physical sites of stimulation, as in deep brain stimulation therapy, and phase-shifted stimuli were delivered to each subpopulation in a random sequence. We explored how stimulation frequency and the number of stimulation sites affect the efficacy of RVS CR at desynchronizing the network. We demonstrate that RVS CR efficacy is sensitive to the depression-to-potentiation ratio in the STDP rule, which may be an important parameter to tune when reconciling simulations with experimental data. Numerical simulation of neuronal networks is constrained by computational resources when models demand large networks. This work proposes a model that demonstrates similar utility with a relatively small network, enabling researchers to study pathological neuronal activity and treatments more efficiently.

The integration of contextual information is crucial for coherent perception and cognition. The morphology and conductance properties of cortical pyramidal cells suggest that they operate as "two-point neurons" (TPNs), asymmetrically combining driving sensory input at basal dendrites with modulating context at apical compartments. We present a mechanistic computational TPN model that captures the causal cell-internal apical-basal integration. The model is extended incorporating the interactions between pyramidal cells and local inhibitory interneuron circuits of PV, SOM, and VIP cells. The model rests on guiding principles of asymmetric feedforward-feedback integration, contextual feedback, and pooled inhibition to implement local competition and global cooperation supporting the selective amplification of coherent signals. We validate our approach against detailed multi-compartment pyramidal cell simulations reproducing key electrophysiological phenomena. We then extend it to interacting TPN populations with joint spatial and feature selectivity. In such networks, contextual signals propagate through structured lateral recurrence and top-down feedback, exhibiting contextual integration, coherence formation, and evidence propagation. To support larger-scale network simulations, we derive a reduced mathematical model that preserves the core computational principles of TPNs, while substantially reducing complexity. We demonstrate the models applicability in biological vision, showing how it explains motion integration and incremental grouping--processes requiring dynamic resolution of perceptual ambiguity. Finally, we discuss how the proposed framework connects cellular and circuit-level mechanisms of pyramidal neurons to broader questions about cortical computation, the formation of representations for globally consistent perceptual states, and the potential for embedding TPN principles into artificial neural network architectures. HighlightsO_LIMechanistic TPN model integrates basal driving input and apical context modulation. C_LIO_LILocal inhibitory circuits (PV/SOM/VIP) regulate competition and cooperation. C_LIO_LINetworks of TPN populations exhibit global coherence via context propagation. C_LIO_LIReduced models retain core computations for efficient large-scale vision networks. C_LIO_LILinks pyramidal cell mechanisms to cortical computation and AI models. C_LI Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=76 SRC="FIGDIR/small/721094v1_ufig1.gif" ALT="Figure 1"> View larger version (20K): org.highwire.dtl.DTLVardef@18a10b2org.highwire.dtl.DTLVardef@14e33a1org.highwire.dtl.DTLVardef@11f9afborg.highwire.dtl.DTLVardef@1f7dc7e_HPS_FORMAT_FIGEXP M_FIG C_FIG

Biological and robotic systems must solve two related computations to move: inverse dynamics, which determines the forces or torques needed to produce a desired movement, and forward dynamics, which maps applied forces to motion. Although these computations are coupled by the same equations of motion, they are usually estimated or implemented as distinct inverse and forward mappings, in both model-based and data-driven formulations. This separation can obscure the shared structure that constrains both problems. Here, we present ANNet, a physics-informed neural network that places both computations on a common learned representation by learning a single scalar quantity from classical mechanics--Appell acceleration energy. The network maps kinematic state and candidate accelerations to this scalar function, and inverse dynamics is obtained by differentiating the learned energy function with respect to acceleration to recover joint torques. Forward dynamics is then calculated without retraining by embedding the same learned energy landscape in an optimization objective whose unconstrained minimum satisfies the Gibbs- Appell equation. The resulting accelerations are integrated forward in time. We evaluate ANNet on a double pendulum paradigm. In trials unseen by the network during training, inverse and optimization-based forward simulations are real-time accurate. Our results provide a first-principles route for using a single learned representation to support both prediction and control. SignificanceRobots and animals must solve two problems to move: computing the forces or torques needed for a desired motion (inverse dynamics) and determining the motion produced by applied forces (forward dynamics), which are usually modeled separately. We show that both problems can be expressed using a single scalar function from classical mechanics, Appell acceleration energy. A neural network trained so that the derivative of this learned function matches reference joint torques performs inverse dynamics. The same network then computes forward dynamics by minimizing an objective built from the learned energy landscape, without retraining. This framework provides a unified representation for prediction and control in both neuroscience and robotics.

Improving long-term memory in artificial neural networks remains an open challenge. To address this, we developed a novel brain-inspired framework for memory prioritization based on the principle of emotional valence. Our framework includes: (i) a valence-weighted cross-entropy loss that scales the learning signal by the valence magnitude, analogous to neuromodulation; (ii) an amygdala-inspired module that learns high-dimensional valence embeddings; and (iii) a hippocampus-inspired module that integrates valence embeddings into the attention mechanism to modulate information retrieval. We demonstrated the generalization of our framework across spatial, episodic, and language-based memory tasks, consistently improving memory prioritization and long-term retention of high-salience information. In addition to improving long-term memory, we also showed that our framework can help mitigate the "lost-in-the-middle" problem in language modeling. More generally, this research provides further evidence of the potential of brain-inspired algorithms to advance the field of machine learning.

Growing interest to describe the electrical behavior of glial cells, mainly astrocytes, in intact brain tissue poses more and more challenges to commonly accepted belief they only respond in a linear manner in uptake of the excess of extracellular potassium and maintenance of their network equipotentiality. Their highly conductive mutual interconnections via gap junction (GJ) connections introduce yet another class of nonlinear elements. As more studies report nonlinearities in membrane voltage Vm dependence of both, the membrane and junctional conductances, the need to formulate minimal dynamical models of their transient behavior is getting more acute. Since ODE models of coupled cells, even in simplest 1-d arrays, require simplified descriptions and small set of parameters, rare quantitative studies on glia makes the task even more difficult. This study attempts to qualify a self-coupled cell, or a glial cell coupled to fixed voltage as useful system for detecting the nature of instabilities and transitions coming from coupling. In a novel biophysical model of coupled astrocyte, we introduce nonlinear kinetics of deactivation for large junctional voltages for the first time. We found that N-shaped nonlinearities and corresponding fold structure in the vector field of isolated cell serves as a baseline on top of which coupling nonlinearities enrich the bifurcation picture. Numerical simulations of 1-d array of coupled astrocytes show that coupling increases the propensity of astrocytic Vm to bistability and front propagation. We believe that presented illustrations of possible effects of coupling nonlinearities will motivate neurobiologists to further explore their impact in disease. Significance statementTransient changes in membrane voltage of glial cells may produce significant transient voltage difference between directly coupled cells. Nonlinear steady-state conductance of their interconnection elements, the gap junctions, introduce nonlinear current profiles which are very difficult to measure and quantitate using the available methods due to marked permeability of the junctions and leakiness of glial membrane in general. We propose a minimal model of glial membrane extended with a self-coupled feedback loop, which under realistic simplifying assumptions could serve for qualitative analysis of the impact of coupling, on the stability of resting membrane voltage. Neuronal cells of the brain and spinal cord cannot exist and function without supportive and neuromodulatory functions of the diverse population of glial cells. This applies to virtually all physiological processes on cell level - from cell development, metabolic support, membrane signaling, slow molecular signal transduction, ion homeostasis, neurovascular coupling, myelination, to mention only a few, manifest neuro-glial interaction. Even though all glial cell types are interconnected, the most abundant ones, the astrocytes are massively interconnected by gap junctions to form ordered networks. Electrically, astrocytic networks display membrane voltage equipotentiality, which is considered system-wide resting state for given neuro-glial circuit or unit. With molecular and cellular substrates of glial connectivity being slowly elucidated, network science and dynamical modeling are slowly "invading" that area with many important issues left open. In this study using classical dynamical systems approaches we give indications how nonlinear intercellular coupling between astrocytes affects physiological resting state and its instabilities compared to isolated, uncoupled cell. We strongly believe the suggested minimal model could fill the gap in ODE modeling of neuro-glial circuits, within broadest scope of hypothesis-driven research in cell-level neuroscience.

Despite extensive study of cellular mechanisms underlying long-term potentiation, no single specific protein or gene has been identified which encodes an individual unit of information, or memory bit. Indeed, the brain engram remains a knowledge gap. The theory of exclusion led us to cancel one-by-one several unrealistic biological options, suggesting that the explanation resides somewhere else. Superposition of up to concentric 300 myelin layers, spiraled, and highly compacted wrapping a single axon and each wrap could host hundreds to thousands of niches, as memory cells, collectively consisting of a massive array of cells. The disjointed 3D spatial superposition allows storage of charges, nodes not facing from a layer to next. The thickness of a single myelin layer ranges from 7.0 to 20 nm. The dimension scale is approximately the exact dimensions of the charge trap, the tunnel and dielectric also equipping current AI microchips. Stored charges are positive ions, with similar effect whether charges are negative or positive charges creating an electromagnetic field. To write data, following an action potential, this voltage applies to the control gates of the myelin layers producing an ionic charge injection. This causes charges to gain energy and tunnel through the myelin layer across Ranvier nodes, via quantum tunneling, and deep into the concentric myelin multilayers. This is creating an insulated trapping of K+ ions isolated from the system. In a long white matter tract bundle, the near-perfect isolation of millions of axons within compressed myelin wrap-ion channel K+/Na+ systems provides quantum coherence and precision of asynchronous firing property. The injected ionic charges (K+) become physically stuck in traps within the myelin layers. The K+ ions may not move freely, completely trapped after AP ceases. Mirroring a single-bit, single-level-cell, a trapped ionic charge (ions K+) may represent a 1, while an empty cell (absence of K+) represents a 0. The trial-and-error process, with a Bayesian inference which may have also been the core evolution of the learning human brain. Based on selected mathematical equations, we analyzed the general scheme on how deep learning may be embedded in the brain