Model design for networks of heterogeneous Hodgkin–Huxley neurons

Mathematical generation of data-driven hippocampal CA1 pyramidal neurons and interneurons copies via A-GLIF models for large-scale networks covering the experimental variability range

Efficient and accurate large-scale networks are a fundamental tool in modeling brain areas, to advance our understanding of neuronal dynamics. However, their implementation faces two key issues: computational efficiency and heterogeneity. Computational efficiency is achieved using simplified neurons, whereas there are no practical solutions available to solve the problem of reproducing in a large-scale network the experimentally observed heterogeneity of the intrinsic properties of neurons. This is important, because the use of identical nodes in a network can generate artifacts which can hinder an adequate representation of the properties of a real network. To this aim, we introduce a mathematical procedure to generate an arbitrary large number of copies of simplified hippocampal CA1 pyramidal neurons and interneurons models, which exhibit the full range of firing dynamics observed in these cells - including adapting, non-adapting and bursting. For this purpose, we rely on a recently published adaptive generalized leaky integrate-and-fire (A-GLIF) modeling approach, leveraging on its ability to reproduce the rich set of electrophysiological behaviors of these types of neurons under a variety of different stimulation currents. The generation procedure is based on a perturbation of model's parameters related to the initial data, firing block, and internal dynamics, and suitably validated against experimental data to ensure that the firing dynamics of any given cell copy remains within the experimental range. A classification procedure confirmed that the firing behavior of most of the pyramidal/interneuron copies was consistent with the experimental data. This approach allows to obtain heterogeneous copies with mathematically controlled firing properties. A full set of heterogeneous neurons composing the CA1 region of a rat hippocampus (approximately 1.2 million neurons), are provided in a database freely available in the live paper section of the EBRAINS platform. By adapting the underlying A-GLIF framework, it will be possible to extend the numerical approach presented here to create, in a mathematically controlled manner, an arbitrarily large number of non-identical copies of cell populations with firing properties related to other brain areas.

A Josephson junction-coupled neuron with double capacitive membranes

The channel currents have distinct magnetic field effect and any changes of the electromagnetic field or electirc stimulus will change the membrane potential effectively. A feasible neuron model considers the distinct physical characteristic is more suitable to mimic the neural activities accompanying with shift in energy level. A Josephson junction (JJ) is connected to a neural circuit for estimating the effect of external magnetic field and two capacitors are connected via a linear resistor for mimicing the capacitive field beside two sides of the cell membrane. Its equivalent Hamilton energy is calculated to show the relation between firing mode and energy level. Noisy disturbance is imposed to predict the occurrence of coherence resonance, and the biophysical neuron is excited to present higher energy level. This new neuron model can address the field effect and the biophysical property of cell membrane considered as combination of capacitive fields in double capacitors. It can mimic the physical property of outer and inner membranes, and energy exchange across the double membranes explains the energy mechanism in neural activities. Time-varying energy diveristy between capacitive field is crucial for supporting continuous firing activities. The JJ channel discerns slight changes in external magnetic field and regularity is stabilized under coherence resonance in presence of noisy excitation on the membrane or ion channels.

A Novel Robotic Controller Using Neural Engineering Framework-Based Spiking Neural Networks

This paper investigates spiking neural networks (SNN) for novel robotic controllers with the aim of improving accuracy in trajectory tracking. By emulating the operation of the human brain through the incorporation of temporal coding mechanisms, SNN offer greater adaptability and efficiency in information processing, providing significant advantages in the representation of temporal information in robotic arm control compared to conventional neural networks. Exploring specific implementations of SNN in robot control, this study analyzes neuron models and learning mechanisms inherent to SNN. Based on the principles of the Neural Engineering Framework (NEF), a novel spiking PID controller is designed and simulated for a 3-DoF robotic arm using Nengo and MATLAB R2022b. The controller demonstrated good accuracy and efficiency in following designated trajectories, showing minimal deviations, overshoots, or oscillations. A thorough quantitative assessment, utilizing performance metrics like root mean square error (RMSE) and the integral of the absolute value of the time-weighted error (ITAE), provides additional validation for the efficacy of the SNN-based controller. Competitive performance was observed, surpassing a fuzzy controller by 5% in terms of the ITAE index and a conventional PID controller by 6% in the ITAE index and 30% in RMSE performance. This work highlights the utility of NEF and SNN in developing effective robotic controllers, laying the groundwork for future research focused on SNN adaptability in dynamic environments and advanced robotic applications.

Critically synchronized brain waves form an effective, robust and flexible basis for human memory and learning

The effectiveness, robustness, and flexibility of memory and learning constitute the very essence of human natural intelligence, cognition, and consciousness. However, currently accepted views on these subjects have, to date, been put forth without any basis on a true physical theory of how the brain communicates internally via its electrical signals. This lack of a solid theoretical framework has implications not only for our understanding of how the brain works, but also for wide range of computational models developed from the standard orthodox view of brain neuronal organization and brain network derived functioning based on the Hodgkin-Huxley ad-hoc circuit analogies that have produced a multitude of Artificial, Recurrent, Convolution, Spiking, etc., Neural Networks (ARCSe NNs) that have in turn led to the standard algorithms that form the basis of artificial intelligence (AI) and machine learning (ML) methods. Our hypothesis, based upon our recently developed physical model of weakly evanescent brain wave propagation (WETCOW) is that, contrary to the current orthodox model that brain neurons just integrate and fire under accompaniment of slow leaking, they can instead perform much more sophisticated tasks of efficient coherent synchronization/desynchronization guided by the collective influence of propagating nonlinear near critical brain waves, the waves that currently assumed to be nothing but inconsequential subthreshold noise. In this paper we highlight the learning and memory capabilities of our WETCOW framework and then apply it to the specific application of AI/ML and Neural Networks. We demonstrate that the learning inspired by these critically synchronized brain waves is shallow, yet its timing and accuracy outperforms deep ARCSe counterparts on standard test datasets. These results have implications for both our understanding of brain function and for the wide range of AI/ML applications.

Spiking Neural Networks and Mathematical Models

Neural networks are applied in various scientific fields such as medicine, engineering, pharmacology, etc. Investigating operations of neural networks refers to estimating the relationship among single neurons and their contributions to the network as well. Hence, studying a single neuron is an essential process to solve complex brain problems. Mathematical models that simulate neurons and the way they transmit information are proven to be an indispensable tool for neuroscientists. Constructing appropriate mathematical models to simulate information transmission of a biological neural network is a challenge for researchers, as in the real world, identical neurons in terms of their electrophysiological characteristics in different brain regions do not contribute in the same way to information transmission within a neural network due to the intrinsic characteristics. This review highlights four mathematical, single-compartment models: Hodgkin-Huxley, Izhikevich, Leaky Integrate, and Fire and Morris-Lecar, and discusses comparison among them in terms of their biological plausibility, computational complexity, and applications, according to modern literature.