Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism

Pulse Shape and Voltage-Dependent Synchronization in Spiking Neuron Networks

Pulse-coupled spiking neural networks are a powerful tool to gain mechanistic insights into how neurons self-organize to produce coherent collective behavior. These networks use simple spiking neuron models, such as the θ-neuron or the quadratic integrate-and-fire (QIF) neuron, that replicate the essential features of real neural dynamics. Interactions between neurons are modeled with infinitely narrow pulses, or spikes, rather than the more complex dynamics of real synapses. To make these networks biologically more plausible, it has been proposed that they must also account for the finite width of the pulses, which can have a significant impact on the network dynamics. However, the derivation and interpretation of these pulses are contradictory, and the impact of the pulse shape on the network dynamics is largely unexplored. Here, I take a comprehensive approach to pulse coupling in networks of QIF and θ-neurons. I argue that narrow pulses activate voltage-dependent synaptic conductances and show how to implement them in QIF neurons such that their effect can last through the phase after the spike. Using an exact low-dimensional description for networks of globally coupled spiking neurons, I prove for instantaneous interactions that collective oscillations emerge due to an effective coupling through the mean voltage. I analyze the impact of the pulse shape by means of a family of smooth pulse functions with arbitrary finite width and symmetric or asymmetric shapes. For symmetric pulses, the resulting voltage coupling is not very effective in synchronizing neurons, but pulses that are slightly skewed to the phase after the spike readily generate collective oscillations. The results unveil a voltage-dependent spike synchronization mechanism at the heart of emergent collective behavior, which is facilitated by pulses of finite width and complementary to traditional synaptic transmission in spiking neuron networks.

Possible mechanisms to improve sleep spindles via closed loop stimulation during slow wave sleep: A computational study

Sleep spindles are one of the prominent EEG oscillatory rhythms of non-rapid eye movement sleep. In the memory consolidation, these oscillations have an important role in the processes of long-term potentiation and synaptic plasticity. Moreover, the activity (spindle density and/or sigma power) of spindles has a linear association with learning performance in different paradigms. According to the experimental observations, the sleep spindle activity can be improved by closed loop acoustic stimulations (CLAS) which eventually improve memory performance. To examine the effects of CLAS on spindles, we propose a biophysical thalamocortical model for slow oscillations (SOs) and sleep spindles. In addition, closed loop stimulation protocols are applied on a thalamic network. Our model results show that the power of spindles is increased when stimulation cues are applied at the commencing of an SO Down-to-Up-state transition, but that activity gradually decreases when cues are applied with an increased time delay from this SO phase. Conversely, stimulation is not effective when cues are applied during the transition of an Up-to-Down-state. Furthermore, our model suggests that a strong inhibitory input from the reticular (RE) layer to the thalamocortical (TC) layer in the thalamic network shifts leads to an emergence of spindle activity at the Up-to-Down-state transition (rather than at Down-to-Up-state transition), and the spindle frequency is also reduced (8-11 Hz) by thalamic inhibition.

Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits. A tutorial

In this study we focus on two subnetworks common in the circuitry of swim central pattern generators (CPGs) in the sea slugs, Melibe leonina and Dendronotus iris and show that they are independently capable of stably producing emergent network bursting. This observation raises the question of whether the coordination of redundant bursting mechanisms plays a role in the generation of rhythm and its regulation in the given swim CPGs. To address this question, we investigate two pairwise rhythm-generating networks and examine the properties of their fundamental components: cellular and synaptic, which are crucial for proper network assembly and its stable function. We perform a slow-fast decomposition analysis of cellular dynamics and highlight its significant bifurcations occurring in isolated and coupled neurons. A novel model for slow synapses with high filtering efficiency and temporal delay is also introduced and examined. Our findings demonstrate the existence of two modes of oscillation in bicellular rhythm-generating networks with network hysteresis: i) a half-center oscillator and ii) an excitatory-inhibitory pair. These 2-cell networks offer potential as common building blocks combined in modular organization of larger neural circuits preserving robust network hysteresis.

Mechanism of an Intrinsic Oscillation in Rat Geniculate Interneurons

Depolarizing current injections produced a rhythmic bursting of action potentials - a bursting oscillation - in a set of local interneurons in the lateral geniculate nucleus (LGN) of rats. The current dynamics underlying this firing pattern have not been determined, though this cell type constitutes an important cellular component of thalamocortical circuitry, and contributes to both pathologic and non-pathologic brain states. We thus investigated the source of the bursting oscillation using pharmacological manipulations in LGN slices in vitro and in silico. 1. Selective blockade of calcium channel subtypes revealed that high-threshold calcium currentsI L andI P contributed strongly to the oscillation. 2. Increased extracellular K+ concentration (decreased K+currents) eliminated the oscillation. 3. Selective blockade of K+ channel subtypes demonstrated that the calcium-sensitive potassium current (I A H P ) was of primary importance. A morphologically simplified, multicompartment model of the thalamic interneuron characterized the oscillation as follows: 1. The low-threshold calcium currentI T provided the strong initial burst characteristic of the oscillation. 2. Alternating fluxes through high-threshold calcium channels andI A H P then provided the continuing oscillation's burst and interburst periods respectively. This interplay betweenI L andI A H P contrasts with the current dynamics underlying oscillations in thalamocortical and reticularis neurons, which primarily involveI T andI H , orI T andI A H P respectively. These findings thus point to a novel electrophysiological mechanism for generating intrinsic oscillations in a major thalamic cell type. Because local interneurons can sculpt the behavior of thalamocortical circuits, these results suggest new targets for the manipulation of ascending thalamocortical network activity.

Is the Papez circuit the location of the elusive episodic memory engram?

All of the brain structures and white matter that make up Papez' circuit, as well as the circuit as a whole, are implicated in the literature in episodic memory formation and recall. This paper shows that Papez' circuit has the detailed structure and connectivity that is evidently required to support the episodic memory engram, and that identifying Papez' circuit as the location of the engram answers a number of long-standing questions regarding the role of medial temporal lobe structures in episodic memory. The paper then shows that the process by which the episodic memory engram may be formed is a network-wide Hebbian potentiation termed "racetrack potentiation", whose frequency corresponds to that observed in vivo in humans for memory functions. Further, by considering the microcircuits observed in the medial temporal lobe structures forming Papez' circuit, the paper establishes the neural mechanisms behind the required functions of sensory information storage and recall, pattern completion, pattern separation, and memory consolidation. The paper shows that Papez' circuit has the necessary connectivity to gather the various elements of an episodic memory occurring within Pöppel's experienced time or "quantum of experience". Finally, the paper shows how the memory engram located in Papez' circuit might be central to the formation of a duplicate engram in the cortex enabling consolidation and long-term storage of episodic memories.

Emergence of complex oscillatory dynamics in the neuronal networks with long activity time of inhibitory synapses

The brain displays complex dynamics, including collective oscillations, and extensive research has been conducted to understand their generation. However, our understanding of how biological constraints influence these oscillations is incomplete. This study investigates the essential properties of neuronal networks needed to generate oscillations resembling those in the brain. A simple discrete-time model of interconnected excitable elements is developed, capable of closely resembling the complex oscillations observed in biological neural networks. In the model, synaptic connections remain active for a duration exceeding individual neuron activity. We show that the inhibitory synapses must exhibit longer activity than excitatory synapses to produce a diverse range of the dynamical states, including biologically plausible oscillations. Upon meeting this condition, the transition between different dynamical states can be controlled by external stochastic input to the neurons. The study provides a comprehensive explanation for the emergence of distinct dynamical states in neural networks based on specific parameters.

The role of extracellular glutamate homeostasis dysregulated by astrocyte in epileptic discharges: a model evidence

Glutamate (Glu) is a predominant excitatory neurotransmitter that acts on glutamate receptors to transfer signals in the central nervous system. Abnormally elevated extracellular glutamate levels is closely related to the generation and transition of epileptic seizures. However, there lacks of investigation regarding the role of extracellular glutamate homeostasis dysregulated by astrocyte in neuronal epileptic discharges. According to this, we propose a novel neuron-astrocyte computational model (NAG) by incorporating extracellular Glu concentration dynamics from three aspects of regulatory mechanisms: (1) the Glu uptake through astrocyte EAAT2; (2) the binding and release Glu via activating astrocyte mGluRs; and (3) the Glu free diffusion in the extracellular space. Then the proposed model NAG is analyzed theoretically and numerically to verify the effect of extracellular Glu homeostasis dysregulated by such three regulatory mechanisms on neuronal epileptic discharges. Our results demonstrate that the neuronal epileptic discharges can be aggravated by the downregulation expression of EAAT2, the aberrant activation of mGluRs, and the elevated Glu levels in extracellular micro-environment; as well as various discharge states (including bursting, mixed-mode spiking, and tonic firing) can be transited by their combination. Furthermore, we find that such factors can also alter the bifurcation threshold for the generation and transition of epileptic discharges. The results in this paper can be helpful for researchers to understand the astrocyte role in modulating extracellular Glu homeostasis, and provide theoretical basis for future related experimental studies.

Spontaneous slow wave oscillations in extracellular field potential recordings reflect the alternating dominance of excitation and inhibition

In the resting state, cortical neurons can fire action potentials spontaneously but synchronously (Up state), followed by a quiescent period (Down state) before the cycle repeats. Extracellular recordings in the infragranular layer of cortex with a micro-electrode display a negative deflection (depth-negative) during Up states and a positive deflection (depth-positive) during Down states. The resulting slow wave oscillation (SWO) has been studied extensively during sleep and under anaesthesia. However, recent research on the balanced nature of synaptic excitation and inhibition has highlighted our limited understanding of its genesis. Specifically, are excitation and inhibition balanced during SWOs? We analyse spontaneous local field potentials (LFPs) during SWOs recorded from anaesthetised rats via a multi-channel laminar micro-electrode and show that the Down state consists of two distinct synaptic states: a Dynamic Down state associated with depth-positive LFPs and a prominent dipole in the extracellular field, and a Static Down state with negligible (≈ 0 mV $ \approx 0{\mathrm{\;mV}}$ ) LFPs and a lack of dipoles extracellularly. We demonstrate that depth-negative and -positive LFPs are generated by a shift in the balance of synaptic excitation and inhibition from excitation dominance (depth-negative) to inhibition dominance (depth-positive) in the infragranular layer neurons. Thus, although excitation and inhibition co-tune overall, differences in their timing lead to an alternation of dominance, manifesting as SWOs. We further show that Up state initiation is significantly faster if the preceding Down state is dynamic rather than static. Our findings provide a coherent picture of the dependence of SWOs on synaptic activity. KEY POINTS: Cortical neurons can exhibit repeated cycles of spontaneous activity interleaved with periods of relative silence, a phenomenon known as 'slow wave oscillation' (SWO). During SWOs, recordings of local field potentials (LFPs) in the neocortex show depth-negative deflection during the active period (Up state) and depth-positive deflection during the silent period (Down state). Here we further classified the Down state into a dynamic phase and a static phase based on a novel method of classification and revealed non-random, stereotypical sequences of the three states occurring with significantly different transitional kinetics. Our results suggest that the positive and negative deflections in the LFP reflect the shift of the instantaneous balance between excitatory and inhibitory synaptic activity of the local cortical neurons. The differences in transitional kinetics may imply distinct synaptic mechanisms for Up state initiation. The study may provide a new approach for investigating spontaneous brain rhythms.

Plasticity in inhibitory networks improves pattern separation in early olfactory processing

Distinguishing between nectar and non-nectar odors presents a challenge for animals due to shared compounds in complex mixtures, where changing ratios often signify differences in reward. Changes in nectar production throughout the day and potentially many times within a forager's lifetime add to the complexity. The honeybee olfactory system, containing less than a 1000 of principal neurons in the early olfactory relay, the antennal lobe (AL), must learn to associate diverse volatile blends with rewards. We used a computational network model and live imaging of the honeybee's AL to explore the neural mechanisms and functions of the AL plasticity. Our findings revealed that when trained with a set of rewarded and unrewarded odors, the AL inhibitory network suppresses shared chemical compounds while enhancing responses to distinct compounds. This results in improved pattern separation and a more concise and efficient neural code. Our Ca2+ imaging data support our model's predictions. Furthermore, we applied these contrast enhancement principles to a Graph Convolutional Network (GCN) and found that similar mechanisms could enhance the performance of artificial neural networks. Our model provides insights into how plasticity at the inhibitory network level reshapes coding for efficient learning of complex odors.

A realistic computational model for the formation of a Place Cell

Hippocampal Place Cells (PCs) are pyramidal neurons showing spatially localized firing when an animal gets into a specific area within an environment. Because of their obvious and clear relation with specific cognitive functions, Place Cells operations and modulations are intensely studied experimentally. However, although a lot of data have been gathered since their discovery, the cellular processes that interplay to turn a hippocampal pyramidal neuron into a Place Cell are still not completely understood. Here, we used a morphologically and biophysically detailed computational model of a CA1 pyramidal neuron to show how, and under which conditions, it can turn into a neuron coding for a specific cue location, through the self-organization of its synaptic inputs in response to external signals targeting different dendritic layers. Our results show that the model is consistent with experimental findings demonstrating PCs stability within the same spatial context over different trajectories, environment rotations, and place field remapping to adapt to changes in the environment. To date, this is the only biophysically and morphologically accurate cellular model of PCs formation, which can be directly used in physiologically accurate microcircuits and large-scale model networks to study cognitive functions and dysfunctions at cellular level.

Predicting the Behavior of Sparsely-Sampled Systems Across Neurobiology and Epidemiology

Inference is a term that encompasses many techniques including statistical data assimilation (SDA). Unlike machine learning, which is designed to harness predictive power from extremely large data sets, SDA is designed for sparsely-sampled systems. This is the realm of study of nonlinear dynamical systems in nature. Formulated as an optimization procedure, SDA can be considered a path-integral approach to state and parameter estimation. Within this formulation, we can use the physical principle of least action to identify optimal solutions: solutions that are consistent with both measurements and a dynamical model assumed to give rise to those measurements. I review examples from neurobiology and an epidemiological model tailored to the coronavirus SARS-CoV-2, to demonstrate the versatility of SDA across the sciences, and how these distinct applications possess commonalities that can inform one another.

A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics

Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either (1) top-down and interpretable, but not flexible enough to account for experimental data, or (2) bottom-up and biologically realistic, but too intricate to interpret and hard to fit to data. To avoid the shortcomings of these approaches, we present a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to predict plasticity outcomes. We apply this readout to a multi-timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols, animal ages, and experimental conditions. Our model also predicts that in vivo-like spike timing irregularity strongly shapes plasticity outcome. This geometrical readout modelling approach can be readily applied to other excitatory or inhibitory synapses to discover their synaptic plasticity rules.

Analysis of Network Models with Neuron-Astrocyte Interactions

Neural networks, composed of many neurons and governed by complex interactions between them, are a widely accepted formalism for modeling and exploring global dynamics and emergent properties in brain systems. In the past decades, experimental evidence of computationally relevant neuron-astrocyte interactions, as well as the astrocytic modulation of global neural dynamics, have accumulated. These findings motivated advances in computational glioscience and inspired several models integrating mechanisms of neuron-astrocyte interactions into the standard neural network formalism. These models were developed to study, for example, synchronization, information transfer, synaptic plasticity, and hyperexcitability, as well as classification tasks and hardware implementations. We here focus on network models of at least two neurons interacting bidirectionally with at least two astrocytes that include explicitly modeled astrocytic calcium dynamics. In this study, we analyze the evolution of these models and the biophysical, biochemical, cellular, and network mechanisms used to construct them. Based on our analysis, we propose how to systematically describe and categorize interaction schemes between cells in neuron-astrocyte networks. We additionally study the models in view of the existing experimental data and present future perspectives. Our analysis is an important first step towards understanding astrocytic contribution to brain functions. However, more advances are needed to collect comprehensive data about astrocyte morphology and physiology in vivo and to better integrate them in data-driven computational models. Broadening the discussion about theoretical approaches and expanding the computational tools is necessary to better understand astrocytes' roles in brain functions.

GluN2B-NMDAR subunit contribution on synaptic plasticity: A phenomenological model for CA3-CA1 synapses

Synaptic plasticity is believed to be a key mechanism underlying learning and memory. We developed a phenomenological N-methyl-D-aspartate (NMDA) receptor-based voltage-dependent synaptic plasticity model for synaptic modifications at hippocampal CA3-CA1 synapses on a hippocampal CA1 pyramidal neuron. The model incorporates the GluN2A-NMDA and GluN2B-NMDA receptor subunit-based functions and accounts for the synaptic strength dependence on the postsynaptic NMDA receptor composition and functioning without explicitly modeling the NMDA receptor-mediated intracellular calcium, a local trigger of synaptic plasticity. We embedded the model into a two-compartmental model of a hippocampal CA1 pyramidal cell and validated it against experimental data of spike-timing-dependent synaptic plasticity (STDP), high and low-frequency stimulation. The developed model predicts altered learning rules in synapses formed on the apical dendrites of the detailed compartmental model of CA1 pyramidal neuron in the presence of the GluN2B-NMDA receptor hypofunction and can be used in hippocampal networks to model learning in health and disease.

Energy-efficiency computing of up and down transitions in a neural network

Spontaneous periodic up and down transitions of membrane potentials are considered to be a significant spontaneous activity of slow-wave sleep. Previous theoretical studies have shown that stimulation frequency and the dynamics of intrinsic currents have a major influence on synchronicity and firing rate of spontaneous fluctuation. Energy consumption is driven by internal spontaneous activity. However, its energy consumption and energy efficiency are not clear. Therefore, this article simulates the up and down transitions based on a neural network and discusses the energy consumption and energy efficiency. It is found that the dynamics of intrinsic currents have a great impact on the energy consumption and energy efficiency in the process. The energy consumption is influenced by the size of the period and the average power consumption of the state. The average power consumption by the up state is always greater than the consumption by the down state, and the energy consumption of the transition is more than firing. In addition, the lower average proportion of duration of the up state in the cycle leads to higher energy efficiency. Energy consumption is reduced and energy efficiency is enhanced by adjusting parameters of the network. The study helps us to understand and further explore the metabolic consumption of spontaneous activities.NEW & NOTEWORTHY We use a more biological neural network to explore energy consumption and energy efficiency of up and down transitions. Specifically, we find that average energy consumption is more than that caused by action potentials, which proves that metabolic consumption is acquired substantially in the resting state as well. We also find that energy efficiency is influenced by the proportion of duration of the up state in the cycle. These findings may further improve the economy of the nervous system.

A mean-field model of glutamate and GABA synaptic dynamics for functional MRS

Advances in functional magnetic resonance spectroscopy (fMRS) have enabled the quantification of activity-dependent changes in neurotransmitter concentrations in vivo. However, the physiological basis of the large changes in GABA and glutamate observed by fMRS (>10%) over short time scales of less than a minute remain unclear as such changes cannot be accounted for by known synthesis or degradation metabolic pathways. Instead, it has been hypothesized that fMRS detects shifts in neurotransmitter concentrations as they cycle from presynaptic vesicles, where they are largely invisible, to extracellular and cytosolic pools, where they are detectable. The present paper uses a computational modelling approach to demonstrate the viability of this hypothesis. A new mean-field model of the neural mechanisms generating the fMRS signal in a cortical voxel is derived. The proposed macroscopic mean-field model is based on a microscopic description of the neurotransmitter dynamics at the level of the synapse. Specifically, GABA and glutamate are assumed to cycle between three metabolic pools: packaged in the vesicles; active in the synaptic cleft; and undergoing recycling and repackaging in the astrocytic or neuronal cytosol. Computational simulations from the model are used to generate predicted changes in GABA and glutamate concentrations in response to different types of stimuli including pain, vision, and electric current stimulation. The predicted changes in the extracellular and cytosolic pools corresponded to those reported in empirical fMRS data. Furthermore, the model predicts a selective control mechanism of the GABA/glutamate relationship, whereby inhibitory stimulation reduces both neurotransmitters, whereas excitatory stimulation increases glutamate and decreases GABA. The proposed model bridges between neural dynamics and fMRS and provides a mechanistic account for the activity-dependent changes in the glutamate and GABA fMRS signals. Lastly, these results indicate that echo-time may be an important timing parameter that can be leveraged to maximise fMRS experimental outcomes.

Differential thalamocortical interactions in slow and fast spindle generation: A computational model

Cortical slow oscillations (SOs) and thalamocortical sleep spindles are two prominent EEG rhythms of slow wave sleep. These EEG rhythms play an essential role in memory consolidation. In humans, sleep spindles are categorized into slow spindles (8-12 Hz) and fast spindles (12-16 Hz), with different properties. Slow spindles that couple with the up-to-down phase of the SO require more experimental and computational investigation to disclose their origin, functional relevance and most importantly their relation with SOs regarding memory consolidation. To examine slow spindles, we propose a biophysical thalamocortical model with two independent thalamic networks (one for slow and the other for fast spindles). Our modeling results show that fast spindles lead to faster cortical cell firing, and subsequently increase the amplitude of the cortical local field potential (LFP) during the SO down-to-up phase. Slow spindles also facilitate cortical cell firing, but the response is slower, thereby increasing the cortical LFP amplitude later, at the SO up-to-down phase of the SO cycle. Neither the SO rhythm nor the duration of the SO down state is affected by slow spindle activity. Furthermore, at a more hyperpolarized membrane potential level of fast thalamic subnetwork cells, the activity of fast spindles decreases, while the slow spindles activity increases. Together, our model results suggest that slow spindles may facilitate the initiation of the following SO cycle, without however affecting expression of the SO Up and Down states.

Computational models of neurotransmission at cerebellar synapses unveil the impact on network computation

The neuroscientific field benefits from the conjoint evolution of experimental and computational techniques, allowing for the reconstruction and simulation of complex models of neurons and synapses. Chemical synapses are characterized by presynaptic vesicle cycling, neurotransmitter diffusion, and postsynaptic receptor activation, which eventually lead to postsynaptic currents and subsequent membrane potential changes. These mechanisms have been accurately modeled for different synapses and receptor types (AMPA, NMDA, and GABA) of the cerebellar cortical network, allowing simulation of their impact on computation. Of special relevance is short-term synaptic plasticity, which generates spatiotemporal filtering in local microcircuits and controls burst transmission and information flow through the network. Here, we present how data-driven computational models recapitulate the properties of neurotransmission at cerebellar synapses. The simulation of microcircuit models is starting to reveal how diverse synaptic mechanisms shape the spatiotemporal profiles of circuit activity and computation.

Neural Information Processing and Computations of Two-Input Synapses

Information processing in artificial neural networks is largely dependent on the nature of neuron models. While commonly used models are designed for linear integration of synaptic inputs, accumulating experimental evidence suggests that biological neurons are capable of nonlinear computations for many converging synaptic inputs via homo- and heterosynaptic mechanisms. This nonlinear neuronal computation may play an important role in complex information processing at the neural circuit level. Here we characterize the dynamics and coding properties of neuron models on synaptic transmissions delivered from two hidden states. The neuronal information processing is influenced by the cooperative and competitive interactions among synapses and the coherence of the hidden states. Furthermore, we demonstrate that neuronal information processing under two-input synaptic transmission can be mapped to linearly nonseparable XOR as well as basic AND/OR operations. In particular, the mixtures of linear and nonlinear neuron models outperform the fashion-MNIST test compared to the neural networks consisting of only one type. This study provides a computational framework for assessing information processing of neuron and synapse models that may be beneficial for the design of brain-inspired artificial intelligence algorithms and neuromorphic systems.

State-dependent activity dynamics of hypothalamic stress effector neurons

The stress response necessitates an immediate boost in vital physiological functions from their homeostatic operation to an elevated emergency response. However, the neural mechanisms underlying this state-dependent change remain largely unknown. Using a combination of in vivo and ex vivo electrophysiology with computational modeling, we report that corticotropin releasing hormone (CRH) neurons in the paraventricular nucleus of the hypothalamus (PVN), the effector neurons of hormonal stress response, rapidly transition between distinct activity states through recurrent inhibition. Specifically, in vivo optrode recording shows that under non-stress conditions, CRH_PVN neurons often fire with rhythmic brief bursts (RB), which, somewhat counterintuitively, constrains firing rate due to long (~2 s) interburst intervals. Stressful stimuli rapidly switch RB to continuous single spiking (SS), permitting a large increase in firing rate. A spiking network model shows that recurrent inhibition can control this activity-state switch, and more broadly the gain of spiking responses to excitatory inputs. In biological CRH_PVN neurons ex vivo, the injection of whole-cell currents derived from our computational model recreates the in vivo-like switch between RB and SS, providing direct evidence that physiologically relevant network inputs enable state-dependent computation in single neurons. Together, we present a novel mechanism for state-dependent activity dynamics in CRH_PVN neurons.

Bio-Inspired Autonomous Learning Algorithm With Application to Mobile Robot Obstacle Avoidance

Spiking Neural Networks (SNNs) are often considered the third generation of Artificial Neural Networks (ANNs), owing to their high information processing capability and the accurate simulation of biological neural network behaviors. Though the research for SNNs has been quite active in recent years, there are still some challenges to applying SNNs to various potential applications, especially for robot control. In this study, a biologically inspired autonomous learning algorithm based on reward modulated spike-timing-dependent plasticity is proposed, where a novel rewarding generation mechanism is used to generate the reward signals for both learning and decision-making processes. The proposed learning algorithm is evaluated by a mobile robot obstacle avoidance task and experimental results show that the mobile robot with the proposed algorithm exhibits a good learning ability. The robot can successfully avoid obstacles in the environment after some learning trials. This provides an alternative method to design and apply the bio-inspired robot with autonomous learning capability in the typical robotic task scenario.

Neuron-Glia Interactions and Brain Circuits

Recent evidence suggests that glial cells take an active role in a number of brain functions that were previously attributed solely to neurons. For example, astrocytes, one type of glial cells, have been shown to promote coordinated activation of neuronal networks, modulate sensory-evoked neuronal network activity, and influence brain state transitions during development. This reinforces the idea that astrocytes not only provide the "housekeeping" for the neurons, but that they also play a vital role in supporting and expanding the functions of brain circuits and networks. Despite this accumulated knowledge, the field of computational neuroscience has mostly focused on modeling neuronal functions, ignoring the glial cells and the interactions they have with the neurons. In this chapter, we introduce the biology of neuron-glia interactions, summarize the existing computational models and tools, and emphasize the glial properties that may be important in modeling brain functions in the future.

Cell type-specific mechanisms of information transfer in data-driven biophysical models of hippocampal CA3 principal neurons

The transformation of synaptic input into action potential output is a fundamental single-cell computation resulting from the complex interaction of distinct cellular morphology and the unique expression profile of ion channels that define the cellular phenotype. Experimental studies aimed at uncovering the mechanisms of the transfer function have led to important insights, yet are limited in scope by technical feasibility, making biophysical simulations an attractive complementary approach to push the boundaries in our understanding of cellular computation. Here we take a data-driven approach by utilizing high-resolution morphological reconstructions and patch-clamp electrophysiology data together with a multi-objective optimization algorithm to build two populations of biophysically detailed models of murine hippocampal CA3 pyramidal neurons based on the two principal cell types that comprise this region. We evaluated the performance of these models and find that our approach quantitatively matches the cell type-specific firing phenotypes and recapitulate the intrinsic population-level variability in the data. Moreover, we confirm that the conductance values found by the optimization algorithm are consistent with differentially expressed ion channel genes in single-cell transcriptomic data for the two cell types. We then use these models to investigate the cell type-specific biophysical properties involved in the generation of complex-spiking output driven by synaptic input through an information-theoretic treatment of their respective transfer functions. Our simulations identify a host of cell type-specific biophysical mechanisms that define the morpho-functional phenotype to shape the cellular transfer function and place these findings in the context of a role for bursting in CA3 recurrent network synchronization dynamics.

The hippocampus is comprised of numerous types of neurons, which constitute the cellular substrate for its rich repertoire of network dynamics. Among these are sharp waves, sequential activations of ensembles of neurons that have been shown to be crucially involved in learning and memory. In the CA3 area of the hippocampus, two types of excitatory cells, thorny and a-thorny neurons, are preferentially active during distinct phases of a sharp wave, suggesting a differential role for these cell types in phenomena such as memory consolidation. Using a strictly data-driven approach, we built biophysically realistic models of both thorny and a-thorny cells and used them to investigate the integrative differences between these two cell types. We found that both neuron classes have the capability of integrating incoming synaptic inputs in a supralinear fashion, although only a-thorny cells respond with bursts of action potentials to spatially and temporally clustered synaptic inputs. Additionally, by using a computational approach based on information theory, we show that, owing to this propensity for bursting, a-thorny cells can encode more information in their spiking output than their thorny counterpart. These results shed new light on the computational capabilities of two types of excitatory neurons and suggest that thorny and a-thorny cells may play distinct roles in the generation of hippocampal network synchronization.

A theory of synaptic transmission

Rapid and precise neuronal communication is enabled through a highly synchronous release of signaling molecules neurotransmitters within just milliseconds of the action potential. Yet neurotransmitter release lacks a theoretical framework that is both phenomenologically accurate and mechanistically realistic. Here, we present an analytic theory of the action-potential-triggered neurotransmitter release at the chemical synapse. The theory is demonstrated to be in detailed quantitative agreement with existing data on a wide variety of synapses from electrophysiological recordings in vivo and fluorescence experiments in vitro. Despite up to ten orders of magnitude of variation in the release rates among the synapses, the theory reveals that synaptic transmission obeys a simple, universal scaling law, which we confirm through a collapse of the data from strikingly diverse synapses onto a single master curve. This universality is complemented by the capacity of the theory to readily extract, through a fit to the data, the kinetic and energetic parameters that uniquely identify each synapse. The theory provides a means to detect cooperativity among the SNARE complexes that mediate vesicle fusion and reveals such cooperativity in several existing data sets. The theory is further applied to establish connections between molecular constituents of synapses and synaptic function. The theory allows competing hypotheses of short-term plasticity to be tested and identifies the regimes where particular mechanisms of synaptic facilitation dominate or, conversely, fail to account for the existing data for the paired-pulse ratio. The derived trade-off relation between the transmission rate and fidelity shows how transmission failure can be controlled by changing the microscopic properties of the vesicle pool and SNARE complexes. The established condition for the maximal synaptic efficacy reveals that no fine tuning is needed for certain synapses to maintain near-optimal transmission. We discuss the limitations of the theory and propose possible routes to extend it. These results provide a quantitative basis for the notion that the molecular-level properties of synapses are crucial determinants of the computational and information-processing functions in synaptic transmission.

Multiscale dynamic mean field (MDMF) model relates resting-state brain dynamics with local cortical excitatory-inhibitory neurotransmitter homeostasis

Previous computational models have related spontaneous resting-state brain activity with local excitatory–inhibitory balance in neuronal populations. However, how underlying neurotransmitter kinetics associated with E–I balance govern resting-state spontaneous brain dynamics remains unknown. Understanding the mechanisms by virtue of which fluctuations in neurotransmitter concentrations, a hallmark of a variety of clinical conditions, relate to functional brain activity is of critical importance. We propose a multiscale dynamic mean field (MDMF) model—a system of coupled differential equations for capturing the synaptic gating dynamics in excitatory and inhibitory neural populations as a function of neurotransmitter kinetics. Individual brain regions are modeled as population of MDMF and are connected by realistic connection topologies estimated from diffusion tensor imaging data. First, MDMF successfully predicts resting-state functional connectivity. Second, our results show that optimal range of glutamate and GABA neurotransmitter concentrations subserve as the dynamic working point of the brain, that is, the state of heightened metastability observed in empirical blood-oxygen-level-dependent signals. Third, for predictive validity the network measures of segregation (modularity and clustering coefficient) and integration (global efficiency and characteristic path length) from existing healthy and pathological brain network studies could be captured by simulated functional connectivity from an MDMF model.

How changes in neurotransmitter kinetics impact the organization of large-scale neurocognitive networks is an open question in neuroscience. Here, we propose a multiscale dynamic mean field (MDMF) model that incorporates biophysically realistic kinetic parameters of receptor binding in a dynamic mean field model and captures brain dynamics from the “whole brain.” MDMF could reliably reproduce the resting-state brain functional connectivity patterns. Further employing graph theoretic methods, MDMF could qualitatively explain the idiosyncrasies of network integration and segregation measures reported by previous clinical studies.

A Complex-Valued Oscillatory Neural Network for Storage and Retrieval of Multidimensional Aperiodic Signals

Recurrent neural networks with associative memory properties are typically based on fixed-point dynamics, which is fundamentally distinct from the oscillatory dynamics of the brain. There have been proposals for oscillatory associative memories, but here too, in the majority of cases, only binary patterns are stored as oscillatory states in the network. Oscillatory neural network models typically operate at a single/common frequency. At multiple frequencies, even a pair of oscillators with real coupling exhibits rich dynamics of Arnold tongues, not easily harnessed to achieve reliable memory storage and retrieval. Since real brain dynamics comprises of a wide range of spectral components, there is a need for oscillatory neural network models that operate at multiple frequencies. We propose an oscillatory neural network that can model multiple time series simultaneously by performing a Fourier-like decomposition of the signals. We show that these enhanced properties of a network of Hopf oscillators become possible by operating in the complex-variable domain. In this model, the single neural oscillator is modeled as a Hopf oscillator, with adaptive frequency and dynamics described over the complex domain. We propose a novel form of coupling, dubbed "power coupling," between complex Hopf oscillators. With power coupling, expressed naturally only in the complex-variable domain, it is possible to achieve stable (normalized) phase relationships in a network of multifrequency oscillators. Network connections are trained either by Hebb-like learning or by delta rule, adapted to the complex domain. The network is capable of modeling N-channel electroencephalogram time series with high accuracy and shows the potential as an effective model of large-scale brain dynamics.

Assessment of optogenetically-driven strategies for prosthetic restoration of cortical vision in large-scale neural simulation of V1

The neural encoding of visual features in primary visual cortex (V1) is well understood, with strong correlates to low-level perception, making V1 a strong candidate for vision restoration through neuroprosthetics. However, the functional relevance of neural dynamics evoked through external stimulation directly imposed at the cortical level is poorly understood. Furthermore, protocols for designing cortical stimulation patterns that would induce a naturalistic perception of the encoded stimuli have not yet been established. Here, we demonstrate a proof of concept by solving these issues through a computational model, combining (1) a large-scale spiking neural network model of cat V1 and (2) a virtual prosthetic system transcoding the visual input into tailored light-stimulation patterns which drive in situ the optogenetically modified cortical tissue. Using such virtual experiments, we design a protocol for translating simple Fourier contrasted stimuli (gratings) into activation patterns of the optogenetic matrix stimulator. We then quantify the relationship between spatial configuration of the imposed light pattern and the induced cortical activity. Our simulations in the absence of visual drive (simulated blindness) show that optogenetic stimulation with a spatial resolution as low as 100 [Formula: see text]m, and light intensity as weak as [Formula: see text] photons/s/cm[Formula: see text] is sufficient to evoke activity patterns in V1 close to those evoked by normal vision.

On the potential role of lateral connectivity in retinal anticipation

We analyse the potential effects of lateral connectivity (amacrine cells and gap junctions) on motion anticipation in the retina. Our main result is that lateral connectivity can-under conditions analysed in the paper-trigger a wave of activity enhancing the anticipation mechanism provided by local gain control (Berry et al. in Nature 398(6725):334-338, 1999; Chen et al. in J. Neurosci. 33(1):120-132, 2013). We illustrate these predictions by two examples studied in the experimental literature: differential motion sensitive cells (Baccus and Meister in Neuron 36(5):909-919, 2002) and direction sensitive cells where direction sensitivity is inherited from asymmetry in gap junctions connectivity (Trenholm et al. in Nat. Neurosci. 16:154-156, 2013). We finally present reconstructions of retinal responses to 2D visual inputs to assess the ability of our model to anticipate motion in the case of three different 2D stimuli.

Local glutamate-mediated dendritic plateau potentials change the state of the cortical pyramidal neuron

Dendritic spikes in thin dendritic branches (basal and oblique dendrites) are traditionally inferred from spikelets measured in the cell body. Here, we used laser-spot voltage-sensitive dye imaging in cortical pyramidal neurons (rat brain slices) to investigate the voltage waveforms of dendritic potentials occurring in response to spatially restricted glutamatergic inputs. Local dendritic potentials lasted 200-500 ms and propagated to the cell body, where they caused sustained 10- to 20-mV depolarizations. Plateau potentials propagating from dendrite to soma and action potentials propagating from soma to dendrite created complex voltage waveforms in the middle of the thin basal dendrite, comprised of local sodium spikelets, local plateau potentials, and backpropagating action potentials, superimposed on each other. Our model replicated these voltage waveforms across a gradient of glutamatergic stimulation intensities. The model then predicted that somatic input resistance (Rin) and membrane time constant (tau) may be reduced during dendritic plateau potential. We then tested these model predictions in real neurons and found that the model correctly predicted the direction of Rin and tau change but not the magnitude. In summary, dendritic plateau potentials occurring in basal and oblique branches put pyramidal neurons into an activated neuronal state ("prepared state"), characterized by depolarized membrane potential and smaller but faster membrane responses. The prepared state provides a time window of 200-500 ms, during which cortical neurons are particularly excitable and capable of following afferent inputs. At the network level, this predicts that sets of cells with simultaneous plateaus would provide cellular substrate for the formation of functional neuronal ensembles.NEW & NOTEWORTHY In cortical pyramidal neurons, we recorded glutamate-mediated dendritic plateau potentials with voltage imaging and created a computer model that recreated experimental measures from dendrite and cell body. Our model made new predictions, which were then tested in experiments. Plateau potentials profoundly change neuronal state: a plateau potential triggered in one basal dendrite depolarizes the soma and shortens membrane time constant, making the cell more susceptible to firing triggered by other afferent inputs.

A system identification analysis of optogenetically evoked electrocorticography and cerebral blood flow responses

OBJECTIVE

The main objective of this research was to study the coupling between neural circuits and the vascular network in the cortex of small rodents from system engineering point of view and generate a mathematical model for the dynamics of neurovascular coupling. The model was adopted to implement closed-loop blood flow control algorithms.

APPROACH

We used a combination of advanced technologies including optogenetics, electrocorticography, and optical coherence tomography to stimulate selected populations of neurons and simultaneously record induced electrocorticography and hemodynamic signals. We adopted system identification methods to analyze the acquired data and investigate the relation between optogenetic neural activation and consequential electrophysiology and blood flow responses.

MAIN RESULTS

We showed that the developed model, once trained by the acquired data, could successfully regenerate subtle spatio-temporal features of evoked electrocorticography and cerebral blood flow responses following an onset of optogenetic stimulation.

SIGNIFICANCE

The long term goal of this research is to open a new line for computational analysis of neurovascular coupling particularly in pathologies where the normal process of blood flow regulation in the central nervous system is disrupted including Alzheimer's disease.

A Computational Model to Investigate GABA-Activated Astrocyte Modulation of Neuronal Excitation

Gamma-aminobutyric acid (GABA) is critical for proper neural network function and can activate astrocytes to induce neuronal excitability; however, the mechanism by which astrocytes transform inhibitory signaling to excitatory enhancement remains unclear. Computational modeling can be a powerful tool to provide further understanding of how GABA-activated astrocytes modulate neuronal excitation. In the present study, we implemented a biophysical neuronal network model to investigate the effects of astrocytes on excitatory pre- and postsynaptic terminals following exposure to increasing concentrations of external GABA. The model completely describes the effects of GABA on astrocytes and excitatory presynaptic terminals within the framework of glutamatergic gliotransmission according to neurophysiological findings. Utilizing this model, our results show that astrocytes can rapidly respond to incoming GABA by inducing Ca²⁺ oscillations and subsequent gliotransmitter glutamate release. Elevation in GABA concentrations not only naturally decreases neuronal spikes but also enhances astrocytic glutamate release, which leads to an increase in astrocyte-mediated presynaptic release and postsynaptic slow inward currents. Neuronal excitation induced by GABA-activated astrocytes partly counteracts the inhibitory effect of GABA. Overall, the model helps to increase knowledge regarding the involvement of astrocytes in neuronal regulation using simulated bath perfusion of GABA, which may be useful for exploring the effects of GABA-type antiepileptic drugs.

Energy features in spontaneous up and down oscillations

Spontaneous brain activities consume most of the brain's energy. So if we want to understand how the brain operates, we must take into account these spontaneous activities. Up and down transitions of membrane potentials are considered to be one of significant spontaneous activities. This kind of oscillation always shows bistable and bimodal distribution of membrane potentials. Our previous theoretical studies on up and down oscillations mainly looked at the ion channel dynamics. In this paper, we focus on energy feature of spontaneous up and down transitions based on a network model and its simulation. The simulated results indicate that the energy is a robust index and distinguishable of excitatory and inhibitory neurons. Meanwhile, one the whole, energy consumption of neurons shows bistable feature and bimodal distribution as well as the membrane potential, which turns out that the indicator of energy consumption encodes up and down states in this spontaneous activity. In detail, energy consumption mainly occurs during up states temporally, and mostly concentrates inside neurons rather than synapses spatially. The stimulation related energy is small, indicating that energy consumption is not driven by external stimulus, but internal spontaneous activity. This point of view is also consistent with brain imaging results. Through the observation and analysis of the findings, we prove the validity of the model again, and we can further explore the energy mechanism of more spontaneous activities.

Axonal Na+ channels detect and transmit levels of input synchrony in local brain circuits

Sensory processing requires mechanisms of fast coincidence detection to discriminate synchronous from asynchronous inputs. Spike threshold adaptation enables such a discrimination but is ineffective in transmitting this information to the network. We show here that presynaptic axonal sodium channels read and transmit precise levels of input synchrony to the postsynaptic cell by modulating the presynaptic action potential (AP) amplitude. As a consequence, synaptic transmission is facilitated at cortical synapses when the presynaptic spike is produced by synchronous inputs. Using dual soma-axon recordings, imaging, and modeling, we show that this facilitation results from enhanced AP amplitude in the axon due to minimized inactivation of axonal sodium channels. Quantifying local circuit activity and using network modeling, we found that spikes induced by synchronous inputs produced a larger effect on network activity than spikes induced by asynchronous inputs. Therefore, this input synchrony-dependent facilitation may constitute a powerful mechanism, regulating synaptic transmission at proximal synapses.

The Unexplored Territory of Neural Models: Potential Guides for Exploring the Function of Metabotropic Neuromodulation

The space of possible neural models is enormous and under-explored. Single cell computational neuroscience models account for a range of dynamical properties of membrane potential, but typically do not address network function. In contrast, most models focused on network function address the dimensions of excitatory weight matrices and firing thresholds without addressing the complexities of metabotropic receptor effects on intrinsic properties. There are many under-explored dimensions of neural parameter space, and the field needs a framework for representing what has been explored and what has not. Possible frameworks include maps of parameter spaces, or efforts to categorize the fundamental elements and molecules of neural circuit function. Here we review dimensions that are under-explored in network models that include the metabotropic modulation of synaptic plasticity and presynaptic inhibition, spike frequency adaptation due to calcium-dependent potassium currents, and afterdepolarization due to calcium-sensitive non-specific cation currents and hyperpolarization activated cation currents. Neuroscience research should more effectively explore possible functional models incorporating under-explored dimensions of neural function.

Dynamic clamp constructed phase diagram for the Hodgkin and Huxley model of excitability

Excitability-a threshold-governed transient in transmembrane voltage-is a fundamental physiological process that controls the function of the heart, endocrine, muscles, and neuronal tissues. The 1950s Hodgkin and Huxley explicit formulation provides a mathematical framework for understanding excitability, as the consequence of the properties of voltage-gated sodium and potassium channels. The Hodgkin-Huxley model is more sensitive to parametric variations of protein densities and kinetics than biological systems whose excitability is apparently more robust. It is generally assumed that the model's sensitivity reflects missing functional relations between its parameters or other components present in biological systems. Here we experimentally assembled excitable membranes using the dynamic clamp and voltage-gated potassium ionic channels (Kv1.3) expressed in Xenopus oocytes. We take advantage of a theoretically derived phase diagram, where the phenomenon of excitability is reduced to two dimensions defined as combinations of the Hodgkin-Huxley model parameters, to examine functional relations in the parameter space. Moreover, we demonstrate activity dependence and hysteretic dynamics over the phase diagram due to the impacts of complex slow inactivation kinetics. The results suggest that maintenance of excitability amid parametric variation is a low-dimensional, physiologically tenable control process. In the context of model construction, the results point to a potentially significant gap between high-dimensional models that capture the full measure of complexity displayed by ion channel function and the lower dimensionality that captures physiological function.

Effects of Cholinergic Neuromodulation on Thalamocortical Rhythms During NREM Sleep: A Model Study

It has been suggested that cholinergic neurons shape the oscillatory activity of the thalamocortical (TC) network in behavioral and electrophysiological experiments. However, theoretical modeling demonstrating how cholinergic neuromodulation of thalamocortical rhythms during non-rapid eye movement (NREM) sleep might occur has been lacking. In this paper, we first develop a novel computational model (TC-ACH) by incorporating a cholinergic neuron population (CH) into the classical thalamo-cortical circuitry, where connections between populations are modeled in accordance with existing knowledge. The neurotransmitter acetylcholine (ACH) released by neurons in CH, which is able to change the discharge activity of thalamocortical neurons, is the primary focus of our work. Simulation results with our TC-ACH model reveal that the cholinergic projection activity is a key factor in modulating oscillation patterns in three ways: (1) transitions between different patterns of thalamocortical oscillations are dramatically modulated through diverse projection pathways; (2) the model expresses a stable spindle oscillation state with certain parameter settings for the cholinergic projection from CH to thalamus, and more spindles appear when the strength of cholinergic input from CH to thalamocortical neurons increases; (3) the duration of oscillation patterns during NREM sleep including K-complexes, spindles, and slow oscillations is longer when cholinergic input from CH to thalamocortical neurons becomes stronger. Our modeling results provide insights into the mechanisms by which the sleep state is controlled, and provide a theoretical basis for future experimental and clinical studies.

Statistical data assimilation for estimating electrophysiology simultaneously with connectivity within a biological neuronal network

A method of data assimilation (DA) is employed to estimate electrophysiological parameters of neurons simultaneously with their synaptic connectivity in a small model biological network. The DA procedure is cast as an optimization, with a cost function consisting of both a measurement error and a model error term. An iterative reweighting of these terms permits a systematic method to identify the lowest minimum, within a local region of state space, on the surface of a nonconvex cost function. In the model, two sets of parameter values are associated with two particular functional modes of network activity: simultaneous firing of all neurons and a pattern-generating mode wherein the neurons burst in sequence. The DA procedure is able to recover these modes if: (i) the stimulating electrical currents have chaotic waveforms and (ii) the measurements consist of the membrane voltages of all neurons in the circuit. Further, this method is able to prune a model of unnecessarily high dimensionality to a representation that contains the maximum dimensionality required to reproduce the provided measurements. This paper offers a proof-of-concept that DA has the potential to inform laboratory designs for estimating properties in small and isolatable functional circuits.

Cholinergic Modulation Promotes Attentional Modulation in Primary Visual Cortex- A Modeling Study

Attention greatly influences sensory neural processing by enhancing firing rates of neurons that represent the attended stimuli and by modulating their tuning properties. The cholinergic system is believed to partly mediate the attention contingent improvement of cortical processing by influencing neuronal excitability, synaptic transmission and neural network characteristics. Here, we used a biophysically based model to investigate the mechanisms by which cholinergic system influences sensory information processing in the primary visual cortex (V1) layer 4C. The physiological properties and architectures of our model were inspired by experimental data and include feed-forward input from dorsal lateral geniculate nucleus that sets up orientation preference in V1 neural responses. When including a cholinergic drive, we found significant sharpening in orientation selectivity, desynchronization of LFP gamma power and spike-field coherence, decreased response variability and correlation reduction mostly by influencing intracortical interactions and by increasing inhibitory drive. Our results indicated that these effects emerged due to changes specific to the behavior of the inhibitory neurons. The behavior of our model closely resembles the effects of attention on neural activities in monkey V1. Our model suggests precise mechanisms through which cholinergic modulation may mediate the effects of attention in the visual cortex.

Phenomenological models of NaV1.5. A side by side, procedural, hands-on comparison between Hodgkin-Huxley and kinetic formalisms

Computational models of ion channels represent the building blocks of conductance-based, biologically inspired models of neurons and neural networks. Ion channels are still widely modelled by means of the formalism developed by the seminal work of Hodgkin and Huxley (HH), although the electrophysiological features of the channels are currently known to be better fitted by means of kinetic Markov-type models. The present study is aimed at showing why simplified Markov-type kinetic models are more suitable for ion channels modelling as compared to HH ones, and how a manual optimization process can be rationally carried out for both. Previously published experimental data of an illustrative ion channel (Na_V1.5) are exploited to develop a step by step optimization of the two models in close comparison. A conflicting practical limitation is recognized for the HH model, which only supplies one parameter to model two distinct electrophysiological behaviours. In addition, a step by step procedure is provided to correctly optimize the kinetic Markov-type model. Simplified Markov-type kinetic models are currently the best option to closely approximate the known complexity of the macroscopic currents of ion channels. Their optimization can be achieved through a rationally guided procedure, and allows to obtain models with a computational burden that is comparable with HH models one.

Linear response in neuronal networks: From neurons dynamics to collective response

We review two examples where the linear response of a neuronal network submitted to an external stimulus can be derived explicitly, including network parameters dependence. This is done in a statistical physicslike approach where one associates, to the spontaneous dynamics of the model, a natural notion of Gibbs distribution inherited from ergodic theory or stochastic processes. These two examples are the Amari-Wilson-Cowan model [S. Amari, Syst. Man Cybernet. SMC-2, 643-657 (1972); H. R. Wilson and J. D. Cowan, Biophys. J. 12, 1-24 (1972)] and a conductance based Integrate and Fire model [M. Rudolph and A. Destexhe, Neural Comput. 18, 2146-2210 (2006); M. Rudolph and A. Destexhe, Neurocomputing 70(10-12), 1966-1969 (2007)].

Intrinsic temporal tuning of neurons in the optic tectum is shaped by multisensory experience

For a biological neural network to be functional, its neurons need to be connected with synapses of appropriate strength, and each neuron needs to appropriately respond to its synaptic inputs. This second aspect of network tuning is maintained by intrinsic plasticity; yet it is often considered secondary to changes in connectivity and mostly limited to adjustments of overall excitability of each neuron. Here we argue that even nonoscillatory neurons can be tuned to inputs of different temporal dynamics and that they can routinely adjust this tuning to match the statistics of their synaptic activation. Using the dynamic clamp technique, we show that, in the tectum of Xenopus tadpole, neurons become selective for faster inputs when animals are exposed to fast visual stimuli but remain responsive to longer inputs in animals exposed to slower, looming, or multisensory stimulation. We also report a homeostatic cotuning between synaptic and intrinsic temporal properties of individual tectal cells. These results expand our understanding of intrinsic plasticity in the brain and suggest that there may exist an additional dimension of network tuning that has been so far overlooked.NEW & NOTEWORTHY We use dynamic clamp to show that individual neurons in the tectum of Xenopus tadpoles are selectively tuned to either shorter (more synchronous) or longer (less synchronous) synaptic inputs. We also demonstrate that this intrinsic temporal tuning is strongly shaped by sensory experiences. This new phenomenon, which is likely to be mediated by changes in sodium channel inactivation, is bound to have important consequences for signal processing and the development of local recurrent connections.

Curated Model Development Using NEUROiD: A Web-Based NEUROmotor Integration and Design Platform

Decades of research on neuromotor circuits and systems has provided valuable information on neuronal control of movement. Computational models of several elements of the neuromotor system have been developed at various scales, from sub-cellular to system. While several small models abound, their structured integration is the key to building larger and more biologically realistic models which can predict the behavior of the system in different scenarios. This effort calls for integration of elements across neuroscience and musculoskeletal biomechanics. There is also a need for development of methods and tools for structured integration that yield larger in silico models demonstrating a set of desired system responses. We take a small step in this direction with the NEUROmotor integration and Design (NEUROiD) platform. NEUROiD helps integrate results from motor systems anatomy, physiology, and biomechanics into an integrated neuromotor system model. Simulation and visualization of the model across multiple scales is supported. Standard electrophysiological operations such as slicing, current injection, recording of membrane potential, and local field potential are part of NEUROiD. The platform allows traceability of model parameters to primary literature. We illustrate the power and utility of NEUROiD by building a simple ankle model and its controlling neural circuitry by curating a set of published components. NEUROiD allows researchers to utilize remote high-performance computers for simulation, while controlling the model using a web browser.

Dendritic computations captured by an effective point neuron model

Modeling single-neuron dynamics is the first step to quantitatively understand brain computation. Yet, the existing point neuron models fail to capture dendritic effects, which are crucial for neuronal information processing. We derive an effective point neuron model, which incorporates an additional synaptic integration current arising from the nonlinear interaction between synaptic currents across spatial dendrites. Our model captures the somatic voltage response of a neuron with complex dendrites and is capable of performing rich dendritic computations. Besides its computational efficiency in simulations, our model suggests reexamination of previous studies involving the decomposition of excitatory and inhibitory synaptic inputs based on the existing point neuron framework, e.g., the inhibition is often underestimated in experiment.

Complex dendrites in general present formidable challenges to understanding neuronal information processing. To circumvent the difficulty, a prevalent viewpoint simplifies the neuronal morphology as a point representing the soma, and the excitatory and inhibitory synaptic currents originated from the dendrites are treated as linearly summed at the soma. Despite its extensive applications, the validity of the synaptic current description remains unclear, and the existing point neuron framework fails to characterize the spatiotemporal aspects of dendritic integration supporting specific computations. Using electrophysiological experiments, realistic neuronal simulations, and theoretical analyses, we demonstrate that the traditional assumption of linear summation of synaptic currents is oversimplified and underestimates the inhibition effect. We then derive a form of synaptic integration current within the point neuron framework to capture dendritic effects. In the derived form, the interaction between each pair of synaptic inputs on the dendrites can be reliably parameterized by a single coefficient, suggesting the inherent low-dimensional structure of dendritic integration. We further generalize the form of synaptic integration current to capture the spatiotemporal interactions among multiple synaptic inputs and show that a point neuron model with the synaptic integration current incorporated possesses the computational ability of a spatial neuron with dendrites, including direction selectivity, coincidence detection, logical operation, and a bilinear dendritic integration rule discovered in experiment. Our work amends the modeling of synaptic inputs and improves the computational power of a modeling neuron within the point neuron framework.

Alternating activity patterns and a chimeralike state in a network of globally coupled excitable Morris-Lecar neurons

Spatiotemporal chaos collapses to either a rest state or a propagating pulse in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Adding global varying synaptic coupling to the ring network reveals complex transient behavior. Spatiotemporal chaos collapses into a transient pulse that reinitiates spatiotemporal chaos to allow sequential pattern switching until a collapse to the rest state. A domain of irregular neuron activity coexists with a domain of inactive neurons forming a transient chimeralike state. Transient spatial localization of the chimeralike state is observed for stronger synapses.

Leveraging heterogeneity for neural computation with fading memory in layer 2/3 cortical microcircuits

Complexity and heterogeneity are intrinsic to neurobiological systems, manifest in every process, at every scale, and are inextricably linked to the systems' emergent collective behaviours and function. However, the majority of studies addressing the dynamics and computational properties of biologically inspired cortical microcircuits tend to assume (often for the sake of analytical tractability) a great degree of homogeneity in both neuronal and synaptic/connectivity parameters. While simplification and reductionism are necessary to understand the brain's functional principles, disregarding the existence of the multiple heterogeneities in the cortical composition, which may be at the core of its computational proficiency, will inevitably fail to account for important phenomena and limit the scope and generalizability of cortical models. We address these issues by studying the individual and composite functional roles of heterogeneities in neuronal, synaptic and structural properties in a biophysically plausible layer 2/3 microcircuit model, built and constrained by multiple sources of empirical data. This approach was made possible by the emergence of large-scale, well curated databases, as well as the substantial improvements in experimental methodologies achieved over the last few years. Our results show that variability in single neuron parameters is the dominant source of functional specialization, leading to highly proficient microcircuits with much higher computational power than their homogeneous counterparts. We further show that fully heterogeneous circuits, which are closest to the biophysical reality, owe their response properties to the differential contribution of different sources of heterogeneity.

Determination of effective synaptic conductances using somatic voltage clamp

The interplay between excitatory and inhibitory neurons imparts rich functions of the brain. To understand the synaptic mechanisms underlying neuronal computations, a fundamental approach is to study the dynamics of excitatory and inhibitory synaptic inputs of each neuron. The traditional method of determining input conductance, which has been applied for decades, employs the synaptic current-voltage (I-V) relation obtained via voltage clamp. Due to the space clamp effect, the measured conductance is different from the local conductance on the dendrites. Therefore, the interpretation of the measured conductance remains to be clarified. Using theoretical analysis, electrophysiological experiments, and realistic neuron simulations, here we demonstrate that there does not exist a transform between the local conductance and the conductance measured by the traditional method, due to the neglect of a nonlinear interaction between the clamp current and the synaptic current in the traditional method. Consequently, the conductance determined by the traditional method may not correlate with the local conductance on the dendrites, and its value could be unphysically negative as observed in experiment. To circumvent the challenge of the space clamp effect and elucidate synaptic impact on neuronal information processing, we propose the concept of effective conductance which is proportional to the local conductance on the dendrite and reflects directly the functional influence of synaptic inputs on somatic membrane potential dynamics, and we further develop a framework to determine the effective conductance accurately. Our work suggests re-examination of previous studies involving conductance measurement and provides a reliable approach to assess synaptic influence on neuronal computation.

To understand synaptic mechanisms underlying neuronal computations, a fundamental approach is to use voltage clamp to measure the dynamics of excitatory and inhibitory input conductances. Due to the space clamp effect, the measured conductance in general deviates from the local input conductance on the dendrites, hence its biological interpretation is questionable, as we demonstrate in this work. We further propose the concept of effective conductance that is proportional to the local input conductance on the dendrites and reflects directly the synaptic impact on spike generation, and develop a framework to determine the effective conductance reliably. Our work provides a biologically plausible metric for elucidating synaptic influence on neuronal computation under the constraint of the space clamp effect.