Stochastic and deterministic dynamics of intrinsically irregular firing in cortical inhibitory interneurons

A thermodynamical model of non-deterministic computation in cortical neural networks

Neuronal populations in the cerebral cortex engage in probabilistic coding, effectively encoding the state of the surrounding environment with high accuracy and extraordinary energy efficiency. A new approach models the inherently probabilistic nature of cortical neuron signaling outcomes as a thermodynamic process of non-deterministic computation. A mean field approach is used, with the trial Hamiltonian maximizing available free energy and minimizing the net quantity of entropy, compared with a reference Hamiltonian. Thermodynamic quantities are always conserved during the computation; free energy must be expended to produce information, and free energy is released during information compression, as correlations are identified between the encoding system and its surrounding environment. Due to the relationship between the Gibbs free energy equation and the Nernst equation, any increase in free energy is paired with a local decrease in membrane potential. As a result, this process of thermodynamic computation adjusts the likelihood of each neuron firing an action potential. This model shows that non-deterministic signaling outcomes can be achieved by noisy cortical neurons, through an energy-efficient computational process that involves optimally redistributing a Hamiltonian over some time evolution. Calculations demonstrate that the energy efficiency of the human brain is consistent with this model of non-deterministic computation, with net entropy production far too low to retain the assumptions of a classical system.

A universal workflow for creation, validation, and generalization of detailed neuronal models

Detailed single-neuron modeling is widely used to study neuronal functions. While cellular and functional diversity across the mammalian cortex is vast, most of the available computational tools focus on a limited set of specific features characteristic of a single neuron. Here, we present a generalized automated workflow for the creation of robust electrical models and illustrate its performance by building cell models for the rat somatosensory cortex. Each model is based on a 3D morphological reconstruction and a set of ionic mechanisms. We use an evolutionary algorithm to optimize neuronal parameters to match the electrophysiological features extracted from experimental data. Then we validate the optimized models against additional stimuli and assess their generalizability on a population of similar morphologies. Compared to the state-of-the-art canonical models, our models show 5-fold improved generalizability. This versatile approach can be used to build robust models of any neuronal type.

Constrained disorder principle-based variability is fundamental for biological processes: Beyond biological relativity and physiological regulatory networks

The constrained disorder principle (CDP) defines systems based on their degree of disorder bounded by dynamic boundaries. The principle explains stochasticity in living and non-living systems. Denis Noble described the importance of stochasticity in biology, emphasizing stochastic processes at molecular, cellular, and higher levels in organisms as having a role beyond simple noise. The CDP and Noble's theories (NT) claim that biological systems use stochasticity. This paper presents the CDP and NT, discussing common notions and differences between the two theories. The paper presents the CDP-based concept of taking the disorder beyond its role in nature to correct malfunctions of systems and improve the efficiency of biological systems. The use of CDP-based algorithms embedded in second-generation artificial intelligence platforms is described. In summary, noise is inherent to complex systems and has a functional role. The CDP provides the option of using noise to improve functionality.

Controlling the spontaneous firing behavior of a neuron with astrocyte

Mounting evidence in recent years suggests that astrocytes, a sub-type of glial cells, not only serve metabolic and structural support for neurons and synapses but also play critical roles in the regulation of proper functioning of the nervous system. In this work, we investigate the effect of astrocytes on the spontaneous firing activity of a neuron through a combined model that includes a neuron-astrocyte pair. First, we show that an astrocyte may provide a kind of multistability in neuron dynamics by inducing different firing modes such as random and bursty spiking. Then, we identify the underlying mechanism of this behavior and search for the astrocytic factors that may have regulatory roles in different firing regimes. More specifically, we explore how an astrocyte can participate in the occurrence and control of spontaneous irregular spiking activity of a neuron in random spiking mode. Additionally, we systematically investigate the bursty firing regime dynamics of the neuron under the variation of biophysical facts related to the intracellular environment of the astrocyte. It is found that an astrocyte coupled to a neuron can provide a control mechanism for both spontaneous firing irregularity and burst firing statistics, i.e., burst regularity and size.

Recurrence-Based Synchronization Analysis of Weakly Coupled Bursting Neurons Under External ELF Fields

We investigate the response characteristics of a two-dimensional neuron model exposed to an externally applied extremely low frequency (ELF) sinusoidal electric field and the synchronization of neurons weakly coupled with gap junction. We find, by numerical simulations, that neurons can exhibit different spiking patterns, which are well observed in the structure of the recurrence plot (RP). We further study the synchronization between weakly coupled neurons in chaotic regimes under the influence of a weak ELF electric field. In general, detecting the phases of chaotic spiky signals is not easy by using standard methods. Recurrence analysis provides a reliable tool for defining phases even for noncoherent regimes or spiky signals. Recurrence-based synchronization analysis reveals that, even in the range of weak coupling, phase synchronization of the coupled neurons occurs and, by adding an ELF electric field, this synchronization increases depending on the amplitude of the externally applied ELF electric field. We further suggest a novel measure for RP-based phase synchronization analysis, which better takes into account the probabilities of recurrences.

Toward a More General Understanding of Bohr's Complementarity: Insights from Modeling of Ion Channels

Some contemporary theorists such as Mazzocchi, Theise and Kafatos are convinced that the reformed complementarity may redefine how we might exploit the complexity theory in 21st-century life sciences research. However, the motives behind the profound re-invention of "biological complementarity" need to be substantiated with concrete shreds of evidence about this principle's applicability in real-life science experimentation, which we found missing in the literature. This paper discusses such pieces of evidence by confronting Bohr's complementarity and ion channel modeling practice. We examine whether and to what extent this principle might assist in developing ion channel models incorporating both deterministic and stochastic solutions. According to the "mutual exclusiveness of experimental setups" version of Bohr's complementarity, this principle is needed when two mutually exclusive perspectives or approaches are right, necessary in a particular context, and are not contradictory as they arise in mutually exclusive conditions (mutually exclusive experimental or modeling setups). A detailed examination of the modeling practice reveals that both solutions are often used simultaneously in a single ion channel model, suggesting that the opposite conceptual frameworks can coexist in the same modeling setup. We concluded that Bohr's complementarity might find applications in these complex modeling setups but only through its realistic phenomenological interpretation that allows applying different modes of description regardless of the nature of the underlying ion channel opening process. Also, we propose the combined use of complementarity and Complex thinking in building the multifaceted ion channel models. Overall, this paper's results support the efforts to establish a more general form of complementarity to meet today's complexity theory-inspired life sciences modeling demands.

A dopamine gradient controls access to distributed working memory in the large-scale monkey cortex

Dopamine is required for working memory, but how it modulates the large-scale cortex is unknown. Here, we report that dopamine receptor density per neuron, measured by autoradiography, displays a macroscopic gradient along the macaque cortical hierarchy. This gradient is incorporated in a connectome-based large-scale cortex model endowed with multiple neuron types. The model captures an inverted U-shaped dependence of working memory on dopamine and spatial patterns of persistent activity observed in over 90 experimental studies. Moreover, we show that dopamine is crucial for filtering out irrelevant stimuli by enhancing inhibition from dendrite-targeting interneurons. Our model revealed that an activity-silent memory trace can be realized by facilitation of inter-areal connections and that adjusting cortical dopamine induces a switch from this internal memory state to distributed persistent activity. Our work represents a cross-level understanding from molecules and cell types to recurrent circuit dynamics underlying a core cognitive function distributed across the primate cortex.

Firing statistics in the bistable regime of neurons with homoclinic spike generation

Neuronal voltage dynamics of regularly firing neurons typically has one stable attractor: either a fixed point (like in the subthreshold regime) or a limit cycle that defines the tonic firing of action potentials (in the suprathreshold regime). In two of the three spike onset bifurcation sequences that are known to give rise to all-or-none type action potentials, however, the resting-state fixed point and limit cycle spiking can coexist in an intermediate regime, resulting in bistable dynamics. Here, noise can induce switches between the attractors, i.e., between rest and spiking, and thus increase the variability of the spike train compared to neurons with only one stable attractor. Qualitative features of the resulting spike statistics depend on the spike onset bifurcations. This paper focuses on the creation of the spiking limit cycle via the saddle-homoclinic orbit (HOM) bifurcation and derives interspike interval (ISI) densities for a conductance-based neuron model in the bistable regime. The ISI densities of bistable homoclinic neurons are found to be unimodal yet distinct from the inverse Gaussian distribution associated with the saddle-node-on-invariant-cycle bifurcation. It is demonstrated that for the HOM bifurcation the transition between rest and spiking is mainly determined along the downstroke of the action potential-a dynamical feature that is not captured by the commonly used reset neuron models. The deduced spike statistics can help to identify HOM dynamics in experimental data.

Chronic unpredictable stress induces depression-related behaviors by suppressing AgRP neuron activity

Previous studies have shown that AgRP neurons in the arcuate nucleus (ARC) respond to energy deficits and play a key role in the control of feeding behavior and metabolism. Here, we demonstrate that chronic unpredictable stress, an animal model of depression, decreases spontaneous firing rates, increases firing irregularity and alters the firing properties of AgRP neurons in both male and female mice. These changes are associated with enhanced inhibitory synaptic transmission and reduced intrinsic neuronal excitability. Chemogenetic inhibition of AgRP neurons increases susceptibility to subthreshold unpredictable stress. Conversely, chemogenetic activation of AgRP neurons completely reverses anhedonic and despair behaviors induced by chronic unpredictable stress. These results indicate that chronic stress induces maladaptive synaptic and intrinsic plasticity, leading to hypoactivity of AgRP neurons and subsequently causing behavioral changes. Our findings suggest that AgRP neurons in the ARC are a key component of neural circuitry involved in mediating depression-related behaviors and that increasing AgRP neuronal activity coule be a novel and effective treatment for depression.

Characterizing the brain's dynamical response from scalp-level neural electrical signals: a review of methodology development

The brain displays dynamical system behaviors at various levels that are functionally and cognitively relevant. Ample researches have examined how the dynamical properties of brain activity reflect the neural cognitive working mechanisms. A prevalent approach in this field is to extract the trial-averaged brain electrophysiological signals as a representation of the dynamical response of the complex neural system to external stimuli. However, the responses are intrinsically variable in latency from trial to trial. The variability compromises the accuracy of the detected dynamical response pattern based on trial-averaged approach, which may mislead subsequent modelling works. More accurate characterization of the brain's dynamical response incorporating single trial variability information is of profound significance in deepening our understanding of neural cognitive dynamics and brain's working principles. Various methods have been attempted to address the trial-to-trial asynchrony issue in order to achieve an improved representation of the dynamical response. We review the latest development of methodology in this area and the contribution of latency variability-based decomposition and reconstruction of dynamical response to neural cognitive researches.

Chronic mild stress alters synaptic plasticity in the nucleus accumbens through GSK3β-dependent modulation of Kv4.2 channels

Although major depressive disorder (MDD) is highly prevalent, its pathophysiology is poorly understood. Recent evidence suggests that glycogen-synthase kinase 3β (GSK3β) plays a key role in memory formation, yet its role in mood regulation remains controversial. Here, we investigated whether GSK3β activity in the nucleus accumbens (NAc) is associated with depression-like behaviors and synaptic plasticity. We performed whole-cell patch-clamp recordings of medium spiny neurons (MSNs) in the NAc and determined the role of GSK3β in spike timing-dependent long-term potentiation (tLTP) in the chronic unpredictable mild stress (CUMS) mouse model of depression. To assess the specific role of GSK3β in tLTP, we used in vivo genetic silencing by an adeno-associated viral vector (AAV2) short hairpin RNA against GSK3β. In addition, we examined the role of the voltage-gated potassium Kv4.2 subunit, a molecular determinant of A-type K⁺ currents, as a potential downstream target of GSK3β. We found increased levels of active GSK3β and augmented tLTP in CUMS mice, a phenotype that was prevented by selective GSK3β knockdown. Furthermore, knockdown of GSK3β in the NAc ameliorated depressive-like behavior in CUMS mice. Electrophysiological, immunohistochemical, biochemical, and pharmacological experiments revealed that inhibition of the Kv4.2 channel through direct phosphorylation at Ser-616 mediated the GSK3β-dependent tLTP changes in CUMS mice. Our results identify GSK3β regulation of Kv4.2 channels as a molecular mechanism of MSN maladaptive plasticity underlying depression-like behaviors and suggest that the GSK3β-Kv4.2 axis may be an attractive therapeutic target for MDD.

Persistent sodium current blockers can suppress seizures caused by loss of low-threshold D-type potassium currents: Predictions from an in silico study of Kv1 channel disorders

Objective

Ion channels belonging to subfamily A of voltage‐gated potassium channels (K_v1) are highly expressed on axons, where they play a key role in determining resting membrane potential, in shaping action potentials, and in modulating action potential frequency during repetitive neuronal firing. We aimed to study the genesis of seizures caused by mutations affecting K_v1 channels and searched for potential therapeutic targets.

Methods

We used a novel in silico model, the laminar cortex model (LCM), to examine changes in neuronal excitability and network dynamics associated with loss‐of‐function mutations in K_v1 channels. The LCM simulates the activities of a network of tens of thousands of interconnected neurons and incorporates the kinetics of 11 types of ion channel and three classes of neurotransmitter receptor. Changes in two types of potassium currents conducted by K_v1 channels were examined: slowly inactivating D‐type currents and rapidly inactivating A‐type currents. Effects on neuronal firing rate, action potential shape, and neuronal oscillation state were evaluated. A systematic parameter scan was performed to identify parameter changes that can reverse the effects of the changes.

Results

Reduced axonal D‐type currents led to lower firing threshold and widened action potentials, both lowering the seizure threshold. Two potential therapeutic targets for treating seizures caused by loss‐of‐function changes in K_v1 channels were identified: persistent sodium channels and NMDA receptors. Blocking persistent sodium channels restored the firing threshold and reduced action potential width. NMDA receptor antagonists reduced excitatory postsynaptic currents from excessive glutamate release related to widened action potentials.

Significance

Riluzole reduces persistent sodium currents and excitatory postsynaptic currents from NMDA receptor activation. Our results suggest that this FDA‐approved drug can be repurposed to treat epilepsies caused by mutations affecting axonal K_v1 channels.

Cortical reliability amid noise and chaos

Typical responses of cortical neurons to identical sensory stimuli appear highly variable. It has thus been proposed that the cortex primarily uses a rate code. However, other studies have argued for spike-time coding under certain conditions. The potential role of spike-time coding is directly limited by the internally generated variability of cortical circuits, which remains largely unexplored. Here, we quantify this internally generated variability using a biophysical model of rat neocortical microcircuitry with biologically realistic noise sources. We find that stochastic neurotransmitter release is a critical component of internally generated variability, causing rapidly diverging, chaotic recurrent network dynamics. Surprisingly, the same nonlinear recurrent network dynamics can transiently overcome the chaos in response to weak feed-forward thalamocortical inputs, and support reliable spike times with millisecond precision. Our model shows that the noisy and chaotic network dynamics of recurrent cortical microcircuitry are compatible with stimulus-evoked, millisecond spike-time reliability, resolving a long-standing debate.

Kv4.2 channel activity controls intrinsic firing dynamics of arcuate kisspeptin neurons

Key points

Neurons in the hypothalamus of the brain which secrete the peptide kisspeptin are important regulators of reproduction, and normal reproductive development.

Electrical activity, in the form of action potentials, or spikes, leads to secretion of peptides and neurotransmitters, influencing the activity of downstream neurons; in kisspeptin neurons, this activity is highly irregular, but the mechanism of this is not known.

In this study, we show that irregularity depends on the presence of a particular type of potassium ion channel in the membrane, which opens transiently in response to electrical excitation.

The results contribute to understanding how kisspeptin neurons generate and time their membrane potential spikes, and how reliable this process is.

Improved understanding of the activity of kisspeptin neurons, and how it shapes their secretion of peptides, is expected to lead to better treatment for reproductive dysfunction and disorders of reproductive development.

Abstract

Kisspeptin neurons in the hypothalamus are critically involved in reproductive function, via their effect on GnRH neuron activity and consequent gonadotropin release. Kisspeptin neurons show an intrinsic irregularity of firing, but the mechanism of this remains unclear. To address this, we carried out targeted whole‐cell patch‐clamp recordings of kisspeptin neurons in the arcuate nucleus (Kiss1^Arc), in brain slices isolated from adult male Kiss‐Cre:tdTomato mice. Cells fired irregularly in response to constant current stimuli, with a wide range of spike time variability, and prominent subthreshold voltage fluctuations. In voltage clamp, both a persistent sodium (NaP) current and a fast transient (A‐type) potassium current were apparent, activating at potentials just below the threshold for spiking. These currents have also previously been described in irregular‐spiking cortical interneurons, in which the A‐type current, mediated by Kv4 channels, interacts with NaP current to generate complex dynamics of the membrane potential, and irregular firing. In Kiss1^Arc neurons, A‐type current was blocked by phrixotoxin, a specific blocker of Kv4.2/4.3 channels, and consistent expression of Kv4.2 transcripts was detected by single‐cell RT‐PCR. In addition, firing irregularity was correlated to the density of A‐type current in the membrane. Using conductance injection, we demonstrated that adding Kv4‐like potassium conductance (g_Kv4) to a cell produces a striking increase in firing irregularity, and excitability is reduced, while subtracting g_Kv4 has the opposite effects. Thus, we propose that Kv4 interacting dynamically with NaP is a key determinant of the irregular firing behaviour of Kiss1^Arc neurons, shaping their physiological function in gonadotropin release.

Neurons in the hypothalamus of the brain which secrete the peptide kisspeptin are important regulators of reproduction, and normal reproductive development.

Electrical activity, in the form of action potentials, or spikes, leads to secretion of peptides and neurotransmitters, influencing the activity of downstream neurons; in kisspeptin neurons, this activity is highly irregular, but the mechanism of this is not known.

In this study, we show that irregularity depends on the presence of a particular type of potassium ion channel in the membrane, which opens transiently in response to electrical excitation.

The results contribute to understanding how kisspeptin neurons generate and time their membrane potential spikes, and how reliable this process is.

Improved understanding of the activity of kisspeptin neurons, and how it shapes their secretion of peptides, is expected to lead to better treatment for reproductive dysfunction and disorders of reproductive development.

Computational models of O-LM cells are recruited by low or high theta frequency inputs depending on h-channel distributions

Although biophysical details of inhibitory neurons are becoming known, it is challenging to map these details onto function. Oriens-lacunosum/moleculare (O-LM) cells are inhibitory cells in the hippocampus that gate information flow, firing while phase-locked to theta rhythms. We build on our existing computational model database of O-LM cells to link model with function. We place our models in high-conductance states and modulate inhibitory inputs at a wide range of frequencies. We find preferred spiking recruitment of models at high (4-9 Hz) or low (2-5 Hz) theta depending on, respectively, the presence or absence of h-channels on their dendrites. This also depends on slow delayed-rectifier potassium channels, and preferred theta ranges shift when h-channels are potentiated by cyclic AMP. Our results suggest that O-LM cells can be differentially recruited by frequency-modulated inputs depending on specific channel types and distributions. This work exposes a strategy for understanding how biophysical characteristics contribute to function.

Functional Diversity of Neurotrophin Actions on the Oculomotor System

Neurotrophins play a principal role in neuronal survival and differentiation during development, but also in the maintenance of appropriate adult neuronal circuits and phenotypes. In the oculomotor system, we have demonstrated that neurotrophins are key regulators of developing and adult neuronal properties, but with peculiarities depending on each neurotrophin. For instance, the administration of NGF (nerve growth factor), BDNF (brain-derived neurotrophic factor) or NT-3 (neurotrophin-3) protects neonatal extraocular motoneurons from cell death after axotomy, but only NGF and BDNF prevent the downregulation in ChAT (choline acetyltransferase). In the adult, in vivo recordings of axotomized extraocular motoneurons have demonstrated that the delivery of NGF, BDNF or NT-3 recovers different components of the firing discharge activity of these cells, with some particularities in the case of NGF. All neurotrophins have also synaptotrophic activity, although to different degrees. Accordingly, neurotrophins can restore the axotomy-induced alterations acting selectively on different properties of the motoneuron. In this review, we summarize these evidences and discuss them in the context of other motor systems.