Systematic analysis of the contributions of stochastic voltage gated channels to neuronal noise

Response sub-additivity and variability quenching in visual cortex

Sub-additivity and variability are ubiquitous response motifs in the primary visual cortex (V1). Response sub-additivity enables the construction of useful interpretations of the visual environment, whereas response variability indicates the factors that limit the precision with which the brain can do this. There is increasing evidence that experimental manipulations that elicit response sub-additivity often also quench response variability. Here, we provide an overview of these phenomena and suggest that they may have common origins. We discuss empirical findings and recent model-based insights into the functional operations, computational objectives and circuit mechanisms underlying V1 activity. These different modelling approaches all predict that response sub-additivity and variability quenching often co-occur. The phenomenology of these two response motifs, as well as many of the insights obtained about them in V1, generalize to other cortical areas. Thus, the connection between response sub-additivity and variability quenching may be a canonical motif across the cortex.

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.

Hydrophobic Gating and 1/f Noise of the Anthrax Toxin Channel

"Pink" or 1/f noise is a natural phenomenon omnipresent in physics, economics, astrophysics, biology, and even music and languages. In electrophysiology, the stochastic activity of a number of biological ion channels and artificial nanopores could be characterized by current noise with a 1/f power spectral density. In the anthrax toxin channel (PA₆₃), it appears as fast voltage-independent current interruptions between conducting and nonconducting states. This behavior hampers potential development of PA₆₃ as an ion-channel biosensor. On the bright side, the PA₆₃ flickering represents a mesmerizing phenomenon to investigate. Notably, similar 1/f fluctuations are observed in the channel-forming components of clostridial binary C2 and iota toxins, which share functional and structural similarities with the anthrax toxin channel. Similar to PA₆₃, they are evolved to translocate the enzymatic components of the toxins into the cytosol. Here, using high-resolution single-channel lipid bilayer experiments and all-atom molecular dynamic simulations, we suggest that the 1/f noise in PA₆₃ occurs as a result of "hydrophobic gating" at the ϕ-clamp region, the phenomenon earlier observed in several water-filled channels "fastened" inside by the hydrophobic belts. The ϕ-clamp is a narrow "hydrophobic ring" in the PA₆₃ lumen formed by seven or eight phenylalanine residues at position 427, conserved in the C2 and iota toxin channels, which catalyzes protein translocation. Notably, the 1/f noise remains undetected in the F427A PA₆₃ mutant. This finding can elucidate the functional purpose of 1/f noise and its possible role in the transport of the enzymatic components of binary toxins.

Circadian Modulation of Neurons and Astrocytes Controls Synaptic Plasticity in Hippocampal Area CA1

Most animal species operate according to a 24-h period set by the suprachiasmatic nucleus (SCN) of the hypothalamus. The rhythmic activity of the SCN modulates hippocampal-dependent memory, but the molecular and cellular mechanisms that account for this effect remain largely unknown. Here, we identify cell-type-specific structural and functional changes that occur with circadian rhythmicity in neurons and astrocytes in hippocampal area CA1. Pyramidal neurons change the surface expression of NMDA receptors. Astrocytes change their proximity to synapses. Together, these phenomena alter glutamate clearance, receptor activation, and integration of temporally clustered excitatory synaptic inputs, ultimately shaping hippocampal-dependent learning in vivo. We identify corticosterone as a key contributor to changes in synaptic strength. These findings highlight important mechanisms through which neurons and astrocytes modify the molecular composition and structure of the synaptic environment, contribute to the local storage of information in the hippocampus, and alter the temporal dynamics of cognitive processing.

Conserved Expression of Nav1.7 and Nav1.8 Contribute to the Spontaneous and Thermally Evoked Excitability in IL-6 and NGF-Sensitized Adult Dorsal Root Ganglion Neurons In Vitro

Sensory neurons respond to noxious stimuli by relaying information from the periphery to the central nervous system via action potentials driven by voltage-gated sodium channels, specifically Nav1.7 and Nav1.8. These channels play a key role in the manifestation of inflammatory pain. The ability to screen compounds that modulate voltage-gated sodium channels using cell-based assays assumes that key channels present in vivo is maintained in vitro. Prior electrophysiological work in vitro utilized acutely dissociated tissues, however, maintaining this preparation for long periods is difficult. A potential alternative involves multi-electrode arrays which permit long-term measurements of neural spike activity and are well suited for assessing persistent sensitization consistent with chronic pain. Here, we demonstrate that the addition of two inflammatory mediators associated with chronic inflammatory pain, nerve growth factor (NGF) and interleukin-6 (IL-6), to adult DRG neurons increases their firing rates on multi-electrode arrays in vitro. Nav1.7 and Nav1.8 proteins are readily detected in cultured neurons and contribute to evoked activity. The blockade of both Nav1.7 and Nav1.8, has a profound impact on thermally evoked firing after treatment with IL-6 and NGF. This work underscores the utility of multi-electrode arrays for pharmacological studies of sensory neurons and may facilitate the discovery and mechanistic analyses of anti-nociceptive compounds.

Theoretical Aspects of Resting-State Cardiomyocyte Communication for Multi-Nodal Nano-Actuator Pacemakers

The heart consists of billions of cardiac muscle cells-cardiomyocytes-that work in a coordinated fashion to supply oxygen and nutrients to the body. Inter-connected specialized cardiomyocytes form signaling channels through which the electrical signals are propagated throughout the heart, controlling the heart's beat to beat function of the other cardiac cells. In this paper, we study to what extent it is possible to use ordinary cardiomyocytes as communication channels between components of a recently proposed multi-nodal leadless pacemaker, to transmit data encoded in subthreshold membrane potentials. We analyze signal propagation in the cardiac infrastructure considering noise in the communication channel by performing numerical simulations based on the Luo-Rudy computational model. The Luo-Rudy model is an action potential model but describes the potential changes with time including membrane potential and action potential stages, separated by the thresholding mechanism. Demonstrating system performance, we show that cardiomyocytes can be used to establish an artificial communication system where data are reliably transmitted between 10 s of cells. The proposed subthreshold cardiac communication lays the foundation for a new intra-cardiac communication technique.

Psychoanalysis and Neuroscience: The Bridge Between Mind and Brain

In 1895 in the Project for a Scientific Psychology, Freud tried to integrate psychology and neurology in order to develop a neuroscientific psychology. Since 1880, Freud made no distinction between psychology and physiology. His papers from the end of the 1880s to 1890 were very clear on this scientific overlap: as with many of his contemporaries, Freud thought about psychology essentially as the physiology of the brain. Years later he had to surrender, realizing a technological delay, not capable of pursuing its ambitious aim, and until that moment psychoanalysis would have to use its more suitable clinical method. Also, he seemed skeptical about phrenology drift, typical of that time, in which any psychological function needed to be located in its neuroanatomical area. He could not see the progresses of neuroscience and its fruitful dialogue with psychoanalysis, which occurred also thanks to the improvements in the field of neuroimaging, which has made possible a remarkable advance in the knowledge of the mind-brain system and a better observation of the psychoanalytical theories. After years of investigations, deriving from research and clinical work of the last century, the discovery of neural networks, together with the free energy principle, we are observing under a new light psychodynamic neuroscience in its exploration of the mind-brain system. In this manuscript, we summarize the important developments of psychodynamic neuroscience, with particular regard to the free energy principle, the resting state networks, especially the Default Mode Network in its link with the Self, emphasizing our view of a bridge between psychoanalysis and neuroscience. Finally, we suggest a discussion by approaching the concept of Alpha Function, proposed by the psychoanalyst Wilfred Ruprecht Bion, continuing the association with neuroscience.

Chaos versus noise as drivers of multistability in neural networks

The multistable behavior of neural networks is actively being studied as a landmark of ongoing cerebral activity, reported in both functional Magnetic Resonance Imaging (fMRI) and electro- or magnetoencephalography recordings. This consists of a continuous jumping between different partially synchronized states in the absence of external stimuli. It is thought to be an important mechanism for dealing with sensory novelty and to allow for efficient coding of information in an ever-changing surrounding environment. Many advances have been made to understand how network topology, connection delays, and noise can contribute to building this dynamic. Little or no attention, however, has been paid to the difference between local chaotic and stochastic influences on the switching between different network states. Using a conductance-based neural model that can have chaotic dynamics, we showed that a network can show multistable dynamics in a certain range of global connectivity strength and under deterministic conditions. In the present work, we characterize the multistable dynamics when the networks are, in addition to chaotic, subject to ion channel stochasticity in the form of multiplicative (channel) or additive (current) noise. We calculate the Functional Connectivity Dynamics matrix by comparing the Functional Connectivity (FC) matrices that describe the pair-wise phase synchronization in a moving window fashion and performing clustering of FCs. Moderate noise can enhance the multistable behavior that is evoked by chaos, resulting in more heterogeneous synchronization patterns, while more intense noise abolishes multistability. In networks composed of nonchaotic nodes, some noise can induce multistability in an otherwise synchronized, nonchaotic network. Finally, we found the same results regardless of the multiplicative or additive nature of noise.

Sparse bursts optimize information transmission in a multiplexed neural code

Many cortical neurons combine the information ascending and descending the cortical hierarchy. In the classical view, this information is combined nonlinearly to give rise to a single firing-rate output, which collapses all input streams into one. We analyze the extent to which neurons can simultaneously represent multiple input streams by using a code that distinguishes spike timing patterns at the level of a neural ensemble. Using computational simulations constrained by experimental data, we show that cortical neurons are well suited to generate such multiplexing. Interestingly, this neural code maximizes information for short and sparse bursts, a regime consistent with in vivo recordings. Neurons can also demultiplex this information, using specific connectivity patterns. The anatomy of the adult mammalian cortex suggests that these connectivity patterns are used by the nervous system to maintain sparse bursting and optimal multiplexing. Contrary to firing-rate coding, our findings indicate that the physiology and anatomy of the cortex may be interpreted as optimizing the transmission of multiple independent signals to different targets.

Neuroaging through the Lens of the Resting State Networks

Resting state functional magnetic resonance imaging (rs-fMRI) allows studying spontaneous brain activity in absence of task, recording changes of Blood Oxygenation Level Dependent (BOLD) signal. rs-fMRI enables identification of brain networks also called Resting State Networks (RSNs) including the most studied Default Mode Network (DMN). The simplicity and speed of execution make rs-fMRI applicable in a variety of normal and pathological conditions. Since it does not require any task, rs-fMRI is particularly useful for protocols on patients, children, and elders, increasing participant's compliance and reducing intersubjective variability due to the task performance. rs-fMRI has shown high sensitivity in identification of RSNs modifications in several diseases also in absence of structural modifications. In this narrative review, we provide the state of the art of rs-fMRI studies about physiological and pathological aging processes. First, we introduce the background of resting state; then we review clinical findings provided by rs-fMRI in physiological aging, Mild Cognitive Impairment (MCI), Alzheimer Dementia (AD), and Late Life Depression (LLD). Finally, we suggest future directions in this field of research and its potential clinical applications.

Relationships between short and fast brain timescales

Brain electric activity exhibits two important features: oscillations with different timescales, characterized by diverse functional and psychological outcomes, and a temporal power law distribution. In order to further investigate the relationships between low- and high- frequency spikes in the brain, we used a variant of the Borsuk-Ulam theorem which states that, when we assess the nervous activity as embedded in a sphere equipped with a fractal dimension, we achieve two antipodal points with similar features (the slow and fast, scale-free oscillations). We demonstrate that slow and fast nervous oscillations mirror each other over time via a sinusoid relationship and provide, through the Bloch theorem from solid-state physics, the possible equation which links the two timescale activities. We show that, based on topological findings, nervous activities occurring in micro-levels are projected to single activities at meso- and macro-levels. This means that brain functions assessed at the higher scale of the whole brain necessarily display a counterpart in the lower ones, and vice versa. Our topological approach makes it possible to assess brain functions both based on entropy, and in the general terms of particle trajectories taking place on donut-like manifolds. Condensed brain activities might give rise to ideas and concepts by combination of different functional and anatomical levels. Furthermore, cognitive phenomena, as well as social activity can be described by the laws of quantum mechanics; memories and decisions exhibit holographic organization. In physics, the term duality refers to a case where two seemingly different systems turn out to be equivalent. This topological duality holds for all the types of spatio-temporal brain activities, independent of their inter- and intra-level relationships, strength, magnitude and boundaries, allowing us to connect the physiological manifestations of consciousness to the electric activities of the brain.

Methodology of Recurrent Laguerre-Volterra Network for Modeling Nonlinear Dynamic Systems

In this paper, we have introduced a general modeling approach for dynamic nonlinear systems that utilizes a variant of the simulated annealing algorithm for training the Laguerre-Volterra network (LVN) to overcome the local minima and convergence problems and employs a pruning technique to achieve sparse LVN representations with l₁ regularization. We tested this new approach with computer simulated systems and extended it to autoregressive sparse LVN (ASLVN) model structures that are suitable for input-output modeling of nonlinear systems that exhibit transitions in dynamic states, such as the Hodgkin-Huxley (H-H) equations of neuronal firing. Application of the proposed ASLVN to the H-H equations yields a more parsimonious input-output model with improved predictive capability that is amenable to more insightful physiological/biological interpretation.

Anti-correlations in the degree distribution increase stimulus detection performance in noisy spiking neural networks

Neuronal circuits in the rodent barrel cortex are characterized by stable low firing rates. However, recent experiments show that short spike trains elicited by electrical stimulation in single neurons can induce behavioral responses. Hence, the underlying neural networks provide stability against internal fluctuations in the firing rate, while simultaneously making the circuits sensitive to small external perturbations. Here we studied whether stability and sensitivity are affected by the connectivity structure in recurrently connected spiking networks. We found that anti-correlation between the number of afferent (in-degree) and efferent (out-degree) synaptic connections of neurons increases stability against pathological bursting, relative to networks where the degrees were either positively correlated or uncorrelated. In the stable network state, stimulation of a few cells could lead to a detectable change in the firing rate. To quantify the ability of networks to detect the stimulation, we used a receiver operating characteristic (ROC) analysis. For a given level of background noise, networks with anti-correlated degrees displayed the lowest false positive rates, and consequently had the highest stimulus detection performance. We propose that anti-correlation in the degree distribution may be a computational strategy employed by sensory cortices to increase the detectability of external stimuli. We show that networks with anti-correlated degrees can in principle be formed by applying learning rules comprised of a combination of spike-timing dependent plasticity, homeostatic plasticity and pruning to networks with uncorrelated degrees. To test our prediction we suggest a novel experimental method to estimate correlations in the degree distribution.

New Perspectives on Spontaneous Brain Activity: Dynamic Networks and Energy Matter

Spontaneous brain activity has received increasing attention as demonstrated by the exponential rise in the number of published article on this topic over the last 30 years. Such “intrinsic” brain activity, generated in the absence of an explicit task, is frequently associated with resting-state or default-mode networks (DMN)s. The focus on characterizing spontaneous brain activity promises to shed new light on questions concerning the structural and functional architecture of the brain and how they are related to “mind”. However, many critical questions have yet to be addressed. In this review, we focus on a scarcely explored area, specifically the energetic requirements and constraints of spontaneous activity, taking into account both thermodynamical and informational perspectives. We argue that the “classical” definitions of spontaneous activity do not take into account an important feature, that is, the critical thermodynamic energetic differences between spontaneous and evoked brain activity. Spontaneous brain activity is associated with slower oscillations compared with evoked, task-related activity, hence it exhibits lower levels of enthalpy and “free-energy” (i.e., the energy that can be converted to do work), thus supporting noteworthy thermodynamic energetic differences between spontaneous and evoked brain activity. Increased spike frequency during evoked activity has a significant metabolic cost, consequently, brain functions traditionally associated with spontaneous activity, such as mind wandering, require less energy that other nervous activities. We also review recent empirical observations in neuroscience, in order to capture how spontaneous brain dynamics and mental function can be embedded in a non-linear dynamical framework, which considers nervous activity in terms of phase spaces, particle trajectories, random walks, attractors and/or paths at the edge of the chaos. This takes us from the thermodynamic free-energy, to the realm of “variational free-energy”, a theoretical construct pertaining to probability and information theory which allows explanation of unexplored features of spontaneous brain activity.

Modulation of BK Channels by Small Endogenous Molecules and Pharmaceutical Channel Openers

Voltage- and Ca(2+)-activated K(+) channels of big conductance (BK channels) are abundantly found in various organs and their relevance for smooth muscle tone and neuronal signaling is well documented. Dysfunction of BK channels is implicated in an array of human diseases involving many organs including the nervous, pulmonary, cardiovascular, renal, and urinary systems. In humans a single gene (KCNMA1) encodes the pore-forming α subunit (Slo1) of BK channels, but the channel properties are variable because of alternative splicing, tissue- and subcellular-specific auxiliary subunits (β, γ), posttranslational modifications, and a multitude of endogenous signaling molecules directly affecting the channel function. Initiatives to develop drugs capable of activating BK channels (channel openers) therefore need to consider the tissue-specific variability of BK channel structure and the potential interference with endogenously produced regulatory factors. The atomic structural basis of BK channel function is only beginning to be revealed. However, building on detailed knowledge of BK channel function, including its single-channel characteristics, voltage- and Ca(2+) dependence of channel gating, and modulation by diffusible messengers, a multi-tier allosteric model of BK channel gating (Horrigan and Aldrich (HA) model) has become a valuable tool in studying modulation of the channel. Using the conceptual framework of the HA model, we here review the functional impact of endogenous modulatory factors and select small synthetic compounds that regulate BK channel activity. Furthermore, we devise experimental approaches for studying BK channel-drug interactions with the aim to classify BK-modulating substances according to their molecular mode of action.

A Microscopic Capacitor Model of Voltage Coupling in Membrane Proteins: Gating Charge Fluctuations in Ci-VSD

The voltage sensitivity of membrane proteins is reflected in the response of the voltage sensing domains (VSDs) to the changes in membrane potential. This response is implicated in the displacement of positively charged residues, associated with the conformational changes of VSDs. The displaced charges generate nonlinear (i.e., voltage-dependent) capacitance current called the gating current (and its corresponding gating charge), which is a key experimental quantity that characterizes voltage activation in VSMP. However, the relevant theoretical/computational approaches, aimed to correlate the structural information on VSMP to electrophysiological measurements, have been rather limited, posing a broad challenge in computer simulations of VSMP. Concomitant with the development of our coarse-graining (CG) model of voltage coupling, we apply our theoretical framework for the treatments of voltage effects in membrane proteins to modeling the VSMP activation, taking the VSDs (Ci-VSD) derived from the Ciona intestinalis voltage sensitive phosphatase (Ci-VSP) as a model system. Our CG model reproduces the observed gating charge of Ci-VSD activation in several different perspectives. In particular, a new closed-form expression of the gating charge is evaluated in both nonequilibrium and equilibrium ways, while considering the fluctuation-dissipation relation that connects a nonequilibrium measurement of the gating charge to an equilibrium measurement of charge fluctuations (i.e., the voltage-independent linear component of membrane capacitance). In turn, the expression uncovers a novel link that connects an equilibrium measurement of the voltage-independent linear capacitance to a nonequilibrium measurement of the voltage-dependent nonlinear capacitance (whose integral over voltage is equal to the gating charge). In addition, our CG model yields capacitor-like voltage dependent free energy parabolas, resulting in the free energy difference and the free energy barrier for the Ci-VSD activation at "zero" (depolarization) membrane potential. Significantly, the resultant voltage dependent energetics enables a direct evaluation of capacitance-voltage relationship (C-V curve) as well as charge-voltage relationship (Q-V curve) that is in a good agreement with the observed measurement of Ci-VSD voltage activation. Importantly, an extension of our kinetic/thermodynamic model of voltage dependent activation in VSMP allows for novel derivations of voltage-dependent rate constants, whose parameters are expressed by the intrinsic properties of VSMP. These novel closed-form expressions offer a physicochemical foundation for the semiempirical Eyring-type voltage dependent rate equations that have been the cornerstone for the phenomenological (kinetic) descriptions of gating and membrane currents in the mechanistic study of ion channels and transporters. Our extended theoretical framework developed in the present study has potential implications on the roles played by gating charge fluctuations for the spike generations in nerve cells within the framework of the Hodgkin-Huxley-type model.

Balanced ionotropic receptor dynamics support signal estimation via voltage-dependent membrane noise

Encoding behaviorally relevant stimuli in a noisy background is critical for animals to survive in their natural environment. We identify core biophysical and synaptic mechanisms that permit the encoding of low-frequency signals in pyramidal neurons of the weakly electric fish Apteronotus leptorhynchus, an animal that can accurately encode even miniscule amplitude modulations of its self-generated electric field. We demonstrate that slow NMDA receptor (NMDA-R)-mediated excitatory postsynaptic potentials (EPSPs) are able to summate over many interspike intervals (ISIs) of the primary electrosensory afferents (EAs), effectively eliminating the baseline EA ISI correlations from the pyramidal cell input. Together with a dynamic balance of NMDA-R and GABA-A-R currents, this permits stimulus-evoked changes in EA spiking to be transmitted efficiently to target electrosensory lobe (ELL) pyramidal cells, for encoding low-frequency signals. Interestingly, AMPA-R activity is depressed and appears to play a negligible role in the generation of action potentials. Instead, we hypothesize that cell-intrinsic voltage-dependent membrane noise supports the encoding of perithreshold sensory input; this noise drives a significant proportion of pyramidal cell spikes. Together, these mechanisms may be sufficient for the ELL to encode signals near the threshold of behavioral detection.

A temperature rise reduces trial-to-trial variability of locust auditory neuron responses

The neurophysiology of ectothermic animals, such as insects, is affected by environmental temperature, as their body temperature fluctuates with ambient conditions. Changes in temperature alter properties of neurons and, consequently, have an impact on the processing of information. Nevertheless, nervous system function is often maintained over a broad temperature range, exhibiting a surprising robustness to variations in temperature. A special problem arises for acoustically communicating insects, as in these animals mate recognition and mate localization typically rely on the decoding of fast amplitude modulations in calling and courtship songs. In the auditory periphery, however, temporal resolution is constrained by intrinsic neuronal noise. Such noise predominantly arises from the stochasticity of ion channel gating and potentially impairs the processing of sensory signals. On the basis of intracellular recordings of locust auditory neurons, we show that intrinsic neuronal variability on the level of spikes is reduced with increasing temperature. We use a detailed mathematical model including stochastic ion channel gating to shed light on the underlying biophysical mechanisms in auditory receptor neurons: because of a redistribution of channel-induced current noise toward higher frequencies and specifics of the temperature dependence of the membrane impedance, membrane potential noise is indeed reduced at higher temperatures. This finding holds under generic conditions and physiologically plausible assumptions on the temperature dependence of the channels' kinetics and peak conductances. We demonstrate that the identified mechanism also can explain the experimentally observed reduction of spike timing variability at higher temperatures.

Spontaneous Action Potentials and Neural Coding in Unmyelinated Axons

The voltage-gated Na and K channels in neurons are responsible for action potential generation. Because ion channels open and close in a stochastic fashion, spontaneous (ectopic) action potentials can result even in the absence of stimulation. While spontaneous action potentials have been studied in detail in single-compartment models, studies on spatially extended processes have been limited. The simulations and analysis presented here show that spontaneous rate in unmyelinated axon depends nonmonotonically on the length of the axon, that the spontaneous activity has sub-Poisson statistics, and that neural coding can be hampered by the spontaneous spikes by reducing the probability of transmitting the first spike in a train.