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Current carried by sodium and potassium ions through the membrane of the giant axon of Loligo

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... With the advances in technology applied to the electrophysiology field, the origin of the action potential evidences the activity of certain proteins situated in the cell's surface interchanging ions: Ion channels [9]. These proteins were first hypothesized as pores and then extensively studied during the golden analogical era of electrophysiology [21][22][23][24][25][26][27][28][29][30]. Decades after, with strong and convincing shreds of evidence, the pore-like function was confirmed by the patch-clamp technique in the 70-80's decades [31][32][33][34][35]. From then on, the catalog of ion channels identities associated with biological functions has grown-up thanks to understanding their biophysical, pharmacological, genetic, and structural characterization, confirming their presence in all kinds of cells [9,36]. ...
... Hodgkin and Huxley understood the sodium channels (Na + channels) at the very beginning of an era in which it was not possible to study their molecular structure as they were studied only by voltage-current amplification, physics equations, and saline solutions [23,25,26]. Nowadays, with a common profile completed, we know that Na + channels serve as activators, inhibitors, or allosteric modulators of their voltage-dependent gating processes. ...
... Potassium channels (K + channels) are responsible to reequilibrate the resting potential of the cell after the depolarization caused by sodium or calcium at the beginning of the action potential [23,24,26,[40][41][42]. Their structure is smaller and less complicated with respect to other types of channels and this superfamily is found in bacteria kingdom to the higher vertebrates [42]. ...
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Polyglutamine (polyQ) diseases are a family composed of nine neurodegenerative inherited disorders (NDDs) caused by pathological expansions of cytosine-adenine-guanine (CAG) trinucleotide repeats which encode a polyQ tract in the corresponding proteins. CAG polyQ repeat expansions produce neurodegeneration via multiple downstream mechanisms; among those the neuronal activity underlying the ion channels is affected directly by specific channelopathies or indirectly by secondary dysregulation. In both cases, the altered excitability underlies to gain- or loss-of-function pathological effects. Here we summarize the repertoire of ion channels in polyQ NDDs emphasizing the biophysical features of neuronal excitability and their pathogenic role. The aim of this review is to point out the value of a deeper understanding of those functional mechanisms and processes as crucial elements for the designing and targeting of novel therapeutic avenues.
... La forme du PA ainsi que la fréquence de décharge dépendent du type de canaux ioniques sensibles au potentiel membranaire qui sont exprimés dans le neurone (Bean, 2007). sont dus à 1/ l'activation de la conduction au sodium Na + 2/ l'activation de la conductance au potassium K + et enfin 3/ l'inactivation de la conductance au sodium (Hodgkin and Huxley, 1945) (Hodgkin and Huxley, 1952). Ils obtiennent le prix Nobel en 1963 pour l'ensemble de leurs travaux. ...
... Toutefois les canaux au potassium n'étant pas inactivés au moment où la cellule retourne à son potentiel de repos, les ions potassium continuent à quitter la cellule et provoquent ainsi une légère hyperpolarisation, le temps que la perméabilité au potassium retrouve sa valeur de repos. Cette hyperpolarisation est appelée afterhyperpolarisation (AHP) et permet de contrôler la fréquence de décharge des neurones (Hodgkin and Huxley, 1952) (Bean, 2007). In vivo, les neurotransmetteurs sont libérés par l'élément pré-synaptique. ...
... En réponse à une dépolarisation, le canal sodique s'active ce qui permet l'entrée d'ions sodium dans la cellule et donc la génération de potentiels d'action. Quelques millisecondes plus tard (1 à 2ms) le canal s'inactive, les ions sodium ne peuvent plus entrer à l'intérieur de la cellule évitant ainsi la génération de décharges répétitives (Hodgkin and Huxley, 1952). En 1988, le groupe de WA Catterall montre, en utilisant des anticorps dirigés contre différents peptides de la sous-unité α, que la boucle intracellulaire reliant le segment S6 de DIII au segment S1 de DIV est directement impliquée dans le processus d'inactivation rapide (Vassilev et coll., 1988). ...
Thesis
Les gènes codant pour les canaux sodiques potentiel-dépendants (Nav) présents dans le système nerveux central sont la cible de mutations conduisant à divers phénotypes. L’objectif de mon travail de thèse est de comprendre pourquoi des mutations d’un même gène peuvent conduire à des pathologies distinctes afin d’envisager le développement de nouvelles approches thérapeutiques. Le gène SCN1A codant pour le canal Nav1.1, exprimé principalement dans les interneurones GABAergiques (IN GABA), est la cible de mutations responsables de syndromes épileptiques et de la migraine hémiplégique familiale (MHF-3), une forme rare de migraine avec aura. Il a été montré que les mutations responsables de l’épilepsie induisent une perte de fonction du canal, ce qui conduit à une hypoexcitabilité des IN GABA dont résulte une hyperexcitabilité du réseau neuronal. L’analyse fonctionnelle de mutations responsables de la MHF-3 a montré qu’elles induisent un gain de fonction du canal et une hyperexcitabilité des IN GABA pouvant être à l’origine d’une dépression corticale envahissante, un mécanisme pathologique de la migraine. En particulier, l’étude de la mutation L1649Q a montré qu’elle induit une réduction importante de la densité de courant des canaux Nav1.1 (défaut d’expression des canaux). L’analyse des propriétés biophysiques des canaux mutés après récupération de la densité de courant a mis en évidence que l’effet de la mutation correspond à un gain de fonction allant dans le sens d’une hyperexcitabilité des IN GABA (Cestèle et al.2013 PNAS). Afin d’identifier si d’autres mutations MHF-3 possèdent le même mécanisme (perte/gain de fonction), la 1ère partie de ma thèse a consisté en la caractérisation fonctionnelle d’une nouvelle mutation responsable de la MHF-3, L1670W. Cette mutation conduit à un défaut d’expression des canaux Nav1.1 (perte de fonction) cependant, après récupération de la densité de courant, la mutation induit un gain de fonction des canaux Nav1.1. Ces résultats ont permis de mettre en évidence que la mutation L1670W induit un défaut d’expression des canaux à la membrane et un gain de fonction renforçant ainsi l’hypothèse selon laquelle ce mécanisme pourrait être généralisé à d’autres mutations MHF-3. Le gène SCN2A codant pour le canal Nav1.2, exprimé principalement dans les neurones excitateurs, est la cible de mutations responsables de différentes pathologies telles que les épilepsies bénignes, les encéphalopathies épileptiques et les troubles du spectre de l’autisme (TSA). A ce jour, les mécanismes responsables de ces pathologies restent flous. Dans le but d’élucider la relation génotype/phénotype, nous avons étudié les effets fonctionnels de 23 mutants SCN2A responsables de ces différentes pathologies. Nos résultats montrent que toutes les mutations responsables de TSA induisent une perte presque totale de densité de courant tandis que pour les autres pathologies les effets sont hétérogènes. Dans le but de reproduire les conditions hétérozygotes, nous avons étudié la co-expression des canaux wild-type (WT) avec chaque canal muté. Nos résultats ont mis en évidence une réduction de la densité de courant des canaux WT uniquement en présence de canaux porteurs de mutations responsables de TSA. Par conséquent, seules les mutations responsables de TSA induisent un phénomène de dominance négative sur les canaux WT. Afin de déterminer si ce mécanisme de dominance négative est dû à l’interaction de 2 sous-unités α décrite récemment (Clatot et coll., 2018 Nat Commun), nous avons utilisé différentes stratégies pour inhiber cette interaction. Les résultats obtenus ont montré que l'effet de dominance négative des mutants responsables de TSA n’est plus observé lorsque α-α est inhibée. Par conséquent, nos résultats permettent de décrire pour la 1ère fois que les mutations des canaux Na+ responsables de TSA agissent par un mécanisme de dominance négative, lequel est médié par l’interaction entre les canaux WT et mutés.
... Neuronal action potential modelling was based on a modified Hodgkin-Huxley model (Hodgkin & Huxley, 1952;Verma et al., 2020). The model was modified to match the properties of DRG cells (Hodgkin & Huxley, 1952;Verma et al., 2020). ...
... Neuronal action potential modelling was based on a modified Hodgkin-Huxley model (Hodgkin & Huxley, 1952;Verma et al., 2020). The model was modified to match the properties of DRG cells (Hodgkin & Huxley, 1952;Verma et al., 2020). ...
... To test the effects of CBG on neuronal excitability, we used a modified version of the Hodgkin-Huxley model to simulate a DRG neuron's excitability, which includes both TTX-R and TTX-S currents (Hodgkin & Huxley, 1952;Verma et al., 2020). We ran two simulations of the CBG condition, at 2 and 15 μM. ...
Article
Background and purpose: Cannabigerol (CBG), a non-psychotropic phytocannabinoid and a precursor for ∆9-tetrahydrocannabinol and cannabidiol, has been suggested to act as an analgesic. A previous study reported that CBG (10 μM) blocks voltage-gated sodium (Nav) currents in CNS neurons; however, the underlying mechanism is not well-understood. Genetic and functional studies have validated Nav1.7 as an opportune target for analgesic drug development. The effects of CBG on Nav1.7 channels, which may contribute to its analgesic properties, have not been previously investigated. Experimental approach: To determine the effects of CBG on Nav channels, we used stably transfected HEK cells and primary dorsal root ganglion (DRG) neurons to characterize compound effects using experimental and computational techniques. These included patch-clamp, multielectrode array, and action potential modelling. Key results: We found that CBG is a ~10-fold state-dependent Nav inhibitor (KI -KR : ~2-20 μM) with an average Hill-slope of ~2. We determined that at lower concentrations, CBG predominantly blocks sodium Gmax and slows recovery from inactivation; however, as the concentration is increased, CBG also induces a hyperpolarizing shift in half-voltage of inactivation. Our modeling and multielectrode array recordings suggest that CBG attenuates DRG excitability. Conclusions and implications: Inhibition of Nav1.7 in DRG neurons may underlie CBG-induced neuronal hypoexcitability. As most Nav1.7 channels are inactivated at DRG resting membrane potential, they are more likely to be inhibited by lower CBG concentrations, suggesting functional selectivity against Nav1.7 compared to other Navs (via Gmax block).
... As expected from sodium channel inactivation, for both RGC types, spikes elicited from more depolarized potentials were smaller ( Figure 5H) and had shallower slopes ( Figure 5I). Maximum action potential slope is proportional to sodium current multiplied by membrane capacitance (Hille, 2001;Hodgkin and Huxley, 1952). Membrane capacitance was similar between the two RGC types (p = 0.45, see Table S1), thus, the fact that bSbC RGCs had spikes with smaller slopes than those OFFsA RGCs across voltages indicated that the total sodium conductance in the bSbC RGCs was lower than that in OFFsA RGCs. ...
... Voltage gated potassium channels are an even more diverse class than Na V channels (Hille, 2001), and they could also contribute to differences in susceptibility to depolarization block between bSbC and OFFsA RGCs. Our decision to leave K + channel diversity out of our model was influenced by the fact that we observed significant differences in the rising phase of action potentials (Figures 5,7) which is controlled primarily by Na V channels (Hodgkin and Huxley, 1952). Therefore, while our model did not capture all aspects of intrinsic properties of RGCs, it provided a useful tool for studying the contributions of components that are not easily isolated experimentally. ...
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The output of spiking neurons depends both on their synaptic inputs and on their intrinsic properties. Retinal ganglion cells (RGCs), the spiking projection neurons of the retina, comprise over 40 different types in mice and other mammals, each tuned to different features of visual scenes. The circuits providing synaptic input to different RGC types to drive feature selectivity have been studied extensively, but there has been substantially less research aimed at understanding how the intrinsic properties of RGCs differ and how those differences impact feature selectivity. Here, we introduce an RGC type in the mouse, the Bursty Suppressed-by-Contrast (bSbC) RGC, whose contrast selectivity is shaped by its intrinsic properties. Surprisingly, when we compare the bSbC RGC to the OFF sustained alpha (OFFsA) RGC that receives similar synaptic input, we find that the two RGC types exhibit starkly different responses to an identical stimulus. We identified spike generation as the key intrinsic property behind this functional difference; the bSbC RGC undergoes depolarization block in conditions where the OFFsA RGC maintains a high spike rate. Pharmacological experiments, imaging, and compartment modeling demonstrate that these differences in spike generation are the result of differences in voltage-gated sodium channel conductances. Our results demonstrate that differences in intrinsic properties allow these two RGC types to detect and relay distinct features of an identical visual stimulus to the brain.
... However, the low pass filtering assumption is rooted in the treatment of neurons as linear, time-invariant systems near resting membrane potential. If the transmembrane potential departs significantly from the resting value, then the neuron must be modeled as an active electrical system which, by virtue of voltage-dependent membrane resistance, requires nonlinear models (e.g., Hodgkin and Huxley, 1952). Furthermore, neurons need not pass kHz frequency components to have an effect upon the transmembrane potential. ...
... First, high frequency signals could be passed during short intervals. As the membrane potential nears threshold (due to synaptic input) the sodium ion membrane conductance can increase by two orders of magnitude 29 . This will effectively decrease the membrane time constant (the product of membrane resistance and capacitance) and increase the cutoff frequency by the same factor. ...
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We report a novel subthreshold non-invasive brain stimulation approach that we refer to as kilohertz transcranial magnetic perturbation, or kTMP. kTMP is a magnetic induction method that delivers kHz-frequency cortical E-fields and, through amplitude modulation of the kHz carrier frequency, may mimic E-fields at physiological frequencies. To evaluate the efficacy of kTMP, we used suprathreshold TMS to elicit motor-evoked potentials (MEP) in a peripheral muscle, comparing the amplitude of the MEPs before and after kTMP stimulation. In Experiment 1, we used non-modulated kTMP with an E-field amplitude of 2 V/m over motor cortex. Ten minutes of kTMP stimulation resulted in an increase in cortical excitability in a frequency-specific manner. We replicated this effect in Experiment 2 and found that amplitude-modulation at 20 Hz produced an additional boost in cortical excitability. The only percept associated with kTMP is a faint auditory tone, making kTMP ideal for double-blind experimentation.
... Families of Na V 1.8 sodium currents recorded in the control experiment and after extracellular application of TP1 and TP2 at 100 nM are shown in Figure 1a,b. Normalized peak current-voltage characteristics of sodium currents plotted using the regular protocol [10] demonstrate a slight shift of the left branch along the voltage axis, which indicates that both tripeptides modulate voltage sensitivity of the Na V 1.8 channel activation gating device (Figure 1c,d). ...
... The stationary characteristics of transitions between the states of the Na V 1.8 channel activation gating device are assumed in this case to be determined by the voltage dependence of the chord conductance. To obtain the Z eff values herein, we have implemented a different approach, first suggested by the authors of the membrane ionic theory [10] and later modified [11]. The protocol of Z eff evaluation is illustrated in Figure 2c,d. ...
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Two short arginine-containing tripeptides, H-Arg-Arg-Arg-OH (TP1) and Ac-Arg-Arg-Arg-NH2 (TP2), have been shown by the patch-clamp method to modulate the NaV1.8 channels of DRG primary sensory neurons, which are responsible for the generation of nociceptive signals. Conformational analysis of the tripeptides indicates that the key role in the ligand-receptor binding of TP1 and TP2 to the NaV1.8 channel is played by two positively charged guanidinium groups of the arginine side chains located at the characteristic distance of ~9 Å from each other. The tripeptide effect on the NaV1.8 channel activation gating device has been retained when the N- and C-terminal groups of TP1 were structurally modified to TP2 to protect the attacking peptide from proteolytic cleavage by exopeptidases during its delivery to the molecular target, the NaV1.8 channel. As demonstrated by the organotypic tissue culture method, the agents do not affect the DRG neurite growth, which makes it possible to expect the absence of adverse side effects at the tissue level upon administration of TP1 and TP2. The data obtained indicate that both tripeptides can have great therapeutic potential as novel analgesic medicinal substances.
... After the pioneering and groundbreaking achievements by Hodgkin and Huxley (HH) regarding the properties of voltage dependence of Na + and K + currents in squid giant axon [1,2] and their mathematical model [3], a countless number of works have been devoted to the structure of K + channels and their modeling. These models can be loosely classified into structural and kinetic models. ...
... We simulated the same experiment by first fitting the curve of the ON ionic current density j i on against time t at the depolarization potential V = 60 mV and 20 ° C, reported by WB in Fig. 2 of [15] (apart from the initial blip). In this connection, it should be noted that the electric potential values in HH work [1][2][3] are referred to a resting potential taken conventionally equal to zero, whereas in WB work [15] they are true transmembrane potentials ϕ m , with the holding potential set equal to ϕ m = -− 60 mV. Hence, in what follows, the WB values will be increased by + 60 mV in order to approximately compare them with the corresponding HH values. ...
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1.1 Introduction After the pioneering and groundbreaking achievements by Hodgkin and Huxley (HH) regarding the properties of voltage dependence of Na + and K + currents in squid giant axon [1,2] and their mathematical model [3], a countless number of works have been devoted to the structure of K + channels and their modeling. These models can be loosely classified into structural and kinetic models. Structural models are based on crystal structures of K + channels and use molecular dynamics simulations [4,5], molecular docking [5], continuum electrostatic free energy calculations [6], etc. Their predictions can be usefully employed to better understand several aspects of K + channel function, such as permeation, selectivity, block and gating [7]. K + channels are aggregates of four of their components, called 'subunits', each consisting of six α-helical segments, S1-S6, which span the membrane and maintain a transmembrane disposition at all voltages. Four of them, S1-S4, constitute the voltage-sensor domain, and the remaining two, S5 and S6, contribute to the formation of the pore. According to the 'sliding helix' model of gating [8], the opening of the K + channel is accompanied by a slight outward movement of the positively charged S4 segments, elicited by a positive shift of the transmembrane potential ϕ m on the inner side of the membrane. The S4 segment moves along a hydrophilic pathway formed by the negatively charged residues of the S1, S2 and S3 segments. The outward movement of the S4 segments is equivalent to that of a positive charge, and is responsible for the passage of the ion channel from a closed to an open state. The transmembrane segments of K + channels are considered to affect the membrane voltage profile. The free energy F(X,ϕ m) for a given configuration X of the channel is considered to consist of the sum of a contribution F(X,0), at zero transmembrane potential ϕ m , and a voltage dependent contribution ΔF(X,ϕ m) = ϕ m Q(X) [9,10]. The 'effective charge' Q(X) is a sum of all charges q i of the given configuration, each multiplied by a dimensionless fraction ϕ x (r) of ϕ m at the position r i of the given charge, with ϕ x varying from 0 on the intracellular side of the membrane to 1 on its extracellular side. The ϕ x (r) profile is calculated on the basis of a linearized Poisson-Boltzmann equation that ignores the presence of charges within the hydrocarbon tail region and considers diffuse-layer charges on the two sides of the membrane, with space-dependent dielectric coefficient ε(r) and Debye-Hückel ionic screening factor κ(r). After taking the positions of the charges q i for a given configuration X from a trajectory generated from an all-atom molecular dynamics simulation with no transmembrane potential, these positions are used to calculate both ϕ x (r) via the Poisson-Boltzmann equation and the corresponding free energy contribution ΔF(X,ϕ m). By following the above procedure with a Kv1.2 channel in a lipid membrane, Jogini and Roux [11] concluded that the two outermost arginine residues of the S4 segments of all four subunits of the K + channel in its open configuration adopt an interfacial position, where they are well hydrated and establish salt bridges with the lipid headgroups. The negatively charged residues of the S1-S3 segments interact with the positively charged residues of S4 that are within the membrane, whereas the lipid headgroups interact with those that are located at the membrane interface. The ϕ x (r) profile sensed by the charged residues of the voltage sensor along the axis normal to the membrane Abstract A kinetic model accounting for all salient features of the K + channel of the squid giant axon, including the rising phase of the ON gating charge and the Cole-Moore effect, is provided. Upon accounting for a significant feature distinguishing K + , Na + and Ca 2 + channels from channel-forming peptides modeled in our previous 2016 BBA paper, the nucleation-and-growth kinetic model developed therein is extended to simulate ON ionic and gating currents of the K + channel of the squid giant axon at different depolarization potentials by the use of only two free parameters. K + channel opening is considered to proceed by progressive aggregation of single subunits, while they are moving their gating charge outward under depolarizing conditions within their tetrameric structure; K + channel closing proceeds in the opposite direction, by repolarization-induced disaggregation of subunits, accompanied by inward movement of their gating charge.
... e neuron model is very important to further analyze the electrical activity and synchronization of neurons, and even help to understand the potential mechanism of disease. Since the last century, great progress has been made in the building and research of neuron models, and all kinds of improved mathematical models have been established successively, such as Hodgkin-Huxley (HH) model [3][4][5], FitzHugn-Nagmno (FHN) model [6][7][8], Hindmash-Rose (HR) model [9,10], and Morris-Lecar (ML) model [11]. Researchers have built various nonlinear circuits based on these theoretical models to reproduce the same characteristics of electrical activity as in biological neurons [12,13]. ...
... When I and d are taken as variable parameters, the corresponding two-parameter bifurcation diagrams are shown in Figures 4(a)∼4(f ) on the parameter plane of I ∈ [3,5] and d ∈ [4,6]. System (4) reveals rich and complex firing characteristics and looks horizontally at Figure 4(a) is shown in Figure 6(a). ...
Article
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Neurons encode and transmit signals through chemical synaptic or electrical synaptic connections in the actual nervous system. Exploring the biophysical properties of coupling channels is of great significance for further understanding the rhythm transitions of neural network electrical activity patterns and preventing neurological diseases. From the perspective of biophysics, the activation of magnetic field coupling is the result of the continuous release and propagation of intracellular and extracellular ions, which is very similar to the activation of chemical synaptic coupling through the continuous release of neurotransmitters. In this article, an induction coil is used to connect two HR neurons to stimulate the effect of magnetic field coupling. It is inevitable that time delays can affect the coupling process in the transmission of information, and it should be considered in the coupled model. Firstly, the firing characteristics and bifurcation modes of two coupled HR neurons are studied by using one parameter and two parameters bifurcation. With the increase of propagation delay and coupling gain, the chaotic state of neurons disappears and the high-period window decreases due to the influence of energy transfer between neurons. Then, the synchronization patterns of two HR neurons with different stimulation are analyzed by error diagrams and time series diagrams. It is confirmed that the synchronous pattern has certain regularity and is related not only to the neurons with large stimulation current but also to the time delay and coupling gain. The research conclusions of this article will provide the corresponding theoretical basis for medical experiments.
... Huxley (Hodgkin & Huxley, 1952a). ...
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In this work it proposes a mathematical model for ion channels based on two concepts, the Hodgkin and Huxley's as well as the Law of Mass Action in addition, we consider the kinetics of channels as a dynamic process of Markov`s chain. With the previous premises, a system of differential equations is proposed that when it is solved, all properties of the macroscopic currents are determined. The activation, deactivation, inactivation, and recovery of the inactivation concepts remain as processes that are part of a chemical reaction. With this system of equations, all the experimental protocols used in electrophysiology to characterize macroscopic currents can be modeled. Another advantage is that the model allows, with the same system of equations, to determine the properties of voltage-dependent channels regardless of the type of ion that pass through in the channel. Keywords: Marcov`s Chain, differentials equation system, ionic channels, macroscopic currents, kinetic of channel. RESUMEN En este trabajo se propone un modelo matemático para los canales iónicos basado en dos conceptos, el de Hodgkin y el de Huxley, así como en la Ley de Acción de Masas, además se considera la cinética de los canales como un proceso dinámico de cadena de Markov. Con las premisas anteriores, se propone un sistema de ecuaciones diferenciales que al resolverlo se determinan todas las propiedades de las corrientes macroscópicas. Los conceptos de activación, desactivación, inactivación y recuperación de la inactivación quedan como procesos que forman parte de una reacción química. Con este sistema de ecuaciones se pueden modelar todos los protocolos experimentales utilizados en electrofisiología para caracterizar las corrientes macroscópicas. Otra ventaja es que el modelo permite, con el mismo sistema de ecuaciones, determinar las propiedades de los canales dependientes de voltaje independientemente del tipo de ion que pase por el canal. Palabras clave: Cadena de Marcov, sistema de ecuaciones diferenciales, canales iónicos, corrientes macroscópicas, cinética del canal.
... This critique foretold the intellectual skepticism and challenge that all biophysicists can encounter in their work: While enjoying the quantitative, how do we stay rooted in relevant biological questions? I had already read the 1952 papers of Hodgkin & Huxley (44)(45)(46)(47)(48), which modeled exponential relaxations of hidden gating variables to explain electrical excitability of axons. Their Nobel Prize-winning story was demeaned for the first decade by the elephant's tail critique before its full impact was appreciated. ...
Article
Biophysics is a way of approaching biological problems through numbers, physical laws, models, and quantitative logic. In a long scientific career, I have seen the formation and fruition of the ion channel concept through biophysical study. Marvelous discoveries were made as our instruments evolved from vacuum tubes to transistors; computers evolved from the size of an entire building to a few chips inside our instruments; and genome sequencing, gene expression, and atom-level structural biology became accessible to all laboratories. Science is rewarding and exhilarating. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
... En bas : un courant traversant le canal ouvert. (Adapté de (Hodgkin and Huxley, 1952). ...
Thesis
Parmi les différentes familles de canaux potassiques, la famille des canaux à deux domaines pore, K2P, est la dernière à avoir été découverte à l’IPMC. Ces canaux sont responsables des courants dits « de fond » qui maintiennent le potentiel membranaire négatif réduisant ainsi l’excitabilité cellulaire. Les fonctions physiologiques qui dépendent de ces canaux sont nombreuses (transmission des messages nerveux, fonction cardiaque, homéostasie rénale, développement…). Ils ont été impliqués dans plusieurs conditions physiopathologiques (dépression, douleur, migraine…) et de ce fait, ils représentent des cibles pharmacologiques importantes en recherche thérapeutique.La famille des canaux K2P compte 15 sous-unités différentes classées dans 6 groupes en fonction de leur homologie de séquences et de quelques-unes de leurs propriétés biophysique et pharmacologique. Les canaux K2P homomériques se présentent sous la forme de dimères composés de deux sous-unités identiques. En plus des 15 canaux K2P homomériques (TREK1, TREK2, TRAAK, THIK1, THIK2, TWIK1, TWIK2, TWIK3, TALK1, TALK2, TASK2, TASK1, TASK2, TASK5, TRESK) des canaux hétéromériques, formés de deux sous-unités différentes, ont récemment été rapportés (THIK1/THIK2 ; TREK1/TREK2…). Ces possibilités d’hétéromérisation permettent de nouvelles régulations des fonctions physiologiques et élargissent le spectre des cibles thérapeutiques possibles. Pour la recherche fondamentale ils ouvrent de nouvelles possibilités d’étude de ces canaux.Durant mes travaux de thèse, je me suis intéressée aux propriétés d’hétéromérisation des sous-unités TALK1, TALK2 et TASK2 qui composent le groupe des canaux de type TALK. Grâce à l’utilisation des techniques de « ligation de proximité » in situ (PLA) et de dominant négatifs des canaux TALK, j’ai pu mettre en évidence les capacités d’hétéromérisation dans cette sous-famille (TALK1/TALK2 ; TALK1/TASK2 et TALK2/TASK2). Des interactions entre les canaux TALK et d’autres sous-unités des canaux K2P ont également été trouvées qui devront être confirmées et approfondies (TALK1/THIK2). La construction de tandem et de chimères de ces canaux m’a aussi permis d’étudier la distribution cellulaire et les propriétés biophysiques et pharmacologiques des hétéromères dans les cellules de mammifères et dans les ovocytes de xénopes. De manière intéressante, les canaux TALK hétéromériques présentent des propriétés différentes des canaux homomériques du même groupe. Ces « nouveaux canaux » apportent une plus grande diversité fonctionnelle et donc des possibilités de régulation différentes des fonctions physiologiques influencées par ces canaux.
... channels) that provide major channels for cells to communicate and coordinate with other cells for major biological functions [22][23][24][25][26]52,59]. Ion channels are nano valves for life [7,12,13,15,31,32,36]. ...
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In this work, for ionic flows through ion channels involving three ion species (two cations with different valences and one anion), we examine how channel structure (permanent charge distribution) interacts with boundary conditions to affect individual fluxes. This is analyzed via a quasi-one-dimensional classical Poisson–Nernst–Planck model and, as an early step, the focus is on finding of new phenomena presented by the biological settings with three ion species (comparing to two ion species). Permanent charges are taken to be piecewise constant with three regions: zeros over two end regions of the channel including the baths and a constant over the middle region. For ionic flows involving two ion species (one cation and one anion), the topic has been recently examined and important phenomena, some counterintuitive, were revealed. For ionic flows involving three ion species treated in this work, even for small permanent charges and for a special case of boundary conditions, several striking phenomena are discovered and the study also immediately leads to a number of questions. We hope and believe the rich behavior revealed in this work for the special case will stimulate a great deal of research along this line in the near future.
... This dual role of the S4 segment is tightly integrated [15][16][17][18][19][20]. After a prolonged depolarization, P-loop and S5-S6 linker change their position with reference to the membrane, and Na v 1.5 channels enter in a "slow inactivation", leading to the termination of the Na + current flow [15,21]. ...
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Nav1.5 is the predominant cardiac sodium channel subtype, encoded by the SCN5A gene, which is involved in the initiation and conduction of action potentials throughout the heart. Along its biosynthesis process, Nav1.5 undergoes strict genomic and non-genomic regulatory and quality control steps that allow only newly synthesized channels to reach their final membrane destination and carry out their electrophysiological role. These regulatory pathways are ensured by distinct interacting proteins that accompany the nascent Nav1.5 protein along with different subcellular organelles. Defects on a large number of these pathways have a tremendous impact on Nav1.5 functionality and are thus intimately linked to cardiac arrhythmias. In the present review, we provide current state-of-the-art information on the molecular events that regulate SCN5A/Nav1.5 and the cardiac channelopathies associated with defects in these pathways.
... Implicit in this explanation is the presupposition that the deer walking through the snow caused the marks. Similarly, Alan Hodgkin and Andrew Huxley (1952), for example, postulated lower-level fluxes of sodium and potassium ions because such fluxes would explain the higher-level neuronal action potentials. In this case, the implicit assumption of the explanation is that the ion fluxes compose (or, as the New Mechanists often put it, "mechanistically constitute") the action potential. ...
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Some New Mechanists have proposed that claims of compositional relations are justified by combining the results of top-down and bottom up interlevel interventions. But, what do scientists do when they can perform, say, a cellular intervention, but not a subcellular detection? In such cases, paired interlevel interventions are unavailable. We propose that scientists use abduction and we illustrate its use through a case study of the ionic theory of resting and action potentials.
... In recent decades, studying the nervous system through neuronal mathematical models has become a very common and effective method. Morris-Lecar (M-L) model [1] is one of the simplified versions of the classic Hodgkin-Huxley (H-H) model [2,3]. The M-L model can behave like a real neuron by adjusting different system parameters. ...
Article
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Based on a modified Morris–Lecar neural model, the synchronization modes transitions between two coupled neurons or star-coupled neural network connected by weak electrical and chemical coupling are, respectively, investigated. For the two coupled neurons, by increasing the calcium conductivity, it is found that the period-2 synchronization of the action potential is transformed to desynchronization first, and then to period-3 synchronization. By increasing the potassium conductivity, however, the synchronization mode transition is a reversal direction process as mentioned above. The corresponding inter-spike interval shows the synchronization modes transition is induced by the chaos. The stronger the coupling strength is, the smaller the period-2 synchronization region in the parameters plane is, while the larger the period-3 synchronization region will be. For the star-coupled neural network, in the presence of weak electrical coupling, it can exhibit the completely synchronized mode, desynchronized mode, and drum head mode under different parameter values, respectively. In the presence of chemical synapse, however, the completely synchronized mode cannot be observed. Our results might provide novel insights into synchronization modes transition and related biological experiments.
... The Na + Channels of β-cells Na + channels mediate the classic, fast activating, and inactivating inward current first identified by Alan Hodgkin and Andrew Huxley in the squid giant axon, where they mediate the rapid upstroke of the sodium spike (109,110). Na + channels are expressed in human, rat, and mouse β-cells (36,71,213,308). However, there is a consensus that they play only Volume 11, October 2021 a minor role in mouse β-cell excitability because their steady state inactivation(or h-infinity curve) is quite left-shifted in mouse β-cells (93,213); Na + current can thus only be elicited by de-inactivating the channels using very negative holding potentials. ...
Article
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ATP-sensitive K⁺ (K(ATP)) channels were first reported in the beta-cells of pancreatic islets in 1984, and it was soon established that they are the primary means by which the blood glucose level is transduced to cellular electrical activity and consequently insulin secretion. However, the role that the K(ATP) channels play in driving the bursting electrical activity of islet beta-cells, which drives pulsatile insulin secretion, remains unclear. One difficulty is that bursting is abolished when several different ion channel types are blocked pharmacologically or genetically, making it challenging to distinguish causation from correlation. Here, we demonstrate a means for determining whether activity-dependent oscillations in K(ATP) conductance play the primary role in driving electrical bursting in beta-cells. We use mathematical models to predict that if K(ATP) is the driver, then, contrary to intuition, the mean, peak and nadir levels of ATP/ADP should be invariant to changes in glucose within the concentration range that supports bursting. We test this in islets using Perceval-HR to image oscillations in ATP/ADP. We find that mean, peak and nadir levels are indeed approximately invariant, supporting the hypothesis that oscillations in K(ATP) conductance are the main drivers of the slow bursting oscillations typically seen at stimulatory glucose levels in mouse islets. In conclusion, we provide, for the first time, causal evidence for the role of K(ATP) channels not only as the primary target for glucose regulation, but also for their role in driving bursting electrical activity and pulsatile insulin secretion.
... The second paper (Hodgkin and Huxley 1952a) followed up on the 'sodium hypothesis' proposed earlier by Hodgkin and Katz (1949). The latter two had found evidence that an influx of sodium ions is causally involved in the upstroke of the action potential, and that an efflux of potassium ions plays a critical role in the downstroke. ...
... For simplicity, the functional states of Na V channels can be classified into three major conformations: resting/closed, activated/open, and inactivated/closed, with different parts and modules in the structure adopting unique conformations required for each functional step ( Figure 2). Here we briefly discuss our current understanding of key processes originally described by Hodgkin and Huxley (Hodgkin and Huxley, 1952a;Hodgkin and Huxley, 1952b;Hodgkin and Huxley, 1952c;Hodgkin and Huxley, 1952d;Hodgkin and Huxley, 1952e;Hodgkin et al., 1952) that facilitate the transitions of Na V channels from one conformation to the next in light of recent molecular details from high-resolution structural studies. ...
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Voltage-gated ion channels are important drug targets because they play crucial physiological roles in both excitable and non-excitable cells. About 15% of clinical drugs used for treating human diseases target ion channels. However, most of these drugs do not provide sufficient specificity to a single subtype of the channels and their off-target side effects can be serious and sometimes fatal. Recent advancements in imaging techniques have enabled us for the first time to visualize unique and hidden parts of voltage-gated sodium channels in different structural conformations, and to develop drugs that further target a selected functional state in each channel subtype with the potential for high precision and low toxicity. In this review we describe the druggability of voltage-gated sodium channels in distinct functional states, which could potentially be used to selectively target the channels. We review classical drug receptors in the channels that have recently been structurally characterized by cryo-electron microscopy with natural neurotoxins and clinical drugs. We further examine recent drug discoveries for voltage-gated sodium channels and discuss opportunities to use distinct, state-dependent receptor sites in the voltage sensors as unique drug targets. Finally, we explore potential new receptor sites that are currently unknown for sodium channels but may be valuable for future drug discovery. The advancement presented here will help pave the way for drug development that selectively targets voltage-gated sodium channels.
... Nearly seven decades ago, the pioneering works of Hodgkin and Huxley (Hodgkin and Huxley, 1952) on the giant squid axon established that the generation and propagation of action potentials in electrically excitable cells is absolutely dependent on the ionic currents of sodium and potassium. ...
Thesis
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Schizophrenia is a heterogeneous psychiatric disorder which affects at least 1% of the global population. Its complex pathology involves impaired neuronal communication that leads to the onset of debilitating symptoms affecting behaviour and cognition. Voltage-gated potassium (Kv) channels are fundamental to neuronal communication because of their intricate roles in regulating neuronal excitability, thereby governing information processing in the brain. The cerebellum has a significant influence over how this information is communicated across the brain because of its interconnectivity with virtually all brain regions. To expand our understanding of Kv channels, this thesis investigates the regulation of three alpha subunits of voltage-gated potassium channels Kv2.1, Kv6.4, and Kv3.1b in the cerebellar cortex of a phencyclidine-induced mouse model of schizophrenia and explores their potential role in schizophrenia symptoms. In Chapter 3 we show using immunohistochemistry that Kv2.1 is expressed in the Purkinje cells and granule cells as membrane-bound clusters in the soma and proximal dendrites, whereas the Kv6.4 are mainly present in the cytosol. Additionally, using proximity ligation we demonstrated for the first time that Kv6.4 arrange with Kv2.1 to form heteromeric channels on the perisomatic membrane of Purkinje cells. These findings suggest that Kv2.1 and Kv6.4 may act as neuronal ‘transistors’ thereby controlling the frequency of neuronal firing in these cell populations. In Chapter 4 we describe the behavioural phenotype of our CBA/CA phencyclidine model to include altered exploratory patterns, changes in locomotor activity, and changes in rearing and grooming behaviours. We also observed dysregulation of NMDA-receptor genes in frontal cortex and the cerebellum, and abnormalities in several features of the cerebellum of the model mice. Additionally, we describe the effectiveness of concomitant antipsychotic agents haloperidol and clozapine in attenuating the acute changes in behaviour induced by phencyclidine, and we introduce specific motor function tests to assess cerebellar involvement in the model. Together, these findings support several aspects of face, construct, and predictive validity expected of a schizophrenia model. Finally in Chapter 5 we investigate the cerebellar regulation of the three Kv subunits in our animal model, where we found Kv2.1 downregulation in the cerebellar cortex which is consistent with findings from human schizophrenia subjects and from animal studies. Strikingly, we found that the Kv6.4 is upregulated in several regions of the cerebellum that was supported by upregulated Kcng4 gene, which may indicate a compensatory mechanism for Kv2.1 loss. Additionally, we observed downregulation of the Kv3.1b in the granule cell layer of the right cerebellar lateral hemisphere, which may indicate a local functional demand. In conclusion, this thesis demonstrates, by using a range of behavioural, histological, and biomolecular investigations, the cerebellar pathology resulting from subchronic phencyclidine treatment, and also elucidates the functional role of Kv channels in a schizophrenia-like pathological state.
... Voltage-gated sodium (Na V ) channels are a family of integrated membrane proteins, which selectively conduct sodium ions across cell membrane in response to depolarizing stimuli (Catterall, 2000;Hille, 2001). The primary function of Na V channels was related to the generation of action potentials (Hodgkin And Huxley, 1952a;Hodgkin And Huxley, 1952b). Subsequently, the voltage-dependent activation, sodium selectivity, fast inactivation and components of Na V channels were characterized by extensive biophysical and biochemical studies Tamkun and Catterall, 1981;Weigele and Barchi, 1982;Hartshorne and Catterall, 1984;Stühmer et al., 1987). ...
Article
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Voltage-gated sodium (NaV) channels are responsible for the rapid rising-phase of action potentials in excitable cells. Over 1,000 mutations in NaV channels are associated with human diseases including epilepsy, periodic paralysis, arrhythmias and pain disorders. Natural toxins and clinically-used small-molecule drugs bind to NaV channels and modulate their functions. Recent advances from cryo-electron microscopy (cryo-EM) structures of NaV channels reveal invaluable insights into the architecture, activation, fast inactivation, electromechanical coupling, ligand modulation and pharmacology of eukaryotic NaV channels. These structural analyses not only demonstrate molecular mechanisms for NaV channel structure and function, but also provide atomic level templates for rational development of potential subtype-selective therapeutics. In this review, we summarize recent structural advances of eukaryotic NaV channels, highlighting the structural features of eukaryotic NaV channels as well as distinct modulation mechanisms by a wide range of modulators from natural toxins to synthetic small-molecules.
... Oscillatory dynamics is ubiquitous in biological systems, from simple predator-prey models to the more complex descriptions of how neurons transmit electrical signal spikes, such as the Hodgkin-Huxley model or its two-dimensional counterpart, the Fitzhugh-Nagumo model [31,32]. Indeed, recently, a sustained oscillatory behavior of bacteria in a viscoelastic fluid was reported and studied using both a full hydrodynamic active viscoelastic model [23], and the Fitzhugh-Nagumo oscillator. ...
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Models of active nematics in biological systems normally require complexity arising from the hydrodynamics involved at the microscopic level as well as the viscoelastic nature of the system. Here we show that a minimal, space-independent, model based on the temporal alignment of active and polymeric particles provides an avenue to predict and study their coupled dynamics within the framework of dynamical systems. In particular, we examine, using analytical and numerical methods, how such a simple model can display self-sustained oscillations in an activity-driven viscoelastic shear flow.
... However, although this theory did not consider that molecules might move across the plasma membrane, we learned that certain molecules freely cross the plasma membrane soon after publication. Indeed, evidence of the existence of membrane channels was finally reported in the mid-20th century primarily by the studies of Alan L. Hodgkin and coworkers [4][5][6][7][8]; rev. in [9,10]. ...
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The history of direct cell-cell communication has evolved in several small steps. First discovered in the 1930s in invertebrate nervous systems, it was thought at first to be an exception to the “cell theory”, restricted to invertebrates. Surprisingly, however, in the 1950s, electrical cell-cell communication was also reported in vertebrates. Once more, it was thought to be an exception restricted to excitable cells. In contrast, in the mid-1960s, two startling publications proved that virtually all cells freely exchange small neutral and charged molecules. Soon after, cell-cell communication by gap junction channels was reported. While gap junctions are the major means of cell-cell communication, in the early 1980s, evidence surfaced that some cells might also communicate via membrane pores. Questions were raised about the possible artifactual nature of the pores. However, early in this century, we learned that communication via membrane pores exists and plays a major role in medicine, as the structures involved, “tunneling nanotubes”, can rescue diseased cells by directly transferring healthy mitochondria into compromised cells and tissues. On the other hand, pathogens/cancer could also use these communication systems to amplify pathogenesis. Here, we describe the evolution of the discovery of these new communication systems and the potential therapeutic impact on several uncurable diseases.
... The AP is often considered as a binary signal that propagates down the motor axon to the nerve terminal, causing a release of neurotransmitters into the synapse upon reaching the nerve terminal [12][13][14]. However, it is clear even from early work on the squid giant axon AP [15][16][17][18][19][20][21] that the size, shape, and conduction velocity of the AP play an important role in regulating communication. Neurons regulate the propagation and shape of the AP with a heterogeneous distribution of ion channels, and the shape of the AP waveform can vary greatly between different neuron types [22] and within different regions of the same neuron [12,[23][24][25]. ...
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The mouse neuromuscular junction (NMJ) has long been used as a model synapse for the study of neurotransmission in both healthy and disease states of the NMJ. Neurotransmission from these neuromuscular nerve terminals occurs at highly organized structures called active zones (AZs). Within AZs, the relationships between the voltage-gated calcium channels and docked synaptic vesicles govern the probability of acetylcholine release during single action potentials, and the short-term plasticity characteristics during short, high frequency trains of action potentials. Understanding these relationships is important not only for healthy synapses, but also to better understand the pathophysiology of neuromuscular diseases. In particular, we are interested in Lambert-Eaton myasthenic syndrome (LEMS), an autoimmune disorder in which neurotransmitter release from the NMJ decreases, leading to severe muscle weakness. In LEMS, the reduced neurotransmission is traditionally thought to be caused by the antibody-mediated removal of presynaptic voltage-gated calcium channels. However, recent experimental data and AZ computer simulations have predicted that a disruption in the normally highly organized active zone structure, and perhaps autoantibodies to other presynaptic proteins, contribute significantly to pathological effects in the active zone and the characteristics of chemical transmitters.
... Another model widely used in the neuroscience community is the Hodgkin-Huxley membrane model [32]. This model takes into account three different types of ion currents -potassium current, sodium current and current leak. ...
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One of the main broad applications of deep learning is function regression. However, despite their demonstrated accuracy and robustness, modern neural network architectures require heavy computational resources to train. One method to mitigate or even resolve this inefficiency has been to draw further inspiration from the brain and reformulate the learning process in a more biologically-plausible way, developing what are known as Spiking Neural Networks (SNNs), which have been gaining traction in recent years. In this paper we present an SNN-based method to perform regression, which has been a challenge due to the inherent difficulty in representing a function's input domain and continuous output values as spikes. We use a DeepONet - neural network designed to learn operators - to learn the behavior of spikes. Then, we use this approach to do function regression. We propose several methods to use a DeepONet in the spiking framework, and present accuracy and training time for different benchmarks.
... In the resting state, the resting membrane potential is determined by the movement of potassium ions [33]. Additionally, the sAP amplitude relies on the entry of sodium at the rising phase and exiting of potassium channel [34], and implying that MEHP might regulate the sodium activity. In our sAP data, the MEHP-induced depolarization and MEHP-induced amplitude reduction of sAP indicated that MEHP may have the ability to regulate sodium or potassium channels. ...
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Mono-(2-ethylhexyl) phthalate (MEHP) is one of the main active metabolites of di-(2-ethylhexyl) phthalate (DEHP). In our previous works, by using rat and Drosophila models, we showed a disruption of neural function due to DEHP. However, the exact neural effects of MEHP are still unclear. To explore the effects of MEHP on the central nervous system, the electrophysiological properties of spontaneous action potential (sAP), mini-excitatory postsynaptic currents (mEPSCs), ion channels, including Na+, Ca2+, and K+ channels from rat CA3 hippocampal neurons area were assessed. Our data showed that MEHP (at the concentrations of 100 or 300 μM) decreased the amplitude of sAP and the frequency of mEPSCs. Additionally, MEHP (100 or 300 μM) significantly reduced the peak current density of Ca2+ channels, whereas only the concentration of 300 μM decreased the peak current density of Na+ and K+ channels. Therefore, our results indicate that exposure to MEHP could affect the neuronal excitability and synaptic plasticity of rat CA3 hippocampal neurons by inhibiting ion channels’ activity, implying the distinct role of MEHP in neural transmission.
... The FitzHugh-Nagumo equation is a nonlocal PDE describing the dynamics of interacting neurons structured with two variables: the membrane potential (or voltage) v and the adaptation (or recovery) variable x. The model is proposed in [36,54] as a simplified version of the celebrated Hodgkin-Huxley model [45]. The latter is proposed by Alan Hodgkin and Andrew Huxley in 1952, and led them to receive a ''Nobel Prize in Physiology or Medicine'' in 1963. ...
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This review concerns recent results on the quantitative study of convergence towards equilibrium for spatially in-homogeneous linear kinetic equations. We focus on analytical results obtained by means of certain probabilistic techniques from the ergodic theory of Markov processes. These techniques are sometimes referred to as Harris-type theorems. They provide constructive proofs for convergence results in L1 (or total variation) setting for a wide class of initial data. The convergence rates can be made explicit (both for geometric and sub-geometric rates) by tracking the constants appearing in the hypotheses. Harris-type theorems are particularly well-adapted for equations exhibiting non-explicit and non-equilibrium steady states since they do not require prior information on the existence of stationary states. This allows for significant improvements of some already-existing results by relaxing assumptions and providing explicit convergence rates. We aim at presenting Harris-type theorems, providing a guideline on how to apply these techniques on kinetic equations at hand, presenting an exposition of recent quantitative results obtained for kinetic equations in gas theory and mathematical biology, as well as giving some perspectives on potential extensions to non-linear equations.
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In his Transmembrane Electrostatically Localized Proton hypothesis (TELP), James W. Lee has modeled the bioenergetic membrane as a simple capacitor. According to this model, the surface concentration of protons is completely independent of proton concentration in the bulk phase, and is linearly proportional to the transmembrane potential. Such a proportionality runs counter to the results of experimental measurements, molecular dynamics simulations, and electrostatics calculations. We show that the TELP model dramatically overestimates the surface concentration of protons, and we discuss the electrostatic reasons why a simple capacitor is not an appropriate model for the bioenergetic membrane.
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This retrospective traces the hypothesis of ion channels from an early statement in a 1970 essay in this journal (Hille, B., 1970, Prog. Biophys. Mol. Biol. 21, 1–32) to its realization today in biophysical, molecular, biochemical, and structural terms. The Na⁺ and K⁺ channels of the action potential have been isolated, reconstituted, cloned, mutated, and expressed. Refined atomic structures of several conformational states are known. The discoveries over this half century history illustrate the growth of a field from initial ideas to a mature discipline of biology, physiology, and biomedical science.
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Based on a modified Morris–Lecar neural model, the synchronization modes transitions between two coupled neurons or star-coupled neural network connected by weak electrical and chemical coupling are respectively investigated. For the two coupled neurons, by increasing the calcium conductivity, it is found that the period-2 synchronization of action potential of neurons is transformed to desynchronization first, and then to period-3 synchronization. By increasing the potassium conductivity, however, the synchronization mode transition is a reversal direction process as mentioned above. The bifurcation analysis of inter-spike interval shows that the synchronization modes transition is induced by the chaos. The stronger the coupling strength is, the smaller the period-2 synchronization region in the parameters plane is, while the larger the period-3 synchronization region will be. For the star-coupled neural network, in the presence of weak electrical coupling, it can exhibit the complete synchronization, desynchronization, and drum head mode states under different parameter values, respectively. In the presence of chemical synapse, however, the completely synchronized state can not be observed in the star-coupled neural network. Our results might provide novel insights into synchronization modes transition and related biological experiments.
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The comparative method, closely identified with Darwinian evolutionary biology, also has a long pre-Darwinian history. The method derives its scientific power from its ability to interpret comparative observations with reference to a theory of relatedness among the entities being compared (the comparates). Such scientifically powerful strong comparison is distinguished from weak comparison, which lacks such theoretical grounding. This paper examines the history of the strong comparison permitted by the comparative method from the early modern period to the threshold of the Darwinian revolution in the mid nineteenth century. It interprets the work of early pioneers such as Belon, Willis, Perrault, and Tyson from this methodological perspective, rather than focusing on their particular anatomical findings. Although these early writers made formative scientific contributions through their comparative investigations, the more theoretically grounded application of the comparative method by Geoffroy, Cuvier, and Owen was instrumental in laying the foundation for its later incorporation into Darwinian evolutionary theory.
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Locomotion is a fundamental movement in vertebrates produced by spinal networks known as central pattern generators (CPG). During fictive locomotion cat lumbar motoneurons (MNs) exhibit changes in membrane properties, including hyperpolarization of voltage threshold, reduction of afterhyperpolarization and input resistance, and amplification of nonlinear membrane properties. Both modeling and electrophysiological studies suggest that these changes can be produced by upregulating voltage-gated sodium channel (VGSC), persistent sodium (NaP), or L-type calcium channel (LTCC) or downregulating delayed-rectifier potassium (K(DR)) or calcium-dependent potassium channel (KCa) in spinal MNs. Further studies implicate that these channel modulations increase motor output and facilitate MN recruitment. However, it remains unknown how the channel modulation of CPG networks or MN pools affects the rhythmic generation of locomotion and force production of skeletal muscle during locomotion. In order to investigate this issue, we built a two-level CPG model composed of excitatory interneuron pools (Exc-INs), coupled reciprocally with inhibitory interneuron pools (Inh-INs), and projected to the flexor-extensor MN pools innervating skeletal muscles. Each pool consisted of 100 neurons with membrane properties based on cat spinal neurons. VGSC, K(DR), NaP, KCa, LTCC, and H-current channels were included in the model. Simulation results showed that (1) upregulating VGSC, NaP, or LTCC or downregulating KCa in MNs increased discharge rate and recruitment of MNs, thus facilitating locomotor pattern formation, increased amplitude of electroneurogram (ENG) bursting, and enhanced force generation of skeletal muscles. (2) The same channel modulation in Exc-INs increased the firing frequency of the Exc-INs, facilitated rhythmic generation, and increased flexor-extensor durations of step cycles. (3) Contrarily, downregulation of NaP or LTCC in MNs or Exc-INs or both CPG (Exc-INs and Inh-INs) and MNs disrupted locomotor pattern and reduced or even blocked the ENG bursting of MNs and force generation of skeletal muscles. (4) Pharmacological experiments showed that bath application of 25 μM nimodipine or 2 μM riluzole completely blocked fictive locomotion in isolated rat spinal cord, consistent with simulation results. We concluded that upregulation of VGSC, NaP, or LTCC or downregulation of KCa facilitated rhythmic generation and force production during walking, with NaP and LTCC playing an essential role.
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Complementary developments in microscopy and mathematical modeling have been critical to our understanding of cardiac excitation–contraction coupling. Historically, limitations imposed by the spatial or temporal resolution of imaging methods have been addressed through careful mathematical interrogation. Similarly, limitations imposed by computational power have been addressed by imaging macroscopic function in large subcellular domains or in whole myocytes. As both imaging resolution and computational tractability have improved, the two approaches have nearly merged in terms of the scales that they can each be used to interrogate. With this review we will provide an overview of these advances and their contribution to understanding ventricular myocyte function, including exciting developments over the last decade. We specifically focus on experimental methods that have pushed back limits of either spatial or temporal resolution of nanoscale imaging (e.g., DNA-PAINT), or have permitted high resolution imaging on large cellular volumes (e.g., serial scanning electron microscopy). We also review the progression of computational approaches used to integrate and interrogate these new experimental data sources, and comment on near-term advances that may unify understanding of the underlying biology. Finally, we comment on several outstanding questions in cardiac physiology that stand to benefit from a concerted and complementary application of these new experimental and computational methods.
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Attractors in nonlinear dynamical systems can be categorized as self-excited attractors and hidden attractors. In contrast to self-excited attractors, which can be located by the standard numerical computational method, hidden attractors are hard to detect due to the fact that its basin of attraction is away from the proximity to equilibrium. In multistable systems, many attractors, including self-excited and hidden ones, co-exist, which makes locating each different oscillation more difficult. Hidden attractors are frequently connected to rare or abnormal oscillations in the system and often lead to unpredicted behaviors in many engineering applications, and, thus, the research in locating such attractors is considerably significant. Previous work has proposed several methods for locating hidden attractors but these methods all have their limitations. For example, one of the methods suggests that perpetual points are useful in locating hidden and co-existing attractors, while an in-depth examination suggests that they are insufficient in finding hidden attractors. In this study, we propose that the method of connecting curves, which is a collection of points of analytical inflection including both perpetual points and fixed points, is more reliable to search for hidden attractors. We analyze several dynamical systems using the connecting curve, and the results demonstrate that it can be used to locate hidden and co-existing oscillations.
Thesis
Neuroscience and cognitive neuroscience is one of the most fascinating fields of science in the last decade. The complexities of the brain and the systems based on it have attracted the attention of researchers in various sciences such as computer science, mathematics, psychology and engineering. Due to the high levels of complexity of this science, various models have been proposed to analyze the behavior of the brain from the surface of a single neuron or a network of neurons that increase scientists insight into understanding the brain and its function. At the same time, many brain diseases are the result of some functional or destructive problems in which there is still no suitable treatment for many of these diseases. Abnormal synchronization of a network of neurons is one of the causes of seizures in epilepsy or severe tremors in Parkinson’s. In this dissertation, Meshless methods have been developed to simulate neuronal models, coupling and neuronal synchronization systems, as well as a definite and stochastic control system for neuronal synchronization and its efficiency has been demonstrated. Also, from the technological point of view and the product of this dissertation, a package based on MATLAB software has been implemented to develop control models in order to (de)synchronize a network of neural oscillators, which researchers in medical sciences and dynamic systems can evaluate the accuracy of their defined controls (without the need for professional coding), so that these new control mechanisms can be used in the treatment of neurological diseases such as epilepsy and Parkinson’s
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Idealization is commonly understood as distortion: representing things differently than how they actually are. In this paper, we outline an alternative artifactual approach that does not make misrepresentation central for the analysis of idealization. We examine the contrast between the Hodgkin-Huxley (1952a, b, c) and the Heimburg-Jackson (2005, 2006) models of the nerve impulse from the artifactual perspective, and argue that, since the two models draw upon different epistemic resources and research programs, it is often difficult to tell which features of a system the central assumptions involved are supposed to distort. Many idealizations are holistic in nature. They cannot be locally undone without dismantling the model, as they occupy a central position in the entire research program. Nor is their holistic character mainly related to the use of mathematical and statistical modeling techniques as portrayed by Rice (2018, 2019). We suggest that holistic idealizations are implicit theoretical and representational assumptions that can only be understood in relation to the conceptual and representational tools exploited in modeling and experimental practices. Such holistic idealizations play a pivotal role not just in individual models, but also in defining research programs.
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Bio-inspired recipes are being introduced to artificial neural networks for the efficient processing of spatio-temporal tasks. Among them, Leaky Integrate and Fire (LIF) model is the most remarkable one thanks to its temporal processing capability, lightweight model structure, and well investigated direct training methods. However, most learnable LIF networks generally take neurons as independent individuals that communicate via chemical synapses, leaving electrical synapses all behind. On the contrary, it has been well investigated in biological neural networks that the inter-neuron electrical synapse takes a great effect on the coordination and synchronization of generating action potentials. In this work, we are engaged in modeling such electrical synapses in artificial LIF neurons, where membrane potentials propagate to neighbor neurons via convolution operations, and the refined neural model ECLIF is proposed. We then build deep networks using ECLIF and trained them using a back-propagation-through-time algorithm. We found that the proposed network has great accuracy improvement over traditional LIF on five datasets and achieves high accuracy on them. In conclusion, it reveals that the introduction of the electrical synapse is an important factor for achieving high accuracy on realistic spatio-temporal tasks.
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The matrix method used in many studies of wave theory, for easy calculations, is described and used in the shallow water breaking theory. We deal with shallow water wave breaking and the method of unimodular matrix. Introducing a class of nonlinear water waves, the solution in the stratification regions using matrix method through unimodularity is given. In this paper, we present the stratification approximated by n-layers. Our method firstly involves a 2x2 matrix. Taking the production of n 2x2 matrices, we choose the layers with linear variation. The main part of our work covers the fact that energy conservation law is satisfied. For this, the unimodularity of the matrices is used. The models are tested against experiments concerning periodic wave transformation. The density and the speed of waves vary exponentially with depth. We conclude with experiments and some important conclusions.
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The matrix method used in many studies of wave theory, for easy calculations, is described and used in the shallow water breaking theory. We deal with shallow water wave breaking and the method of unimodular matrix. Introducing a class of nonlinear water waves, the solution in the stratification regions using matrix method through unimodularity is given. In this paper, we present the stratification approximated by n-layers. Our method firstly involves a 2x2 matrix. Taking the production of n 2x2 matrices, we choose the layers with linear variation.The main part of our work covers the fact that energy conservation law is satisfied. For this, the unimodularity of the matrices is used. The models are tested against experiments concerning periodic wave transformation. The density and the speed of waves vary exponentially with depth. We conclude with experiments and some important conclusions.
Article
Hodgkin-Huxley model is a system of four non-linear coupled differential equations which describes and explains the threshold and action potential by a stimulus arising in a single neuron. The solution and analysis of Hodgkin-Huxley equations is a formidable task because of the coupling between non-linear differential equations, lots of unknowns and their dependence on many physical parameters. Although this model has been solved by numerical methods, finding an analytic solution is interesting due to the challenges that the continuum model offers. In this paper, first order semi analytic solution of this model, in space-clamped situation, is derived by Homotopy Perturbation Method. We applied this technique in piece wise manner due to the strong and complex coupling between the variables in the model. Without this modification, finding an accurate analytic solution is impossible for this neural model. Results show that computed analytic solution has excellent agreement with higher order numerical solution. Robustness of the computed analytic solution in different physical scenarios is examined. Further, this analytic solution can describe many key properties such as the threshold potential, the action potential and the refractory period. MATLAB software is used to simulate the solution.
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Analyses have been made, with respect to the principal inorganic constituents, of the blood and urine of Carcinus, when living in normal sea water, diluted sea water, and sea water modified by the addition of magnesium sulphate. The composition of the blood of individuals living in normal sea water is as follows (the concentration of each ion being expressed as a percentage of the concentration that would be expected if the blood were in dialysis equilibrium with the external medium): Na 110%, K 118%, Ca 108%, Mg 34%, Cl 104%, SO4 61%. This ionic regulation is the resultant of the following processes: active absorption by the gills of sodium, potassium, calcium and chloride at a rate greater than that at which they are lost by diffusion; differential excretion by the antennary gland, which tends to conserve potassium and eliminate magnesium and sulphate; inward diffusion across the gills of magnesium and sulphate in accordance with the concentration gradient. In normal conditions there is active absorption of water. In dilute media, when osmoregulation begins, this is suspended, and possibly there is a fall in the passive permeability of the gills to water. In other respects osmoregulation is brought about by an intensification of the processes responsible for ionic regulation. The permeability of the cuticle under physiological conditions is such that it does not affect the salt and water exchange of the animal, which is controlled by the branchial epithelium. The structure of the gills of four species of Decapoda is described, and correlated with their powers of osmotic and ionic regulation.
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SUMMARY1Four methods of determining the potential difference across the surface membrane of living cells are described.2In a wide range of excitable tissues the resting membrane potential is of the order of 50–100 mV. and the action potential of the order of 80–130 mV.3At the height of activity the potential difference across the membrane is reversed by 30–50 mV.4The potassium concentration inside most excitable cells is 20–50 times greater than that in the external medium; sodium is 3–15 times more concentrated outside than it is inside, while chloride is 5–50 times more concentrated outside than inside. Isolated fibres lose potassium and gain sodium and chloride ions.5Potassium appears to exist as a free ion inside nerve and muscle fibres.6The nature of the organic anions which balance the high concentration of potassium inside excitable cells is still largely unknown. In certain cases amino-acids such as aspartic acid are present in high concentrations.7The resting membrane behaves as though it were moderately permeable to K+ and Cl- but sparingly permeable to Na+. The absolute magnitude of the resting potential is similar to that calculated from the potassium concentrations if allowance is made for the contributions of chloride and other ions. Movements of K+ and Cl- as determined by radioactive tracers or by chemical methods agree with a quantitative formulation of this hypothesis.8It is necessary to suppose that sodium is continuously pumped out of excitable cells by a process which depends on metabolism.9Electrical activity is due to a large and specific increase in the permeability to sodium. The reversed potential difference across the active membrane arises from the concentration difference of sodium and varies with the external concentration of sodium in the same manner as the theoretical potential of a sodium electrode.10In many cells, conduction of impulses is impossible if the external medium does not contain sodium or lithium ions.11The rate of rise of the action potential varies with the concentration of sodium ions in the external medium.12Sodium enters a nerve fibre when it is active. The quantity entering 1 cm.2 of membrane during one impulse is of the order of 3 μμmol.13Entry of sodium is approximately balanced by the leakage of a corresponding quantity of potassium.14It is suggested that sodium enters the nerve fibre during the rising phase of the action potential and that potassium leaves during the falling phase.15The permeability changes during the action potential probably consist of a rapid but transient increase in the permeability to sodium and a delayed increase in the permeability to potassium. It is suggested that both permeability changes vary with membrane potential in a graded but reversible manner. This hypothesis is applied to the phenomena of subthreshold activity, accomodation and oscillatory behaviour.16In vertebrate myelinated fibres there is much evidence to show that conduction is saltatory; this suggests that sodium entry is confined to the nodes of Ranvier, and that the internodes are depolarized by local circuit action.17Provided that nerves are not stimulated at a high rate, recovery heat production is sufficient to account for the metabolic extrusion of sodium after activity.
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The direct current longitudinal resistance of the squid giant axon was measured as a function of the electrode separation. Large sea water electrodes were used and the inter-electrode length was immersed in oil. The slope of the resistance vs. separation curve is large for a small electrode separation, but becomes smaller and finally constant as the separation is increased. An analysis of the resistance vs. length curves gives the following results. The nerve membrane has a resistance of about 1000 ohm cm.(2) The protoplasm has a specific resistance of about 1.4 times that of sea water. The resistance of the connective tissue sheath outside the fiber corresponds to a layer of sea water about 20micro in thickness. The characteristic length for the axon is about 2.3 mm. in oil and 6.0 mm. in sea water.
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Alternating current impedance measurements have been made over a wide frequency range on the giant axon from the stellar nerve of the squid, Loligo pealii, during the passage of a nerve impulse. The transverse impedance was measured between narrow electrodes on either side of the axon with a Wheatstone bridge having an amplifier and cathode ray oscillograph for detector. When the bridge was balanced, the resting axon gave a narrow line on the oscillograph screen as a sweep circuit moved the spot across. As an impulse passed between impedance electrodes after the axon had been stimulated at one end, the oscillograph line first broadened into a band, indicating a bridge unbalance, and then narrowed down to balance during recovery. From measurements made during the passage of the impulse and appropriate analysis, it was found that the membrane phase angle was unchanged, the membrane capacity decreased about 2 per cent, while the membrane conductance fell from a resting value of 1000 ohm cm.(2) to an average of 25 ohm cm.(2) The onset of the resistance change occurs somewhat after the start of the monophasic action potential, but coincides quite closely with the point of inflection on the rising phase, where the membrane current reverses in direction, corresponding to a decrease in the membrane electromotive force. This E.M.F. and the conductance are closely associated properties of the membrane, and their sudden changes constitute, or are due to, the activity which is responsible for the all-or-none law and the initiation and propagation of the nerve impulse. These results correspond to those previously found for Nitella and lead us to expect similar phenomena in other nerve fibers.
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This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre (Hodgkinet al., 1952,J. Physiol.116, 424–448; Hodgkin and Huxley, 1952,J. Physiol.116, 449–566). Its general object is to discuss the results of the preceding papers (Section 1), to put them into mathematical form (Section 2) and to whow that they will account for conduction and excitation in quantitative terms (Sections 3–6).
Membrane electrophoresis in relation to bio-electrical polarization effects
TEORELL, T. (1949b). Membrane electrophoresis in relation to bio-electrical polarization effects. Arch. Sci. phyl. 3, 205-218.
The distinction bv means of tracers between active transport and diffusion
USSIN, H. H. (1949). The distinction bv means of tracers between active transport and diffusion. Acta physiol. 8cand. 19, 43-56.
The sodium and potassium content of sea water
WEBB, D. A. (1939). The sodium and potassium content of sea water. J. exp. Biol. 16,178-183.
Ueber wechselseitige Diffusion von Elektrolyten in verdunnten wasserigen L6sungen, inebesondere uber Diffusion gegen das Concentrationsgefalle
BE~HN, U. (1897). Ueber wechselseitige Diffusion von Elektrolyten in verdunnten wasserigen L6sungen, inebesondere uber Diffusion gegen das Concentrationsgefalle. Ann. Phy8., Lpz., N.F. 62, 54-67.