A simple integrative electrophysiological model of bursting GnRH neurons

In this paper a modular model of the GnRH neuron is presented. For the aim of simplicity, the currents corresponding to fast time scales and action potential generation are described by an impulsive system, while the slower currents and calcium dynamics are described by usual ordinary differential equations (ODEs). The model is able to reproduce the depolarizing afterpotentials, afterhyperpolarization, periodic bursting behavior and the corresponding calcium transients observed in the case of GnRH neurons.     

Ionic mechanisms of endogenous bursting in CA3 hippocampal pyramidal neurons: a model study

A critical property of some neurons is burst firing, which in the hippocampus plays a primary role in reliable transmission of electrical signals. However, bursting may also contribute to synchronization of electrical activity in networks of neurons, a hallmark of epilepsy. Understanding the ionic mechanisms of bursting in a single neuron, and how mutations associated with epilepsy modify these mechanisms, is an important building block for understanding the emergent network behaviors. We present a single-compartment model of a CA3 hippocampal pyramidal neuron based on recent experimental data. We then use the model to determine the roles of primary depolarizing currents in burst generation. The single compartment model incorporates accurate representations of sodium (Na(+)) channels (Na(V)1.1) and T-type calcium (Ca(2+)) channel subtypes (Ca(V)3.1, Ca(V)3.2, and Ca(V)3.3). Our simulations predict the importance of Na(+) and T-type Ca(2+) channels in hippocampal pyramidal cell bursting and reveal the distinct contribution of each subtype to burst morphology. We also performed fast-slow analysis in a reduced comparable model, which shows that our model burst is generated as a result of the interaction of two slow variables, the T-type Ca(2+) channel activation gate and the Ca(2+)-dependent potassium (K(+)) channel activation gate. The model reproduces a range of experimentally observed phenomena including afterdepolarizing potentials, spike widening at the end of the burst, and rebound. Finally, we use the model to simulate the effects of two epilepsy-linked mutations: R1648H in Na(V)1.1 and C456S in Ca(V)3.2, both of which result in increased cellular excitability.     

Low dimensional model of bursting neurons

A computationally efficient, biophysically-based model of neuronal behavior is presented; it incorporates ion channel dynamics in its two fast ion channels while preserving simplicity by representing only one slow ion current. The model equations are shown to provide a wide array of physiological dynamics in terms of spiking patterns, bursting, subthreshold oscillations, and chaotic firing. Despite its simplicity, the model is capable of simulating an extensive range of spiking patterns. Several common neuronal behaviors observed in vivo are demonstrated by varying model parameters. These behaviors are classified into dynamical classes using phase diagrams whose boundaries in parameter space prove to be accurately delineated by linear stability analysis. This simple model is suitable for use in large scale simulations involving neural field theory or neuronal networks.     

A basic biophysical model for bursting neurons

Presented here is a basic biophysical cell model for bursting, an extension of our previous model (Av-Ron et al. 1991) for excitability and oscillations. By changing a limited set of model parameters, one can describe different patterns of bursting behavior in terms of the burst cycle, the durations of oscillation and quiescence, and firing frequency.     

Investigations of the ionic mechanisms of bursting activity in Helix pomatia neurons

Steady-state current-voltage characteristics of the membrane and ionic currents arising during changes in membrane potential in bursting neurons ofHelix pomatia were studied by the voltage clamp method. The steady-state current-voltage characteristics of the membrane were shown to have a nonlinear region. Replacement of sodium ions by Tris-HC1 ions in the external solution completely abolishes this nonlinearity. Hyperpolarization of the membrane under voltage clamp conditions leads to the development of an outward current which reaches a maximum and then is inactivated. This current has a reversal potential in the region of the potassium equilibrium potential. Depolarization of the membrane to the threshold value for excitation of uncontrollable regions of the axon hillock causes the appearance of a slow inward current. After reaching a maximum, the inward current falls to zero. A model of generation of waves in a bursting neuron is suggested.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 10, No. 2, pp. 193–202, March–April, 1978.     

A unified model for two modes of bursting in GnRH neurons

Gonadotropin-releasing hormone (GnRH) neurons exhibit at least two intrinsic modes of action potential burst firing, referred to as parabolic and irregular bursting. Parabolic bursting is characterized by a slow wave in membrane potential that can underlie periodic clusters of action potentials with increased interspike interval at the beginning and at the end of each cluster. Irregular bursting is characterized by clusters of action potentials that are separated by varying durations of interburst intervals and a relatively stable baseline potential. Based on recent studies of isolated ionic currents, a stochastic Hodgkin-Huxley (HH)-like model for the GnRH neuron is developed to reproduce each mode of burst firing with an appropriate set of conductances. Model outcomes for bursting are in agreement with the experimental recordings in terms of interburst interval, interspike interval, active phase duration, and other quantitative properties specific to each mode of bursting. The model also shows similar outcomes in membrane potential to those seen experimentally when tetrodotoxin (TTX) is used to block action potentials during bursting, and when estradiol transitions cells exhibiting slow oscillations to irregular bursting mode in vitro. Based on the parameter values used to reproduce each mode of bursting, the model suggests that GnRH neurons can switch between the two through changes in the maximum conductance of certain ionic currents, notably the slow inward Ca²⁺ current I _s, and the Ca²⁺ -activated K⁺ current I _KCa. Bifurcation analysis of the model shows that both modes of bursting are similar from a dynamical systems perspective despite differences in burst characteristics.     

Pacemaker neurons and neuronal networks: an integrative view

Rhythmically active neuronal networks give rise to rhythmic motor activities but also to seemingly non-rhythmic behaviors such as sleep, arousal, addiction, memory and cognition. Many of these networks contain pacemaker neurons. The ability of these neurons to generate bursts of activity intrinsically lies in voltage- and time-dependent ion fluxes resulting from a dynamic interplay among ion channels, second messenger pathways and intracellular Ca2+ concentrations, and is influenced by neuromodulators and synaptic inputs. This complex intrinsic and extrinsic modulation of pacemaker activity exerts a dynamic effect on network activity. The nonlinearity of bursting activity might enable pacemaker neurons to facilitate the onset of excitatory states or to synchronize neuronal ensembles--an interactive process that is intimately regulated by synaptic and modulatory processes.     

Environmental carcinogenesis: an integrative model.

An integrative theory is proposed in which environmental carcinogenesis is viewed as a process by which the genetic control of cell division and differentiation is altered by carcinogens. In this theory, carcinogens include physical, chemical, and viral "mutagens," as well as chemical and viral gene modulators. Existing explanations of carcinogenesis can be considered either as somatic mutation theories or as epigenetic theories. Evidence seems to support the hypothesis that both mutations and epigenetic processes are components of carcinogenesis. The mutational basis of cancer is supported by the clonal nature of tumors, the mutagenicity of most carcinogens, high mutation frequencies in cells of cancer-prone human fibroblasts lacking DNA repair enzymes, the correlation of in vitro DNA damage and in vitro mutation and transformation frequencies with in vivo tumorigenesis, age-related incidences of various hereditary tumors, and the correlation between photoreactivation of DNA damage and the biological amelioration of UV-induced neoplasms. Since both mutagens and gene modulators can be carcinogenic it may be that carcinogens affect genes which control cell division. An integration of the mutation and epigenetic theories of cancer with the "two-stage" theory and Comings's general theory of carcinogenesis is proposed. This integrative theory postulates that carcinogens can affect regulatory genes which control a series of "transforming genes." A general hypothesis is advanced that involves a common mechanism of somatic mutagenesis via error-prone repair of DNA damage which links carcinogenesis, teratogenesis, atherosclerosis and aging. Various concepts are presented to provide a framework for evaluating the scientific, medical, and social implications of cancer.     

An integrate-and-fire model for synchronized bursting in a network of cultured cortical neurons

It has been suggested that spontaneous synchronous neuronal activity is an essential step in the formation of functional networks in the central nervous system. The key features of this type of activity consist of bursts of action potentials with associated spikes of elevated cytoplasmic calcium. These features are also observed in networks of rat cortical neurons that have been formed in culture. Experimental studies of these cultured networks have led to several hypotheses for the mechanisms underlying the observed synchronized oscillations. In this paper, bursting integrate-and-fire type mathematical models for regular spiking (RS) and intrinsic bursting (IB) neurons are introduced and incorporated through a small-world connection scheme into a two-dimensional excitatory network similar to those in the cultured network. This computer model exhibits spontaneous synchronous activity through mechanisms similar to those hypothesized for the cultured experimental networks. Traces of the membrane potential and cytoplasmic calcium from the model closely match those obtained from experiments. We also consider the impact on network behavior of the IB neurons, the geometry and the small world connection scheme. Action Editor: David Golomb     

Possible interaction between synaptic and pacemaker mechanisms of electrical activity in bursting neurons of Helix pomatia

Membrane hyperpolarization induced by short pulses of inward current, by stimulation of the anal nerve, which leads to the appearance of a long IPSP in the neuron, and developing during the appearance of spontaneous IPSPs in the neuron was investigated in neuron RPa1 ofHelix pomatia. Short-term hyperpolarization of the neuron membrane by an inward current (10 msec) led to the development of self-maintained (regenerative) membrane hyperpolarization lasting several seconds. The amplitude and duration of regenerative hyperpolarization increased with an increase in amplitude and duration of the pulse of inward current. The time course of IPSPs arising spontaneously in the neuron and in response to stimulation of the anal nerve was similar to that of regenerative hyperpolarization evoked by a pulse of inward current. It is suggested that regenerative hyperpolarization associated with activation of endogenous mechanisms of regulation of the bursting activity of the neuron may be due not only to short-term membrane hyperpolarization of the test neuron by the electric current, but also to hyperpolarization occurring during IPSP generation.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 13, No. 1, pp. 67–74, January–February, 1981.     

2 types of neurons differing in their plastic properties: study of ionic mechanisms

Plasticity ionic mechanisms of 2 types of neurones identified in the brain of snail Helix pomatia: habituating and non-habituating to rhythmic intracellular stimulation by DC pulses were studied. It has been shown that the development of habituation is due to entering of Ca2+ into the cell and by its activation of Ca-dependent K-conductivity of the membrane, leading to hyperpolarization, decrease of input resistance and elimination of spike response to stimulation. Depression of Ca-dependent K-conductivity by quinine totally blocks the ability of the neurons to habituate to stimulation. The data obtained on non-habituating neurons testify that their non-habituation to intracellular stimulation results from their absence or weak manifestation of Ca-dependent K-conductivity in their membrane. Ca2+ entering non-habituating cells during electrical stimulation may have depolarizing and facilitating effects.     

Two independent mechanisms down-regulate the intrinsic SecA ATPase activity

SecA initiates protein translocation by interacting with ATP, preprotein, and the SecYEG membrane components. Under such conditions, it undergoes a conformational change characterized as membrane insertion, which is then followed by hydrolysis of ATP, enabling the release of the preprotein and deinsertion of SecA itself for the next cycle of reactions. Without ongoing translocation, the ATPase activity of SecA is kept very low. Previously, it was shown that the C-terminal 34-kDa domain of SecA interacts with the N-terminal 68-kDa ATPase domain to down-regulate the ATPase. Here, we show, using a deregulated SecA mutant, that the intrinsic ATPase activity is subject to dual inhibitory mechanisms. Thus, the proposed second ATP-binding domain down-regulates the ATPase activity executed by the primary ATPase domain. This regulation, within the N-terminal ATPase domain, operates independently of the C-terminal domain-mediated regulation. The absence of both the mechanisms resulted in a 50-fold elevation of translocation-uncoupled ATP hydrolysis.     

Predictive features of persistent activity emergence in regular spiking and intrinsic bursting model neurons

Proper functioning of working memory involves the expression of stimulus-selective persistent activity in pyramidal neurons of the prefrontal cortex (PFC), which refers to neural activity that persists for seconds beyond the end of the stimulus. The mechanisms which PFC pyramidal neurons use to discriminate between preferred vs. neutral inputs at the cellular level are largely unknown. Moreover, the presence of pyramidal cell subtypes with different firing patterns, such as regular spiking and intrinsic bursting, raises the question as to what their distinct role might be in persistent firing in the PFC. Here, we use a compartmental modeling approach to search for discriminatory features in the properties of incoming stimuli to a PFC pyramidal neuron and/or its response that signal which of these stimuli will result in persistent activity emergence. Furthermore, we use our modeling approach to study cell-type specific differences in persistent activity properties, via implementing a regular spiking (RS) and an intrinsic bursting (IB) model neuron. We identify synaptic location within the basal dendrites as a feature of stimulus selectivity. Specifically, persistent activity-inducing stimuli consist of activated synapses that are located more distally from the soma compared to non-inducing stimuli, in both model cells. In addition, the action potential (AP) latency and the first few inter-spike-intervals of the neuronal response can be used to reliably detect inducing vs. non-inducing inputs, suggesting a potential mechanism by which downstream neurons can rapidly decode the upcoming emergence of persistent activity. While the two model neurons did not differ in the coding features of persistent activity emergence, the properties of persistent activity, such as the firing pattern and the duration of temporally-restricted persistent activity were distinct. Collectively, our results pinpoint to specific features of the neuronal response to a given stimulus that code for its ability to induce persistent activity and predict differential roles of RS and IB neurons in persistent activity expression.     

Interval analysis of bursting discharges in aplysia neurons

Time intervals of 12 records of bursting discharges in Aplysia neurons were analysed by digital computer to determine the interrelations between the burst period, the interburst interval and the burst duration. The effects of membrane potential changes on the parameters of bursting discharges were examined also. A low correlation was found between burst duration and burst period in the majority of cases, and this was interpreted as an indication of probable independence between the mechanisms governing these parameters. Also, a specific temporal organization of interspike intervals seems to be present in each type of neuron. The results suggest that the mechanism governing the burst period is characterized by a slow membrane potential oscillation resembling that observed in bursting neurons when actions potentials are blocked by tetrodotoxin. The burst duration would be determined by the response of the neuron to suprathreshold depolarization.     

Possible mechanism of bursting suppression in nociceptive neurons

The use of the mathematical model of rat nociceptive neuron membrane allowed us to predict a new mechanism of suppression of ectopic bursting discharges, which arise in neurons of dorsal root ganglia and are one of the causes of neuropathic pain. The treatment with comenic acid leads to switching off the ectopic bursting discharges due to a decrease in the effective charge transferring via the activation gating structure of the slow sodium channels (Na _V1.8a). Comenic acid is a drug substance of a new non-opioid analgesic [1] Thus, this analgesic not only reduces the frequency of rhythmic discharges of nociceptive neuron membrane [2] but also it suppresses its ectopic bursting discharges.     

Two independent type III secretion mechanisms for YopE in Yersinia enterocolitica

Pathogenic Yersinia species escape the infected host's defense mechanisms by targeting cytotoxic Yop proteins into the cytoplasm of macrophages via a type III secretion pathway. Two separate secretion signals contained in YopE were identified, each of which were sufficient but not necessary for the secretion of reporter molecules. One signal is located within the coding sequence of the first 15 amino acids and is sufficient for the secretion of fusion proteins but not required for YopE secretion. The second signal is located downstream at residues 15–100 of YopE and is only recognized by the type III machinery when it is bound to SycE. We propose the existence of two independent mechanisms that allow for the secretion of Yop proteins.     

Model predictions of the ionic mechanisms underlying the beating and bursting pacemaker characteristics of molluscan neurons

The general properties of the excitable membrane on molluscan pacemaker neurons can be described on the basis of a fair amount of experimental evidence available in the literature. The neuronal membrane exhibits under voltage clamp an initial inward current carried by both Na⁺ and Ca²⁺ ions, the time- and voltage-dependent characteristics of which are similar to that of other excitable structures. The conductance mechanism for the two ion species and the transport kinetics appear to be closely similar. The time course and amplitude of the delayed outward current carried by K⁺ ions shows a marked dependence on the membrane potential. Characteristic for the molluscan neurons is the existence of an additional fast transient outward current which is only activated by hyperpolarizing shifts from the membrane potential. A regular beating discharge over a wide range of frequencies can be predicted by making the assumption of a metabolically controlled driving of the Na⁺ conductance. Bursting pacemaker characteristics can be correctly simulated by the model if sinusoidal variations of an additional Na⁺ and Ca²⁺ conductances g _Na and g _Ca, and periodic variations of the K⁺ conductance g _K, governed by the known operation of a metabolic substrate cycle are introduced. The close approximation of experimentally observed impulse bursts requires that the actual inpulse-frequency and the amplitude of the after-spike hyperpolarization are determined by the temporal pattern of g _Na, while the spike amplitude is controlled by g _Na which (although of similar time course) is lagging in phase behing g _Na. The periodic changes in additional K⁺ conductance g _K, are responsible for burst termination and the changes in inter-burst interval, to the effect that spike doublets, triplets and multi-spike bursts can be simulated by a suitable choice for the time characteristics of g _K. The model makes use of the finding that the Ca²⁺ inflow associated with a spike discharge actually activates g _K, so that large postburst hyperpolarizations can be obtained in high-frequency bursts.Supported by the Deutsche Forschungsgemeinschaft (Grant Ch 25/1)