A minimal,compartmental model for a dendritic origin of bistability of motoneuron firing patterns

Various nonlinear regenerative responses, including plateau potentials and bistable repetitive firing modes, have been observed in motoneurons under certain conditions. Our simulation results support the hypothesis that these responses are due to plateau-generating currents in the dendrites, consistent with a major role for a noninactivating calcium L-type current as suggested by experiments. Bistability as observed in the soma of low- and higher-frequency spiking or, under TTX, of near resting and depolarized plateau potentials, occurs because the dendrites can be in a near resting or depolarized stable steady state. We formulate and study a two-compartment minimal model of a motoneuron that segregates currents for fast spiking into a soma-like compartment and currents responsible for plateau potentials into a dendrite-like compartment. Current flows between compartments through a coupling conductance, mimicking electrotonic spread. We use bifurcation techniques to illuminate how the coupling strength affects somatic behavior. We look closely at the case of weak coupling strength to gain insight into the development of bistable patterns. Robust somatic bistability depends on the electrical separation since it occurs only for weak to moderate coupling conductance. We also illustrate that hysteresis of the two spiking states is a natural consequence of the plateau behavior in the dendrite compartment.     

The role of a transient potassium current in a bursting neuron model

Presented here is a biophysical cell model which can exhibit low-frequency repetitive activity and bursting behavior. The model is developed from previous models (Av-Ron et al. 1991, 1993) for excitability, oscillations and bursting. A stepwise development of the present model shows the contribution of a transient potassium current (I _A ) to the overall dynamics. By changing a limited set of model parameters one can describe different firing patterns; oscillations with frequencies ranging from 2–200 Hz and a wide range of bursting behaviors in terms of the durations of bursting and quiescence, peak firing frequency and rate of change of the firing frequency.     

A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties

The integrate-and-fire neuron model describes the state of a neuron in terms of its membrane potential, which is determined by the synaptic inputs and the injected current that the neuron receives. When the membrane potential reaches a threshold, an action potential (spike) is generated. This review considers the model in which the synaptic input varies periodically and is described by an inhomogeneous Poisson process, with both current and conductance synapses. The focus is on the mathematical methods that allow the output spike distribution to be analyzed, including first passage time methods and the Fokker–Planck equation. Recent interest in the response of neurons to periodic input has in part arisen from the study of stochastic resonance, which is the noise-induced enhancement of the signal-to-noise ratio. Networks of integrate-and-fire neurons behave in a wide variety of ways and have been used to model a variety of neural, physiological, and psychological phenomena. The properties of the integrate-and-fire neuron model with synaptic input described as a temporally homogeneous Poisson process are reviewed in an accompanying paper (Burkitt in Biol Cybern, 2006).     

Ion channels and information processing in GnRH neuron dendrites

Recent findings indicate that a majority of action potentials originate from dendrites of GnRH neurons. This localization of the dendrite as the principle site of action potential initiation has sparked considerable interest in the nature of ionic channels throughout GnRH neurons. This paper will review the ionic conductances described within GnRH neurons and their implications for physiological output, such as sensitivity to steroids and diurnal state. To date, a majority of information regarding ionic conductances in GnRH neurons pertains to somata and the first 50–100 µm of dendrite length. Thus, unraveling the tapestry created by the nature and distribution of dendritic conductances in GnRH neurons lies at the forefront of understanding the control of reproductive hormone secretion.     

对一个气孔经验模型的电学类比分析和模拟检验

对Ｂａｌｌ等人提出的气孔经验模型进行了分析和模拟检验,分析是通过电学类比实现的,在引进叶片边界层导度很大等假设后可以从气孔内外ＣＯ２浓度之比保持恒定的实验事实推导出这个经验模型的表达式;在其它类似的实验事实的基础上已可作同样的推导。模拟检验中采用的是由我们建立的人为完整的气孔对环境响应的机理性定态数学模型。两种方法得出的结论是一致的：Ｂａｌｌ等人的经验模型有一定的局限性,因为它不能模拟边界层阻力和叶温对气孔导度的影响。由此我们指出叶片表面的风速是影响气孔导度的重要环境因子之一。一个完整的气孔模型必须包括它的影响。     

Motor neuron degeneration in a mouse model of seipinopathy

Heterozygosity for missense mutations (N88S/S90L) in BSCL2 (Berardinelli–Seip congenital lipodystrophy type 2)/Seipin is associated with a broad spectrum of motoneuron diseases. To understand the underlying mechanisms how the mutations lead to motor neuropathy, we generated transgenic mice with neuron-specific expression of wild-type (tgWT) or N88S/S90L mutant (tgMT) human Seipin. Transgenes led to the broad expression of WT or mutant Seipin in the brain and spinal cord. TgMT, but not tgWT, mice exhibited late-onset altered locomotor activities and gait abnormalities that recapitulate symptoms of seipinopathy patients. We found loss of alpha motor neurons in tgMT spinal cord. Mild endoreticular stress was present in both tgMT and tgWT neurons; however, only tgMT mice exhibited protein aggregates and disrupted Golgi apparatus. Furthermore, autophagosomes were significantly increased, along with elevated light chain 3 (LC3)-II level in tgMT spinal cord, consistent with the activation of autophagy pathway in response to mutant Seipin expression and protein aggregation. These results suggest that induction of autophagy pathway is involved in the cellular response to mutant Seipin in seipinopathy and that motoneuron loss is a key pathogenic process underlying the development of locomotor abnormalities.     

An analysis of a dendritic neuron model with an active membrane site

We formulate and analyze a mathematical model that couples an idealized dendrite to an active boundary site to investigate the nonlinear interaction between these passive and active membrane patches. The active site is represented mathematically as a nonlinear boundary condition to a passive cable equation in the form of a space-clamped FitzHugh-Nagumo (FHN) equation. We perform a bifurcation analysis for both steady and periodic perturbation at the active site. We first investigate the uncoupled space-clamped FHN equation alone and find that for periodic perturbation a transition from phase locked (periodic) to phase pulling (quasiperiodic) solutions exist. For the model coupling a passive cable with a FHN active site at the boundary, we show for steady perturbation that the interval for repetitive firing is a subset of the interval for the space-clamped case and shrinks to zero for strong coupling. The firing rate at the active site decreases as the coupling strength increases. For periodic perturbation we show that the transition from phase locked to phase pulling solutions is also dependent on the coupling strength.This work was supported in part by NSF Grants MCS 83-00562 and MDS 85-01535     

Coding of odor intensity in a steady-state deterministic model of an olfactory receptor neuron

The coding of odor intensity by an olfactory receptor neuron model was studied under steady-state stimulation. Our model neuron is an elongated cylinder consisting of the following three components: a sensory dendritic region bearing odorant receptors, a passive region consisting of proximal dendrite and cell body, and an axon. First, analytical solutions are given for the three main physiological responses: (1) odorant-dependent conductance change at the sensory dendrite based on the Michaelis-Menten model, (2) generation and spreading of the receptor potential based on a new solution of the cable equation, and (3) firing frequency based on a Lapicque model. Second, the magnitudes of these responses are analyzed as a function of odorant concentration. Their dependence on chemical, electrical, and geometrical parameters is examined. The only evident gain in magnitude results from the activation-to-conductance conversion. An optimal encoder neuron is presented that suggests that increasing the length of the sensory dendrite beyond about 0.3 space constant does not increase the magnitude of the receptor potential. Third, the sensivities of the responses are examined as functions of (1) the concentration at half-maximum response, (2) the lower and upper concentrations actually discriminated, and (3) the width of the dynamic range. The overall gain in sensitivity results entirely from the conductance-to-voltage conversion. The maximum conductance at the sensory dendrite appears to be the main tuning constant of the neuron because it determines the shift toward low concentrations and the increase in dynamic range. The dynamic range of the model cannot exceed 5.7 log units, for a sensitivity increase at low odor concentration is compensated by a sensitivity decrease at high odor concentration.     

Dendritic synchrony and transient dynamics in a coupled oscillator model of the dopaminergic neuron

Transient increases in spontaneous firing rate of mesencephalic dopaminergic neurons have been suggested to act as a reward prediction error signal. A mechanism previously proposed involves subthreshold calcium-dependent oscillations in all parts of the neuron. In that mechanism, the natural frequency of oscillation varies with diameter of cell processes, so there is a wide variation of natural frequencies on the cell, but strong voltage coupling enforces a single frequency of oscillation under resting conditions. In previous work, mathematical analysis of a simpler system of oscillators showed that the chain of oscillators could produce transient dynamics in which the frequency of the coupled system increased temporarily, as seen in a biophysical model of the dopaminergic neuron. The transient dynamics was shown to be consequence of a slow drift along an invariant subset of phase space, with rate of drift given by a Lyapunov function. In this paper, we show that the same mathematical structure exists for the full biophysical model, giving physiological meaning to the slow drift and the Lyapunov function, which is shown to describe differences in intracellular calcium concentration in different parts of the cell. The duration of transients was long, being comparable to the time constant of calcium disposition. These results indicate that brief changes in input to the dopaminergic neuron can produce long lasting firing rate transients whose form is determined by intrinsic cell properties.     

Pyramidal neuron morphogenesis requires a septin network that stabilizes filopodia and suppresses lamellipodia during neurite initiation

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Orexin decreases mRNA expressions of NMDA and AMPA receptor subunits in rat primary neuron cultures

Orexin is one of the orexigenic neuropeptides in the hypothalamus. Orexin neurons in the lateral hypothalamus (LH) project into the cerebral cortex and hippocampus in which the receptors are distributed in high concentrations. Therefore, to elucidate the actions of orexin in the cerebral cortex, we examined its effects on the mRNA expressions of N-methyl-d-aspartate (NMDA) receptor subunits (NR1, NR2A, NR2B) and α-amino-3-hydroxy-5-methylisoxazole-4-propionate (AMPA) receptor subunits (GluR1, GluR2) following 6-day application of orexin-A or orexin-B to rat primary cortical neuron cultures. The mRNAs of NR1 and NR2A subunits were significantly decreased by orexin-A and orexin-B at concentrations over 0.1 μM and 0.01 μM, respectively. The mRNA expression of NR2B subunit was also significantly decreased by orexin-A and orexin-B only at the concentration of 1 μM. Moreover, orexin-A and orexin-B at concentrations over 0.01 μM significantly decreased the mRNA expressions of AMPA receptor subunits, GluR1 and GluR2. The present study demonstrated that orexins significantly suppressed RNA expressions of NMDA and AMPA receptor subunits in cortical neuron cultures, suggesting that orexin may regulate the higher functions of the cerebral cortex as well as be involved in energy regulation in the hypothalamus.     

Calcium spikes in a leech nonspiking neuron

The NS neurons are nonspiking cells, present as pairs in each midbody ganglion of the leech nervous system, which display a very extensive arborization. They were shown to regulate the coactivation of motoneurons. Here we have investigated the electrophysiological properties of these neurons under the hypothesis that transmission along the extensive neurites requires the aid of voltage-dependent conductances. The results indicate that NS neurons respond to electrical stimulation with a spike-like event, which was not an all-or-none but rather a graded phenomenon that depended on the intensity and duration of the electrical stimulus. The spike-like response was activated at a membrane potential of approximately −50 mV; its amplitude was a logarithmic function of the extracellular Ca²⁺ concentration and was unaffected by a broad range of changes in the extracellular Na⁺ concentration; intracellular application of tetraethylammonium (TEA) caused a large increase in its amplitude and duration. These data indicate that NS neurons bear voltage-dependent low-threshold Ca²⁺ and TEA-sensitive K⁺ conductances that could contribute to shaping synaptic signals, or transmission along the extensive neuritic tree.     

Psilocybin induces rapid and persistent growth of dendritic spines in frontal cortex in vivo

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Farnesylated peptides in model membranes: a biophysical investigation

Protein prenylation plays an important role in signal transduction, protein-protein interactions, and the localization and association of proteins with membranes. Using three different techniques, this study physically characterizes the interactions between model dimyristoylphosphatidylcholine membranes and a series of farnesylated peptides. Magic angle spinning nuclear Overhauser enhancement spectroscopy and differential scanning calorimetry reveal that both charged [Ac-Asn-Lys-Asn-Cys-(farnesyl)-OMe and Ac-Asn-Lys-Asn-Cys-(farnesyl)-NH(2)] and uncharged [Ac-Cys-(farnesyl)-OMe and farnesol] species partition into dimyristoylphosphatidylcholine bilayers. Calorimetry and vesicle fluctuation analysis of giant unilamellar vesicles show that the charged peptides modestly decrease the main gel-fluid phase transition and markedly increase the bending rigidity of large unilamellar vesicles. Uncharged species, on the other hand, dramatically decrease the main phase transition and modestly decrease the bending rigidity. No difference with carboxyl methylation is detected.     

Electrical signals in the ER are cell type and stimulus specific with extreme spatial compartmentalization in neurons

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Electrical characteristics of the apical and basal-lateral membranes in the turtle bladder epithelial cell layer

(1) The active transport of Na⁺ across the turtle bladder epithelial cell layer consists of a passive entry step through a Na⁺-selective path in the apical membrane and an active extrusion step through Na⁺ pump-containing path in the basal-lateral membrane together with some back-leakage through the paracellular spaces and tight junctions between the epithelial cells. This hypothesis has now been verified qualitatively and to some extent, quantitatively by the use of an intracellularly-located microelectrode in conjunction with a conventional assembly of extracellularly-located macroelectrodes mainly in short-circuited bladders bathed by Na⁺-rich Ringer media. Under these conditions, the intracellular potential (V_sc) averaged 38.4 mV with the cell electronegative; the fractional resistance of the apical membrane ($\text{?R}{}_{\mathrm{<mtext>a</mtext>}}$) averaged 0.55; while the concomitant transepithelial parameters, short circuiting current (I_sc) and electrical conductance (G_t), average 68.6 μA/cm² and 0.98 mS/cm², respectively. (2) The relation between these parameters and the transepithelial flow of Na⁺ (orI_sc) is evoked by blocking Na⁺ entry into the cell (by the mucosal addition of amiloride or removal of mucosal Na⁺). Amiloride-induced blockade of the Na⁺ entry step results in a rapid hyperpolarization of the cell interior during which V_sc = —79.1 mV and $\text{?R}{}_{\mathrm{<mtext>a</mtext>}}\text{= 0.92}$. I_sc and G_t (equivalent to the shunt conductance under these conditions) averaged 5 μA/cm² and 0.35 mS/cm², respectively. The entire process is reversible on re-admission of Na⁺ entry into the cell. (3) A slow depolarization of the cell interior in the period of blocked transapical Na⁺ entry is opposite to that expected from an electroneutral Na⁺-K⁺ exchanging pump; but instead is the predictable response of an electrogenic Na⁺ pump in parallel with a passive K⁺-selective conductance in the basal-lateral membrane. (4) The electrogenicity concept is substantiated after pretreatment of the bladder with serosal ouabain, which changes the response of V_sc to amiloride (from the aforementioned biphasic response) to a step-function response, attributable mainly to the development of a slowly dissipating K⁺ diffusion potential across the basallateral membrane. (5) Under open-circuit conditions, the electronegativity of cell to mucosa (V_a) is a linear inverse function of the electropositivity of serosa to mucosa (V_t). For V_t ? 100 mV, V_a is positive; and for V_t between ?30 and 90 mV, V_a is negative.     

Spiking neural network model for memorizing sequences with forward and backward recall

We present an oscillatory network of conductance based spiking neurons of Hodgkin–Huxley type as a model of memory storage and retrieval of sequences of events (or objects). The model is inspired by psychological and neurobiological evidence on sequential memories. The building block of the model is an oscillatory module which contains excitatory and inhibitory neurons with all-to-all connections. The connection architecture comprises two layers. A lower layer represents consecutive events during their storage and recall. This layer is composed of oscillatory modules. Plastic excitatory connections between the modules are implemented using an STDP type learning rule for sequential storage. Excitatory neurons in the upper layer project star-like modifiable connections toward the excitatory lower layer neurons. These neurons in the upper layer are used to tag sequences of events represented in the lower layer. Computer simulations demonstrate good performance of the model including difficult cases when different sequences contain overlapping events. We show that the model with STDP type or anti-STDP type learning rules can be applied for the simulation of forward and backward replay of neural spikes respectively.     

Allelopathy of bacteria in a lattice population: Competition between colicin-sensitive and colicin-producing strains

We analyse the population dynamics of two strains of bacteria (Escherichia coli): one strain produces a toxin (called colicin) that increases the mortality of a colicin-sensitive strain in the neighbourhood, but does not harm the colicin-producing strain itself. On the other hand, in the absence of colicin in the environment, the colicin-sensitive strain enjoys a higher population growth rate. The model is closely related to the evolutionary dynamics of social interaction. It has been established previously that a perfectly mixing population shows bistability; that is, whichever strain dominates initially tends to defeat the other. On the other hand, empirical and computer simulation results in lattice structured populations show neither co-existence nor bistability of the two strains. In this paper, we analyse the lattice model based on pair approximation (forming a system of ordinary differential equations of global densities and local densities), and by the direct c omputer simulation of the spatial stochastic model. Both the pair approximation dynamics and the computer simulation show that, for most regions of parameter values, one strain defeats the other, irrespective of the initial abundance. However, the pair approximation analysis also suggests a relatively narrow parameter region of bistability, which should disappear when the model is considered on a lattice of infinitely large size. The biological implications of the results and the relationship of the present model with other models of the evolution of spite or altruistic behaviours are discussed. This suggests that the dynamics reflected by the spatially explicit lattice model may be sufficient, perhaps even necessary, to support the evolution of colicin.     

Responses of olfactory receptor neurons in the spiny lobster to binary mixtures are predictable using a noncompetitive model that incorporates excitatory and inhibitory transduction pathways

Coding of binary mixtures by a population of olfactory receptor neurons in the spiny lobster (Panulirus argus) was examined. Extracellular single-unit responses of 50 neurons to seven compounds and their binary mixtures were recorded. The ability of a noncompetitive model with correction for binding inhibition to predict responses to mixtures based on responses to their components was compared with the predictive abilities of other models. This model assumes that different compounds activate different transduction processes in the same neuron leading to excitation or inhibition, and it includes a term quantifying the degree to which binding of an odorant to its receptor sites is inhibited by other compounds. The model accurately predicted the absolute response magnitude of the population of neurons for 13 of 15 mixtures assessed, which is superior to the predictive power of any of the other models. The model also accurately predicted the across neuron patterns generated by the binary mixtures, as evaluated by multidimensional scaling analysis. The results suggest that there is no emergence of unique qualities for binary mixtures relative to components of these mixtures.Abbreviations AMP or A adenosine-5-monophosphate - ANP across neuron pattern - ARM absolute response magnitude - ASW artificial sea water - Bet or B betaine - Cys or C L-cysteine - Glu or G L-glutamate - MDS multidimensional scaling - MID mixture interaction distance - NC model noncompetitive model - NCBI model noncompetitive model with correction for binding inhibition - C model competitive model - CBI model competitive model with correction for binding inhibition - MEC more effective component - NH ₄ or N ammonium chloride - ORN olfactory receptor neuron - Suc or S DL-succinate - Tau or T taurine     

S100, a brain-specific protein: Localization and possible role in the snail nervous system

Immunofluorescence techniques were used to show that S100 is present on the surface of neuronal and glial membranes of Helix pomatia in vitro. By the method of rocket immunoelectrophoresis of aqueous, Trition, and n-pentanol extracts of snail nervous tissue, S100 was demonstrated to be mainly in the membrane fraction. Anti-S100 antiserum inhibited the electrical activity of identified neurons, pointing to a relationship of this protein with ionic channels of the excitable membrane. The effect of anti-S100 antiserum on the membrane was potential dependent and controlled by the Ca²⁺ concentration.