Accurate and fast simulation of channel noise in conductance-based model neurons by diffusion approximation

Stochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically detailed model neurons calls for the availability of fast numerical methods. In fact, exact techniques employ the microscopic simulation of the random opening and closing of individual ion channels, usually based on Markov models, whose computational loads are prohibitive for next generation massive computer models of the brain. In this work, we operatively define a procedure for translating any Markov model describing voltage- or ligand-gated membrane ion-conductances into an effective stochastic version, whose computer simulation is efficient, without compromising accuracy. Our approximation is based on an improved Langevin-like approach, which employs stochastic differential equations and no Montecarlo methods. As opposed to an earlier proposal recently debated in the literature, our approximation reproduces accurately the statistical properties of the exact microscopic simulations, under a variety of conditions, from spontaneous to evoked response features. In addition, our method is not restricted to the Hodgkin-Huxley sodium and potassium currents and is general for a variety of voltage- and ligand-gated ion currents. As a by-product, the analysis of the properties emerging in exact Markov schemes by standard probability calculus enables us for the first time to analytically identify the sources of inaccuracy of the previous proposal, while providing solid ground for its modification and improvement we present here.     

Stability of the memory of eye position in a recurrent network of conductance-based model neurons

Studies of the neural correlates of short-term memory in a wide variety of brain areas have found that transient inputs can cause persistent changes in rates of action potential firing, through a mechanism that remains unknown. In a premotor area that is responsible for holding the eyes still during fixation, persistent neural firing encodes the angular position of the eyes in a characteristic manner: below a threshold position the neuron is silent, and above it the firing rate is linearly related to position. Both the threshold and linear slope vary from neuron to neuron. We have reproduced this behavior in a biophysically plausible network model. Persistence depends on precise tuning of the strength of synaptic feedback, and a relatively long synaptic time constant improves the robustness to mistuning.     

Behavior of delayed current under voltage clamp in the supramedullary neurons of puffer

Depolarizations applied to voltage-clamped cells bathed in the normal solution disclose an initial inward current followed by a delayed outward current. The maximum slope conductance for the peak initial current is about 30 times the leak conductance, but the maximum slope conductance for the delayed current is only about 10 times the leak conductance. During depolarizations for as long as 30 sec, the outward current does not maintain a steady level, but declines first exponentially with a time constant of about 6 msec; it then tends to increase for the next few seconds; finally, it declines slowly with a half-time of about 5 sec. Concomitant with the changes of the outward current, the membrane conductance changes, although virtually no change in electromotive force occurs. Thus, the changes in the membrane conductance represent two phases of K inactivation, one rapidly developing, the other slowly occurring, and a phase of K reactivation, which is interposed between the two inactivations. In isosmotic KCl solution after a conditioning hyperpolarization there occurs an increase in K permeability upon depolarization. When the depolarizations are maintained, the increase of K permeability undergoes changes similar to those observed in the normal medium. The significance of the K inactivation is discussed in relation to the after-potential of the nerve cells.     

Patch clamp recording from enteric neurons in situ

The study of enteric neurons is key to understanding intestinal motility anGutn of therapeutic strategies for dealing with neurogenic disorders. However, enteric neurons have historically been inaccessible to patch-clamp recording. We report here the first technique that allows patch-clamp recording of neurons from the intact myenteric plexus of the mouse duodenum. The mucosa, submucosa and circular muscles are removed, exposing the myenteric plexus on the longitudinal muscle. Proteolytic treatment of exposed ganglia combined with gentle cell-surface cleaning allows gigaseal formation. Compared with previous studies using intracellular microelectrode recordings or cultured myenteric neurons, this technique provides an opportunity to explore properties of single or multiple ion channels in myenteric neurons in their native environment. The protocol-from the tissue preparation to patch-clamp recording-can be completed in ～4 h.     

Inactivation of calcium current in the somatic membrane of snail neurons

The decline of calcium inward currents evoked by a long-lasting membrane depolarization was studied on isolated snail neurons internally perfused with a K+-free solution. Two exponential components superimposed on a steady inward current could be distinguished, a slow decline with a time constant of several hundreds of milliseconds, observed at all the testing potentials used, and a fast one with a time constant of several dozens of milliseconds, which appeared at depolarizations to about -10 mV and above. When the calcium current was blocked by extracellular Cd2+ or verapamil, an outward current could be recorded at the same depolarizations. Subtraction of the latter current from the total current, recorded prior to the blockage, largely reduced the fast component of the decline of the total current. An increase in pHi from 7.3 to 8.1 led to the elimination of both the outward current and the fast component of the calcium current decline. The slow component remained practically unchanged, with its rate depending upon the current amplitude. It was slowed following intracellular administration of EDTA, and after equimolar substitution of Ba2+ for Ca2+. It is concluded that the fast component of the calcium inward current decline is mainly due to the superposition of the outward current produced by low selective channels. Only the slow component represents an actual decline of the inward current through calcium channels; it is due to ion accumulation at the inner surface of the cell membrane.     

The somatic shunt cable model for neurons.

The derivation of the equations for an electrical model of nerve cells is presented. The model consists of an equivalent cylinder, a lumped somatic impedance, and a variable shunt at the soma. This shunt was introduced to take into account the fast voltage decays observed following the injections of current pulses in some motoneurons and hippocampal granule cells that could not be explained by existing models. The shunt can be interpreted either by penetration damage with the electrode or by a lower membrane specific resistance at the soma than in the dendrites. A solution of the model equations is presented that allows the estimation of the electrotonic length L, the membrane time constant tau m, the dendritic dominance ratio rho, and the shunt parameter epsilon, based only on the measurement of the first two coefficients and time constants in the multiexponential voltage response to injected current pulses.     

A cable model for coupled neurons with somatic gap junctions

A cable model is presented for a pair of electrotonically coupled neurons to investigate the spatial effects of soma-somatic gap junctions. The model extends that of Poznanski et al.(1995) in which each neuron is represented by a tapered equivalent cable attached to an isopotential soma with the two somas being electrically coupled. The model is posed generally, so that both active and passive properties can be considered. In the active case a system of nonlinear integral equations is derived for the voltage, whilst in the passive case these have an exact solution that also holds for inputs modelled as synaptic reversal potentials. Analytical and numerical methods are used to examine the sensitivity of the soma potentials (in particular) to the coupling resistance.     

Voltage dependence of calcium current deactivation in the somatic membrane of mouse sensory neurons

Voltage dependence of the deactivation kinetics of calcium inward currents was investigated in the somatic membrane of murine spinal ganglia neurons. It was found that deactivation of high threshold calcium current has a slower component (=0.80–0.85 msec at a repolarizing potential of –80 mV) as well as the principal transient exponential component (130 sec at the same potential repolarizing level). A dissimilar relationship exists between amplitudes of the transient and slower exponential components, describing deactivation of high threshold calcium current and degree of activation of the depolarizing shift in membrane potential; the former dependence is expressed by a sigmoid and the latter by a V-shaped curve. The slower component of deactivation of high threshold current was inhibited substantially by perfusing the cell with a Tris-PO₄-containing solution. Low-threshold calcium tail current undergoes slower deactivation (=1.1–1.2 msec) at a repolarizing potential of –160 mV. A relationship between the time constant of low threshold current deactivation and the type of penetrating cation used was observed. A kinetic model of calcium current deactivation is suggested, taking account of the three different types of calcium channels, (one low and two high threshold) present in the somatic membrane.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 20, No. 2, pp. 185–193, March–April, 1988.     

Quantitative description of the slowly inactivated barium current through the somatic membrane of molluscan neurons

The potential-dependent slowly inactivated barium current through the somatic membrane of identified neurons of the molluskHelix pomatia was investigated under voltage clamp conditions. The experimental data were analyzed by the equations of Hodgkin and Huxley. Steady-state values of the inactivation variable of this current were shown to be a function, described approximately by an analytical equation, of membrane potential. The slowly inactivated barium current was shown to be proportional to the third power of the activation variable. The dependence of the time constant of activation of this current on membrane potentials was investigated.     

Investigations of excitability of isolated and non-isolated neurons from the terminal ganglion of Periplaneta americana by current/voltage clamp and intracellular perfusion

It was shown by means of current and voltage clamp measurements in combination with the intracellular perfusion method that the isolated motoneuron nerve cell bodies of the cockroach Periplaneta americana show overshoot action potentials. A regenerative Na current was found to be responsible for the excitability of these membranes; however, the results are not in agreement with a de novo synthesis of these channels.     

Efficient induction of functional neurons from adult human fibroblasts

Cellular reprogramming is a rapidly developing technology by which somatic cells are turned into pluripotent stem cells or other somatic cell types through expression of specific combinations of genes. This allows for the generation of patient-specific cell lines that can serve as tools for understanding disease pathogenesis, for drug screens and, potentially, for cell replacement therapies. Several cellular models of neurological disorders based on induced pluripotent cells (iPS cells) have been developed, and iPS-derived neurons are being explored as candidates for transplantation. Recent findings show that neurons can also be induced directly from embryonic and postnatal somatic cells by expression of defined combinations of genes. This conversion does not occur through a pluripotent stem cell stage, which eliminates the risk for tumor formation. Here, we demonstrate for the first time that functional neurons can be generated via direct conversion of fibroblasts also from adult individuals. Thus, this technology is an attractive alternative to iPS cells for generating patient- and disease-specific neurons suitable for disease modeling and autologous transplantation.     

Two types of calcium-dependent channels of potassium outward current in the somatic membrane of Helix pomatia neurons

Characteristics of delayed potassium outward current were investigated during voltage clamp experiments on nonidentified intracellularly perfused neurons isolated from the snailHelix pomatia. A calcium-dependent potassium curent displaying special properties was shown to exist, apart from the voltage-operated potassium currents dependent on intracellular calcium ions . This type of current increases with a rise in the extracellular concentration of calcium ions , is not blocked by intracellular application of 10 mM EGTA and 77 mM fluoride, and may be suppressed by adding 1.5 mM cobalt ions to the extracellular fluid. This current, unlike , only takes a few milliseconds to peak, after which it fades to a steady level, comparable with that of .A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 19, No. 2, pp. 185–191, March–April, 1987.     

Whole-cell voltage clamp measurements of anthrax toxin pore current

Protective antigen (PA) of anthrax toxin binds cellular receptors and forms pores in target cell membranes, through which catalytic lethal factor (LF) and edema factor (EF) are believed to translocate to the cytoplasm. Using patch clamp electrophysiological techniques, we assayed pore formation by PA in real time on the surface of cultured cells. The membranes of CHO-K1 cells treated with activated PA had little to no electrical conductivity at neutral pH (7.3) but exhibited robust mixed ionic currents in response to voltage stimuli at pH 5.3. Pore formation depended on specific cellular receptors and exhibited voltage-dependent inactivation at large potentials (>60 mV). The pH requirement for pore formation was receptor-specific as membrane insertion occurs at significantly different pH values when measured in cells specifically expressing tumor endothelial marker 8 (TEM8) or capillary morphogenesis protein 2 (CMG2), the two known cellular receptors for anthrax toxin. Pores were inhibited by an N-terminal fragment of LF and by micromolar concentrations of tetrabutylammonium ions. These studies demonstrated basic biophysical properties of PA pores in cell membranes and served as a foundation for the study of LF and EF translocation in vivo.     

Mechanisms of voltage transients during current clamp inNecturus gallbladder

Summary Microelectrode techniques were employed to study the mechanisms of the transepithelial voltage transients (V _ms ) observed during transmural current clamps in the isolatedNecturus gallbladder. The results indicate that: a) part of V _ms is due to a transepithelial resistance change (R _t ), and part to a tissue emf change. b) R _t is entirely caused by changes of the resistance of the paracellular pathway. At all current densities employed, the measured changes are probably due to changes in both fluid conductivity and width of the lateral intercellular spaces. At high currents, in addition to the effects on the lateral spaces, the resistance of other elements of the pathway (probably the limiting junction) drops, regardless of the direction of the current. c) The magnitude and polarity of the R _t -independent transepithelial and cell membrane potential transients indicate that the largest emf change takes place at the basolateral membrane (E _b ), with smaller changes at the luminal membrane (E _a ) and the paracellular (shunt) pathway (E _s ). It is shown that two-thirds of the transient are caused by E _s , and one-third by (E _b –E _a ). E _s can be explained by a diffusion potential generated by a current-dependent NaCl concentration gradient across the tissue. E _a and E _b are caused by [K] changes, mainly at the unstirred layer in contact with the basolateral membrane.