Solutions for transients in arbitrarily branching cables: II. Voltage clamp theory

Analytical solutions are derived for arbitrarily branching passive neurone models with a soma and somatic shunt, for synaptic inputs and somatic voltage commands, for both perfect and imperfect somatic voltage clamp. The solutions are infinite exponential series. Perfect clamp decouples different dendritic trees at the soma: each exponential component exists only in one tree; its time constant is independent of stimulating and recording position within the tree; its amplitude is the product of a factor constant over that entire tree and factors dependent on stimulating and recording positions. Imperfect clamp to zero is mathematically equivalent to voltage recording with a shunt. As the series resistance increases, different dendritic trees become more strongly coupled. A number of interesting response symmetries are evident. The solutions reveal parameter dependencies, including an insensitivity of the early parts of the responses to specific membrane resistivity and somatic shunt, and an approximately linear dependence of the slower time constants on series resistance, for small series resistances. The solutions are illustrated using a “cartoon” representation of a CA1 pyramidal cell and a two-cylinder + soma model.     

Cooperative polymerization reactions. Analytical approximations, numerical examples, and experimental strategy

How does one obtain kinetic rate constants from the time course of a reversible and cooperative polymerization reaction? We examine a simple version of the homogeneous nucleation-elongation model with both analytical and numerical techniques to test some common assumptions and develop an experimental strategy. The assumption of irreversible polymer formation is found to be a useful and adequate approximation for the numerical determination of monomer disappearance. The assumption of early "pre-equilibrium" between monomer and seed, however, is shown numerically and analytically to produce significant errors over a wide range of parameters, particularly for small seed lengths. We exhibit numerical solutions for many different parameters, and also discuss analytical techniques that allow approximate solutions for several conditions: the high-concentration limit; the long-time limit; and the long-seed-length, lows concentration limit. The overall reaction simplifies when the monomer concentration is large. An experimental strategy for elucidating the seed size and the rate constants for polymerization and depolymerization is presented.     

Axons Amplify Somatic Incomplete Spikes into Uniform Amplitudes in Mouse Cortical Pyramidal Neurons

Background

Action potentials are the essential unit of neuronal encoding. Somatic sequential spikes in the central nervous system appear various in amplitudes. To be effective neuronal codes, these spikes should be propagated to axonal terminals where they activate the synapses and drive postsynaptic neurons. It remains unclear whether these effective neuronal codes are based on spike timing orders and/or amplitudes.

Methodology/Principal Findings

We investigated this fundamental issue by simultaneously recording the axon versus soma of identical neurons and presynaptic vs. postsynaptic neurons in the cortical slices. The axons enable somatic spikes in low amplitude be enlarged, which activate synaptic transmission in consistent patterns. This facilitation in the propagation of sequential spikes through the axons is mechanistically founded by the short refractory periods, large currents and high opening probability of axonal voltage-gated sodium channels.

Conclusion/Significance

An amplification of somatic incomplete spikes into axonal complete ones makes sequential spikes to activate consistent synaptic transmission. Therefore, neuronal encoding is likely based on spike timing order, instead of graded analogues.     

Using a five-state model for fitting amplitude histograms from MaxiK channels: β-distributions reveal more than expected

Fast gating of ion channels with rate constants higher than the corner frequency of the recording set-up can be evaluated by fitting so-called beta distributions to measured amplitude histograms. Up to now, this was preferentially done for O–C Markov sub-models with one open and one closed state. Here, a fit of the amplitude histograms from MaxiK (BK) single-channel records was achieved with a five-state model with two open and three closed states including three open–close transitions with rate constants higher than the corner frequency (20 kHz) of the inevitable low-pass filter of the recording system. The numerical values of the rate constants of these transitions enabled a nearly one-to-one relationship between typical regions of the histograms and the reactions in the Markov model. These characteristic features are the width of the peak at the apparent single-channel current, the side slopes at the open and at the closed peak, and the depth of the valley between the two peaks. However, the simplex routine alone was incapable of finding the solution but could do so if guided by hand along a suggested strategy.     

Crystallization of Escherichia coli catabolite gene activator protein with its DNA binding site. The use of modular DNA

To obtain crystals of the Escherichia coli catabolite gene activator protein (CAP) complexed with its DNA-binding site, we have searched for crystallization conditions with 26 different DNA segments greater than or equal to 28 base-pairs in length that explore a variety of nucleotide sequences, lengths, and extended 5' or 3' termini. In addition to utilizing uninterrupted asymmetric lac site sequences, we devised a novel approach of synthesizing half-sites that allowed us to efficiently generate symmetric DNA segments with a wide variety of extended termini and lengths in the large size range (greater than or equal to 28 bp) required by this protein. We report three crystal forms that are suitable for X-ray analysis, one of which (crystal form III) gives measurable diffraction amplitudes to 3 A resolution. Additives such as calcium, n-octyl-beta-D-glucopyranoside and spermine produce modest improvements in the quality of diffraction from crystal form III. Adequate stabilization of crystal form III is unexpectedly complex, requiring a greater than tenfold reduction in the salt concentration followed by addition of 2-methyl-2,4-pentanediol and then an increase in the concentration of polyethylene glycol.     

Membrane voltage changes in a compartmental chain model of a neurone

A mathematical model of the neurone has been developed using the method of subdivision of the neurone into a number of equivalent circuit compartments. Compartmental characteristics have been investigated by calculating the shape indices of the output produced in response to a given somatic input conductance change. A generalised form of compartmental chain has been chosen to allow calculation of the shape indices produced by a variety of geometrical configurations including the straight and tapering chain forms. Equations have been deduced from the computations made on a CDC 6600 computer relating the peak amplitude of the output response to the compartmental diameter for both the straight and tapering chain forms. The effect of variation in the location of the input conductance injection site has also been related to the peak amplitude of the somatic response. The optimum characteristics of the input conductance pulse shape have been computed initially using a rectangular pulse and later the more physiologically relevant double exponential shape. The effect of alteration in the end compartmental terminal impedances over the range from open to short circuit conditions was also calculated. The establishment of optimum single compartmental chain criteria allows the future investigation of multiple chain and pyramidal cell configurations.     

Correlation between dendrite diameter and action potential amplitude in sex pheromone specific receptor neurons in male Ostrinia nubilalis (Lepidoptera: Pyralidae)

Outer dendritic segments of olfactory receptor neurons tuned to sex pheromone components were measured morphometrically on the antenna of male European corn borers. Ostrinia nubilalis, to determine if a correlation exists between the diameter of the outer dendritic segment and the spike amplitude. The olfactory sensilla investigated each contained three receptor cells. Two cells were each specific for one of the two pheromone components, (Z)-11-tetradecenyl acetate (Z11-14:OAc) and (E)-11-tetradecenyl acetate (E11-14:OAc). Two strains of cornborers (Z and E) differ as to which of the two pheromone components is the main one. In both strains a large difference could be observed between the spike amplitudes elicited in the receptor cells by the two pheromone components, the main component always eliciting the large spike. In F1-hybrids (EZ) of these two strains, producing both pheromone components in similar quantities, the spike amplitudes were equal in the two pheromone-specific receptor cells. The third cell responded specifically to a behavioural antagonist. (Z)-9-tetradecenyl acetate (Z9-14:OAc) in both the parental and hybrid strains, and always showed the smallest spike amplitude. In a morphometric study, the outer dendritic segments were shown to differ more in diameter between the largest and second largest cell in the two parental strains than in the hybrid strain, while the smallest diameter cell did not differ between the different strains. These results imply that receptor cells with larger diameter produce spikes with greater amplitude. The data also show that all three types of receptor neurons display outer dendritic segments with strong variation in the diameter along the length of the segment, and with a pronounced taper towards the tip.     

Elementary transcallosal connections of the rabbit sensomotor cortex]

Antidromic responses of two callosal neurones to a local electrical stimulation of the rabbit sensorimotor cortex may be recorded simultaneously with one microelectrode in the homotopic cortical area. In such recording conditions the relative amplitude of extracellularly recorded action potentials of the two neurones is determined primarily by the distance between these neurones and the electrode's tip. In response to the stimulation of the symmetrical area transcallosal monosynaptic excitation of the callosal neurone may occur; two callosal neurones may exite monosynaptically one and the same recorded neurone. The results suggest the existence of clusters or columns, formed jointly by the bodies and terminals of callosal neurones; a functional interconnection between symmetrical clusters or columns may exist, in particular a positive feedback.     

Local changes in the transmembrane ion currents in plastic reorganization of electrogenesis in isolated neurons of the pond snail

Transmembrane ion currents were studied on limited (pore diameter 6-15 mcm) areas of isolated neurone's soma membrane. The significant differences of the amplitude and correlation of input and output currents of various areas of the cell membrane were observed. The different directions of transmembrane ion currents' local changes were recorded only in the site of action stimulus during the formation of plastic changes of neurone responses. Natural heterogeneity of total ion current of cell membrane, rapid changes of current components values at local influences probably testify to the possibility of selective plasticity of separate neurone areas.     

Excitable dynein model with multiple active sites for large-amplitude oscillations and bend propagation in flagella

The formal excitable dynein model proposed by Murase et al. (1989, J. theor. Biol. 139, 413-430) is modified to produce large-amplitude oscillations and excitability. The present model assumes that (i) each dynein arm has multiple active sites, which are distributed along most of the 24-nm distance between adjacent B-subtubule attachment sites; and (ii) any given dynein molecule tends to produce force continuously during interdoublet sliding in one direction and to produce little force during sliding in the opposite direction. Since no sliding motion occurs without superthreshold perturbations in the form of the sliding displacement, this new model also possesses an excitable nature. Once passive elastic components (e.g. nexin links and radial spokes) are incorporated into this model, oscillations with large amplitudes result. To test the ability of the model for bend propagation without a curvature-control mechanism, forced oscillations are applied to the basal end of the flagellum by the sliding displacement. It is found that bend propagation can occur even in the absence of a curvature-control mechanism.     

Extracellular potentials from single spinal motoneurons

Extracellular action potentials found close to the surface of motoneurons are related to the intracellular spikes. Evidence is cited to support the assumption that the extracellular spikes have the same time course as the membrane current at the site of recording. Simultaneously recorded intracellular and extracellular spikes are compared. Intracellular spikes are transformed, by means of a circuit which is equivalent to the extracellular recording situation, into transients that are like those appearing extracellularly. Evidence is given that the recordings are from the cell bodies of motoneurons. The results show that the membrane at the extracellular recording site does not produce a spike since the time course of the extracellular potentials is determined by the passive properties of the membrane.     

Changes in miniature endplate potential frequency during repetitive nerve stimulation in the presence of Ca2+, Ba2+, and Sr2+ at the frog neuromuscular junction

Miniature endplate potentials (MEPPs) were recorded from frog sartorious neuromuscular junctions under conditions of reduced quantal contents to study the effect of repetitive nerve stimulation on asynchronous (tonic) quantal transmitter release. MEPP frequency increased during repetitive stimulation and then decayed back to the control level after the conditioning trains. The decay of the increased MEPP frequency after 100-to 200-impulse conditioning trains can be described by four components that decayed exponentially with time constants of about 50 ms, 500 ms, 7 s, and 80 s. These time constants are similar to those for the decay of stimulation-induced changes in synchronous (phasic) transmitter release, as measured by endplate potential (EPP) amplitudes, corresponding, respectively, to the first and second components of facilitation, augmentation, and potentiation. The addition of small amounts of Ca2+ or Ba2+ to the Ca2+-containing bathing solution, or the replacement of Ca2+ with Sr2+, led to a greater increase in the stimulation-induced increases in MEPP frequency. The Sr-induced increase in MEPP frequency was associated with an increase in the second component of facilitation of MEPP frequency; the Ba-induced increase with an increase in augmentation. These effects of Sr2+ and Ba2+ on stimulation-induced changes in MEPP frequency are similar to the effects of these ions on stimulation- induced changes in EPP amplitude. These ionic similarities and the similar kinetics of decay suggest that stimulation induced changes in MEPP frequency and EPP amplitude have some similar underlying mechanisms. Calculations are presented which show that a fourth power residual calcium model for stimulation-induced changes in transmitter release cannot readily account for the observation that stimulation- induced changes in MEPP frequency and EPP amplitude have similar time- courses.     

Electrical consequences of spine dimensions in a model of a cortical spiny stellate cell completely reconstructed from serial thin sections

We built a passive compartmental model of a cortical spiny stellate cell from the barrel cortex of the mouse that had been reconstructed in its entirety from electron microscopic analysis of serial thin sections (White and Rock, 1980). Morphological data included dimensions of soma and all five dendrites, neck lengths and head diameters of all 380 spines (a uniform neck diameter of 0.1 m was assumed), locations of all symmetrical and asymmetrical (axo-spinous) synapses, and locations of all 43 thalamocortical (TC) synapses (as identified from the consequences of a prior thalamic lesion). In the model, unitary excitatory synaptic inputs had a peak conductance change of 0.5 nS at 0.2 msec; conclusions were robust over a wide range of assumed passive-membrane parameters. When recorded at the soma, all unitary EPSPs, which were initiated at the spine heads, were relatively iso-efficient; each produced about 1 mV somatic depolarization regardless of spine location or geometry. However, in the spine heads there was a twentyfold variation in EPSP amplitudes, largely reflecting the variation in spine neck lengths. Synchronous activation of the TC synapses produced a somatic depolarization probably sufficient to fire the neuron; doubling or halving the TC spine neck diameters had only minimal effect on the amplitude of the composite TC-EPSP. As have others, we also conclude that from a somato-centric viewpoint, changes in spine geometry would have relatively little direct influence on amplitudes of EPSPs recorded at the soma, especially for a distributed, synchronously activated input such as the TC pathway. However, consideration of the detailed morphology of an entire neuron indicates that, from a dendro-centric point of view, changes in spine dimension can have a very significant electrical impact on local processing near the sites of input.     

The parameter identification problem for the somatic shunt model

The somatic shunt model, a generalized version of the Rall equivalent cylinder model, is used commonly to describe the passive electrotonic properties of neurons. Procedures for determining the parameters of the somatic shunt model that best describe a given neuron typically rely on the response of the cell to a small step of hyperpolarizing current injected by an intrasomatic recording electrode. In this study it is shown that the problem of estimating model parameters for the somatic shunt model using physiological data is ill-posed, in that very small errors in measured data can lead to large and unpredictable errors in parameter estimates. If the somatic shunt is assumed to be a real property of the intact neuron, the effects of these errors are not severe when predicting EPSP waveshapes resulting from synaptic input at a given location. However, if the somatic shunt is assumed to be a consequence of a leakage pathway around the recording electrode, and a correction for the shunt is applied, then the instability of the inverse problem can introduce large errors in estimates of EPSP waveshape as a function of synaptic location in the intact cell. Morphological constraints can be used to improve the accuracy of the inversion procedure in terms of both parameter estimates and predicted EPSP responses.     

Quantitation of pharyngeal motor function in normal human subjects.

A need exists for accurate pressure recording of pharyngeal motor events. Results of this study indicate that accurate quantitation of pharyngeal motor activity is not possible using a water-filled catheter system, even when high infusion rates are used. An intraluminal strain gauge system, however, achieves high-fidelity recording. Quantitation of pharyngeal peristalsis using the intraluminal strain gauge system reveals peristaltic pressure amplitudes higher than those hitherto recorded. In normal subjects, peristaltic amplitude averages about 200 mmHg in the hypopharynx, complexes in one subject being as high as 600 mmHg. A zone of relatively low pressure exists in the oropharynx. Mean pharyngeal wave duration decreases progressively in an aboral direction, from 1.0 to 0.3 s, and peristaltic wave speeds range between 9 and 25 cm/s. Accurate quantitation of pharyngeal peristaltic variables provides the necessary basis for characterization and assessment of pharyngeal motor disorders.     

Kinetic investigations on the phase transition of phospholipid bilayers

Pressure-jump experiments were performed on vesicles and liposomes of dimyristoyl phosphatidylcholine and dipalmitoyl phosphatidylcholine following the time course of solution turbidity. For both lipids two relaxation effects were evaluated the time constants of which exhibit clear maxima at the midpoint of the phase transition. The time constants lie for vesicles in the 100 μs and 1 ms ranges and for liposomes in the 1 ms and 10 ms ranges. The processes are slightly faster for dimyristoyl phosphatidylcholine than for dipalmitoyl phosphatidylcholine. All relaxation times are concentration-independent. The time constant and amplitude behaviours indicate that all processes are cooperative in agreement with previous interpretations. It is demonstrated that cooperative units can be evaluated from the relaxation amplitudes. These are of the same order of magnitude as those obtained from static experiments. On the grounds of the present kinetic investigation we can state that the application of the linear Ising model to two-dimensional processes as attempted for the static lipid phase transition is inadequate.     

An inexpensive electronic device for measuring electroantennogram responses to sex pheromone components with a voltmeter

ABSTRACT. An inexpensive, portable device which allows measurement of electroantennogram (EAG) maximum amplitudes with a voltmeter instead of an oscilloscope is described. Potential advantages of the device include more rapid recording, low-cost construction of additional EAG recording systems for a laboratory with several users, and portability allowing studies in the field and occasional bench top use. The device is intended for use in conventional EAG recording, where EAG signals with rapid depolarizations are being measured, and where the maximum amplitude of the EAG signal is the only parameter of interest.     

Detection of major and minor sex pheromone components by the male codling moth Cydia pomonella (Lepidoptera: Tortricidae)

Electroantennograms (EAGs) recorded from the antennae of male Cydia pomonella L. in response to stimulation with doses of the main sex pheromone component E8,E10-dodecadienol (Codlemone) ranging from 5ng to 500&mgr;g did not differ in their amplitudes from responses obtained to a synthetic 7-component pheromone blend containing the same absolute quantities of Codlemone. Based on differences in spike amplitudes obtained in Single Cell recordings (SCR), Sensilla trichodea on the antenna of males were found to contain at least three receptor neurone types. Two olfactory receptor neurones were tuned to Codlemone, while the third failed to be stimulated by Codlemone or by the minor components of the pheromone blend. As spike activity of the neurones in the S. trichodea stimulated by the 7-component blend did not differ from that of stimulation by Codlemone alone it appears that none of the receptor neurones is sensitive to any of the minor components tested. Scanning-electron-microscopical (SEM) examination of Sensilla auricillica on the antennae of Cydia males revealed two morphologically distinct types: rabbit eared shoehorn and regular shoehorn. SCR from these sensilla showed that only olfactory receptor neurones located in the rabbit-eared shoehorn type were tuned to the minor components. Differences in spike amplitudes (large, intermediate, small) allowed three types of neurones to be distinguished. Only the spike frequency of the intermediate receptor neurone was increased by application of the minor components E8-dodecenol, E9-dodecenol, dodecanol, tetradecanol, hexadecanol and E8,E10-dodecadienal. None were stimulated by Codlemone. These results are discussed in relation to the behavioural role of the minor pheromone components of C. pomonella.     

Characteristics of electrical activity in different sections of nerve endings in the frog

In experiments on frog sartorius neuromuscular preparations, the evoked electrical responses of nerve endings were recorded by extracellular microelectrodes. It was shown that in proximal parts of the nerve ending, the three-phase response (+ - +) with a high amplitude negative phase occurred due to motor nerve stimulation. With movement of the extracellular electrode in distal direction a certain increase of the initial positive phase and a significant decrease of the negative one were observed. At the end of the terminal that response transformed to the monophasic one (+). On local iontophoretic application of tetrodotoxin (TTX) to the recording site two components of the nerve ending response were revealed: TTX-insensitive and TTX-sensitive. A significant decrease of the TTX-sensitive component occurred along the course of the nerve ending. That component was absent from the distal synaptic areas. It is concluded that in frog nerve ending, the action potential propogates with decrement while depolarization of the end parts of the terminal is passive in nature.     

Model calculations on the kinetics of oligonucleotide double helix coil transitions. Evidence for a fast chain sliding reaction

Relaxation data obtained previously for the double helix coil transition of oligoriboadenylates and oligoribouridylates are compared to the results of numerical calculations according to various models. In these models the helix coil transition is described by individual rate constants for the first steps of helix formation, whereas the rate constants of the following steps of helix chain growth are assumed to be uniform. The existence of various helix intermediates containing the same number of base pairs is accounted for by statistical factors. First a quasistationary treatment of a zipper model is used for an analysis of the influence of various model parameters. Then relaxation spectra are calculated including helix coil intermediates explicitly without any assumption of quasistationarity. The relaxation spectrum calculated for any chain length N comprises N—1 fast processes with time constants in the range of 0.1 to 0.5 μs and one slow process with a time constant τ depending upon the nucleotide concentration (τ is usually in the ms time range). The fast processes are associated mainly with the unzippering at helix ends and are usually characterized by relatively small amplitudes, whereas the slow process represents the overall helix coil transition usually characterized by a very large amplitude.Consideration of staggered helix series (where the different helix scries are coupled to each other by the single stranded state) leads to a spectrum of slow relaxation processes with one separate relaxation process for each helix series. It is shown that this “non-sliding” staggering zipper model is not consistent with the experimental results. The measured relaxation curves can be represented by single exponentials for nucleotide chain lengths 8 to 11 (within experimental accuracy). This is also true for conditions where several, clearly separated time constants should be expected according to the theoretical model. The experimental data suggest the existence of a direct coupling between different series of staggered helices by a chain sliding mechanism with a time constant < 1ms. Chain sliding may be explained by diffusion of helix defects along the double helix such as diffusion of small loops. A simple model calculation for the diffusion of a bulge loop assuming quasistationarity suggests a sliding time constant around 100 μs for a helix comprising 10 base pairs.Finally some thermodynamic and kinetic parameters are evaluated according to the “sliding” staggering zipper model: The negative activation enthalpy observed for helix recombination can he described using a series of nucleation parameters indicating reduced stability constants for the first three base pairs. Nucleation may usually be achieved with the formation of the third or fourth base pair depending upon the magnitude of the chain growth parameter. The rate constant of helix chain growth is around 10⁶ s^?1 at 0.05 M [Na⁺] and increases to about 4 × 10⁶ s^?1 at 0.17 M [Na⁺].