Cable properties of cat spinal motoneurones measured by combining voltage clamp, current clamp and intracellular staining

Techniques for the application of the analytical solution to the multicylinder somatic shunt cable model for passive neurones

The general solution for the voltage response to a generic impulse current input in a multicylinder somatic shunt cable model for passive neurones has been developed in [1]. In this paper we consider the application of the multicylinder solution to examples previously considered by other authors for the single cylinder case: long and short current input and synaptic input modeled by an alpha-function and a multi-exponential function. Simple expansions appropriate for small and large times are found and efficient means of obtaining these expansions are clearly demonstrated. The dependence of the small and large time solutions upon the dimensionless parameters appearing in the conservation of current condition at the soma is investigated. Relevant limits of these dimensionless parameters which further simplify the small and large time solutions are related back to equivalent dimensional problems of interest to the practitioner. The well-posedness of the dimensionless inverse problem is investigated and a method proposed for the solution of the dimensional inverse problem for the somatic shunt.

Three-dimensional imaging and image analysis of hippocampal neurons: confocal and digitally enhanced wide field microscopy

The microscopy of biological specimens has traditionally been a two-dimensional imaging method for analyzing what are in reality three-dimensional (3-D) objects. This has been a major limitation of the application of one of science's most widely used tools. Nowhere has this limitation been more acute than in neurobiology, which is dominated by the necessity of understanding both large- and small-scale 3-D anatomy. Fortunately, recent advances in optical instrumentation and computational methods have provided the means for retrieving the third dimension, making full 3-D microscopic imaging possible. Optical designs have concentrated on the confocal imaging mode while computational methods have made 3-D imaging possible with wide field microscopes using deconvolution methods. This work presents a brief review of these methods, especially as applied to neurobiology, and data using both approaches. Specimens several hundred micrometers thick can be sampled allowing essentially intact neurons to be imaged. These neurons or selected components can be contrasted with either fluorescent, absorption, or reflection stains. Image analysis in 3-D is as important as visualization in 3-D. Automated methods of cell counting and analysis by nuclear detection as well as tracing of individual neurons are presented.

Solutions for transients in arbitrarily branching cables: IV. Nonuniform electrical parameters

Solutions for transients in arbitrarily branching passive cable neurone models with a soma are extended to models with nonuniform electrical parameters and multiple dendritic shunts. The response to an injected current can again be represented as an infinite series of exponentially decaying components with system time constants obtained from the roots of a recursive transcendental equation. The reciprocity relations and global parameter dependencies are the same as for uniform models. Infinitely many "raw" electro-morphological models map onto a given "core" electrotonic model; local as well as global raw parameter trade-offs are now possible. The solutions are illustrated by means of biologically relevant examples: (i) the effects of nonuniform electrical parameters in a two-cylinder + soma cortical pyramidal cell model, (ii) the errors that can occur when uniformity is incorrectly assumed in a single cylinder model, (iii) nonsumming interactions between cells and electrodes that can dramatically increase the duration of the effective capacitative electrode artefact, and (iv) shunting inhibition and double impalements in a hippocampal CA1 pyramidal cell "cartoon" representation. These solutions should complement compartmental modelling techniques.

Automated tracing and volume measurements of neurons from 3-D confocal fluorescence microscopy data

Three-dimensional (3-D) image analysis algorithms and experimental results that demonstrate the feasibility of fully automated tracing of neurons from fluorescence confocal microscopy data are presented. The input to the automated analysis is a set of successive optical slices that have been acquired using a confocal scanning laser microscope. The output of the system is a labelled graph representation of the neuronal topology that is spatially aligned with the 3-D image data. A variety of topological and metric analyses can be carried out using this representation. For instance, precise measurements of volumes, lengths, diameters and tortuosities can be made over specific portions of the neuron that are specified in terms of the graph representation. The effectiveness of the method is demonstrated for a set of sample fields featuring selectively stained neurons. Additional work will be needed to refine the method for unsupervised use with complex data involving multiple intertwined neurons and extremely fine dendritic structures.

Analytical solutions to the multicylinder somatic shunt cable model for passive neurones with differing dendritic electrical parameters

The multicylinder somatic shunt cable model for passive neurones with differing time constants in each cylinder is considered in this paper. The solution to the model with general inputs is developed, and the parameteric dependence of the voltage response is investigated. The method of analysis is straightforward and follows that laid out in Evans et al. (1992, 1994): (i) The dimensional problem is stated with general boundary and initial conditions. (ii) The model is fully non-dimensionalised, and a dimensionless parameter family which uniquely governs the behaviour of the dimensionless voltage response is obtained. (iii) The fundamental unit impulse problem is solved, and the solutions to problems involving general inputs are written in terms of the unit impulse solution. (iv) The large and small time behaviour of the unit impulse solution is examined. (v) The parametric dependence of the unit impulse upon the dimensionless parameter family is explored for two limits of practical interest. A simple expression for the principle relationship between the dimensionless parameter family is derived and provides insight into the interaction between soma and cylinders. A well-posed method for the solution of the dimensional inverse problem is presented.

Physiology, morphology and detailed passive models of guinea-pig cerebellar Purkinje cells

1. Purkinje cells (PCs) from guinea-pig cerebellar slices were physiologically characterized using intracellular techniques. Extracellular caesium ions were used to linearize the membrane properties of PCs near the resting potential. Under these conditions the average input resistance, RN, was 29 M omega, the average system time constant, tau 0, was 82 ms and the average cable length, LN, was 0.59. 2. Three PCs were fully reconstructed following physiological measurements and staining with horseradish peroxidase. Assuming that each spine has an area of 1 micron 2 and that the spine density over the spiny dendrites is ten spines per micrometre length, the total membrane area of each PC is approximately 150,000 microns 2, of which approximately 100,000 microns 2 is in the spines. 3. Detailed passive cable and compartmental models were built for each of the three reconstructed PCs. Computational methods were devised to incorporate globally the huge number of spines into these models. In all three cells the models predict that the specific membrane resistivity, Rm, of the soma is much lower than the dendritic Rm (approximately 500 and approximately 100,000 omega cm2 respectively). The specific membrane capacitance, Cm, is estimated to be 1.5-2 muF cm-2 and the specific cytoplasm resistivity, Ri, is 250 omega cm. 4. The average cable length of the dendrites according to the model is 0.13 lambda, suggesting that under caesium conditions PCs are electrically very compact. Brief somatic spikes, however, are expected to attenuate 30-fold when spreading passively into the dendritic terminals. A simulated 200 Hz train of fast, 90 mV somatic spikes produced a smooth 12 mV steady depolarization at the dendritic terminals. 5. A transient synaptic conductance increase, with a 1 nS peak at 0.5 ms and a driving force of 60 mV, is expected to produce approximately 20 mV peak depolarization at the spine head membrane. This EPSP then attenuates between 200- and 900-fold into the soma. Approximately 800 randomly distributed and synchronously activated spiny inputs are required to fire the soma. 6. The passive model of the PC predicts a poor resolution of the spatio-temporal pattern of the parallel fibre input. An equally sized, randomly distributed group of approximately 1% of the parallel fibres, activated within a time window of a few milliseconds, would result in approximately the same composite EPSP at the soma.

Quantal components of unitary EPSCs at the mossy fibre synapse on CA3 pyramidal cells of rat hippocampus

1. Excitatory postsynaptic currents (EPSCs) were recorded in CA3 pyramidal cells of hippocampal slices of 15- to 24-day-old rats (22 degrees C) using the whole-cell configuration of the patch clamp technique. 2. Composite EPSCs were evoked by extracellular stimulation of the mossy fibre tract. Using the selective blockers 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) and D-2-amino-5-phosphonopentanoic acid (APV), a major alpha-amino-3-hydroxy-5-methylisoxazole-4-propionate (AMPA)/kainate receptor-mediated component and a minor NMDA receptor-mediated component with slower time course were distinguished. For the AMPA/kainate receptor-mediated component, the peak current-voltage (I-V) relation was linear, with a reversal potential close to 0 mV. The half-maximal blocking concentration of CNQX was 353 nM. 3. Unitary EPSCs of the mossy fibre terminal (MF)-CA3 pyramidal cell synapse were evoked at membrane potentials of -70 to -90 mV by low-intensity extracellular stimulation of granule cell somata using fine-tipped pipettes. The EPSC peak amplitude as a function of stimulus intensity showed all-or-none behaviour. The region of low threshold was restricted to a few micrometres. This suggests that extracellular stimulation was focal, and that the stimulus-evoked EPSCs were unitary. 4. Latency and rise time histograms of EPSCs evoked by granule cell stimulation showed narrow unimodal distributions within each experiment. The mean latency was 4.2 +/- 1.0 ms, and the mean 20-80% rise time was 0.6 +/- 0.1 ms (23 cells). When fitted within the range 0.7 ms to 20 ms after the peak, the decay of the EPSCs with the fastest rise (rise time 0.5 ms or less) could be described by a single exponential function; the mean time constant was in the range 3.0-6.6 ms with a mean of 4.8 ms (8 cells). 5. Peak amplitudes of the EPSCs evoked by suprathreshold granule cell stimulation fluctuated between trials. The apparent EPSC peak conductance in normal extracellular solution (2 mM Ca2+, 1 mM Mg2+), excluding failures, was 1 nS. Reducing the Ca2+ concentration and increasing the Mg2+ concentration reduced the mean peak amplitude in a concentration-dependent manner. 6. Peaks in EPSC peak amplitude distributions were apparent in low Ca2+ and high Mg2+. Using the criteria of equidistance and the presence of peaks and dips in the autocorrelation function, five of nine EPSC peak amplitude distributions were judged to be quantal.(ABSTRACT TRUNCATED AT 400 WORDS)

Stochastic geometry and electronic architecture of dendritic arborization of brain stem motoneuron

We describe how the stochastic geometry of dendritic arborization of a single identified motoneuron of the rat affects the local details of its electrotonic structure. After describing the 3D dendritic geometry at high spatial resolution, we simulate the distribution of voltage gradients along dendritic branches under steady-state and transient conditions. We show that local variations in diameters along branches and asymmetric branchings determine the non-monotonous features of the heterogeneous electrotonic structure. This is defined by the voltage decay expressed as a function of the somatofugal paths in physical distances (voltage gradient). The fan-shaped electrotonic structure demonstrates differences between branches which are preserved when simulations are computed from different values of specific membrane resistivity although the absolute value of their voltages is changed. At given distances from soma and over long paths, some branches display similar voltages resulting in their grouping which is also preserved when specific membrane resistivity is changed. However, the mutual relation between branches inside the group is respecified when different values of specific membrane resistivity are used in the simulations. We find that there are some invariant features of the electrotonic structure which are related to the geometry and not to the electrical parameters, while other features are changed by altering the electrical parameters. Under transient conditions, the somatofugal invasion of the dendritic tree by a somatic action potential shifts membrane potentials (above 10 mV) of dendritic paths for unequal distances from the soma during several milliseconds. Electrotonic reconfigurations and membrane shifts might be a mechanism for postsynaptic plasticity.

Modulation of EPSP shape and efficacy by intrinsic membrane conductances in rat neocortical pyramidal neurons in vitro

1. Intracellular recordings were made from pyramidal neurons in layers II/III and V of rat visual cortical slices. Distal and proximal excitatory postsynaptic potentials (EPSPs) were evoked using extracellular bipolar electrodes placed on the slice horizontal to each cell, near the apical and basal dendrites respectively. Experiments were conducted in the presence of 2-amino-5-phosphonopentanoate, picrotoxin and, in most cases, 2-hydroxy-saclofen. 2. For layer II/III pyramidal neurons, voltage undershoots following distal and proximal EPSPs (n = 7 pairs) and injected somatic pulses were rarely apparent. In layer V pyramidal neurons substantial voltage undershoots were recorded following distal and proximal EPSPs (n = 27 pairs) and injected somatic pulses, with undershoot being greatest for apical inputs (P = 0.001). The greater undershoots following apical EPSPs were also apparent in semilogarithmic plots of voltage decay where the slope of decay for apical EPSPs was quicker than the voltage decay following pulses of current injected at the soma. There was no significant difference in the shapes of distal and proximal EPSPs in layer II/III or layer V pyramidal cells under control conditions. 3. Pharmacological agents were used to reduce voltage undershoots. The most successful of these was alinidine, a putative blocker of the slow inward rectifier (IH) conductance. In the presence of bath-applied 100 microM alinidine, undershoots were significantly reduced and it became possible to distinguish the relative origins of EPSPs on the basis of their shape. Distally generated EPSPs (n = 14) had rise times and half-widths that were 2.8 and 1.5 times longer respectively than those evoked proximally (n = 10; P = 0.001 for both parameters). 4. These results confirm previous theoretical simulations of somatic recordings in passive model neurons where distal EPSPs display slower rise times and longer half-widths than proximal EPSPs. The present results suggest that, at least in pyramidal neurons of layer V, distal synaptic inputs can be specifically modulated by intrinsic membrane conductances.

Signal transmission in lobster olfactory receptor cells: functional significance of electrotonic structure analysed by a compartmental model

The electrotonic structure of lobster olfactory receptor cells was evaluated using general purpose simulation software in a compartmental model derived from electron-microscopic reconstruction. The model with non-uniform membrane resistance (Rm) was used to (i) simulate current spread and (ii) determine if the electronic structure of the cell improves signal recognition in the soma. The odor-evoked conductance change in dendrites was calculated according to the Michaelis-Menten equation with the assumption that the outer dendritic segments function as independent stimulus detectors. The inflection point of the concentration-response function measured in the soma was shifted to lower concentrations relative to that measured in the ciliary (outer dendritic) arbor. The shift, which was greater for inputs with lower efficacy (represented in the model by smaller Hill coefficients) and for the dynamic phase of the response than for the steady-state phase, effectively increased the selectivity of the somatic response. Randomized input distributed uniformly to progressively more restricted areas of the ciliary arbor showed that stimulation of larger areas (presumably the entire ciliary arbor) decreased the statistical variability of the somatic response.

Solutions for transients in arbitrarily branching cables: I. Voltage recording with a somatic shunt

An analytical solution is derived for voltage transients in an arbitrarily branching passive cable neurone model with a soma and somatic shunt. The response to injected currents can be represented as an infinite series of exponentially decaying components with different time constants and amplitudes. The time constants of a given model, obtained from the roots of a recursive transcendental equation, are independent of the stimulating and recording positions. Each amplitude is the product of three factors dependent on the corresponding root: one constant over the cell, one varying with the input site, and one with the recording site. The amplitudes are not altered by interchanging these sites. The solution reveals explicitly some of the parameter dependencies of the responses. An efficient recursive root-finding algorithm is described. Certain regular geometries lead to "lost" roots; difficulties associated with these can be avoided by making small changes to the lengths of affected segments. Complicated cells, such as a CA1 pyramid, produce many closely spaced time constants in the range of interest. Models with large somatic shunts and dendrites of unequal electrotonic lengths can produce large amplitude waveform components with surprisingly slow time constants. This analytic solution should complement existing passive neurone modeling techniques.

Solutions for transients in arbitrarily branching cables: III. Voltage clamp problems

Branched cable voltage recording and voltage clamp analytical solutions derived in two previous papers are used to explore practical issues concerning voltage clamp. Single exponentials can be fitted reasonably well to the decay phase of clamped synaptic currents, although they contain many underlying components. The effective time constant depends on the fit interval. The smoothing effects on synaptic clamp currents of dendritic cables and series resistance are explored with a single cylinder + soma model, for inputs with different time courses. "Soma" and "cable" charging currents cannot be separated easily when the soma is much smaller than the dendrites. Subtractive soma capacitance compensation and series resistance compensation are discussed. In a hippocampal CA1 pyramidal neurone model, voltage control at most dendritic sites is extremely poor. Parameter dependencies are illustrated. The effects of series resistance compound those of dendritic cables and depend on the "effective capacitance" of the cell. Plausible combinations of parameters can cause order-of-magnitude distortions to clamp current waveform measures of simulated Schaeffer collateral inputs. These voltage clamp problems are unlikely to be solved by the use of switch clamp methods.

The electrical geometry, electrical properties and synaptic connections onto rat V motoneurones in vitro

1. We have developed a tissue slice preparation which allows the study of the actions of single presynaptic neurones onto single trigeminal motoneurones in the immature rat. Our aim in this first stage of the work has been to assess the validity of this preparation as a model for responses obtained in vivo from trigeminal motoneurones in adult rats. We have quantified the integrative properties of the motoneurones and also the variability in transmission at synapses of single presynaptic neurones onto the motoneurones. This data has then been compared to similar published data obtained from adult (rat) trigeminal motoneurones in vivo. 2. Quantitative reconstructions were made of the morphology of three motoneurones which had been labelled with biocytin by intracellular injection. The neurones gave off six to nine dendrites, of mean length 522 microns (S.D. = 160; n = 22), which branched on average 10.5 times to produce 11.45 end-terminations per dendrite (S.D. = 8.57; n = 22). The mean surface area of the dendrites was 0.92 x 10(4) microns2 (S.D. = 0.67; n = 22), and, for individual cells, the ratio of the combined dendritic surface area to the total neuronal surface area ranged from 98.3 to 99.2% (n = 3). At dendritic branch points the ratio of the summed diameters of the daughter dendrites to the 3/2 power against the parent dendrite to the 3/2 power was 1.09 (S.D. = 0.21; n = 217), allowing branch points to be collapsed into a single cylinder. The equivalent cylinder diameter of the combined dendritic tree remained approximately constant over the proximal 25-40% of the equivalent electrical length of the dendritic tree and then showed tapering. The tapering could be ascribed to termination of dendrites at different electrical distances from the soma. 3. Electrical properties were determined for a total of eighty-seven motoneurones, all with membrane potentials more negative than 60 mV (mean = 66.0 mV; S.D. = 5.2) and spikes which overshot zero (mean spike amplitude = 77 mV; S.D. = 10.5; n = 87). The spikes were followed by after-hyperpolarizations (AHPs) of mean amplitude 2.2 mV (S.D. = 1.7; n = 47), and mean duration 54.1 ms (S.D. = 9.5; n = 47). The mean input resistance of the neurones was 7.5 M omega (S.D. = 2.5; n = 69), the mean membrane time constant was 3.5 ms (S.D. = 2.2; n = 35), and the mean rheobase was 1.6 nA (S.D. = 1.1; n = 56).(ABSTRACT TRUNCATED AT 400 WORDS)

On trees as equivalent cables

By means of a suitable transformation, any passive dendritic tree may be reduced to an equivalent, possibly non-uniform cable. Under certain conditions the equivalent cable has disjoint sections of which only one communicates with the soma. Inputs that map on to the disconnected sections cannot be seen by the soma. Ralls's equivalent cylinder and its generalizations emerge naturally as the simplest cases of this behaviour. Even where, as is more usual, decomposition does not occur exactly the equivalent cable together with the input mapping from the tree to the cable provides a readily visualisable and intuitively appealing description of quite subtle relationships on the tree. The structure of the equivalent cable is dominated by approximate geometric symmetries of the tree. These symmetries cause well-defined subspaces of the total space of synaptic inputs to arrive at the soma at different times, thus allowing them, in principle, to be reflected, for example in the temporal statistics of the neurons' spike output.

Quantitative synaptology of functionally different types of cat medial gastrocnemius alpha-motoneurons

The aim of this ultrastructural investigation was to study quantitatively the synaptology of the cell bodies and dendrites of cat medial gastrocnemius (MG) alpha-motoneurons of functionally different types. In electrophysiologically classified and intracellularly HRP-labelled MG alpha-motoneurons of the FF (fast twitch, fatigable), FR (fast twitch, fatigue resistant) and S (slow twitch, very fatigue resistant) types, the synaptic covering of the soma as well as that of dendritic segments located within 100 microns and at 300, 700, and 1,000 microns distance, respectively from the soma, was analyzed. The synaptic boutons were classified into the L-(apposition length > 4 microns) and S-types (< 4 microns) with spherical synaptic vesicles, and the F-type with flat or pleomorphic synaptic vesicles. The length of apposition towards the motoneuron membrane was measured for each bouton profile. Approximately 1,000 boutons contacted the soma and a similar number of boutons contacted the proximal dendrites within 50 microns from the soma. The number of dendritic boutons was larger at the 300 microns distance than at the 100 and 700 microns distances. The three types of motoneurons showed similar values for percentage synaptic covering and synaptic packing density in the proximal dendrites, while in the most distal dendritic regions the S motoneurons had more than 50% higher values for percentage covering, packing density and total number of boutons. The S motoneurons also exhibited a larger preponderance of F-type boutons on the soma. The ratio between the F- and S-types of boutons decreased somatofugally along the dendrites in the type FF and FR motoneurons, while in the S motoneurons it remained fairly constant.

Different proportions of N-methyl-D-aspartate and non-N-methyl-D-aspartate receptor currents at the mossy fibre-granule cell synapse of developing rat cerebellum

The mossy fibre-granule cell synapse undergoes major developmental changes during the second and third weeks after birth. We investigated synaptic transmission during postnatal days 10-22 by means of whole-cell patch-clamp recordings from granule cells in situ. Parasagittal slices were cut from rat cerebellar vermis, and excitatory postsynaptic currents were evoked in granule cells by mossy fibre stimulation with 1.2 mM Mg++ in the extracellular solution. In the majority of granule cells recorded at postnatal days 16-22, excitatory currents were characterized by a fast initial peak followed by a slower component, while in many of the cells recorded at more immature stages, the fast peak was virtually absent. Pharmacological and kinetic data indicated that the fast and slow components were mediated by non-N-methyl-D-aspartate and N-methyl-D-aspartate receptor activation, respectively. The magnitude of the non-N-methyl-D-aspartate current increased with developmental age, while the magnitude of the NMDA current did not change markedly. The age-dependent change of the non-N-methyl-D-aspartate currents could not be accounted for by changes in recording conditions or granule cell electrotonic properties. Furthermore, from postnatal day 11 to 16 the extent of Mg++ block on the N-methyl-D-aspartate receptor did not change, and could not explain the increasing non-N-methyl-D-aspartate/N-methyl-D-aspartate current ratio. We concluded therefore that the age-dependent increase of the non-N-methyl-D-aspartate current was the main cause of the different postsynaptic current waveforms observed at different ages. The developmental change in the proportion of N-methyl-D-aspartate and non-N-methyl-D-aspartate currents may be relevant to the processes regulating granule cell maturation and excitability.

Reduced compartmental models of neocortical pyramidal cells

Model neurons composed of hundreds of compartments are currently used for studying phenomena at the level of the single cell. Large network simulations require a simplified model of a single neuron that retains the electrotonic and synaptic integrative properties of the real cell. We introduce a method for reducing the number of compartments of neocortical pyramidal neuron models (from 400 to 8-9 compartments) through a simple collapsing method based on conserving the axial resistance rather than on the surface area of the dendritic tree. The reduced models retain the general morphology of the pyramidal cells on which they are based, allowing accurate positioning of synaptic inputs and ionic conductances on individual model cells, as well as construction of spatially accurate network models. The reduced models run significantly faster than the full models, yet faithfully reproduce their electrical responses.

Simulation of the Effect of Synapses: the Significance of the Dendritic Diameter in Impulse Propagation

The effectiveness of synapses at various sites of the dendritic tree was studied using a segmental cable model with a program developed by Hines (Int. J. Biomed. Comput., 24, 55 - 68, 1989). The model rendered possible a high-fidelity simulation of the dendritic geometry of a frog motoneuron described in the accompanying paper (Birinyi et al., Eur. J. Neurosci., 1003 - 1012, 1992). The model was used in the passive membrane mode and the synaptic activity was simulated with current injections into large and small diameter dendrites at proximal and distal locations. Synaptic efficiency was defined by the charge transfer ratio expressed as the proportion of the injected current which appeared at the soma. The charge transfer ratio was determined with uniform and non-uniform distribution of specific membrane resistance over the soma - dendrite surface while the diameter of selected dendrite segments changed. The best charge transfer ratio was found with the largest dendrite membrane resistance, and the maximum efficiency of synaptic activity appeared at the original size of the dendrite segment stimulated. The amount of current that flowed in the proximal and distal directions from the segment stimulated depended on the diameter of that segment. The increase in diameter of proximal dendrites increased synaptic efficiency on distal dendrites, whereas the reverse caused a decline in synaptic efficiency on proximal dendrites. In addition to the diameter of dendrites, the arborization pattern also played a significant role in this mechanism. It is concluded that the cellulipetal increase in dendrite diameter greatly increases synaptic efficiency.

Dendritic morphology of pyramidal neurones of the visual cortex of the rat. IV: Electrical geometry

Features of the dendritic morphology of pyramidal neurones of the visual cortex of the rat that are relevant to the development of models of their passive electrical geometry were investigated. The sample of 39 neurones that was used came from layers 2/3 and 5. They had been recorded from and injected intracellularly with horseradish peroxidase (HRP) in vitro as part of a previous study (Larkman and Mason, J. Neurosci 10:1407, 1990). These cells had been reconstructed and measured previously by light microscopy. The relationship between the diameters of parent and daughter dendrites during branching was examined. It was found that most dendrites did not closely obey the "3/2 branch power relationship" required for representation of the dendrites as single equivalent cylinders. Estimates of total neuronal membrane area ranged from 27,100 +/- 7,900 microns2 for layer 2/3 cells to 52,200 +/- 11,800 microns2 for thick layer 5 cells. Dendritic spines contributed approximately half the total membrane area. Both neuronal input resistance and the ratio of membrane time constant to input resistance were correlated with neuronal membrane area as measured anatomically. The relative electrical lengths of the different dendrites of individual neurones were investigated, by using simple transformations to take account of the differences in diameter and spine density between dendritic segments. A novel "morphotonic" transformation is described that represents the purely morphological component of electrotonic length. Morphotonic lengths can be converted into electrotonic lengths by division by a "morphoelectric factor" ([Rm/Ri]1/2). This procedure has the advantage of separating the steps involving anatomical and electrical parameters. These transformations indicated that the dendrites of the apical terminal arbor were much longer electrically than the basal or apical oblique dendrites. In relative electrical terms, most apical oblique trees arose extremely close to the soma, and terminated at similar distances to the basals. These results indicate that the dendrites of these pyramidal cells cannot be represented as single equivalent cylinders. The electrotonic lengths of the dendrites were calculated by using the electrical parameters specific membrane capacitance (Cm), intracellular resistivity (Ri), and specific membrane resistivity (Rm). Conventional values were assumed for Cm (1.0 muFcm-2) and Ri (100 omega cm), but three different Rm values were used for each cell. Two of these were within the conventionally accepted range (10,000-20,000 omega cm2), while the third value was an order of magnitude higher, in line with some recent evidence from modeling and whole-cell recording studies.(ABSTRACT TRUNCATED AT 400 WORDS)

Estimation of electrotonic parameters of neurons using an inverse Fourier transform technique

The objective of this paper is to estimate the passive electrotonic parameters of hippocampal granule cells. Accurate estimation of these parameters is important in understanding the information processing of neurons. A shunt cable model, where the somatic and dendritic time constants can be different, is used to describe the potential changes in the soma and along the dendritic tree. For this model, parameter values are estimated by nonlinear least-squares fitting of the model output to the voltage response of the stimulated cell to current pulses. The solutions are obtained in a two-step process: First, the sensitivity functions are derived from the Laplace transform solution of the theoretical model. Second, the time domain solutions are obtained numerically by an inverse FFT. A sensitivity analysis indicates that accurate estimates require the use of a short current pulse injected at the soma and the sampling of the voltage response close to the end of that pulse. This parameter estimation procedure has been tested on hippocampal granule cells. It yields accurate estimation of neural parameters and will be a useful tool for measuring passive properties of neurons.

Restorative effects of reinnervation on the size and dendritic arborization patterns of axotomized cat spinal alpha-motoneurons

In a preceding paper [Brännström, et al. (1992) J. Comp. Neurol. 318:439-451] a marked reduction in dendritic size was observed in cat spinal motoneurons following permanent axotomy. The aim of the present study was to analyse the possible restorative effects of peripheral reinnervation on the size and dendritic branching patterns of cat spinal motoneurons which had been deprived of neuromuscular contact for an extended period of time. In adult cats the medial gastrocnemius (MG) nerve was transected and ligated. After 6 weeks the nerve was allowed to reinnervate its muscle through a nerve graft. With approximately 6 weeks needed for muscle reinnervation [Foehring, et al. (1986) J. Neurophysiol. 55:947-965], the MG motoneurons were devoid of neuromuscular contact for altogether about 12 weeks. Two years later reinnervated MG alpha-motoneurons were intracellularly labelled with horseradish peroxidase to allow quantitative analyses of the cell bodies and dendritic trees. Comparisons were made with previous data from normal and permanently axotomized MG motoneurons. The reinnervated motoneurons exhibited positive correlations between dendritic stem diameter, on one hand, and combined length, volume, membrane area, and number of end branches of the whole dendrite, on the other. By using the regression equations for these correlations, the total dendritic size of whole reinnervated motoneurons could be estimated. Such calculations showed that in comparison with the reduction in dendritic size found at 12 weeks after permanent axotomy (Brännström et al., see above), peripheral reinnervation caused the dendritic volume and membrane area to return to normal values. However, the values for combined dendritic length and number of dendritic end branches were still reduced by more than 25% as compared to the normal situation. The results indicate that following reinnervation of the target muscle, the axotomized motoneurons did not recover their original number of dendritic branches. The normalization of dendritic membrane area and volume was instead accomplished by two other mechanisms, namely an increase in dendritic diameters and an increased number of dendrites per neuron.

Changes in size and dendritic arborization patterns of adult cat spinal alpha-motoneurons following permanent axotomy

This study was performed to analyse quantitatively the changes in dimensions and dendritic branching patterns of adult cat spinal alpha-motoneurons following permanent axotomy, i.e., in a situation in which the transected motoraxons are prevented from reinnervating their peripheral target muscle. After transection and ligation of the medial gastrocnemius nerve of adult cats, homonymous alpha-motoneurons were intracellularly labelled with horseradish peroxidase and subjected to quantitative light microscopic analyses. The cell bodies and proximal dendrites were studied at 3, 6, and 12 weeks after the axotomy. An initial increase in cell body size at 3 weeks was followed by a gradual return towards normal values. The mean diameter of the stem dendrites was decreased at all time periods studied, and the combined diameter of the stem dendrites was reduced at 12 weeks after the axotomy. Entire dendritic trees were reconstructed at 12 weeks postoperatively, and the regression equations describing the correlations between dendritic stem diameter, on one hand, and the size of the entire dendrite, on the other, were used to calculate the total dendritic length, volume, and membrane area of whole axotomized motoneurons. The dendritic branching patterns were also analysed. In comparison with normal medial gastrocnemius alpha-motoneurons, the dendritic membrane area and volume of the axotomized cells had decreased by 36% and 29%, respectively, at 12 weeks after the axotomy. This reduction in dendritic size was due to a loss of preterminal and terminal dendritic segments. Abnormal dendritic elongations were observed in 2 of 16 completely reconstructed dendrites.

Cable properties of arborized Retzius cells of the leech in culture as probed by a voltage-sensitive dye

Retzius cells of Hirudo medicinalis were cultivated on extracellular matrix protein so that extended arborizations were formed. The propagation of voltage transients along 1-microns-thick neurites was observed at a resolution of 8 microns at 10 kHz by use of a voltage-sensitive dye. Delay and width of the fluorescence transients caused by hyperpolarization of the soma are described by passive spread of voltage in a homogeneous cable (time constant, 10 ms; space constant, 320 microns). The local sensitivity of the dye was determined from a comparison of the amplitudes of fluorescence and of fitted voltage. The fluorescence transients caused by depolarization were scaled using the sensitivity profile. Action potentials were found to pervade the neurites without significant change of amplitude but with enhanced pulse width.

Propagation of action potentials along complex axonal trees. Model and implementation

Axonal trees are typically morphologically and physiologically complicated structures. Because of this complexity, axonal trees show a large repertoire of behavior: from transmission lines with delay, to frequency filtering devices in both temporal and spatial domains. Detailed theoretical exploration of the electrical behavior of realistically complex axonal trees is notably lacking, mainly because of the absence of a simple modeling tool. AXONTREE is an attempt to provide such a simulator. It is written in C for the SUN workstation and implements both a detailed compartmental modeling of Hodgkin and Huxley-like kinetics, and a more abstract, event-driven, modeling approach. The computing module of AXONTREE is introduced together with its input/output features. These features allow graphical construction of arbitrary trees directly on the computer screen, and superimposition of the results on the simulated structure. Several numerical improvements that increase the computational efficiency by a factor of 5-10 are presented; most notable is a novel method of dynamic lumping of the modeled tree into simpler representations ("equivalent cables"). AXONTREE's performance is examined using a reconstructed terminal of an axon from a Y cell in cat visual cortex. It is demonstrated that realistically complicated axonal trees can be handled efficiently. The application of AXONTREE for the study of propagation delays along axonal trees is presented in the companion paper (Manor et al., 1991).

The size and dendritic structure of HRP-labeled gamma motoneurons in the cat spinal cord

We report quantitative data obtained from 60 fully reconstructed dendritic trees belonging to eight gamma-motoneurons (gamma-MNs) and six additional gamma-MNs that were not completely reconstructed. The cells were labeled intracellularly with horseradish peroxidase (HRP). These data are compared to measurements from 79 reconstructed dendrites belonging to seven documented alpha-motoneurons (alpha-MNs), supplemented by a larger sample of alpha-MNs labeled intracellularly or by retrograde transport with HRP. As expected from earlier studies, the soma dimensions and total membrane area of gamma-MNs were smaller than those of alpha-MNs. Although gamma-MN dendrites were, on average, slightly but significantly longer than those of alpha-MNs, the former had, on average, smaller diameter stem dendrites, less membrane area, and less profuse branching, and they tended to branch closer to the soma and to terminate farther from the soma. These differences were evident even when subsets of dendrites with similar stem diameters were compared. Some of the anatomical distinctions suggest that gamma-MNs are qualitatively as well as quantitatively different from alpha-MNs, even though the distributions of many of the morphological variables examined showed no abrupt discontinuities between the two motoneuron groups.

Uneven distribution of excitatory amino acid receptors on ventral horn neurones of newborn rat spinal cord

1. The distribution of excitatory amino acid receptors on ventral horn neurones was investigated using slices of newborn rat spinal cord. 2. The neurone and the tip of the pipette used to inject amino acids were visualized using Lucifer Yellow under a fluorescent microscope. The pipette was precisely located on the soma and dendrite of the neurone under visual control, and L-glutamate (Glu), L-aspartate (Asp), N-methyl-D-aspartate (NMDA), kainate (KA) and quisqualate (Quis) were ionophoretically applied with a short pulse. The potential changes were intracellularly recorded from the soma. 3. Sensitivity to Glu as tested with short pulses (1-2 ms) was almost the same at the soma and along dendrites. 4. The amplitude of the responses to NMDA produced at the soma and the proximal part of the dendrite was about the same as that of Glu, but smaller than that of Glu at the distal part of the dendrite. Suppression of the Glu potential by an NMDA receptor antagonist, 2-amino-5-phosphonovaleric acid (APV), was greater at the soma than at the dendrite, suggesting that the contribution of NMDA receptors to the Glu potential was greater at the soma. 5. Sensitivity to Asp was about one-half that to Glu sensitivity on the soma and even less on the dendrite. Sensitivity to KA was high at the soma and low at the dendrite. However, Quis responses were produced throughout the neurone. 6. The Quis response induced by the application of a short pulse showed two phases: a fast response followed by a very slow depolarization that lasted more than 10 s. 7. The fast Quis response was easily desensitized and insensitive to APV. The time course of the fast Quis potential was shorter than that of Glu. 8. The slow Quis response was more pronounced at the dendrites than at the soma and was reduced by the intracellular injection of EGTA, suggesting the contribution of Ca2+ in the cell, possibly mediated by a second messenger system. 9. Experimental results suggest that the distribution of excitatory amino acid receptors differs between the soma and the dendrites of spinal neurones.

Morphology and frequency of axon terminals on the somata, proximal dendrites, and distal dendrites of dorsal neck motoneurons in the cat

The purpose of the present study was to compare the frequency of different classes of axon terminals on selected regions of the somatodendritic surface of dorsal neck motoneurons. Single motoneurons supplying neck extensor muscles were antidromically identified and intracellularly stained with horseradish peroxidase. By using light microscopic reconstructions as a guide, axon terminals on the somata, proximal dendrites (within 250 microns of the soma), and distal dendrites (more than 540 microns from the soma) were examined at the electron microscopic level. Axon terminals were divided into several classes based on the shape, density, and distribution of their synaptic vesicles. The proportion of axon terminals belonging to each axon terminal class was similar on the somata and proximal dendrites. However, there were major shifts in the relative frequency of most classes of axon terminals on the distal dendrites. The most common classes of axon terminals on the somata and proximal dendrites contained clumps of either spherical or pleomorphic vesicles. These types of axon terminals accounted for more than 60% of the axon terminals on these regions. In contrast, only 11% of the axon terminals found on distal dendrites belonged to these types of axon terminals. The most commonly encountered axon terminal on distal dendrites contained a dense collection of uniformly distributed spherical vesicles. These types of axon terminals accounted for 40% of all terminals on the distal dendrites, but only 5-7% of the axon terminals on the somata and proximal dendrites. Total synaptic density on each of the three regions examined was similar. However, the percentage of membrane in contract with axon terminals was approximately four times smaller on distal dendrites than somata or proximal dendrites. Axon terminals (regardless of type) were usually larger on somata and proximal dendrites than distal dendrites. These results indicate that there are major differences in the types and arrangement of axon terminals on the proximal and distal regions of dorsal neck motoneurons and suggest that afferents from different sources may preferentially contact proximal or distal regions of the dendritic trees of these cells.

Dendritic morphology of pyramidal neurones of the visual cortex of the rat: II. Parameter correlations

This study concerns the correlations between the various morphometric parameters obtained for the dendrites of neocortical pyramidal cells. The primary aims were to uncover underlying design principles in dendritic morphology, to see if these differed between different types of dendrite, and to see if estimates of parameters such as total dendritic shaft membrane area could be obtained from a limited number of measurements, avoiding the need to measure every dendritic segment. The data were from a sample of 39 pyramidal neurones, from layers 2/3 and 5 of the visual cortex of the rat, that had been injected with horseradish peroxidase, reconstructed, and measured with the light microscope as part of an earlier study (Larkman and Mason, '90: J. Neurosci. 10:1407-1414). Correlations between the somal area or the combined diameters of the stem segments and measures of the overall size of the dendrites were generally weak. For basal dendrites, the size of a tree was correlated with both its number of tips and the diameter of its stem segment, but these correlations were weaker for apical dendrites. Within individual cells, the diameter of any basal segment was closely related to the size of the tree arising from it, and quantitatively similar relations applied to apical oblique trees from the same cell. Terminal arbor trees showed relations that were similar in pattern but differed quantitatively, whereas apical trunk segment diameter correlations were often weak. In all cases, the number of tips in a tree was closely related to its size. Segment lengths, however, were not closely related to the size of the trees arising from them. It appears that at least some aspects of pyramidal dendritic morphology obey simple design rules. There was heterogeneity between trees of different types, although basal and oblique trees were very similar in most respects. It should prove possible to make use of correlations to estimate the sizes of basal, oblique, and terminal arbor trees from a limited number of measurements, but this does not seem to be possible for apical trunks.

The morphology and electrical geometry of rat jaw-elevator motoneurones

1. The aim of this work was to quantify both the morphology and electrical geometry of the dendritic trees of jaw-elevator motoneurones. To do this we have made intracellular recordings from identified motoneurones in anaesthetized rats, determined their membrane properties and then filled them with horseradish peroxidase by ionophoretic ejection. Four neurones were subsequently fully reconstructed and the lengths and diameters of all the dendritic segments measured. 2. The mean soma diameter was 25 microns and values of mean dendritic length for individual cells ranged from 514 to 773 microns. Dendrites branched on average 9.1 times to produce 10.2 end-terminations. Dendritic segments could be represented as constant diameter cylinders between branch points. Values of dendritic surface area ranged from 1.08 to 2.52 x 10(5) microns 2 and values of dendritic to total surface area from 98 to 99%. 3. At branch points the ratio of the summed diameters of the daughter dendrites to the 3/2 power against the parent dendrite to the 3/2 power was exactly 1.0. Therefore the individual branch points could be collapsed into a single cylinder. Furthermore for an individual dendrite the diameter of this cylinder remained constant with increasing electrical distance from the soma. Thus individual dendrites can be represented electrically as cylinders of constant diameter. 4. However dendrites of a given neurone terminated at different electrical distances from the soma. The equivalent-cylinder diameter of the combined dendritic tree remained constant over the proximal half and then showed a pronounced reduction over the distal half. The reduction in equivalent diameter could be ascribed to the termination of dendrites at differing electrical distances from the soma. Therefore the complete dendritic tree of these motoneurones is best represented as a cylinder over the proximal half of their electrical length but as a cone over the distal half.

Changes in size and shape during histochemical preparation for light and electron microscopy of neurons intracellularly labelled with horseradish peroxidase

In this study we show that neurons labelled intracellularly with horseradish peroxidase react differently from surrounding unlabelled neurons in vibratome sections during histological preparations for light and electron microscopy. The diameters and cross-sectional area of the cell bodies of intracellularly horseradish peroxidase-labelled neurons increased by about 6 and 11% respectively, while the surrounding unlabelled neurons decreased by the same amount. Also, the caliber of the proximal dendrites of horseradish peroxidase-labelled neurons increased during the histological preparation while dendritic path lengths remained unchanged. Since the surrounding tissue shrunk, the dendritic path shapes became more tortuous during histological processing. The demonstrated reaction of horseradish peroxidase-labelled neurons is suggested to be caused by the horseradish peroxidase reaction product.

The membrane properties and firing characteristics of rat jaw-elevator motoneurones

1. We have determined the membrane and firing properties of fifty-six jaw-elevator motoneurones in rats that were anaesthetized with pentobarbitone, paralysed and artificially ventilated. 2. Forty-two neurones were identified as masseter motoneurones and fourteen as masseter synergist motoneurones. The membrane potentials for the sample ranged from -60 to -86 (mean = -68; S.D. = 7.3; n = 56), and spike amplitudes from 50 to 95 mV. The duration of the after-hyperpolarization following antidromic spikes in masseter motoneurones ranged from 15 to 50 ms (mean = 30; S.D. = 12.8) and their amplitudes from 1.0 to 4.5 mV (mean = 2.7; S.D. = 2.2; n = 42). 3. The mean input resistance for the total sample was 2.3 M omega (S.D. = 0.9; n = 56), membrane time constant 3.9 ms (S.D. = 0.9; n = 48) and rheobase 4.2 nA (S.D. = 2.6; n = 56). The distribution of these parameters was independent of membrane potential. We found no significant interrelationships between the membrane properties and one interpretation of this is that our sample may be drawn from a homogenous population of motoneurones. We also suggest that elevator motoneurones may have a lower Rm (specific membrane resistivity) value than cat hindlimb motoneurones because they have a similar range of input resistance values but only half the total surface area. 4. Forty-six out of forty-nine neurones fired repetitively to a depolarizing current pulse at a mean threshold of 1.6 x rheobase. Current-frequency plots were constructed for thirteen neurones and all but one showed a primary and secondary range in the firing of the first interspike interval. The mean slope in the primary range was 31 impulses s-1 nA-1 and 77 impulses s-1 nA-1 for the secondary range. The mean minimal firing frequency for steady firing was 26 impulses s-1 and, in response to an increase of stimulation, the rate increased monotonically with a slope of 11 impulses s-1 nA-1. 5. The dynamic sensitivity of twelve neurones was assessed from their response to ramp waveforms of current of constant amplitude but varying frequencies (0.2-2 Hz). Firing initially increased along a steep slope up to a frequency of between 40 and 60 impulses s-1 and then increased along a much shallower slope. Both the threshold for eliciting firing and the firing at the transition point of the two slopes remained constant with changes in ramp frequency.(ABSTRACT TRUNCATED AT 400 WORDS)

Tuberal supraoptic neurons--II. Electrotonic properties

The electrotonic properties of tuberal supraoptic neurons were studied from conventional intracellular recordings made in the hypothalamo-neurohypophysial explant in vitro. The cable parameters electrotonic dendritic length, and the dendritic to somatic conductance ratio, were estimated using the slopes and intercepts of the first two peeled exponentials of the voltage transients generated by current steps. The estimations were made assuming an equivalent cylinder model consisting of a soma and an attached, lumped dendrite of finite length. An equalizing time constant was resolved in 12 of 17 neurons, allowing calculation of both cable parameters. In only one of these 12 was it necessary to assume a somatic shunt to account for the data. The average value of the dendritic electrotonic length was 1.02, and that of the dendritic to somatic conductance ratio, 4.11. In the remaining five neurons, an equalizing time constant could not be peeled and consequently the dendritic cable parameters could not be estimated. The average input resistance of these 12 neurons was 162 M omega and the average membrane time constant was 11.86 ms. Principal Components Analysis revealed that the variance of input resistance and time constant was largely explained by one factor, while that of dendritic electrotonic length and the dendritic to somatic conductance ratio was explained by a separate, independent factor, suggesting a separation of electrical and morphological parameters, respectively. In addition, the variability of the data indicates that considerable differences in the morphology and specific membrane resistivity exist across supraoptic neurons. An analysis of spontaneously occurring postsynaptic potentials revealed that the shapes of these potentials could not be explained simply by assuming that they were determined by their passive decay from some point along the equivalent cable to the soma. In conclusion, dendrites make a significant and previously unappreciated contribution to the electrotonic behavior of supraoptic neurons. These electrotonic properties are similar to those of many other, morphologically diverse, central nervous system neurons.

A non-uniform equivalent cable model of membrane voltage changes in a passive dendritic tree

A non-uniform equivalent cable model of membrane voltage changes in a passive dendritic tree extending Rall's equivalent cylinder model is presented. It is obtained from a combination of cable theory with the continuum approach. Replacing the fine structure of the branching dendrites by an equivalent, conductive medium characterized by averaged electrical parameters, the one-dimensional cable equations with spatially varying parameters are derived. While these equations can be solved in general only numerically, we were able to formulate a general branching condition (comprising Rall's 3/2 power relationship as a special case) under which analytical solutions can be deduced from those of the equivalent cylinder model. This model allows dendritic trees with a greater variety of branching patterns than before to be analytically treated.

Reduction by baclofen of monosynaptic EPSPs in lumbosacral motoneurones of the anaesthetized cat

1. Monosynaptic excitatory postsynaptic potentials (EPSPs) were elicited in lumbosacral motoneurones of pentobarbitone anaesthetized cats by stimulating group Ia muscle afferents with most of the dorsal roots severed. In some experiments Ia EPSPs were recorded together with monosynaptic EPSPs elicited by stimulating the ipsilateral ventral quadrants (VQ) of the thoracic spinal cord. Injection of (+/-) baclofen (1 mg kg-1 I.V.) caused a reduction in the peak amplitudes of both Ia and VQ EPSPs, which started immediately upon injection and progressed gradually. No recovery in EPSP amplitude was seen during the recording period, which lasted up to 60 min. 2. The Ia EPSP peak amplitude was reduced by 18-61% (mean +/- S.D., 38 +/- 14%; n = 30), while VQ EPSPs were reduced by 7-42% (23 +/- 13%; n = 5). Baclofen had a significantly larger effect on Ia EPSPs than VQ EPSPs (P less than 0.001; t test). 3. Baclofen did not cause any consistent change in the membrane potential, nor in the membrane time constant, as estimated from the exponential decay of the tail of the EPSP. There was no tendency for the reduction in peak EPSP amplitude to be related to the estimated electrical distance on the dendritic tree at which the synaptic current was injected. 4. For two I a and two VQ EPSPs, the trial-to-trial fluctuation in the peak amplitude was resolved into quantal parameters before and after baclofen was administered. The reduction in peak amplitude was in all cases accounted for by a reduction in the probability of release of neurotransmitter, with no change in quantal size. Other EPSPs either showed negligible trial-to-trial amplitude fluctuation, or could not be resolved into quantal parameters without ambiguity. 5. By comparing the variance components of the EPSP peak amplitude distribution, the hypothesis was tested that the entire action of baclofen was to reduce quantal amplitude. This was rejected for sixteen out of thirty Ia and three out of five VQ EPSPs (P less than 0.05). 6. These results support a presynaptic site of action of baclofen on the terminals of Ia afferents, by decreasing the probability of release of neurotransmitter. They also indicate a similar, although weaker, action on VQ terminals. No evidence was found for an action on the postsynaptic membrane properties or synaptic conductance.

Monosynaptic EPSPs in cat lumbosacral motoneurones from group Ia afferents and fibres descending in the spinal cord

1. Excitatory postsynaptic potentials (EPSPs) were elicited in lumbosacral motoneurones of pentobarbitone-anaesthetized cats by stimulating the ventral quadrants (VQ) of the thoracic spinal cord. These EPSPs were compared with monosynaptic EPSPs from small numbers of group Ia afferents, obtained by stimulating hindlimb muscle nerves with most of the dorsal roots severed. 2. EPSPs with average peak amplitude less than 1 mV were selected for fluctuation analysis. Three out of fourteen (21%) VQ EPSPs with peak voltage less than 150 mu V fluctuated in amplitude from trial to trial no more than could be accounted for by the background intracellular noise. Similarly, nine out of thirty-nine (23%) Ia EPSPs smaller than 150 mu V fluctuated to a comparable extent as the noise. These results are consistent with the view that there is little variation in the postsynaptic signal produced by an individual transmitter release event. 3. Of the EPSPs which did fluctuate more than the background noise, maximum likelihood estimates were obtained for the fluctuation patterns of ten VQ and fourteen Ia EPSPs. This was achieved by assuming that synaptic signals sum linearly with noise, but without constraining the results to conform to a statistical description of transmitter release. The fluctuation of both VQ and Ia EPSPs was made up of discrete amplitudes separated by roughly equal increments, in accordance with the quantal hypothesis of synaptic transmission. 4. Fluctuation patterns were obtained simultaneously for VQ and Ia EPSPs in seven motoneurones. The amplitudes of the quanta, defined as the mean increments between discrete amplitudes, were correlated (r = 0.90), suggesting common postsynaptic mechanisms. 5. For most EPSPs the time course of the voltage transient could be used to estimate the electrical distance from the soma at which the synaptic current was injected. There was a comparable distribution for VQ and Ia EPSPs. For those in which a quantal analysis was performed (nine VQ and eleven Ia), quantal size measured at the soma appeared to be independent of the deduced site of origin. 6. The results indicate no qualitative or quantitative differences in the behaviour of VQ and Ia EPSPs.