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.     

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.     

Analysis of membrane heterogeneity and non-linearity of summation of postsynaptic potentials in a simulation model of the Purkinje cell

Propagation and summation of EPSP was studied by means of a numerical model of rat Purkinje neuron. It was shown that the difference between the membrane resistivity of the soma and dendrites can be determined experimentally by the character of EPSP attenuation, while comparing intra- and extracellular recordings. It was also shown that at an increase of synaptic input the nonlinear increase of the potential is more pronounced in the soma that in the synaptic region. The role of this fact for the interpretation of the experimental data is discussed.     

Manufacturing and Using Piggy-back Multibarrel Electrodes for In vivo Pharmacological Manipulations of Neural Responses

In vivo recordings from single neurons allow an investigator to examine the firing properties of neurons, for example in response to sensory stimuli. Neurons typically receive multiple excitatory and inhibitory afferent and/or efferent inputs that integrate with each other, and the ultimate measured response properties of the neuron are driven by the neural integrations of these inputs. To study information processing in neural systems, it is necessary to understand the various inputs to a neuron or neural system, and the specific properties of these inputs. A powerful and technically relatively simple method to assess the functional role of certain inputs that a given neuron is receiving is to dynamically and reversibly suppress or eliminate these inputs, and measure the changes in the neuron''s output caused by this manipulation. This can be accomplished by pharmacologically altering the neuron''s immediate environment with piggy-back multibarrel electrodes. These electrodes consist of a single barrel recording electrode and a multibarrel drug electrode that can carry up to 4 different synaptic agonists or antagonists. The pharmacological agents can be applied iontophoretically at desired times during the experiment, allowing for time-controlled delivery and reversible reconfiguration of synaptic inputs. As such, pharmacological manipulation of the microenvironment represents a powerful and unparalleled method to test specific hypotheses about neural circuit function.Here we describe how piggy-back electrodes are manufactured, and how they are used during in vivo experiments. The piggy-back system allows an investigator to combine a single barrel recording electrode of any arbitrary property (resistance, tip size, shape etc) with a multibarrel drug electrode. This is a major advantage over standard multi-electrodes, where all barrels have more or less similar shapes and properties. Multibarrel electrodes were first introduced over 40 years ago ^1-3, and have undergone a number of design improvements ^2,3 until the piggy-back type was introduced in the 1980s ^4,5. Here we present a set of important improvements in the laboratory production of piggy-back electrodes that allow for deep brain penetration in intact in vivo animal preparations due to a relatively thin electrode shaft that causes minimal damage. Furthermore these electrodes are characterized by low noise recordings, and have low resistance drug barrels for very effective iontophoresis of the desired pharmacological agents.     

Targeted patch-clamp recordings and single-cell electroporation of unlabeled neurons in vivo

Here we describe an approach for making targeted patch-clamp recordings from single neurons in vivo, visualized by two-photon microscopy. A patch electrode is used to perfuse the extracellular space surrounding the neuron of interest with a fluorescent dye, thus enabling the neuron to be visualized as a negative image ('shadow') and identified on the basis of its somatodendritic structure. The same electrode is then placed on the neuron under visual control to allow formation of a gigaseal ('shadowpatching'). We demonstrate the reliability and versatility of shadowpatching by performing whole-cell recordings from visually identified neurons in the neocortex and cerebellum of rat and mouse. We also show that the method can be used for targeted in vivo single-cell electroporation of plasmid DNA into identified cell types, leading to stable transgene expression. This approach facilitates the recording, labeling and genetic manipulation of single neurons in the intact native mammalian brain without the need to pre-label neuronal populations.     

Role of excitatory amino acid receptors in synaptic transmission in area CA1 of rat hippocampus

The new antagonist 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX), which blocks responses to kainate and quisqualate, has been used in conjunction with D-2-amino-5-phosphonovalerate (APV), which blocks selectively responses to N-methyl-D-aspartate (NMDA), to determine the role of excitatory amino acid receptors in synaptic transmission. An excitatory postsynaptic potential (EPSP)-inhibitory postsynaptic potential (IPSP) sequence was evoked in CA1 neurons by stimulation of the Schaffer collateral-commissural pathway in rat hippocampal slices. CNQX (10 microM) substantially reduced the EPSP without having any effect on input resistance or membrane potential. The IPSP was also reduced provided that the stimulating electrode was place approximately 1 mm from the recording electrode. The EPSP that remained in the presence of CNQX had characteristics of an NMDA receptor-mediated potential; it had a slow timecourse, summated at high frequencies, was blocked reversibly by APV, increased greatly in size in Mg2+-free medium, and showed an anomalous voltage dependence in Mg2+-containing medium. In the presence of CNQX, an APV-sensitive polysynaptic GABAergic IPSP could be evoked, indicating that NMDA receptors can mediate suprathreshold EPSPS in inhibitory interneurons. It is suggested that either NMDA or non-NMDA receptors can, under different circumstances, mediate the synaptic excitation of pyramidal neurons and inhibitory interneurons in area CA1 of the hippocampus.     

Spine calcium transients induced by synaptically-evoked action potentials can predict synapse location and establish synaptic democracy

CA1 pyramidal neurons receive hundreds of synaptic inputs at different distances from the soma. Distance-dependent synaptic scaling enables distal and proximal synapses to influence the somatic membrane equally, a phenomenon called "synaptic democracy". How this is established is unclear. The backpropagating action potential (BAP) is hypothesised to provide distance-dependent information to synapses, allowing synaptic strengths to scale accordingly. Experimental measurements show that a BAP evoked by current injection at the soma causes calcium currents in the apical shaft whose amplitudes decay with distance from the soma. However, in vivo action potentials are not induced by somatic current injection but by synaptic inputs along the dendrites, which creates a different excitable state of the dendrites. Due to technical limitations, it is not possible to study experimentally whether distance information can also be provided by synaptically-evoked BAPs. Therefore we adapted a realistic morphological and electrophysiological model to measure BAP-induced voltage and calcium signals in spines after Schaffer collateral synapse stimulation. We show that peak calcium concentration is highly correlated with soma-synapse distance under a number of physiologically-realistic suprathreshold stimulation regimes and for a range of dendritic morphologies. Peak calcium levels also predicted the attenuation of the EPSP across the dendritic tree. Furthermore, we show that peak calcium can be used to set up a synaptic democracy in a homeostatic manner, whereby synapses regulate their synaptic strength on the basis of the difference between peak calcium and a uniform target value. We conclude that information derived from synaptically-generated BAPs can indicate synapse location and can subsequently be utilised to implement a synaptic democracy.     

Central nervous sensitization and dishabituation of reflex action in an insect by the neuromodulator octopamine

Habituation of excitatory synaptic inputs onto identified motor neurons of the locust metathoracic ganglion, driven electrically and by natural stimuli, was examined using intracellular recording. Rapid progressive reduction in amplitude of EPSPs from a variety of inputs onto fast-type motor neurons occurred. The habituated EPSPs were quickly dishabituated by iontophoretic release of octopamine from a microelectrode into the neuropilar region of presumed synaptic action. The zone within which release was effective for a given neuron was narrowly-defined. With larger amounts of octopamine applied at a sensitive site the EPSP became larger than normal, and in many instances action potentials were initiated by the sensitized response. Very small EPSPs onto a motor neuron, which were associated with proprioceptive feedback, and which were originally too small to be detected above the noise, were potentiated to a level of several mV by the iontophoresed octopamine. A DUM neuron (presumed to be octopaminergic) was found, whose direct stimulation was followed by a strong dishabituating and sensitizing action leading to spikes, of inputs to an identified flexor tibiae motor neuron. The action and its time course were closely similar to those evoked by octopamine iontophoresed into the neuropil in the region of synaptic inputs to the motor neuron. It is concluded that DUM (octopaminergic) neurons exert large potentiating actions on central neuronal excitatory synaptic transmission in locusts.     

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.     

刺激鲫鱼小脑腹外侧区诱发的Mauthner细胞兴奋性突触后电位

实验采用微电极胞内记录技术探查鲫鱼Mauthner细胞(M-细胞)对小脑刺激的电反应特征。电刺激鲫鱼小脑腹外侧部,可在双侧M-细胞胞体、腹侧树突和外侧树突近端记录到一种复合性兴奋性突触后电位(小脑诱发性EPSP)。小脑诱发性EPSP潜伏期较短(0.63±0.09 ms),持续时间较长(5.49±1.13 ms),幅度分级和刺激频率依从等特征。以较高强度刺激小脑常引起M-细胞顺向激活。多点胞内连续穿刺实验显示小脑诱发性EPSP起源于腹侧树突远端。实验结果提示,小脑-M-细胞通路可能包含一组长短不等的神经元链,它们根据链的短或长,由近及远依次投射在腹侧树突远端。     

A persistent postsynaptic modification mediates long-term potentiation in the hippocampus

Long-term potentiation (LTP) is a long-lasting enhancement of synaptic transmission that can be induced by brief repetitive stimulation of excitatory pathways in the hippocampus. One of the most controversial points is whether the process underlying the enhanced synaptic transmission occurs pre- or postsynaptically. To examine this question, we have taken advantage of the novel physiological properties of excitatory synaptic transmission in the CA1 region of the hippocampus. Synaptically released glutamate activates both NMDA and non-NMDA receptors on pyramidal cells, resulting in an excitatory postsynaptic potential (EPSP) with two distinct components. A selective increase in the non-NMDA component of the EPSP was observed with LTP. This result suggests that the enhancement of synaptic transmission during LTP is caused by an increased sensitivity of the postsynaptic neuron to synaptically released glutamate.     

Synaptic depression increases the selectivity of a neuron to its preferred pattern and binarizes the neural code

The preferred pattern of a neuron is defined here by the set of features detected by its excitatory inputs. It is shown that the Leaky integrate-and-fire (LIF) model of a neuron has a poor selectivity to its preferred pattern. Its response is determined by the total current injected by input spike trains. Thus, a few inputs with a high activity (an incomplete pattern) can elicit the same response as many inputs (a complete pattern) with a weak activity. A theoretical model of depressing synapse with linear recovery is proposed which eliminates this problem. Using this model, the time-averaged current injected in the soma by a spike train becomes independent on its frequency. The neural code thus becomes binary, and the response strength of the target neuron depends only on the number of active inputs. Simulations show that a biological model of strong synaptic depression has effects similar to those of the ideal linear model. The best selectivity is obtained with long somatic decay time constants (>50 ms) and with depression recovery time constants larger or equal to the somatic decay time constant. Thus, by eliminating information carried in the input firing rate, a neuron can improve its pattern recognition performance.     

Synaptic organization of retinotectal connections of the frog application of pulse triggered averaging

Pulse-triggered averaging technique was applied to retinotectal connections of the frog. An extracellular single unit was first isolated from the terminals of retinal fibers, and then intracellular responses were recorded from a tectal neuron in the vicinity of the extracellular recording electrode. Intracellular potentials in response to a moving stimulus were averaged by triggering with the isolated presynaptic impulses. The results show that "on-off" retinal fibers monosynaptically excite E-E type (EPSP at "on" and "off" of light) and EI-EI type (EPSP-IPSP at "on" and "off" of light). One of the E-E type neurons was identified as a large ganglionic neuron in layer 8.     

Estimates of a Treatment Effect Based on Censored Data Rank Tests

Linear rank test statistics are applied to the problem of estimating a treatment effect if two sets of censored failure time data are compared and the distributions of the log-failure times of the two samples are assumed to differ only in location. Rank tests for this accelerated failure time model are reviewed and Hodges-Lehmann type estimates for the shift parameter are proposed. Properties of these estimates are investigated, computational aspects are discussed and an example is presented.     

Multiplicity of pacemaker zones in Helix pomatia neurons

Intracellular microelectrode recordings from neurons ofHelix pomatia revealed several local zones of action potential generation both on the soma and on some of the branches of the neurons. Under certain conditions the activity of individual loci of the neuron membrane was synchronized to produce a normal action potential. It is suggested that the somatic membrane of neurons is heterogeneous in structure and consists of separate loci of an electrically excitable membrane, incorporating active and latent pacemaker zones. Neurons ofH. pomatia are characterized by two types of action potential with different triggering mechanisms: one (synaptic) type is generated under the influence of the EPSP, the other (pacemaker) arises through activation of endogenous factors for the neuron (pacemaker potentials). The interaction between synaptic and pacemaker potentials during integrative activity of the neuron is discussed.M. V. Lomonosov Moscow State University. Translated from Neirofiziologiya, Vol. 5, No. 1, pp. 88–94, January–February, 1973.     

Imaging Inhibitory Synaptic Potentials Using Voltage Sensitive Dyes

Studies of the spatio-temporal distribution of inhibitory postsynaptic potentials (IPSPs) in a neuron have been limited by the spatial information that can be obtained by electrode recordings. We describe a method that overcomes these limitations by imaging IPSPs with voltage-sensitive dyes. CA1 hippocampal pyramidal neurons from brain slices were loaded with the voltage-sensitive dye JPW-1114 from a somatic patch electrode in whole-cell configuration. After removal of the patch electrode, we found that neurons recover their physiological intracellular chloride concentration. Using an improved voltage-imaging technique, dendritic GABAergic IPSPs as small as 1 mV could be resolved optically from multiple sites with spatial averaging. We analyzed the sensitivity of the technique, in relation to its spatial resolution. We monitored the origin and the spread of IPSPs originating in different areas of the apical dendrite and reconstructed their spatial distribution. We achieved a clear discrimination of IPSPs from the dendrites and from the axon. This study indicates that voltage imaging is a uniquely suited approach for the investigation of several fundamental aspects of inhibitory synaptic transmission that require spatial information.     

Generating oscillatory bursts from a network of regular spiking neurons without inhibition

Avian nucleus isthmi pars parvocellularis (Ipc) neurons are reciprocally connected with the layer 10 (L10) neurons in the optic tectum and respond with oscillatory bursts to visual stimulation. Our in vitro experiments show that both neuron types respond with regular spiking to somatic current injection and that the feedforward and feedback synaptic connections are excitatory, but of different strength and time course. To elucidate mechanisms of oscillatory bursting in this network of regularly spiking neurons, we investigated an experimentally constrained model of coupled leaky integrate-and-fire neurons with spike-rate adaptation. The model reproduces the observed Ipc oscillatory bursting in response to simulated visual stimulation. A scan through the model parameter volume reveals that Ipc oscillatory burst generation can be caused by strong and brief feedforward synaptic conductance changes. The mechanism is sensitive to the parameter values of spike-rate adaptation. In conclusion, we show that a network of regular-spiking neurons with feedforward excitation and spike-rate adaptation can generate oscillatory bursting in response to a constant input.     

Dipole characterization of single neurons from their extracellular action potentials

The spatial variation of the extracellular action potentials (EAP) of a single neuron contains information about the size and location of the dominant current source of its action potential generator, which is typically in the vicinity of the soma. Using this dependence in reverse in a three-component realistic probe + brain + source model, we solved the inverse problem of characterizing the equivalent current source of an isolated neuron from the EAP data sampled by an extracellular probe at multiple independent recording locations. We used a dipole for the model source because there is extensive evidence it accurately captures the spatial roll-off of the EAP amplitude, and because, as we show, dipole localization, beyond a minimum cell-probe distance, is a more accurate alternative to approaches based on monopole source models. Dipole characterization is separable into a linear dipole moment optimization where the dipole location is fixed, and a second, nonlinear, global optimization of the source location. We solved the linear optimization on a discrete grid via the lead fields of the probe, which can be calculated for any realistic probe + brain model by the finite element method. The global source location was optimized by means of Tikhonov regularization that jointly minimizes model error and dipole size. The particular strategy chosen reflects the fact that the dipole model is used in the near field, in contrast to the typical prior applications of dipole models to EKG and EEG source analysis. We applied dipole localization to data collected with stepped tetrodes whose detailed geometry was measured via scanning electron microscopy. The optimal dipole could account for 96% of the power in the spatial variation of the EAP amplitude. Among various model error contributions to the residual, we address especially the error in probe geometry, and the extent to which it biases estimates of dipole parameters. This dipole characterization method can be applied to any recording technique that has the capabilities of taking multiple independent measurements of the same single units.     

Phenomenological Incorporation of Nonlinear Dendritic Integration Using Integrate-and-Fire Neuronal Frameworks

It has been discovered recently in experiments that the dendritic integration of excitatory glutamatergic inputs and inhibitory GABAergic inputs in hippocampus CA1 pyramidal neurons obeys a simple arithmetic rule as , where , and are the respective voltage values of the summed somatic potential, the excitatory postsynaptic potential (EPSP) and the inhibitory postsynaptic potential measured at the time when the EPSP reaches its peak value. Moreover, the shunting coefficient in this rule only depends on the spatial location but not the amplitude of the excitatory or inhibitory input on the dendrite. In this work, we address the theoretical issue of how much the above dendritic integration rule can be accounted for using subthreshold membrane potential dynamics in the soma as characterized by the conductance-based integrate-and-fire (I&F) model. Then, we propose a simple I&F neuron model that incorporates the spatial dependence of the shunting coefficient by a phenomenological parametrization. Our analytical and numerical results show that this dendritic-integration-rule-based I&F (DIF) model is able to capture many experimental observations and it also yields predictions that can be used to verify the validity of the DIF model experimentally. In addition, the DIF model incorporates the dendritic integration effects dynamically and is applicable to more general situations than those in experiments in which excitatory and inhibitory inputs occur simultaneously in time. Finally, we generalize the DIF neuronal model to incorporate multiple inputs and obtain a similar dendritic integration rule that is consistent with the results obtained by using a realistic neuronal model with multiple compartments. This generalized DIF model can potentially be used to study network dynamics that may involve effects arising from dendritic integrations.