In the classical model of impulse propagation along a chain of neurons, information is carried by axons in the form of action potentials, where the strength of the stimulus may be encoded in the frequency of these all or none potentials. Historically, graded potentials were believed to be generated in the dendrites of the postsynaptic neuron. The combination of inhibitory and excitatory inputs to the dendritic tree of the postsynaptic cell are integrated at the site of action potential generation, which was presumed to be the initial segment of the axon (axon hillock). The dendrites of mammalian neurons have been considered to be electrically passive structures, which funnel synaptic potentials to the soma and axon initial segment, which was proposed by Coombs et al. (1957) to be the site of action potential generation in spinal motor neurons. Thus the term `dendritic' classically implied passive membrane and current flow in a centripetal direction, most usually to the soma/ axon initial segment; whilst the term axon is commonly used to refer to the portion of active membrane leading from the initial segment towards the presynaptic terminal. If the combined inputs depolarised the cell beyond its threshold potential, action potentials are generated which are then propagated to other neurons. The classical model holds that the passive dendrite cables weight synaptic input in proportion to the proximity of the synapse to the soma, with proximal dendrites having a greater weight upon action potential generation than distal ones. However, in the retina this distinction breaks down, as, although not possessing `true' axons, elicit action potentials in response to illumination. The membranes of bipolar cells, in contrast, are believed to be passive, responding to inputs with only sustained, graded potentials. Many investigators have now reported the presence of active Na⁺ and Ca²⁺ conductances within dendrites (e.g. Llinas & Sugimori, 1980; Stuart & Sakmann, 1994; Regehr et al., 1993), and the classical model of the dendritic tree as a passive funnel for the propagation of graded synaptic potentials is now untenable.

Evidence for excitable Na⁺ channels in dendrites

Much evidence has now accumulated to suggest that the dendrites of many neurons, both vertebrate and invertebrate, contain excitable Na⁺, K⁺ and Ca²⁺ channels. This has recently been demonstrated directly by recordings from outside-out patches excised from the apical dendrite of layer V neocortical pyramidal neurons (Stuart & Sakmann, 1994). These were found to contain voltage-activated TTX-sensitive Na⁺ channels, present at around the same density as found in the soma (Stuart & Sakmann, 1994). However, Richardson and fellows (1987) used current density source analysis of hippocampal CA1 pyramidal neurons, to suggest that the presence of excitable dendritic channels is not a sufficient condition to make the dendrites the locus of action potential generation. Regehr and collaborators (1992) showed that TTX-sensitive action potentials are elicited in poorly voltage-clamped regions of cerebellar Purkinje cells, by applying a 3ms voltage step from -65mV to -37mV, which could be prevented by holding the soma at more hyperpolarised potentials. Thus, they concluded that TTX-sensitive Na⁺ channels are present at a sufficiently high density to support Na⁺-dependent action potentials. Furthermore, simultaneous whole-cell recordings at the dendrite and soma by Stuart and Sakmann (1994), showed that the component of the action potential recorded at the dendrite was blocked by the intracellular Na⁺ channel blocker QX-314 introduced via the dendritic patch pipette, before the component recorded at the soma, again consistent with the presence of an excitable dendritic membrane.

Several laboratories have used electrophysiological techniques to provide evidence that Ca²⁺-dependent action potentials may be elicited in the dendritic tree. Laurent and colleagues (1993) showed that small, slow (20-30 ms) regenerative potentials could be evoked in the dendrites of locust non-spiking local interneurons when depolarised positive to -40mV, and that these were resistant to 1m M TTX and inhibited by Ca²⁺ channel blockers. Coleman and Miller (1989) similarly identified a TTX-insensitive spike component in retinal ganglion cells that was inhibited by 3mM Co²⁺. A further point of interest was raised, in that the TTX-insensitive transient had a higher threshold for activation than the TTX-sensitive action potential, and they suggested that such a Ca²⁺ conductance was unlikely to be activated by synaptic currents alone (Coleman & Miller, 1989). Stuart and Sakmann (1994) showed that dendritic Ca²⁺ spikes could be evoked in isolation from the soma in whole-cell recordings when 1mM QX-314 was present in the patch-pipette, which were inhibited by 200m M Cadmium chloride. This showed that the dendrites of layer V neocortical pyramidal cells contain voltage-activated Ca²⁺ channels in addition to Na⁺ channels. Simultaneous measurements of membrane potential and calcium transients in Purkinje cell dendrites have also suggested that Na⁺ and Ca²⁺-dependent action potentials may occur together during plateau potentials in the dendrite (Ross et al., 1990). Ross and co-workers reported that in the dendrites of Purkinje cells, free Ca²⁺ increases only slowly during plateau depolarisations, probably associated with a non-inactivating Na⁺ conductance (Llinas & Sugimori, 1980), indicating that plateau potentials are not sufficient to open voltage-gated Ca²⁺ channels. However, intracellular Ca²⁺ rises quickly during bursts of action potentials, with sharp incremental increases in free Ca²⁺ apparently associated with individual action potentials. The jumps in Ca²⁺ were reported to be coincident with the peaks of the slower action potentials, whilst no large increase was associated the fast spikes (Ross et al., 1990), suggesting that fast spikes correspond to Na⁺-dependent action potentials, whilst the slower spikes describe Ca²⁺-dependent action potentials.

Regehr and Armstrong used an ingenious method to isolate the dendritic action potential. They voltage-clamped layer V pyramidal cells at the soma in thin slices of rat motor cortex, to prevent the spread of activity to and from the soma, and under these conditions action potentials were seen when the dendrite was stimulated by an extracellular electrode located 400m m from the cell body, near the apical dendrite (Regehr et al., 1993). By selectively inhibiting Na⁺ channels in the soma and proximal dendrite of the pyramidal cell with TTX, the dendritic component of the regenerative activity was isolated. The inward current spike could also be separated into two components, and the later and larger of the two components of the synaptic response could be eliminated by hyperpolarising the soma or by improving the access resistance compensation, suggesting that the larger spike component was generated in the soma when the cell body was not efficiently voltage-clamped. Regehr and colleagues concluded that synaptic input or extracellular stimulation far out on the apical dendrite, triggers current spikes under conditions where the soma is voltage-clamped. This evidence strongly supports the contention that the dendrites have a sufficiently high density of Na⁺ channels to support action potentials.

The technique used by Regehr and Armstrong (1992), provides a potentially useful electrophysiological approach to determine whether the ganglion cell dendrites contain excitable membrane conductances. Regehr and partners clamped the soma of axotomised rat cerebellar Purkinje cells at a command voltage below the resting potential, so that threshold potential could not be reached. The use of suitably low resistance electrodes of 0.5-2.6 MW allowed good voltage control of the soma after compensation of around 70% of the access resistance (see Appendix I), but poor control over the dendrites and axon stump. However, the axon stump is effectively isolated from regenerative activity in the dendritic tree by the voltage clamp on the soma. Thus, the inadequacy of the space-clamp was harnessed as a means of isolating regenerative potentials within the dendrite. Two alternative strategies may be used to trigger action potentials in the dendrites without eliciting an action potential in the soma. Firstly, depolarising voltage steps may be applied from a hyperpolarised clamp potential, which are too short to elicit an action potential in the soma, but are sufficiently long to elicit an action potential in the dendrites if not adequately space-clamped. The duration may be incremented until the threshold for regenerative activity in the dendrite is reached. Alternatively, as poorly space-clamped dendrites are closer to threshold than the soma when clamped below resting potential, depolarising voltage steps of longer duration may be applied incrementally to the soma, which may trigger an action potential in the dendrite before the soma reaches threshold potential, provided the duration of the step is insufficient to elicit a somatic action potential. Regehr and co-workers observed that the latency of the regenerative current spike increased as the holding potential was made more hyperpolarised, and became shorter as the as the holding potential was made more depolarised.

Cerebellar Purkinje cells respond to a long depolarising pulse with a burst of fast Na⁺-dependent action potentials (previously believed to be somatic), and slower Ca²⁺-dependent dendritic action potentials (believed to be mainly dendritic in location), in addition to plateau potentials resulting from conductance increases to each of these ions (Llinas & Sugimori, 1980). When combined, the segregated conductances produce potentials of variable waveform in different dendritic regions (e.g. Llinas & Sugimori, 1980), and such a heterogeneous distribution of active conductances combined with the cell's complex dendritic architecture makes the simplified model of synaptic integration based upon compact passive dendrites untenable (Lev-Ram et al., 1992).

The current body of evidence has now laid to rest the idea that dendritic membranes are invariably passive membrane structures. However, the new findings raise two important possibilities; that a specific region, or regions of the dendritic arbor, may function as the decision point in the generation of an action potential, and that the dendritic component of the action potential may travel in an anterograde (from synapse to soma), or retrograde (from soma to dendrite) direction following generation of the action potential. In consideration of this first question, Regehr and fellows concluded that action potentials can begin in the dendrite and propagate to the soma, indicating that the initial segment is not necessarily the decision point for the action potential, at least not in pyramidal cells. However, Stuart & Sakmann produced strong evidence that action potentials are produced in the soma before the dendrite in response to depolarising current pulses in neocortical pyramidal cells. Stuart and Sakmann made simultaneous whole-cell current-clamp recordings from both the soma and dendrite, and found that action potentials elicited by short dendritic current pulses were observed first at the soma. However, using larger current pulses that depolarised the dendrites close to 0mV, it was possible to elicit action potentials that first appeared in the dendrite. Action potentials could also be initiated by EPSP's in the very distal parts of the dendritic tree by stimulating layer I of the neocortex. These action potentials always appeared initially in the soma and then propagated back into the dendritic tree. Thus the role of the dendrite as an anterograde conduit for regenerative potentials triggered by excitatory synaptic potentials, and as a decision point in the generation of action potentials may vary between neuronal cell types, and upon experimental methodology. Stuart & Sakmann concluded that action potential initiation occurs at or near the soma. Introduction of the intracellular Na⁺ channel blocker QX-314 into the dendritic patch pipette (1mM), led to a decline in the amplitude of the action potential in the dendrite before the soma, supporting their contention that Na⁺ channels in the dendrite support the back propagation of somatic action potentials into the dendrites. From their observations they proposed that dendritic Na⁺ channels serve to boost the amplitude of dendritic action potentials as they propagate back into the dendritic tree.

If the neuron is modelled as an equivalent cylinder, the electrotonic length (L) can be estimated, giving an effective measure of the electrical distance of synapses from the soma. As is explained in appendix III, the electrotonic length increases in direct proportion to the cytoplasmic resistivity (around 200-400 W cm in measurements from hippocampal pyramidal cells), and decreases as the specific membrane resistance increases. The propagation of potentials in dendrites is very dependent upon signal speed and frequency, with both faster and higher frequency events being attenuated to a much greater extent than slower or steady-state voltage changes (e.g. graded potentials). However, at lower frequencies, an increase in specific membrane resistance (R_m) will reduce the degree of attenuation, as R_m is determined by the type and density of ion channels in the membrane that are open near the resting potential. A change in R_m affects the attenuation of an electrical event in two ways; by changing the effective electrotonic distance, and secondly, by slowing the time course of the event. However, as the action potential is very fast, increasing R_m has little effect upon its time course. Increasing R_m however, has the undesirable effect of slowing the measured synaptic current, as R_m increases t_m, thus slowing the decay of the membrane potential.

Most synapses in the CNS are located in the dendrites at distances where it is impossible to achieve adequate voltage control with a somatic voltage-clamp. However, higher R_m values result in a shorter steady-state electrotonic distance of the synapse, improving the quality of the voltage-clamp for slow synaptic events, although faster events are still susceptible to severe attenuation and filtering due to the inadequacy of the space clamp. Further, an inadequate space-clamp also induces errors in the measured reversal potential of synaptic events. A fall in R_m is accompanied by a posoitive shift in the reversal potential and a fall in conductance.

Retinal ganglion cells are projection neurons that integrate excitatory and inhibitory post-synaptic potentials and generate action potentials which are then channeled to the cortex for higher processing. Ganglion cells then function as the output neurons of the retinal neuroepithelium, which functions to transduce an optical image of the environment into a neural image. Ganglion cells are found primarily in the ganglion cell layer, proximal to the inner nuclear and plexiform layers, to which their dendritic fields are restricted. However, up to 50% of cells in the ganglion cell layer may be displaced amacrine cells, which are generally of smaller size. Displaced ganglion cells may also be found at the inner margins of the inner plexiform layer.

Functional classification of retinal ganglion cells.

Ganglion cells can be subdivided into two general types on the basis of the morphology of their dendritic trees; those that have diffuse dendritic trees that spread throughout the inner plexiform layer, and those with stratified dendritic arbors that spread on one or only a few levels of the inner plexiform layer. Three general classifications of cell types can be made on the basis of ganglion cell receptive field properties: On-cells, Off-cells and On-Off cells. Both On-centre and Off-centre ganglion cells give generally sustained responses to illumination at the center of their receptive fields, whilst On-Off cells give very transient responses at the onset and cessation of illumination, reflecting the activity of transient amacrine cells, and may be movement and/or direction-sensitive. Cold-blooded vertebrates have predominantly transient On-Off ganglion cells, whilst those in the cat and monkey retina exhibit mainly sustained behaviour. The best known ganglion cells found in the cat retina are called a (Y) and ß (X) cells. ß-cells have a bushy dendritic tree 30m m in diameter, which arborizes in either the outer third of the IPL (sublamina a), or in the inner two-thirds of the IPL (sublamina b). In contrast a -cells have larger perikarya and wider, radiating dendritic arbors of around 180m m diameter, which similarly terminate in sublaminas a or b. Ganglion cells whose dendrites terminate in sublamina a fire action potentials at light "off", whilst those terminating in sublamina b fire action potentials at light "on".

The photo-receptive field of a ganglion cell, usually around 1mm in diameter, is organised both concentrically and antagonistically, so that illuminating different regions of the receptive field alters the firing rate of the ganglion cell. Extensive overlap occurs between the receptive fields of adjacent ganglion cells. Thus a given photoreceptor cell contributes to the responses of a number of ganglion cells (signal divergence). Illuminating the centre of the receptive field with a spot increases the firing rate of an On-ganglion cell, whilst decreasing the firing rate of an Off-ganglion cell for the duration of illumination. The frequency of firing is dependent upon the light intensity, and the derived intensity-response curves can be fitted to Michaelis-Menten kinetics. Such analysis shows that transient On-Off ganglion cells show a steeper intensity-response curve than do sustained ganglion cells. Illuminating both the centre and surround regions with more diffuse light antagonises the response to the centre, and the cell responds most dramatically when there is maximum contrast between the illumination of the centre and surround regions.

The ß-cell gives both a strong transient and a sustained response in bright light, but an a -cell gives primarily a transient and a much less sustained component. Sustained, contrast-sensitive ß cells receive approximately 70% bipolar and 30% amacrine input, whilst other cells (e.g. a -cells) receive around 75% amacrine input (cat retina). There are several additional classes of ganglion cells that have been described according to their receptive field properties. For example, Barlow (1964) described large-field unit On-ganglion cells, that are direction-sensitive, and respond to dark or light spots over a large receptive field.

Ganglion cell activity reflects the two basic types of processing that occur in the retina; inner and outer plexiform layer processing. Ganglion cells receive their inputs from either bipolar cells (sustained outputs reflecting primarily OPL processing) and amacrine cells (transient outputs reflecting primarily IPL processing). Certain ganglion cells receive a predominantly amacrine cell input (conventional synapses onto dendritic tree), whilst others receive an abundant bipolar cell input (ribbon synapses). In cold-blooded vertebrates, ganglion cells receive a predominantly amacrine input, whilst in primates, bipolar input is relatively more abundant. In an alternative classification of ganglion cells, so-called G₁ ganglion cells receive a predominantly bipolar input; G₂ cells receive a more even mixture of bipolar and amacrine inputs, and G₃ cells receive a predominantly amacrine cell input.

In retinas where a simple, sustained, contrast-sensitive receptive field predominates, bipolar cells make numerous direct contacts with ganglion cell dendrites; whereas when complex direction and motion-sensitive receptive fields predominate, there are relatively fewer direct bipolar-ganglion cell contacts, more amacrine synapses and amacrine-amacrine cell interactions. The transient On-Off ganglion (G₃) cell receives a strong inhibitory input from amacrine cells, and an excitatory input from both amacrine and bipolar cells, and it is believed that the amacrine cells, with their transient activity, are responsible for mediating motion and direction sensitivity.

Synapses to the mammalian ganglion cell are directed exclusively towards the dendrites, thus setting it apart from the Purkinje cell and motor neuron, which both receive extensive somatic inputs, and indicating that light will not evoke EPSC's directly on the soma. It has been postulated that retinal ganglion (and amacrine) cells receive both excitatory inputs from On-bipolar cells, utilising glutamate as a neurotransmitter (Massey & Miller, 1988); and inhibitory inputs from Off-bipolar cells, which may release glycine (Bolz et al., 1985; Cohen & Sterling, 1986), in what amounts to a `push-pull' mechanism. However, amacrine cells are also present which release GABA or glycine. There are amacrine cells that store, either exclusively or in combination (and hence presumably release), GABA, glycine, acetylcholine (starburst), indoleamine and dopamine, forming a basis for their classification. The excitatory input to transient On-Off ganglion cells appears to be mediated mainly by acetylcholine, although this has not been demonstrated in the salamander; whilst the inhibitory input is mainly GABAergic. The effects of neurotransmitters and their analogues (e.g. nicotine, AMPA) may be studied in the intact retina by the addition of 20m M CdCl₂ to the bathing medium, which effectively blocks synaptic transmission (Mittmann et al., 1990).

As ganglion cell receptive fields appear to extend at least as far as the dendritic field (Lukasiewicz & Werblin, 1990); it follows that there must be excellent communication between the dendritic synapses and the spike initiation zone. This suggests that either the ganglion cell must effectively be a single isopotential compartment, or alternatively is anisopotential and possesses an excitable dendritic membrane. The presence of an excitable dendritic membrane, as has been demonstrated in cerebellar Purkinje cells, layer V neocortical pyramidal neurons and layer V pyramidal motor neurons, makes distal synapses more effective in influencing the excitability of neurons. However, Coleman and Miller (1989) have suggested from their measurements of specific membrane resistance in retinal neurons, that the ganglion and amacrine cells of the inner nuclear layer are essentially isopotential, and thus operate with a uniform spread of potential within the cell, thereby involving the entire dendritic field in the light-evoked response of a ganglion cell.

Intracellular microelectrode recordings made by Carras and co-workers (1992) also supported the view that the ganglion cell conforms to the classical model of the neuron. Hyperpolarising pulses were injected into ganglion cells to modulate the form of the light-generated action potentials. Using this technique, they found that as they hyperpolarised the cell, an inflection appeared initially in the rising phase of the action potential, which then became abruptly smaller in amplitude as the magnitude of the hyperpolarising stimulus was increased. Stimulation of the cell's axon, whilst recording from the soma, revealed that an increase in the hyperpolarising current produced a significant delay in the arrival of the impulse at the soma, and produced a more marked inflection in the rising phase. They concluded that moderate hyperpolarisations slowed, but did not block the action potential. With greater hyperpolarisations they concluded that they had prevented the soma from reaching threshold, and that the smaller, earlier peaking response was a signal that had been passively propagated from the last active site to the recording site. They concluded that the orthodromic action potential had originated in the axon, at some `electrical' distance from the cell body. They discounted the possibility that the notch in the action potential had been generated by an active membrane in the dendrites, due to the similarity in the appearance of the responses after orthodromic and antidromic stimulation, and to the failure of the dendritic compartments to sustain a regenerative response. Carras and co-workers concluded that their data supported the classical notion that the nerve impulse is generated in the initial segment of the axon, and then spreads to activate a retrograde somatic impulse and an anterograde axonal impulse.

Mittman and colleagues claimed that they were unable to compensate for the series resistance or membrane capacitance due to the anisopotentiality of ganglion cells. In contrast, Coleman and Miller measured passive membrane parameters in salamander ganglion cells, from which they concluded that these cells may be essentially isopotential. Exponentials were fitted to charging curves to determine whether these cells behave in an isopotential fashion. In their experiments, 65% of cells were described by a single exponential, whereas 35% were not, although these were believed to be due to inadequate access resistance compensation. An input resistance (R_m) of between 500 and 5,000 W .cm² was calculated following injection of hyperpolarising current pulses. The charging curve induced by injecting hyperpolarising current pulses was fitted to a single exponential to derive the membrane time constant (t_m), which was typically around 70ms. The R_m was then calculated from t_m and from the specific membrane capacitance, which was assumed to be 1m F/cm². Using the average experimentally determined value of t, R_m values of around 68,000 W .cm² were calculated. The R_m values were estimated to be sufficiently high for some cells to effectively behave as an isopotential compartment.

To justify their argument for isopotentiality, Coleman and Miller modelled the dendrite as a single equivalent cylinder with a diameter of 1m m and a length of 240m m, to allow them to estimate the expected passive decay of graded potentials arising at different distances from the soma. They argued that for a specific membrane resistance of 2,500 W .cm², a steady-state voltage applied at the end of the dendrite will decay to 23% of its original value at the soma, compared to only 10% when the R_m is around 70,000 W .cm². Thus, Coleman and Miller concluded that the high value of R_m reduced the ganglion cell structure to within 2% of being isopotential, although their estimate of the internal resistivity may have been favourable to their conclusions. They predicted from their analysis that a reasonable space clamp of the ganglion cell had been achieved, as the electrotonic length of the dendrites was close to 0.2 space constants (Appendix III). They argued that this provides the basis for the excellent communication that exists between the distal dendrites and the spike initiation zone. However, in the same publication, Coleman and Miller showed that the rising phase of the light-evoked action potential could be separated into two components, and that stepping from a holding potential of -45 to -31 mV evoked a large inward current, the peak of which was preceded by a transient in the voltage record. These observations were interpreted as being consistent with an inadequate space clamp, contradicting their later arguments, and suggested that the action potential had been initiated at a site spatially distinct from the soma. However, they argued that an adequate space clamp had been achieved for action potentials produced by the soma (Coleman & Miller, 1989).

The patch-clamp technique can be used to characterise the various cell types present in the ganglion cell layer. Coleman and Miller (1989) obtained stable resting potential measurements from ganglion cells by applying alternating light and current pulses, and thus provided a constant state of light adaption. In their measurements, On-ganglion cells had a mean dark resting potential of -70mV, Off-ganglion cells -55mV and On-Off ganglion cells -65mV. Mittman et al (1990) also claimed that they were able to distinguish the light responses of On and On-Off ganglion cells in both current-clamp and voltage-clamp recordings. In response to a 2.5s step increase in illumination, On-Off ganglion cells responded with a transient depolarisation accompanied by a volley of action potentials at both the onset and cessation of the stimulus; whilst On-cells responded with a sustained depolarisation accompanied by action potentials which often showed accommodation of the spike rate. When voltage-clamped near the resting potential, these cells respond to the same stimulus with inward currents similar to the potential responses (i.e. transient EPSC's in On-Off ganglion cells, and a sustained EPSC in On-ganglion cells), reflecting the shaping of the potential responses by synaptically-activated conductances. They found that in the salamander, On-Off ganglion cells constitute 86% of the cell population and On-cells 14%, with only small numbers of Off-ganglion cells encountered.

One potential experimental approach to evaluate whether the dendritic membrane is excitable, may be to illuminate the intact retina to stimulate the ganglion cell, using Ringer containing 100m M bicuculline and 500nM strychnine to block IPSC's (Mittman et al., 1990). Under these conditions it may be possible to see if regenerative currents are elicited in a well voltage-clamped ganglion cell upon a step increase in illumination. If regenerative activity or a TTX-sensitive component is detected, then this will be consistent with a dendritic origin, irrespective of the presence of an intact axon or stump. Such experiments may therefore require that retinal preparations be dissected and maintained in the dark.

Alternative experiments may be designed to investigate the nature of the dendritic membrane. The ganglion cell layer may be voltage clamped at between -60 and -70 mV, and the potential stepped to more depolarised values in small increments to determine the threshold, latency and sub-components of any inward current spikes induced. The intracellular Na⁺ channel inhibitor QX-314 (1mM) may be employed in the patch-pipette to isolate any regenerative components of the dendritic current that are due to the activation of voltage-dependent Ca²⁺ channels, which may be amplified by increasing the Ba²⁺ concentration in the bathing solution. Inhibitors of voltage-activated Ca²⁺ channels may be used to characterise any voltage-dependent Ca²⁺ conductance that is present. Alternatively, the soma may be voltage-clamped at a potential just beyond threshold, where a Na⁺ spike current may be elicited, and the clamp potential may be held at this potential to maintain the voltage-dependent Na⁺ channels in the soma in an inactivated state. From this depolarised holding potential, using Regehr's argument that the dendrites, if poorly space-clamped, should still be below threshold, further regenerative activity will be evoked if a series of small depolarising voltage pulses is applied to the cell membrane. If other regenerative components are elicited, then TTX or Ca²⁺ channel blockers may be used to determine whether these components are due to the activation of Na⁺ or Ca²⁺ currents. This raises the difficulty of selectively perfusing the axon and nearby soma with TTX (200-400nM). One strategy might be to use a separate perfusion nozzle to pass a stream of Ringer containing TTX, together with a marker dye such as fast green, across the surface of the ganglion cell layer of the intact retina, in the presence of a fast bulk solution flow. This would allow the comparison of regenerative transients elicited before and after superficial TTX application. This may be followed by the general bath application of TTX to determine the magnitude of the regenerative Na⁺ current in the dendritic tree, by subtracting the global TTX-insensitive regenerative current from the superficial TTX-insensitive current. This may be followed by a recovery experiment to show that changes are reversible.

A heterogeneous distribution of active conductances within the dendritic membrane produces a dilemma for the physiologist, as invasive techniques, such as microelectrode impalements, only measure electrical events in isolated regions of the dendrite or soma. However, non-invasive techniques, such as fluorescence imaging using Ca²⁺-sensitive dyes, allows simultaneous multi-site recordings. Thus patterns of excitation across the entire dendritic field can be measured, to give an insight into the spatial distribution of Ca²⁺ transients. Lev-Ram et al (1992) used a general bath perfusion of 1m M TTX to isolate Ca²⁺-dependent electrical activity in Purkinje cells loaded with 2mM fura-2 (free acid), whilst simultaneously monitoring the entire dendritic tree with epifluorescence optics. The cells were fed a hyperpolarising DC bias current (<1nA) to prevent occasional spontaneous firing. Ross and co-workers devised a system, wherein changes in the free Ca²⁺ levels could be monitored simultaneously with electrical events at the soma, allowing spike potentials to be correlated with changes in cytosolic free Ca²⁺.

To measure free Ca²⁺ changes, Lev-Ram et al (1992) used single wavelength recordings of fast Ca²⁺ transients to maximise their signal to noise ratio. Background (auto)fluorescence (F_auto) was determined by measuring the intensity at a location away from the neuron, and was subtracted from the measured resting fluorescence (F_tot), allowing the true resting fluorescence (F_r) to be calculated. These measurements allow both the time course and location of the fluorescence to be determined, although a transformation between the change in F and [Ca²⁺]_i can be made, if both the resting [Ca²⁺]_r and the fluorescence change for a maximal [Ca²⁺]_i are known. The change in F can be related to the change in free [Ca²⁺]_i in a particular location, because F is proportional to the volume when the resting [Ca²⁺]_i and dye distribution are uniform. However, it must be borne in mind that spatial resolution in dendritic arbors is limited by the absence of true two-dimensionality in the dendritic tree, leading to focusing difficulties, blurring of the cell's image due to light-scattering by overlying tissue, and a reduction in the signal to noise ratio of the transients because pixels of a smaller area are necessary.

Ross and co-workers (1990) argued that as all dendritic elements of cerebellar Purkinje cells recorded a sharp Ca²⁺ change in response to spontaneous or evoked events, whilst the somatic signal was weak or absent. As Ca²⁺ diffuses slowly in the cytoplasm, and changes in [Ca²⁺]_i are detected throughout the dendritic field, then, they concluded, the site of [Ca²⁺]_i change must be close to the site of Ca²⁺ entry, and therefore Ca²⁺ channels must be present all over the dendritic membrane. If Ca²⁺ channels are distributed throughout the dendritic arbor, then the failure to detect a transient in a particular region is a good indication that the Ca²⁺ transient failed to propagate actively into that region. Synaptically-generated Ca²⁺ transients could result from entry via ligand-gated channels, voltage-gated channels or indirectly, via the mobilisation of intracellular messengers. Thus, Miyakawa and co-workers concluded from the fast rise and fall times of the Ca²⁺ transients stimulated in Purkinje cells by Parallel and Climbing Fibre inputs, and from the close linkage to electrical transients, that Ca²⁺ enters through voltage-gated Ca²⁺ channels.

True Ca²⁺ transients are sharper than fluorescence measurements indicate, as the dye and Ca²⁺ are not in equilibrium within the cell during very fast transients. As the recovery process is slower than the rate of rise, for fast transients the change in [Ca²⁺]_i is proportional to the integral of the inward Ca²⁺ current. However, for plateau potentials and burst spikes, the change in F will reflect the integral of the difference between the rate of Ca²⁺ influx and the recovery process. It has been reported that the soma (Kaneda et al., 1990) and dendrites (Bossu et al., 1989) of isolated Purkinje cells may have two types of Ca²⁺ conductance, which underlie both high threshold Ca²⁺ spikes and low threshold Ca²⁺ potentials, and many workers have found Ca²⁺ channels located in the soma of isolated Purkinje cells (e.g. Regan, 1991). However, in contrast to the arguments of Tank et al (1988), Lev-Ram et al (1992) argued that due to the absence of a phase shift in the appearance of Ca²⁺ in the fine processes and the peak of the action potential, that these conductances were distributed similarly, or were the same. Time-dependent measurements of membrane Ca²⁺ currents can be related to conventional electrophysiological measurements, only if the increase in Ca²⁺ is due to entry through the cell membrane, and not due to release from intracellular stores (Berridge, 1993), and if the buffering process is slow relative to the entry process and is linear over a physiological range of free Ca²⁺ concentrations (Ross et al., 1990). Where the rate of Ca²⁺ entry is considerably greater than the rate of efflux, the membrane current is likely to be proportional to the derivative of the Ca²⁺ signal, which is not the case during plateau potentials. Another factor which must be considered when measuring Ca²⁺ transients is the surface area to volume ratio of the dendrite. Free [Ca²⁺]_i rises much more slowly in thick dendrites than in thinner dendrites, although in thinner dendrites the rate of decline in [Ca²⁺]_i is faster than in the thick dendrites, as might be predicted from surface area to volume ratio considerations (Lev-Ram et al., 1992).

Slow increases in free Ca²⁺ are generated during Purkinje cell plateau potentials, which are widespread, but it is difficult to accurately determine which regions generate these transients due to their small size. Such subthreshold plateau potentials can be generated in the presence of TTX, and the distribution of Ca²⁺ conductances underlying spike and plateau potentials are the same, or distributed similarly in the dendrites (Lev-Ram et al., 1992). Similarly in the presence of global TTX, a stimulus pulse elicited a regenerative, slowly decaying response that did not reflect the passive membrane time-constant, presumably reflecting Ca²⁺-dependent electrical activity (Lev-Ram et al., 1992). The relatively low amplitude of the Ca²⁺-dependent plateau potential evoked in the presence of TTX, is consistent with their conclusion that Ca²⁺ action potentials propagate electronically into the soma.

Lev-Ram and colleagues (1992) reported that significant increases in free intracellular Ca²⁺ were recorded in the soma and dendritic shaft of the Purkinje cell during bursts of Na⁺-dependent action potential activity, in contrast to the sharp changes in dendritic fluorescence intensity that correspond to Ca²⁺-dependent action potentials. Lev-Ram and associates argued that this was largely due to Ca²⁺ entry through Na⁺ channels during action potentials, although significant entry may also have occurred through voltage-gated Ca²⁺ channels activated by fast Na⁺ action potentials, or via an electrogenic Na⁺/Ca²⁺ exchange mechanism.

Whether Ca²⁺-dependent action potentials occur physiologically in response to synaptic stimulation, was raised from observations of Ca²⁺-dependent action potentials elicited in voltage-clamp recordings in response to depolarisations in the presence of TTX. Investigators have claimed that, under some circumstances, Ca²⁺ action potentials can be elicited in dendrites (Llinas & Sugimori, 1980), although Regehr and fellows concluded that prolonged and heavy current injection at the soma was necessary to reach the threshold for Ca²⁺ electrogenesis. Coleman and Miller (1989) concluded that communication between the distal dendrites and soma of ganglion cells did not appear to depend upon regenerative voltage-sensitive conductances, and that high threshold dendritic Ca²⁺ spikes were unlikely to be activated by synaptic potentials. If, however, Na⁺ action potentials are elicited then this would almost certainly indicate that the threshold for Ca²⁺ electrogenesis will be reached. These questions can be addressed in the ganglion cell using Ca²⁺ imaging techniques to detect regenerative transients in response to step increases in illumination.

However, it has been shown in hippocampal pyramidal neurons that Ca²⁺ channels are activated in distal dendrites when the synaptic depolarisation is prolonged, as the action potential propagates more effectively into these dendritic regions (Jaffe et al., 1992). Miyakawa and coworkers (1992) argued that the amplitude and spatial distribution of Ca²⁺ signals is directly related to the active spread of potential changes in the dendrites. From the restricted distribution of many CF and PF signals they suggested that these synaptic potentials often produce only locally regenerative responses, which may in turn summate to elicit complex regenerative responses. The appearance and amplitude of distal Climbing Fibre-evoked Ca²⁺ signals was more variable than proximal signals, indicating a failure of reliable spread to the fine distal branches. This appeared to be a property of the postsynaptic membrane as it was enhanced by intrasomatic depolarising pulses (Miyakawa et al., 1992). The stimulation of both Parallel and Climbing Fibres led to the appearance of regenerative components at higher stimulus intensities which were reversibly blocked by 2m M CNQX (a potent inhibitor of non-NMDA `AMPA' glutamate receptors). Whenever Lev-Ram and co-workers (1992) saw Ca²⁺ transients in a Purkinje cell dendritic branch, the sharpest jumps were observed in the finest twigs, implying that the potentials must have spread to the tips either actively or passively. However, after climbing fibre activation, sharp transients are often not detected in the finest dendrites, suggesting that passive spread is not in itself sufficient to generate signals there. Occasionally, the dendritic Ca²⁺ spikes fail to propagate into regions of fine branches, indicating that electrically distinct regions exist in the stem dendrites and fine branches, and that Ca²⁺ action potentials can be regenerative in restrictive parts of the dendritic field (Ross et al., 1990; Lev-Ram et al., 1992). Lev-Ram and colleagues (1992) believe that the sharp Ca²⁺ changes that occur in fine dendrites are primarily due to Ca²⁺ action potentials at that location (Ross et al., 1990), whilst Tank and collaborators (1988) observed a phase shift between the appearance of Ca²⁺ changes in the fine and thick dendrites, and argued that plateau potentials in the thin dendrites activated action potentials in the thick dendrites, which then propagated back over the finer processes.

In order to understand how synaptically evoked, and intrinsically generated electrical events are integrated in complex dendritic fields, it is essential to understand how potentials originating in different parts of the field propagate and are combined within the cell. The dendritic tree functions as a junctionally complex integrative unit for the thousands of synaptic inputs, which induce differing excitatory and inhibitory, slow and fast, and electrical and biochemical events in the dendritic membrane. Two critical factors affect the integrative function of dendrites: the distribution of voltage-gated ion channels in the dendrites, and the passive electrical properties, or `electrotonic structure' of the dendritic tree. Evidence from perforated-patch experiments in hippocampal neurons shows that the input resistance and membrane time constant are larger at relatively depolarised potentials, and smaller at relatively hyperpolarised potentials, and are therefore not truly passive membrane parameters (Spruston & Johnston, 1992). This is probably due to the activation of K⁺ channels by membrane hyperpolarisation. In cortical neurons it has been shown that dendritic channels activated by hyperpolarisation can affect the shape of the EPSP (Rall & Segev, 1985). Similarly, the activation of dendritic ion channels by ligands or second messengers could affect the R_m of large parts of the dendritic tree (e.g. by diffuse release of neurotransmitters), or very locally (by GABA-modulated shunt inhibition, or the activation of K⁺ channels following action potentials). In this way the PSP shape could be altered by changes in the electrotonic structure of the dendritic tree, changes in the time course of synaptic potentials, or in the active response to synaptically-mediated membrane potential changes.

In general the `twigs' that are derived from a single small branch originating on one of the stem dendrites fire together. Lev-Ram and colleagues (1992) have suggested that subtle variations in Ca²⁺ channel density, in the distribution of K⁺ conductances and impedance mismatches at branch points are possible factors explaining why action potentials sometimes only fire in restricted dendritic regions. One explanation for the propagation failures that occur in the dendritic tree, is that there are low Ca²⁺ channel densities at the origins of branches from stem dendrites. Llinas and Sugimori (1980) have proposed that there are electrically distinct regions and heterogeneous sites of action potential generation in the neuron, from the variety of shapes and amplitudes of different spikes recorded by the electrode. If only selective dendrites, or specific regions of dendrites, act as trigger zones, then this may skew the spatial properties of the receptive field. However, if the site of action potential generation is more remote from the site(s) of dendritic integration, then receptive field properties should be less sensitive to local events at the dendritic level (Carras et al., 1992). Intracellular microelectrode recordings from locust nonspiking local interneurons (Laurent et al., 1993) suggested the presence of multiple initiation sites for regenerative potentials , separated by regions of inexcitable membrane, allowing decremental conduction and the passive fusion of spike envelopes.

There is much evidence that the K⁺ conductance plays a role in modulating dendritic excitability. In turtle Purkinje cells a transient hyperpolarisation, or A-like current, has been shown to be a critical component in determining the magnitude and spatial configuration of CF-induced Ca²⁺ spikes (Chan et al., 1989). If a K⁺ conductance in Purkinje cells had similar properties to I_A or I_D, then it would inhibit the spread of locally regenerative CF or PF responses, until inactivated by small plateau potentials or synaptic potentials. Dendritic spikes come at the end of a stimulus pulse, or ride on top of a plateau, either of which would inactivate the K⁺ conductance(s) present. The activation of K⁺ conductances in certain dendritic branches after conducting action potentials will make them refractory to further stimulation. Synaptic potentials would also serve to introduce shunting conductances at specific dendritic locations, and thus directly affect spreading potentials. Each dendrite will tend to drain off a portion of the stimulating current, which will charge adjacent membrane regions and cause them to depolarise. Ca²⁺-dependent spikes in Purkinje cells are followed by a strong after-hyperpolarisation, most likely representing a Ca²⁺-activated K⁺ conductance (Ross et al., 1990). Such Ca²⁺-dependent K⁺ conductances could be turned on faster in the fine dendrites, and persist for longer in the thick dendrites. These differences may have profound influences on the spread of potentials from one region to another. The Ca²⁺ influx associated with the Na⁺ spike bursts may have a self-regulating role, as the activation of a Ca²⁺-dependent K⁺ conductance would serve to limit the level of the Na⁺ potential plateau, and thus will profoundly influence the firing rate of the fast Na⁺ spikes (Llinas & Sugimori, 1980).

Finally, the observations of Stuart and Sakmann (1994) have raised the possibility that the dendritic action potential functions as a feedback mechanism. According to the data of Stuart and Sakmann (1994) somatic action potentials invade the dendritic tree via the activation of dendritic, TTX-sensitive Na⁺ channels. This may provide a retrograde signal that could modulate the computational properties of neurons in both the long and short term. For example the activation of voltage-activated Ca²⁺ channels could shunt out parts of the dendritic tree by opening Ca²⁺-activated K⁺ conductances. Similarly the entry of Na⁺ could open Na⁺-activated K⁺ conductances, which will also tend to hyperpolarise the dendritic membrane and make it refractory to further stimulation. Long-term changes in synaptic strength could be induced by the activation of dendritic voltage-activated Ca²⁺ channels, or by the relief of the Mg²⁺ blockade of NMDA receptor channels, leading to phosphorylation events and the modulation of synaptic elements.

Unless either I_clamp or R_access+R_external is zero, the membrane potential is not equal to the clamping potential V_clamp. The series resistance error can be detected through the decay time of the membrane capacity current transient, which has a time constant (t) given by R_access*C_m. Thus the charging/ discharging time of the membrane depends upon the degree to which the R_access is compensated. R_access prevents the voltage clamp circuit from drawing off all the inflowing current, thereby allowing charging of the membrane capacitance, and causing a change in V_m which leads to the series resistance error.

The series resistance error may be partially compensated (by 70-90%) by applying a briefly and rapidly rising current pulse to the membrane, and measuring the jump in V_m = I_step * R_access. Alternatively, a voltage step may be applied to the membrane, allowing the time constant to be measured which is equal to the product of the C_m and the R_access. The R_access is usually at least twice the pipette resistance and must be determined after initial compensation to evaluate the residual series R error. The resistance to ground must also be minimised to reduce the R_access.

If the membrane potential of an infinitely long, cable-like cell, with uniform properties and no voltage-dependent channels, is driven away from the resting membrane potential by current injection at one point in the cytoplasm, the steady-state voltage as one progresses away from the control point decays back to the resting level as the exponential function of distance. An electrical half distance can thus be defined as the point at which the voltage displacement has decayed to half its control point level.

If the electrical distance of a synapse from the soma is one space constant, then the signal at the soma will be only 37% of the synaptic signal if the dendrite can be considered to be a passive cable, with infinite membrane resistance and no membrane capacitance. If we assume that the space constant is infinite, then a synapse that depolarises the local membrane to 0 mV from a membrane potential of -60mV will produce an initial current equal to:

I = 60mV/R_ax.

R_ax is the axial resistance, where R_ax = x.(200 W cm/p r²); the resistivity of the cytoplasm is taken as 200 W cm, x is the distance of the synaptic input from the soma and r is the radius of the dendrite. According to the passive cable theory, the further the dendrite is from the initial segment, the smaller the current reaching the trigger point will be. Thus the charging rate of the somatic capacitance by a distal synapse will be many times slower than for a proximal one, as only a small proportion of the initial current is delivered by the distal synapse. Thus a distal synapse will be far less effective than if only the space constant were considered, and slower still if the dendritic capacitance is taken into account.

The neuron can be modelled as an equivalent cylinder, allowing the electrotonic length (L) to be calculated, from which we can derive an effective measure of the electrical distance of synapses from the soma. In order to calculate L, we need to accurately determine the passive membrane parameters of the neuron, particularly the specific membrane resistivity (R_m) and the specific membrane capacitance (C_m). The value of R_m can be calculated from the slowest time constant (t_o) that can be derived from the passive voltage response to a step current injection;

given that t_o = R_m.C_m, where C_m is close to 1.0m F/cm². In addition the input resistance (R_N) at the soma, which is determined by R_m, the internal resistivity (R_i), and the morphology of the neuron, can be calculated from the steady-state voltage response to a step of current. Both t_o and R_N are affected by the leak conductance of patch-clamp recordings.

The electrotonic length L is defined as l/s, where l is the length of the equivalent cylinder and s the space constant (given in cm); where s is equal to the square root of (r.R_m/2R_i), r is the radius in cm, R_m is the specific membrane resistance (W .cm²), and R_i the internal resistivity. The space constant is the distance along an infinite cylinder over which a steady-state voltage decays less than e-fold per s. However, estimates of L are in error, due to difficulties in extracting the appropriate time constants from the infinite series of exponentials that theoretically determine membrane-charging, and the lack of a uniform L for all dendritic branches.

Gottesman and Miller used CLSPA collagenase of a low tryptic activity with hyaluronidase to remove the vitreous humour from the retina, before preparing slices (1992), although type IA collagenase appears more effective in our hands. They used a long working distance objective modified for Hoffman modulation contrast, and a multi-reservoir system permitting continuous oxygenation of all solutions to record from cells. The ganglion cell's physiological state was evaluated in the current-clamp mode, allowing the rejection of cells that did not display good spike amplitude and repetitive spiking.

Mittman and colleagues used pipette solutions containing (mM) 84 CsF, 3.4 NaCl, 400m M MgCl₂, 400m M CaCl₂, 11 EGTA and 10 NaHEPES (due to the low solubility of MgCl₂ free [Mg²⁺] was around 1m M) to produce more stable recordings from ganglion cells. Regehr and co-workers used 20m M bicuculline to eliminate inhibitory synaptic conductances and an internal solution containing 90mM KF to improve the stability of whole-cell recordings from pyramidal cells and to allow them to use larger recording electrodes. Using a `U-tube' system to perfuse individual ganglion cells gives a more economical means of perfusing cells with a more rapid response time than a general bath perfusion, avoiding global contamination. After perfusing the retinal preparation with Ringer containing 120 U/ml of type 1A collagenase and 465 U/ml of hyaluronidase, to remove the vitreous, a cleaning pipette can be used to lift the remaining vitreous overlying the ganglion cell layer, and to break the axons along their axis to the optic nerve fibre head, thus improving access to the underlying ganglion cell layer. Lucifer yellow (1mM) may be used in the patch pipette to determine the rate of diffusion into and the extent of the dendritic field, and the type of ganglion or displaced amacrine cell patched.