INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Action potentials (AP) are classically viewed as the functional output units propagating down the axon, but they can also propagate across the soma and dendritic regions of many neuron types. Somatodendritic APs constitute a major element of dialog between input and output regions, with different functional implications when traveling in one direction or another (Herreras 1990; Larkum et al. 1999; Markram et al. 1997; Mel 1999; Schiller et al. 2000; Schwindt and Crill 1998; Stuart and Hausser 2001). The biophysical aspects of AP propagation in axons have been well studied (see Swadlow 1980 for review) but little attention has been given to their spread through the electrically and geometrically heterogeneous somatodendritic cell axis. In general, a higher reliability of AP backpropagation over forward conduction of dendritic APs is assumed based on the asymmetric geometry and/or the weaker excitability of soma and dendrites (e.g., Segev and Rall 1998). Some cell types, however, display safe AP forward conduction (Chen et al. 1997; Martina et al. 2000), and in others, such as CA1 and neocortical pyramidal cells, both forward and backward APs have been reported (e.g., Golding and Spruston 1998; Herreras 1990).

Previous theoretical work partially addressed this issue within the generic perspective of AP propagation in weakly excitable dendrites (Mainen et al. 1995; Segev and Rall 1998; Shen et al. 1999; Vetter et al. 2001). Here we used modeling techniques to study the influence of the structural inhomogeneities along the more critical regions of transition between input and output zones, i.e., the proximal axon, soma, and main dendrite. Since the discrepancies found in the literature concerning the predominant AP direction appear related to the choice of intra and extracellular recording techniques (see Johnston et al. 1996 for review), we have focused on a spike parameter that enables a direct correlation of both techniques, the current flow underlying APs. This variable is a more sensitive index of the interactions between different subcellular regions than membrane potential. Also, the current flow constitutes the obligatory nexus between intra- and extracellular compartments and is central to the understanding of the relations between intracellular electrogenic events and extracellular field potentials (FPs). These are widely used for the study of APs in the hippocampus (e.g., Fujita and Sakata 1962; Herreras 1990; Kloosterman et al. 2001; Leung 1979). The well-known population spike (PS) (Andersen et al. 1971; Lorente de Nó 1947) is in fact generated by the extracellular addition of all I_ms during synchronous AP firing. Hence ortho- and antidromically evoked PSs should mirror whatever differences exist between the single cell I_ms obtained during forward- and backpropagated spikes.

For an integral view of AP-associated currents, we require a comprehensive treatment of unitary currents on both sides of the cellular membrane generators. Our recently developed integral model of the CA1 region describes all the different current components (ionic and capacitive) in different cell compartments and their participation in the macroscopic extracellular FPs (Varona et al. 2000). The theoretical grounds linking intra- and extracellular currents are as follows. During AP firing, the underlying current flows in closed loops within, out, and across the neuron membranes. Due to fast propagation, the spatial stretch occupied by a spreading AP is very large, causing the overlap of action (V-dependent channel-mediated) and return passive (capacitive and leak) currents along the irregular morphology. The external component of the circulating currents (sinks and sources) generates FPs in the extracellular space (ES), e.g., the PS. There, the currents spread in all directions, and the FPs, although dominated by local I_m, are also contributed by currents from different subcellular regions.

Specifically, we have studied how the geometrical inhomogeneities influence the current flow components during forward and backward APs, and how each of these components relates to the PS in the CA1 region. To this purpose, we first analyzed the current flow in a pyramidal single-cell model whose parameters were optimized by large-scale extrapolation to reconstruct the PS in a simulated volume conductor (Varona et al. 2000; see also Rall and Shepherd 1968). The effects of geometrical and electrical heterogeneities were dissociated by using simplified models of homogeneous excitability. Finally, we tested the predictions of the model by comparing the theoretical results with the basic in vivo features of the anti- and orthodromic PS and their extracellular population currents (I_CSD) obtained using current source density (CSD) analysis. Intracellular recordings were also used to compare model and experimental AP waveforms. We found that somatodendritic currents are entirely different during forward and backward APs. Single-cell somatic inward currents and PSs are smaller during apical AP initiation than during antidromic activation. There is a dramatic difference in the rate and timing of capacitive and V-dependent ion currents, for the most part due to the different geometrical inhomogeneities "seen" by forward or backward APs.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Pyramidal cell model

The single-neuron model reproduced the detailed pyramidal cell morphology, with an average dendritic branching pattern, total dendritic length, dendritic tapering, and distribution of spine density obtained from detailed morphometric studies (Bannister and Larkman 1995a,b; Trommald et al. 1995). The three dimensional (3-D) morphology was simulated using 265 compartments distributed in an axon [consisting of myelinated portions, Ranvier nodes, axon initial segment (AIS), and axon hillock], soma, and apical and basal dendritic trees (see the 2-D projection in Fig. 5). The apical shaft diameter decreased from 3.5 µm at the soma junction to 2.4 µm at the main bifurcation located 250 µm distal. Compartmental spatial coordinates can be found at http://navier.ucsd.edu/colis. Total effective area of the neuron was 66,800 µm². The electrotonic parameters were R_i = 75  · cm and C_m = 0.75 µF/cm². The value of R_m was set as variable according to Stuart and Spruston (1998), with R_msomatic = 70,000  · cm² and a half-decay at 150 µm distal. Spines were collapsed into the parent dendrites, whose values of R_m and C_m were compensated accordingly.

We used seven types of ionic channels to simulate the active properties of the somatodendritic membrane: fast sodium (Na⁺), calcium (Ca²⁺), and five potassium currentsdelayed rectifier (DR), small persistent muscarinic (M), A-type transient (A, proximal and distal), short-duration [Ca]- and voltage-dependent (C), and long duration [Ca]-dependent (AHP). Conductance variables were described with Hodgkin-Huxley type formalism (see details of the kinetics at the website listed above). Most of them were taken from Warman et al. (1994), with some modifications to account for the faster rising slope of APs in vivo. The channel distribution along the cell morphology was continuously tuned in a feedback manner. Briefly, Na⁺ channel density was uniform in soma and dendrites and slightly higher in the axon. A somatodendritic gradient of the A-type K⁺ current was used as described in Hoffman et al. (1997). The detailed distributions for the neuron prototype can be obtained from the same website as listed above. Simulation of antidromic stimuli was made by 1-nA, 0.1-ms-long pulses in a distal Ranvier node for each cell in the population. Alpha functions were used to simulate synaptic activation as follows: g_syn(t) = _syn(t/_syn)[exp(1  t/_syn)]. The synaptic currents were defined as I_syn = g_syn(t)(V_m  E_syn). GABA_A synaptic currents had a reversal potential of 75 mV and _syn of 7 ms. Synapses were distributed in the soma and proximal apical and basal dendrites and were initiated 1.5 ms after anti- and orthodromic activation. The AMPA-type synaptic excitation was simulated with _syn of 2 ms and reversal potential at 0 mV. For apical AP initiation, the AMPA currents were distributed from 150 to 250 µm below the soma and _syn = 0.7 mS/cm². For AIS-AP initiation, the AMPA currents were distributed from 25 to 175 µm, and _syn = 1.0 mS/cm².

CA1 aggregate model and the calculation of field potentials

The dorsal CA1 region was modeled as reported earlier (Varona et al. 2000). We used an aggregate of 16,966 morphologically identical model neurons arranged in a 3-D realistic manner, using a cell density of 44 neurons in a 50 × 50 µm antero-lateral section (Boss et al. 1987), which represents a "slice" of 1 × 1 mm of tissue. The dorso-ventral extension was set to 0.8 mm. This aggregate size yields almost maximum FP amplitude; the underestimation of neglecting further contributions is <5%. Cell somata were arranged in four uneven layers with 75% in the apical one-half.

A set of 16 "recording" points 50 µm apart simulated a vertical track at the center of the population in parallel to the somatodendritic axis and spanning from 250 µm above to 500 µm below the stratum pyramidale. The value of the FP measured () at each point was calculated as follows
where I_mij is the total transmembrane current at the jth compartment of neuron i, and r_ij is the distance from the recording point to that compartment. Thus compartments are treated as point sources into a medium of homogeneous conductivity (), and the value of the FP at each point is calculated as the summation of all compartmental transmembrane currents (I_ms) weighted by the distance to each recording point. I_ms were calculated with a time step of 0.1 µs using the GENESIS simulator (Bower and Beeman 1998), and the calculation of FPs was programmed in C code. For a thorough model description, see http://navier.ucsd.edu/colis.

Optimization of model parameters

Single-cell parameters were initially set to reproduce the basic physiology of pyramidal cells (current-evoked and synaptic responses). This can be achieved using multiple combinations and wide ranges of several parameters that define passive and active properties. A severe restriction of the parametric space is indeed necessary (see e.g., Shen et al. 1999). For the present study, we used an iterative method with the most significant parameters so that optimized calculations met two criteria. First, AP waveform along the somatodendritic axis reproduced actual AP values during backpropagation of axonally initiated spikes. Using the AP waveforms as templates caused only a moderate parametric restriction and does not solve the problem of the variability and reliability of intracellular experimental results. Second, the extrapolation of the single-cell compartmental I_ms to the aggregate level yielded a calculated FP that fitted the in vivo somatodendritic values for the antidromic PS. This method is very powerful because it uses as a template the steady and reproducible experimental PS, a reflection of I_ms, which are much more sensitive to parameter changes than V_m. At the single-cell level, we used the amplitude, half-width, and rates of rise and fall of the AP measured at the soma in vivo. Reliable AP measurements at dendritic levels in vivo are not available, thus an initial approximation was made using the in vitro AP estimates (Spruston et al. 1995; Turner et al. 1991) and later modified as required to match the computed model FP maps and the experimental PS. At the aggregate level, we measured the amplitude, width, and latency of the PS at the s. pyramidale and stratum radiatum. The fitting of realistic AP waveforms to obtain the I_m is analogous to the use of AP waveform commands in clamp experiments. In a way, the model is more realistic since a different AP waveform was "imposed" to each membrane sub-region, what cannot be achieved in actual experiments. This model has two major advantages over available single-cell models of CA1 pyramidal cells. First, it is calibrated using in vivo somatodendritic physiology, which presents some differences when compared with in vitro physiology, especially as it concerns to the unitary AP parameters and the site of AP initiation. Second, it uses a double optimization procedure by comparing not only the single cell features but also the reconstructed macroscopic PS, which strongly accentuates small errors that go unnoticed in single cell models.

The influence of unitary firing jitter on the PS amplitude has been shown in our previous study to be small (Varona et al. 2000).

Experimental recordings and CSD in vivo

Female Sprague-Dawley rats, weighing 200-250 g, were anesthetized with urethane (1.2-1.5 g/kg ip). Surgical and stereotaxic procedures were as previously described (Herreras 1990). Antidromic and orthodromic activation of the CA1 were achieved by stimuli (0.07-0.1 ms, 0.3-0.5 mA) delivered in the alvear region and in the ipsilateral CA3, respectively (see scheme of electrodes in Fig. 6A). Recording was made with micropipettes (filled with 150 mM NaCl; 3-6 M) connected to DC-coupled field effect transistor (FET) input stages. For CSD-analysis two pipettes were employed: one remained stationary in the CA1 s. pyramidale to test the constancy of the evoked PS amplitude and the other was used to explore dorso-ventral trajectories in 25- or 50-µm steps. After filtering (1 Hz-5 kHz band-pass) and amplification, signals were recorded on VCR, acquired to a computer (20-40 kHz acquisition rate, Digidata 1200, Axon Instruments, Burlingame, CA), processed by Axotape and Axoscope software (Axon Instruments), and further analyzed by the Axum program (Trimetrix, Seattle, WA). Depth profiles of evoked potentials were used for CSD analysis (Nicholson and Freeman 1975). A highly precise reference for electrode position was obtained by using characteristic FP landmarks (<10 µm error; see López-Aguado et al. 2001). Extracellular current sinks and sources correspond to inward and outward transmembrane currents, terms that will be referred to interchangeably throughout the text. Active currents are those caused by channel opening, either synaptic or V-dependent, while passive currents are return currents (capacitive and leak). A detailed account of technical and theoretical considerations for the calculation of CSD in vivo has been presented elsewhere (Herreras 1990). We have used the customary 1-D approach for the calculation of the extracellular currents (Freeman and Nicholson 1975). Differences in tissue resistivity within the s. pyramidale were not taken in account since these would only significantly affect the currents generated in a very narrow band (10-20 µm; López-Aguado et al. 2001). Smoothing procedures aiming to decrease high spatial noise were not used because they introduce major perturbations in the relative amplitude and spatial distribution of high-frequency components, i.e., action currents (Herreras 1990).

We used the intracellular recordings made previously in vivo (López-Aguado et al. 2000, 2001; Varona et al. 2000) to compare some parameters of the experimental and model APs.

Statistical comparisons were made using the Student t-test with a level of significance of 95%. Measurements of some basic PS parameters have been gathered in this and previous studies (large n).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Compartmental somatodendritic currents are larger during backward than forward spikes

All model parameters remained the same during ortho- and antidromic activation so that the only possible modulation of APs is the opposite sequence of the compartments invaded when spreading in one direction or another. While antidromic activation always gives backward APs (Fig. 1, Anti), the orthodromic may initiate forward (Syn-Fwd) or backward (Syn-Bckwd) APs. The single-cell model reproduced the general features reported in single-cell studies in vitro, including the gradual attenuation of backpropagating AP in dendrites (see V_m). The precise AP waveform (rising slope and half-width) was forced to reproduce the faster kinetics shown in vivo. The synaptic input was first tuned to reproduce the experimental findings in vivo, i.e., initiation of AP in the apical shaft at approximately 150-200 µm below the soma (Syn-Fwd), and then modified so that the AP was initiated in the axon and backpropagated into the soma and apical dendrites (Syn-Bckwd). This is the pattern more frequently reported in vitro.

View larger version (28K): [in this window] [in a new window]   Fig. 1. Comparative study of antidromic and synaptically initiated action potentials (APs) at different levels of complexity [Vm and Im at the single cell level, and the field potential (FP) at the aggregate level] by model reconstruction. Thick traces correspond to the soma, and apical (ap) positions are labeled with the distance to the soma in micrometers. Antidromic activation (Anti) caused somatodendritic AP invasion with attenuating amplitude and increased duration. Synaptic activation was adjusted to obtain forward propagation of APs initiated in the apical shaft (Syn-Fwd) as in vivo, or the AP backpropagation more often reported in vitro (Syn-Bckwd). Inset: AP direction. With minor differences, backpropagation behaves similarly to antidromically elicited APs. Forward propagation is slower and lacks the precedent outward currents along dendritic compartments. The soma Im, however, is preceded by a strong outward current (arrowhead). Total and net inward current are smaller than during antidromic APs (horizontal dashed lines), matching the corresponding population spike (PS).

The most outstanding result is that somatic I_m was always larger during backward (whether anti- or orthodromically initiated) than during forward conduction. Thus the somatic inward current was preceded by a marked accelerating outward current in forward (arrowhead) but not backward APs, decreasing the net inward current in the former mode. In addition, the I_m along the apical shaft compartments during forward conduction of synaptically initiated APs overlapped far less than during backward conduction, indicating a slower AP velocity.

As expected, the macroscopic FPs and the compartmental I_ms in the synaptic-backward mode became much alike those obtained during antidromic activation. The somatic I_m was somewhat smaller, indicating an additional effect of the concurrent synaptic currents onto spike-related somatic currents.

Resolving somatic I_m: the flow of axial currents during backward or forward conduction is entirely different

To understand the differences on I_m, we examined the current components in the soma. This compartment is invaded from geometrically different structures (the AIS or the apical shaft), and its intermediate position and large size makes it critical for AP spread. Figure 2 shows the somatic I_m (thick black trace) resolved into its axial components from the apical shaft (green), the AIS (red), and the basal dendrites (orange). Somatic current is depicted as positive and negative when entering or leaving the compartment, respectively, whether it flows into another compartment (axial) or to the ES (transmembrane). Some schemes have been drawn to facilitate spatial comparison (only currents entering/leaving the soma have been depicted for simplicity). When comparing the time course of I_m and V_m (thick and thin black traces, respectively), it was evident that, quantitatively, net current flow occurred mainly during the depolarizing phase of the AP. Following antidromic activation, the AP advanced heralded by a wave front of axial current on its path to the soma (Fig. 2, Anti, red is positive). Most of this current ran across the still inactive soma directly into the apical and basal dendrites (orange and green traces are negative) that presented lower overall resistance than the soma membrane (Fig. 2, anti-scheme 1). Only when the AP actively invaded the soma (opening of local Na⁺ channels) did a strong inward I_m set off (I_m trace crosses 0 value) that was also drained into the apical and basal dendrites (Fig. 2, anti-scheme 2, green and orange traces are negative) preceding active backpropagation. In turn, the subsequent apical activation (Fig. 2, anti-scheme 3) injected axial current back into the soma, causing the cancellation and subsequent reversion of this axial current (note the shorter time-course in the green vs. the orange trace, arrows in Fig. 2, Anti).

View larger version (23K): [in this window] [in a new window]   Fig. 2. Somatic transmembrane current flow resolved into its axial components during different modes of activation. The AP trace (thin trace) is superimposed to allow the temporal comparison of Vm, Im (black thick trace), and axial currents. Green, red, and orange traces correspond to axial currents from the apical shaft, axon initial segment (AIS), and basal dendrites, respectively. Current entering and leaving the soma is depicted positive and negative, respectively (note that Im has opposite polarity to other figures). Selected instants have been schematically represented in a spatially graphic manner using arrows of different width to denote the magnitude of the currents. Current flow is largest in the depolarizing phase of the AP. Left: during axonal AP initiation (Anti), the AIS injects axial current into the soma, most of which is directly drained out into the apical and basal dendrites (1). Instant (2) marks the transition when no net current flows through the soma membrane and strong axial currents are balanced in the soma. During the active phase of the soma (3), the strong inward Im is also drained out into both dendritic compartments. Subsequently, the AP invaded the apical shaft (note the different time course of green and orange at the arrows). Middle: when the AP is initiated in the apical shaft (Syn-Fwd), a strong axial current is injected into the soma from which it is drained out to the basal dendrites (orange) and into the extracellular compartment across the membrane (1). Active soma invasion begins at a strongly depolarized level, when the outward Im ceased to increase (arrowhead). Between instants 1 and 2, the AIS also becomes active (the AP "jumped" from the apical shaft into the AIS) and injects axial current into the soma (arrow in red tracing). At a later time (3), soma invasion is completed, and the inward Im is drained out into the basal dendrites. Somatic axial currents are entirely different at the instant of zero Im (2). Right: when the AP is initiated in the AIS following synaptic activation (Syn-Bckwd), the pattern of currents is similar to that of antidromic invasion.

When the AP began in the apical shaft (Syn-Fwd), the resulting axial current was injected into the soma, leaving across its membrane (outward I_m) and into the basal dendrites (black and orange traces are negative, see scheme 1 in Syn-Fwd). The active soma invasion was marked by the beginning of the inward I_m (arrowhead), which must first cancel the strong outward current originated by the incoming apical spike before achieving net inward polarity. Curiously, before this event, a notable axial current entered the soma also from the AIS (compare arrow and arrowhead in red and black traces). This current entered across the AIS membrane (not shown), and indicated that the apical spike "jumped" from the apical shaft into the AIS before the soma invasion. Figure 2, scheme 2, illustrates the instant when the net I_m at the soma is zero despite the AP being active in all three regions: apical shaft, soma, and AIS. Subsequently, inward currents dominated in the soma (black is positive) as those in the apical shaft subsided (scheme 3).

The right panel of Fig. 2 (Syn-Bckwd) illustrates the currents when the AP is first initiated in the AIS following synaptic activation of the apical shaft. The overall pattern is similar to that of antidromic activation. However, the shorter duration of the axial current entering the soma from the AIS (red) indicated a facilitated soma invasion, an effect caused by the concurrent axial current injected from the apical (synaptic) region (green is slightly positive before the soma fired). Note the abrupt decrease of the current drained into the apical shaft (green trace) compared with that of the basal dendrites (orange), again caused by backpropagation-mediated cancellation of soma-to apical axial currents.

Somatic AP depolarizing phase is dominated by capacitive or channel-mediated currents during forward or backward spikes, respectively

We can also examine the composition of transmembrane currents with the model. Figure 3 shows the somatic I_m (thick black trace) resolved into its capacitive (I_cap, blue) and resistive (I_ion, red) components (leak current was negligible). The former indicates the rate of membrane charging and the second the net flow of charge through V-dependent open channels. The short duration of I_ion was caused by the near complete balance of inward Na⁺ and outward K⁺ currents except on the initial depolarizing phase, when I_Na strongly dominated (black thin trace corresponds to V_m). The I_cap transient was smaller when the AP entered the soma from the AIS (Fig. 3A, Anti and Syn-Bckwd) than from the apical shaft (Syn-Fwd). This effect was caused by the larger diameter of the apical shaft-soma compared with the AIS-soma junctions. When the AP entered from the AIS, the current flowed toward the lowest impedance path, i.e., the thick apical dendrite. On the contrary, when the AP entered the soma from the later, it did not encounter a low impedance path, flowing out as capacitive current. Hence, the soma charged faster.

View larger version (21K): [in this window] [in a new window]   Fig. 3. Different dominance of capacitive and ionic currents during the depolarizing phase of APs depends on its direction. A: Im (thick black trace) was resolved into its capacitive (blue) and ionic (red) components. To facilitate comparison with the evolution of axial currents, the same instants have been marked as in Fig. 2 (vertical dashed lines). Ionic currents were larger when the AP entered the soma from the AIS (Anti and Syn-Bckwd), while the capacitive current dominated the depolarizing phase when the AP entered from the apical shaft (Syn-Fwd). Small horizontal arrows mark the depolarization level on the Vm trace at which Im became net inward (zero crossing). Note also the strong difference in the depolarizing level at which the regenerative acceleration of local inward currents began. In all cases, Icap peaked slightly earlier, but Iion was larger during antidromic activation. B: dominance of capacitive currents during orthodromic activation is also reflected in the steeper rising slope of the AP, both in the model and in the experiment. Thin and thick traces correspond to the Vm and its first derivative, respectively.

The different charging rate caused the V-dependent channels to open at a different depolarizing level in the rising phase of the AP. Thus in forward APs, I_m became inward at a V_m depolarized by approximately 35-40 mV compared with backward APs (compare small horizontal arrows in Fig. 3A). Consequently, the driving force in the first case was smaller, yielding a smaller I_ion.

Despite the similarity of the V_m waveforms during backward and forward spikes, there was a marked difference in the rate of rise and final magnitude of the current I_ion and I_cap components. The regenerative acceleration of local inward currents at the soma began at approximately 15-20 mV more depolarized on the rising phase of forward spikes.

Since I_cap is proportional to the rate of change of V_m, its dynamics during apical or axonal AP invasion of the soma must also be reflected on the corresponding APs. We thus compared the rate of rise of APs in the model and in real cells. In Fig. 3B, the V_m (thin traces) is superimposed to its first derivative (thick traces) to accentuate the variations of the rate of V_m change. In both model and experiment, the maximum AP slope was 30-40% larger during ortho- than antidromic activation.

A simplified model discloses the role of the heterogeneous cell axis geometry

The dissimilar current flow and membrane charging during backward and forward spikes must be related to the different sequence of geometric inhomogeneities and/or regional excitability. Since our unit model had a realistic heterogeneous excitability, we unveiled the role of geometry with simplified models that preserved the dimensions and electrotonic parameters of the simulated structures (Fig. 4) but used a homogeneous channel distribution. In all cases, the AP was initiated by short current pulses, i.e., without concurrent synaptic input. We first explored the behavior of I_m in the simplest geometry, a cylinder of constant diameter. The AP was initiated in one end and spread rather uniformly except when approaching the opposite end, where the depolarizing slope and amplitude increased (Fig. 4A, left) because of the faster membrane charging effect of sealed ends. The plots of the corresponding compartmental currents (only 1 of every 5 is represented) show a diphasic outward/inward current of constant magnitude and velocity except at the end, where a larger I_cap (outward) took over a decreasing inward I_ion (arrowhead and curved arrow in Fig. 4A, right). We then simulated an isolated apical shaft presenting a realistic flare (Fig. 4B). The AP waveforms changed little when the AP was initiated at either end (data not shown), but notable variations were found on the velocity and the relative magnitude of I_cap and I_ion depending on the AP direction. The velocity gradually increased or decreased for flaring (left) or tapering (right) diameters, respectively (simulating ortho- and antidromic conduction). As a whole, the AP was slower or faster, respectively, than in the equivalent apical shaft of constant diameter. Notably, flaring shafts boosted I_m, the two components increasing in parallel to roughly twofold the initial magnitude, except when approaching the opposite end. Here again, I_cap increased much more while I_ion began to decrease (curved arrow in Fig. 4B, left). In tapering shafts, the same sealed end effect was observed, but the current components decreased instead (Fig. 4B, right).

View larger version (29K): [in this window] [in a new window]   Fig. 4. Different dominance of capacitive and ionic currents can be explained by geometrical inhomogeneities. Results obtained with a simplified geometrical model of uniform excitability. The AP was initiated by short current pulses in one end, and Vm and Im of selected compartments are plotted superimposed. A: AP runs uniformly along a cylinder of constant diameter (2.5 µm) except at the sealed end where the rising phase accelerated. Corresponding Im showed a characteristic diphasic outward/inward pattern that remained constant except near the sealed end where outward (capacitive) current increased markedly (arrowhead) and inward current decreased in parallel (curved arrow). B: in a more realistic apical shaft represented by a cylinder of moderately variable diameter (1.5-3.5 µm), the underlying currents behaved entirely different. When the AP initiated in the narrow edge (simulating apical forward conduction, left plots) the speed gradually accelerated and the two components of Im were boosted, except when approaching to the sealed end that behaved as above. The opposite behavior of Im occurred when the AP was initiated in the thick edge (i.e., simulating backpropagation, right plots), except again at the sealed end. C and D: soma and axon were connected to the flaring apical shaft to simulate forward (C) and backward (D) AP conduction. Currents behaved similarly within the apical shaft except near the soma. During forward conduction, a large capacitive outward current dominated in the soma, while inward ion current did it during antidromic AP invasion (thick traces correspond to the soma). In this case, AP invasion was delayed. The AP at the axon segment nearest to the soma was smaller (arrows on Vm traces), allowing a large inward current to develop (arrowhead) that caused the heralding capacitive outward current in the soma (arrow).

We then introduced the soma and AIS compartments. During forward AP conduction (Fig. 4C), the soma acted as a large capacitor, accumulating most of the axial charge injected by the incoming dendritic AP. The result is that the depolarizing phase of the AP is almost entirely due to capacitive charging of the soma membrane (compare thick traces in Fig. 4C, left and right). As expected, the closer segment of the apical shaft did not show the sealed-end effect, but developed instead a large inward I_ion that was injected into the soma (arrow in Fig. 4C). The subsequent invasion of the AIS regained the diphasic pattern of current flow.

During antidromic AP spread, there was a notable increase in magnitude and duration of the net inward I_m at the axon segments near the soma (approximately twofold at the peak, arrowhead, Fig. 4D) compared with more distal segments. In the soma, this increase of axonal I_m is reflected as a notable capacitive component (small arrow in Fig. 4D) that is soon overbalanced by a huge ionic inward current (approximately 14-fold of that in the axon, thick trace). The density of current per unit membrane was, however, reduced in the soma to about one-half of that in the axon. The strong impedance mismatch at the AIS/soma boundary caused most of the current generated in the proximal segments to be drained out into the soma, hampering its own depolarization and the delay of invasion (arrows in Fig. 4D, left). The reduced AP enabled a strong unbalanced increase of Na⁺ and K⁺ currents that resulted in the strong and lasting inward current (dominated by Na⁺ inflow). Except for this strong delay of AIS-to-soma AP invasion, the results obtained with this simplified model matched those in the realistic model.

Forward AP conduction is safe in the main apical shaft regardless of the concurrent synaptic currents

Since the moderate realistic flare of the apical shaft caused forward conduction to be more reliable than expected, we investigated whether it was modified by the concurrent synaptic conductance in the realistic model of heterogeneous excitability. For this purpose, we initiated the spike using an AP waveform as a voltage command (V_comm in Fig. 5) in one compartment of the apical shaft. When it was initiated at any point along the main apical shaft (250 µm), we found a successful and highly reliable sequential conduction to the soma/axon (Fig. 5, right). Similar results were obtained for more distal initiation loci using different cell morphologies designed with longer primary dendrites. However, when the AP was initiated behind the primary bifurcation, the AP failed to invade not only the soma, but also the main dendrite (Fig. 5, left). The threshold for apical conduction and soma invasion was not much different, however, since slight modulations in several parameters, such as the basal excitability, restored successful forward conduction.

View larger version (18K): [in this window] [in a new window]   Fig. 5. Forward conduction is safe when the AP reaches the apical shaft. To avoid the upholding effect of synaptic conductance on AP forward conduction along the apical shaft, we used the realistic model unit to initiate an AP in the apical shaft by using an AP waveform as a voltage command (Vcomm). APs so initiated at any point within the main apical shaft (150 µm distal) were safely conducted to the soma/axon (right plots). However, when initiated 200 µm distal, below the main bifurcation (left plots), the AP failed to invade.

We also investigated the effect of "evoked" inhibitory conductance by comparing simulations in which GABA_A and GABA_B synaptic conductances were set to zero. No significant differences were found. Ongoing inhibition was not included in this study.

Testing predictions: antidromic activation yields larger PSs than synaptic activation in vivo

The above theoretical results predict that the antidromic PS should be larger than the orthodromic PS in situ. We tested this prediction in vivo by carefully optimizing recordings and comparing the maximal amplitude of the PS recorded in the soma layer. In vivo, orthodromic (synaptic) and antidromic (axonal) activation modes are paradigms of AP initiation in the apical dendrites and the axon, respectively (Herreras 1990; Leung 1979). We invariably found that an optimized antidromic PS is 30% larger than the orthodromic PS (24.5 ± 0.41 and 18.54 ± 0.34 mV, respectively, n = 32). For these values to be comparable, we had to identify the neuron populations activated on each case. Synaptic activation from the ipsilateral CA3 raised a somatic PS of similar amplitude throughout the entire latero-medial extension of the CA1, while alvear (axonal) stimuli activated cells within a narrow band (see Fig. 6A), whose width varied according to the electrode properties and stimulus intensity. In our conditions, this was approximately 500 µm wide, and as we showed earlier, it can yield a nearly saturated PS (Varona et al. 2000).

View larger version (21K): [in this window] [in a new window]   Fig. 6. PS evoked in the CA1 hippocampus in vivo. A: electrical stimulation of the pyramidal axons running in parallel within the alvear region (Alv, S1) elicited a large antidromic PS (red) in the pyramidal cell layer (SPyr) within a narrowband (1), its amplitude decaying steeply toward lateral positions (2 and 3). Activation of Schaffer collaterals (Sch, S2) by stimulating the ipsilateral CA3 region elicited an orthodromic (synaptic) PS (blue) of smaller but homogeneous amplitude throughout the lateromedial extension of the CA1 region. B: collision test. Antidromic volleys (marked by small arrows) were delivered at decreasing intervals from a previous orthodromic shock until respective APs that propagate in opposite directions collided in the axon, avoiding antidromic invasion. Numbers indicate time in milliseconds from occurrence of the orthodromic PS. Note that the antidromic PS disappeared completely at very short intervals (2 ms). Stimulus artifacts have been deleted for clarity.

It is possible that maximal synaptic activation could not bring to fire as many neurons as an axonic volley or that they would fire less synchronously. The latter was found irrelevant in a previous study (Varona et al. 2000). The former possibility was tested by a collision test (Fig. 6B). An antidromic shock was delivered at decreasing intervals after an orthodromic volley. At short delays the first AP collided against that initiated in the axon, preventing its further propagation and somatic invasion. In all cases (n = 12) a maximal ortho-PS totally obliterated the anti-PS, even when this was much larger, as in the center of the activated lamella (Fig. 6A). Therefore all neurons that contributed to the anti-PS had also fired within the ortho-PS, and the amplitude difference must be accounted by factors other than the number of cells.

Experimental population currents reproduce the qualitative features of the subcellular currents predicted by the model

The parallelism between anti- and orthodromic PS differences might not be comparable in experiments and models unless the respective population and compartmental currents coincided in their temporal relation with the FPs. A detailed comparative CSD analysis in vivo validated the comparison. Figure 7 shows the temporal relation between the population I_CSD and the corresponding PS at the soma layer. In all cases, the PS-related sink (transmembrane inward current) was always shorter than the corresponding FP. During antidromic activation, the sink began at the same time as the PS, while during orthodromic activation it began later, followed a fast source (arrowhead), and reached smaller amplitude. Consequently, inward currents dominated the negative-going phase of the somatic antidromic PS while they were delayed to the peak and positive-going phase of the ortho-PS. Note the different onsets for the respective negative limbs in the orthodromic PS and I_CSD (vertical dashed lines in Fig. 7). The orthodromic diphasic somatic currents rode on a slower source (outlined by the dotted line in Fig. 7, ortho) that corresponded to the capacitive charging by synaptic and other V-dependent dendritic currents (Herreras 1990).

View larger version (17K): [in this window] [in a new window]   Fig. 7. Different temporal mismatch of somatic FP and population currents (ICSD) during anti and orthodromic (synaptic) PSs in the soma layer. The sinks (inward current) are always shorter than the PSs, but initiate at the same time during antidromic activation, while it is delayed during synaptic volleys. Fast sources are marked by arrowheads. Sink/source pattern in the former case is caused by sequential invasion of soma and dendrites, while the precedent sources in the later represent outward currents from the incoming AP before active invasion of somata. Active soma invasion is marked by the beginning of the negative going phase in the local sink that differed markedly from that of the local PS (vertical dashed lines). A slower source can be unmasked (slashed trace), which reflects outward currents from dendritic synaptic and slower V-dependent currents. This can be discerned from the fast spike-related sources (arrow). The total (peak-to-peak) and the net inward currents (shaded area) are smaller during synaptic PS (horizontal dashed lines), causing a smaller negative contribution to the local FP.

The differences in somatic population currents were closely related to those in apical dendritic regions. Figure 8 shows the details in a representative experiment. During both anti- and orthodromic activation, the negative component of the PS decreased in amplitude from the soma layer to about 150 µm below. Note that the apparent increase of negativity during orthodromic activation is caused by the increasing negativity of the field excitatory postsynaptic potential (fEPSP) envelope component. The distribution of peak latencies was entirely different, however. While the synaptically initiated spike increased in a somatopetal direction, the antidromic PS did it in a somatofugal way.

View larger version (27K): [in this window] [in a new window]   Fig. 8. Comparison of PS and population currents (ICSD) along the somatodendritic axis during anti- and orthodromic (synaptic) activation. The peak latency of the PS increased/decreased from the soma toward the stratum radiatum (curved arrows). Inset: complete traces of the orthodromic FPs (horizontal bar: 5 ms). Scaled drawing in the center indicates the approximated locations of recording. Compare the smooth and abrupt transition toward negative values of the PS and ICSD, respectively (arrowheads). In all dendritic locations, the active inward currents (sink) are preceded by a fast source only during antidromic activation (*), while it is absent for the apically initiated PS. The source corresponds in time to a strong sink in a nearby locus. During synaptically elicited PSs, this is only true for the soma and the nearest apical region (shaded areas). Note the slower propagation speed of the forward (ortho) than the backward sink. A strong temporal overlap of sinks at the soma layer and the nearest 100 µm (ap50 and ap100) indicate an almost simultaneous activation, in contrast to a clear sequential activation during forward PSs.

The corresponding population currents showed dendritic sinks that were slower when the spike was initiated in the apical shaft (ortho-synaptic), while they overlapped extensively from the soma up to 100 µm below during antidromic invasion (small arrows in Fig. 8, I_CSD). Dendritic backpropagation was characterized by preceding sources (asterisk), which were only observed ahead of the forward sink on its arrival to the soma layer during synaptic activation (arrowhead). The fast source corresponds in all cases to the outward currents during capacitive charging of the membrane ahead of the incoming AP. The hatched areas illustrate the opposite inward and outward currents in the soma and apical shaft. The strong leading net source in the apical shaft region during backpropagation and at the soma layer during forward conduction caused the respective subsequent sinks to be smaller (Fig. 8, compare ap50 and ap100 in both modes). All these features resemble closely the behavior of the computed compartmental currents (Fig. 1).

Experimentally, synaptic backward conduction cannot be obtained in vivo using bulk stimulation.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

This study shows that rigorous analysis of current flows in inhomogeneous structures is essential for understanding the propagation of APs through the axo-somato-dendritic axis of neurons. The main result is that the somatic I_m is entirely different during backward and forward AP propagation; in the former case is larger and dominated by ionic currents, whereas in the second case, capacitive currents are more notable. From a functional point of view, the heterogeneous geometry of the activated cell subregions (AIS, soma, and apical dendrite) implies that the main cell axis behaves as a totally different conducting cable when the AP propagates in one direction or another. Contrary to current views, a moderately flaring apical shaft is a suitable structure that facilitates AP forward conduction.

Dominance of capacitive or ionic components of current flow in somatic APs during apical and axonal initiation

The electrical behavior of inhomogeneous structures has been analyzed earlier within the context of AP conduction in axonal trees (Goldstein and Rall 1974; Joyner et al. 1980; Moore and Westerfield 1983; Moore et al. 1983; Parnas et al. 1976). The present study shows that the somatodendritic region behaves qualitatively as axonal membranes. A minimum level of excitability is obviously the absolute requirement in any case, but the relevant issue is that the heterogeneous somatodendritic cable behaves totally different when the AP is initiated in the axon or in the apical shaft. Most features of the current flow computed by the realistic model unit were reproduced in a simplified model of homogeneous excitability. We may then conclude that the specific geometrical constraints are critical to define whether and how APs propagate along the apical shaft, especially in weakly excitable dendrites as those of pyramidal cells.

An added value of the present work is that we focused on the current flow, the membrane potential being used only as an intermediate template during the necessary restriction of parameters of the model. This approach allowed the comprehensive description of electrical events in and out of the neuron. During backpropagated spikes, the current supplied by the AIS flows directly into the low resistance apical dendrite (Fig. 2). The abrupt impedance mismatch at the AIS-soma makes this transition to occur with a low safety factor and the AP typically delayed (Fig. 4D). If invasion occurs, the somatic I_m is scarcely heralded by capacitive currents because the rapid onset of local inward ionic current (Figs. 1-4). The bulk of soma charging is then caused by current entering from the ES through ionic channels, and a large extracellular sink appears with little or no precedent source (Figs. 1, 7, and 8). This large somatic current charges the tapering apical shaft, and the AP propagates led by a large but decreasing capacitive current (Figs. 1 and 4). The increasing internal resistance forces more axial current to leave across the membrane (Fig. 2), which together with the decreasing surface available to regenerate currents may cause the blockade of the AP at some point.

When the AP is initiated in the apical shaft, the flaring gradually boosts the I_m and the decreasing internal resistance drives the inward current toward the soma that is rapidly charged (Figs. 1 and 4). The small section of the AIS and basal dendrites makes the large capacitance of the soma act as a sealed end, further accelerating its charging. Consequently, the somatic I_m and the AP depolarizing phase are now dominated by capacitive outward currents (Fig. 3). The opening of V-dependent channels occurs later in the depolarizing ramp because of the fast membrane charging, resulting in a reduced driving force and a smaller inward current that, in addition, has to cancel the strong outward capacitive current (Figs. 3 and 4). As a result, the extracellular sink is smaller and begins riding on a large extracellular source, i.e., less field negativity (Figs. 1, 7, and 8).

A notable discrepancy between model and experiment is worth mentioning. Compartmental dendritic I_m during apical AP initiation in the simplified model is preceded by a sizable capacitive current (Fig. 4), but this is barely detectable in the realistic model or in the experiment (Figs. 1 and 8). In the first case, the AP was elicited by a short depolarizing pulse of current, while in the latter, the activation of a slower long-lasting synaptic conductance was used. The abolition of the leading capacitive current is not a simple consequence of the shunt caused by synaptic activation, since when this initiated the AP in the AIS, the backpropagated spikes still preserved the heralding outward currents. The complexity of this interaction requires further study.

The somatic AP waveform elicited by ortho- or antidromic activation is rather similar in amplitude and total duration. A conspicuous difference was the faster rate of rise in the former case. This apparently small difference is, however, bound to an entirely different I_m and its capacitive and ionic components, as well as the axial components. It becomes obvious that fitting AP waveforms on single-cell models is far from sufficient to grant a reliable reproduction of the electrical behavior in real neurons (see also Shen et al. 1999). Certainly, backpropagating APs can be supported by weakly excitable dendrites (e.g., Rapp et al. 1996). The point is whether the parameters used actually reflect the dendritic excitability in vivo. In a preliminary study, we have reconstructed the PS by extrapolation of the I_ms obtained with several pyramidal cell models available in the literature (Herreras et al. 2001). The differences with actual in vivo PS were striking. Along this line, one must be cautious when using in vitro recordings as templates for modeling, since AP parameters are differentnotably the AP rising slope.

Somatodendritic interactions and APs: is geometry decisive for the role of the apical shaft?

The role played by the AP machinery in the thick apical shaft is crucial since many synaptic inputs converge there before reaching the output zone at the soma/axon. Whether the AP is first initiated in the apical shaft or the axon is not a trivial question because it defines when a neuron operates as a multiplexing device or as a simple integrator. Neither is irrelevant to know whether the apical shaft is geometrically and electrically designed to conduct or to fade APs out. In neocortical pyramidal cells, Larkum et al. (2001) have proposed that the proximal portion of the apical shaft is a strongly interactive coupling zone between two other triggering regions located in the distal dendrites and the AIS. Subtle voltage modulations in this zone may control the passage of distally initiated APs and also be initiated there (Golding and Spruston 1998; Larkum et al. 2001; Regher et al. 1993; Shen et al. 1999). Using mild damage specifically targeted to the apical shaft of CA1 pyramidal cells in vivo, we suggested earlier that this region operates as a true gateway for apical inputs (Herreras and Somjen 1993). Since boosting and output-deciding capabilities have been unequivocally demonstrated in various degrees (Golding and Spruston 1998; Herreras 1990; Herreras and Somjen 1993; Lipowsky et al. 1996; Oviedo and Reyes 2002; Regehr et al. 1993; Stuart and Sakmann 1994) it only remains to be determined the precise conditions under which they occur in vivo. Some evidence has already been advanced (Kamondi et al. 1998).

The results shown here support the view that once the AP has been initiated in the primary apical dendrite it is safely conveyed to the soma/axon, their particular geometry being critical on this task. On this condition, the moderate flare of the apical shaft acts as an efficient amplifier for action currents, strong enough to counteract the blocking effect of the increasing surface. In fact, a very strong flaring is required to block AP conduction (Goldstein and Rall 1974). The amount of current generated is thus large enough to spare the vast soma capacitance without risking blockade. The AP may even "jump" from the apical shaft to the axon before the soma is activated (e.g., Golding and Spruston 1998; Shen et al. 1999; this report). In addition, the limited number of branches in the apical shaft and their reduced diameter (Bannister and Larkman 1995a) facilitate the efficient delivery of charge to the soma.

The situation is different during backpropagation since cumulative impedance mismatches at successive bifurcations and the large capacitive load cause the AP blockade at some point. The same applies during forward propagation of spikes initiated in distal dendrites (e.g., Segev and Rall 1998; Vetter et al. 2001). We examined only a few loci just below the main bifurcation and found a similar fading behavior in the forward direction. However, our results agree with other authors (e.g., Larkum et al. 2001) in that subtle local modulations may be critical to allow or block the passage of a somatodendritic AP. For instance, even if the initiation of an AP per se in certain dendritic loci would not be enough to ensure the final output, the concurrent synaptic depolarization that fired it up constitutes a continuous upholding factor that increases the overall excitability along the cable. In a separate modeling work, we found an ample repertoire of synaptic input patterns that ensure successful AP invasion to the soma/axon (Ibarz, López-Aguado, and Herreras, unpublished observations). This applies for secondary moderately thick dendrites and not for the thicker apical shaft that always showed a high safety factor, even in absence of the concurrent synaptic depolarization.

It may be argued that the reliability of forward conduction lies on the basal excitability that may be locally controlled by ongoing stratum-specific inhibition. Changes in the AP threshold, initiation locus, or the extent of dendritic backpropagation may happen (e.g., Tsubokawa and Ross 1996). In a computational analysis performed by Shen et al. (1999), it was shown that the main impact of basal excitability is to shift the AP initiation locus between the AIS and the primary dendrite. However, once the AP was initiated in the primary dendrite, forward conduction was granted, even if they used a lower Na⁺ channel density. In summary, a safe forward AP conduction requires the combination of favorable geometric, synaptic, and regenerative properties, all of which can be found in the apical shaft of CA1 pyramidal cells in vivo.

Practical consequences of structural inhomogeneities on the shape of PS

As noted in the INTRODUCTION, the PS is the result of all compartmental I_m's added in the ES, and therefore it must reflect the average behavior and modulations of the component currents. Using a careful optimization of stimulating/recording positions, this is the first systematic study that reported a consistently larger antidromic than orthodromic PS despite firing about the same number of neurons. The possibility that higher synchronization of antidromically activated units will cause a larger instantaneous current-density in the ES was studied before and found to be irrelevant within the physiological ranges of temporal dispersion (see Varona et al. 2000).

We used here anti- and orthodromic activation as paradigms of axonal and apical initiation of the AP, respectively (Herreras 1990; Leung 1979). This may not be the case in vitro, where bulk synaptic activation appears to initiate the AP in the AIS or the apical shaft depending on the strength of the stimulus (Golding and Spruston 1998; Turner et al. 1991). Our model results indicate that changing the locus of AP firing from the apical shaft to the AIS during synaptic activation caused an antidromic-like pattern of somatodendritic current flow and a PS increase. This result should be considered when using PSs under experimental manipulations that may cause a shift in the AP initial locus, such as during repetitive activation or states of increased excitability (e.g., López-Aguado et al. 2001). It may also account for basal differences of in vivo and in vitro preparations.

More important than the population firing jitter is the different time dispersion of subcellular action currents along the somatodendritic axis. It was found here that the population current sink as well as the compartmental inward currents along the apical shaft span through a much shorter period during AP backpropagation, i.e., propagation is faster. As shown with the simplified model, the increasing internal resistance along the apical taper causes a deceleration of the AP, but the velocity is always faster than for an equivalent cylinder of constant diameter. This result is consistent with previous calculations made to simulate the electrical behavior of inhomogeneous axons (Goldstein and Rall 1974). On the contrary, AP conduction accelerates along flaring cables, but the overall velocity is slower, resulting on a decreased temporal overlapping of compartmental I_ms, as when the AP is initiated in the apical shaft. In the end, the different somatodendritic temporal overlap will increase or decrease the instantaneous current density in the ES, modifying the PS amplitude. This finding is analogous to the dramatic increase of the model PS by lowering the internal resistance (Varona et al. 2000), known to cause increased AP velocity (Goldstein and Rall 1974; Moore et al. 1983).

Finally, the reconstruction of FPs from unitary elemental currents establishes a practical framework to link field and cable theory extended to excitable membranes. This technique provides a more comprehensive view of neuronal electrogenic phenomena and a detailed correlation of intra- and extracellular events, classically analyzed from a simple temporal coincidence framework that neglects the rich behavior of current flow in cable-like structures and volume conductors.