The Journal of Neurophysiology Vol. 79 No. 5 May 1998, pp. 2809-2813
Copyright ©1998 by the American Physiological Society

RAPID COMMUNICATION

Temporal Integration Can Readily Switch Between Sublinear and Supralinear Summation

Michael Margulis and Cha-Min Tang

Department of Neurology, University of Maryland School of Medicine Baltimore, Maryland 21201

	ABSTRACT

Abstract Introduction Methods Results Discussion References

Margulis, Michael and Cha-Min Tang. Temporal integration can readily switch between sublinear and supralinear summation. J. Neurophysiol. 79: 2809-2813, 1998. Temporal summation at dendrites of cultured rat hippocampal neurons was examined as a function of the interval separating two dendritic inputs. A novel method that relies on single-mode optical fibers to achieve rapid photorelease of glutamate was developed. Dendritic excitation achieved with this approach resembles that associated with miniature excitatory postsynaptic currents (mEPSCs), but the strengths, sites, and timing of the inputs can be precisely controlled. Dendritic summation deviated markedly from behavior predicted by passive cable theory. Subthreshold temporal summation varied as a triphasic function of the interpulse interval. As the interpulse interval decreased, local dendritic Na⁺ conductances were recruited to generate a marked transition from sublinear to supralinear summation. These results suggest that active dendritic conductances acting in concert with passive cable properties may serve to boost coincident synaptic inputs and attenuate noncoincident inputs.

	INTRODUCTION

Abstract Introduction Methods Results Discussion References

The mechanism by which synaptic inputs that are separated in time are combined by dendrites of central neurons is fundamental to neurophysiology, having important implications for both neural computation and the pathogenesis of neuronal hyperexcitability. Whether temporal summation is fundamentally a linear, sublinear, or supralinear process remains controversial. Whereas the precedent at the nerve-muscle synapse is for linear temporal summation, passive cable theory predicts that summation at central neurons will be sublinear for many physiologically relevant circumstances (Rall 1970). On the other hand, the abundance of voltage-gated conductances expressed on dendrites suggests that temporal summation may be supralinear (Johnston et al. 1996; Magee and Johnston 1995; Miles and Wong 1986). In theory, given sufficient information on the distribution and gating properties of active dendritic conductances and reliable data on R_i, R_m, and C_m of dendrites, it should be possible to determine the nature of temporal summation through computer simulations of compartmental models. However, data on these parameters are incomplete (Yuste and Tank 1996). Temporal summation could be approached directly by paired-pulse stimulation if it was possible to control precisely the strengths, sites, and timing of the individual dendritic inputs. However, methods currently available for probing synaptic function cannot adequately control these three parameters. For example, in "paired-pulse" afferent fiber stimulation paradigms, the transmitter release probabilities are likely to differ for two closely timed inputs (Stevens and Wang 1995), and the sites of transmitter release may change. Furthermore, when two closely timed action potentials are generated in the presynaptic cell, the second action potential may not always propagate down the same axon terminals as the first. An ideal approach to circumvent these difficulties arising on the presynaptic side would be to activate the postsynaptic receptors directly. However, the available methods of direct dendritic stimulation, including iontophoresis and photorelease of glutamate, lack the necessary temporal-spatial resolution and dynamic range. We have now developed a method for rapid focal photolysis of caged glutamate compounds, with the use of "single-mode" optical fibers, that can simulate dendritic excitation by two excitatory synaptic inputs. With this novel approach, we have examined temporal summation as a function of the interpulse interval.

	METHODS

Abstract Introduction Methods Results Discussion References

Photolysis

An argon ion laser (Coherent I90-5) configured to emit light at wavelength of 351-364 nm was used as the light source for photolysis. The output of the laser was attenuated to 40-100 mW by reducing the aperture and the tube current. The beam was gated by a fast laser shutter (NM Laser Products, LST200) to control the pulse duration, and was split and directed into the back aperture of two ultraviolet (UV) objectives (Newport, U-27X) mounted on two fiber launchers. The two beams were launched separately into two single-mode optical fibers and were gated by a second pair of laser shutters (Uniblitz LS2), one set to be normally open and the other normally closed. These secondary shutters determine which fiber will receive the first and second light pulses. The timing and duration of both the primary and secondary shutters were controlled with PClamp6 software. Experimental UV single-mode optical fibers were obtained from PointSource (UV 2/125). Each fiber was etched in concentrated hydrofluoric acid until the 2-µm-diam core was reached. The fiber tip was then cleaved to form a flat front surface by inserting the etched tip into the molten glass bead of a microforge followed by cooling the glass bead.

Two light pulses separated by a variable interval were separately directed at two adjacent dendritic sites ~15 µm apart. Two adjacent sites, rather than a single site, were stimulated to avoid possible interpretative complications due to receptor saturation and desensitization. The two fiber tips were positioned at a 80° angle with respect to the bottom of the dish and brought to within 10 µm of the target site. A micropuffer made from a large patch pipette tip (~5-10 µm) was filled with --carboxy-2-nitrobenzyl (-CNB)-Glu (250 µM) (Weiboldt et al. 1994). A suction pipette with a tip opening of 10-20 µm was placed opposite the micropuffer to create a local laminar flow orthogonal to the dendrite, which helps to minimize the duration of the evoked response and eliminates the possibility of transmitter cross talk. The sites of photostimulation were 100-200 µm from the soma. The peak amplitudes of the two evoked responses were adjusted to ~5 mV by varying the intensity of the laser output. The relative amplitudes of the two light-evoked responses were then adjusted more precisely by varying the relative durations of the two light pulses under voltage-clamp conditions until the two current responses were equal at 200 ms.

View larger version (35K): [in this window] [in a new window]   FIG. 1. Delivery of well-collimated light with high spatial resolution and elicitation of miniature excitatory postsynaptic current (mEPSC)-like dendritic excitation by "single-mode" optical fibers. A: optical fibers were etched and then cleaved to a size similar to that of a large patch-clamp electrode. In this figure, the fiber was positioned slightly above the bottom of a Petri dish, at a 15° angle to the bottom, to best illustrate the beam. Red blood cells (diameter, ~7 µm) were placed at the bottom of the dish as one means of calibrating the microscopic dimensions of the fiber tip and light beam. Cascade blue was added to the solution to reveal the ultraviolet beam. The beam appears to end when it exits the Cascade blue-filled dish. B: the attenuated beam was directed at a thin (2-4 µm) film prepared from an emulsion of fluorescein and clear nail polish smeared evenly on a glass coverslip to calibrate its intensity profile in a more objective manor. The fluorescent image was captured by a charge-coupled device camera. C: a line scan through the center of the spot (B) revealed the half and1/e2 peak intensity diameters of the beam to be 2.1 and 3.4 µm, respectively. D: a pair of 1-ms light pulses (indicated by vertical bars above the trace) was directed at a dendrite under voltage-clamp conditions while -CNB-Glu (500 µM) was applied under laminar flow. The light-evoked responses closely mimic the incidently recorded spontaneous mEPSC. (Calibration bars, 20 pA and 90 ms; holding potential, 70 mV.) E: identical photostimulation at the same dendritic site results in slower voltage responses under current-clamp conditions. The light-evoked responses are indistinguishable from a spontaneous miniature excitatory postsynaptic potential. (Calibration bars, 1.8 mV and 90 ms; membrane potential, 70 mV.)

Cells, solutions, and electrophysiological recordings

Experiments were performed on hippocampal neurons that were dissociated from 20-day-old rat embryos, plated on 35-mm dishes, and maintained in culture for 2-4 wk (Tang et al. 1994). The extracellular solution contained (in mM) 150 NaCl, 3 KCl, 2 CaCl₂, 1 MgCl₂, and 10 N-2-hydroxyethylpiperazine-N'-2-ethanesulfonic acid (HEPES), titrated to pH 7.3. The internal pipette solution comprised of 135 KGluconate (or CsGluconate), 10 KCl, 5 bis-(o-aminophenoxy)-N,N,N',N'-tetraacetic acid (BAPTA), 0.5 CaCl₂, 1 MgCl₂, 2 MgATP, and 10 NaHEPES, titrated to pH 7.3.

Electrodes were prepared from borosilicate glass to a resistance of 4-6 M for whole cell patch recordings. Series resistance was compensated to 80-90% in whole cell recordings. The signals were filtered at 2 kHz, sampled at 5 kHz, and analyzed with pClamp software.

	RESULTS

Abstract Introduction Methods Results Discussion References

A novel method for eliciting dendritic excitation

A UV-transmitting single-mode optical fiber with a 2-µm-diam core was used to deliver light pulses for rapid focal photolysis of caged glutamate. The advantages of single-mode optical fibers relative to multimode fibers are that light pulses of greater intensity and increased spatial resolution can be delivered for photolysis. An advantage of using optical fibers for light delivery rather than using conventional method of focusing through a microscope objective is that multiple spots of light can be positioned independently. The calibration of the temporal-spatial resolution of this approach is shown in Fig. 1. Figure 1A provides a perspective on the microscopic dimension of the etched optical fiber and the well-collimated beam exiting from its tip. Figure 1, B and C, provides a more objective measurement of the beam dimension and its light-density profile. An emulsion of fluorescein and clear nail polish was smeared evenly on a glass coverslip and allowed to dry into a thin film (thickness,2-4 µm). The fiber tip was positioned close to the film without touching it. An attenuated beam was directed through the fiber, and the fluorescent image from the thin emulsion was recorded using a charge-coupled device (CCD) camera (Fig. 1B). A line scan of the light intensity through the middle of the fluorescent image is shown in Fig. 1C. The half and 1/e² peak intensity diameters of the beam were 2.1 and 3.4 µm, respectively. The coupling efficiency and UV transmission over a 1-m length of the fiber combined to give a transmission efficiency of ~20%. The output of the laser was attenuated so that the power of light leaving the tip of the etched fiber was between 1 and 5 mW. Caged glutamate (-CNB-Glu) was ejected under pressure through a micropuffer directed at a dendritic site and removed by an adjacent suction pipette. A 1-ms light pulse was able to induce photolysis of -CNB-Glu with sufficient speed and yield to mimic spontaneous miniature excitatory postsynaptic currents (mEPSCs) and miniature excitatory postsynaptic potentials (mEPSPs; Fig. 1, D and E). The decay time constants for the light-evoked currents and spontaneous mEPSCs were 4.7 and 4.5 ms, respectively. Under current-clamp conditions, kinetic differences between the light-evoked voltage responses and spontaneous mEPSPs could not be detected (Fig. 1E).

Triphasic pattern of temporal summation

The voltage response to dendritic excitation with a pair of light pulses was monitored at the soma as the interpulse interval was incrementally varied between 0 and 200 ms. The interlaced responses at each interval were averaged. A total of 27 cells was studied, with 4-6 different intervals tested for each. An example of responses of a single cell to interpulse intervals of 150, 25, 10, and 0 ms is shown in Fig. 2A. The amplitude of the second response remained approximately the same as that of the first response when the interpulse interval was >100 ms. At intervals between 15 and 100 ms, the amplitude of the second response (measured from takeoff to peak) was less than that of the first response. However, at an interpulse interval of 10 ms, the amplitude of the 2nd response was greater than that of the 1st response in 16 of the 27 cells studied. Figure 2B shows the ratio of the 2 responses (V₂/V₁) plotted as a function of the interpulse interval for these 16 cells. The triphasic pattern of summation, with the abrupt transition between sublinear and supralinear summation, is a departure from the predictions of passive cable theory (Geiger et al. 1997).

View larger version (11K): [in this window] [in a new window]   FIG. 2. Temporal summation as a function of the interstimulus interval. A: rapid focal photolysis of -CNB-Glu was induced with a variable interval at 2 adjacent dendritic sites. Examples of somatic voltage response recorded at 4 intervals (150, 25, 10, and 0 ms) are shown. Each trace is the average of 3 individual recordings. There was a prominent switch between sublinear summation at 25 ms to supralinear summation at 10 ms. Baseline membrane potential, 79 to 83 mV. Calibration bar, 5 mV. B: responses (means ± SE) from 16 cells each tested at 4 or 5 different intervals. Temporal summation is plotted as the ratio (V2/V1) of the 2nd response to the 1st response, measured from the point of takeoff to the peak. The ratio varies in a triphasic manner, with a sharp transition between sublinear and supralinear summation between 10 and 15 ms.

Mechanisms underlying nonlinear summation

Pharmacological and voltage-clamp studies were performed to dissect the mechanisms responsible for sublinear and supralinear summation. The tetrodotoxin (TTX) sensitivity of nonlinear summation was examined in seven cells (Fig. 3A). In each of these 7 cells, 2-5 individual responses before and during TTX application were averaged for comparison. The mean ± SD of summation at 10 ms was 1.49 ± 0.37 without TTX and 0.99 ± 0.34 with TTX, a statistically significant difference (paired t-test, P < 0.005). TTX did not significantly affect summation at 20 ms in these same seven cells. Voltage-clamp studies with the membrane potential held at 80 and 45 mV were carried out in six cells to examine the effects of Na⁺ channel inactivation on supralinear summation. Summation at an interpulse interval of 10 ms was 1.42 ± 0.13 at 80 mV and 0.91 ± 0.13 at 45 mV, a statistically significant difference (paired t-test, P < 0.005). These two observations suggest that classic voltage-dependent Na⁺ channels play a critical role in mediating supralinear summation.

View larger version (13K): [in this window] [in a new window]   FIG. 3. Role of dendritic voltage-dependent Na+ channels in supralinear temporal summation. A: tetrodotoxin (TTX; 1 µM) eliminated the supralinear summation at 10 ms but had no effect on sublinear summation at 20 ms. (Calibration, 5 mV; membrane potential, 72 to 74 mV.) B: partial depolarization to a membrane potential (45 mV) that inactivates most voltage-dependent Na+ channels attenuated supralinear summation but had no effect on sublinear summation. (Calibration, 35 pA.)

View larger version (11K): [in this window] [in a new window]   FIG. 4. Role of passive cable properties and K+ conductances in sublinear temporal summation. A: neurons were dialyzed internally with a Cs+-containing solution to block K+ conductances to assess the role of the latter in sublinear temporal summation. Seven cells were examined in the same manner as described in Fig. 2. An example of the responses to dendritic stimulation at 4 intervals is shown. (Calibration, 35 pA.) B: responses (means ± SE) of the 7 Cs+-dialyzed cells are plotted together with the data shown in Fig. 2B. Cs+ eliminated sublinear summation at 50 ms (P < 0.023, t-test) but did not have a significant effect on the sublinear process at 20 ms.

The manner of Na⁺ channels recruitment during temporal summation differs from that during action-potential initiation. The demonstration that supralinear summation occurs under somatic voltage-clamp conditions (Fig. 3B) suggests that subthreshold temporal summation is a local dendritic phenomenon that involves dendritic Na⁺ channels rather than somatic and axonal channels. Previous studies have shown that the dendritic membrane can undergo transient substantial depolarization without markedly perturbing the somatic membrane (Spruston et al. 1994), which may explain why supralinear temporal summation could be elicited at somatic membrane potentials ranging from the resting membrane potential to more negative than 100 mV.

Supralinear summation was not observed under conditions of excessive stimulation, such as when the individual evoked depolarization responses detected at the soma were >10-15 mV (data not shown). A single strong input may fully activate available neighboring dendritic Na⁺ channels, thereby precluding their activation in response to a closely timed second input. Strong dendritic excitation may also cause the attenuating passive cable properties to become dominant. Supralinear summation was also not observed when both inputs were directed to the same dendritic site, probably because receptor saturation and desensitization decrease the response to the second stimulus. In addition, supralinear summation was not detected with immature neurons, presumably because Na⁺ channels are not yet sufficiently abundant in their dendrites.

The role of K⁺ conductances in nonlinear temporal summation was examined by replacing intracellular K⁺ with Cs⁺. The effectiveness of Cs⁺ in blocking K⁺ conductances was monitored by the broadening of the action potential. The blockade of K⁺ conductances resulted in the elimination of a component of sublinear summation (Fig. 4). This change was especially marked at interpulse intervals close to 50 ms (P < 0.023, t-test). Blockade of K⁺ conductances did not prevent supralinear summation, nor did it eliminate the component of sublinear summation apparent at 20 ms. A reduced driving force and increased shunting likely underlie the earlier component of sublinear summation not sensitive to TTX or Cs⁺.

	DISCUSSION

Abstract Introduction Methods Results Discussion References

Passive cable theory is a useful starting point for analyzing dendritic excitability and dendritic integration. It predicts that, during temporal summation, the amplitude of the response to the second input will decrease monotonically as the interpulse interval decreases (Rall 1970). Our present data deviated from this prediction in two respects. Temporal summation was supralinear at short intervals and was sublinear at intervals longer than would be expected based on passive dendritic attenuation. Our results suggest that dendritic voltage-gated Na⁺ and K⁺ conductances, respectively, are largely responsible for these two deviations. The persistence of sublinear summation at intermediate interpulse intervals despite blockade of these Na⁺ and K⁺ conductances suggests that passive dendritic attenuation is primarily responsible for sublinear summation at interpulse intervals close to 20 ms.

It has been proposed that the expression of Na⁺ channels in dendrites serves to boost synaptic signals from distant synapses (Schwindt and Crill 1995) and to promote the back-propagation of action potentials from the soma toward dendritic branches (Stuart and Sakmann 1994). Our data suggest that boosting of temporally and spatially coincident dendritic inputs may be another physiological role of dendritic Na⁺ channels. Temporally and spatially coincident dendritic excitation, however, also generates conditions that allow maximal attenuation by passive cable properties. The juxtaposition of these two opposing nonlinear processes likely underlies the sharp transition between sublinear and supralinear summation. This sharp transition may reflect an elementary but highly sensitive mechanism for discriminating signals separated slightly in time and for retrieving temporally encoded signals arriving on the dendrites of central neurons.

In the present study, a novel photolysis method based on unique properties of "single-mode" optical fibers was developed, calibrated, and applied. "Single-mode" optical fibers comprise fused silica fibers with core diameters that approach the wavelength of the light they transmit. Light confined within such a narrow cavity propagates with high efficiency and low temporal dispersion, rendering these fibers indispensable components of modern telecommunication. Unlike "multimode" optical fibers, single-mode optical fibers have not previously been used for photolysis. We have now demonstrated the high temporal-spatial resolution that can be achieved with photolysis using single-mode fibers. This approach, combined with several other recently developed photolysis strategies (Denk 1994; Pettit et al. 1997), creates new opportunities for applying photolysis to problems in neurobiology.

	ACKNOWLEDGEMENTS

  We thank R. Tang for fabricating the tapered optical fiber tips and for developing the method for cleaving their front tips.

  This work was supported by a grant from the Veterans Affairs Medical Research Service.

	FOOTNOTES

  Address reprint requests to C.-M. Tang.

  Received 10 December 1997; accepted in final form 16 January 1998.

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