Input summation by cultured pyramidal neurons is linear and position-independent

Abstract

The role of dendritic morphology in integration and processing of neuronal inputs is still unknown. Models based on passive cable theory suggest that dendrites serve to isolate synapses from one another. Because of decreases in driving force or resistance, two inputs onto the same dendrite would diminish their joint effect, resulting in sublinear summation. When on different dendrites, however, inputs would not interact and therefore would sum linearly. These predictions have not been rigorously tested experimentally. In addition, recent results indicate that dendrites have voltage-sensitive conductances and are not passive cables. To investigate input integration, we characterized the effects of dendritic morphology on the summation of subthreshold excitatory inputs on cultured hippocampal neurons with pyramidal morphologies. We used microiontophoresis of glutamate to systematically position inputs throughout the dendritic tree and tested the summation of two inputs by measuring their individual and joint effects. We find that summation was surprisingly linear regardless of input position. For small inputs, this linearity arose because no significant shunts or changes in driving force occurred and no voltage-dependent channels were opened. Larger inputs also added linearly, but this linearity was caused by balanced action of NMDA and IA potassium conductances. Therefore, active conductances can maintain, paradoxically, a linear input arithmetic. Furthermore, dendritic morphology does not interfere with this linearity, which may be essential for particular neuronal computations.

Fig. 1.

Iontophoretic potentials resemble spontaneous EPSPs and are spatially localized. A, Photomicrograph of a 12 d in vitro cultured hippocampal neuron showing a pyramidal morphology, with a single large apical dendrite and several smaller basal dendrites. Scale bar, 40 μm. B, Examples of action potentials elicited from two different neurons using either a short (left) or long (right) glutamate depolarization. Fast, large action potentials that accommodated in frequency with long depolarizations were present in the cultured neurons. Calibration: 10 mV, 10 msec for left; 10 mV, 1 sec for right. C, Spontaneous EPSPs (top set) and iontophoretically induced potentials (bottom set) from five different cells. Note that the two sets of potentials are nearly identical in waveform.D, Peak amplitude of the average of five iontophoretic pulses as the pipette was moved vertically in 1 μm increments away from the point of maximal amplitude. Data from 10 cells was fit with a single exponential. Inset shows the decreases of the responses of a representative cell as the pipette was moved 5 μm from the original location. Note how the response decreasese-fold in ∼5 μm. Calibration for C, D: 5 mV, 30 msec.

Fig. 2.

Synaptic summation is independent of input position. A, Diagram of the experiment. Two microiontophoresis pipettes were positioned on the dendritic tree of a pyramidal neuron in culture. Glutamate was ejected first from each pipette individually and then from both simultaneously. The algebraic sum of the individual potentials was then compared with the actual potential recorded with simultaneous stimuli. B, Averaged results from a representative cell (5 trials). The twolower lines are the responses from each of the pipettes, the dashed line indicates their algebraic sum, and thetop solid line is the simultaneous response measured. Note the overlap between the expected and actual summed depolarizations, indicating linear summation. Calibration: 2 mV, 25 msec. C, Schematic diagram of a neuron showing pipette locations studied, including apical (Ap), second or higher order branches (S), and basal dendrites (B). D, Histogram of the linearity of the summed responses, measured by the ratio of actual to expected peak amplitudes, for different input configurations. No significant deviations from linearity are observed (ANOVA, p < 0.05; number of experiments in parentheses).

Fig. 3.

Linearity of summation is independent of intrapipette distance and response amplitude. A, Percent linearity of the summation of two inputs in all spatial configurations as a function of distance between the pipettes. Distance was measured as the shortest length along the neuron between the two inputs.Dashed line indicates linearity. No systematic correlation is observed. B, Percent linearity of the summation of two inputs as a function of combined peak amplitude. No significant deviation from linearity is seen. Each pointrepresents a single experiment. More than one experiment may be performed on a given cell in either different positions or amplitudes. These data include 75 different experiments on 40 different cells and are the same data as those plotted in Figure 2.

Fig. 4.

Mechanisms underlying linear summation. Effects of APV, TTX, NiCl₂, TEA, 4-AP, and hyperpolarization on the linearity of two inputs on the apical dendrite. A, For combined events <10 mV, none of the manipulations produced a significant change from control conditions or from experiments performed with APV (ANOVA, p < 0.01). This suggests that NMDA, Na⁺, Ca²⁺, and K⁺ conductances do not contribute significantly to the summation. B, For combined events >10 mV, application of APV produced a significance sublinearity compared with controls (*). TEA, 4-AP, and hyperpolarization produced a significant block of the APV effect (**). The presence of all types of blockers revealed a significant sublinearity, compared with theTEA+APV experiments (^†, for all cases, ANOVA, p < 0.002). These results suggests that the normal linearity for large amplitude events is produced by a balanced action of NMDA and K⁺ conductances. Blockade of all conductances reveals a sublinearity that could be attributable to driving force reduction or conductance shunting. Number of experiments in parentheses.