INTRODUCTION

TOP ABSTRACT INTRODUCTION Methods RESULTS DISCUSSION REFERENCES

Diverse dendritic geometry is a characteristic feature of central neurons. Dendritic geometry is one of the main factors that determine the properties and functions of neurons. This is because dendrites are sites where computation of synaptic signals takes place and also because dendritic structures themselves are critical for neuronal firing properties (Mainen and Sejnowski 1996). Because most neurons have complicated dendritic arborization, it has been difficult to evaluate the function that certain dendritic structures subserve, although there have been demonstrations of dendritic contribution to neuronal function in several systems (Archie and Mel 2000; Henze et al. 1996).

The corpus glomerulosum is an expansive thalamic nucleus in teleosts; it has been suggested that it is involved in visual information processing (Sakamoto and Ito 1982). Previous comparative studies of this nucleus in several teleost species (Ito 1978; Ito and Kishida 1975) have shown that it can be classified into three types according to the degree of laminar organization, with type III representing the most clearly laminated type. The nucleus contains only two cell types. The "large cell" in the most clearly laminated group (type III) has a massive enlargement at the tip of the dendrite that often exceeds 60 µm in diameter and that has been referred to as a star-like structure (Fig. 1A). The large cells in the other nuclear types do not have such a tip structure (Ito and Kishida 1975, 1977). The dendritic tip is the postsynaptic component of the glomerulus and the large cell receives the majority of excitatory synaptic input in this location (Ito and Kishida 1977; Tsutsui et al. 2001). It has been shown that the tip has only passive properties whereas the soma fires a fast Na⁺ spike (Tsutsui et al. 2001). Thus, this extremely large dendritic tip is one of the most simple and remarkable dendritic structures among central neurons and it may serve as a good model system by which to explore the significance of dendritic geometry on the physiology of neurons. The aim of the present study is to use a computational approach to evaluate the possible functions of this characteristic dendritic geometry.

View larger version (92K): [in this window] [in a new window]   Fig. 1. A: typical morphology of the large cell with an extremely large dendritic tip. A patch pipette was used to fill the cell with biocytin in the soma of a Stephanoplepis cirrhifer brain slice preparation (250 µm). Arrows, course of the dendritic stalk that connects the soma and the tip. The axon was not visible in this cell because it was cut by the slicing procedure. Bar = 100 µm. See Tsutsui et al. (2001) for detailed methods. B: compartmental model used in the present study.

	Methods

TOP ABSTRACT INTRODUCTION Methods RESULTS DISCUSSION REFERENCES

The typical morphology of the large cell is shown in Fig. 1A (for detail see Tsutsui et al. 2001). The axon is not visible in the figure because it was cut during tissue sectioning. However, it has previously been demonstated that the axon of the large cell projects to the inferior lobe of the hypothalamus (Sakamoto and Ito 1982). The anatomical dimensions of the cell were abstracted and a multi-compartmental model was constructed that consisted of four compartments: axon, soma, dendritic stalk, and dendritic tip (Fig. 1B). Based on the morphology of several cells, we used the following values for the dimensions of the compartments: 1,000 × 1 µm (length × diameter) for the axon, 30 × 30 µm for the soma, and 500 × 2 µm for the dendritic stalk. The tip dimension was varied from 2 × 2 to 96 × 96 µm to determine the effects of changing the dendritic geometry. One-tenth of the alternative current (AC) length constant at 100 Hz was used as a maximum length for the spatial grid. Consequently, the dendritic stalk and the axon were segmented into 13 and 37 segments, respectively, and the other compartments were modeled as one segment. We used the passive membrane parameters as follows: conductance (G_m) = 0.15 mS/cm², capacitance (C_m) = 1 µF/cm², axial resistance (R_a) = 100 cm, and E_pas (equilibrium potential for G_m) = 65 mV. As a result, input resistance and capacitance measured at the soma were 78 M and ~35 pF, respectively, which is similar to the real parameters described in Tsutsui et al. (2001). To incorporate synaptic inputs, an excitatory synapse, modeled by an alpha function (Koch and Segev 1998) with time constant of 0.1 ms, was introduced into the center of the dendritic tip. The equilibrium potential for the synaptic conductance was set at 0 mV. Although the main interest of the present study was in analyzing passive propagation of the postsynaptic potential (PSP) by using a model in which no region had any active conductance [whole-passive (WP) model], conventional Hodgkin-Huxley (HH) type Na⁺ and K⁺ channels (Hodgkin and Huxley 1952) were used for incorporating active conductance in preliminary simulations, as explained in the DISCUSSION. E_Na and E_K were set at 50 and 77 mV, respectively, for all of the regions. Values used for channel densities in these simulations ranged from 33 to 4,000 and 10 to 900 mS/cm² for the Na⁺ and K⁺ channels, respectively. Models were simulated using the NEURON program (Hines 1993; http://neuron.duke.edu/), with an integration time step of 25 µs, on a standard personal computer. As the convention in NEURON, the expression "stalk(x)" was used to specify a location in the stalk, where x is the ratio of total stalk length to distance along the dendrite from the soma.

	RESULTS

TOP ABSTRACT INTRODUCTION Methods RESULTS DISCUSSION REFERENCES

First, we focused on passive propagation of PSP from the tip to the soma through the stalk. When we consider the tip without the interconnecting stalk, a low total synaptic conductance (equivalent to a small number of synaptic inputs) is enough to produce a certain amplitude of PSP at a small tip with high-input resistance, and a high synaptic conductance is necessary at a large tip with low-input resistance. Thus, depending on the tip geometry, there should be a large difference in the amount of charge influx that produces PSP of the same amplitude. In contrast, the time course of PSP should be independent of the geometry because the membrane time-constant remains the same (note that R_m  r² and C_m  r², where r is tip diameter, and therefore  = R_mC_m = const). However, when the tip is connected to the soma by the stalk, through which charge can flow out, the difference in the charge influx to the tip should affect the amplitude and the time course of the PSP at the tip and, consequently, passive propagation to the soma. In Fig. 2A, the WP model is used to show simulated responses to synaptic inputs of different conductance. When tip geometry was set to 2 × 2 µm, the PSP at the tip decayed faster than did the membrane time constant ( = 6.67 ms) (Fig. 2A, dotted line), which means that a large portion of the charge influx from the synaptic conductance flowed out to the stalk. At a 64 × 64-µm tip, the decay phase of the PSP was close to the exponential decay with a time constant of  because the current outflow from the tip is much smaller compared with the large amount of charge influx. Consequently, the postsynaptic responses at the stalk (0.9) and at the soma in a cell with a small tip were smaller both in peak amplitude and in time to peak than were those in a cell with a large tip (Fig. 2A). Because the cell did not have any nonlinear active conductance, the ratio of the peak amplitude of the postsynaptic response at any location to that at the tip was independent of synaptic conductance. The ratio at the soma was nearly 2.4 times larger in the 64 × 64-µm tip than it was in the 2 × 2-µm tip. These ratios and the time-to-peak amplitude at the tip, stalk (0.9), and stalk (0.5) and soma for various tip geometries are plotted in Fig. 2B. It should be pointed out that both the ratio and the time-to-peak curve versus the tip geometry were S-shaped. There are upper limits to these values when the tip dimension is large enough, so that current outflow from the tip could be totally neglected and PSP at the tip decays exponentially with a time constant of . Furthermore, note that, in the simulations shown in Fig. 2A, to produce PSP of nearly the same amplitude the synaptic conductance was only 10-fold larger in a 64 × 64-µm tip (0.2-0.6 µS) than it was in a 2 × 2-µm tip (0.02-0.06 µS), even though the membrane resistance of a 64 × 64-µm tip is 1,000 (32²)-fold lower. Thus, there was a great difference in the density of synaptic conductance (i.e., synaptic conductance/tip membrane area) required to produce a certain amplitude of PSP at the tip, which should be constant when the tip alone is considered. This is caused by current outflow through the stalk that occurs before the PSP reaches its peak. Figure 2C is a plot of PSP amplitude at the tip versus synaptic densities for various tip geometries. It shows that a nearly 100-fold higher synaptic density was required to produce a PSP of 20 mV amplitude in the 2 × 2-µm tip than was required in the tip without the stalk, whereas almost the same density was required in the 64 × 64-µm tip, as seen in Fig. 2A. Thus, from Fig. 2, B₁ and C₁, a remarkable "boosting" effect that depends on the tip geometry is demonstrated. A more than 350-fold difference in synaptic density is required to produce 4 mV PSP at the soma with a 2 × 2-µm tip compared with a 64 × 64-µm tip (Fig. 2C₂).

View larger version (22K): [in this window] [in a new window]   Fig. 2. A: simulated synaptic potentials. Tip dimension is 2 × 2 µm (left) and 64 × 64 µm (right). The top, middle, and bottom traces are responses at the tip, stalk (0.9), and soma, respectively. Responses to 3 different synaptic conductances are superimposed. The conductance was varied from 0.02 to 0.06 µS (left) and 0.2 to 0.6 µS (right). Dotted lines, exponential decay with time constant  (=6.67 ms). The postsynaptic potentials (PSPs) decayed faster and the somatic responses were attenuated to a greater extent in the 2 × 2-µm tip than in the 64 × 64-µm tip. B1: ratio of the peak PSP amplitudes at three different positions [soma, stalk (0.5), and stalk (0.9)] to those at the tip. B2: time to peak at four different positions [soma, stalk (0.5), stalk (0.9), and tip] vs. tip dimension (=diameter = length). C: plot of the peak PSP amplitude at the tip (C1) and at the soma (C2) vs. synaptic density (i.e., synaptic conductance/tip membrane area). The number beside each curve indicates tip dimension. The curve indicated as "tip" in C1 indicates simulations without the stalk (note that the curve for "tip" is independent of tip geometry).

Another predictable effect of large dendritic tip diameter includes back-propagated action potentials from the active region that are caused by the large current sink at the tip. Although physiological data on the active conductance are needed for a quantitative evaluation, we performed a preliminary analysis of the responses to supra-threshold synaptic inputs. To do this we used models that incorporated HH channels in soma, axon, and stalk (if any) with a different combination of densities in physiological ranges. As expected, back-propagated action potentials from PSP-induced spikes were attenuated to a great extent in the 64 × 64-µm tip in all of the simulations. We then used the models with HH channels to simulate somatic current injections to determine the effects of dendritic geometry on somatic firing properties. When the dendritic tip was connected to the soma by a normal stalk (500 ×2 µm), we found that it was almost impossible (even with a 96 × 96-µm or larger tip) to significantly affect the firing properties in the soma, although a slight increase or decrease in the firing frequency was observed in some simulations. In contrast, a remarkable decrease in firing frequency was observed when a large tip (32 × 32 µm) was connected by a stalk of shorter length (100 µm) (data not shown). Thus, it is less likely that the large tip has a significant effect on somatic firing properties, although information on the distribution of active conductance is also required for a quantitative evaluation.

	DISCUSSION

TOP ABSTRACT INTRODUCTION Methods RESULTS DISCUSSION REFERENCES

As shown in the present study, a large-diameter dendritic tip has a large area of postsynaptic membrane that not only receives many synaptic inputs but also can "boost" the somatic response via passive mechanisms. Since the distal part of the dendritic stalk [e.g., stalk (0.9)] is also boosted to some extent (Fig. 2, A and B₁), it is highly probable that the boosting effect works in the real cell independent of the existence of active conductance in the dendritic stalk. It seems that the large cells without enlarged tips in the two other laminar-type groups in teleost species (i.e., type I and II) do not have a very long stalk, as shown in Fig. 1A, because the corpus glomerulosum nuclei in these groups do not have a laminated histological organization (Ito and Kishida 1975). Therefore, it may be possible that the tip structure has evolved to propagate PSP for a long distance to the soma in the laminated nucleus. It is interesting that the effect on the attenuation of back-propagated action potential counteracts the boosting effect; the postsynaptic depolarization is less attenuated in smaller tips. However, the general physiological significance of back-propagation is not yet clear. Thus, in principle, the back-propagated potential in a small dendritic tip can efficiently couple delayed synaptic inputs to depolarize the membrane and to activate voltage-dependent processes [e.g., N-methyl-D-aspartate (NMDA) receptor activation] where large synaptic conductance is required otherwise.

The present study also suggests that a dendritic tip with larger dimensions has a broader time window for temporal summation of the PSP when it receives multiple synaptic inputs in succession because the PSP decays slower in the larger tip (Fig. 2A). On the other hand, it has been suggested that the large cell may encode temporal aspects of afferent inputs (Tsutsui et al. 2001). Thus, the time course of PSP decay, which is dependent on tip geometry, may have a significant effect on the detection of the coherence of afferent inputs.