The Extracellular Space of A Simple Molluscan Nervous System and Its Permeability to Potassium

The surface of both the soma and axon of the giant gastro-oesophageal neurone (G cell) of Anisodoris nobilis is greatly infolded (Mirolli & Talbott, 1972). Gorman & Mirolli (1972 a) concluded that the specific resistance and capacitance of the G cell is considerably different from the values previously estimated for molluscan neurones. This conclusion was based on the assumption that the diffusion of small ions is not severely restricted in the infoldings. Qualitative evidence for this assumption has been given. Thus, the possibility that the space of the infoldings is completely or partially closed (Amoroso et al. 1963) can be excluded because lanthanum, an electron-microscopical marker of the extracellular space (Revel & Karnowsky, 1967), diffuses in the entire extracellular space of the gastro-oesophageal nervous system (Mirolli & Crayton, 1968). Furthermore, small ions such as Na+ and K+, diffuse rapidly from the external solution bathing the ganglion and from the nerve to the surface of the G cell, and vice versa (Gorman & Marmor, 1970a). However, neither of these findings can be used to exclude the possibility that the extracellular space of the infoldings constitutes a separate compartment where diffusion occurs at a slower rate than elsewhere in the tissues surrounding the G cell. The purpose of this paper is to examine this possibility and to provide a quantitative estimate for the ionic permeability of the extracellular space in the gastro-oesophageal ganglion and nerve of Anisodoris. A preliminary report of these findings has been published elsewhere (Gorman & Mirolli, 1972b).

A description of the G cell of Anisodoris nobilis (MacFarland) can be found in the papers of Gorman & Mirolli (1969) and Mirolli & Talbott (1972). The extracellular space in the tissue was marked with lanthanum by incubating the living gastro- oesophageal ganglion and nerve with artificial sea water to which 5 mM LaCl had been added (Mirolli & Crayton, 1968). After 5‐10 min. of exposure the lanthanum was precipitated and the preparation was fixed by rinsing with a 2·5 % solution of glutaraldehyde in collidine phosphate buffer at pH 7·8. After 1 h the specimens were rinsed in buffer, post-fixed in osmium, dehydrated, and then embedded in Maraglass for electron microscopy. Histochemical tests for the PAS reaction indicative of the presence of mucopolyaccharides (Pearse, 1968), were made on sections of material embedded in paraffin.

When [K_o] is changed, the K+ concentration in the fluid layer adjacent to the G cell membrane, [K_e], will change at a rate which is uniquely determined by the diffusive properties of the tissues surrounding the cell. Corresponding to the changes in [K_o], V will also change, reaching a new stable level, V_∞ at a time At t_œ we can assume that [K_o] × [K_e], Thus, a graph of V versus [K₀] will give, for every cell examined, a calibration curve through which the instantaneous values of [K_e], during the voltage transient following a change in [Ko], can be estimated.

The diffusion coefficient for KC1 in aqueous solution depends on a number of variables (see Harned & Owen, 1958). The two most important of these for evaluating our data are temperature and concentration effects. A plot of the relation between the diffusion coefficient for KC1 and temperature is shown in Text-fig. 2. The open triangles represent values for the diffusion coefficient determined with dilute solutions by a number of authors (Washburn, 1929), and the closed circles represent values for stronger concentrations from data given by Harned and his associates (Harned & Blake, 1950; Harned & Owen, 1958). The variation of the diffusion coefficient with changes in concentration can be seen to be much less than with changes in temperature.

A thin connective sheath and several glial layers are interposed between the fluid bathing the ganglion, and the surface of the G cell. When lanthanum is added to the external solution and then precipitated, a fine electron-dense deposit is found in the sheath as well as in the intercellular clefts of the underlying glial layers and in the space between the glia and the neurones.

The avascular connective sheath is 3–10 μm thick (Pl. 1 A, cs). Its bulk is made up of an amorphous matrix with only a few interspersed cellular elements. This matrix is positive for the PAS reaction indicating the presence of acid mucopolysaccharides (Pearse, 1968). Lanthanum deposits are found dispersed throughout this matrix without evidence of specialized channels. Collagen-like fibrils are abundant in the sheath covering the nerve and in the lower half of the sheath covering the ganglion. They are rare or absent in the upper half of the sheath around the ganglion.

The glial cells have a small perikaryon out of which radiate broad, leaf-like processes which in section appear as thin (0·2‐0·μm) profiles, 5–15 μm long. At the surface of the ganglion and the nerve the glia is tightly packed into concentric shells, forming a distinctive layer (Pl. 1 A, ogl). This outer glial layer is 3–8 μm thick in the ganglion and 2–5 μm in the nerve. Immediately underneath the boundary with the sheath the membranes of adjacent glial cells are finely folded and interdigitated to form characteristic crenated junctions (Pl. 1B and C) where the width of the extracellular clefts is about 50 to 100 Å. Below these junctions the extracellular space is wider (between 150 and 200 Å) and at some points expands into large lacunae as much as 500 Å in width. The extracellular pathways which can be traced in the outer glial layer are extremely tortuous, their lengths being on the average 5·25 times the overall thickness of the outer glia layer in the ganglion and 6·40 times the thickness of this layer in the nerve.

Below the outer layer the glia is organized into bundles of finger-like or laminar processes, variously oriented, which separate the individual neurones and penetrate their surface foldings (Pl. 2A, Pl. 3 A). The extracellular pathways which can be traced from the outer glial layer to any region of the G cell’s surface are almost straight (Pl. 2B). The cleft between the glial cells is 150 to 200 Å wide; as in the outer layer, there are numerous lacunae which may be as much as 1000 A in width. Also common are points of close contact between adjacent glial cells, but these are never more than 1–2 μm long (Pl. 2B).

The space between the plasma membrane of the neurone and that of the surrounding glial cells (extraneuronal space) is of uniform width, about 150 to 200 Å (Pl. 3 B). The extraneuronal space is everywhere marked by a dense lanthanum precipitate (Pl. 3 B). No specialized coating of the membranes of either the glial cells or the neurones can be demonstrated and there are no specialized junctions between the glia and the neurones, either inside or outside the infoldings.

Estimates for the average length of the extracellular channels from the outer face of the sheath to the extraneuronal space of the G cell soma and axon were obtained from light microphotographs of representative sections of the ganglion and of the nerve (see Methods). The channels were approximated by straight line segments in the sheath and in the inner glia ; in the outer glial layer their lengths were calculated from the thickness of the layer itself, multiplied by the correction factors given above. For cells of approximately the same dimension as those used in the physiological experiments the average length, l, for the extracellular channels was 94 μm for the soma, and 68 μm for the axon. The frequency distribution of the somatic channels was distinctly skewed, ranging from 30 to 230 μm, with a peak around l = 50 μm; that of the axon was more compact and symmetrical ranging from 25 to 116 μm with more than 70 % of the measured lengths clustered within + 20 μm of the average.

From measurements of electron micrographs, the extracellular space was calculated to be 8·9 % of the total volume of the glia layer in the ganglion and 8·6 % of the glia layer in the nerve. In the sheath around the ganglion the extracellular space was calculated to be 83 % of the total volume and that around the nerve 75 %.

The electrical events observed in the gastro-oesophageal ganglion when [K_o] was changed, depended on the position of the recording electrode. When it was located extracellularly, next to the G cell, only a small shift in potential (0·5–1·0mV) was observed (Text-fig. 3 A; top trace), indicating that the layers surrounding the G cell have a high, non-selective, ionic permeability. In contrast, the electrode recorded a prompt and massive voltage change when it was located in an intracellular position (Text-fig. 3 A; lower trace).

Both the depolarization following an increase in [K_o] and the repolarization associated with its decrease were completed in about 50 to 100 seconds. The final potential level attained, V_∞, was dependent on [K_o]. For all the cells examined the relationship between [K_o] and e^VFlRT was linear, as predicted by equation (1) (Text-fig. 3 B). Thus the K+ concentration in the extraneuronal space of the G cell corresponding to any given time, t, [K_e]_t could be estimated from records such as that presented in Text-fig. 3 A. For the time interval corresponding to the cell spike discharge a smooth line was drawn through the spike’s baseline. The experimental points in a plot of [K_e]_t versus time could always be fitted to a sigmoid curve (Text fig. 4; see legend to the figure and discussion), which could be characterized by two parameters: (1) latency of onset, defined as the time interval between a change in [K_o,] from [K_o]_o to a new value [K_o] ∞ and (2) the half-time (t₀·₅), defined as the time interval between the onset and when the change in [K_e] calculated from equation (1) reached a value equal to [K_o] ∞Thus, t₀·₅ corresponds to a value of the ratio, {[K_o]_t-[K_o]_o}/{[K_o]_∞-[K_o]_o}, equal to 0-5. The magnitude of t_0·.7 depends on how fast [K_e] changes and gives important insights into the nature of the process of diffusion of K⁺ in the ganglion (Nicholls & Kuffler, 1964; Treherne et al. 1970).

The latency of onset is an important indication of the experimental conditions. Both this parameter and, to a lesser extent, the half-time were dependent on the flow rate of the solution in the chamber in the sense that short latencies and briefer half-times were consistently observed with higher flow rates (Text-fig. 5 A, B). In the case illustrated in Text-fig. 5 the flow rate was increased from 0·5 to approximately 2·7 ml per minute (cc/min). The latency of onset and t_{0· 5} approached a stable value only at the highest flow rate. However, in most cases the flow rates had to be restricted to values less than 2·7 cc/min in order to maintain the temperature at o °C and to minimize the likelihood of dislodgement of the micro-electrode. Therefore in all probability our data overestimate the actual t₀·₅.

Complete experiments were made on four cells. The average half-time for the inflow of K+ (K+ raised in the external bath) was 14 sec and that for the outflow (K⁺ decreased) was 21 sec. In the experiment with the fastest flow rate, t₀·₅ was 9·4 sec for the inflow and 12 sec for the outflow. The reasons for this difference between inflow and outflow values (see also Nicholls & Kuffler, 1964), are unclear. It may be explained, at least in part, by the active membrane phenomenon associated with the spike discharge and by the experimental conditions.

The system of extracellular channels of the Amsodoris nervous system departs from the model described by equations (2a) and (2b) because the channels have neither a constant width nor equal lengths. The mathematical difficulties introduced by these complications make any attempt to obtain a precise quantitative model futile. However, experimentally it is found that the diffusion data can be fitted by theoretical curves calculated from equation (2) (see Text-fig. 4). In the best case (corresponding to the experiments with the fastest flow rate), the agreement is good. The curves calculated for the same value of L fit both outflow and inflow data except, in the latter, during the period of spike discharge (see Text-figs. 3 and 4). In the other cases the agreement was also satisfactory, but it was necessary to use a value of L longer for the outflow than for the inflow data. Since in these cases the flow rate was not optimal, it is possible that the difference between the inflow and the outflow depends, at least in part, on the experimental conditions.

According to the measured average half-time for K+ inflow, L = 200 μ m; for the outflow the half-time corresponds to L = 240 μ m. L can be compared to the length of the extracellular channels measured by anatomical methods (Z). Since the input conductance of the G cell is dominated by the axon (Gorman & Mirolli, 1972 a; Mirolli & Talbott, 1972) it seems reasonable to compare the values given for L to the average length of the axonal channels (70 μ m) rather than to the greater length of the somatic channels (95μ m). On this basis the restriction factor (A) for the diffusion of K+ given by the ratio A = L/l in the nervous system of Anisodoris is 2· 9 for the inflow and 3· 4 for the outflow. A restriction of this order of magnitude is minor. By way of comparison, in the leech ganglion where diffusion is also thought to be practically unrestricted and to occur entirely via extracellular channels (Nicholls & Kuffler, 1964), the restriction factor is 2· 4. Furthermore, the average L is almost certainly an overestimate ; if we use the L corresponding to the best experiment (175 μ m) the restriction factor for Amsodoris is 2· 5.

It should be emphasized that the model described by equation (2) is not the only one that can be fitted to our data. For instance, either the model of diffusion in channels closed by a terminal reservoir, examined by Treherne et al. (1970), or that of diffusion in a semi-infinite medium used by Nicholls & Kuffler (1964) could be used. These however, would result in smaller values of the estimated L, thus making the restriction factor for diffusion even smaller.

The present findings may have some relevance to other systems where the extracellular space appears to be limited. A superficial examination of the anatomy of the G cell with its numerous surface infoldings, many of which seemingly having no direct contact with the surrounding extracellular space, might have suggested that diffusion to and from much of the cell surface was severely restricted. Our results suggest a different interpretation. The extracellular space of the gastro-oesophageal ganglion and nerve of Anisodoris, even in the deeply infolding regions of the G cell membrane, behaves as an aqueous layer where diffusion to small ions is essentially free. Moreover, diffusion is sufficiently rapid so that under most conditions it is unlikely that a sizable difference in ionic concentration is established between the extraneuronal layer surrounding the G cell and the fluid bathing the ganglion.

We are grateful for comments on an earlier draft of this paper from Dr M. Marmor and for the technical assistance of Mrs M. Marti-Volkoff and Miss S. Talbott.