- Email: [email protected]
Chapter 3 Chapter Two different ways evolution makes neurons larger
J . Storm-Mathisen, J . Zimmer and O.P. Ottersen (Eds.) Progress in Brain Research, Vol. 83 0 1990 Elsevier Science Publishers B.V. (Biomedical Division)
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CHAPTER 3
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Two different ways evolution makes neurons larger John M. Bekkers and Charles F. Stevens* Section of Molecular Neurobiology, Howard Hughes Medical Institute at Yale University School of Medicine, 333 Cedar Street, New Haven, CT 06510, U.S.A.
As evolution makes larger brains it also increases the size of many of the individual neurons that make up the brain. How neurons are made larger can give clues about design principles of the brain’s circuits. One way of making a larger neuron is called conservative scaling. If evolution magnifies a particular type of neuron by a factor of two - that is, each dendrite is made twice as long - then the neuron is scaled conservatively if the magnified neuron has dendrites with 4 times the diameter of their unscaled counterparts. This type of scaling leaves the passive cable properties of the neuron unchanged and so maintains a balance in effectiveness between proximal and distal dendritic inputs. One might imagine that, for some types of circuits, maintaining such a balance would be necessary to use just the same neuronal interconnections in both large and small brains. We have compared dentate granule cells and CAI pyramidal neurons in cat and human to establish how these cell types are, in fact, scaled. Both cell types are larger in human than in cat, even though their general form is conserved. Pyramidal neurons scale conservatively, but dentate granule cells do not. The CAI circuits seem, then, to require conservation of the passive cable properties of their elements, whereas dentate does not. We suggest that the reason CAI neurons scale conservatively is that, for this region, each individual synaptic input exerts a significant effect on the cell’s output, whereas in dentate the neuronal output represents the average of a large number of anonymous individual inputs.
Introduction The brains of mammals, from pigmy tree shrew to man, range in size over about 4 orders of magnitude. Although the various mammalian brains have greatly different capabilities, most workers nevertheless believe they all conform to a generally uniform design; this belief is the basis for comparative neuroanatomy, and provides the justification for using, for example, rat or cat brains as models in neurobiological experiments intended to enlighten us about the workings of the human nervous system. To make any computational machine, including a brain, a thousand times larger is a difficult task, and the way this magnification is achieved can give some clues about the underlying principles used for designing
* Present address: C.F. Stevens, The Salk Institute, 10010 North Torrey Pines Road, La Jolla, CA 92037, U.S.A.
the computing circuitry. The goal of this chapter is to explore one aspect of this scaling problem related to altered cable properties in neurons that are magnified. Some background information will be necessary before we can give a precise statement of the problem we wish to investigate. As brains grow in size, so do the nerve cells of which they are composed (Hardesty, 1902; Bok, 1959). The brain is unu‘sual in this regard because the cells used to construct other organs - liver or gut, for example - d o no differ very much in size between small and large animals (Teissier, 1939; Altman and Dittmer, 1961). The cell bodies of spinal motoneurons have about half the diameter in a small animal like a mouse than they have in man, and cortical neurons generally differ by about the same amount. In fact, the thickness of the cerebral cortex varies approximately as the 0.1 power of the cortical surface area (Stevens, 1989) so that if one brain is a thousand times larger than
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another (mouse to man), its cortFx is twice as thick and the corresponding neurons have dendritic trees that are double in length. Why do large brains have larger neurons? One likely explanation is that the increase in cell body size reflects the need for a larger biosynthetic capacity to maintain the larger axonal tree that must reach over longer distances. This presumably is at least part of the reason why spinal motoneurons and Betz cells are so large compared to other neurons in the same brain. Why then must cortical neurons have longer dendritic trees? The answer here is perhaps that the cortex must be thicker to accommodate larger and more rapidly conducting axons that communicate over greater distances in the large brain. Different parts of a neuron’s dendritic tree commonly have quite specific inputs (see, for example: Blackstad, 1956; Andersen et al., 1966; Blackstad et al., 1970; Blackstad, 1975). The most distal part, for example, might receive information from one brain region and the more proximal parts from another. The distal information is somewhat more attenuated by the neuron’s cable properties than that arriving over proximal inputs. A particular distal synapse might, for example, have half the effect at the soma of a proximal synapse. In this case, if one neuron has a dendritic tree that is twice as long as that of another, and if the dendrites had the same diameters in both cases, then the distal input in the larger neuron would have only one fourth the effect of a proximal synapse. The relative influence of proximal and distal synapses, then, might be quite different for large and small neurons, and this difference could be of great functional significance if the circuitry assumed a particular balance between the influences of nearby and distant synapses. Thus larger brains must, whenever inputs are stratified as they generally are in cortex, deal with the problem of maintaining a constant balance between distal and proximal inputs. We wish to investigate theoretically and experimentally this scaling problem. Our goal, then, is to ask how neurons differ between small and large brains, to estimate how significant cable at-
tenuation of distal signals is likely to be in particular classes of neuron, to propose several ways the brain might deal with the problem of keeping proximal and distal inputs in balance, and to ask which methods are used in fact. Our preliminary observations suggest that different classes of neurons deal with the size problem in different ways, and this in turn indicates that the various parts of the brain may not have just the same organizational principles. The following discussion is organized in 4 parts. In the first part we present experimental data, gathered in a new way, that provides estimates of the cable characteristics of hippocampal neurons, and also presents measurements on the magnitude of depolarization produced by a single quantum of neurotransmitter. These data will highlight the implications of dendritic cable properties for neuronal function and provide the physiological basis for the consideration of morphological features that follows. The second part presents a theoretical analysis of the functional implications of making a neuron larger and develops the concept of “conservative scaling”, a set of rules according to which a larger neuron would be electrically equivalent to a smaller one of the same shape. This section is needed to indicate what morphological features of a dendritic tree must be measured to gain insight into the functional implications of neuronal size changes. The third section gives some preliminary measurements that indicate what rules neurons actually follow when they are enlarged by evolution. We will conclude that not all neurons follow the same rules. In the final section we speculate on the implication of our observations for neuronal function. We shall suggest that the rules a neuron follows in being evolutionarily enlarged may give clues to differences in function. We have chosen the hippocampus as a model system in which to investigate these questions because of its importance and simple structure. We shall consider neuronal properties in the dentate granule cells and pyramidal cells of the CA1 region in cat and human.
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Attenuation of synaptic signals by dendrites This section will present some preliminary data on the cable properties of hippocampal pyramidal cells in tissue culture. These results were obtained using a technique that should make immediately clear the issues in cable attenuation of synaptic signals. In particular, we will- show directly the dramatic effect of cable filtering when a synaptic current is injected far out on the dendritic tree. Briefly, the experimental procedure was as follows. Pyramidal cells from the CA1 and CA3 fields of the hippocampi of neonatal rats were maintained in culture for up to 3 weeks using the methods described by Jahr and Stevens (1987). The cell density was sufficiently low that the dendritic field of each cell could be traced without much ambiguity, i.e. cells were separated, on average, by several hundred microns. Membrane currents were measured from a cell via a patch electrode, sealed onto the cell body, in the whole-cell configuration as described by Bekkers and Stevens (1989). The objective was to inject a known current at different places on the dendritic tree and measure the cabledistorted form of it that reached the soma. This was done using a trick suggested by a finding made at the neuromuscular junction: Fatt and Katz (1952) showed that applying hypertonic solutions increased the frequency of miniature endplate potentials, an effect possibly due to osmotic shrinkage causing asynchronous exocytosis of presynaptic, neurotransmitter-loaded vesicles. We found that a similar process occurred in our culture system. When we applied a narrow stream of hypertonic solution to a place close to the voltage-clamped soma of a pyramidal cell, we usually observed a sudden increase in small, rapid currents. We have shown elsewhere that these currents are evoked local to the flow of solution, and have all the features of miniature excitatory postsynaptic currents (“mini EPSCs”) (Bekkers and Stevens, 1989). Use can be made of these solution-evoked currents to study cable properties if one makes the following assumption: that the currents have a
constant mean size, as seen at their site of origin, no matter where on the dendritic tree they are elicited. This is equivalent to supposing that all excitatory synapses, wherever they are located, possess similar amounts of the same kind of receptor. This seems reasonable, and is also supported by studies of synaptic currents in these cultures (Bekkers and Stevens, unpublished). Local solution application now becomes equivalent to the local injection of a known current, equal to the mean mini EPSC amplitude, at known places on the cell, allowing direct estimation of dendritic cable properties. Examples of hypertonic solution-evoked mini EPSCs are shown in Fig. 1. Panel A shows a train of mini EPSCs recorded at the soma when applying the solution close to the soma, i.e. when cable distortion is minimal. The currents vary markedly in size - we think this is mainly due to a distribuA
B 90pm
L
c J 170 $m
50 PA
50 ms
Fig. 1. Miniature EPSCs elicited by the application of hypertonic solution at the soma (A) and at the indicated distances from the soma down a dendrite (B,C). The soma was voltage clamped at - 70 mV; the patch electrode contained CsCI. The hypertonic solution was bath solution (standard mammalian Ringers) plus 0.5 M sucrose, and was applied in short bursts from a puffer pipette and removed via a nearby suction pipette, localizing its flow to a narrow (20 - 30 pm) plume.
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tion in the sizes of presynaptic vesicles at one or a few synapses - but their shapes are similar. Panels B and C show mini EPSCs recorded when the solution is applied on the same dendrite but at 90 pm and 170 pm, respectively, from the soma. The currents now look much smaller and slower, and this is, by the above assumption, entirely due to the cable distortion of the dendrite. The traces in Fig. 1 thus show directly what current the cell body “sees” when a presynaptic impulse arrives at a synapse located proximally (panel A) or increasingly distally (panels B and C). A preliminary analysis of data like these was done as follows. The patch pipette contained, in addition to the usual electrolyte solution, a fluorescent dye (Lucifer yellow) that allowed us to measure accurately the lengths and diameters of all the dendrites of the cell. Usually we applied the hypertonic solution to a dendrite that extended for a couple of hundred microns from the soma without branching or tapering significantly (total dendritic length was typically 300 - 600 pm); thus, to a first approximation the dendrite could be treated as a semi-infinite cable with the diameter we measured (Rall, 1962). The decrement of voltage (DC) along such a cable, when a constant voltage Vo is applied at the sealed end, is given by V(x) = Voexp( -xA) where x is distance and X is the DC length constant. It can be shown that the time integral of current reaching the sealed end (or soma) from distance x (i.e. the charge transfer) behaves the same as V(x). Thus, the DC length constant can be extracted from our voltage clamp data by integrating the currents evoked at different distances along the dendrite and fitting an exponential to a plot of this charge versus distance. Results are shown in Fig. 2A for 3 different cells. The vertical axis is charge transfer to the soma normalized to the mean charge measured from synapses located on the soma. (Each open symbol represents an average of 60-100 individual integrated currents.) Note the logarithmic scale. The horizontal axis is distance from the soma at which the minis were elicited, normalized to a dendrite diameter of 1 pm (because X depends
Charge
A
L , 100
5
0.1
2
0
200
300
Normolized distance from soma
0
Peak current
0
100
200
300
Normalized distance from soma
Fig. 2. Dependence of charge transfer to the soma (A) and peak current at the soma (B) on distance between the soma and the point on the dendrite at which current was injected using the hypertonic solution technique described in the text. Actual distances have been normalized to equivalent distances for a 1pm-diameter dendrite. Data are from 3 different cells and each of the 3 symbol types refers to one of the 3 neurons.
on diameter; see later on). Data from 3 cells are shown, with actual dendrite diameters of 0.5 pm, 1 pm and 1.9 pm. The straight line is fitted by eye and gives X = 1000 pm for a 1 pm diameter dendrite. Also shown in the figure (filled symbols) are the same data analyzed in a slightly different way: the transfer function for a semi-infinite cable was used to calculate the expected distortion of mini EPSCs elicited at different distances, and X was varied for each cell until the calculated and measured currents looked similar. The agreement between the two methods was good, supporting the validity of the semi-infinite cable approximation. Fig. 2B shows data from the same 3 cells as in Fig. 2A except that instead of charge transfer, the peak mini current is plotted against normalized distance to the injection site. It can immediately be
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noted that the peak of the current seen at the soma falls off much more rapidly with distance than does the charge transfer. The transient length constant estimated from these data (from the slope of the straight line in the figure) is about 170 pm for the unit diameter dendrite. Note that the transient length constant, although a useful descriptive term, is not a true constant. It depends on the temporal form of the input signal, and changes (becomes smaller) as distance from the synapse is increased. The technique used above causes single quanta of neurotransmitter to be released and permits us to produce releases close to the recording site. This means that we can, in the same experiments, measure the depolarization produced by a single quantum of transmitter, the smallest effect that a synapse can have on its target neuron. We find that the mean mini EPSP amplitude is about 2 mV for releases induced close to the soma although mini amplitudes can sometimes exceed 10 mV. Since the average number of quanta released at hippocampal synapses is unknown, we cannot estimate the effect of a single impulse arrival on a hippocampal pyramidal cell. Nevertheless, we note that the depolarization caused by a single quantum is at least an order of magnitude larger than reported in spinal motoneurons (Kuno, 1964; Edwards et al., 1976; Jack et al., 1981), and that the coincident release of only a few quanta would be sufficient to cause the cell to fire. We also note that our minis are somewhat larger than those reported by Sayer et al. (1989); this discrepancy may result from differences between cultured neurons and those in slices, or from the fact that the intracellular electrodes cause a larger shunt conductance than do patch electrodes. In summary, these results show directly the effects of cable distortion on physiological inputs at varying distances out on a dendrite. In particular, they emphasize that different features of synaptic transmission are affected differently by this distortion: charge transfer to the soma is attenuated much less significantly than is peak current.
How might a neuron scale? For convenience in discussion, we will take the neurons in an animal with a particular size as a reference, and refer to these neurons as “standard”; we take the cat as our reference and will compare human neurons to this standard. Thus, we will note, for example, that human dentate granule cells have dendrites that are about three and a half times the standard length, and that mouse granule cells would be smaller than standard. As discussed in the preceding section, distal inputs into a cortical neuron’s dendritic tree can be quite strikingly attenuated. If the length of a standard dendrite were doubled, the effect on inputs to the distal third, say, would be comparatively smaller than in the standard dendrite if the dendritic diameter were unchanged. In order to have some guidance as to what morphological characteristics to examine in neurons of different sizes, we start with a theoretical treatment of how a neuron might be scaled up in such a way as to preserve its passive electrical properties. We assume for simplicity that the neuron’s dendritic tree can be treated as being constructed of nontapering cylinders with uniform membrane properties and intracellular resistivity, and that the resistance of the extracellular space can be neglected. The obvious way to keep peripheral and distal inputs in balance as a neuron is made larger is to increase the dendritic diameter so that the length of the neuron’s dendritic cable remains the same as the standard. The DC length constant for a cable is (see Rall, 1962): A =
J””4r
where R is the membrane resistance (Q . cm2), d is the dendrite diameter, and r is the resistivity of the cm). In our cultured dendritic cytoplasm (Q neurons, we found the length constant to be about
-
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1 mm for d = 1 pm. If a neuron is magnified from the standard by a factor m, the length constant must also be magnified by m to keep the electrotonic length of the dendrites unchanged. The new length constant is related to the standard one by X = mX,
(2)
The new dendritic diameter d must then be related to the standard diameter d, by the relation (which arises by substituting equation 1 for 2 with the appropriate subscripts)
dd
=
mdd, or d
=
m2d,
(3)
Thus, dendritic diameters must scale like the square of the magnification factor. For example, if a particular neuron is twice as large as the standard, it must have dendrites that have 4 times the standard diameter (not twice) for the entire neuron to have the same electrotonic length and thus achieve the same balance between distal and proximal inputs. When a neuron has dendrites with increased diameter, however, it has a much greater surface area, and a correspondingly lower input resistance. This means that each synapse providing a standard amount of current would have a smaller effect on a magnified neuron than it would on the standard neuron. More specifically, the input resistance of a cable varies in proportion to the length constant and inversely as the dendritic diameter squared (see equation 3.06 of Rall, 1977). When a neuron’s linear dimensions are magnified by a factor m and the dendritic diameters by m2, the input resistance therefore varies inversely with m3. For a particular synapse to have the same effect in the magnified neuron, then, it must provide current that is m3 times larger than the standard. For example, a neuron that has twice the linear dimensions as standard with 4 times the dendritic diameter (to have a standard electrotonic length for its dendritic
tree) would require 8 times the strength of each synapse in order for the synapses to cause a standard depolarization. The required m3-fold increase in effectiveness could be achieved in two ways. First, each synapse could have a sufficiently increased conductance to provide the required current. Since the synapses in large and small brains seem about the same size, this possibility seems unlikely. Alternatively, each synapse could be functionally duplicated m3-fold times. In the example given above where m = 2, each synaptic type could be represented 8 times as often on the cell dendrites. When a neuron’s linear dimensions are increased by m and its dendritic diameters increased by m2, the surface area increases by the product m3. Thus, if dendrites had a constant number of synapses per unit surface area, the required functional increase in synaptic current could be achieved by appropriate reduplication of contacts. We shall term magnification of this sort longitudinal dimensions (that is, dendritic lengths) magnified by m and dendritic diameters by m2 conservative scaling because the dendritic cable properties and receptive surface area vary jointly in a way that could leave the neuron’s integrative electrical properties unchanged. Note that, because the cable equation can be written in terms of length constant and time constant units, all passive electrical properties of a neuron are unchanged by conservative scaling. One way a brain could increase the size of its neurons and leave them functionally unchanged, then, is by conservative scaling. Other alternatives are more difficult to evaluate. For example, membrane properties could in principle be altered, or synaptic patterns on a neuron’s dendrites could perhaps be rearranged in a way to achieve the same end. The preceding theory has indicated one way a neuron can deal with the problems that arise when it is magnified, and we now know which morphological characteristic to measure to determine the extent to which conservative scaling is used.
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How do neurons scale? The human hippocampus has about 5 times as many neurons as the cat's (Seress, 1988). Are hippocampal neurons magnified when the hippocampal size is increased? Measurements of cat dentate gyrus show that the dendritic layer is about 155 pm thick whereas comparable measurements on human hippocampus give a value of 540 pm; the dendritic layer in human is thus about 3.5 times 'thicker, suggesting that the dendrites are 3 - 4 times longer in humans. For the CA1 region, the cat dendritic layer averaged about 440 pm while that for the human, in a comparable region, was about 610 pm, a ratio of about one and a third. Clearly, then, human hippocampal neurons are larger than those in cat with the disparity being considerably greater for dentate granule cells than for CA1 pyramidal neurons. The magnification factor rn used in the preceding section cannot, however, be estimated simply from the dendritic layer thickness. Because dendrites do not run normal to the cortical surface but rather at an angle, a dendrite that traversed the entire dendritic layer of a cortex would have a length increased by a further factor of l/cos(A) where A is the angle relative to the surface. We therefore have compared the longitudinal and lateral extent of cat and human dendritic trees in Golgi - Cox preparations. The forms of dentate granule cells are strikingly similar in the two species and, in fact, the human cells are, in terms of dendritic length, simply magnified versions of the cat neurons so that the magnification factor, in fact, can be obtained directly from the dendritic layer thickness. For the dentate, the dendrites of both species fit in a cone with an angle at its apex of approximately 90". The similarity of granule cell forms in cat and human is well illustrated by the very typical examples shown superimposed in Fig. 3. Pyramidal cells have dendritic trees with more complex forms, but here again one is struck by the great similarity in shapes. For both species, the
apical dendrites mostly fit in a cone with an apical angle of about 65", and most basal dendrites are contained in a cone characterized by a 75" angle (although a few dendrites stray outside their cones in both cases). In summary, then, both human dentate granule cells and pyramidal neurons have the same form as the corresponding cells in the cat but are magnified 3.5 and 1.4 times respectively. Because dendrites vary considerably in diameter, a complete comparison of the diameters between cat and human is quite difficult. If the neurons investigated here scaled conservatively, the human granule cells should have dendritic diameters 3 .52 = 12.3 times larger than the cat, and the human pyramidal neurons should have dendritic diameters 1.42 = 2 times larger than the cat. Since the expected effects are rather large, we adopted a simpler approach: for all of the cell types, the diameters of a population of dendrites were measured at a point in the dendritic layer that is one half the entire extent of the dendritic length. This approach avoids the complete reconstruction of a large number of neurons and provides a preliminary quantitative test of the hypothesis that
Fig. 3. A typical cat dentate granule cell drawn (dotted) superimposed on a corresponding human neuron. Note that many of the human neuron dendrites are truncated because they have left the plane of the section. Scale bar = 0.1 mm.
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a particular neuronal class scales conservatively. For the human granule cells the dendritic diameter at half tree averaged 0.89 pm k 0.06 pm (mean 2 S.E.M.) whereas for the cat it was 0.79 pm f 0.05 pm. Although these measurements are subject to many errors, the human dendritic diameters clearly were not appreciably different from those in the cat, and certainly nothing like the twelve-fold ratio of diameters required by conservative scaling. We conclude, then, that dentate granule cells have much longer dendrites in the large human brain than in the small cat brain, but that the dendritic diameters are not different in the two cases. This conclusion is immediately obvious from an examination of the Golgi - Cox preparations. Although the human CA1 pyramids had (in the areas compared) dendrites that were only 40% longer than those in the cat, the dendritic diameters at half tree were very different in the two cases: 1.6 pm k 0.17 pm (mean k S.E.M.) for human and 0.64 pm f 0.02 pm for cat. If these neurons scaled conservatively the cat neurons should have half the diameter of the human neurons as indicated above. Thus conservative scaling predicts the cat dendritic diameter half way out the dendritic tree should be 0.78 pm f 0.12 pm whereas the observed diameter is 0.64 pm f 0.02 pm; clearly the observed dendritic diameters are not significantly different from the conservation scaling predictions. Again, the h u m a d c a t difference is immediately apparent from the histological sections. CA1 pyramids seem, then, to conform to the expectations of conservative scaling. Although we have not made measurements on CA3 pyramids or on the pyramidal neurons of the subiculum, they appear, on inspection, to follow conservative scaling. Functional implications
To summarize briefly: hippocampal pyramidal cells (in culture) have a DC length constant of about 1 mm for a 1-pm-diameter dendrite, but a transient length constant about 5 times smaller. A
single quantum of transmitter produces a mean depolarization, at the site of origin, of about 2 mV, a value more than an order of magnitude greater than that reported for spinal motoneurons. The hippocampal pyramidal neurons scale conservatively, but neighboring dentate granule cells do not. What can these observations mean? If synaptic inputs to a neuron are unstratified, or if the stratification of inputs is of no particular functional importance (although it may have developmental significance, for example), then maintaining the precise balance between inputs that are proximal and those that are distal on the dendritic tree may not be necessary for the circuits to function properly. Here, simply the net input may be what is significant, so conservative scaling would not be needed. Dentate granule cells perhaps are of this type. Alternatively, if keeping the various proximal and distal inputs equivalent in their influence on the neuron’s output is required for the circuits to function properly, then conservative scaling would be appropriate. An interesting feature of hippocampal neuronal function is that a single quantum of transmitter can have such a large effect on the membrane potential. As noted above, quanta1 size in the central nervous system seems to vary quite considerably, so that some individual quanta can approach the size necessary to fire a neuron single-handedly. In cases where the weights of specific inputs can be so important - in contradistinction to spinal motoneurons where individual synaptic events play little role in determining neuronal firing - keeping a balance between the various inputs assumes increased importance. Since our hippocampal pyramidal neurons seem to have outputs that can be determined by only a few inputs, we suggest that they must scale conservatively for just this reason. Thus, hippocampal pyramidal cells may well need to use conservative scaling to maintain the effectiveness of distal inputs since each individual synapse can be significant in determining the neuron’s output. We would suggest, then, that neurons like the dentate granule cells, which do not
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scale conservatively, effectively integrate synaptic currents and depend less on the synchronous activation of spike generation by only a few inputs. It will be interesting to investigate the electrophysiological properties of dentate neurons. We propose that conservative scaling is used by neurons in which a balance between distal and proximal inputs must be maintained as neuronal size is altered and particularly when neuronal output is determined by the synchronous activation of only a few inputs. Alternatively, neurons whose outputs depend just on the net synaptic activation with little importance attached to the source of individual inputs need not scale conservatively. Hippocampal pyramidal neurons in the CA1 field would be an example in the first category and dentate granule cells in the second. If this proposal is correct, then considerable information about how a neuron behaves can be deduced from how evolution changes its size.
References Altman, P.L. and Dittmer, D.S. (Eds.) (1961) Blood and Other Body Fluids. Federation of American Societies for Experimental Biology, Bethesda, MD. Andersen, P., Blackstad, T.W. and Lomo, T. (1966) Location and identification of excitatory synapses on hippocampal pyramidal cells. Exp. Brain Rex, 1: 236-248. Bekkers, J.M. and Stevens, C.F. (1989) NMDA and nonNMDA receptors are colocalized at individual excitatory synapses in cultured rat hippocampus. Nature (Lond.), 341 : 230-233. Blackstad, T.W. (1956) Commissural connections of the hippocampus of the rat, with special reference to their mode of termination. J. Comp. Neurol., 105: 417 - 538. Blackstad, T.W. (1975) Electron microscopy of experimental axonal degeneration in photochemically modified Golgi preparations: a procedure for precise mapping of nervous
connections. Brain Res., 95: 191 - 210. Blackstad, T.W., Brink, K., Hem, J. and Jeune, B. (1970) Distribution of hippocampal mossy fibers in the rat. An experimental study with silver impregnation methods. J. Comp. Neurol., 138: 433 -449. Bok, S.T. (1959) Histonomy of the Cerebral Cortex. Elsevier, Amsterdam. Edwards, F.R., Redman, S.J. and Walmsley, B. (1976) Statistical fluctuations in charge transfer at Ia synapses on spinal motoneurones. J. Physiol. (Lond.), 259: 665 - 688. Fatt, P. and Katz, B. (1952) Spontaneous subthreshold activity at motor nerve endings. J . Physiol. (Lond.), 117: 109- 128. Hardesty, I . (1902) Observations on the medulla spinalis of the elephant with some comparative studies of the intumescentia cervicalis and the neurones of the columna anterior. J. Comp. Neurol., 12: 125 - 182. Jack, J.J.B., Redman, S.J. and Wong, K. (1981) The components of synaptic potentials evoked in cat spinal motoneurones by impulses in single group Ia fibres. J . Physiol. (Lond.), 321: 65 - 96. Jahr, C.E. and Stevens, C.F. (1987) Glutamate activates multiple single channel conductances in hippocampal neurons. Nature (Lond.), 325: No. 6104, 522-525. Kuno, M. (1964) Quanta1 components of excitatory potentials in spinal motoneurones. 1.Physiol. (Lond.), 175: 81 - 99. Rall, W. (1962)Theory of physiological properties of dendrites. Ann. N . Y . Acad. Sci., 96: 1071-1092. Rall, W. (1977) Core conductor theory and cable properties of neurons. In J.M.Brookhart and V.B. Mountcastle (Eds.), Handbook of Physiology. The Nervous System, Cellular Biology of Neurons, Vol. I , Part I , Am. Physiol. SOC., Bethesda, MD, pp. 39- 97. Sayer, R.J., Redman, S.J. and Andersen, P . (1989) Amplitude fluctuations in small EPSPs recorded from CAI pyramidal cells in the guinea pig hippocampal slice. J. Neurosci., 9: 840 - 850. Seress, L. (1988) Interspecies comparison of the hippocampal formation shows increased emphasis on the Regio superior in the Ammon’s horn of the human brain. J. Hirnforsch., 29: 335 - 340. Stevens, C.F. (1989) How cortical interconnectedness varies with network size. Neural Computation, 1: 473 - 479. Teissier, G. (1939) Biometrie de la cellule. Tabulae Biol., 19: 1-64.
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CHAPTER 3
*
Two different ways evolution makes neurons larger John M. Bekkers and Charles F. Stevens* Section of Molecular Neurobiology, Howard Hughes Medical Institute at Yale University School of Medicine, 333 Cedar Street, New Haven, CT 06510, U.S.A.
As evolution makes larger brains it also increases the size of many of the individual neurons that make up the brain. How neurons are made larger can give clues about design principles of the brain’s circuits. One way of making a larger neuron is called conservative scaling. If evolution magnifies a particular type of neuron by a factor of two - that is, each dendrite is made twice as long - then the neuron is scaled conservatively if the magnified neuron has dendrites with 4 times the diameter of their unscaled counterparts. This type of scaling leaves the passive cable properties of the neuron unchanged and so maintains a balance in effectiveness between proximal and distal dendritic inputs. One might imagine that, for some types of circuits, maintaining such a balance would be necessary to use just the same neuronal interconnections in both large and small brains. We have compared dentate granule cells and CAI pyramidal neurons in cat and human to establish how these cell types are, in fact, scaled. Both cell types are larger in human than in cat, even though their general form is conserved. Pyramidal neurons scale conservatively, but dentate granule cells do not. The CAI circuits seem, then, to require conservation of the passive cable properties of their elements, whereas dentate does not. We suggest that the reason CAI neurons scale conservatively is that, for this region, each individual synaptic input exerts a significant effect on the cell’s output, whereas in dentate the neuronal output represents the average of a large number of anonymous individual inputs.
Introduction The brains of mammals, from pigmy tree shrew to man, range in size over about 4 orders of magnitude. Although the various mammalian brains have greatly different capabilities, most workers nevertheless believe they all conform to a generally uniform design; this belief is the basis for comparative neuroanatomy, and provides the justification for using, for example, rat or cat brains as models in neurobiological experiments intended to enlighten us about the workings of the human nervous system. To make any computational machine, including a brain, a thousand times larger is a difficult task, and the way this magnification is achieved can give some clues about the underlying principles used for designing
* Present address: C.F. Stevens, The Salk Institute, 10010 North Torrey Pines Road, La Jolla, CA 92037, U.S.A.
the computing circuitry. The goal of this chapter is to explore one aspect of this scaling problem related to altered cable properties in neurons that are magnified. Some background information will be necessary before we can give a precise statement of the problem we wish to investigate. As brains grow in size, so do the nerve cells of which they are composed (Hardesty, 1902; Bok, 1959). The brain is unu‘sual in this regard because the cells used to construct other organs - liver or gut, for example - d o no differ very much in size between small and large animals (Teissier, 1939; Altman and Dittmer, 1961). The cell bodies of spinal motoneurons have about half the diameter in a small animal like a mouse than they have in man, and cortical neurons generally differ by about the same amount. In fact, the thickness of the cerebral cortex varies approximately as the 0.1 power of the cortical surface area (Stevens, 1989) so that if one brain is a thousand times larger than
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another (mouse to man), its cortFx is twice as thick and the corresponding neurons have dendritic trees that are double in length. Why do large brains have larger neurons? One likely explanation is that the increase in cell body size reflects the need for a larger biosynthetic capacity to maintain the larger axonal tree that must reach over longer distances. This presumably is at least part of the reason why spinal motoneurons and Betz cells are so large compared to other neurons in the same brain. Why then must cortical neurons have longer dendritic trees? The answer here is perhaps that the cortex must be thicker to accommodate larger and more rapidly conducting axons that communicate over greater distances in the large brain. Different parts of a neuron’s dendritic tree commonly have quite specific inputs (see, for example: Blackstad, 1956; Andersen et al., 1966; Blackstad et al., 1970; Blackstad, 1975). The most distal part, for example, might receive information from one brain region and the more proximal parts from another. The distal information is somewhat more attenuated by the neuron’s cable properties than that arriving over proximal inputs. A particular distal synapse might, for example, have half the effect at the soma of a proximal synapse. In this case, if one neuron has a dendritic tree that is twice as long as that of another, and if the dendrites had the same diameters in both cases, then the distal input in the larger neuron would have only one fourth the effect of a proximal synapse. The relative influence of proximal and distal synapses, then, might be quite different for large and small neurons, and this difference could be of great functional significance if the circuitry assumed a particular balance between the influences of nearby and distant synapses. Thus larger brains must, whenever inputs are stratified as they generally are in cortex, deal with the problem of maintaining a constant balance between distal and proximal inputs. We wish to investigate theoretically and experimentally this scaling problem. Our goal, then, is to ask how neurons differ between small and large brains, to estimate how significant cable at-
tenuation of distal signals is likely to be in particular classes of neuron, to propose several ways the brain might deal with the problem of keeping proximal and distal inputs in balance, and to ask which methods are used in fact. Our preliminary observations suggest that different classes of neurons deal with the size problem in different ways, and this in turn indicates that the various parts of the brain may not have just the same organizational principles. The following discussion is organized in 4 parts. In the first part we present experimental data, gathered in a new way, that provides estimates of the cable characteristics of hippocampal neurons, and also presents measurements on the magnitude of depolarization produced by a single quantum of neurotransmitter. These data will highlight the implications of dendritic cable properties for neuronal function and provide the physiological basis for the consideration of morphological features that follows. The second part presents a theoretical analysis of the functional implications of making a neuron larger and develops the concept of “conservative scaling”, a set of rules according to which a larger neuron would be electrically equivalent to a smaller one of the same shape. This section is needed to indicate what morphological features of a dendritic tree must be measured to gain insight into the functional implications of neuronal size changes. The third section gives some preliminary measurements that indicate what rules neurons actually follow when they are enlarged by evolution. We will conclude that not all neurons follow the same rules. In the final section we speculate on the implication of our observations for neuronal function. We shall suggest that the rules a neuron follows in being evolutionarily enlarged may give clues to differences in function. We have chosen the hippocampus as a model system in which to investigate these questions because of its importance and simple structure. We shall consider neuronal properties in the dentate granule cells and pyramidal cells of the CA1 region in cat and human.
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Attenuation of synaptic signals by dendrites This section will present some preliminary data on the cable properties of hippocampal pyramidal cells in tissue culture. These results were obtained using a technique that should make immediately clear the issues in cable attenuation of synaptic signals. In particular, we will- show directly the dramatic effect of cable filtering when a synaptic current is injected far out on the dendritic tree. Briefly, the experimental procedure was as follows. Pyramidal cells from the CA1 and CA3 fields of the hippocampi of neonatal rats were maintained in culture for up to 3 weeks using the methods described by Jahr and Stevens (1987). The cell density was sufficiently low that the dendritic field of each cell could be traced without much ambiguity, i.e. cells were separated, on average, by several hundred microns. Membrane currents were measured from a cell via a patch electrode, sealed onto the cell body, in the whole-cell configuration as described by Bekkers and Stevens (1989). The objective was to inject a known current at different places on the dendritic tree and measure the cabledistorted form of it that reached the soma. This was done using a trick suggested by a finding made at the neuromuscular junction: Fatt and Katz (1952) showed that applying hypertonic solutions increased the frequency of miniature endplate potentials, an effect possibly due to osmotic shrinkage causing asynchronous exocytosis of presynaptic, neurotransmitter-loaded vesicles. We found that a similar process occurred in our culture system. When we applied a narrow stream of hypertonic solution to a place close to the voltage-clamped soma of a pyramidal cell, we usually observed a sudden increase in small, rapid currents. We have shown elsewhere that these currents are evoked local to the flow of solution, and have all the features of miniature excitatory postsynaptic currents (“mini EPSCs”) (Bekkers and Stevens, 1989). Use can be made of these solution-evoked currents to study cable properties if one makes the following assumption: that the currents have a
constant mean size, as seen at their site of origin, no matter where on the dendritic tree they are elicited. This is equivalent to supposing that all excitatory synapses, wherever they are located, possess similar amounts of the same kind of receptor. This seems reasonable, and is also supported by studies of synaptic currents in these cultures (Bekkers and Stevens, unpublished). Local solution application now becomes equivalent to the local injection of a known current, equal to the mean mini EPSC amplitude, at known places on the cell, allowing direct estimation of dendritic cable properties. Examples of hypertonic solution-evoked mini EPSCs are shown in Fig. 1. Panel A shows a train of mini EPSCs recorded at the soma when applying the solution close to the soma, i.e. when cable distortion is minimal. The currents vary markedly in size - we think this is mainly due to a distribuA
B 90pm
L
c J 170 $m
50 PA
50 ms
Fig. 1. Miniature EPSCs elicited by the application of hypertonic solution at the soma (A) and at the indicated distances from the soma down a dendrite (B,C). The soma was voltage clamped at - 70 mV; the patch electrode contained CsCI. The hypertonic solution was bath solution (standard mammalian Ringers) plus 0.5 M sucrose, and was applied in short bursts from a puffer pipette and removed via a nearby suction pipette, localizing its flow to a narrow (20 - 30 pm) plume.
40
tion in the sizes of presynaptic vesicles at one or a few synapses - but their shapes are similar. Panels B and C show mini EPSCs recorded when the solution is applied on the same dendrite but at 90 pm and 170 pm, respectively, from the soma. The currents now look much smaller and slower, and this is, by the above assumption, entirely due to the cable distortion of the dendrite. The traces in Fig. 1 thus show directly what current the cell body “sees” when a presynaptic impulse arrives at a synapse located proximally (panel A) or increasingly distally (panels B and C). A preliminary analysis of data like these was done as follows. The patch pipette contained, in addition to the usual electrolyte solution, a fluorescent dye (Lucifer yellow) that allowed us to measure accurately the lengths and diameters of all the dendrites of the cell. Usually we applied the hypertonic solution to a dendrite that extended for a couple of hundred microns from the soma without branching or tapering significantly (total dendritic length was typically 300 - 600 pm); thus, to a first approximation the dendrite could be treated as a semi-infinite cable with the diameter we measured (Rall, 1962). The decrement of voltage (DC) along such a cable, when a constant voltage Vo is applied at the sealed end, is given by V(x) = Voexp( -xA) where x is distance and X is the DC length constant. It can be shown that the time integral of current reaching the sealed end (or soma) from distance x (i.e. the charge transfer) behaves the same as V(x). Thus, the DC length constant can be extracted from our voltage clamp data by integrating the currents evoked at different distances along the dendrite and fitting an exponential to a plot of this charge versus distance. Results are shown in Fig. 2A for 3 different cells. The vertical axis is charge transfer to the soma normalized to the mean charge measured from synapses located on the soma. (Each open symbol represents an average of 60-100 individual integrated currents.) Note the logarithmic scale. The horizontal axis is distance from the soma at which the minis were elicited, normalized to a dendrite diameter of 1 pm (because X depends
Charge
A
L , 100
5
0.1
2
0
200
300
Normolized distance from soma
0
Peak current
0
100
200
300
Normalized distance from soma
Fig. 2. Dependence of charge transfer to the soma (A) and peak current at the soma (B) on distance between the soma and the point on the dendrite at which current was injected using the hypertonic solution technique described in the text. Actual distances have been normalized to equivalent distances for a 1pm-diameter dendrite. Data are from 3 different cells and each of the 3 symbol types refers to one of the 3 neurons.
on diameter; see later on). Data from 3 cells are shown, with actual dendrite diameters of 0.5 pm, 1 pm and 1.9 pm. The straight line is fitted by eye and gives X = 1000 pm for a 1 pm diameter dendrite. Also shown in the figure (filled symbols) are the same data analyzed in a slightly different way: the transfer function for a semi-infinite cable was used to calculate the expected distortion of mini EPSCs elicited at different distances, and X was varied for each cell until the calculated and measured currents looked similar. The agreement between the two methods was good, supporting the validity of the semi-infinite cable approximation. Fig. 2B shows data from the same 3 cells as in Fig. 2A except that instead of charge transfer, the peak mini current is plotted against normalized distance to the injection site. It can immediately be
41
noted that the peak of the current seen at the soma falls off much more rapidly with distance than does the charge transfer. The transient length constant estimated from these data (from the slope of the straight line in the figure) is about 170 pm for the unit diameter dendrite. Note that the transient length constant, although a useful descriptive term, is not a true constant. It depends on the temporal form of the input signal, and changes (becomes smaller) as distance from the synapse is increased. The technique used above causes single quanta of neurotransmitter to be released and permits us to produce releases close to the recording site. This means that we can, in the same experiments, measure the depolarization produced by a single quantum of transmitter, the smallest effect that a synapse can have on its target neuron. We find that the mean mini EPSP amplitude is about 2 mV for releases induced close to the soma although mini amplitudes can sometimes exceed 10 mV. Since the average number of quanta released at hippocampal synapses is unknown, we cannot estimate the effect of a single impulse arrival on a hippocampal pyramidal cell. Nevertheless, we note that the depolarization caused by a single quantum is at least an order of magnitude larger than reported in spinal motoneurons (Kuno, 1964; Edwards et al., 1976; Jack et al., 1981), and that the coincident release of only a few quanta would be sufficient to cause the cell to fire. We also note that our minis are somewhat larger than those reported by Sayer et al. (1989); this discrepancy may result from differences between cultured neurons and those in slices, or from the fact that the intracellular electrodes cause a larger shunt conductance than do patch electrodes. In summary, these results show directly the effects of cable distortion on physiological inputs at varying distances out on a dendrite. In particular, they emphasize that different features of synaptic transmission are affected differently by this distortion: charge transfer to the soma is attenuated much less significantly than is peak current.
How might a neuron scale? For convenience in discussion, we will take the neurons in an animal with a particular size as a reference, and refer to these neurons as “standard”; we take the cat as our reference and will compare human neurons to this standard. Thus, we will note, for example, that human dentate granule cells have dendrites that are about three and a half times the standard length, and that mouse granule cells would be smaller than standard. As discussed in the preceding section, distal inputs into a cortical neuron’s dendritic tree can be quite strikingly attenuated. If the length of a standard dendrite were doubled, the effect on inputs to the distal third, say, would be comparatively smaller than in the standard dendrite if the dendritic diameter were unchanged. In order to have some guidance as to what morphological characteristics to examine in neurons of different sizes, we start with a theoretical treatment of how a neuron might be scaled up in such a way as to preserve its passive electrical properties. We assume for simplicity that the neuron’s dendritic tree can be treated as being constructed of nontapering cylinders with uniform membrane properties and intracellular resistivity, and that the resistance of the extracellular space can be neglected. The obvious way to keep peripheral and distal inputs in balance as a neuron is made larger is to increase the dendritic diameter so that the length of the neuron’s dendritic cable remains the same as the standard. The DC length constant for a cable is (see Rall, 1962): A =
J””4r
where R is the membrane resistance (Q . cm2), d is the dendrite diameter, and r is the resistivity of the cm). In our cultured dendritic cytoplasm (Q neurons, we found the length constant to be about
-
42
1 mm for d = 1 pm. If a neuron is magnified from the standard by a factor m, the length constant must also be magnified by m to keep the electrotonic length of the dendrites unchanged. The new length constant is related to the standard one by X = mX,
(2)
The new dendritic diameter d must then be related to the standard diameter d, by the relation (which arises by substituting equation 1 for 2 with the appropriate subscripts)
dd
=
mdd, or d
=
m2d,
(3)
Thus, dendritic diameters must scale like the square of the magnification factor. For example, if a particular neuron is twice as large as the standard, it must have dendrites that have 4 times the standard diameter (not twice) for the entire neuron to have the same electrotonic length and thus achieve the same balance between distal and proximal inputs. When a neuron has dendrites with increased diameter, however, it has a much greater surface area, and a correspondingly lower input resistance. This means that each synapse providing a standard amount of current would have a smaller effect on a magnified neuron than it would on the standard neuron. More specifically, the input resistance of a cable varies in proportion to the length constant and inversely as the dendritic diameter squared (see equation 3.06 of Rall, 1977). When a neuron’s linear dimensions are magnified by a factor m and the dendritic diameters by m2, the input resistance therefore varies inversely with m3. For a particular synapse to have the same effect in the magnified neuron, then, it must provide current that is m3 times larger than the standard. For example, a neuron that has twice the linear dimensions as standard with 4 times the dendritic diameter (to have a standard electrotonic length for its dendritic
tree) would require 8 times the strength of each synapse in order for the synapses to cause a standard depolarization. The required m3-fold increase in effectiveness could be achieved in two ways. First, each synapse could have a sufficiently increased conductance to provide the required current. Since the synapses in large and small brains seem about the same size, this possibility seems unlikely. Alternatively, each synapse could be functionally duplicated m3-fold times. In the example given above where m = 2, each synaptic type could be represented 8 times as often on the cell dendrites. When a neuron’s linear dimensions are increased by m and its dendritic diameters increased by m2, the surface area increases by the product m3. Thus, if dendrites had a constant number of synapses per unit surface area, the required functional increase in synaptic current could be achieved by appropriate reduplication of contacts. We shall term magnification of this sort longitudinal dimensions (that is, dendritic lengths) magnified by m and dendritic diameters by m2 conservative scaling because the dendritic cable properties and receptive surface area vary jointly in a way that could leave the neuron’s integrative electrical properties unchanged. Note that, because the cable equation can be written in terms of length constant and time constant units, all passive electrical properties of a neuron are unchanged by conservative scaling. One way a brain could increase the size of its neurons and leave them functionally unchanged, then, is by conservative scaling. Other alternatives are more difficult to evaluate. For example, membrane properties could in principle be altered, or synaptic patterns on a neuron’s dendrites could perhaps be rearranged in a way to achieve the same end. The preceding theory has indicated one way a neuron can deal with the problems that arise when it is magnified, and we now know which morphological characteristic to measure to determine the extent to which conservative scaling is used.
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How do neurons scale? The human hippocampus has about 5 times as many neurons as the cat's (Seress, 1988). Are hippocampal neurons magnified when the hippocampal size is increased? Measurements of cat dentate gyrus show that the dendritic layer is about 155 pm thick whereas comparable measurements on human hippocampus give a value of 540 pm; the dendritic layer in human is thus about 3.5 times 'thicker, suggesting that the dendrites are 3 - 4 times longer in humans. For the CA1 region, the cat dendritic layer averaged about 440 pm while that for the human, in a comparable region, was about 610 pm, a ratio of about one and a third. Clearly, then, human hippocampal neurons are larger than those in cat with the disparity being considerably greater for dentate granule cells than for CA1 pyramidal neurons. The magnification factor rn used in the preceding section cannot, however, be estimated simply from the dendritic layer thickness. Because dendrites do not run normal to the cortical surface but rather at an angle, a dendrite that traversed the entire dendritic layer of a cortex would have a length increased by a further factor of l/cos(A) where A is the angle relative to the surface. We therefore have compared the longitudinal and lateral extent of cat and human dendritic trees in Golgi - Cox preparations. The forms of dentate granule cells are strikingly similar in the two species and, in fact, the human cells are, in terms of dendritic length, simply magnified versions of the cat neurons so that the magnification factor, in fact, can be obtained directly from the dendritic layer thickness. For the dentate, the dendrites of both species fit in a cone with an angle at its apex of approximately 90". The similarity of granule cell forms in cat and human is well illustrated by the very typical examples shown superimposed in Fig. 3. Pyramidal cells have dendritic trees with more complex forms, but here again one is struck by the great similarity in shapes. For both species, the
apical dendrites mostly fit in a cone with an apical angle of about 65", and most basal dendrites are contained in a cone characterized by a 75" angle (although a few dendrites stray outside their cones in both cases). In summary, then, both human dentate granule cells and pyramidal neurons have the same form as the corresponding cells in the cat but are magnified 3.5 and 1.4 times respectively. Because dendrites vary considerably in diameter, a complete comparison of the diameters between cat and human is quite difficult. If the neurons investigated here scaled conservatively, the human granule cells should have dendritic diameters 3 .52 = 12.3 times larger than the cat, and the human pyramidal neurons should have dendritic diameters 1.42 = 2 times larger than the cat. Since the expected effects are rather large, we adopted a simpler approach: for all of the cell types, the diameters of a population of dendrites were measured at a point in the dendritic layer that is one half the entire extent of the dendritic length. This approach avoids the complete reconstruction of a large number of neurons and provides a preliminary quantitative test of the hypothesis that
Fig. 3. A typical cat dentate granule cell drawn (dotted) superimposed on a corresponding human neuron. Note that many of the human neuron dendrites are truncated because they have left the plane of the section. Scale bar = 0.1 mm.
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a particular neuronal class scales conservatively. For the human granule cells the dendritic diameter at half tree averaged 0.89 pm k 0.06 pm (mean 2 S.E.M.) whereas for the cat it was 0.79 pm f 0.05 pm. Although these measurements are subject to many errors, the human dendritic diameters clearly were not appreciably different from those in the cat, and certainly nothing like the twelve-fold ratio of diameters required by conservative scaling. We conclude, then, that dentate granule cells have much longer dendrites in the large human brain than in the small cat brain, but that the dendritic diameters are not different in the two cases. This conclusion is immediately obvious from an examination of the Golgi - Cox preparations. Although the human CA1 pyramids had (in the areas compared) dendrites that were only 40% longer than those in the cat, the dendritic diameters at half tree were very different in the two cases: 1.6 pm k 0.17 pm (mean k S.E.M.) for human and 0.64 pm f 0.02 pm for cat. If these neurons scaled conservatively the cat neurons should have half the diameter of the human neurons as indicated above. Thus conservative scaling predicts the cat dendritic diameter half way out the dendritic tree should be 0.78 pm f 0.12 pm whereas the observed diameter is 0.64 pm f 0.02 pm; clearly the observed dendritic diameters are not significantly different from the conservation scaling predictions. Again, the h u m a d c a t difference is immediately apparent from the histological sections. CA1 pyramids seem, then, to conform to the expectations of conservative scaling. Although we have not made measurements on CA3 pyramids or on the pyramidal neurons of the subiculum, they appear, on inspection, to follow conservative scaling. Functional implications
To summarize briefly: hippocampal pyramidal cells (in culture) have a DC length constant of about 1 mm for a 1-pm-diameter dendrite, but a transient length constant about 5 times smaller. A
single quantum of transmitter produces a mean depolarization, at the site of origin, of about 2 mV, a value more than an order of magnitude greater than that reported for spinal motoneurons. The hippocampal pyramidal neurons scale conservatively, but neighboring dentate granule cells do not. What can these observations mean? If synaptic inputs to a neuron are unstratified, or if the stratification of inputs is of no particular functional importance (although it may have developmental significance, for example), then maintaining the precise balance between inputs that are proximal and those that are distal on the dendritic tree may not be necessary for the circuits to function properly. Here, simply the net input may be what is significant, so conservative scaling would not be needed. Dentate granule cells perhaps are of this type. Alternatively, if keeping the various proximal and distal inputs equivalent in their influence on the neuron’s output is required for the circuits to function properly, then conservative scaling would be appropriate. An interesting feature of hippocampal neuronal function is that a single quantum of transmitter can have such a large effect on the membrane potential. As noted above, quanta1 size in the central nervous system seems to vary quite considerably, so that some individual quanta can approach the size necessary to fire a neuron single-handedly. In cases where the weights of specific inputs can be so important - in contradistinction to spinal motoneurons where individual synaptic events play little role in determining neuronal firing - keeping a balance between the various inputs assumes increased importance. Since our hippocampal pyramidal neurons seem to have outputs that can be determined by only a few inputs, we suggest that they must scale conservatively for just this reason. Thus, hippocampal pyramidal cells may well need to use conservative scaling to maintain the effectiveness of distal inputs since each individual synapse can be significant in determining the neuron’s output. We would suggest, then, that neurons like the dentate granule cells, which do not
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scale conservatively, effectively integrate synaptic currents and depend less on the synchronous activation of spike generation by only a few inputs. It will be interesting to investigate the electrophysiological properties of dentate neurons. We propose that conservative scaling is used by neurons in which a balance between distal and proximal inputs must be maintained as neuronal size is altered and particularly when neuronal output is determined by the synchronous activation of only a few inputs. Alternatively, neurons whose outputs depend just on the net synaptic activation with little importance attached to the source of individual inputs need not scale conservatively. Hippocampal pyramidal neurons in the CA1 field would be an example in the first category and dentate granule cells in the second. If this proposal is correct, then considerable information about how a neuron behaves can be deduced from how evolution changes its size.
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connections. Brain Res., 95: 191 - 210. Blackstad, T.W., Brink, K., Hem, J. and Jeune, B. (1970) Distribution of hippocampal mossy fibers in the rat. An experimental study with silver impregnation methods. J. Comp. Neurol., 138: 433 -449. Bok, S.T. (1959) Histonomy of the Cerebral Cortex. Elsevier, Amsterdam. Edwards, F.R., Redman, S.J. and Walmsley, B. (1976) Statistical fluctuations in charge transfer at Ia synapses on spinal motoneurones. J. Physiol. (Lond.), 259: 665 - 688. Fatt, P. and Katz, B. (1952) Spontaneous subthreshold activity at motor nerve endings. J . Physiol. (Lond.), 117: 109- 128. Hardesty, I . (1902) Observations on the medulla spinalis of the elephant with some comparative studies of the intumescentia cervicalis and the neurones of the columna anterior. J. Comp. Neurol., 12: 125 - 182. Jack, J.J.B., Redman, S.J. and Wong, K. (1981) The components of synaptic potentials evoked in cat spinal motoneurones by impulses in single group Ia fibres. J . Physiol. (Lond.), 321: 65 - 96. Jahr, C.E. and Stevens, C.F. (1987) Glutamate activates multiple single channel conductances in hippocampal neurons. Nature (Lond.), 325: No. 6104, 522-525. Kuno, M. (1964) Quanta1 components of excitatory potentials in spinal motoneurones. 1.Physiol. (Lond.), 175: 81 - 99. Rall, W. (1962)Theory of physiological properties of dendrites. Ann. N . Y . Acad. Sci., 96: 1071-1092. Rall, W. (1977) Core conductor theory and cable properties of neurons. In J.M.Brookhart and V.B. Mountcastle (Eds.), Handbook of Physiology. The Nervous System, Cellular Biology of Neurons, Vol. I , Part I , Am. Physiol. SOC., Bethesda, MD, pp. 39- 97. Sayer, R.J., Redman, S.J. and Andersen, P . (1989) Amplitude fluctuations in small EPSPs recorded from CAI pyramidal cells in the guinea pig hippocampal slice. J. Neurosci., 9: 840 - 850. Seress, L. (1988) Interspecies comparison of the hippocampal formation shows increased emphasis on the Regio superior in the Ammon’s horn of the human brain. J. Hirnforsch., 29: 335 - 340. Stevens, C.F. (1989) How cortical interconnectedness varies with network size. Neural Computation, 1: 473 - 479. Teissier, G. (1939) Biometrie de la cellule. Tabulae Biol., 19: 1-64.