{"title": "Network activity determines spatio-temporal integration in single cells", "book": "Advances in Neural Information Processing Systems", "page_first": 43, "page_last": 50, "abstract": null, "full_text": "Network activity determines \n\nspatio-temporal integration in single cells \n\nOjvind Bernander, Christof Koch * \n\nComputation and Neural Systems Program, \n\nCalifornia Institut.e of Technology, \n\nPasadena, Ca 91125, USA. \n\nRodney J. Douglas \n\nAnatomical Neuropharmacology Unit, \n\nDept. Pharmacology, \n\nOxford, UK. \n\nAbstract \n\nSingle nerve cells with static properties have traditionally been viewed \nas the building blocks for networks that show emergent phenomena. In \ncontrast to this approach, we study here how the overall network activity \ncan control single cell parameters such as input resistance, as well as time \nand space constants, parameters that are crucial for excitability and spatio(cid:173)\ntemporal integration. Using detailed computer simulations of neocortical \npyramidal cells, we show that the spontaneous background firing of the \nnetwork provides a means for setting these parameters. The mechanism \nfor this control is through the large conductance change of the membrane \nthat is induced by both non-NMDA and NMDA excitatory and inhibitory \nsynapses activated by the spontaneous background activity. \n\n1 \n\nINTRODUCTION \n\nBiological neurons display a complexity rarely heeded in abstract network models. \nDendritic trees allow for local interactions, attenuation, and delays. Voltage- and \n\n*To whom all correspondence should be a.ddressed. \n\n43 \n\n\f44 \n\nBernander, Koch, and Douglas \n\ntime-dependent conductances can give rise to adaptation, burst-firing, and other \nnon-linear effects. The extent of temporal integration is determined by the time \nconstant, and spatial integration by the \"leakiness\" of the membrane. It is unclear \nwhich cell properties are computationally significant and which are not relevant \nfor information processing, even though they may be important for the proper \nfunctioning of the cell. However, it is crucial to understand the function of the \ncomponent cells in order to make relevant abstractions when modeling biological \nIn this paper we study how the spontaneous background firing of the \nsystems. \nnetwork as a whole can strongly influence some of the basic integration properties \nof single cells. \n\n1.1 Controlling parameters via background synaptic activity \n\nThe input resistance, RJn, is defined as ~, where dV is the steady state voltage \nchange in response to a small current step of amplitude dI. RJn will vary throughout \nthe cell, and is typically much larger in a long, narrow dendrite than in the soma. \nHowever, the somatic input resistance is more relevant to the spiking behavior of \nthe neuron, since spikes are initiated at or close to the soma, and hence Rin,.oma \n(henceforth simply referred to as Rin) will tell us something of the sensitivity of the \ncell to charge reaching the soma. \n\nThe time constant, Tm , for a passive membrane patch is Rm . em, the membrane \nresistance times the membrane capacitance. For membranes containing voltage(cid:173)\ndependent non-linearities, exponentials are fitted to the step response and the \nlargest. time constant is taken to be the membrane time constant. A large time \nconstant implies that any injected charge leaks away very slowly, and hence the cell \nhas a longer \"memory\" of previous events. \n\nThe parameters discussed above (Rin, Tm) clearly have computational significance \nand it would be convenient to be able to chanfe them dynamically. Both depend \ndirectly on the membrane conductance G m = Jr.;' so any change in G m will change \nthe \u00b7parameters. Traditionally, however, G m has been viewed as static, so these \nparameters have also been considered static. How can we change Gm dynamically? \n\nIn traditional models, G m has two components: active (time- and voltage(cid:173)\ndependent) conductances and a passive \"leak\" conductance. Synapses are mod(cid:173)\neled as conductance changes, but if only a few are activated, the cable structure \nof the cell will hardly change at all. However, it is well known that neocortical \nneurons spike spontaneously, in the absence of sensory stimuli, at rates from 0 to \n10 Hz. Since neocortical neurons receive on the order of 5,000 to 15,000 excitatory \nsynapses (Larkman, 1991), this spontaneous firing is likely to add up to a large total \nconductance (Holmes & Woody, 1989) . This synaptic conductance becomes crucial \nif the non-synaptic conductance components are small. Recent evidence show in(cid:173)\ndeed that the non-synaptic conductances are relatively small (when the cell is not \nspiking) (Anderson et aI., 1990). Our model uses a leak Rm = 100,000 kOcm2 , \ninstead of more conventional values in the range of 2,500-10,000 kOcm2 \u2022 These \ntwo facts, high Rm and synaptic background activity, allow R in and Tm to change \nby more than ten-fold, as described below in this paper. \n\n\fNerwork activity determines spatio-temporal integration in single cells \n\n45 \n\n2 MODEL \n\nA typical layer V pyramidal cell (fig. 2) in striate cortex was filled with HRP dur(cid:173)\ning in vivo experiments in the anesthetized, adult cat (Douglas et aI., 1991). The \n3-D coordinates and diameters of the dendritic tree were measured by a computer(cid:173)\nassisted method and each branch was replaced by a single equivalent cylinder. This \nmorphological data was fed into a modified version of NEURON, an efficient sin(cid:173)\ngle cell simulator developed by Hines (1989). The dendrites were passive, while the \nsoma contained seven active conductances, underlying spike generation, adaptation, \nand slow onset for weak stimuli. The model included two sodium conductances (a \nfast spiking current and a. fJlower non-inactivating current), one calcium conduc(cid:173)\ntance, and four potassium conductances (delayed rectifier, slow 'M' and 'A' type \ncurrents, and a calcium-dependent current). The active conductances were modeled \nusing a Hodgkin-Huxley-like formalism. \nThe model used a total of 5,000 synapses. The synaptic conductance change \nin time was modeled with an alpha function, get) = \n~., ... e te- tlt.,.... 4,000 \nsynapses were fast excitatory non-NMDA or AMPA-type (tped = 1.5 msec, gpeaJ: = \n0.5 nS, EretJ = 0 mV), 500 were medium-slow inhibitory GABAA (tpe4k = \n10 msec, gpeole = 1.0 nS, EretJ = -70 mV), and 500 were slow inhibitory GABAB \n(tpeok = 40 msec, gpeok = 0.1 nS, E,.etJ = -95 mV). The excitatory synapses were \nless concentrated towards the soma, while the inhibitory ones were more so. For a \nmore detailed description of the model, see Bernander et al. (1991). \n120r------------------------------, \n\n~~-----------------------, \n\n. ., .. . \n\n100 \n\nRIn, no~NMDA \nRin, no~MDA and NMDA \n\n-\" ..... \n\n\" \n\n./ \n\ni 40 \n\n20 \n\n..... -\n----\n\n'\"-- ----\n\n60 \n\ni 140 \n\n20 \n\n2 \n\n3 \n\n4 \n\n5 \n\n6 \n\n7 \n\n2 \n\n, 3 \n\n4 \n\n5 \n\n6 \n\n7 \n\nBackground \n\nfrequency (Hz) \n\nBackground \n\nfrequency (Hz) \n\nFigure 1: Input resistance and time constant as a function of background \nfrequency. In (a), the solid line corresponds to the \"standard\" model with passive \ndendrites, while the dashed line includes active NMDA synapses as described in the \ntext. \n\n\f46 \n\nBernander, Koch, and Douglas \n\n3 RESULTS \n\n3.1 R,n and Tm change with background frequency \n\nFig. 1 illustrates what happens to ~n and Tm when the synaptic background activ(cid:173)\nities of all synaptic types are varied simultaneously. In the absence of any synaptic \ninput, ~n = 110 Mn and Tm = 80 msec. At 1 Hz background activity, on av(cid:173)\nerage 5 synaptic events are impinging on the cell every msec, contributing a total \nof 24 nS to the somatic input conductance Gin. Because of the reversal potential \nof the excitatory synapses (0 mV), the membrane potential throughout the cell is \npulled towards more depolarizing potentials, activating additional active currents. \nAlthough these trends continue as f is increased, the largest change can be observed \nbetween 0 and 2 Hz. \n\nFigure 2: Spatial integration as a function of background frequency. \n\nEach dendrite has been \"stretched\" so that its apparent length corresponds to its \nelectrotonic length. The synaptic background frequency was 0 Hz (left) and 2 Hz \n(right). The scale bar corresponds to 1 A (length constant). \n\nActivating synaptic input has two distinct effects: \nsynaptic membrane increases and the membrane is depolarized. The system can, \nat least in principle, independently control these two effects by differentially vary(cid:173)\ning the spontaneous firing frequencies of excitatory versus inhibitory inputs. Thus, \nincreasing f selectively for the GABAB inhibition will further increase the mem(cid:173)\nbrane conductance but move the resting potential towards more hyperpolarizing \n\nthe conductance of the post(cid:173)\n\n\fNetwork activity determines spatio-temporal integration in single cells \n\n47 \n\npotentials. \nNote that the 0 Hz ca\u00a3c corresponds to experiments made with in vitro slice prepa(cid:173)\nrations or culture. In this case incoming fibers have been cut off and the spontaneous \nfiring rate is very small. Careful studies have shown very large values for Rin and \nTm under these circumstances (e.g. Spruston &. Johnston, 1991). In vivo prepara(cid:173)\ntions, on the other hand, leave the cortical circuitry intact and much smaller values \nof R,n and Tm are usually recorded. \n\n3.2 Spatial integration \n\nVarying synaptic background activity can have a significant impact on the electro(cid:173)\ntonic structure of the cell (fig. 2). We plot the electrotonic distance of any particular \npoint from the cell body, that is the sum of the electrotonic length's L, = Ej(lj/Aj) \nassociated with each dendritic segment i, where Aj = J ~m.R~j is the electrotonic \nlength constant of compartment i, Ij its anatomical length and the sum is taken \nover all compartments between the soma and compartment i. \nIncreasing the synaptic background activity from I = 0 to f = 2 Hz has the effect \nof stretching the \"distance\" of any particular synapse t.o the soma by a factor of \nabout 3, on average. Thus, while a distal synapse has an associated L value of \nabout 2.6 at 2 Hz it shrinks to 1.2 if all network activity is shut off, while for a \nsynapse at the tip of a basal dendrite, L shrinks from 0.7 t.o 0.2. In fact, the EPSP \ninduced by a single excitatory synapse at that location goes from 39 to 151 J,lV, a \ndecrease of about 4. Thus, when the overall network activity is low, synapses in the \nsuperficial layer of cortex could have a significant effect on somatic discharge, while \nhaving only a weak modulatory effect on the soma if the overall network activity is \nhigh. Note that basal dendrites, which receive a larger number of synapses, stretch \nmore than apical dendrites. \n\n3.3 Temporal integration \n\nThat the synaptic background activity can also modify the temporal integration \nbehavior of the cell is demonstrated in fig. 3. At any part.icular background fre(cid:173)\nquency I, we compute the minimal number of additional excitatory synapses (at \ngpeal: = 0.5 nS) necessary to barely generate one action potential. These synapses \nwere chosen randomly from among all excitatory synapses throughout the cell. We \ncompare the case in which all synapses are activated simultaneously (solid line) \nwith the case in which the inputs arrive asynchronously, smeared out over 25 msec \n(dashed line). If I = 0, it requires 115 synapses firing simultaneously to generate \na single action potential, while 145 are needed if the input is desynchronized. This \nsmall difference between inputs arriving synchronized and at random is due to the \nlong integration period of the cell. \nIf the background activity increases to f = 1 Hz, 113 synchronized synaptic \ninputs-spread out all over the cell-are sufficient to fire the cell. \nIf, however, \nthe synaptic input is spread out over 25 msec, 202 synapses are now needed in \norder to trigger a response from the cell. This is mainly due to the much smaller \nvalue of Tm relative to the period over which the synaptic input is spread out. Note \n\n\f48 \n\nBernander, Koch, and Douglas \n\nthat the difference in number of simultaneous synaptic inputs needed to fire the \ncell for f = 0 compared to f = 1 is small (i.e. 113 vs. 115), in spite of the more \nthan five-fold decrease in somatic input resistance. The effect of the smaller size of \nthe individual EPSP at higher values of f is compensated for by the fact that the \nresting potential of the cell has been shifted towards the firing threshold of the cell \n(about -49 mY). \n\n,~----------------------------------------------, \n\nUnsynchronized Input \nSynchronized input \n\n800 \n\n600 \n\no -: \n\nI \n! \n=-... \nJ \nE :;, z \n\n-\n\n\u00b0OL-------'------~2------~3~----~4------~5~----~I~----~7 \n\nBackground \n\nfrequency \n\n(Hz) \n\nFigure 3: Phase detection. \n\nA variable number of excitatory synapses were fired superimposed onto a constant \nbackground frequency of 1 Hz. They fired either simultaneously (solid line) or \nspread out in time uniformly during a 25 msec interval (dashed line). The y axis \nshows the minimum number of synapses necessary to cause the cell to fire. \n\n3.4 NMDA synapses \n\nFast excitatory synaptic input in cortex is mediated by both AMPA or non-NMDA \nas well as NMDA receptors (Miller et aI., 1989). As opposed to the AMPA synapse, \nthe NMDA conductance change depends not only on time but also on the post(cid:173)\nsynaptic voltage: \n\n(1) \n\nwhere '1'1 = 40 msec, '1'2 = 0.335 msec, '1 = 0.33 mM-t, [M g2+] -\n1 mM, \nr = 0.06 mV-1. During spontaneous background activity many inputs impinge \non the cell and we can time-average the equation above. We will then be left with \na purely voltage-dependent conductance. \nWe measured the somatic input resistance, Rin, by injecting a small current pulse in \nthe soma (fig. 4) in the standard model. All synapses fired at a 0.5 Hz background \nfrequency. Next we added 4,000 NMDA synapses in addition to the 4,000 non-\n\n\fNetwork activity determines spatio-temporal integration in single cells \n\n49 \n\nNMDA synapses, also at 0.5 Hz, and again injected a current pulse. The voltage \nresponse is now larger by about 65%, corresponding to a smaller input conducta.nce, \neven though we are adding the positive NMDA conductance. This seeming paradox \ndepends on two effects. First, the input conductance is, by definition, ~ = G(V)+ \ndi) . (V - Ern), where G(V) is the conductance specified in eq. (1). For the \n\nN DA synapse this derivative is negative below about -35 mV. Second, due to the \nexcitation the membrane voltage has drifted towards more depolarized values. This \nwill cause a change in the activation of the other voltage-dependent currents. Even \nthough the summed conductance of these active currents will be larger at the new \n\nvoltage, the derivative '*\" will be smaller at that point. In other words, activation \n\nof NMDA synapses gives a negative contribution to the input conductance, even \nthough more conductances have opened up. \nNext we replaced 2,000 of the 4,000 non-NMDA synapses in the old model with \n2,000 NMDA synapses and recomputed the input resistance as a function of synap(cid:173)\ntic background activity. The result is overlaid in figure 1a (dashed line). The curve \nshifts toward larger values of Rin for most values of f. This shift varies between \n50 % - 200 %. The cell is more excitable than before. \n\n-60 \n\n> \n\n- -62 \nE -\n\n-63 \n\n-61 \n\nE \n> \n\n-64 \n\n-65 \n\n-66 \n\n0 \n\n200 \n\n400 \nt \n\n600 \n\n800 \n\n1000 \n\nlmsecl \n\nFigure 4: Negative input conductance from NMDA activation. \n\nAt times t = 250 msec and t = 750 msec a 0.05 nA current pulse was injected \nat the soma and the somatic voltage response was recorded. At t = 500 msec, \none NMDA synapse was activated for each non-NMDA synapse, for a total of 8,000 \nexcitatory synaptic inputs. The background frequency was 0.5 Hz for all synapses. \n\n4 DISCUSSION \n\nWe have seen that parameters such as Rtn, 7'm, and L are not static, but can \nvary over about one order of magnitude under network control. The potential \ncomputational possibilities could be significant. \n\n\f50 \n\nBernander, Koch, and Douglas \n\nFor example, if a low-contrast stimulus is presented within the receptive field of \nthe cell, the synaptic input rate will be small and the signal-t~noise ratio (SNR) \nlow. In this case, to make the cell more sensitive to the inputs we might want to \nincrease R;n. This would automatically be achieved as the total network activation \nis low. We can improve the SNR by integrating over a longer time period, i.e. by \nincreasing Tm. This would also be a consequence of the reduced network activity. \nThe converse argument can be made for high-contrast stimuli, associated with high \noverall network activity and low R;n and Tm values. \n\nMany cortical cells are tuned for various properties of the stimulus, such as orien(cid:173)\ntation, direction, and binocular disparity. As the effective membrane conductance, \nG m , changes, the tuning curves are expected to change. Depending on the exact \ncircuitry and implementation of the tuning properties, this change in background \nfrequency could take many forms. One example of phase-tuning was given above. \nIn this case the temporal tuning increases with background frequency. \n\nAcknowledgements \n\nThis work was supported by the Office of Naval Research, the National Science \nFoundation, the James McDonnell Foundation and the International Human Fron(cid:173)\ntier Science Program Organization. Thanks to Tom Tromey for writing the graphic \nsoftware and to Mike Hines for providing us with NEURON. \n\nReferences \n\nP. Anderson, M. Raastad &, J. F. Storm. (1990) Excitatory synaptic integration in \nhippocampal pyramids and dentate granule cells. Symp. Quant. Bioi. 55, Cold \nSpring Harbor Press, pp. 81-86. \nO. Bernander, R. J. Douglas, K. A. C. Martin &, C. Koch. \n(1991) Synaptic \nbackground activity influences spatiotemporal integration in single pyramidal cells. \nP.N.A.S, USA 88: 11569-11573. \nR. J. Douglas, K. A. C. Martin &, D. Whitteridge. (1991) An intracellular analysis \nof the visual responses of neurones in cat visual cortex. J. Physiol. 440: 659-696. \n\nM. Hines. \ngeometries. Int. J. Biomed. Comput. 24: 55-68. \n\n(1989) A program for simulation of nerve equations with branching \n\nW. R. Holmes &, C. D. Woody. (1989) Effects of uniform and non-uniform synap(cid:173)\ntic activation-distributions on the cable properties of modeled cortical pyramidal \nneurons. Brain Research 505: 12-22. \n\nA. U. Larkman. (1991) Dendritic morphology of pyramidal neurones of the visual \ncortex of the rat: III. Spine distributions. J. Compo Neurol. 306: 332-343. \n\nK. D. Miller, B. Chapman &, M. P. Stryker. (1989) Responses of cells in cat visual \ncortex depend on NMDA receptors. P.N.A.S. 86: 5183-5187. \n\nN. Spruston &, D. Johnston. (1992) Perforated patch-clamp analysis of the passive \nmembrane properties of three classes of hippocampal neurons. J. Netlrophysiol., in \npress. \n\n\f", "award": [], "sourceid": 541, "authors": [{"given_name": "\u00d6jvind", "family_name": "Bernander", "institution": null}, {"given_name": "Christof", "family_name": "Koch", "institution": null}, {"given_name": "Rodney", "family_name": "Douglas", "institution": null}]}