{"title": "Amplifying and Linearizing Apical Synaptic Inputs to Cortical Pyramidal Cells", "book": "Advances in Neural Information Processing Systems", "page_first": 519, "page_last": 526, "abstract": null, "full_text": "Amplifying and Linearizing Apical \n\nSynaptic Inputs \n\nto Cortical Pyramidal Cells. \n\nOjvind Bernander, Christof Koch ... \n\nComputation and Neural Systems Program, \nCalifornia Institute of Technology, 139-74 \n\nPasadena, Ca 91125, USA. \n\nRodney J. Douglas \n\nAnatomical Neuropharmacology Unit, \n\nDept. Pharmacology, \n\nOxford, UK. \n\nAbstract \n\nIntradendritic electrophysiological recordings reveal a bewildering \nrepertoire of complex electrical spikes and plateaus that are dif(cid:173)\nficult to reconcile with conventional notions of neuronal function. \nIn this paper we argue that such dendritic events are just an exu(cid:173)\nberant expression of a more important mechanism - a proportional \ncurrent amplifier whose primary task is to offset electrotonic losses. \nUsing the example of functionally important synaptic inputs to the \nsuperficial layers of an anatomically and electrophysiologically re(cid:173)\nconstructed layer 5 pyramidal neuron, we derive and simulate the \nproperties of conductances that linearize and amplify distal synap(cid:173)\ntic input current in a graded manner. The amplification depends \non a potassium conductance in the apical tuft and calcium conduc(cid:173)\ntances in the apical trunk. \n\n\u00b7To whom all correspondence should be addressed. \n\n519 \n\n\f520 \n\nBemander, Koch, and Douglas \n\n1 \n\nINTRODUCTION \n\nAbout half the pyramidal neurons in layer 5 of neocortex have long apical dendrites \nthat arborize extensively in layers 1-3. There the dendrites receive synaptic input \nfrom the inter-areal feedback projections (Felleman and van Essen, 1991) that play \nan important role in many models of brain function (Rockland and Virga, 1989). \nAt first sight this seems to be an unsatisfactory arrangement. In light of traditional \npassive models of dendritic function the distant inputs cannot have a significant \neffect on the output discharge of the pyramidal cell. The distal inputs are at least \none to two space constants removed from the soma in layer 5 and so only a small \nfraction of the voltage signal will reach there. Nevertheless, experiments in cortical \nslices have shown that synapses located in even the most superficial cortical layers \ncan provide excitation strong enough to elicit action potentials in the somata of \nlayer 5 pyramidal cells (Cauller and Connors, 1992, 1994). These results suggest \nthat the apical dendrites are active rather than passive, and able to amplify the \nsignal en route to the soma. Indeed, electrophysiological recordings from cortical \npyramidal cells provide ample evidence for a variety of voltage-dependent dendritic \nconductances that could perform such amplification (Spencer and Kandel, 1961; \nRegehr et al., 1993; Yuste and Tank, 1993; Pockberger, 1991; Amitai et al., 1993; \nKim and Connors, 1993). \n\nAlthough the available experimental data on the various active conductances pro(cid:173)\nvide direct support for amplification, they are not adequate to specify the mecha(cid:173)\nnism by which it occurs. Consequently, notions of dendritic amplification have been \ninformal, usually favoring voltage gain, and mechanisms that have a binary (high \ngain) quality. In this paper, we formalize what conductance properties are required \nfor a current amplifier, and derive the required form of their voltage dependency by \nanalysis. \n\nWe propose that current amplification depends on two active conductances: a \nvoltage-dependent K+ conductance, gK, in the superficial part of the dendritic \ntree that linearizes synaptic input, and a voltage-dependent Ca 2+ conductance, \ngc a, in layer 4 that amplifies the result of the linearization stage. Spencer and Kan(cid:173)\ndel (1961) hypothesized the presence of dendritic calcium channels that amplify \ndistal inputs. More recently, a modeling study of a cerebellar Purkinje cell suggests \nthat dendritic calcium counteracts attenuation of distal inputs so that the somatic \nresponse is independent of synaptic location (De Schutter and Bower, 1992). A \ngain-control mechanism involving both potassium and calcium has also been pro(cid:173)\nposed in locust non-spiking interneurons (Laurent, 1993). In these cells, the two \nconductances counteract the nonlinearity of graded transmitter release, so that the \noutput of the interneuron was independent of its membrane voltage. The principle \nthat we used can be explained with the help of a highly simplified three compart(cid:173)\nment model (Fig. 1A). The leftmost node represents the soma and is clamped to \n-50 m V. The justification for this is that the time-averaged somatic voltage is re(cid:173)\nmarkably constant and close to -50 m V for a wide range of spike rates. The middle \nnode represents the apical trunk containing gCa, and the rightmost node represents \nthe apical tuft with a synaptic induced conductance change gsyn in parallel with \ngK. For simplicity we assume that the model is in steady-state, and has an infinite \nmembrane resistance, Rm. \n\n\fAmplifying and Linearizing Apical Synaptic Inputs to Cortical Pyramidal Cells \n\n521 \n\n150ma \n\n9 \n\n9 \n\nVsoma \n\n--\n\nEea \n\nEK T Esyn \n\n~----~--~I----~----\n\nB PaSSlve response and targets \n\nc \n\nActlvation curves \n\nLinearized and amplified \n\n~ 1 \no \nUl \nH \n\n, , \n, , \n\n30 \n\n10 \n\n100 \n\ngsyn (nS) \n\n200 \n\nO~--~--~--~----~L-~--~ \n10 \n-50 \n\nv (mV) \n\nFigure 1: Simplified model used to demonstrate the concepts of saturation, \nlinearization, and amplification. (A) Circuit diagram. The somatic compart(cid:173)\nment was clamped to V$oma = -50 mV with ECa = 115 mV, EK = -95 mV, \nE$yn = 0 m V, and g = 40 nS. The membrane capacitance was ignored, since \nonly steady state properties were studied, and membrane leak was not included for \nsimplicity. (B) Somatic current, I$oma, in response to synaptic input. The pas(cid:173)\nsive response (thin dashed line) is sublinear and saturates for low values of gsyn. \nThe linearized response (thick solid line) is obtained by introducing an inactivating \npotassium conductance, OK (\"gA\" in c). A persistent persistent OK results in a \nsomewhat sub-linear response (thick dashed line; \"gM\" in c). The addition of a cal(cid:173)\ncium conductance amplifies the response (thin solid line). (C) Analytically derived \nactivation curves. The inactivating potassium conductance (\"IA\") was derived, but \nthe persistent version (\" IM\") proved to be more stable. \n\n\f522 \n\nBemander, Koch, and Douglas \n\n2 RESULTS \n\nFig. 1B shows the computed relationship between the excitatory synaptic input \nconductance and the axial current, I soma , flowing into the somatic (leftmost) com(cid:173)\npartment. The synaptic input rapidly saturates; increasing gsyn beyond about 50 nS \nleads to little further increase in Isoma. This saturation is due to the EPSP in the \ndistal compartment reducing the effective synaptic driving potential. We propose \nthat the first goal of dendritic amplification is to linearize this relationship, so that \nthe soma is more sensitive to the exact amount of excitatory input impinging on \nthe apical tuft, by introducing a potassium conductance that provides a hyper(cid:173)\npolarizing current in proportion to the degree of membrane depolarization. The \nvoltage-dependence of such a conductance can be derived by postulating a linear \nrelationship between the synaptic current flowing into the somatic node and the \nsynaptic input, i.e. Isoma = constant\u00b7 gsyn. In conjunction with Ohm's law and \ncurrent conservation, this relation leads to a simple fractional polynominal for the \nvoltage dependency of gK (labeled \"gA\" in Fig. 1C). As the membrane potential \ndepolarizes, gK activates and pulls it back towards EK . At large depolarizations gK \ninactivates, similar to the \"A\" potassium conductance, resulting overall in a linear \nrelationship between input and output (Fig. 1B). As the slope conductance of this \nparticular form of gK can become negative, causing amplification of the synaptic \ninput, we use a variant of gK that is monotonized by leveling out the activation \ncurve after it has reached its maximum, similar to the \"M\" current (Fig. IC). Incor(cid:173)\nporating this non-inactivating K+ conductance into the distal compartment results \nin a slightly sublinear relationship between input and output (Fig. 1B). \n\nWith gK in place, amplification of Isoma is achieved by introducing an inward \ncurrent between the soma and the postsynaptic site. The voltage-dependency of the \namplification conductance can be derived by postulating Isoma = gain \u00b7 constant\u00b7 \ngsyn' This leads to the non-inactivating gCa shown in Fig. 1C, in which the overall \nrelationship between synaptic input and somatic output current (Fig. 1B) reflects \nthe amplification. \n\nWe extend this concept of deriving the form of the required conductances to a \ndetailed model of a morphologically reconstructed layer 5 pyramidal cell from cat \nvisual cortex (Douglas et al., 1991, Fig. 2A;). We assume a passive dendritic tree, \nand include a complement of eight common voltage-dependent conductances in its \nsoma. 500 non-NMDA synapses are distributed on the dendritic tuft throughout \nlayers 1, 2 and 3, and we assume a proportionality between the presynaptic firing \nfrequency fin and the time-averaged synaptic induced conductance change. When \nfin is increased, the detailed model exhibits the same saturation as seen in the \nsimple model (Fig. 2B). Even if an 500 synapses are activated at fin = 500 Hz only \n0.65 nA of current is delivered to the soma. This saturation is caused when the \nsynaptic input current flows into the high input resistances of the distal dendrites, \nthereby reducing the synaptic driving potential. Layer 1 and 2 input together can \ncontribute a maximum of 0.25 nA to the soma. This is too little current to cause \nthe cell to spike, in contrast with the experimental evidence (Cauller and Connors, \n1994), in which spike discharge was evoked reliably. Electrotonic losses make only \na minor contribution to the small somatic signal. Even when the membrane leak \ncurrent is eliminated by setting Rm to infinity, Isoma only increases a mere 2% to \n0.66 nA. \n\n\fAmplifying and Linearizing Apical Synaptic Inputs to Cortical Pyramidal Cells \n\n523 \n\n~8r2layer1 \n\n\u00b7 \nM \n.jJ \nu \nIII \n\n.-i \nIII \n\u00a7 \n\nM \n.jJ \nU \nIII \n'\"' \n'H \n\nQ60 \n\n40 \n\n30 \n\n20 \n\n10 \n\nN :r: \n\n'-\" \n\n.jJ \n~ \n0 \n'H \n\nActive, \npredicted \n\nActive \ndendrite \n\n00 \n\n50 \n\nPassive dendrlte \n\n150 \n\n200 \n\nV (mV) \n\nFigure 2: Amplification in the detailed model. (A) The morphology of this \nlayer V pyramidal cell was reconstructed from a HRP-stained cell in area 17 of the \nadult cat (Douglas et ai., 1991). The layers are marked in alternating black and \ngrey. The boundaries between superficial layers are not exact, but rough estimates \nand were chosen at branch points; a few basal dendrites may reach into layer 6. \nAxon not shown. (B) Current delivered to the soma by stimulation of 500 AMPA \nsynapses throughout either layer 5 or layers 1-3. (C) Derived activation curves for \ngK and gCa' Sigmoidal fits of the form g(V) = 1/(1 + e(Vhcll/-V)/K), resulted in \n]{K = 3.9 mY, Vhalj,K = -51 mY, KCa = 13.7 mY, Vhalj,Ca = -14 mY. (D) \nOutput spike rate as a function of input activation rate of 500 AMPA synapses \nin layers 1-3, with and without the derived conductances. The dashed line shows \nthe lout rate predicted by using the linear target Isoma as a function of lin in \ncombination with the somatic f - I relationship. \n\n\f524 \n\nBemander, Koch, and Douglas \n\no \n\nVrn \n\n(rnV) \n\n-50 \n\n100 \n\n200 \n\nt \n\n(rnsec) \n\nFigure 3: Dendritic calcium spikes. All-or-nothing dendritic Ca 2+ calcium \nspikes can be generated by adding a voltage-independent but Ca 2+ -dependent K+ \nconductance to the apical tree with gma~ = 11.4 nS. The trace shown is in response \nto sustained intradendritic current injection of 0.5 nA. For clamp currents of 0.3 nA \nor less, no calcium spikes are triggered and only single somatic spikes are obtained \n(not shown). These currents do not substantially affect the current amplifier effect. \n\nBy analogy with the simple model of Fig. 1, we eliminate the saturating response by \nintroducing a non-inactivating form of gK spread evenly throughout layers 1-3. The \nresulting linearized response is amplified by a Ca2+ conductance located at the base \nof the apical tuft, where the apical dendrite crosses from layer 4 to layer 3 (Fig. 2A). \nThis is in agreement with recent calcium imaging experiments, which established \nthat layer 5 neocortical pyramidal cells have a calcium hot spot in the apical tree \nabout 500-600 pm away from the soma (Tank et ai., 1988). Although the derivation \nof the voltage-dependency of these two conductances is more complicated than in \nthe three compartment model, the principle of the derivation is similar (Bernander, \n1993, Fig. 2C;). We derive a Ca 2+ conductance, for a synaptic current gain of \ntwo, resembling a non-inactivating, high-threshold calcium conductance. The curve \nrelating synaptic input frequency and axial current flowing into the soma (Fig. 2B) \nshows both the linearized and amplified relationships. \n\nOnce above threshold, the model cell has a linear current-discharge relation with a \nslope of about 50 spikes per second per nA, in good agreement with experimental \nobservations in vitro (Mason and Larkman, 1990) and in vivo (Ahmed et a/., 1993). \nGiven a sustained synaptic input frequency, the somatic f-I relationship can be used \nto convert the synaptic current flowing into the soma 130ma into an equivalent output \nfrequency (Abbott, 1991; Powers et a/., 1992; Fig. 2D). This simple transformation \naccounts for all the relevant nonlinearities, including synaptic saturation , interaction \nand the threshold mechanism at the soma or elsewhere. We confirmed the validity \nof our transformation method by explicitly computing the expected relationship \nbetween lin and lout, without constraining the somatic potential, and comparing \nthe two. Qualitatively, both methods lead to very similar results (Fig. 2D): in the \n\n\fAmplifying and Linearizing Apical Synaptic Inputs to Cortical Pyramidal Cells \n\n525 \n\npresence of dendritic gCa superficial synaptic input can robustly drive the cell, in a \nproportional manner over a large input range. \n\nThe amplification mechanism derived above is continuous in the input rate. It does \nnot exhibit the slow calcium spikes described in the literature (Pockberger, 1991; \nAmitai et ai., 1993; Kim and Connors, 1993). However, it is straightforward to add a \ncalcium-dependent potassium conductance yielding such spikes. Incorporating such \na conductance into the apical trunk leads to calcium spikes (Fig. 3) in response to \nan intradendritic current injection of 0.4 nA or more, while for weaker inputs no \nsuch events are seen. In response to synaptic input to the tuft of 120 Hz or more, \nthese spikes are activated, resulting in a moderate depression (25% or less) of the \naverage output rate, lout (not shown). \n\nIn our view, the function of the dendritic conductances underlying this all-or-none \nvoltage event is the gradual current amplification of superficial input, without am(cid:173)\nplifying synaptic input to the basal dendrites (Bernander, 1993). Because gCa \ndepolarizes the membrane, further activating gCa, the gain of the current amplifier \nis very sensitive to the density and shape of the dendritic gCa. Thus, neuromod(cid:173)\nulators that act upon gCa control the extent to which cortical feedback pathways, \nacting via superficial synaptic input, have access to the output of the cell. \n\nAcknowledgements \n\nThis work was supported by the Office of Naval Research, the National Institute of \nMental Health through the Center for Neuroscience, the Medical Research Council \nof the United Kingdom, and the International Human Frontier Science Program. \n\nReferences \n\n[1] L.F. Abbott. Realistic synaptic inputs for model neuronal networks. Network, \n\n2:245-258, 1991. \n\n[2] B. Ahmed, J .C. Anderson, R.J. Douglas, K.A.C. Martin, and J .C. Nelson. \nThe polyneuronal innervation of spiny steallate neurons in cat visual cortex. \nSubmitted, 1993. \n\n[3] Y. Amitai, A. Friedman, B.W. Connors, and M.J. Gutnick. Regenerative ac(cid:173)\n\ntivity in apical dendrites of pyramidal cells in neocortex. Cerebral Cortex, \n3:26-38, 1993. \n\n[4] 6 Bernander. 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In \nNeuroscience Abstr. 19, page 616.2, 1993. \n\n\f", "award": [], "sourceid": 717, "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}]}