FAST KINETIC MODELS FOR SIMULATING AMPA, NMDA, Zachary F. Mainen and Terrence J. Sejnowski*

Transcription

1 2 FAST KINETIC MODELS FOR SIMULATING AMPA, NMDA, GABA A AND GABA B RECEPTORS Alain Destexhe, Zachay F. Mainen and Teence J. Sejnowski* The Salk Institute fo Biological Studies and The Howad Hughes Medical Institute, Noth Toey Pines Road, La Jolla, Califonia * also in the Depatment of Biology, Univesity of Califonia San Diego In: The Neuobiology of Computation, Edited by Bowe, J., Kluwe Academic Pess, Nowell MA, pp. 914, Abstact Since the intoduction of the alpha function by Rall in 1967 ë12ë, thee has been signiæcant pogess in ou undestanding of the molecula events undelying synaptic tansmission. Paticula ecepto types have been identiæed and thei activation kinetics chaacteized. It is now possible to develop models of these eceptos, using a fomalism simila to that intoduced by Hodgkin and Huxley ë9ë. In this pape, we pesent ecentlyintoduced models obtained by simplifying moe detailed biophysical models of postsynaptic eceptos ë7ë. The simpliæed models ae fully compatible with the HodgkinHuxley fomalism, ae vey eæcient to simulate, and account fo impotant phenomena such as synaptic summation and desensitization. These models should be useful in lagescale netwok simulations. Fast kinetic models In a pevious pape ë7ë, we developed a model of synaptic tansmission that incopoated the kinetics of voltagedependent channels, the kinetics of exocytosis of neuotansmitte in the synapse, diæusion of the neuotansmitte and binding to postsynaptic eceptos, and ænally the kinetics of activation of these eceptos. It was shown that intoducing simplifying assumptions leads to much simple kinetic models fo a vaiety of ecepto types, including fast tansmission and neuomodulation. Synaptic eceptos activate o deactivate ion channels located in the postsynaptic cell. In the case of ëfast" synaptic tansmission, the ecepto and the channel ae pat of the same potein complex. In these socalled ionotopic eceptos, the ligand is a neuotansmitte and its binding to the complex leads to the opening of the associated ionophoe. Ionotopic eceptos include the glutamate AMPAèkainate and NMDA types, the fast GABAegic eceptos 9

2 10 Chapte 2 ègaba A è and nicotinic acetylcholine èachè eceptos. Howeve, fo a vaiety of neuotansmittes, the channel is independent of the ecepto and the gating occus though the poduction of an intacellula second messenge. These socalled metabotopic eceptos include the slow GABAegic type ègaba B è, muscainic ACh eceptos, noadenegic eceptos, seotonegic eceptos, as well as othe types. We have consideed elatively detailed kinetic schemes fo both ionotopic and metabotopic types of synaptic eceptos. Fo both types, we deived simple kinetic schemes that account fo most of thei popeties. The simpliæed models assume that the time couse of the ligand, L, occus as a pulse, tiggeed by the pesynaptic spike. The ligand then gates the opening of a ion channel, accoding to the following possible schemes: C + L O C + L (1) (2) (3) 5 6 D O C + L C In these schemes, C 1 and C 2 epesent the closed states of the channel, O is the open state, D epesents the desensitized state and ae the associated ate constants. The synaptic cuent I syn is obtained fom the elation: I syn = çg syn m èv, E syn è whee çg syn is the maximal synaptic conductance, m is the faction of channels in open state, V is the postsynaptic membane potential and E syn is the evesal potential. The time couse of the ligand L and the kinetic constants distinguish ionotopic fom metabotopic eceptos. In the fome, L epesents the neuotansmitte and occus as a pulse of 1 mm amplitude and 1 ms duation, as estimated fom patchclamp ecodings ë4ë. In the latte, L is a second messenge and occus as a pulse of 1 çm amplitude and ms duation. These values wee estimated fom kinetic data of secondmessenge tansduction. The computational advantage of simple schemes such as è12è is that the time couse of the cuent can be obtained analytically ë6, 7ë. The analytic expessions make these models extemely poweful because they do not equie diæeential equations to be solved numeically èsee ef. ë7ë fo moe detailsè. Anothe advantage is that it is easy to æt model to expeimental data, as descibed in the next section. Adjustment of paametes fo diæeent ecepto types AMPAèkainate glutamate eceptos ae among the most pominent eceptos found in cental synapses and mediate fast excitatoy tansmission. We have æt the above models to aveaged AMPAèkainatemediated postsynaptic cu D 3 4 O

3 Models of AMPA, NMDA, GABA A and GABA B Receptos 11 A 2state 3state 4state AMPA 60 pa 10 ms B NMDA 20 pa 100 ms C GABA A 10 pa 10 ms D GABA B 10 pa 200 ms Figue 1 Fit of simple kinetic schemes to fou types of synaptic cuents. A. AMPAèkainatemediated cuents èobtained fom Z. Xiang, A.C. Geenwood and T. Bown ë14ëè. B. NMDAmediated cuents èobtained fom N.A. Hessle and R. Malinow ë8ëè. C. GABAAmediated cuents èobtained fom T.S. Otis and I. Mody ë11ëè. D. GABABmediated cuents èobtained fom T.S. Otis, Y. De Koninck and I. Mody ë10ëè. The aveaged ecoding of the synaptic cuent ènoisy taces negative cuents upwads fo A and Bè is shown with the best æt obtained using simple kinetics with a simplex algoithm ècontinuous tace paametes given in Table 1è. A and D modiæed fom ë5ë, B unpublished, C modiæed fom ë7ë. ents èpscè fom wholecell ecodings in mossy æbe synapses in hippocampal pyamidal cells ë7ë. Fo this neuotansmittegated channel, two, thee o foustate kinetic schemes gave vey good æts èfig. 1Aè. Howeve, only theeo foustate schemes could account fo phenomena like ecepto desensitization èsee ef. ë7ëè.

4 12 Chapte 2 Table 1 Optimal values of the ate constants obtained by ætting simple gating kinetic schemes to aveaged ecodings of synaptic cuents fo vaious eceptos. The kinetic schemes è13è ae as indicated in the text. The ate constants shown ae fom the best model of this kind that æt the expeimental data using a simplex algoithm èsee Fig. 1è. All kinetic schemes assumed a pulse of ligand è1 mm amplitude and 1 ms duation fo AMPAèkainate, NMDA and GABAA; 1 çm amplitude and, fom top to bottom, 84, 97 and 66 ms duation fo GABABè. Othe eceptos, such as cholinegic muscainic èm2è, noadenegic èæ2è, seotonegic è5ht, 1è, dopaminegic èd2è, adenosinegic èa1è and histaminegic ae likely to act though the same Gpoteinbased mechanisms as GABAB ë2, 3ë and show a simila slow time couse. The units of the ate constants ae as follows: s,1 mm,1 fo 1 ès,1 çm,1 in the case of GABABè; s,1 fo 2, 3, 4 and 5; s,1 fo 6 in scheme è3è; s,1 mm,1 fo 6 in scheme è2è ès,1 çm,1 in the case of GABABè. Recepto Scheme AMPAèkainate è1è è2è è3è NMDA è1è è2è è3è GABAA è1è è2è è3è GABAB è1è è2è è3è NMDA eceptos ae a second type of glutamate ionotopic channel which have a time couse signiæcantly slowe than the AMPAèkainate type. The above models wee æt to an aveaged NMDA PSC obtained by wholecell ecodings in hippocampal slices ë7ë. The NMDA cuent could only be æt well by a foustate scheme, but two and theestate schemes gave acceptable æts èfig. 1Bè. Alpha functions o elated doubleexponential template functions gave identical esults to the theestate scheme. GABA A eceptos ae a pimay mediato of inhibitoy cuents in cental synapses. Kinetic models wee æt to an aveaged PSC obtained by wholecell ecodings fom dentate ganule cells ë5, 7ë. As in the case of fast AMPAèkainatemediated excitatoy channels, fast GABA A ecepto cuents wee well æt by schemes involving two o moe states èfig. 1Cè. Note that the decay of this GABAegic cuent isvey simila to the AMPAèkainate type. We do not expect this to be the case fo all subtypes of GABA A and AMPA eceptos, since the exact kinetic ates can vay among diæeent subtypes ë13ë.

5 Models of AMPA, NMDA, GABA A and GABA B Receptos 13 Fo all the above eceptos, the gating was ionotopic with a elatively fast time couse. In the case of GABA ègaba B è, cholinegic èm2è, noadenegic èalpha2è, seotonegic è5ht1è, dopaminegic èd2è, as well as othe eceptos, a K + channel is gated though the action of a Gpotein subunit ë2, 3ë. If the Gpotein diectly gates the K + channel, then a simple kinetic schemes can be deived, assuming ms pulses of Gpotein. This simpliæed model was found to be vey eæective in ætting aveaged GABA B mediated PSC obtained by wholecell ecodings fom dentate ganule cells ë5, 7ë. As in the case of NMDA channels, the cuent could only be æt well with a foustate scheme, but two and theestate schemes gave acceptable æts èfig. 1Dè. Fitting is also possible using a shot pulse of tansmitte, but in this case the kinetics of the ecepto, Gpotein activation and K + channels must be taken into account, leading to moe complex models ë7ë. Discussion Although it has been possible to develop emakably detailed models of the synapse ë1ë, substantial simpliæcation is necessay fo lagescale netwok simulations involving thousands of synapses. We have descibed hee one type of simpliæed model fo synaptic esponses, based on the kinetics of the ion channel molecules. The time couse of the tansmitte was assumed to be a constant pulse and the kinetics of the synaptic channel wee kept as simple as possible to æt expeimentallyecoded postsynaptic cuents. We used a set of kinetic schemes that, although vey simpliæed, povided good æts of postsynaptic cuents. An advantage of using kinetic models ove othe models, such as the alpha function, is that inteactions between successive events can be easily captued ë6, 7ë. Anothe impotant advantage of these simpliæed models is that they can be computed vey easily, making them good candidates fo lagescale netwok simulations. Togethe with HodgkinHuxleylike equations fo the voltagedependent cuents, the pesent synaptic models allow a whole netwok to be descibed by the same fomalism. Acknowledgments This eseach was suppoted by the Howad Hughes Medical Institute, the Oæce fo Naval Reseach and the National Institutes of Health. We thank Ds. T. Bown, R. Malinow, I. Mody and T. Otis fo making thei data available to us. Pogams that simulate kinetic models of synaptic cuents using the NEURON simulato ae available by anonymous ftp to salk.edu in èpubèalain o in

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