{"title": "Stationarity of Synaptic Coupling Strength Between Neurons with Nonstationary Discharge Properties", "book": "Advances in Neural Information Processing Systems", "page_first": 11, "page_last": 18, "abstract": null, "full_text": "Stationarity of Synaptic Coupling Strength Between \nNeurons with Nonstationary Discharge Properties \n\nMark R. Sydorenko and Eric D. Young \n\nDept. of Biomedical Engineering & Center for Hearing Sciences \n\nThe Johns Hopkins School of Medicine \n\n720 Rutland Avenue \n\nBaltimore. Maryland 21205 \n\nAbstract \n\nBased on a general non-stationary point process model, we computed estimates of \nthe synaptic coupling strength (efficacy) as a function of time after stimulus onset \nbetween an inhibitory interneuron and its target postsynaptic cell in the feline dorsal \ncochlear nucleus. The data consist of spike trains from pairs of neurons responding \nto brief tone bursts recorded in vivo. Our results suggest that the synaptic efficacy is \nnon-stationary. Further. synaptic efficacy is shown to be inversely and \napproximately linearly related to average presynaptic spike rate. A second-order \nanalysis suggests that the latter result is not due to non-linear interactions. Synaptic \nefficacy is less strongly correlated with postsynaptic rate and the correlation is not \nconsistent across neural pairs. \n\n1 \n\nINTRODUCTION \n\nThe aim of this study was to investigate the dynamic properties of the inhibitory effect of \ntype IT neurons on type IV neurons in the cat dorsal cochlear nucleus (DeN). Type IV cells \nare the principal (output) cells of the DCN and type II cells are inhibitory intemeurons (Voigt \n& Young 1990). In particular. we examined the stationarity of the efficacy of inhibition of \nneural activity in a type IV neuron by individual action potentials (APs) in a type II neuron. \nSynaptic efficacy. or effectiveness, is defmed as the average number of postsynaptic (type IV) \nAPs eliminated per presynaptic (type IT) AP . \n\nThis study was motivated by the observation that post-stimulus time histograms of type IV \nneurons often show gradual recovery (\"buildup\") from inhibition (Rhode et al. 1983; Young \n& Brownell 1976) which could arise through a weakening of inhibitory input over time. \n11 \n\n\f12 \n\nSydorenko and Young \n\nCorrelograms of pairs of DCN units using long duration stimuli are reported to display \ninhibitory features (Voigt & Young 1980; Voigt & Young 1990) whereas correlograms using \nshort stimuli are reported to show excitatory features (Gochin et a1. 1989). This difference \nmight result from nonstationarity of synaptic coupling. Finally, pharmacological results \n(Caspary et al. 1984) and current source-density analysis of DCN responses to electrical \nstimulation (Manis & Brownell 1983) suggest that this synapse may fatigue with activity. \n\nSynaptic efficacy was investigated by analyzing the statistical relationship of spike trains \nrecorded simultaneously from pairs of neurons in vivo. We adopt a first order (linear) non(cid:173)\nstationary point process model that does not impose a priori restrictions on the presynaptic \nprocess's distribution. Using this model, estimators of the postsynaptic impulse response to a \npresynaptic spike were derived using martingale theory and a method of moments approach. \nTo study stationarity of synaptic efficacy, independent estimates of the impulse response \nwere derived over a series of brief time windows spanning the stimulus duration. Average \npre- and postsynaptic rate were computed for each window, as well. In this report, we \nsummarize the results of analyzing the dependence of synaptic efficacy (derived from the \nimpulse response estimates) on post-stimulus onset time, presynaptic average rate. \npostsynaptic average rate, and presynaptic interspike interval. \n\n2 \n\nMETHODS \n\n2.1 \n\nDATA COLLECTION \n\nData were collected from unanesthetized cats that had been decerebrated at the level of the \nsuperior colliculus. We used a posterior approach to expose the DCN that did not require \naspiration of brain tissue nor disruption of the local blood supply. Recordings were made \nusing two platinum-iridium electrodes. \n\nThe electrodes were advanced independently until a type II unit was isolated on one electrode \nand a type IV unit was isolated on the other electrode. Only pairs of units with best \nfrequencies (BFs) within 20% were studied. The data consist of responses of the two units to \n500-4000 repetitions of a 100-1500 millisecond tone. The frequency of the tone was at the \ntype II BF and the tone level was high enough to elicit activity in the type II unit for the \nduration of the presentation, but low enough not to inhibit the activity of the type IV unit \n(usually 5-10 dB above the type II threshold). Driven discharge rates of the two units ranged \nfrom 15 to 350 spikes per second. A silent recovery period at least four times longer than the \ntone burst duration followed each stimulus presentation. \n\n2.3 \n\nDATA ANALYSIS \n\nThe stimulus duration is divided into 3 to 9 overlapping or non-overlapping time windows ('a' \nthru 'k' in figure 1). A separate impulse response estimate, presynaptic rate. and postsynaptic \nrate computation is made using only those type II and type IV spikes that fall within each \nwindow. The effectiveness of synaptic coupling during each window is calculated from the \narea bounded by the impulse response feature and the abscissa (shaded area in figure 1). The \neffectiveness measure has units of number of spikes. \n\nThe synaptic impulse response is estimated using a non-stationary method of moments \nalgorithm. The estimation algorithm is based on the model depicted in figure 2. The thick \ngray line encircles elements belonging to the postsynaptic (type IV) cell. The neural network \nsurrounding the postsynaptic cell is modelled as a I-dimensional multivariate counting \nprocess. Each element of the I-dimensional counting process is an input to the postsynaptic \n\n\fStationarity of Synaptic Coupling Strength Between Neurons \n\n13 \n\ncell. One of these input elements is the presynaptic (type II) cell under observation. The \ninput processes modulate the postsynaptic cell's instantaneous rate function, Aj(t). Roughly \nspeaking, A.j(t) is the conditional flring probability of neuron j given the history of the input \nevents up to time t. \n\n200 \n\n~I Vl \n\n'-' \n\n400 \n\n0 a b y,., \n\nSR \n\nU' \nQ) Q) \n~ ~ . . . SR\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7 \n~o. \nVl \n'-' \n\nTYFE II PST \nHISTOGRAM \n\n+ + Post-Stimulus Time \n....... ~ .... - TYFE IV PST \n+ t Post-Stimulus Time \n, \u2022\u2022 F' , , , , , I \n\n~ Kh2(t) \n\n, , , \n\nHISTOGRAM \n\n, , \n\nI \u2022 \n\nFigure 1: Analysis of Non-stationary Synaptic Coupling \n\n,,, \u2022..... _ .... _ ... _-... \n. \n. \n. \\ \n\nN\u00b7 \nJ \n~ \n\n......... , .... \n\nNj+ 1 \n\n.. \n\\\" \nNJ \n\n\"-\n\n\u2022 \n\nNp \n\n. \n. \n. \n\nThe transformation K describes how the \ninput processes influence Aj(t). We model \nthis transformation as a linear sum of an \nintrinsic rate component and the contribution \nof all the presynaptic processes: \n\nAj(t} = KOj(t}+ \u00b1 J Kljk(t,U} dNk{U) \n\nk = 1 \n\n(1) \n\nwhere KO describes the intrinsic rate and the \nK 1 describe the impulse response of the \npostsynaptic cell in response to an input \nevent. The output of the postsynaptic neuron \nis modeled as the integral of this rate \nfunction plus a mean-zero noise process, the \ninnovation martingale (Bremaud 1981): \n\nNj(t} = 11 Aj{U) du + Mj{t). \n\nTO \n\n(2) \n\nAn algorithm for estimating the first order \nkernel, Kl, was derived without assuming \n\nFigure 2 \n\n~ \nNj ... _ ..\u2022\u2022\u2022 \"\" \n\n.. / .... \n\n\f14 \n\nSydorenko and Young \n\nanything about the distribution of the presynaptic process and without assuming stationary \nflrst or second order product densities (Le., without assuming stationary rate or stationary \nauto-correlation). One or more such assumptions have been made in previous method of \nmoments based algorithms for estimating neural interactions (Chornoboy et al. 1988 describe \na maximum likelihood approach that does not require these assumptions). \nSince Kl is assumed to be stationary during the windowed interval (figure 1) while the \nprocess product densities are non-stationary (see PSTHs in figure 1), Kl is an average of \nseparate estimates of K 1 computed at each point in time during the windowed interval: \n\n\".... (Il) \n1 \nKliAt = -\nnil \n\nL \n\n\".... (Il \nIl) \nKliAti, tj \n\n(3) \nwhere K 1 inside the summation is an estimate of the impulse response of neuron i at time t? \n\n~-tf=t'\\ tfeI \n\nto a spike from neuron j at time tf (times are relative to stimulus onset); the digitization bin \nwidth D. (= 0.3 msec in our case) determines the location of the discrete time points as well \nas the number of separate kernel estimates, nL\\, within the windowed interval, I. The time \ndependent kernel, Kl(','), is computed by deconvolving the effects of the presynaptic process \ndistribution, described by rii below, from the estimate of the cross-cumulant density, qij: \n\nKlilt?, tf) = Lqj{vll, tf)f~(t?_VIl,tf)D. \n\nwhere: \n\nqj(UIl,VIl) = Pij(UIl,VIl)- Pi (UIlJPj(VIl)' \nfjj(UIl,VIl) = ~(UIl,VIl) + o(UIl_VIlJPj(vll), \nf~I(UIl,~) = ~-l[ \n\nJ' \n.r[fjj (UIl,VIl)] \n\n1 \n\npj (tf) = # { spike in neuron j during [tf t, tf +~ )} / (#{ trials) D.) , \n\n(4) \n\n(5) \n(6) \n\n(7) \n\n(8) \n\nPij(t?,tf) = \n\n#{ spike in i during [t~.A, t~ +D. ) and spike in j during [tf.A, tf +D. )} \n\n2 \n\n2 \n#{ trials} D. 2 \n\n2 2 , \n\n(9) \nwhere Be-> is the dirac delta function; ~and .r1 are the DFf and inverse DFf, respectively; \nand #{.} is the number of members in the set described inside the braces. If the presynaptic \nprocess is Poisson distributed, expression (4) simplifles to: \nK .. (t~ t~) = qj{t~, tf) \n,., ( Il) \npj tj \n\n11J I, J \n\n(to) \n\nUnder mild (physiologically justiflable) conditions, the estimator given by (3) converges in \nquadratic mean and yields an asymptotically unbiased estimate of the true impulse response \nfunction (in the general, (4), and Poisson presynaptic process, (10), cases). \n\n3 \n\nRESULTS \n\nFigure 3 displays estimates of synaptic impulse response functions computed using tradi tional \ncross-correlation analysis and compares them to estimates computed using the method of \nmoments algorithms described above. (We use the deflnition of cross-correlation given by \nVoigt & Young 1990; equivalent to the function given by dividing expression (10) by \n\n\fStationarity of Synaptic Coupling Strength Between Neurons \n\n15 \n\nexpression (9) after averaging across all tj-) Figure 3A compares estimates computed from \nthe responses of a real type II and type IV unit during the flrst 15 milliseconds of stimulation \n(where nonstationarity is greatest). Note that the cross-correlation estimate is distorted due to \nthe nonstationarity of the underlying processes. This distortion leads to an overestimation of \nthe effectiveness measure (shaded area) as compared to that yielded by the method of \nmoments algorithm below. Figure 3B compares estimates computed using a simulated data \nset where the presynaptic neuron had regular (non-Poisson) discharge properties. Note the \ncharacteristic ringing pattern in the cross-correlation estimate as well as the larger feature \namplitude in the non-Poisson method of moments estimate. \n\n(A) \n\nCross-correlogram \n\n(B) \n\nCross-correlogram \n\n30~--------~----------, \n\n15 \n\nO~~Pri~~++~rHrH~~~ \n\n-15 \n\n-10 \n\n-5 \n\n0 \n\nmilliseconds \n\n5 \n\n10 \n\n-30+T\"\"T\"T\"\"T\"T\"\"T\"\"'1-r-r-r-,r\"\"'T\"\"Il\"'T\"'1l'\"\"T\"\"1l'\"\"T\"\"1r-f \n50 \n\n-50 \n\n-25 \n\n25 \n\n0 \n\nmilliseconds \n\nMethod of Moments \n\nMethod of Moments \n\n30 \n. \n-\n15 \n: \no \n. -\n-15 \n-30 \n\n-50 \n\n\u2022 \n\nI \n\n-25 \n\n-10 \n\n-5 \n\n0 \n\nmilliseconds \n\n5 \n\n10 \n\np ~ \n'T \n\nIf-. \n\n. \nmilliseconds \n\n0 \n\nI \n\n25 \n\n50 \n\nFigure 3 \n\nResults from one analysis of eight different type II / type IV pairs are shown in flgure 4. For \neach pair, the effectiveness and the presynaptic (type ll) average rate during each window are \nplotted and fit with a least squares line. Similar analyses were performed for effectiveness \nversus postsynaptic rate and for effectiveness versus post-stimulus-onset time. The number of \npairs showing a positive or negative correlation of effectiveness with each parameter are \ntallied of table 1. The last column shows the average correlation coefflcient of the lines fit to \nthe eight sets of data. Note that: Synaptic efficacy tends to increase with time; there is no \nconsistent relationship between synaptic efflcacy and postsynaptic rate; \nthere is a strong \ninverse and linear correlation between synaptic efflcacy and presynaptic rate in 7 out of 8 \npairs. \nIf the data appearing in figure 4 had been plotted as effectiveness versus average interspike \ninterval (reciprocal of average rate) of the presynaptic neuron, the result would suggest that \nsynaptic effIcacy increases with average inter-spike interval. This result would be consistent \nwith the interpretation that the effectiveness of an input event is suppressed by the occurrence \nof an input event immediately before it. The linear model initially used to analyze these data \nneglects the possibility of such second order effects. \n\n\f16 \n\nSydorenko and Young \n\nTable 1: Summary of Results \n\nGRAPH \n\nEffectiveness \n\n-vs-\n\nPost Stimulus Onset Time \n\nEffectiveness \n\n-vs-\n\nAverage Postsynaptic Rate \n\nEffectiveness \n\n-vs-\n\nA verage Presynaptic Rate \n\nNUMBER OF NUMBER OF AVERAGE LINEAR \nPAIRS WITH \n\nPAIRS WITH \nNEGATIVE \n\nSLOPE \n\nREGRESSION \nCORRELATION \nCOEFFICIENT \n\nPOSITWE \n\nSLOPE \n\n7/8 \n\n1/8 \n\n5/8 \n\n3 /8 \n\n1/8 \n\n7/8 \n\n0.83 \n\n0.72 \n\n0.89 \n\n0.2 __ - - - - - - - - - - - - , \n\n0.2-r-------------, \n\n0.15 \n\n0.05 \n\n.. \n\u00b7\u00b7t\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7t\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7 \n- ! \n\n! \n\n: \n\n. \n\n. \n\n. \n\n............. _ ................. _ ............... _ ................. . \n\ni I'! \n...... ~~ ..... .)~ .. \nI \nA~J + -. I \n. ~~: : \n-:---- ..... : \n:-\n:\" \n: \n~'~ i \n\n: \n: \n: \ni \n\nO~~~~~~~ .. ~~~~ \n250 \n\n200 \n\n150 \n\n100 \n\n50 \n\nType II Rate (spikes/sec) \n\n...... -----............ _---_ ............. _-_ .......... ............... . \n\n. \n. \n. \n. \n. \n. \n. \n. \n. \n-1 \ni \n\n-\n\n\u00b7 \n\u00b7 \n\u00b7 \n\u00b7 \n\u00b7 \n\u00b7 \n\u00b7 \n\u00b7 \n\u00b7 \n\u00b7 \n: \n: \n!-\n\n. \n. \n. \n. \n. \n. \n. \n. \n. \n. \n! \n\\ \n\n\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7-t\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7.:.\u00b7\u00b7\u00b7~\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7t~\u00b7\u00b7\u00b7\u00b7\u00b7 ....... . \n\n\u00b7 \n\u00b7 \n\u00b7 \n\u00b7 \n\u00b7 \n\u00b7 \n\u00b7 \n\n. \n. \n. \n. \n. \n. \n. \n\ni a \n\n. \n\n+ \n\n~ \n\na\n\n. -\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022. :- \u2022\u2022 +-.Q.-..... ---t \u2022\u2022\u2022\u2022\u2022 -- \u2022\u2022\u2022 -\u2022\u2022\u2022 -.~ \u2022.\u2022 -\u2022\u2022 - ..\u2022\u2022\u2022\u2022\u2022 \u2022. \n+ ==a:=;; \n: \n: \n: -0 \n\u2022 ~ \n\na + + \n, . \n\u2022 \nAi \n\n~ \n: \n: \n\u2022 1 \n\n.J \n\nof' \n\n0.15 \n\n0.05 \n\n0 \n\n0 \n\n20 \nType II Inter-spike Interval (millisec) \n\n10 \n\n15 \n\n5 \n\nFigure 4 \n\nFigure 5 \n\nWe used a modification of the analysis described in the methods to investigate second order \neffects. Rather than window small segments of the stimulus duration as in figure I, the entire \nduration was used in this analysis. Impulse response estimates were constructed conditional \n\n\fStationarity of Synaptic Coupling Strength Between Neurons \n\n17 \n\non presynaptic interspike interval. For example, the first estimate was constructed using \npresynaptic events occurring after alms interspike interval, the second estimate was based \non events after a 2 ms interval, and so on. \n\nThe results of the second order analysis are shown in figure 5. Note that there is no \nsystematic relationship between conditioning interspike interval and effectiveness. In fact. \nlines fitted to these points tend to be horizontal, suggesting that there are no significant \nsecond order effects under these experimental conditions. \n\nOur results suggest that synaptic efficacy is inversely and roughly linearly related to average \npresynaptic rate. We have attempted to understand the mechanism of the observed decrease \nin efficacy in terms of a model that asswnes stationary synaptic coupling mechanisms. The \nmodel was designed to address the following hypothesis: Could the decrease in synaptic \nefficacy at high input rates be due to an increase in the likelihood of driving the stochastic \nintensity below zero, and, hence decreasing the apparent efficacy of the input due to clipping? \nThe answer was pursued by attempting to reproduce the data collected for the 3 best type II / \ntype IV pairs in our data set. Real data recorded from the presynaptic unit are used as input \nto these models. The parameters of the models were adjusted so that the first moment of the \noutput process had the same quantitative trajectory as that seen in the real postsynaptic unit. \nThe simulated data were analyzed by the same algorithms used to analyze the real data. Our \ngoal was to compare the simulated results with the real results. If the simulated data showed \nthe same inverse relationship between presynaptic rate and synaptic efficacy as the real data, \nit would suggest that the phenomenon is due to non-linear clipping by the postsynaptic unit. \nThe simulation algorithm was based on the model described in figure 2 and equation (1) but \nwith the following modifications: \n\n\u2022 \n\nThe experimentally determined type IV PST profile was substituted for KO (this term \nrepresents the average combined influence of all extrinsic inputs to the type IV cell plus \nthe intrinsic spontaneous rate). \n\n\u2022 An impulse response function estimated from the data was substituted for Kl (this kernel \n\n\u2022 \n\nis stationary in the simulation model). \nThe convolution of the experimentally determined type II spikes with the first-order \nkernel was used to perturb the output cell's stochastic intensity: \n\nAl{t) = MAX [0, Pl{t) + L \n\ndN2 (Ui) = s \nwhere: dN2(t) = Real type n cell spike record, and \nPI (t) = PST profile of real type IV cell. \n\nKl 12{t - Ui) 1 \n\n\u2022 \n\nThe output process was simulated as a non-homogeneous Poisson process with ),,1 (t) as \nits parameter. This process was modified by a 0.5 msec absolute dead time. \n\n\u2022 The simulated data were analyzed in the same manner as the real data. \n\nThe dependence of synaptic efficacy on presynaptic rate in the simulated data was compared \nto the corresponding real data. In lout of the 3 cases, we observed an inverse relationship \nbetween input rate and efficacy despite the use of a stationary first order kernel in the \nsimulation. The similarity between the real and simulated results for this one case suggests \nthat the mechanism may be purely statistical rather than physiological (e.g., not presynaptic \ndepletion or postsynaptic desensitization). The other 2 simulations did not yield a strong \ndependence of effectiveness on input rate and, hence, failed to mimic the experimental \nresults. In these two cases, the results suggest that the mechanism is not due solely to \nclipping, but involves some additional, possibly physiological, mechanisms. \n\n\f18 \n\nSydorenko and Young \n\n4 \n\nCONCLUSIONS \n\n1) The amount of inhibition imparted to type IV units by individual presynaptic type II unit \naction potentials (expressed as the expected nwnber of type N spikes eliminated per type \nII spike) is inversely and roughly linearly related to the average rate of the type II unit. \n\n(2) There is no evidence for second order synaptic effects at the type II spike rates tested. In \nother words, the inhibitory effect of two successive type II spikes is simply the linear \nsum of the inhibition imparted by each individual spike. \n\n(3) There is no consistent relationship between type II I type IV synaptic efficacy and \n\npostsynaptic (type IV) rate. \n\n(4) Simulations, in some cases, suggest that the inverse relationship between presynaptic rate \nand effectiveness may be reproduced using a simple statistical model of neural \ninteraction. \n\n(5) We found no evidence that would explain the discrepancy between Voigt and Young's \nresults and Gochin's results in the DCN. Gochin observed correlogram features \nconsistent with monosynaptic excitatory connections within the DCN when short tone \nbursts were used as stimuli. We did not observe excitatory features between any unit \npairs using short tone bursts. \n\nAcknowledgements \n\nDr. Alan Karr assisted in developing Eqns. 1-10. E. Nelken provided helpful comments. \nResearch supported by NIH grant DCOO115. \n\nReferences \n\nBremaud, P. (1981). Point Processes and Queues: Martingale Dynamics. New York, \nSpringer-Verlag. \nCaspary, D.M., Rybak, L.P.et al. (1984). \"Baclofen reduces tone-evoked activity of cochlear \nnucleus neurons.\" Hear Res. 13: 113-22. \nChomoboy, E.S., Schramm, L.P.et al. (1988). \"Maximum likelihood identification of neural \npoint process systems.\" BioI Cybem. 59: 265-75. \nGochin, P.M., Kaltenbach, J.A.et al. (1989). \"Coordinated activity of neuron pairs in \nanesthetized rat dorsal cochlear nucleus.\" Brain Res. 497: 1-11. \nManis, P.B. & Brownell, W.E. (1983). \"Synaptic organization of eighth nerve afferents to cat \ndorsal cochlear nucleus.\" J Neurophysiol. 50: 1156-81. \nRhode, W.S., Smith, P.H.et al. (1983). \"Physiological response properties of cells labeled \nintracellularly with horseradish peroxidase in cat dorsal cochlear nucleus.\" J Comp Neurol. \n213: 426-47. \nVoigt, H.F. & Young, ED. (1980). \"Evidence of inhibitory interactions between neurons in \ndorsal cochlear nucleus.\" J Neurophys. 44: 76-96. \nVoigt, H.F. & Young, E.D. (1990). \"Cross-correlation analysis of inhibitory interactions in \nthe Dorsal Cochlear Nucleus.\" J Neurophys. 54: 1590-1610. \nYoung, E.D. & Brownell, W.E. (1976). \"Responses to tones and noise of single cells in \ndorsal cochlear nucleus of unanesthetized cats.\" J Neurophys. 39: 282-300. \n\n\f", "award": [], "sourceid": 479, "authors": [{"given_name": "Mark", "family_name": "Sydorenko", "institution": null}, {"given_name": "Eric", "family_name": "Young", "institution": null}]}