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180 nips-2002-Selectivity and Metaplasticity in a Unified Calcium-Dependent Model

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Author: Luk Chong Yeung, Brian S. Blais, Leon N. Cooper, Harel Z. Shouval

Abstract: A uniﬁed, biophysically motivated Calcium-Dependent Learning model has been shown to account for various rate-based and spike time-dependent paradigms for inducing synaptic plasticity. Here, we investigate the properties of this model for a multi-synapse neuron that receives inputs with diﬀerent spike-train statistics. In addition, we present a physiological form of metaplasticity, an activity-driven regulation mechanism, that is essential for the robustness of the model. A neuron thus implemented develops stable and selective receptive ﬁelds, given various input statistics 1

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sentIndex sentText sentNum sentScore

1 edu Abstract A uniﬁed, biophysically motivated Calcium-Dependent Learning model has been shown to account for various rate-based and spike time-dependent paradigms for inducing synaptic plasticity. [sent-8, score-0.301]

2 Here, we investigate the properties of this model for a multi-synapse neuron that receives inputs with diﬀerent spike-train statistics. [sent-9, score-0.102]

3 In addition, we present a physiological form of metaplasticity, an activity-driven regulation mechanism, that is essential for the robustness of the model. [sent-10, score-0.117]

4 Activation of NMDA receptors is also essential for functional plasticity in vivo [5]. [sent-12, score-0.315]

5 An inﬂuential hypothesis holds that modest elevations of Ca above the basal line would induce LTD, while higher elevations would induce LTP[6, 7]. [sent-13, score-0.076]

6 In this model, cellular activity is translated locally into the dendritic calcium concentrations Cai , through the voltage and time-dependence of the NMDA channels. [sent-16, score-0.445]

7 The level of Cai determines the sign and magnitude of synaptic plasticity as determined through a function of local calcium Ω(Cai )(see Methods). [sent-17, score-0.614]

8 Implementation of this simple yet biophysical model has shown that it is suﬃcient to account for the outcome of diﬀerent induction protocols of synaptic plasticity in a one-dimensional input space, as illustrated in Figure 1. [sent-19, score-0.45]

9 In the pairing protocol, LTD occurs when LFS is paired with a small depolarization of the postsynaptic voltage while a larger depolarization yields LTP (Figure 1a), due to the voltage-dependence of the NMDA currents. [sent-20, score-0.379]

10 In the rate-based protocol, low-frequency stimulation (LFS) gives rise to LTD while high-frequency stimulation (HFS) produces LTP (Figure 1b), due to the time-integration dynamics of the calcium transients. [sent-21, score-0.226]

11 Finally, STDP gives LTD if a post-spike comes before a pre-spike within a time-window, and LTP if a post-spike comes after a pre-spike (Figure 1c); this is due to the coincidencedetector property of the NMDA receptors and the shape of the BPAP. [sent-22, score-0.12]

12 The Pairing Protocol was simulated with a ﬁxed input rate of 3 Hz; STDP curve is shown for 1 Hz. [sent-26, score-0.123]

13 In this study we investigate characteristics of the Calcium Control Hypothesis such as cooperativity and competition, and examine how they give rise to input selectivity. [sent-28, score-0.137]

14 A neuron is called selective to a speciﬁc input pattern if it responds strongly to it and not to other patterns, which is equivalent to having a potentiated pathway to this pattern. [sent-29, score-0.313]

15 Input selectivity is a general feature of neurons and underlies the formation of receptive ﬁelds and topographic mappings. [sent-30, score-0.327]

16 We demonstrate that using the UCM alone, selectivity can arise, but only within a narrow range of parameters. [sent-31, score-0.196]

17 Metaplasticity, the activity-dependent modulation of synaptic plasticity, is essential for robustness of the BCM model [11]. [sent-32, score-0.261]

18 2 Selectivity to Spike Train Correlations The development of neuronal selectivity, given any learning rule, depends on the statistical structures of the input environment. [sent-36, score-0.109]

19 One method of examining this feature is to generate input spike trains with diﬀerent statistics across synapses. [sent-38, score-0.136]

20 We use a simple scenario in which half of the synapses (group B) receive noisy Poisson spike trains with a mean rate rin , and the other half (group A), receive correlated spikes with the same rate rin . [sent-39, score-0.742]

21 One might expect that, by ﬁring together, group A will gain control of the post-synaptic ﬁring times and thus be potentiated, while group B will be depressed, in a manner similar to the STDP described by Song et al. [sent-41, score-0.124]

22 In addition to the 100 excitatory neurons our neuron receives 20 inhibitory inputs. [sent-43, score-0.235]

23 There exists a range of input frequencies (Figure 2a, left) at which segregation occurs between the correlated and uncorrelated groups. [sent-45, score-0.276]

24 The cooperativity among the synapses in group A enhances its probability of generating a post-spike, which, through the BPAP causes strong depolarization. [sent-46, score-0.313]

25 Since the NMDA channels are still open due to a recent pre-spike, this is likely to potentiates these synapses in a Hebbian-associative fashion. [sent-47, score-0.243]

26 Group B will ﬁre with equal probability before and after a post-spike which, given a suﬃciently low NMDA receptor conductance, ensures that, on average, depression takes place. [sent-48, score-0.113]

27 At the ﬁnal state, the output spike train is irregular (Figure 2a, right) but its rate is stable (Figure 2a, center), indicating that the system had reached a ﬁxed point with a balance between excitation and inhibition. [sent-49, score-0.135]

28 5 0 0 5 10 5 Time (ms x 10 ) 10 2 CV Average weight 1 Output rate (Hz) a) 5 0 0 10 5 5 Time (ms x 10 ) 1 0 10 5 5 Time (ms x 10 ) b) 8 Hz 0. [sent-51, score-0.113]

29 5 0 0 1 2 Time (ms x 10 5 ) 1 Average weight Average weight 1 12 Hz 0. [sent-52, score-0.104]

30 5 0 0 1 2 Time (ms x 10 5 ) Figure 2: Segregation of the synapses for diﬀerent input structures. [sent-53, score-0.238]

31 Left, time evolutions of the average synaptic weight for the groups A (solid) and B (dashed). [sent-55, score-0.314]

32 In fact, a slight change in the value of rin disrupts the segregation described previously (Figure 2b). [sent-61, score-0.306]

33 For too high or too low values of rin , both channels are potentiated and depressed, respectively. [sent-62, score-0.312]

34 3 Metaplasticity In the BCM theory the threshold between LTD and LTP moves as a function of the history of postsynaptic activity [11]. [sent-65, score-0.168]

35 This type of activity-dependent regulation of the properties of synaptic plasticity, or metaplasticity, was developed to ensure selectivity and stability. [sent-66, score-0.466]

36 Experimental results have linked some forms of metaplasticity to the magnitude of the NMDA conductance; it is shown that as the cellular activity increases, NMDA conductance is down-regulated, and vice-versa [15, 16, 13, 17]. [sent-67, score-0.493]

37 Under the Calcium Control Hypothesis, this sets the ground for a more physiological formulation of metaplasticity [18]. [sent-68, score-0.343]

38 NMDA conductance is interpreted here as the total number (gm ) of NMDA channels inserted in the membrane of the postsynaptic terminal. [sent-69, score-0.238]

39 Consider a simple kinetic model in which additional channels can be inserted from an intracellular pool (gi ) or removed and returned to the pool in an activity dependent manner. [sent-70, score-0.133]

40 The ﬁxed point is: gt ∗ gm = (1) k– /(k+ V α ) + 1 If, in this model, cellular activity is translated into Ca, then gm can be loosely interpreted as the inverse of the BCM sliding threshold θm [18]. [sent-72, score-0.717]

41 Notice that in the original form of BCM, θm is the time average of a non-linear function of the postsynaptic the activity level. [sent-73, score-0.203]

42 In order to achieve competition, gm should not depend solely on local (synaptic) variables, but should rather detect changes of the global patterns of cellular activity. [sent-74, score-0.322]

43 Here, the activity-signaling global variable is taken to be postsynaptic membrane potential. [sent-75, score-0.102]

44 Implementation of metaplasticity widens signiﬁcantly the range of input frequencies for which segregation between the weights of correlated and uncorrelated synapses is observed; this is shown in Figure 3a. [sent-76, score-0.755]

45 At low spiking activity, the subthreshold depolarization levels prevent signiﬁcant inward Ca currents. [sent-77, score-0.113]

46 Persistent post-spike generation will lead gm and therefore Ca to decrease, hence scaling the synaptic weights downwards. [sent-79, score-0.45]

47 Competition arises as the system searches for the balance between the selective positive feed-back of a standard Hebbian rule and the overall negative feed-back of a sliding threshold mechanism. [sent-80, score-0.089]

48 However, consistent with the rate-based protocol described before, at too low and too high rin selectivity is disrupted, and the synapses will eventually all depress or potentiate, regardless of the statistical structures of the stimulus. [sent-81, score-0.592]

49 Strengthening the correlation increases segregation (Figure 3b), demonstrating the eﬀects of lateral cooperativity in potentiation. [sent-82, score-0.223]

50 On the other hand, increasing the fraction of correlated inputs weakens the ﬁnal weight of the correlated group (Figure 3c), suggesting that less potentiation is needed to control the output spike-timing. [sent-83, score-0.284]

51 5 Correlation parameter 0 100 50 % of correlated inputs Figure 3: The eﬀects of metaplasticity. [sent-86, score-0.068]

52 (a) The weights segregate within the range of input frequency = [5, 35] Hz in a half correlated (solid), half uncorrelated (dashed) input environment; shown are the average ﬁnal weights within each group, correlation parameter c = 0. [sent-87, score-0.297]

53 (b) The average ﬁnal weight as a function of the correlation parameter, rin = 10 Hz. [sent-89, score-0.274]

54 (c) The average ﬁnal weight as a function of the fraction of correlated inputs, rin = 10 Hz, c = 0. [sent-90, score-0.306]

55 4 Selectivity to patterns of rate distribution An alternative input environment is one in which the rates vary across the synapses and over time. [sent-92, score-0.343]

56 Since the mean switching time is constant and much smaller than the time constant of learning, each synapse receives the same average input over time. [sent-97, score-0.155]

57 However, we observe that, after training, the neuron spontaneously breaks the symmetry, as a subset of synapses becomes potentiated, while others are depressed (Figure 4b). [sent-98, score-0.347]

58 The ﬁnal state of the neuron is one that is selective to the last pattern ( a), left most). [sent-103, score-0.157]

59 5 Discussion Neurons in many cortical areas develop receptive ﬁelds that are selective to a small subset of stimulating inputs. [sent-104, score-0.101]

60 It is likely, therefore, that receptive ﬁeld formation relies on the same type of NMDA-dependent synaptic plasticity observed in vitro [1, 2, 4]. [sent-106, score-0.471]

61 Previous work has shown that these in vitro rate and spike time-induced plasticity can be accounted for by the biologicallyinspired Uniﬁed Calcium Model. [sent-107, score-0.296]

62 Metaplasticity adds robustness to the system and reinforces temporal competition between input patterns [11] , by controlled scaling of NMDAR currents. [sent-109, score-0.17]

63 We have shown here that even in simple input environments there is segregation among the synaptic strengths, depending on the temporal input statistics of diﬀerent channels. [sent-110, score-0.463]

64 Because the UCM is responsive to input rates, in addition to spike-timing, we are able to achieve selectivity for rate-distribution patterns in spiking neurons that is comparable to the selectivity obtained in simpliﬁed, continuous-valued systems [23]. [sent-112, score-0.584]

65 This result suggests that the coexistence and complementarity of rate- and spike time-dependent plasticities, previously demonstrated for a one-dimensional neuron [8], can also be extended to multi-dimensional input environments. [sent-113, score-0.238]

66 We are currently investigating the formation of receptive ﬁelds in more realistic environments, such as natural stimuli and examining how the their statistical properties can be translated into a physiological mechanism for emergence of input selectivity. [sent-114, score-0.221]

67 6 Methods We simulate a single neuron with 20 non-plastic inhibitory synapses and 100 excitatory synapses undergoing the Calcium-Dependent learning rule: wi = η(Cai ) (Ω(Cai ) − λw) , ˙ (2) where wi is the synaptic weight of the synapse i, i = 1, . [sent-115, score-0.964]

68 5; additionally, wi is constrained within hard boundaries: wi ∈ [0, 1] for the cases where no metaplasticity is used. [sent-124, score-0.391]

69 The NMDA-mediated calcium concentration varies as: dCai Cai =I− , dt τCa (3) where I is the NMDA current and τCa = 20 ms is the passive decay time constant [24]. [sent-125, score-0.358]

70 I depends on the association between pre-spike times and postsynaptic depolarization level, described by I = gm f (t, tpre )H(V ) [7]. [sent-126, score-0.4]

71 70% of this value decays with time constant τf = 50 ms, the remaining N decays with time constant τs = 200 ms. [sent-131, score-0.106]

72 57 (4) with the reversal potential for calcium Vrev = 130 mV. [sent-134, score-0.226]

73 If a pre-spike arrives at the max excitatory [inhibitory] synapse i, Gex[in] (t) = Gex[in] (t − 1) + gex[in] gi ; otherwise, Gex and Gin decay exponentially with time constant τ = 5 ms. [sent-136, score-0.145]

74 For excitatory and inhibitory synapses, (gi , g max ) = (wi , 0. [sent-137, score-0.085]

75 75% of this value decays rapidly (τf = 3 ms) and the B remaining decays slowly (τs = 35 ms) [25]. [sent-141, score-0.106]

76 The voltage at the synaptic site is thus given by the sum V = Vm +BPAP. [sent-142, score-0.289]

77 For simulations involving diﬀerent rates, the 100 synapses were ﬁrst divided into 4 channels of 25 synapses. [sent-147, score-0.243]

78 At each epoch, one of the channels was randomly chosen and assigned a mean rate r ∗ , while others receive spike-trains with mean rate r < r∗ . [sent-149, score-0.189]

79 For metaplasticity in Equation 1, we use the parameters: k– /(k+ ) = 9. [sent-150, score-0.303]

80 A synaptic model of memory; long-term potentiation the hippocampus. [sent-162, score-0.261]

81 Homosynaptic long-term depression in area CA1 of hippocampus and the eﬀects on NMDA receptor blockade. [sent-169, score-0.113]

82 Regulation of synaptic eﬃcacy u by coincidence of postsynaptic APs and EPSPs. [sent-180, score-0.329]

83 Synaptic modiﬁcations in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynaptic cell type. [sent-185, score-0.403]

84 Blockade of NMDA receptors disrupts experience-dependent plasticity of kitten striate cortex. [sent-194, score-0.324]

85 A physiological basis for a theory of synapse modiﬁcation. [sent-202, score-0.098]

86 A uniﬁed theory of nmda receptordependent bidirectional synaptic plasticity. [sent-219, score-0.622]

87 Calcium stores regulate the polarity and input speciﬁcity of synaptic modiﬁcation. [sent-232, score-0.289]

88 Rate, timing, and cooperativity o o jointly determine cortical synaptic plasticity. [sent-241, score-0.302]

89 Theory for the development of neuron selectivity: orientation speciﬁcity and binocular interaction in visual cortex. [sent-249, score-0.239]

90 Visual experience and deprivation bidirectionally modify the composition and function of NMDA receptors in visual cortex. [sent-270, score-0.219]

91 Activity dependent increase in NMDA receptor responses during development of visual cotex. [sent-284, score-0.178]

92 Rapid, experiencedependent expression of synaptic NMDA receptors in visual cortex in vivo. [sent-295, score-0.446]

93 Activity co-regulates quantal ampa and nmda currents at neocortical synapses. [sent-310, score-0.395]

94 Converging evidence for a simpliﬁed biophysical model of synaptic plasticity. [sent-322, score-0.227]

95 Early development of visual cortical cells in normal and e dark reared kittens: relationship between orientation selectivity and ocular dominance. [sent-329, score-0.333]

96 Development of orientation preference maps in ferret primary visual cortex. [sent-339, score-0.09]

97 Suppression of cortical nmda receptor function prevents development of orientation selectivity in the primary visual cortex. [sent-351, score-0.803]

98 The role of presynaptic activity in monocular deprivation: Comparison of homosynaptic and heterosynaptic mechanisms. [sent-361, score-0.109]

99 Synaptic plasticity in visual cortex: Comparison of theory with experiment. [sent-373, score-0.217]

100 A synaptically controlled, associative signal for hebbian plasticity in hippocampal neurons. [sent-389, score-0.199]

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Abstract: Cortical neurons have been reported to use both rate and temporal codes. Here we describe a novel mode in which each neuron generates exactly 0 or 1 action potentials, but not more, in response to a stimulus. We used cell-attached recording, which ensured single-unit isolation, to record responses in rat auditory cortex to brief tone pips. Surprisingly, the majority of neurons exhibited binary behavior with few multi-spike responses; several dramatic examples consisted of exactly one spike on 100% of trials, with no trial-to-trial variability in spike count. Many neurons were tuned to stimulus frequency. Since individual trials yielded at most one spike for most neurons, the information about stimulus frequency was encoded in the population, and would not have been accessible to later stages of processing that only had access to the activity of a single unit. These binary units allow a more efficient population code than is possible with conventional rate coding units, and are consistent with a model of cortical processing in which synchronous packets of spikes propagate stably from one neuronal population to the next. 1 Binary coding in auditory cortex We recorded responses of neurons in the auditory cortex of anesthetized rats to pure-tone pips of different frequencies [1, 2]. Each pip was presented repeatedly, allowing us to assess the variability of the neural response to multiple presentations of each stimulus. We first recorded multi-unit activity with conventional tungsten electrodes (Fig. 1a). The number of spikes in response to each pip fluctuated markedly from one trial to the next (Fig. 1e), as though governed by a random mechanism such as that generating the ticks of a Geiger counter. Highly variable responses such as these, which are at least as variable as a Poisson process, are the norm in the cortex [3-7], and have contributed to the widely held view that cortical spike trains are so noisy that only the average firing rate can be used to encode stimuli. Because we were recording the activity of an unknown number of neurons, we could not be sure whether the strong trial-to-trial fluctuations reflected the underlying variability of the single units. We therefore used an alternative technique, cell- a b Single-unit recording method 5mV Multi-unit 1sec Raw cellattached voltage 10 kHz c Single-unit . . . . .. .. ... . . .... . ... . Identified spikes Threshold e 28 kHz d Single-unit 80 120 160 200 Time (msec) N = 29 tones 3 2 1 Poisson N = 11 tones ry 40 4 na bi 38 kHz 0 Response variance/mean (spikes/trial) High-pass filtered 0 0 1 2 3 Mean response (spikes/trial) Figure 1: Multi-unit spiking activity was highly variable, but single units obeyed binomial statistics. a Multi-unit spike rasters from a conventional tungsten electrode recording showed high trial-to-trial variability in response to ten repetitions of the same 50 msec pure tone stimulus (bottom). Darker hash marks indicate spike times within the response period, which were used in the variability analysis. b Spikes recorded in cell-attached mode were easily identified from the raw voltage trace (top) by applying a high-pass filter (bottom) and thresholding (dark gray line). Spike times (black squares) were assigned to the peaks of suprathreshold segments. c Spike rasters from a cell-attached recording of single-unit responses to 25 repetitions of the same tone consisted of exactly one well-timed spike per trial (latency standard deviation = 1.0 msec), unlike the multi-unit responses (Fig. 1a). Under the Poisson assumption, this would have been highly unlikely (P ~ 10 -11). d The same neuron as in Fig. 1c responds with lower probability to repeated presentations of a different tone, but there are still no multi-spike responses. e We quantified response variability for each tone by dividing the variance in spike count by the mean spike count across all trials for that tone. Response variability for multi-unit tungsten recording (open triangles) was high for each of the 29 tones (out of 32) that elicited at least one spike on one trial. All but one point lie above one (horizontal gray line), which is the value produced by a Poisson process with any constant or time varying event rate. Single unit responses recorded in cell-attached mode were far less variable (filled circles). Ninety one percent (10/11) of the tones that elicited at least one spike from this neuron produced no multi-spike responses in 25 trials; the corresponding points fall on the diagonal line between (0,1) and (1,0), which provides a strict lower bound on the variability for any response set with a mean between 0 and 1. No point lies above one. attached recording with a patch pipette [8, 9], in order to ensure single unit isolation (Fig. 1b). This recording mode minimizes both of the main sources of error in spike detection: failure to detect a spike in the unit under observation (false negatives), and contamination by spikes from nearby neurons (false positives). It also differs from conventional extracellular recording methods in its selection bias: With cell- attached recording neurons are selected solely on the basis of the experimenter’s ability to form a seal, rather than on the basis of neuronal activity and responsiveness to stimuli as in conventional methods. Surprisingly, single unit responses were far more orderly than suggested by the multi-unit recordings; responses typically consisted of either 0 or 1 spikes per trial, and not more (Fig. 1c-e). In the most dramatic examples, each presentation of the same tone pip elicited exactly one spike (Fig. 1c). In most cases, however, some presentations failed to elicit a spike (Fig. 1d). Although low-variability responses have recently been observed in the cortex [10, 11] and elsewhere [12, 13], the binary behavior described here has not previously been reported for cortical neurons. a 1.4 N = 3055 response sets b 1.2 1 Poisson 28 kHz - 100 msec 0.8 0.6 0.4 0.2 0 0 ry na bi Response variance/mean (spikes/trial) The majority of the neurons (59%) in our study for which statistical significance could be assessed (at the p<0.001 significance level; see Fig. 2, caption) showed noisy binary behavior—“binary” because neurons produced either 0 or 1 spikes, and “noisy” because some stimuli elicited both single spikes and failures. In a substantial fraction of neurons, however, the responses showed more variability. We found no correlation between neuronal variability and cortical layer (inferred from the depth of the recording electrode), cortical area (inside vs. outside of area A1) or depth of anesthesia. Moreover, the binary mode of spiking was not due to the brevity (25 msec) of the stimuli; responses that were binary for short tones were comparably binary when longer (100 msec) tones were used (Fig. 2b). Not assessable Not significant Significant (p<0.001) 0.2 0.4 0.6 0.8 1 1.2 Mean response (spikes/trial) 28 kHz - 25 msec 1.4 0 40 80 120 160 Time (msec) 200 Figure 2: Half of the neuronal population exhibited binary firing behavior. a Of the 3055 sets of responses to 25 msec tones, 2588 (gray points) could not be assessed for significance at the p<0.001 level, 225 (open circles) were not significantly binary, and 242 were significantly binary (black points; see Identification methods for group statistics below). All points were jittered slightly so that overlying points could be seen in the figure. 2165 response sets contained no multi-spike responses; the corresponding points fell on the line from [0,1] to [1,0]. b The binary nature of single unit responses was insensitive to tone duration, even for frequencies that elicited the largest responses. Twenty additional spike rasters from the same neuron (and tone frequency) as in Fig. 1c contain no multi-spike responses whether in response to 100 msec tones (above) or 25 msec tones (below). Across the population, binary responses were as prevalent for 100 msec tones as for 25 msec tones (see Identification methods for group statistics). In many neurons, binary responses showed high temporal precision, with latencies sometimes exhibiting standard deviations as low as 1 msec (Fig. 3; see also Fig. 1c), comparable to previous observations in the auditory cortex [14], and only slightly more precise than in monkey visual area MT [5]. High temporal precision was positively correlated with high response probability (Fig. 3). a b N = (44 cells)x(32 tones) 14 N = 32 tones 12 30 Jitter (msec) Jitter (msec) 40 10 8 6 20 10 4 2 0 0 0 0.2 0.4 0.6 0.8 Mean response (spikes/trial) 1 0 0.4 0.8 1.2 1.6 Mean response (spikes/trial) 2 Figure 3: Trial-to-trial variability in latency of response to repeated presentations of the same tone decreased with increasing response probability. a Scatter plot of standard deviation of latency vs. mean response for 25 presentations each of 32 tones for a different neuron as in Figs. 1 and 2 (gray line is best linear fit). Rasters from 25 repeated presentations of a low response tone (upper left inset, which corresponds to left-most data point) display much more variable latencies than rasters from a high response tone (lower right inset; corresponds to right-most data point). b The negative correlation between latency variability and response size was present on average across the population of 44 neurons described in Identification methods for group statistics (linear fit, gray). The low trial-to-trial variability ruled out the possibility that the firing statistics could be accounted for by a simple rate-modulated Poisson process (Fig. 4a1,a2). In other systems, low variability has sometimes been modeled as a Poisson process followed by a post-spike refractory period [10, 12]. In our system, however, the range in latencies of evoked binary responses was often much greater than the refractory period, which could not have been longer than the 2 msec inter-spike intervals observed during epochs of spontaneous spiking, indicating that binary spiking did not result from any intrinsic property of the spike generating mechanism (Fig. 4a3). Moreover, a single stimulus-evoked spike could suppress subsequent spikes for as long as hundreds of milliseconds (e.g. Figs. 1d,4d), supporting the idea that binary spiking arises through a circuit-level, rather than a single-neuron, mechanism. Indeed, the fact that this suppression is observed even in the cortex of awake animals [15] suggests that binary spiking is not a special property of the anesthetized state. It seems surprising that binary spiking in the cortex has not previously been remarked upon. In the auditory cortex the explanation may be in part technical: Because firing rates in the auditory cortex tend to be low, multi-unit recording is often used to maximize the total amount of data collected. Moreover, our use of cell-attached recording minimizes the usual bias toward responsive or active neurons. Such explanations are not, however, likely to account for the failure to observe binary spiking in the visual cortex, where spike count statistics have been scrutinized more closely [3-7]. One possibility is that this reflects a fundamental difference between the auditory and visual systems. An alternative interpretation— a1 b Response probability 100 spikes/s 2 kHz Poisson simulation c 100 200 300 400 Time (msec) 500 20 Ratio of pool sizes a2 0 16 12 8 4 0 a3 Poisson with refractory period 0 40 80 120 160 200 Time (msec) d Response probability PSTH 0.2 0.4 0.6 0.8 1 Mean spike count per neuron 1 0.8 N = 32 tones 0.6 0.4 0.2 0 2.0 3.8 7.1 13.2 24.9 46.7 Tone frequency (kHz) Figure 4: a The lack of multi-spike responses elicited by the neuron shown in Fig. 3a were not due to an absolute refractory period since the range of latencies for many tones, like that shown here, was much greater than any reasonable estimate for the neuron’s refractory period. (a1) Experimentally recorded responses. (a2) Using the smoothed post stimulus time histogram (PSTH; bottom) from the set of responses in Fig. 4a, we generated rasters under the assumption of Poisson firing. In this representative example, four double-spike responses (arrows at left) were produced in 25 trials. (a3) We then generated rasters assuming that the neuron fired according to a Poisson process subject to a hard refractory period of 2 msec. Even with a refractory period, this representative example includes one triple- and three double-spike responses. The minimum interspike-interval during spontaneous firing events was less than two msec for five of our neurons, so 2 msec is a conservative upper bound for the refractory period. b. Spontaneous activity is reduced following high-probability responses. The PSTH (top; 0.25 msec bins) of the combined responses from the 25% (8/32) of tones that elicited the largest responses from the same neuron as in Figs. 3a and 4a illustrates a preclusion of spontaneous and evoked activity for over 200 msec following stimulation. The PSTHs from progressively less responsive groups of tones show progressively less preclusion following stimulation. c Fewer noisy binary neurons need to be pooled to achieve the same “signal-to-noise ratio” (SNR; see ref. [24]) as a collection of Poisson neurons. The ratio of the number of Poisson to binary neurons required to achieve the same SNR is plotted against the mean number of spikes elicited per neuron following stimulation; here we have defined the SNR to be the ratio of the mean spike count to the standard deviation of the spike count. d Spike probability tuning curve for the same neuron as in Figs. 1c-e and 2b fit to a Gaussian in tone frequency. and one that we favor—is that the difference rests not in the sensory modality, but instead in the difference between the stimuli used. In this view, the binary responses may not be limited to the auditory cortex; neurons in visual and other sensory cortices might exhibit similar responses to the appropriate stimuli. For example, the tone pips we used might be the auditory analog of a brief flash of light, rather than the oriented moving edges or gratings usually used to probe the primary visual cortex. Conversely, auditory stimuli analogous to edges or gratings [16, 17] may be more likely to elicit conventional, rate-modulated Poisson responses in the auditory cortex. Indeed, there may be a continuum between binary and Poisson modes. Thus, even in conventional rate-modulated responses, the first spike is often privileged in that it carries most of the information in the spike train [5, 14, 18]. The first spike may be particularly important as a means of rapidly signaling stimulus transients. Binary responses suggest a mode that complements conventional rate coding. In the simplest rate-coding model, a stimulus parameter (such as the frequency of a tone) governs only the rate at which a neuron generates spikes, but not the detailed positions of the spikes; the actual spike train itself is an instantiation of a random process (such as a Poisson process). By contrast, in the binomial model, the stimulus parameter (frequency) is encoded as the probability of firing (Fig. 4d). Binary coding has implications for cortical computation. In the rate coding model, stimulus encoding is “ergodic”: a stimulus parameter can be read out either by observing the activity of one neuron for a long time, or a population for a short time. By contrast, in the binary model the stimulus value can be decoded only by observing a neuronal population, so that there is no benefit to integrating over long time periods (cf. ref. [19]). One advantage of binary encoding is that it allows the population to signal quickly; the most compact message a neuron can send is one spike [20]. Binary coding is also more efficient in the context of population coding, as quantified by the signal-to-noise ratio (Fig. 4c). The precise organization of both spike number and time we have observed suggests that cortical activity consists, at least under some conditions, of packets of spikes synchronized across populations of neurons. Theoretical work [21-23] has shown how such packets can propagate stably from one population to the next, but only if neurons within each population fire at most one spike per packet; otherwise, the number of spikes per packet—and hence the width of each packet—grows at each propagation step. Interestingly, one prediction of stable propagation models is that spike probability should be related to timing precision, a prediction born out by our observations (Fig. 3). The role of these packets in computation remains an open question. 2 Identification methods for group statistics We recorded responses to 32 different 25 msec tones from each of 175 neurons from the auditory cortices of 16 Sprague-Dawley rats; each tone was repeated between 5 and 75 times (mean = 19). Thus our ensemble consisted of 32x175=5600 response sets, with between 5 and 75 samples in each set. Of these, 3055 response sets contained at least one spike on at least on trial. For each response set, we tested the hypothesis that the observed variability was significantly lower than expected from the null hypothesis of a Poisson process. The ability to assess significance depended on two parameters: the sample size (5-75) and the firing probability. Intuitively, the dependence on firing probability arises because at low firing rates most responses produce only trials with 0 or 1 spikes under both the Poisson and binary models; only at high firing rates do the two models make different predictions, since in that case the Poisson model includes many trials with 2 or even 3 spikes while the binary model generates only solitary spikes (see Fig. 4a1,a2). Using a stringent significance criterion of p<0.001, 467 response sets had a sufficient number of repeats to assess significance, given the observed firing probability. Of these, half (242/467=52%) were significantly less variable than expected by chance, five hundred-fold higher than the 467/1000=0.467 response sets expected, based on the 0.001 significance criterion, to yield a binary response set. Seventy-two neurons had at least one response set for which significance could be assessed, and of these, 49 neurons (49/72=68%) had at least one significantly sub-Poisson response set. Of this population of 49 neurons, five achieved low variability through repeatable bursty behavior (e.g., every spike count was either 0 or 3, but not 1 or 2) and were excluded from further analysis. The remaining 44 neurons formed the basis for the group statistics analyses shown in Figs. 2a and 3b. Nine of these neurons were subjected to an additional protocol consisting of at least 10 presentations each of 100 msec tones and 25 msec tones of all 32 frequencies. Of the 100 msec stimulation response sets, 44 were found to be significantly sub-Poisson at the p<0.05 level, in good agreement with the 43 found to be significant among the responses to 25 msec tones. 3 Bibliography 1. Kilgard, M.P. and M.M. Merzenich, Cortical map reorganization enabled by nucleus basalis activity. Science, 1998. 279(5357): p. 1714-8. 2. Sally, S.L. and J.B. Kelly, Organization of auditory cortex in the albino rat: sound frequency. J Neurophysiol, 1988. 59(5): p. 1627-38. 3. Softky, W.R. and C. Koch, The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J Neurosci, 1993. 13(1): p. 334-50. 4. Stevens, C.F. and A.M. Zador, Input synchrony and the irregular firing of cortical neurons. Nat Neurosci, 1998. 1(3): p. 210-7. 5. Buracas, G.T., A.M. Zador, M.R. DeWeese, and T.D. Albright, Efficient discrimination of temporal patterns by motion-sensitive neurons in primate visual cortex. Neuron, 1998. 20(5): p. 959-69. 6. 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