Pre- and postsynaptically expressed spiking-timing-dependent plasticity contribute differentially to neuronal learning

A plethora of experimental studies have shown that long-term plasticity can be expressed pre- or postsynaptically depending on a range of factors such as developmental stage, synapse type, and activity patterns. The functional consequences of this diversity are unknown. However, in models of neuronal learning, long-term synaptic plasticity is implemented as changes in connective weights. Whereas postsynaptic expression of plasticity predominantly affects synaptic response amplitude, presynaptic expression alters both synaptic response amplitude and short-term dynamics. In other words, the consideration of long-term plasticity as a fixed change in amplitude corresponds more closely to post- than to presynaptic expression, which means theoretical outcomes based on this choice of implementation may have a postsynaptic bias. To explore the functional implications of the diversity of expression of long-term synaptic plasticity, we modelled spike-timing-dependent plasticity (STDP) such that it was expressed either pre- or postsynaptically, or both. We tested pair-based standard STDP models and a biologically tuned triplet STDP model, and investigated the outcome in a feed-forward setting, with two different learning schemes: either inputs were triggered at different latencies, or a subset of inputs were temporally correlated. Across different STDP models and learning paradigms, we found that presynaptic changes adjusted the speed of learning, while postsynaptic expression was better at regulating spike timing and frequency. When combining both expression loci, postsynaptic changes amplified the response range, while presynaptic plasticity maintained control over postsynaptic firing rates, potentially providing a form of activity homeostasis. Our findings highlight how the seemingly innocuous choice of implementing synaptic plasticity by direct weight modification may unwittingly introduce a postsynaptic bias in modelling outcomes. We conclude that pre- and postsynaptically expressed plasticity are not interchangeable, but enable complimentary functions. Author summary Differences between functional properties of pre- or postsynaptically expressed long-term plasticity have not yet been explored in much detail. In this paper, we used minimalist models of STDP with different expression loci, in search of fundamental functional consequences. Presynaptic expression acts mostly on neurotransmitter release, thereby altering short-term synaptic dynamics, whereas postsynaptic expression affects mainly synaptic gain. We compared cases where plasticity was expressed presynaptically, postsynaptically, or both. We found that postsynaptic plasticity was more effective at changing response times, while both pre- and postsynaptic plasticity were similarly capable of detecting correlated inputs. A model with biologically tuned expression of plasticity also achieved this separation over a range of frequencies without the need of external competitive mechanisms. Postsynaptic spiking frequency was not directly affected by presynaptic plasticity of short-term plasticity alone, however in combination with a postsynaptic component, it helped restrain positive feedback, contributing to activity homeostasis. In conclusion, expression locus may determine distinct coding schemes while also keeping activity within bounds. Our findings highlight the importance of correctly implementing expression of plasticity in modelling, since the locus of expression may affect functional outcomes in simulations.

Learning and memory in the brain, as well as refinement of neuronal circuits and 2 receptive fields during development, are widely attributed to long-term synaptic 3 plasticity [1]. While this notion is not yet formally experimentally proven [2], it has in 4 recent years received strong experimental support in several brain regions, in particular 5 the amygdala [3] and the cerebellum [4]. The notion that synaptic plasticity underlies 6 memory is typically attributed to Hebb [5], but it is in actuality an idea that extends 7 considerably farther back in time, e.g. to Ramon y Cajal and William James [6]. 8 After the discovery by Bliss and Lømo [7] of the electrophysiological counterpart of 9 Hebb's postulate, now known as long-term potentiation (LTP), much effort has been 10 focused on establishing the induction and expression mechanisms of long-term plasticity. 11 In the 1990s, this lead to a heated debate on the precise locus of expression of LTP, 12 with some arguing for postsynaptic expression, whereas others were in favour of a 13 presynaptic locus of LTP [8]. Beginning in the early 2000's, this controversy was 14 gradually resolved by the realisation that plasticity depends critically on several factors, 15 notably animal age, induction protocol, and precise brain region [9][10][11]. Indeed, this 16 resolution has now been developed to the point that it is currently widely accepted that 17 e.g. specific interneuron types have dramatically different forms of long-term 18 plasticity [12, 13], meaning that long-term plasticity in fact depends on the particular 19 synapse type [14]. In retrospect, it is probably not all that surprising that LTP in 20 different circuits is expressed either pre-or postsynaptically, or both, given the diversity 21 of computational functions of different synapses [15]. Nevertheless, the precise 22 functional benefits of having LTP be expressed on one side of the synapse or the other 23 have remained quite poorly explored, with only a handful of classical theoretical papers 24 addressing this point [16][17][18][19][20][21]. 25 Going back several decades, a multitude of highly influential computer models of 26 neocortical learning and development have been proposed, some of them focusing on 27 aspects such as the rate-dependence of induction [22][23][24], while others have emphasised 28 the role of the relative millisecond timing of spikes in connected cells [25][26][27], and some 29 yet have included both [28]. Irrespective of whether timing, rate, or other factors are been the case that -with a few notable exceptions [18,19,21] -the expression of 32 plasticity itself has been regarded as a simple change in the magnitude of synaptic inputs 33 between neurons of the network. In the absence of better information, this is of course a 34 perfectly reasonable approach, as it is a parsimonious assumption that induction of 35 long-term plasticity manifests itself in the alteration of connectivity weights. 36 However, the expression of plasticity is not always well modelled by this simple 37 change of instantaneous magnitude. This is because presynaptically expressed plasticity 38 leads to changes in synaptic dynamics, whereas postsynaptic expression does not 39 (Fig.1B). For instance, during high-frequency bursting, the readily releasable pool of 40 vesicles runs out, leading to short-term depression of synaptic efficacy [29], while at 41 some synapse types short-term facilitation dominates [30]. Such short-term plasticity is 42 important from a functional point of view because it leads to filtering of the information 43 that is transmitted by a synapse [31-33]. Short-term depressing connections are most 44 likely to elicit postsynaptic spikes due to brief non-sustained epochs of activity, whereas 45 facilitating synapses require that presynaptic activity be maintained for some period of 46 time before postsynaptic spikes are elicited. In other words, short-term facilitating 47 connections act as high-pass filtering burst detectors [34,35], while short-term depression 48 provides low-pass filtering inputs suitable for correlation detection and automatic 49 gain-control [36-38]. As a corollary, it follows that presynaptic expression of plasticity 50 may change the computational properties of a given synaptic connection. In this case, 51 increasing the probability of release by LTP induction will lead to more prominent 52 short-term depression due to readily-releasable pool depletion, and as a consequence to 53 a gradual bias towards correlation detection at the expense of burst detection [39,40]. Postsynaptic response to the same stimulus after plasticity depends on expression loci. A -Representation of pre-(red) and postsynaptic (blue) sides of a synapse. B -Initial responses are illustrated in grey, while potentiated ones are in colour. In this example, the amplitude of the first response after learning was set to be the same after both pre-(red) and postsynaptic (blue) potentiation. Whereas with postsynaptic potentiation the gain was increased by the same amount for all responses in a high-frequency burst, with presynaptic potentiation the efficacy of the response train was shifted toward the beginning, enhancing the first response but resulting in no changes over the summed input.
It is long known that the induction of neocortical long-term plasticity may alter 55 short-term depression [16,41]. While the functional consequences of short-term 56 plasticity itself are quite well described [39,42], the theoretical implications of changes 57 in short-term plasticity due to the induction of long-term plasticity are less well 58 described. Yet, as outlined above, the vast majority of theoretical studies of long-term 59 plasticity assumes that synaptic amplitudes, but not synaptic dynamics, are altered by 60 cellular learning rules. One of the motivations of our present study is the observation 61 that this seemingly innocuous assumption may not be neutral, but in effect a bias, 62 because changing weights in theoretical models of long-term plasticity is equivalent to 63 assuming that synaptic plasticity is solely postsynaptically expressed. This begs the 64 question: What are the functional implications of pre-versus postsynaptically expressed 65 long-term plasticity? Providing answers to this central issue is important for 66 understanding brain functioning, as well as for knowing when weight-only changes in 67 computer modelling is warranted, and when it is not.

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Here, we use computational modelling to explore the consequences of expressing 69 plasticity pre-or postsynaptically in a single neuron under two simple paradigms Fig.   70 2), a time-locked stimulus [26, 43,44] or the detection of a rate-correlated 71 stimulus [45][46][47]. Initially, we compare and contrast relatively artificial scenarios, for 72 which the locus of expression is either solely presynaptic, solely postsynaptic, or equally 73 October 18, 2018 3/16 divided between both sides. We then move on to investigating the functional impact of 74 a model with separate pre-and postsynaptic components that were tuned to biological 75 data from connections between neocortical layer-5 pyramidal cells.

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Presynaptic expression modelled as changes in stochastic release 78 For the first set of simulations, we explored the simplest possible differentiation between 79 pre-and postsynaptic efficacy changes. Here, we considered the probability of vesicle 80 release (P j ) and the quantal amplitude (q j ) pre-and postsynaptic quantities 81 respectively. Plasticity was expressed either exclusively on each side or equally divided 82 between both sides.

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Since postsynaptic activity depends on the average input across many synapses, one 84 might expect that any differences between pre-or postsynaptic changes should vanish Change of stochastic neurotransmitter release probability lead to faster presynaptic plasticity. The graphs here and below are colour-coded: only presynaptic plasticity (red), only postsynaptic plasticity (blue), or simultaneous preand postsynaptic plasticity (black) are implemented. A-F: Latency reduction configuration. A -Example traces of the postsynaptic membrane potential before (grey) and after (black) plasticity. Initial latency of response is marked by a green dashed line. B -Shortening of postsynaptic latency to spike in comparison to the initial state. C -Synaptic weight distribution after 200 trials, normalized for each kind of plasticity expression and sorted by the fixed presynaptic delay. D -Postsynaptic response duration (interval between first and last spike in each trial). E -Postsynaptic intraburst frequency. F -Potentiation of average synaptic weight among early presynaptic inputs (i.e. that arrived within the first half of the stimulus). G-I: Correlated input configuration. G -Input rasterplot sample: correlated inputs shown in black and uncorrelated in gray. H -Histogram of total correlated and uncorrelated presynaptic activities. I -Potentiation of the average synaptic weight among correlated inputs.
In the correlated stimuli paradigm ( Fig. 3G and H), potentiation was similarly faster 97 with presynaptic expression of plasticity (Fig. 3I). This happened because plasticity was 98 triggered only after a signal was transmitted, which in the presynaptic case resulted in a 99 The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/450825 doi: bioRxiv preprint positive feedback loop as the probability of potentiation was higher for a more 100 potentiated synapse. This is a consequence of potentiation requiring glutamate release, 101 so that in a high-p synapse, there is an intrinsic propensity for more potentiation.

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Conversely, depression was slower as the probability of plasticity tended to decrease 103 (Fig. 3F).

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Presynaptic expression modelled as changes in short-term 105 plasticity 106 We next explored the effects of altering short-term plasticity. This adds another degree 107 of biological realism, since short-term plasticity takes into account the history of 108 presynaptic activity [16]. In this scenario, presynaptic changes generate redistribution of 109 synaptic resources used over a certain time period, instead of an overall amplification. 110 Even if the amplitude of an individual EPSP were affected equally by pre-or by 111 postsynaptically expressed plasticity, the total input from a burst would still differ 112 dramatically depending on the site of expression (Fig. 1B). 113 Correspondingly, in this case, results differed considerably depending on the specific 114 locus of plasticity in the latency configuration. Postsynaptic expression alone provided 115 the largest latency reduction, and also achieved it faster than the other plasticity  Nevertheless, synaptic efficacy was still potentiated faster and depressed slower in 122 the presynaptic case (Fig. 1E). This was similar to the stochastic case, although less 123 pronounced. This means that even if the rate of learning was effectively faster, 124 presynaptic expression affected timing less efficiently than postsynaptic expression did 125 (Fig. 1F). Change of short-term plasticity was less efficient at reducing latency. Graphs here and in subsequent figures are colour-coded: red denotes presynaptic plasticity alone, blue postsynaptic plasticity alone, and black combined pre-and postsynaptic plasticity. A -Example traces of postsynaptic activity before (grey) and after plasticity (coloured). Initial response latency is illustrated by a vertical dashed line. B -Latency reduction was more marked for postsynaptic (blue) than for presynaptic (red) or combined (black) plasticity. C -Combined and presynaptic plasticity reduced response duration better than with postsynaptic expression. D -Burst frequency was similarly increased with all three forms of plasticity, although rate change was faster with postsynaptic plasticity. E -Time course of average synaptic weights for early (left) and late (right) inputs. F -Normalized synaptic weight distribution, according to presynaptic delay. G -Time course of average synaptic weights for correlated (left, "corr") and uncorrelated (right, "unc") inputs.
On the other hand, plasticity rates in the correlated inputs paradigm evolved 127 differently compared to the stochastic case (Fig. 1G), even though the overall effect on 128 the covariance between pre-and postsynaptic activity was similar (not shown). With 129 depression acting via short-term plasticity, the postsynaptic rate of change was slightly 130 faster than the presynaptic change. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/450825 doi: bioRxiv preprint Contextualization with a biologically tuned model 132 For an improved biological plausibility, we investigated the interplay between pre-and 133 postsynaptic plasticity in a model that was fitted to data from rodent V1 pyramidal 134 neurons [19,48]. To isolate the effects of each component, we simply blocked either pre-135 or postsynaptic changes instead of normalising the total synaptic change in each side, so 136 as to not disrupt of the parameter tuning. We still found that both pre-and 137 postsynaptic plasticity components independently lead to the shortening of postsynaptic 138 latency (Figs. 5B and 5C). As with the above, more abstract modelling scenarios, 139 postsynaptic changes appeared to be more effective at affecting spike timing. When 140 both pre-and postsynaptic plasticity were active, the presence of postsynaptic 141 potentiation enhanced the response compared to presynaptic plasticity alone.

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As postsynaptic plasticity in the tuned model lacked the capacity to depress [49], it 143 also lead to inflated postsynaptic frequency and duration if implemented alone (Figs. 5D 144 and E). However, the inclusion of presynaptic LTD was enough to avoid saturation, and 145 the whole model was able to produce a sharpened response. In this case, postsynaptic 146 changes developed faster (Fig. 5F) because of increased postsynaptic frequency. In the second configuration, we observed a separation between synaptic efficacy of 148 correlated and uncorrelated inputs (Fig. 6A) without the need of added mechanism of 149 competition [46,50]. This only occurred when both pre-and postsynaptic components 150 were implemented. This is not achieved through other models with physiologically 151 compatible parameters [47]. We quantified this capacity with a linear separator for the 152 average and variance of p values (Fig. 6B).

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The presynaptic frequency range for optimal separation was between 50 and 80 Hz. 154 On the lower end it was bounded by the correlation time scale, as interspike intervals 155 longer than 20 ms were unable to represent the minimal interval of correlation. On the 156 other end, higher presynaptic frequency yielded overall potentiation that included 157 uncorrelated inputs, limiting the separation from the more potentiated correlated 158 population (see appendix). The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/450825 doi: bioRxiv preprint produced no such effect. In combination with postsynaptic plasticity, presynaptic 162 plasticity performed a kind of output control, as its introduction helped to maintain a 163 lower postsynaptic frequency even if q saturated (Fig. 6C). 164

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In recent years, it has become eminently clear that diversity in LTP expression is both 166 ubiquitous and considerable, depending on factors such as animal age, induction 167 protocol, and precise brain region [9][10][11]15]. In this work, we explored a few possible 168 functional consequences of pre-or postsynaptic locus of plasticity expression, and found 169 that even in a single neuron scenario overall dynamics may be affected by it. Plasticity 170 has in the typical phenomenological model been implemented as a straightforward standard assumption has been that that locus of expression does not matter appreciably 174 for the modelling scenario at hand. Our findings thus challenge this standard 175 assumption, highlighting when it is valid, and when it is not. 176 We investigated two different learning paradigms, one with differently timed inputs, 177 in which postsynaptic latency to spike was used as a learning measurement, and another 178 under constant stimulation, where a subset of inputs were correlated and potentiated 179 together. We worked with simplified conceptual models, first a simple stochastic STDP 180 implementation and later a more realistic, biologically tuned model of long-term 181 plasticity at in which pre-and postsynaptic components were fitted to connections 182 between neocortical layer 5 pyramidal cells [19]. 183 Our study showed that the locus of expression of plasticity determined affinity for uncorrelated inputs without the need for a competitive mechanism, in an optimal range 210 of input frequencies that depended on input frequency and correlation times.
Since it is possible to specifically block pre-or postsynaptic STDP 212 pharmacologically [41,49], several of our findings related to the locus of expression of 213 plasticity are experimentally testable. For example, at connections between neocortical 214 layer-5 pyramidal cells, it is possible to block nitric oxide signalling to abolish pre-but 215 not postsynaptic expression of LTP [49]. It is also possible to use GluN2B-specific 216 blockers such as ifenprodil or Ro25-6581 to block presynaptic NMDA receptors necessary 217 for presynaptically expressed LTD without affecting postsynaptic NMDA receptors that 218 are needed for LTP [41,55]. As a proxy for learning rate, one could explore in vitro how 219 blockade of different forms of plasticity expression impacts the number of pairings 220 required for plasticity, or alternatively how the magnitude of plasticity is affected for a 221 given number of pairings [49,52]. In vivo, the impact on cortical receptive fields could 222 similarly be explored. For example, we predict that receptive field discriminability is 223 poorer when presynaptic LTP is abolished by nitric oxide signalling blockade [19].

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In conclusion, we challenged the standard assumption of modelling synaptic 225 plasticity as a straightforward weight change by considering plasticity as pre-or 226 postsynaptically expressed, or both. As our collective understanding of LTP expression 227 improves, it is important to understand its overall consequences on circuit dynamics and 228 global functioning of neural networks [56]. We found that even in a simple feed-forward 229 network, the locus of expression could have considerable impact on learning outcome. 230 We speculate that the effect will only be greater in recurrent networks, where 231 presynaptic plasticity at loops and re-entrant pathways will exacerbate the effects of 232 changes in synaptic dynamics due to alterations of the accumulated difference. This 233 additional level of complexity may in particular complicate very large recurrent network 234 models [57,58]. As the locus of expression of long-term plasticity has been relatively 235 poorly studied, our study highlights the general need for more detailed modelling of the 236 role of the site of expression. In modelling long-term plasticity, correctly implementing 237 changes in weight is thus a matter of gravity.

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Inputs were accounted as conductance-based excitatory contributions with reversal 248 potential E e = 0 mV, amplitude q j , summed after the l th spike of presynaptic neuron j, 249 that decayed exponentially with a time constant of τ g = 5ms: In the the last section, we used the adaptative exponential integrate-and-fire 251 model [59] for increased bursting stability: The corresponding parameters for a pyramidal neuron were C = 281 pF, g L = 30 nS, 253 E L = −70.6 mV, ∆ T = 2mV, c = 4nS, τ W = 144ms. Spiking threshold was V T = −50.4 254 mV, and after each spike V was reset to the resting potential E L while z increased by 255 the quantity b = 0.0805 nA (as in [59]). Results, curves that represent latency shift, intraburst frequency or burst duration were 265 smoothed using a moving average filter with a window of three points.

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The second type of stimulation paradigm was based on [45] (Fig. 2B). This Each increment to the synaptic weights W ij (since there was only one postsynaptic 274 cell we consider W j = W ij for the rest of this paper) was computed after a pair of pre-275 and postsynaptic spikes, and the parameters were set to τ ST DP = 20ms, c pot = 0.005, 276 and c dep = −0.00525. We separated the synaptic weight W j as a product between pre-277 and postsynaptic counterparts, probability of release P j (0, 1] and quantal amplitude 278 q j (0, q max ] respectively, so that W j = q j P j . The probability of release was simulated in 279 two different ways, one by regulating the probability of stochastic interactions and the 280 other by short-term plasticity.

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When the weight convergence rates were compared, we had to ensure that 282 ∆W = W f − W i per time step was the same for all simulations. Therefore, we 283 normalized the chages so that if only q was changed: and if only P was changed, The initial value of all simulations was the same for P and q, so in these cases 286 ∆P = ∆q ≡ ∆. This amount was equally divided between P and q when both were 287 changed simultaneously: so that The largest possible change for P or q separately was ∆ tot = 1 − q i . To keep the 290 same range of W for changing P and q simultaneously, we limited the maximal values P 291 and q in this case at q max = P max = q i .

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Biologically tuned STDP model 293 We compared the results of the straightforward additive model to a slightly more 294 complex STDP model that acts separately over pre-and postsynaptic factors [19].

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Parameters were fitted to experimental data from connections between pyramidal cells 296 from layer 5 of V1 [41,48,49]. The equations for pre-and postsynaptic changes followed: 297 where X j (t) = l δ(t − t l j ) is increased at each spike from the presynaptic neuron j and 298 Y (t) = k δ(t − t k i ) at each spike from the postsynaptic neuron. is to emphasize that 299 ∆W was calculated before x j+ and y − were updated, upon the arrival of a new spike. 300 y + and y − are postsynaptic traces, with decay times τ y+ and τ y− respectively, and x j+ was a presynaptic trace with decay 302 time τ x+ : The Presynaptic control of the probability of release per stimulus was implemented either as 310 a Markovian process or as short-term plasticity. In the former case, probability (P j ) of 311 stochastic neurotransmitter vesicle release followed a binomial distribution. Each 312 presynaptic neuron had N = 5 release sites that functioned independently. In the 313 second we considered a dynamic modulation of the EPSPs through STP. The 314 probability P j was decomposed into the product of instantaneous probability of release 315 p j (t) and availability of local resources r j (t), resulting in the following synaptic efficacy: 316 W j (t) = q j p j (t)r j (t) .
In the latter case, the dynamics of p j (t) and r j (t) followed the model proposed by 317 Tsodyks and Markram [60]: neurons [61]. The resulting short-term plasticity could be either depressing, if P j > P C , 321 or facilitating, if P j < P C . For the values of τ D and τ F used, P C ≈ 0.3.

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Supporting information 323 S1 Appendix. Rate model A simple firing rate model with linear response was 324 able to illustrate how correlated and uncorrelated input separation was achieved 325 without competition between the two populations. Considering independent Poisson 326 inputs with fixed firing rate we found there is a determined, non-zero average value for 327 P . The LTP model (eqs. 10 and 11) was converted to time-averaged values:
Postsynaptic output ν was then considered as a simple firing rate model with linear 329 relation to average input I, weighted by average synaptic efficacy (eq. 15): where α and β (for fixed values of q and P ) were fitted to data from simulations 331 without plasticity. Since I was fixed, we could consider stationary values for r(t) and 332 p(t),r andp, from eqs. 16 and 17: We thus have < dq > (P, q, I) and < dP > (P, q, I) for LTP: 334 ν ≈ α + βqIP (1 + Iτ F ) 1 + P Iτ F + P Iτ D (1 + Iτ F ) .
In the vector field dP × dq (Fig. 7A), it is visible that P tends to the a specific value 335 (P * ) at the intersection of the higher* p-nullcline and the maximum value q max which 336 corresponds to the average value of P for uncorrelated inputs. This is in contrast to 337 correlated inputs, which tend to potentiate to the maximum. This value tends to 338 increase with frequency, limiting the range of separation of the more potentiated 339 correlated population.