Understanding how neural populations encode sensory information thereby leading to perception and behavior (i. e. , the neural code) remains an important problem in neuroscience. When investigating the neural code, one must take into account the fact that neural activities are not independent but are actually correlated with one another. Such correlations are seen ubiquitously and have a strong impact on neural coding. Here we investigated how differences in the antagonistic center-surround receptive field (RF) organization across three parallel sensory maps influence correlations between the activities of electrosensory pyramidal neurons. Using a model based on known anatomical differences in receptive field center size and overlap, we initially predicted large differences in correlated activity across the maps. However, in vivo electrophysiological recordings showed that, contrary to modeling predictions, electrosensory pyramidal neurons across all three segments displayed nearly identical correlations. To explain this surprising result, we incorporated the effects of RF surround in our model. By systematically varying both the RF surround gain and size relative to that of the RF center, we found that multiple RF structures gave rise to similar levels of correlation. In particular, incorporating known physiological differences in RF structure between the three maps in our model gave rise to similar levels of correlation. Our results show that RF center overlap alone does not determine correlations which has important implications for understanding how RF structure influences correlated neural activity.
Encoding sensory stimuli and integrating this information into suitable behavior is a highly complex task that is continuously solved by our nervous system. Nonetheless, the mechanisms by which this is achieved (i. e. the neuronal code) remain poorly understood. There is a growing body of evidence that perception and behavior are determined by the integrated activity of large neural populations [1]. However, our understanding of such population codes is complicated by the fact that neural responses are often correlated and not independent of one another. Correlations between the spike counts of neurons have traditionally been separated into two components: signal correlations (i. e. , correlations between the average responses of neurons) which are due to similarities in stimulus-response properties, and noise correlations (i. e. , correlations between the trial-to-trial variabilities of the neural responses) that are due to shared synaptic input [2]. Noise correlations have been observed ubiquitously across systems and species [1,3] and there is general agreement that they will strongly influence sensory processing [2,3]. However, the fact that these strongly depend on factors such as the organism’s behavioral state [1,4] as well as stimulus statistics [5–8] greatly complicates understanding their impact on coding in general. Much effort has gone into the investigation of how shared neural input gives rise to noise correlations. Modeling studies have shown that the balance between excitatory and inhibitory inputs is critical towards determining the sign and magnitude of noise correlations [9,10]. Other studies have instead focused on understanding how the spiking nonlinearity influences correlation transfer [11]. In contrast, much less is known about how receptive field (RF) structure influences correlated activity [12,13]. Thus, studies performed in sensory systems with well-characterized RF structure and anatomical correlates can aid our understanding as to how RF structure and organization influences neural correlations. For this we use the weakly electric fish Apteronotus leptorhynchus, which benefits from a well-characterized anatomy and physiology [14–17]. These fish sense amplitude modulations of a self-generated electric organ discharge (EOD) through an array of electroreceptors distributed over their body [18–21]. While objects with a conductivity different than that of the surrounding water (e. g. , plants, rocks, prey) cause spatially localized amplitude modulations, interaction between the EODs of conspecifics will instead give rise to spatially diffuse amplitude modulations [22]. Sensory afferents project to the medullary electrosensory lateral line lobe (ELL) where each axon trifurcates and synapses onto pyramidal neurons within three parallel and somatotopically organized sensory maps within the lateral, centro-lateral and centro-medial segment (LS, CLS & CMS, Fig 1A–1C) [23]. Pyramidal cells within each map are differentially tuned [24,25] and mediate appropriate behavioral responses to stimuli occurring in different contexts [26] (see [16] for review). Pyramidal cells in all maps display an antagonistic center-surround receptive field (RF; the area of sensory space within which impinging stimuli cause a neural response) organization, similar to that of retinal ganglion cells in the visual system [22,27–29]. However, both anatomical and physiological studies have shown substantial differences in the RF structure of pyramidal cells across the maps both in terms of size and % overlap (LS: ≤ 65%; CLS: ≤ 36%; CMS ≤ 16%; Fig 1A) [28,30]. These differences are expected to give rise to increasing levels of correlations between pyramidal cell activities when going from CMS to LS. To date, most studies have assumed that noise correlations between pyramidal cell activities are negligible (e. g. , [31,32]), in part because anatomical results have shown low RF % overlap values in both CMS and CLS [30]. Only a few studies have recorded the simultaneous responses of multiple electrosensory neurons and quantified correlations [7,8, 33–35]. These have shown that pyramidal cells can display significant correlation coefficients ranging between 0 and 0. 5 that are at least partially due to RF overlap (Fig 1D) [7,8]. However, these studies have only considered recordings from CLS and LS. Thus, no study to date has systematically quantified and compared correlations between the activities of electrosensory pyramidal neurons across all three ELL maps. Here, using a combination of mathematical modeling and in vivo electrophysiology, we investigated how receptive field structure influences correlations between the activities of pyramidal neurons across the three parallel ELL maps. Experimental data reveals that, contrary to predictions that correlation magnitude increases from CMS to LS based on increasing amounts of RF center overlap, correlations between pyramidal cell pairs are actually not significantly different from one another on average across the three ELL maps. To explain this surprising result, we modeled the contributions of both RF center and surround to determine correlated activity. We found that very different combinations of RF center-surround relative gain and size can give rise to similar correlations because of similar relative amounts of positively and negatively correlated inputs. Importantly, including previously published experimental data on differences between the RF center-surround organization across the maps gave rise to similar average levels of correlations. Our model thus predicts that the similar levels of correlations observed experimentally arise because cells receive similar relative levels of positively and negatively correlated inputs, despite very different RF center-surround organizations.
In this study, we focused on understanding how differences in RF center size and overlap influence correlated ELL pyramidal cell activity. To do so, we focused on correlations between neural activities measured under baseline condition (i. e. , in the absence of stimulation). These are key determinants of noise correlations under stimulation because baseline correlations can be thought of as the limit towards which noise correlations tend to as stimulus intensity goes to zero (see Methods). We used a simple yet accurate phenomenological model of receptor afferent activity [36,37] to simulate a population of peripheral afferents synapsing onto pyramidal cells. Model parameters were adjusted to reproduce experimentally observed heterogeneities in the baseline activities of afferents [38] (see Methods). Afferent activities were then used as input to two ELL pyramidal neurons that were modeled using the leaky integrate-and-fire formalism (see Fig 2A). We initially only included the contribution of the RF center in the model and adjusted both RF size and % overlap according to the available anatomical data [30]. Specifically, we used 640 model afferents as input for LS center, 105 model afferents as input for CLS center, and 25 model afferents as input for CMS center. To further mimic the different degrees of RF overlap, we adjusted the number of common afferent activities within two different populations that serve as input to two pyramidal cells. The % of shared input was high in LS (57%), intermediate in CLS (33. 4%), and low in CMS (13%). Correlations were calculated as spike-count correlations at different timescales (see Methods) from the simulated paired spiking output of the ELL LIF model. Our modeling results predict that the different amounts of RF center overlap for pyramidal neurons in the three different ELL maps will give rise to very different levels of correlated activity (Fig 2B). Indeed, correlation coefficients obtained from our model were always highest for LS, intermediate for CLS and lowest for CMS (Fig 2B & 2C). To test our modeling predictions, we simultaneously recorded spontaneous activity from pyramidal cell pairs within each of the three ELL maps (Fig 3A). For each pair, correlations between spike trains were computed in the same way as for the model. Surprisingly, and in contrast to our model predictions, we found that correlations were identical across the ELL segments (Fig 3B). Indeed, pyramidal cell pairs across the three ELL segments displayed on average similar levels of correlated activity and the distributions of correlation coefficients obtained from each map were not significantly different from one another across multiple timescales (Fig 3B & 3C). We found correlation estimates computed from independent pyramidal cell pairs recorded in different individual animals were not significantly different than those computed using our entire dataset (see Methods and S1 Fig). Further, similar levels of correlated activity were obtained for pairs that were recorded on different electrodes (different-electrode pairs) as compared to pairs that were recorded on the same electrode (same-electrode pairs, S2 Fig), indicating that our measurements of correlated activity do not depend on the recording technique used. Our results show further that the large variability of correlation coefficients within each map originates from heterogeneities between pairs. This is because the time varying correlation coefficients computed for a given pair displayed much lower variance than that seen across pairs (S3 Fig). We also note that differences between the baseline firing rates of neurons within a given pair did not influence magnitude of variability of correlation estimates (S4 Fig). Previous studies have shown that there are two types of pyramidal cells: ON-type cells that are excited and OFF-type cells that are inhibited by increases in EOD amplitude, respectively [39]. To investigate how pyramidal cell type influences correlated activity, we segregated pyramidal cell pairs into three categories: ON-OFF, ON-ON, and OFF-OFF. Overall, we found that opposite type pairs (i. e. , ON-OFF) on average displayed negative correlations, while same type pairs (i. e. , ON-ON and OFF-OFF) displayed positive correlations on average (S5 Fig). All pair types displayed similar levels of correlation magnitude on average (S5 Fig, see black lines). We found that, at small timescales, correlations were weakly related to firing rate (time windows < 75 ms; S6A, S6B, S6D & S6E Fig), which is consistent with results obtained in other systems [11,40]. However, we found that there was no such relationship for larger time windows (S6C, S6D & S6E Fig). In order to explain the discrepancy between our model prediction and our experimental data, we refined our model to account for both RF center and surround. We then systematically varied RF surround size and gain relative to those of RF center to explore how RF center-surround organization influences correlations (Fig 4). This is because experimental data has shown large differences in RF surround size and strength between ELL maps [28]. Our results show that RF surround gain and size strongly influence correlated activity. First, consistent with previous results, correlation coefficient estimates obtained for small RF surround size tended towards those obtained in the absence of surround (compare Fig 4B with Fig 2). Increasing RF surround size decreased correlations for all three segments: estimates were lowest with RF center and surround size being equal. Further increasing surround size increased correlations for all three segments (Fig 4B). Qualitatively similar results were obtained when instead varying RF surround gain: increasing surround gain to a value similar to that of the RF center decreased correlations (Fig 4D). However, when further increasing RF surround gain, correlations increased much less than what observed when increasing surround size (compare Fig 4D & 4B). This is because the impact of the different areas of the RF interactions that determine correlations varies nonlinearly when RF surround size is changed, but linearly when RF surround gain is varied. Correlations varied most strongly for high RF center overlaps (i. e. LS) and less strongly for lower RF center overlaps (e. g. CLS & CMS). These results were qualitatively consistent across time scales (S7 Fig). Thus, our modeling predicts that the RF center-surround balance strongly influences correlations. Our model further predicts that correlations are more sensitive to changes in relative RF surround size than to changes in relative RF surround gain. To test whether different RF geometries can lead to similar levels of correlations, we next varied both RF surround size and gain jointly, while keeping the amount of RF center overlap at constant values corresponding to each of the ELL maps (Fig 5). In all three cases, we found that correlations were close to zero when RF center and surround were matched in strength (center of Fig 5A–5C; dark blue). Correlations increased strongly if the surround gain and size were increased (upper right quadrants in each plot) and less so if surround gain and size were decreased (lower left quadrants). If the surround size was increased while its gain was simultaneously decreased, we found that correlations on average increased in LS and CLS (Fig 5A & 5B; upper left quadrants). If the surround size was decreased while increasing its gain, correlations remained small in all cases (lower right quadrants). While the overall effects of RF surround size and gain on input correlations were qualitatively similar for all three segments, the ranges over which correlations varied differed. Specifically, for LS, we found the largest range of mean correlation coefficients (Fig 5A; ≈ -0. 02–0. 68). For CLS, we found a slightly smaller range (Fig 5B; ≈ -0. 04–0. 52). For CMS, we found the smallest range (Fig 5C; ≈ -0. 07–0. 45). In general, for each segment, our model produced a large range of correlation values that were similar to the experimentally observed range (Fig 3). The values of RF surround gain and size for which correlations matched the average experimentally observed values (i. e. , ≈ 0. 19; blue to green color in Fig 5) however differed between segments. For LS (Fig 5A), physiological values of input correlations were obtained by manipulating center-surround balance in multiple ways. For example, by: strongly decreasing the surround size at a relatively balanced gain (e. g. “I” in Fig 5A); or by decreasing both surround size and gain (“II” Fig 5A); or by decreasing surround gain and increasing surround size (“III” in Fig 5A), or by increasing both surround size and gain (“IV” & “V” in Fig 5A). While similar results were obtained for CLS (Fig 5B) and CMS (Fig 5C), physiological levels of correlation were obtained only when strongly increasing surround size and either decreasing or increasing surround gain. Thus, our model predicts that physiologically realistic values of correlations can be obtained with different combinations of RF surround relative size and gain. Specifically, our model predicts that both weak and strong surround strength (i. e. , in terms of both size and gain) can lead to equal levels of positive correlations. We next determined the correlation transfer in our model: we found that output spike train correlations were effectively linearly scaled by a factor of ~ 0. 49 with respect to the input correlations (i. e. , the correlations between the inputs to both model ELL neurons, S8 Fig). We thus developed a reduced, theoretical model). In this model, the input to each neuron is described by the sum of all RF sub-portions which each are described by the product of its gain and its surface area. It is then possible to obtain an analytical expression for the correlation coefficient (see Methods). The output correlations were then obtained by scaling the input correlations by the factor found empirically in our numerical simulations. Results obtained using this reduced model were qualitatively similar to those obtained using the full model (compare S9 Fig to Fig 5). Thus, our results show that the effects of varying RF geometry on correlations in our full model can be, up to a scaling factor, explained by input correlations computed from the linearly summed inputs from different RF sub-regions. In order to gain further understanding as to how interactions between different RF sub-regions determine output correlations, we considered a model with arbitrary RF geometry (Fig 6A, see Methods). Specifically, we segregated the inputs to both model neurons into those that are positively correlated (i. e. , “+/+”, representing input coming from regions of overlap between both RF centers and overlaps of both surrounds), negatively correlated (i. e. , “+/-“, representing input coming from regions of overlap between RF center with surround), and uncorrelated inputs (i. e. , “+/0” and “0/+” representing regions for which there is no overlap between the RFs). This model allowed us to explore how arbitrary relations between these inputs shape correlations without having the constraints imposed by a particular RF structure (see Methods). We varied the ratio of correlated to anti-correlated input in terms of their amounts (i. e. , “N”) and gain while keeping the total input fixed. In the absence of uncorrelated input (0% independent), the sign and magnitude of correlations was determined by the relative strength (i. e. , that obtained when considering both amount and gain) of correlated and anti-correlated inputs (Fig 6B). Indeed, correlations were positive if the correlated input was dominant and negative if the anti-correlated input was dominant. Correlations were null if both correlated and anti-correlated inputs were matched in strength. Increasing the amount of uncorrelated inputs led to reduced correlations (i. e. , “dilution”) but did not affect these results qualitatively (Fig 6C). In the results shown in Fig 6B and 6C, we independently varied the gain of correlated, anti-correlated, and un-correlated inputs. This however, is physiologically not plausible. For example, the sign and gain of an input to a given cell depend only on whether this input is part of the RF center or surround region and not on the type of interaction with the RF of a neighbouring cell (i. e. , both input sign and gain are “single-cell” properties). We thus considered an alternative model in which the gains and signs of the inputs to a given neuron are mapped as either being part of the RF center or RF surround, but where the amount of input originating from different regions of overlap between the RFs can be varied independently of one another (Fig 6D). For example, correlated inputs now originate both from regions of overlap between the RF centers (i. e. , “+/+” in Fig 6D) and between the RF surrounds (i. e. , “-/-”in Fig 6D). We then varied the ratio of correlated to anti-correlated inputs in terms of their amount while simultaneously varying the gain of the surround relative to that of the center. Our results are in agreement with those obtained using the reduced model in that the relative amount of positively correlated input determined the sign and magnitude of correlations and that addition of uncorrelated input effectively “diluted” correlations but otherwise did not affect results qualitatively (compare Fig 6E & 6F to Fig 6B & 6C, respectively). However, in contrast to the reduced model (Fig 6B & 6C), major differences were observed when varying the relative surround gain: similar levels of correlation were observed when the RF surround was either weak or strong (i. e. , inverting the ratio of center/surround gain did not affect correlation magnitude. Fig 6E & 6F). This is because the net strength of positively correlated input relative to that of negatively correlated input are the same in both cases. It is important to realize however that the source of positively and negatively correlated inputs does vary. For example, the primary source of positively correlated input will come from RF center overlap in the case of weak surround and from RF surround overlap in the case of strong surround. Thus, these results explain why equal levels of correlation can be achieved with widely different RF structures as seen in our numerical simulations (Fig 5). Finally, we tested whether including experimentally measured differences in RF structure across the three ELL maps [28,30] in our model can lead to equal average levels of correlations as found experimentally (Fig 3). The different RF structures are shown in Fig 7A. For LS, RF center size was greatest with large overlap with surround gain approximately to that of the center but with a very small relative size (Fig 7A, left; “I” in Fig 5A). For CLS, RF center size was smaller with a smaller amount of overlap while the surround size was larger with a very weak gain (Fig 7A, middle; “II” in Fig 5B). For CMS, RF center size was smallest with the lowest amount of overlap while RF surround size was large and RF surround gain was strong relative to that of center (Fig 7A, right; “III” in Fig 5C). We found that our model gave rise to correlations that were: 1) similar across all timescales despite these very different RF structures (Fig 7B & 7C) and; 2) similar to the average levels measured experimentally (compare Fig 7B & 7C with Fig 3B & 3C). Furthermore, the different RF structures across ELL maps led to physiologically realistic variations in correlation magnitude when the relative overlap between RF centers was varied (S11 Fig). We conclude that the similar average levels of correlated activity displayed by ELL pyramidal cell pairs in the different ELL maps can be explained by considering differences in both RF center and surround specifically by the differing RF surrounds which influence correlation magnitude in each of the segments differentially. Indeed, including the RF surround led to a decrease in correlations for LS and an increase in correlations in CMS relative to values obtained when only considering the RF center (compare Fig 7 to Fig 2). For LS, our model predicts that correlations are primarily due to the strong positively correlated input originating from the large overlap between the RF centers. For CMS however, correlations are instead primarily due to the strong positively correlated input originating from the large overlap between the RF surrounds. In the case of CLS, the positively correlated input originating from regions of overlap between the RF centers and surrounds are somewhat attenuated by negatively correlated inputs originating from regions of overlap between the RF center and surround. We note that, within each segment, large heterogeneities in correlation magnitude were observed experimentally. These are likely due to heterogeneity in RF center overlap as well as differences in the relative size and gain of surrounds within each map as discussed below.
We investigated the mechanisms that give rise to correlations between the baseline activities of ELL pyramidal neurons within three parallel somatotopic maps of the body surface. Using a simple feedforward model, we initially predicted that the decreasing amounts of RF center interactions from LS to CMS should lead to decreasing levels of correlated activity. In contrast, in vivo recordings revealed that the average levels of correlation between pyramidal neuron activities were nearly identical across all three segments. To explain this surprising result, we considered the effects caused by the antagonistic center-surround organization of RFs. By including and systematically varying the size and gain of a RF surround, we found that very different combinations of RF center-surround balance gave rise to nearly identical correlations between pyramidal neuron activities in our model. Further simulations showed that the sign and magnitude of correlations were largely determined by the relative strength of positively and negatively correlated inputs. However, it is impossible to vary the gains of these independently when considering a physiologically realistic RF center-surround organization. Taking this fact into account showed that, while the relative amount of positively and negatively correlated inputs still largely determined correlation sign and magnitude, relative gain was less important. This was because both a relatively weak or a strong surround gives rise to the same correlation magnitude. Finally, we showed that including the previously published differences in RF center-surround structure across the three ELL maps in our model resulted in physiologically realistic magnitudes of correlations that were similar across segments. Thus, our results strongly suggest that pyramidal cell pairs within different ELL segments display similar average levels of correlated activity because of known differences in RF center-surround organization. Our results show that the RF structure has a strong influence on correlated activity between neurons. It should be noted that we assumed that RFs in our model were circular and organized in an antagonistic center-surround fashion. Experimental data has shown that ELL pyramidal neuron RF centers can be more elongated along the animal’s rostro-caudal axis [22,28]. This is not expected to alter the qualitative nature of our results, as increasing RF eccentricity will lead to relatively greater amounts of RF overlap, thereby scaling both positively and negatively correlated inputs similarly. We further note RF center and surround inputs to pyramidal neurons are excitatory and inhibitory, respectively. Thus, by altering the RF geometry, we effectively altered the balance of excitation and inhibition in the input to ELL neurons. Our modeling results thus agree with previous theoretical studies showing that balanced excitation and inhibition can cause a decorrelated state (i. e. correlations are negligible) [3,9]. The present study characterizes correlations between the baseline activities (i. e. , in the absence of stimulation) of ELL pyramidal neurons. As mentioned above, baseline correlations are the limit towards which noise correlations will tend to as stimulus intensity decreases. Thus, for weak stimulus intensities, baseline and noise correlations will be approximately equal to one another (see Methods). Generally, noise correlations are thought to be caused by shared neuronal input and consequently, experimentally measured correlations were found to depend on the proximity of neurons in visual cortex [4,41] or on the amount of RF center overlap in the retina and the electrosensory system [7,12,42]. We here extend this notion to the RF surround as we have shown that it is the balance between the RF center and the RF surround that can have substantial impact onto determining correlations. We note that the correlation magnitudes observed experimentally within each segment showed considerable heterogeneity. While these can partly be accounted to the varying degree of RF center overlap that RF will show within each segment [7], our model also predicts that differences in the relative surround size and gain will strongly affect correlation magnitude. While differences in size and gain have been observed experimentally [22,28], further studies are needed to verify whether and how these contribute to giving rise to differences in correlation magnitude in vivo. There exists similarities between the electrosensory and other systems (see [17] for review). For example, RFs with an antagonistic center-surround organization are a common feature in the peripheral organization of sensory systems and are found in visual [27], somatosensory systems [43], in the lateral line system of fish [44], and in the auditory system [45]. Consequently, our results showing how differences in RF center-surround structure affect correlated activity are likely to be applicable to other systems. As discussed below, these correlations are expected to strongly affect neural coding. The role of correlations in information coding has been extensively studied and is the focus on much debate (see [2] for review). On the one hand, correlations can be detrimental to coding because of redundancy. On the other hand, more recent studies have uncovered a more positive role for correlations [5,6]. Theoretically it was shown that, in order to assess the effect of noise correlations on coding, one must consider their sign with respect to that of signal correlations [2]. When noise and signal correlations have the same sign, noise correlations introduce additional variability compared to the independent case, and thus reduce coding efficacy. In contrast, when signal and noise correlations have opposite sign, the variability is effectively reduced thereby increasing coding efficacy. However, understanding how noise correlations impact the neural code in general is greatly complicated by the fact that they are plastic and can be modulated by several factors including stimulus properties as well as the animal’s behavioral state [1,4, 7,8, 46]. Recent studies have only begun to uncover the means by which state dependent correlations can aid in the decoding of behaviorally relevant stimuli [5,6]. Our recordings show that pyramidal cells display significant baseline correlations in all three ELL segments. This implies that pyramidal cells will display noise correlations under stimulation, specifically for low stimulus intensities. In fact, the presence of noise correlations under stimulation has previously been shown for CLS and LS neurons [7,8] and this is expected to impact the processing of behaviorally relevant electrosensory stimuli as discussed below. Behavioral studies have shown that weakly electric display excellent (> 90%) accuracy at detecting electrical signals caused by prey [47,48]. At the time of detection, the perturbations of the animal’s own electric field caused by the prey are very weak and will activate only a portion of the animals’ sensory epithelium. This will in turn cause very small perturbations in the activities of afferents and ELL pyramidal neurons in all three ELL maps [16,49]. This is because their frequency tuning [24,28,50] and RF structure [30,49] are optimized to the resulting input statistics. Perturbations to the electric field caused by prey can in theory be accurately predicted by averaging the activities of large ELL pyramidal cell populations [31]. This assumes however, that noise correlations are negligible. Our results strongly suggest that this will not be the case for pyramidal cells in all maps including CMS. The impact of noise correlations on the detection performance of the ELL pyramidal cell population has not been investigated to date and should be included in future studies. In particular, the dependency of noise and signal correlations on the spatial position of a stimulus should be investigated systematically in order to determine the sign relationship between signal and noise correlations and thereby assess their impact on coding, similar to what has been done recently in other systems [5,6]. Beyond prey signals, ELL pyramidal neurons also respond to electro-communication stimuli arising during social interactions between conspecifics. When two fish come into proximity of one another (< 1 m), each fish will experience a sinusoidal amplitude modulation of its EOD (i. e. , a beat). Natural electro-communication signals consisting of brief (< 30 ms) changes in EOD frequency and/or amplitude that will cause transient distortions in this beat signal [51]. While there has been much interest in understanding how electro-communication stimuli are encoded by single electrosensory neurons [52–57], only a few studies have investigated their encoding by neural populations [7,8, 33]. Interestingly, these stimuli will activate most if not the entire animal’s sensory epithelium, and furthermore activate feedback inputs projecting to the ELL pyramidal cells from higher order brain areas [58,59]. Activation of feedback input has been shown to reduce noise correlations in CLS and LS neurons [7,8, 33]. Nonetheless, the resulting “weak” correlation coefficients (~ 0. 1) can still have strong effects on coding when large neural populations are considered [60]. Previous studies have shown that signal and noise correlations have the same sign when stimulated with electro-communication stimuli [7]. Based on theoretical arguments, it could thus be expected that the presence of noise correlations will have a negative impact on the encoding of these signals. However, in naturalistic behavior stimulus intensity will vary dynamically as both conspecifics move with respect to one another [61,62]. It is likely that these changes in stimulus intensity will alter the level of noise correlations dynamically [7,8], which could presumably optimize information processing through a stimulus dependent adaption of correlation levels and/or relations. Further, several recent studies have proposed mechanisms by which correlated activity from electrosensory neurons can be decoded. In particular, it was shown that downstream neurons respond to increases in correlated afferent neuron activity in order to give rise to perception [56,63], leading to the interesting hypothesis that correlated activity carries behaviorally relevant information. In conclusion, the role of correlations in electrosensory stimulus coding is likely to be complex and should be the focus of future studies.
Our model consists of two ELL pyramidal neurons each receiving input from a pool of receptor afferents. We note that this input could be from either feedforward or feedback sources as anatomical studies have shown that the feedback input received by a given pyramidal cell originates from a separate group of pyramidal cells [58]. Thus, any feedback input can effectively be considered a delayed feedforward input [33]. We further note that transmission delays are irrelevant here because on the one hand we are only considering baseline conditions (i. e. , in the absence of stimulation), and on the other hand experiments have shown that the baseline activities of receptor afferents are not correlated with one another [35,56,72]. In general, model parameters were constrained based on available experimental data (see below) such as to fit average values unless otherwise noted. Based on the different regions of overlap between the RFs (see above), the level of correlation arising from the inputs to both model pyramidal neurons can be computed analytically. For the example of two interacting excitatory RF centers with inhibitory surrounds the inputs for each of the pyramidal neurons n1 and n2 can be expressed as: n1=[ (GcN+/+) + (GcN+/−) + (GcN+/0) − (GsN−/−) − (GsN−/+) − (GsN−/0) ] (15) n2=[ (GcN+/+) + (GcN−/+) + (GcN0/+) − (GsN−/−) − (GsN+/−) − (GsN0/−) ] (16) Where N is the number of afferents according to the size of a given area of interaction and G is the gain of the respective area, with Gc used if the area is part of the RF center and Gs if the area is part of the RF surround. Note that the areas are computed using Euclidian geometries based on the intersection between the antagonistic RF structures. The % overlap was varied by changing the distance between the two centers of the circles representing the RF centers. The variances of the inputs are then given by: Var (n1) =GS2[ (GcGsN+/+) 2+ (GcGsN+/−) 2+ (GcGsN+/0) 2+ (N−/−) 2+ (N−/+) 2+ (N−/0) 2] (17) Var (n2) =GS2[ (GcGsN+/+) 2+ (GcGsN−/+) 2+ (GcGsN0/+) 2+ (N−/−) 2+ (N+/−) 2+ (N0/−) 2] (18) The covariance of the signals is then given by: Cov (n1, n2) =Gs2[ (GCGSN+/+) 2+ (N−/−) 2− (GcGsN+/−) 2− (GcGsN−/+) 2] (19) Using the variance and the covariance we calculated the correlation according to: r=k ⋅Cov (n1, n2) Var (n1) Var (n2) (20) Where k is a constant accounting for the correlation transfer from the input to the output stage of the ELL as determined from our LIF model (see S8 Fig). We empirically used k = 0. 4884 based on our numerical simulations. Inspection of Eqs 8–11 makes clear that, while both variance and covariance explicitly depend on Gs and Gc (Eqs 17–19), the correlation coefficient r (Eq 20) only depends on the ratio of Gs and Gc. In order to calculate correlations for the interactions of RFs with arbitrary geometry, we adjusted our mathematical model accordingly. For the calculations shown in Fig 6A–6C, inputs were used according to: n1=[ (G+corr N+corr) − (G−corr N−corr) + (N01) ] (21) n2=[ (G+corr N+corr) + (G−corr N−corr) + (N02) ] (22) With G+corr and N+corr representing the gain and amount of correlated input, G-corr and N-corr represent the gain and amount of anti-correlated input, respectively. N01, N02 are the amounts of uncorrelated inputs to each neuron ni. The variances of inputs n1 and n2 were calculated using: Var (n1) =[ (G+corr N+corr) 2− (G−corr N−corr) 2+ (N01) 2] (23) Var (n2) =[ (G+corrN+corr) 2+ (G−corrN−corr) 2+ (N02) 2] (24) Covariance was calculated using: Cov (n1, n2) = (G+corrN+corr) 2− (G−corrN−corr) 2 (25) The correlation coefficient was then computed according to Eq 20. We note that the parameters G and N are completely interchangeable and thus will have similar effects on correlations in this reduced version of the model. Further, in our investigations, we kept the total amount of input constant (i. e. , Ntot = N+corr + N-corr + N01 + N02 = 1000) and assumed that N01 = N02. Changing the total amount of input had no effect on the shown characteristics of r. For the calculations in Fig 6D–6F, we used the original mathematical model (Eqs 15–20) and split the areas of correlated signals equally between the terms A+/+ and A-/-, areas of anti-correlated inputs between A+/- and A-/+, and uncorrelated input between A+/0, A-/0, A0/+ and A0/-
Growing evidence across nervous systems and species shows that the activities of neighboring neurons are not independent but are correlated with one another, which has important implications for neural coding. Such correlations are generally thought to be due to shared input. However, how this shared input is integrated by neurons in order to give rise to correlated activity is not well understood in general. Here we investigated how receptive field structure determines correlations between the activities of electrosensory pyramidal neurons in weakly electric fish. To do so, we used a combination of mathematical modeling of the known antagonistic center-surround RF structure as well as in vivo electrophysiological recordings. Our results show that the amount of receptive field center overlap alone is not sufficient to explain experimentally observed neural correlations in general. This is because our experimental data shows that pyramidal neurons with very different amounts of receptive field center overlap display almost identical correlations between their activities. Further, our modeling shows that both receptive field center and surround play important roles in determining correlated activity, such that very different combinations of relative RF surround strength and size can generate nearly identical correlations between neural activities. We discuss the implications of our results for sensory processing.
action potentials
medicine and health sciences
membrane potential
social sciences
electrophysiology
neuroscience
fish biology
ganglion cells
membrane electrophysiology
computational neuroscience
bioassays and physiological analysis
vision
zoology
coding mechanisms
research and analysis methods
vertebrate physiology
animal cells
electrophysiological techniques
fish physiology
animal physiology
cellular neuroscience
psychology
electrode recording
cell biology
pyramidal cells
physiology
neurons
biology and life sciences
cellular types
afferent neurons
computational biology
sensory perception
neurophysiology
Differential receptive field organizations give rise to nearly identical neural correlations across three parallel sensory maps in weakly electric fish