Heterogeneities in afferent connectivity dominate local heterogeneities in the emergence of response decorrelation in the dentate gyrus

The ability of a neuronal population to effectuate response decorrelation has been identified as an essential prelude to efficient neural encoding. To what extent are diverse forms of local and afferent heterogeneities essential in accomplishing such response decorrelation in the dentate gyrus (DG)? Here, we incrementally incorporated four distinct forms of biological heterogeneities into conductance-based network models of the DG and systematically delineate their relative contributions to response decorrelation. We incorporated intrinsic heterogeneities by stochastically generating several electrophysiologically-validated basket and granule cell models that exhibited significant parametric variability, and introduced synaptic heterogeneities through randomized local synaptic strengths. In including adult neurogenesis, we subjected the valid model populations to randomized structural plasticity and matched neuronal excitability to electrophysiological data. We assessed networks comprising different combinations of these three local heterogeneities with identical or heterogeneous afferent inputs from the entorhinal cortex. We found that the three forms of local heterogeneities were independently and synergistically capable of mediating significant response decorrelation when the network was driven by identical afferent inputs. Strikingly, however, when we incorporated afferent heterogeneities into the network to account for the unique divergence in DG afferent connectivity, the impact of all three forms of local heterogeneities were significantly suppressed by the dominant role of afferent heterogeneities in mediating response decorrelation. Our results unveil a unique convergence of cellular- and network-scale degeneracy in the emergence of response decorrelation in the DG, and constitute a significant departure from the literature that assigns a critical role for local network heterogeneities in input discriminability. SIGNIFICANCE STATEMENT The olfactory bulb and the dentate gyrus (DG) networks assimilate new neurons in adult rodents, with adult neurogenesis postulated to subserve efficacious information transfer by reducing correlations in neuronal responses to afferent inputs. Heterogeneities emerging from the lateral dendro-dendritic synapses, mediated by locally-projecting neurogenic inhibitory granule cells, are known to play critical roles in channel decorrelation in the olfactory bulb. However, the contributions of different heterogeneities in mediating response decorrelation in DG, comprising neurogenic excitatory granule cells projecting beyond DG and endowed with uniquely divergent afferent inputs, have not been delineated. Here, we quantitatively demonstrate the dominance of afferent heterogeneities, over multiple local heterogeneities, in the emergence of response decorrelation in DG, together unveiling cross-region degeneracy in accomplishing response decorrelation.


ABSTRACT
The ability of a neuronal population to effectuate response decorrelation has been identified as an essential prelude to efficient neural encoding. To what extent are diverse forms of local and afferent heterogeneities essential in accomplishing such response decorrelation in the dentate gyrus (DG)? Here, we incrementally incorporated four distinct forms of biological heterogeneities into conductance-based network models of the DG and systematically delineate their relative contributions to response decorrelation. We incorporated intrinsic heterogeneities by stochastically generating several electrophysiologically-validated basket and granule cell models that exhibited significant parametric variability, and introduced synaptic heterogeneities through randomized local synaptic strengths. In including adult neurogenesis, we subjected the valid model populations to randomized structural plasticity and matched neuronal excitability to electrophysiological data. We assessed networks comprising different combinations of these three local heterogeneities with identical or heterogeneous afferent inputs from the entorhinal cortex. We found that the three forms of local heterogeneities were independently and synergistically capable of mediating significant response decorrelation when the network was driven by identical afferent inputs. Strikingly, however, when we incorporated afferent heterogeneities into the network to account for the unique divergence in DG afferent connectivity, the impact of all three forms of local heterogeneities were significantly suppressed by the dominant role of afferent heterogeneities in mediating response decorrelation. Our results unveil a unique convergence of cellular-and network-scale degeneracy in the emergence of response decorrelation in the DG, and constitute a significant departure from the literature that assigns a critical role for local network heterogeneities in input discriminability.

SIGNIFICANCE STATEMENT
The olfactory bulb and the dentate gyrus (DG) networks assimilate new neurons in adult rodents, with adult neurogenesis postulated to subserve efficacious information transfer by reducing correlations in neuronal responses to afferent inputs. Heterogeneities emerging from the lateral dendro-dendritic synapses, mediated by locally-projecting neurogenic inhibitory granule cells, are known to play critical roles in channel decorrelation in the olfactory bulb. However, the contributions of different heterogeneities in mediating response decorrelation in DG, comprising neurogenic excitatory granule cells projecting beyond DG and endowed with uniquely divergent afferent inputs, have not been delineated. Here, we quantitatively demonstrate the dominance of afferent heterogeneities, over multiple local heterogeneities, in the emergence of response decorrelation in DG, together unveiling cross-region degeneracy in accomplishing response decorrelation.
However, despite the dentate gyrus (DG) being the other prominent brain region expressing adult neurogenesis and despite the widespread literature on the role of DG in pattern separation (7)(8)(9)(19)(20)(21)(22), it is surprising that the impact of distinct forms of local and afferent heterogeneities on channel decorrelation has not been assessed in the DG.
This lacuna in the literature is especially striking because of the stark contrasts in terms of the unique afferent connectivity to the dentate and in the specific roles of adult neurogenesis in the DG vs. the OB (1-3, 7-9, 18-26), although both circuits have been implicated in response decorrelation and express adult neurogenesis. First, there is evidence for adult neurogenesis resulting in both excitatory granule cells and inhibitory basket cells in the dentate, whereas adult neurogenesis results in inhibitory granule cells in the OB. Second, OB granule cells lack axons and make local lateral inhibitory dendrodendritic synapses with other local circuit cells, and do not project outside the OB. In striking contrast, DG cells extend unmyelinated axons connecting both within and beyond (principally to CA3) the DG. It was this feature of the DG granule cells as the principal projection cell to the CA3 that was important in its theoretically postulated role in response decorrelation before inputs are fed to the pattern completing recurrent CA3 network (27,28). Third, neurogenesis results in the replacement of the majority of granule neurons in the olfactory bulb, whereas it leads to a substantial addition of granule neurons to the hippocampal dentate gyrus, suggesting that adult neurogenesis could play distinct roles in the two brain regions (24). Finally, and most importantly, the principal inputs to the olfactory granule cells are the mitral cells through local dendrodendritic synapses, whereas the principal inputs to the ~1.2 billion dentate granule cells are the ~30,000 LII entorhinal cortical neurons. This significant divergence and sparsity of connections in the afferent projections from the excitatory cells in the EC to the excitatory DG granule cells is therefore unique to the DG, and is critical to the analysis in terms of the specific roles of local vs. afferent heterogeneities.
In the DG network, there are at least four distinct forms of heterogeneities that could mediate response decorrelation (the first three are local to the DG network whereas the fourth is afferent onto the network): (i) heterogeneity in intrinsic ion channel and excitability properties of the neurons; (ii) non-uniformities in the local synaptic connectivity; (iii) structural heterogeneities in neurons introduced by adult neurogenesis; and (iv) input-driven heterogeneity that is reflective of the distinct sets of afferent inputs that impinge on different neurons (as a consequence of the unique divergence in DG connectivity). Which of these distinct forms of heterogeneities play a critical role in mediating response decorrelation in the DG? Does a highly divergent, sparsely active network need an additional layer of neurogenesis-induced heterogeneity for effectuating response decorrelation? What is the impact of cell-to-cell variability in ion channel properties and excitability on response decorrelation in the DG network receiving different patterns of inputs?
In this study, we systematically and incrementally incorporate the four different forms of heterogeneities into conductance-based network models of the DG and delineate the impact of each form of heterogeneity on response decorrelation. Specifically, we employed a stochastic search algorithm spanning an exhaustive parametric space (involving experimentally-determined ion channel as well as neurophysiological properties) to reveal cellular-scale degeneracy in the DG, whereby disparate combinations of passive and active properties yielded analogous cellular physiology of excitatory granule (GC) and inhibitory basket cell (BC) populations. Next, we further expanded the parametric search space to encompass biologically observed heterogeneities in local/afferent network connectivity and in neurogenesis-induced alteration to neuronal structure and excitability. We systematically assessed response decorrelation in different DG networks, each built with incremental addition of the four distinct forms of heterogeneities. We found that in the absence of afferent heterogeneities, that is when the DG network was driven by identical afferent inputs, the three forms of local heterogeneities were independently and synergistically capable of mediating significant response decorrelation. Strikingly, however, when we incorporated afferent heterogeneities into the network to account for the unique divergence in DG afferent connectivity, we found that the impact of all three forms of local heterogeneities were suppressed by the dominant role played by afferent heterogeneities in mediating the emergence of response decorrelation. These conclusions on the dominance of afferent heterogeneities constitute a significant departure from the literature that assigns a critical role for local network heterogeneities (including those induced by adult neurogenesis) in input discriminability, and unveils crucial distinctions in the emergence of response decorrelation in the DG vs. the OB network.

RESULTS
In systematically delineating the impact of distinct forms of heterogeneities on response decorrelation, we constructed networks of 500 GCs and 75 BCs from respective conductancebased model populations (Fig. 1A-B). The heterogeneous conductance-based model populations of GC and BC neurons were derived from independent stochastic search procedures that

Degeneracy in single neuron physiology of granule and basket cell model populations
We employed a well-established stochastic search strategy (29-32) to arrive at populations of conductance-based models for GCs and BCs. This exhaustive parametric search procedure was performed on 40 parameters for GCs (Table S1), and 18 parameters for BCs (Table S3), involving ion channel properties derived from respective neuronal subtypes. Nine different measurements, defining excitability and action potential firing patterns ( Fig. 1; Table S2), were obtained from each of the 20,000 stochastically generated unique GC models, and were matched with corresponding electrophysiological GC measurements. We found 126 of the 20,000 models (~0.63%) where all nine measurements were within these electrophysiological bounds (Table   S2), and thus were declared as valid GC models. A similar procedure was employed for BC cells, where 9 different measurements from 8,000 unique models were compared with corresponding electrophysiological BC measurements. Here, we found 54 of the 8,000 models (~0.675%) where all nine measurements were within electrophysiological bounds (Table S4), and declared them as valid BC models. The experimental bounds on physiological measurements for granule (Table S2) and basket (Table S4)  How did these neuronal populations achieve degeneracy? Did they achieve this by pairwise compensation across parameters, or was change in one parameter compensated by changes in several other parameters to achieve robust physiological equivalence? In answering this, we plotted pair-wise scatter plots, independently on valid model parameters of the GC and BC populations (Fig. 3A), and computed pair-wise Pearson's correlation coefficients for each scatter plot ( Fig. 3B-C). We found that a vast majority of these pairs displayed very weak pair-wise correlations (R 2 < 0.25; Fig. 3B-C), suggesting that degeneracy in both populations was achieved through collective changes spanning several parameters. . Surprisingly, we found that introduction of synaptic heterogeneity did not enhance the level of response decorrelation, but allowed response decorrelation to express at a level that was within the bounds set by extreme values of identical synaptic weights ( Fig. 5E; Fig. S3C). Importantly, the level of decorrelation achieved by the introduction of local synaptic heterogeneity into a homogeneous population (no intrinsic heterogeneity) of GCs and BCs was significantly minimal compared to that achieved by the mere presence of intrinsic heterogeneity ( Fig. 5E; Fig. S3C; cf. Fig. 4, Fig.   S2). Together, although the introduction of synaptic heterogeneity critically modulated the level of response decorrelation, these results suggest intrinsic heterogeneity as the dominant form among intrinsic and synaptic forms of heterogeneities in mediating response decorrelation.

Adult neurogenesis-induced structural heterogeneity in neuronal age enhances decorrelation of neuronal responses to identical external inputs
A prominent hypothesis on the specific functions of adult neurogenesis in DG neurons is on their role in response decorrelation. One part of the rationale behind this hypothesis is the distinct excitability properties of new neurons that provide an additional layer of heterogeneity (7-9, 15, 19-21, 39). Although there are lines of evidence linking adult neurogenesis to response decorrelation, the specific role of new neurons and the additional layer of heterogeneity introduced by them in regulating input discriminability has not been systematically assessed.
To introduce neurogenesis-induced heterogeneity into our network, we noted that the excitability of new born neurons in the DG, which could mature to either GCs or BCs, is higher as a consequence of lower surface area reflective of the diminished arborization of immature neurons (9,15,39,40). To quantitatively match the excitability properties of these neurons, we introduced structural plasticity by reducing the surface area of the valid GC and BC models ( Fig.   3) through reduction of their diameter. This reduction in surface area expresses as an increase in input resistance (39, 41, 42) in each of these neurons (Fig. 6A), which in turn translates to increase in firing rate (Fig. 6B).
With the ability to introduce intrinsic, synaptic and neurogenesis-induced forms of heterogeneity into our network, we analyzed three distinct networks (fully mature, fully immature and variable age) to specifically understand the role of neurogenesis-induced heterogeneity on response decorrelation to identical inputs. All three networks were endowed with intrinsic as well as synaptic heterogeneities receiving afferent inputs from the same arena , and the distinction between the three cases was only with reference to neuronal age ( Fig. 6D). In comparing the firing rates of the GCs for different network configurations, we found that the firing rates of all GCs were comparable for all cases where neurogenesis-induced heterogeneities were absent. However, with the introduction of neurogenesis, especially in the scenario where all cells were immature, the firing rates increased and spanned a larger range. In the more physiologically relevant scenario of heterogeneous cellular age, although the firing rates spanned a larger range, a significant proportion of them were in the low firing regime characteristic of GCs (Fig. 6E).
We found that the level of response decorrelation in the fully immature network was significantly (KS test; p<0.001) higher than that achieved in the fully mature network (Fig. 6F). This is to be expected because the structural heterogeneity (effectuated by changes in diameter) would amplify the inherent intrinsic heterogeneity of neurons in the network, thereby enhancing the beneficiary effects of intrinsic heterogeneity that we had observed earlier (Fig. 4).
Importantly, reminiscent of our results with the introduction of synaptic heterogeneity (Fig. 5), in the network that was endowed with variability in neuronal age, the level of decorrelation was intermediate between that obtained with the fully mature and the fully immature networks (Fig.   6F). Together, these results demonstrate that neurogenesis-induced variability in neuronal response properties adds an additional layer of heterogeneity in the DG network, and enhances network decorrelation to identical external inputs.

Input-driven heterogeneity mediated by sparseness of afferent connectivity is a dominant regulator of neuronal response decorrelation
An important defining characteristic of the DG network is the sparseness of the afferent connectivity matrix that is reflective of massive convergence and divergence reflecting the small number of layer II EC cells (~30,000) that project to a large (~1.2 million) number of DG cells, resulting in significant variability in the set of afferent external inputs impinging on each GC (23, 43). Thus far in our analysis, in an effort to delineate the impact of three distinct forms of heterogeneity, we employed an artificial construct where all neurons in the network received identical inputs. To assess the impact of this fourth form of afferent input-driven heterogeneity, we introduced divergence in the set of EC neurons that project onto each GC and BC. This implied that each GC and BC now received distinct sets of EC inputs.
As a consequence of distinct set of inputs impinging on each GC, the firing fields were distinct across different GCs (Fig. 7A) and BCs (Fig. S4), unlike the near-identical firing fields (except for differences in firing frequency or threshold) in the case where neurons received identical inputs (Fig. 4A; Fig. S2). Importantly, when we analyzed pair-wise correlation of firing rates across different neurons, we found that the correlation coefficients were lower irrespective of the presence or absence of different forms of heterogeneity (Fig. 7B). The overall firing rate distributions obtained with either identical (Fig. 6) or distinct (Fig. 7C) afferent inputs were similar, thereby ruling out changes in firing rate as a possible cause for the observed differences in correlation coefficients.
Strikingly, when we plotted the cumulative distributions of correlation coefficients obtained with the introduction of distinct forms of network heterogeneities, we found them to significantly overlap with each other (Fig. 7D). This is in stark contrast to the network receiving identical external inputs (Fig. 5E, Fig. 6F), where introduction of each of intrinsic, synaptic and neurogenesis-induced heterogeneities enhanced or altered the level of response decorrelation.
The negligible impact of the intrinsic or synaptic or age heterogeneities on the overall level of response decorrelation achieved in the presence of input-driven heterogeneities, which was higher than that obtained with identical inputs (Fig. 7E), unveiled the dominance of heterogeneities driven by afferent connectivity in determining response decorrelation.
Were our conclusions on the role of different forms of heterogeneities scalable and invariant to network size? To test this, we repeated our analyses in Figs. 4-7 with a smaller network made of 100 GCs and 15 BCs, and found our conclusions to scale across different network sizes (Fig. S5). Together, our results demonstrate that local heterogeneities in intrinsic, synaptic and neuronal structural (driven by adult neurogenesis) properties contributed to significant levels of response decorrelation in the presence of identical afferent synaptic drive.
However, when the network received heterogeneous external inputs, the impact of local heterogeneities on response decorrelation was strongly suppressed by the dominant role of afferent heterogeneities in mediating neuronal response decorrelation.

Dominance of input-driven heterogeneity and implications for the physiological roles for adult neurogenesis
Our results quantitatively demonstrate a dominant role for afferent heterogeneities, driven specifically by the unique network structure of the DG involving huge number of GCs innervated by the small number of LII EC neurons, in driving response decorrelation in the DG. Within this framework, this dominant connectivity divergence in feed-forward afferents, synergistically coupled to the hetereogeneous intrinsic properties and the sparse GC activity that is sharpened by the local inhibitory network places the DG network as an ideal decorrelating system. Importantly, our conclusions on the dominance of heterogeneous afferent connectivity, with the local network heterogeneities playing secondary roles, pose specific questions on the role of adult neurogenesis in input discriminability, questioning the rationale behind the need for new neurons in a highly divergent, sparsely active network (9).
If adult neurogenesis-induced heterogeneities in neuronal properties were not the dominant contributor to response decorrelation, what is the precise role of adult neurogenesis in the DG? One possibility within our framework is that adult neurogenesis could be a mechanism for implementing afferent heterogeneities across DG neurons, whereby new neurons establish connections to afferent fibers in an activity-dependent manner (14, 44-46), thereby assigning a specific set of active afferent inputs to new neurons of the same time of birth (9, 25, 47). In such a scenario, the afferent heterogeneities would be driven by active assignment of spatial connectivity from the EC to individual DG neurons, whereby the novel contexts encountered by the animal are encoded by the temporal onset of neurons. Such active assignments could be driven by activity-dependent connectivity aided by the hyper-plastic, hyper-excitable nature of new neurons, and the resultant afferent heterogeneities (different neurons get different EC inputs) then plays specific roles in response decorrelation, in encoding temporal context and in controlling memory resolution (9,14,20,25,39,(44)(45)(46)(47). In addition to this, our results suggest that the variability introduced by new neurons in terms of their intrinsic excitability (Figs. 4, 6) and in terms of altered excitation-inhibition balance (Fig. 5) could also be candidate mechanisms through which adult neurogenesis enhances (beyond what is driven by afferent heterogeneities) the degree of response decorrelation achieved in the DG network (8,9,16,20,25,47).

Comparison of mechanisms for decorrelation in the dentate gyrus and in the olfactory bulb
The olfactory bulb (OB) is another brain region that expresses adult neurogenesis and has been postulated to play a critical role in channel decorrelation (referred here as response      For the left and right matrices, which are the same plots as in Fig. 4E and Fig. 4C, respectively, there was no synaptic heterogeneity, with P AMPAR and P GABAAR set at specified fixed values for all excitatory and inhibitory synapses. The matrix represented in the center was computed from a network endowed with intrinsic as well as synaptic heterogeneity (shown in C). (E) Cumulative distribution of correlation coefficients represented in matrices in (E). Plotted are distributions from five different trials of each configuration. Note that except for the homogenous population, all three configurations were endowed with intrinsic heterogeneity. The configurations "Intrinsic + synaptic heterogeneity" and "Homogeneous + synaptic heterogeneity" had randomized synaptic permeabilities; for the other two configurations, the synaptic strengths were fixed at specific values: High P, P AMPAR =5 nm/s and P GABAAR =40 nm/s; Low P, P AMPAR =1 nm/s and P GABAAR =20 nm/s.