Electrophysiological properties of immature GCs and mGCs are known to differ (Mongiat et al., 2009; Yang et al., 2015; Marín-Burgin and Schinder, 2012b). Thus, we wondered whether neurons of different age would produce responses with a different temporal structure to the same stimulus. To investigate this, we performed ex vivo whole cell recordings in mGCs (n=21) and adult-born GCs that were 4 and 5 weeks of age (4wGCs, n=22 and 5wGCs, n=20) (Figure 1A). Adult-born GCs of different ages were labeled using a Ascl1-CreERT2-Tom mice line (Figure 1B, Methods) (Yang et al., 2015). Brain slices were prepared 4 or 5 weeks after tamoxifen injection to obtain tomato expressing GCs of these ages. Excitatory and inhibitory synaptic transmission were blocked pharmacologically with kynurenic acid and picrotoxin, so that differences in recorded activity were only due to differences in the cells intrinsic properties. We measured the passive input resistance and time constant of the GCs by injecting small hyperpolarizing current steps at –70 mV. Both the input resistance and the time constant measured in this way decreased with age (Figure 1—figure supplement 1), consistent with previous reports (Mongiat et al., 2009; Yang et al., 2015). Additionally, when injected with depolarizing current steps, immature GCs fired at higher frequencies than mature ones for the same step amplitude (Figure 1—figure supplement 1).

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Next, we used fluctuating stimuli that we designed from in vivo recordings of the intact network (Pernía-Andrade and Jonas, 2014), which show that GCs receive a wide range of frequencies, with a power spectrum that exhibits a power law decay (Methods). These types of stimuli produced responses with a rich and reproducible temporal structure (Mainen and Sejnowski, 1995). We generated a single stimulus template from an Ornstein-Uhlenbeck process with a short correlation time constant (Figure 1C, Methods). mGCs have smaller input resistances and integrate larger excitatory and inhibitory currents than immature GCs (Figure 1—figure supplement 1; Mongiat et al., 2009; Marín-Burgin et al., 2012a). Therefore, to make the firing rate of the responses comparable across GCs of different ages, we used the same stimulus template for all GCs while adapting its baseline and amplitude (Figure 1—figure supplement 2). We injected nine trials of the template stimulus in each GC and recorded the resulting membrane potentials. From these, we extracted the spike timings that we used to study the responses.

We first studied the alignment between the neural responses and the injected stimulus. For each GC, we smoothed the spike trains with a rectangular sliding window and averaged over trials to obtain a peri-stimulus time histogram (PSTH) (Figure 1D). We then computed the Pearson’s cross-correlation between the injected stimulus and the PSTHs for different time lags (Figure 1E). The lag of the cross-correlation peak reflects the time scale of stimulus integration, and the peak value the degree of alignment between stimulus and response. The lag and the value at the peak of the cross-correlation were negatively and positively correlated with age respectively (Figure 1F). These results indicate that GCs’ responses become faster with maturation and exhibit stronger alignment with the stimulus.

While spike times were often preceded by stimulus upswings, the previous analysis doesn’t explore the variability in the responses across trials and different GCs. To investigate this, we introduced a coincidence ratio between pairs of recordings, each recording consisting of all trials (Figure 1G, Methods; Paiva et al., 2009; Naud et al., 2011). We defined the coincidence ratio as the average proportion of spike coincidences between all possible pairs of trials. A coincidence ratio of 0 means no coincidences between the recordings and a coincidence ratio of 1 means all spikes match their timing. We quantified the reliability in the response of single GCs by computing coincidences between pairs of different trials of the same GC.

The coincidence ratio spanned a wide range of values (Figure 1H). For each GC, we computed its average coincidence ratio with all other GCs of the same age (Figure 1I). Older pairs of GCs exhibited larger coincidence ratios, indicating their responses were more similar to each other. In addition, mixed-age pairs that contain 4wGCs have lower coincidence ratios than pairs of mature neurons alone (Figure 1—figure supplement 2). This could be related to individual immature GCs producing less reproducible responses, which can be quantified by the reliability. GC reliability, determined by the diagonal of Figure 1H, took generally higher values than the coincidence ratio as trials from a single GC were usually more similar to each other than to trials from a different GC. Reliability increased with maturation, taking values $0.29\pm 0.03$ (mean ± 1 s.e.m.) for 4wGCs, $0.38\pm 0.04$ for 5wGCs, and $0.49\pm 0.04$ for mGCs (Figure 1J). Consistent with the cross-correlation analysis, this indicates that GCs are able to produce more robust responses with maturation. This effect could not be attributed to differences in firing rate, as shown by the reliabilities obtained after randomizing the timing of the spikes in every trial (Figure 1—figure supplement 2). Thus, our data indicates that immature GCs are less aligned with the stimulus and produce less reliable responses than mature ones.

The observed differences in the stimulus alignment and reliability of the responses suggest that GCs of different ages do not perform the same stimulus encoding. Thus, we sought to find a functional relationship between the stimulus and the GCs’ responses to characterize their encoding properties, by fitting a spike response model (SRM) to our data (Figure 2; Gerstner, 2014). The SRM is a statistical model in the family of generalized linear models (GLMs) which allow for a direct fitting procedure and have been widely used to provide accurate statistical descriptions of spiking data (Tripathy et al., 2013; Pillow et al., 2008). A key feature of these models is that they provide a quantitative characterization of neural activity in terms of parameters that can be linked to biophysical properties.

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The SRM describes both the subthreshold membrane potential and the spiking response to a current stimulation (Figure 2A, Methods). The stimulus first passes through a membrane filter $k(t)$ that defines how the input current is dynamically transduced in voltage variations. Next, the subthreshold membrane potential is generated by summing the filtered stimulus, a constant bias v_b, and the postspike voltage deflection $h_v(t)$. The bias is a baseline voltage and the postspike voltage deflection accounts for the effect of intrinsic currents occurring after a spike. A moving voltage threshold is then subtracted from the subthreshold membrane potential. The exponential of this difference scaled by a factor $\mathrm{\Delta }v$ sets the time-dependent spiking rate. The moving threshold is the sum of a constant threshold $v_{th}$ and the postspike threshold deflection $h_{th}(t)$ that accounts for threshold refractory effects. Finally, spikes are randomly generated at every discrete time point from the time-dependent spiking rate.

We fitted the SRM to single trial 99 s recordings from individual 4wGCs (n=20), 5wGCs (n=17), and mGCs (n=18), using rapidly fluctuating stimuli generated as described in the previous section. We performed the SRM fitting in two steps: first we extracted the subthreshold parameters v_b, $k(t)$, and $h_v(t)$ using the subthreshold membrane potential (Figure 2B–D, Methods); then we extracted $v_{th}$, $h_{th}(t)$, and $\mathrm{\Delta }v$ by maximizing the likelihood of the spike times while keeping the subthreshold parameters fixed (Figure 2E–G, Methods). The SRM yields predictions on both the subthreshold membrane potential and the spikes of the response. To validate the fits, we used the nine trials 10 s recordings described in the previous section. The SRM captured both the subthreshold membrane potential and spiking responses of the validation data (Figure 2H). We used the validation data to compute the root mean squared error (MSE) of the subthreshold membrane potential prediction and a normalized log-likelihood (Figure 2—figure supplement 1, Methods). To assess the quality of the spike trains generated by the SRM, we also computed the coincidence index $M_d$ between simulated and recorded spike trains (Gerstner, 2014; Naud et al., 2011). The reliability of the simulated spike trains was generally smaller than the reliability of the data but they were linearly correlated, indicating that the differences between GCs were mostly preserved (Figure 2—figure supplement 1).

The parameters obtained from the fit reflect differences in the way that GCs of different ages encode stimuli. While passive properties determine the membrane potential deflection for small current steps in the absence of spikes, the membrane filter $k(t)$ determines how the stimulation current is actively transduced into voltage during spiking activity. $k(t)$ is composed of a rapid decay attributed to the patch pipette (Pozzorini et al., 2015) and a tail that is well approximated by an exponential decay (Figure 2C). The time constant of the slower exponential decay measures the time scale of stimulus integration. The area under the exponential is an electrical resistance and determines the average membrane potential deflection in the absence of spikes. Both the population time constant and the resistance of the filter $k(t)$ decreased with age (Figure 2I, Figure 2—figure supplement 1), consistent with the passive properties’ observations (Figure 1—figure supplement 1; Mongiat et al., 2009; Yang et al., 2015). These properties were correlated with their passive counterparts but were generally smaller (Figure 2—figure supplement 1). Slower membranes could partly explain the observed unreliability of immature GCs, as neurons with longer time constants tend to be less reliable (Figure 2J). The filters $h_v(t)$ and $h_{th}(t)$ quantify the postspike deflections in membrane potential and spiking threshold respectively. We quantified their amplitudes by using the first values of the filters (Figure 2K). While mGCs’ membranes tended to hyperpolarize after a spike, this effect was generally smaller for immature GCs (Figure 2D, K). This hyperpolarization could be attributed to spike-triggered potassium currents, which have been reported to be smaller in immature GCs (Mongiat et al., 2009; Yang et al., 2015). While the threshold after a spike increased for all GCs, the amplitude of the filter $h_{th}(t)$ was also positively correlated with age.

Next, we wanted to explore whether the obtained parameters could be used to discriminate GCs’ ages. We used v_b, $v_{th}$, $\mathrm{\Delta }v$, and the first coefficients of the filters $k(t)$, $h_v(t)$, and $h_{th}(t)$ to classify GCs’ ages using a linear discriminant analysis (LDA) (Figure 2L; Bishop, 2006). SRM parameters could be used to classify mGCs and 4wGCs with cross-validated accuracies of 0.72 and 0.75, respectively. The other 0.28 and 0.25 fractions were classified as 5wGCs indicating that 4wGCs and mGCs were very well discriminated by the LDA. Being maturationally in between, the classification accuracy of 5wGCs was 0.47, with a fraction of 0.41 5wGCs being classified as 4wGCs. This suggests that 5wGCs were closer in parameter space to 4wGCs than to mGCs. The coefficients of the filter $k(t)$ play an important role in the classification as they have large weights in the LDA components (Figure 2—figure supplement 2). The LDA indicates that the SRM parameters reflect maturational differences and can be used to distinguish GCs’ ages with higher than chance accuracy.

We observed that mGCs have a smaller input resistance, a faster membrane, and experience stronger postspike refractory effects. Our results suggest that GCs of different ages might transmit different properties of an afferent stimulus. Besides providing us with parameters that can be compared across ages, the SRM provides us with a statistical description of the GCs. This description can be used to generate spike trains and further explore the way in which GCs represent stimuli. Next, we use the SRM to generate simulated granule cells (SGCs) in a decoding framework to explore the fidelity of stimulus encoding and quantify the information content in the spike trains of the different age groups.

As spiking responses encode information about the stimulus, we wondered, what can we infer about the stimulus by observing the responses of GCs of different ages? To investigate this question, we used the SRM to perform Bayesian model-based decoding (Tripathy et al., 2013; Pillow et al., 2008; Pillow et al., 2011). Model-based decoding finds the most probable stimulus that produced one or more spike trains, given a prior distribution (Figure 3A, Methods). This decoded stimulus can then be compared with the original to evaluate the fidelity of the reconstruction. Furthermore, the procedure can be used to estimate the mutual information between stimulus and responses (Pillow et al., 2011). More broadly, we can use this framework to asses the fidelity of the code, that is to determine how well GCs of different ages encode information about the stimulus in the spike trains they produce.

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We first performed the decoding using single experimentally recorded spike trains. We found the most probable stimulus that produced the spikes and the uncertainty about its value as a function of time (Figure 3B). During intervals in which a GC is silent, there is no information about the stimulus; hence the estimation takes baseline values and the uncertainty is highest. Just before an isolated spike, the stimulus is usually predicted to be above average and the uncertainty is reduced. Averaging over spikes and GCs, we found that the minimum uncertainty about the stimulus before a spike was reduced more in mGCs (Figure 3C).

While recorded spike trains allowed us to perform the decoding of the experimental stimulus, the SRM can be used to simulate responses to multiple different stimuli for decoding. Thus, we obtained SGCs by sampling different stimuli from the same stochastic process that was used experimentally, and repeated the decoding procedure using single spike trains generated with the SRM parameters of each GC. This strategy allows us to quantify decoding performance by estimating the mean coefficient of determination $r^2$ of the reconstruction, and the mutual information between the stimulus and the SGC spike trains (Methods). The coefficient $r^2$ involves computing the error between the reconstructed and the original stimuli to obtain the fraction of the variance explained by the decoded signal. In other words, this quantity captures the proportion of the variation in the stimulus that is predictable with the decoding. The mutual information measures the correspondence between stimulus and response, and quantifies the reduction in uncertainty about the stimulus after observing the given spike trains (Schneidman et al., 2003). Both the total $r^2$ and mutual information strongly correlated with SGC firing rate (Figure 3D, E). This is expected as we used only the spikes to decode the stimulus. Decoding performance using multiple stimuli and SGCs’ spike trains was very similar to the one obtained by using the experimentally recorded stimuli and GCs’ spike trains (Figure 3—figure supplement 1). To study the difference between GCs’ ages, we removed the average contribution of firing rate to decoding performance. For this, we subtracted the linear relationships of Figure 3D, E obtained with all SGCs from the $r^2$ and information of each SGC, obtaining the respective residuals (Figure 3F). Both the residual $r^2$ and information correlated with GC age indicating that for a given firing rate, responses from mGCs generally produced more precise reconstructions and were more informative about the stimulus.

We showed that GCs have different degrees of reliability and the same stimulus will elicit different individual responses from the same neuron (Figure 1C). Is it possible to extract more information from a single GC by observing multiple responses to a single stimulus? Does GC reliability influence this? Using responses to multiple trials of the same stimulus improved both the $r^2$ and the information of the decoding (Figure 3G). For small fold increments in the number of trials used for decoding, the information about the stimulus increased by almost the same fold (Figure 3—figure supplement 2). Immature SGCs benefit more from using multiple trials for decoding as a consequence of their noisier responses. To study age differences while equalizing differences in firing rate, we decoded stimuli using for each SGC a number of trials such that the total number of spikes was 140, on average (Figure 3H, Methods). Consistent with the results of Figure 3F, when equalizing the number of spikes for each SGC, decoding with immature SGCs resulted in lower $r^2$ and information values. When using larger numbers of spikes to equalize the firing rate differences, the correlations between age and decoding performance decreased (Figure 3—figure supplement 2). We also found that when equalizing the number of spikes used for decoding, the resulting $r^2$ and information values were larger in the SGCs that produced more reliable responses (Figure 3I, J).

We next studied how the different age groups complement each other by using pairs of different SGCs to decode. We used a single stimulus to generate 140 spikes on average from each SGC in the pair and performed the decoding (Figure 3—figure supplement 3). Using pairs of SGCs of the same age, we found that more mature pairs achieved higher values of $r^2$ and information. Pairing mature SGCs (mSGCs) with immature SGCs tended to degrade decoding performance resulting in smaller $r^2$ and information values. Coherent with the results from single SGCs, more immature pairs achieved overall worse decoding performance.

Our results indicate that immature GCs produce less precise reconstructions and convey less information about the stimulus, suggesting that they produce generally worse stimuli representations. Moreover, mGCs mostly increase decoding performance when paired with other mGCs rather than with immature ones. Thus, these results cast doubts about whether immature GCs can enhance coding in a population.

Our results so far suggest that mGCs, isolated or in pairs, are generally better than immature GCs for reconstructing stimuli. However, in a larger population there might be synergistic effects, and GCs that did not perform well by themselves could still play a significant role in enhancing population coding. Thus, we wondered whether immature GCs could improve decoding in a population consisting of a larger group of neurons. When building a population, even for a moderate number of neurons, trying all possible combinations between them results in prohibitive computational costs. Hence, we adopted a sequential greedy procedure to construct populations of SGCs that optimize stimulus reconstruction (Tripathy et al., 2013). To build a population, we started with a single mSGC and sequentially added individual neurons from the full pool of mature (n=18) and immature (5wSGCs n=17, 4wSGCs n=20) SGCs in the simulated experiment (Figure 4A, Methods). At each step, using the group built so far, we performed the decoding adding each possible SGC to the population, and kept the one that yielded the largest $r^2$ for the extended group. With this greedy procedure, we sought to evaluate whether immature neurons may contribute to improve the decoding, despite having lower $r^2$ and information values individually. Thus, we did not constrain the proportion of immature neurons in the population to match the in vivo estimation of 3% (van Praag et al., 2002). Rather, we always picked from these given pools the neuron that maximized the population $r^2$. As decoding performance depends on the number of spikes (Figure 3D), we used a different number of trials for each SGC so that the total number of spikes that each one contributed was 1200 on average (Figure 4B). In this way, we reduced the preference for trivially choosing SGCs with high firing rates.

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We built mixed-age populations following the greedy procedure. In the first step, we started with the 18 mSGCs obtained with the SRM fit (Figure 4C). As expected from the results decoding with pairs of SGCs (Figure 3—figure supplement 3), mSGCs were chosen almost exclusively among the full pool in the second step. Unexpectedly, from the third step onward, immature SGCs were chosen by the greedy procedure with increasing preference (Figure 4C). The fraction of immature SGCs in the populations increased at the expense of the mSGCs (Figure 4D). For populations of 12 SGCs, approximately 43% were mSGCs, 32% were 5wSGCs, and 25% were 4wSGCs. We found that 51% of all the SGCs were never chosen in any population by the greedy algorithm, 34.5% of the SGCs were selected between 1 and 10 times, and 14.5% were selected over 10 times (Figure 4—figure supplement 1). This indicates that the final populations strongly differ from random selection, which would have each SGC selected 3.6 times on average. Furthermore, these results highlight the diversity of the final populations, since a large fraction of SGCs were selected a smaller number of times than the number of populations, hence these are not composed of the same neurons. Moreover, although some of the preferentially chosen SGCs achieved large $r^2$ values when used individually, some highly selected SGCs yielded relatively poor reconstructions by themselves (Figure 4E) as well as in pairs (Figure 4—figure supplement 1). These observations indicate that decoding performance is a result of a non-trivial synergy between the GCs composing a population, and optimal performance is not achieved by taking the best individual GCs.

The greedy procedure selected immature SGCs to improve stimulus reconstruction. Both $r^2$ and the mutual information steadily increased with the number of SGCs in the populations, and were clearly larger than those of populations of randomly selected SGCs (Figure 4F, G). This improvement in the decoding that resulted in larger values of $r^2$ can also be contrasted to single simulated neurons, with $r^2\in (0.02,0.12)$ (Figure 3D and Figure 3B), and with multiple trials of single simulated neurons $r^2\in (0.15,0.3)$, (Figure 4E and Figure 3G). Still, the greedy procedure performs a stepwise optimization, therefore choosing immature SGCs over mSGCs early in the construction could result in worse decoding performance for the final populations. We thus compared the decoding performance of the greedy mixed-age populations with exclusively mSGCs’ populations, built following the greedy procedure and starting from the same pool of initial mSGCs. With increasing number of neurons, mixed-age populations achieved consistently larger $r^2$ values in comparison with exclusively mature ones (Figure 4F). This resulted in a steady average decrease in the relative reconstruction error, reaching a final relative improvement of 3% (Figure 4H). Moreover, we found a positive correlation between the $r^2$ of a population and the number of immature SGCs that it contains (Figure 4I). However, the populations of mSGCs achieved larger information values than the mixed-age ones (Figure 4G). The mutual information, unlike the $r^2$, is not quantified by comparing the decoded stimuli with the true stimuli. It is related to the uncertainty about the decoding and the correspondence between decoded and true stimuli, but not to whether it is a good approximation to it. In fact, a decoder could achieve perfect mutual information but result in a poor reconstruction by performing a perfectly scrambled one-to-one mapping of the true stimulus (Schneidman et al., 2003).

After 12 iterations, the greedy procedure produced populations with at least four immature cells (Figure 4I). We wondered whether a smaller fractions of immature cells could still produce a significant effect on decoding. To generate populations with smaller proportions of immature cells, we constrained the greedy procedure by selecting only mature cells in the first steps. Varying the number of steps for which we restrict the selection to mSGCs, we generate populations with a variable number of immature SGCs. For example, for populations of 12 SGCs, if we restrict selection to mSGCs during the first nine steps, we generate populations that can have between zero and three immature SGCs. Although a single immature SGC did not have a significant impact in a 12 SGCs’ population, from 2 immature SGCs onward there was an improvement in decoding as reflected in growing $r^2$ (Figure 4—figure supplement 2). Conversely, the mutual information decayed with increasing number of immature SGCs.

Finally, we wondered if immature SGCs improve decoding performance when the stimulus contains a theta oscillation as it has been observed in hippocampal rhythms (Pernía-Andrade and Jonas, 2014). Thus, we recorded GCs’ responses to a stimulus template containing theta oscillations (Methods) (Figure 4—figure supplement 3). We used the SRM fits obtained in Figure 2 to simulate SGCs’ responses using this same stimuli. We found that the model was able to extrapolate to this theta-modulated stimulus, generating responses that captured the data. In the presence of theta rhythms, stimulus decoding was also improved by the presence of immature SGCs (Figure 4—figure supplement 3).

Thus, while single mGCs perform better than immature ones, mixed-age populations improve stimulus reconstruction, suggesting that the diversity contributed by immature GCs could be beneficial for transmitting distinct properties of stimuli with rich temporal structure.

We showed that the presence of immature GCs in a population can enhance stimulus reconstruction. The dentate gyrus is thought to play a key role in pattern separation (Leutgeb et al., 2007). Ablating neurogenesis affects fine spatial discrimination, that is when the separation between patterns is small, but not when it is large (Clelland et al., 2009). Thus, we wondered whether a downstream region could benefit from reading the output of a mixed-age population to enhance discrimination of similar patterns. We designed a pattern separation task within the decoding framework by using it to discriminate between pairs of correlated stimuli (Figure 5A, Methods). We used mixed-age and mature-only populations of 10 SGCs that we constructed in the previous section. We generated pairs of correlated stimuli and then used one of them to generate spike trains. We then performed the decoding to obtain a stimulus reconstruction. To discriminate, we compared the errors between the reconstruction and each of the two stimuli, expecting that this discrimination task would become increasingly harder as the correlation between stimuli increases.

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We then explored whether the populations could be used to correctly discriminate between the stimuli with different degrees of separation. We defined three degrees of separation (low, medium, and high) that correspond to different correlation values between the jointly generated stimuli (Figure 5B, Methods). For high separation the two stimuli are easily discriminated with almost 100% accuracy both by the mixed-age and mature-only populations. For low separation, stimuli are hard to discriminate and while the obtained accuracy is above chance, the differences between the mixed-age and mature-only populations are small. However, for medium degree of separation the mixed-age populations outperformed the mature-only at the discrimination task, suggesting that age heterogeneity in the dentate gyrus could also be leveraged to separate time-varying stimuli.

Finally, we tested whether immature SGCs could also improve discrimination if the stimulus is corrupted with noise. To do this, for each SGC we produced a different corrupted version of the stimulus used for generating spike trains. As now each spike train is generated with a corrupted version of the stimulus, correct discrimination will depend on the capability of the decoder to average out the noise in the population. For a fixed degree of separation between the pairs of stimuli, adding noise is detrimental to discrimination performance for the populations (Figure 5C). Notably, the mixed-age populations consistently outperform the mature-only for moderate amounts of noise. In summary, our results suggest that immature GCs in the dentate gyrus introduce a degree of heterogeneity at the population level that can be leveraged to reconstruct an incoming stimulus better and, at the same time, discriminate it from others.

Ascl1-CreERT2 mice (Yang et al., 2015) (Jackson Laboratory RRID IMSRJAX:012882) were crossed with CAG-floxStop-tdTomato (Jackson Laboratory RRID IMSRJAX:007914) mice to generate Ascl1-CreERT2-Tom mice. Mice were housed with a running wheel which is known to enhance adult hippocampal neurogenesis (van Praag et al., 1999). Adult mice of either sex were injected with tamoxifen at 6–8 weeks of age. Tamoxifen was delivered intraperitoneally in two 120 μg per mouse gram injections in 2 consecutive days to achieve indelible expression of Tom in newborn GCs. Mice were anesthetized and decapitated at 4 or 5 weeks after injection, depending on the desired age of the GCs. Experimental protocol (2020-03-NE) was evaluated by the Institutional Animal Care and Use Committee of the IBioBA-CONICET according to the Principles for Biomedical Research involving animals of the Council for International Organizations for Medical Sciences and provisions stated in the Guide for the Care and Use of Laboratory Animals. Brains were removed and placed into a chilled solution containing (mM) 110 choline cloride, 2.5 KCl, 2.0 NaH₂PO₄, 25.0 NaHCO₃, 0.5 CaCl₂, 7 MgCl₂, 20 dextrose, 1.3 sodium ascorbate, 0.6 sodium pyruvate. Acute slices 400 μm thick from either hemisphere were cut transversally to the longitudinal axis in a vibratome. Hippocampal slices were then transferred to a chamber containing artificial cerebrospinal fluid (mM): 125 NaCl, 2.5 KCl, 2.3 NaH₂PO₄, 25 NaHCO₃, 2 CaCl₂, 1.3 MgCl₂, 1.3 Na+-ascorbate, 3.1 Na+-pyruvate, and 10 dextrose (315 mOsm). Slices were bubbled with 95% O₂/5% CO₂ and maintained at 30°C for >1 hr before experiments started.

Recorded immature neurons were visually identified by fluorescence. GCs used between 28 and 30 days post injection were labeled as 4w and GCs used between 34 and 36 days post injection were labeled as 5w. The mature population encompassed unlabeled neurons localized in the outer third of the GC layer (Mongiat et al., 2009; Yang et al., 2015). Whole-cell current-clamp recordings were made at room temperature, in the estimated range from 22°C to 26°C. We used microelectrodes (4–6 MΩ) filled with a potassium gluconate internal solution (in mM): 120 potassium gluconate, 4 MgCl₂, 10 HEPES buffer, 0.1 EGTA, 5NaCl, 20KCl, 4ATP-tris, 0.3 GTP-tris, and 10 phosphocreatine (pH = 7.3; 290 mOsm). Excitatory and inhibitory synaptic transmission were blocked pharmacologically with kynurenic acid (Sigma-Aldrich Cat K3375) and picrotoxin (Sigma-Aldrich Cat P1675). Recordings were obtained using Multiclamp 700B amplifiers (Molecular Devices), digitized using Digidata 1550 (Axon instruments), and acquired at 10 kHz onto a personal computer using the pClamp10 software (Molecular Devices). Input resistance was obtained from current traces evoked by a hyperpolarizing step of 10 mV. Series resistance was typically 10–20 MΩ, and experiments were discarded if higher than 40 MΩ. Before starting every protocol of stimulation, the resting membrane potential was kept at around –70 mV by passing a holding current. To compute the reported input resistance and time constants, we injected small current hyperpolarizing steps and performed exponential fits of the resulting membrane potential deviations. Current step amplitude was adapted to each neuron and resulted in a negative membrane potential deviation of 1–4 mV. All electrophysiological recordings are available as raw data from Dryad.

We based the design of the stimulus on in vivo recordings from the intact network (Pernía-Andrade and Jonas, 2014). These recordings show that GCs receive a wide range of frequencies, with a power spectrum that exhibits a power law decay. In vivo recordings have also reported a peak in the spectrum, indicating the presence of theta oscillations. Here, we did not include these oscillations in the stimuli because white noise, or noise with an exponentially decaying autocorrelation, produces better fits with GLMs (Paninski, 2004). We generated fluctuating stimuli from an Ornstein-Uhlenbeck process (Gillespie, 1996)

The process has zero mean, unit variance, and correlation time constant $\tau$. This process was implemented numerically with the discretization

Throughout this work we used a time constant $\tau =3$ ms that was much shorter than neuron membrane time constants. Both in experiments and simulations described below, neurons were injected with currents of the form $i\left(t\right)=\sigma \eta \left(t\right)+\mu$, where μ set the mean value of the current and $\sigma$ determined the amplitude of current fluctuations. Since GCs of different ages have markedly different input resistances, during experiments we adapted μ and $\sigma$ online for each individual GC, seeking to obtain a firing rate of at least 1 Hz.

We generated stimuli with a theta rhythm using the autocovariance function

with $f=8\text{Hz}$ and $\tau =100\text{ms}$. Given discrete time bins $\mathrm{\Delta }t$, we used the autocovariance function to generate a covariance matrix $C$, with $C_{ij}=\rho \left(\left(i-j\right)\mathrm{\Delta }t\right)$. By using the Cholesky decomposition of $C$ to find a matrix $L$, with $C=L{L}^T$, we can then generate stimuli with the desired autocovariance by performing the matrix-vector product $Lϵ$, where $ϵ$ is vector which components are independent and ${\displaystyle {ϵ}_i\sim \mathcal{N}(0,1)}$. An offset μ was added to set the mean value of the current stimuli.

A spike train $s\left(t\right)$ with spike times $\{t_1,t_2,\mathrm{\dots }{t}_s,\mathrm{\dots }\}$ can be represented as the sum of Dirac delta distributions

For two spike trains $s$ and $s^{\prime }$, we defined a coincidence between them as the co-occurrence of two spikes within a predefined time window. We introduced the number of coincident spikes $c(s,s^{\prime })$, defined by the inner product $⟨s,s^{\prime }⟨$ between the spike trains (Gerstner, 2014; Naud et al., 2011),

where $T$ is spike train duration and $K(u,u^{\prime })=h_{\mathrm{\Delta }}\left(u\right)\delta \left(u^{\prime }\right)$ is a kernel with $h_{\mathrm{\Delta }}\left(u\right)=\mathrm{\Theta }\left(u+\mathrm{\Delta }/2\right)\mathrm{\Theta }\left(u-\mathrm{\Delta }/2\right)$ a rectangular function of width $\mathrm{\Delta }$, $\mathrm{\Theta }$ the Heaviside step function, and $\delta$ the Dirac delta distribution. To compute all the quantities introduced here, we always used the time window $\mathrm{\Delta }=8$ ms that is similar to the duration of an action potential. For this choice of kernel and the small time window used, the coincidence of a spike train $s$ with itself always counted the total number of spikes $n\left(s\right)$ in the train, $⟨s,s⟨=n\left(s\right)$ for all spike trains considered. Given two different sets of M spike trains $S=\{s^1,s^2,\mathrm{\dots },s^M\}$ and $S^{\prime }=\{s^{\prime 1},s^{\prime 2},\mathrm{\dots },s^{\prime M}\}$, we define the coincidence ratio between them

where the numerator is the average number of coincidences between the two sets and $N\left(S\right)=\frac{1}{M}{\sum }_{i=1}^{M}n\left(s^i\right)$ is the average number of spikes in the trains of the set $S$. This coincidence ratio is the average number of coincidences between the sets normalized by the average number of spikes in their spike trains. For a single recording $S$ consisting of $M$ trials, we define the reliability as

the average number of coincidences between different spike trains in the recording normalized by the average number of spikes in its spike trains. Thus, this reliability quantifies the variability within a single set of spike trains.

The SRM generates spikes from a Bernoulli probability distribution with an instantaneous rate that is determined from the subthreshold membrane potential. The subthreshold membrane potential is

where $v_b$ is a voltage bias and $k\left(t\right)$ is a membrane filter that is convolved with the stimulus $i\left(t\right)$. A voltage history filter $h_v\left(t\right)$ is added after every spike for the set of spike times $S$. The instantaneous rate or conditional intensity $\lambda \left(t\right)$ is defined from the subthreshold membrane potential as

where $v_{th}$ is a fixed voltage threshold, $h_{th}\left(t\right)$ is the threshold deflection every time there is a spike, and $\mathrm{\Delta }v$ is a voltage scale. Finally, a spike is produced at time $t$ with probability

with a discretized time interval $\mathrm{\Delta }t$.

To fit the SRM we expand the three filters $k\left(t\right)$, $h_v\left(t\right)$, and $h_{th}\left(t\right)$ as linear combinations

where the $f_j\left(t\right)$ are rectangular basis functions with support $[t_j,t_{j+1})$, that is $f_j\left(t\right)=1$ if ${\displaystyle t_j\le t<t_{j+1}}$ and $f_j\left(t\right)=0$ otherwise. We used the same bin size for all the rectangular functions of the same filter. For $k\left(t\right)$ we used 44 bins of 8 ms width from $t_1=0$ ms to $t_{44}=344$ ms, for $h_v\left(t\right)$ we used 17 bins of 25 ms width from $t_1=25$ ms to $t_{17}=425$ ms, and for $h_{th}\left(t\right)$ we used 18 bins of 25 ms width from $t_1=0$ ms to $t_{18}=425$ ms. The predicted subthreshold voltage $\widehat{v}\left(t\right)$ is then a linear combination of the parameters

where ${\displaystyle \mathit{x}(t)\in {\mathbb{R}}^{1+J+L}}$ is the vector

${\displaystyle \mathit{x}(t{)}^{\mathsf{T}}}$ denotes the transposed vector, and ${\displaystyle {\mathit{\theta }}_{\text{sub}}=(v_b,a_1,...,a_J,b_1,...,b_L)}$ is a vector containing the subthreshold model parameters. Introducing the matrix ${\displaystyle \mathit{X}\in {\mathbb{R}}^{N\times 1+J+L}}$ of rows ${\displaystyle \mathit{x}(t)}$, we can write

Here, we distinguish the predicted ${\displaystyle \hat{\mathit{v}}}$ and recorded ${\displaystyle \mathit{v}}$ subthreshold membrane potentials, and introduce vectors to write in compact form the time dependence at discretized times, that is ${\displaystyle \mathit{v}=(v(0),v(\mathrm{\Delta }t),...,v(T))}$ with ${\displaystyle T=(N-1)\mathrm{\Delta }t}$. We determined ${\displaystyle {\mathit{\theta }}_{\text{sub}}}$ from the recorded potential by using linear least squares to minimize the MSE,

after removing the first 25 ms of voltage after every spike.

A set of spike times $S$ defines a spike train ${\displaystyle \mathit{s}=(s(0),s(\mathrm{\Delta }t),...,s(T))}$ with $s\left(t\right)=1$ if there is a spike at time $t$ and $s\left(t\right)=0$ otherwise. The joint probability to observe a spike train ${\displaystyle \mathit{s}}$ as a function of the threshold parameters ${\displaystyle {\mathit{\theta }}_{\text{th}}}$ given the stimulus ${\displaystyle \mathit{i}}$ is the likelihood ${\displaystyle P(\mathit{s}\mid \mathit{i};{\mathit{\theta }}_{\text{th}})}$. The log-likelihood function is (Gerstner, 2014)

Defining

with $\widehat{v}\left(t\right)$ determined by Equation 14, the log-likelihood can be written as

This log-likelihood is concave on the parameters and we can find its global maximum using Newton’s method to perform gradient ascent (Gerstner, 2014). We also added a term to the right-hand side of Equation 18 of the form

to impose a degree of smoothness determined by $\alpha$ over the coefficients of the filter $h_{th}\left(t\right)$. We used the value of $\alpha$ that yielded the largest log-likelihood on the validation data. In this way, each of the two steps of the fitting procedure captures a different aspect of the recording, optimizing a different function. The first step aims to capture the subthreshold membrane potential by minimizing the MSE between predicted and measured, while the second step aims to capture the spiking by maximizing the log-likelihood.

We evaluated our fits by computing the root MSE between the predicted and recorded subthreshold voltage, the log-likelihood and a coefficient $M_d$ which quantifies the degree of similarity between SRM generated and recorded sets of spike trains (Naud et al., 2011; Pozzorini et al., 2015). We reported the log-likelihood relative to the log-likelihood of a Poisson process of the same rate and normalized by the number of spikes,

The degree of similarity $M_d$ was computed using the coincidences with rectangular kernels,

where $c(s,s^{\prime })$ is given by Equation 5, $R\left(S\right)$ by Equation 7, and $N\left(S\right)$ is the average number of spikes in the trains of the set $S$. In contrast to the coincidence ratio, $M_d$ takes into account the reliability within each set of spike trains. The Python custom code developed to perform the model fitting and the decoding is available from Github.

Here, we describe how we decoded a single stimulus $\mathit{\eta }$ from the responses of multiple neurons. Given spike trains ${\displaystyle {\mathit{s}}^j}$ from GCs with SRM parameters ${\displaystyle {\mathit{\theta }}^j}$ produced by stimuli ${\displaystyle {\mathit{i}}^j={\sigma }^j\mathit{\eta }+{\mu }^j}$, we found the maximum a posteriori estimate of $\mathit{\eta }$ as

with

We generated stimuli using Equation 2, resulting in

with

and ${\displaystyle \beta =e^{-\mathrm{\Delta }t/\tau }}$. The log-posterior of Equation 23 with the Gaussian prior of Equation 24 is concave on ${\displaystyle \mathit{\eta }}$, so we found its global maximum using Newton’s method to perform gradient ascent (Pillow et al., 2011). Once we found ${\displaystyle {\mathit{\eta }}_{\text{MAP}}}$, approximating the posterior by a Gaussian as in Pillow et al., 2011, ${\displaystyle P(\mathit{\eta }\mid \{{\mathit{s}}^j\};\{{\mathit{\theta }}^j\})\approx \mathcal{N}({\mathit{\eta }}_{\text{MAP}},\mathit{C})}$ we used

to determine the covariance matrix of the approximation and quantify uncertainty (Pillow et al., 2011). We used the squared root of the diagonal of ${\displaystyle \mathit{C}}$ to quantify the uncertainty in the estimation as a function of time and the determinant of ${\displaystyle \mathit{C}}$ to compute the mutual information. The matrix ${\displaystyle {\mathit{C}}^{-1}}$ is positive semi-definite, symmetric, and banded. We used these properties and implemented the Cholesky decomposition from SciPy (Virtanen et al., 2020) to compute the optimization updates, the diagonal of ${\displaystyle \mathit{C}}$ and the determinant of ${\displaystyle \mathit{C}}$ efficiently, and saving memory.

Given a set of GCs indexed by $j$, we sampled multiple stimuli from Equation 2. For each stimulus we used the currents ${\displaystyle {\mathit{i}}^j={\sigma }^j\mathit{\eta }+{\mu }^j}$ to generate spike trains and performed the decoding. We quantified the reconstruction error using the coefficient of determination,

averaged over all sampled $\mathit{\eta }$. We obtained the mutual information between the spike trains ${\displaystyle \{{\mathit{s}}^j\}}$ and the stimulus $\mathit{\eta }$,

using all the decoded stimuli by computing

We used the Gaussian prior and Gaussian approximation of the posterior to compute the Gaussian entropies

where $|\cdot |$ is the matrix determinant.

Where we sought to compensate for differences in firing rates, we used a different number of trials for each GC to equalize the number of spikes that each one contributes to the decoding. To obtain $n$ spikes on average from a GC with firing rate $\lambda$ in a simulation of duration $T$, we used $\text{round}\left(n/\left(\lambda T\right)\right)$ trials.

To compute the metrics in Figure 3 we repeated the decoding at least 100 times. To compute the metrics in Figure 3—figure supplement 3 we repeated the decoding at least 50 times. To build the populations in Figure 4 we repeated the decoding at least 20 times for each possible population that we tried.

We generated pairs of correlated stimuli $\mathit{\eta }\left(t\right)=({\eta }_1\left(t\right),{\eta }_2\left(t\right))$ following

with ${\displaystyle 0\le \rho <1}$. The two processes have mean value 0, variance 1, time constant $\tau =3$ ms, and correlation $⟨{\eta }_1\left(t\right){\eta }_2\left(t\right)⟨=\rho$. Given the time scales of different filters of the neurons (∼ 100 ms), we decided to use 10 s stimuli, which was sufficiently long to be in a regime where the decoding performance and the pattern discrimination accuracy would not change with stimulus duration. We used only ${\eta }_1\left(t\right)$ to generate spike trains and perform the decoding. We computed the MSE between the reconstruction and both stimuli ${\eta }_1\left(t\right)$ and ${\eta }_2\left(t\right)$. If ${\displaystyle \text{MSE}({\mathit{\eta }}_{\text{MAP}},{\mathit{\eta }}_1)<\text{MSE}({\mathit{\eta }}_{\text{ MAP}},{\mathit{\eta }}_2)}$ then the patterns were correctly discriminated and incorrectly otherwise. By sampling multiple pairs ${\mathit{\eta }}_1$, ${\mathit{\eta }}_2$ we quantified the accuracy of the discrimination task as the percentage of correctly discriminated stimuli. Since we expected the impact of adult-born neurons to be important only for relatively large correlation coefficient values, for quantitation, we introduced three degrees of separation defined as low (ρ=0.9997), medium (ρ=0.999), and high (ρ=0.99). For each population of neurons and each degree of separation and noise corruption in Figure 5, we performed the decoding and stimulus discrimination 200 times.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication. Open access funding provided by Max Planck Society.

We thank Emilio Kropff for valuable comments on the manuscript, and members of the Marin Burgin and Morelli labs for fruitful discussions. This work was supported by IDRC 108878 and ANPCyT grants PICT 2015 0634 and PICT 2018 0880 awarded to AMB, ANPCyT grants PICT 2017 3753 and PICT 2019 0445 awarded to LGM, and FOCEM-Mercosur (COF 03/11) awarded to IBioBA.

Experimental protocol (2020-03-NE) was evaluated by the Institutional Animal Care and Use Committee of the IBioBA-CONICET according to the Principles for Biomedical Research involving animals of the Council for International Organizations for Medical Sciences and provisions stated in the Guide for the Care and Use of Laboratory Animals.

1. Preprint posted: May 13, 2022 (view preprint)
2. Received: May 13, 2022
3. Accepted: August 15, 2023
4. Accepted Manuscript published: August 16, 2023 (version 1)
5. Version of Record published: September 4, 2023 (version 2)

© 2023, Arribas et al.

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