Young adult-born neurons improve odor coding by mitral cells

New neurons are continuously generated in the adult brain through a process called adult neurogenesis. This form of plasticity has been correlated with numerous behavioral and cognitive phenomena, but it remains unclear if and how adult-born neurons (abNs) contribute to mature neural circuits. We established a highly specific and efficient experimental system to target abNs for causal manipulations. Using this system with chemogenetics and imaging, we found that abNs effectively sharpen mitral cells (MCs) tuning and improve their power to discriminate among odors. The effects on MCs responses peaked when abNs were young and decreased as they matured. To explain the mechanism of our observations, we simulated the olfactory bulb circuit by modelling the incorporation of abNs into the circuit. We show that higher excitability and broad input connectivity, two well-characterized features of young neurons, underlie their unique ability to boost circuit computation.

non-injected (right) OBs of a mouse injected with CNO, stimulated with odors and assessed for c-Fos expression 2 hrs later (see Methods for details). Double labeling of abGCs and c-Fos is evident in the control (non-injected) hemisphere (arrows) but less so in the injected OB where abGCs were effectively silenced. Bottommagnifications of white rectangular areas shown at the top. (C) (Left) c-Fos levels in abGCs from virus injected OB vs. the non-injected OB of 1 example mouse at 8WPI. Threshold was determined to be 2-fold higher from baseline level (dotted line).
(Right) Quantification of the data for all mice (8WPI ) exposed to odors and then sacrificed for histology. Proportion of c-Fos levels above threshold are higher in cells not infected by the DREAD virus. Single dots represent measurements from single mice (N=3 mice, n=400 DREADD+ and 400 DREADD-abGCs sampled from 12 slices, p<<.0001, binomial proportions test). (D) Same as C, but for mice 16WPI (N=3 mice, n=530 DREADD+ and 530 DREADD-abGCs sampled from 14 slices, p<<.0001, binomial proportions test). Statistical tests are two sided, and error bars represent the standard error of the mean (SEM  (A) Left-2P micrograph of a representative field of MCs expressing GCamp6f before and after CNO administration. Right-Examples of calcium transients from 8 neurons (marked on the adjacent micrographs) in response to 6 monomolecular odors (black) and 5 natural odors (gray). Odor stimulation is denoted as a black horizontal line under each trace (2 sec). Thin traces are 5 single trials; thick traces are means. Blue/Red asterisks mark a statistically significant response for each condition. Black asterisks mark significant difference between the two conditions. Vertical Scale -100% dF/F. Odors are as described in Fig. 2E. (B) Change in responsiveness (number of responses) due to CNO injection at the absence of DREADD expression N=2 mice, n=42 cells, p=.63, one sample t-test). (C) The difference in absolute response magnitude due to CNO administration, at the absence of DREADD expression. Data shown separately for suppressed and excited responses.(Excited: n=159 cell-odor pairs, p=.84; Suppressed: n=70, p=.19; one sample t-tests). (D) Response magnitude in ranked order before (blue) and after (red) CNO administration, at the absence of DREADD expression. (n=42 cells, p=.77; Wilcoxon signed rank tests on cells curves' standard deviations before vs. after CNO). Statistical tests are two sided, and error bars represent the standard error of the mean (SEM), unless stated otherwise.

SCHEMATIC MODEL
We model a network of Mitral cells (MCs) and Granule cells (GCs). We attempt to model the impact of adult-born Granule cells (abGCs) on the odor tuning properties of the network. The experimental observation is that silencing abGCs leads to a seemingly paradoxical effect, suppressing both inhibitory and excitatory odor-responses by MCs. We argue that this result can be explained quite simply by more "promiscuous" connectivity between MCs and abGCs together with overall elevated excitability of abGCs.
We model the three populations (MCs, GCs, and abGCs) as linear firing-rate neurons with distant-dependant connectivity, which for simplicity we take as having a Gaussian profile. We assume for simplicity that excitatory connections from the two GC populations onto MCs are identical, but we allow for broader MC input onto abGCs than onto GCs.
We assume that the odor input from OSNs is random and uncorrelated with the position of the neurons. For odor, k, neuron i receives input I 0 + I 1 z k i , where Var z k i = 1. Thus the average input to MCs over all odors is I 0 and the standard deviation over odors is I 1 .
The firing rate of neuron i in the MC population in response to odor k is: (1) Meanwhile, the GC firing rates are given by: where g > 1 is the relative input-output gain of abGCs.

Defining Connectivity Profiles
We assume, for mathematical simplicity, that neurons in each population are distributed uniformly on a ring, such that we associate to each neuron j of population X an angle, θ X j = 2πj N X . We define the connectivity strength from a neuron in population Y to a neuron in a population X as a function of the angular distance between them as: where X, Y ∈ {MC, GC, abGC}.
We assume that all spatial spreads are significantly smaller than the full extent of the population, such that the average connectivity from populations Y to X is: For simplicity we assume that J XY is identical for all pairs X, Y .
We assume the connectivity profiles differ only by the spatial spread of the input connectivity from MCs to GCs: σ abGC←MC > σ GC←MC : So we parametrize the relative breadth of abGC connectivity as:

Reduced Model and Fixed Point Solution
Because of the assumption that z k i is independent of θ i , we can assume that the effective input from population Y to neuron i in population X is dominated by the mean: wherer Y is the average firing rate of population Y .
Thus the average firing rate for (ab)GCs is J 0 (ab)GC←MCr MC .
Therefore the firing rate of MC i is approximated by is the proportion of abGCs.
We can rewrite this as where we have written as the effective GC-mediated lateral inhibition of MCs to each other. And as the overall effective excitability of abGCs relative to mature GCs. Note that we have reduced the model to a total of five parameters: Two parameters, I 0 and I 1 , describing the external input onto MCs, and three parameters, J ef f , g ef f and f , describing the recurrent interactions between MCs and abGCs/GCs. Now we can solve forr M , the average MC firing rate: And then we have for individual MC firing rates:

Extent of Tuning and Sharpening Due to abGCs
The extent of tuning is measured by taking the standard deviation over odors, divided by the mean, giving, before silencing abGCs: When silencing abGCs we will have So that the impact of silencing abGCs on MC tuning is Sharpening abGCs = Tuning before

CHERNOFF DISTANCE
We consider two odors, o 1 and o 2 , and assume that the population of neurons fire a number of spikes, n = {n 1 ... n N }, which are independent Poisson distributions with means λ (1) and λ (2) respectively.
The Chernoff Distance between the populations responses to the two odors is defined by: where

Independent, Poisson Variables
In the case where the population is independent this yields: i.e. D α is extensive. Therefore we focus on the per-neuron D (1) α = − log n P α (n|o 1 ) P 1−α (n|o 2 ) , for a single neuron.
Now assume that P (n|o k ) ∼ Poi (λ k ) i.e. P (n|o k ) = λ n k n! exp (−λ k ), then we have Thus the Chernoff Distance of the whole population is where λ k,i is the average spike count of the ith neuron in response to the kth odor.
In our setting, λ B k,i =

I0
1+J eff (1−f ) + I 1 z k i after silencing. We will write These are defined by the random input tuning, z k i , and so we write the expected per-neuron D α between the typical two odors as which simplifies to For small input tuning, I 1 I 0 , we write: We argue that by symmetry D α must be maximized by α = 0.5 (though this is straightforward also to prove), and so we have or to leading order: We see that to leading order D C is inversely proportional to I eff 0 , and so we can compare Before and After: which is identical to the Sharpening abGCs in terms of the tuning curve.

MODEL PARAMETERS
First we note that our empirical data includes a count of the number of labeled abGCs. Based on existing estimates of overal GC density in the OB, we estimate that the monthly addition of abGCs as labeled in our experiments accounts for about 2.5% of GCs. Therefore we set f = 0.025, except where otherwise mentioned.
To interpret experimental data with our model we assume that calcium imaging measurement of ∆F F for a given odor o k , yields an estimate of the change in firing rate relative to baseline: Thus the standard deviation of the odor-evoked responses observed in the experiment yields a direct measure of the "Tuning" for each neuron, as defined above. We find Tuning before−empirical = 0.097 ± .005 (37) Tuning after−empirical = 0.075 ± .004 which are the mean and SEMs before and after silencing abGCs, respectively.
In our model this value depends on the input tuning I1 I0 to which we do not have empirical access, but as shown above, this factor drops out in the measure of Sharpening abGCs ,the ratio of Tuning before to Tuning after . Thus any given value of Sharpening abGCs constrains the phase space of the two parameters, J eff (the effective GC-mediated lateral inhibition) and g ef f (the product of abGCs input broadness and excitability relative to mature GCs) to a single (monotonically decreasing) curve. That curve is given by: Therefore we use this empirical measure to identify a range of confidence for the parameter values, g eff , J eff .
We find the empirical average is Sharpening abGCs−Avg ≡ Avg Tuning before−empirical Avg Tuning after−empirical ≈ 1.31 We define confidence borders on the value of Sharpening abGCs according to Sharpening abGCs−Upper ≡ Avg Tuning before−empirical + SEM Tuning before−empirical Avg Tuning after−empirical − SEM Tuning after−empirical ≈ 1.46 Sharpening abGCs−Lower ≡ Avg Tuning before−empirical − SEM Tuning before−empirical Avg Tuning after−empirical + SEM Tuning after−empirical ≈ 1.17 The resulting range of parameters is displayed in Fig 6F. The solid white line is the curve g iso−Sharpening (J eff ) for Sharpening abGCs−Avg , and the upper and lower dashed curves are those for Sharpening abGCs−Upper and Sharpening abGCs−Lower , respectively.
In Fig 6G we explore the impact of changing the proportion of abGCs, and to that end we focus (somewhat arbitrarily) on the case J eff = 4, and plot the analogous curves f iso−Sharpening (g eff ).
Having set these parameters in order to achieve the Sharpening abGCs , we can now constrain the ratio of I 0 and I 1 by the observed Tuning values. For example, via In Fig 6E we  Deriving a numerical estimate for the Chernoff Distance requires an absolute scale. Firing rates of MCs in the literature are on the order of 20Hz spontaneous, and a single sniff cycle is on the order of 1s, so it may be appropriate to consider 20 spikes as our I eff 0 , which would make I 0 ≈ 80, and therefore I 1 ≈ 1.2 with a potential range of say, [0.5, 5]. We find Assuming independence, the D C of the population of N M C neurons is D C = N MC D (1) C . In Fig 6H we plot as a function of both N MC and f , and mark the "iso-discrimination" curve, N iso−DC (f ), for D baseline C with N baseline M C = 1000 and f baseline = .025 which yields D c ≈ 30. This curve is given by In principle this curve depends on the particular choice of J eff and g eff . Nevertheless, as we show here, this dependence turns out to be very weak.
Near independence of the iso-discrimination curve to choice of parameters To derive the dependence of N iso−DC (f ) on our choice of J eff we substitute g eff with g iso−Sharpening (J eff ) from above, which is a function of f baseline . Importantly f baseline is empirically estimated to be f baseline = 0.025 1. Therefore (writing S ≡ Sharpening abGCs ): Plugging this into N iso−DC (f ) we find We observe that for f f baseline (S − 1) f + f baseline for the entire range of values of f and therefore we expand and simplify to find which shows that the influence of the one free parameter of our model, J eff , on the iso-discrimination curve is as a second-order correction. This relative amplitude of this correction term is bounded by approximately f baseline S−1 ≈ 0.06. Thus resulting iso-discrimination curves are nearly quantitatively identical, independent of J eff .