Scaling Principles of Distributed Circuits

Report

Scaling Principles of Distributed Circuits Highlights d

The number of piriform neurons (n) and bulb glomeruli (g) are related as n  g3/2

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Average number of synapses between each glomerulus and piriform neuron is invariant at 1

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These two properties ensure that discrimination and sensitivity match circuit size

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Conserved relationships show evidence of shared computational and functional properties

Srinivasan & Stevens, 2019, Current Biology 29, 2533–2540 August 5, 2019 ª 2019 Published by Elsevier Ltd. https://doi.org/10.1016/j.cub.2019.06.046

Authors Shyam Srinivasan, Charles F. Stevens

Correspondence [email protected] (S.S.), [email protected] (C.F.S.)

In Brief Two hallmarks of scalable circuits are that relationships between performance and that size and relationships between components are fixed across species. Srinivasan and Stevens show evidence that olfactory circuits are scalable: olfactory bulb glomeruli are related to piriform neurons by a power law, with each glomerulus making 1 synapse with each piriform neuron.

Current Biology

Report Scaling Principles of Distributed Circuits Shyam Srinivasan1,2,3,* and Charles F. Stevens1,2,* 1Salk

Institute for Biological Studies, La Jolla, CA 92037, USA Institute for Brain and Mind, University of California, San Diego, CA 92093, USA 3Lead Contact *Correspondence: [email protected] (S.S.), [email protected] (C.F.S.) https://doi.org/10.1016/j.cub.2019.06.046 2Kavli

SUMMARY

Identifying shared quantitative features of a neural circuit across species is important for 3 reasons. Often expressed in the form of power laws and called scaling relationships [1, 2], they reveal organizational principles of circuits, make insights gleaned from model systems widely applicable, and explain circuit performance and function, e.g., visual circuits [3, 4]. The visual circuit is topographic [5, 6], wherein retinal neurons target and activate predictable spatial loci in primary visual cortex. The brain, however, contains many circuits, where neuronal targets and activity are unpredictable and distributed throughout the circuit, e.g., olfactory circuits, in which glomeruli (or mitral cells) in the olfactory bulb synapse with neurons distributed throughout the piriform cortex [7–10]. It is unknown whether such circuits, which we term distributed circuits, are scalable. To determine whether distributed circuits scale, we obtained quantitative descriptions of the olfactory bulb and piriform cortex in six mammals using stereology techniques and light microscopy. Two conserved features provide evidence of scalability. First, the number of piriform neurons n and bulb glomeruli g scale as n
g3=2 . Second, the average number of synapses between a bulb glomerulus and piriform neuron is invariant at one. Using theory and modeling, we show that these two features preserve the discriminatory ability and precision of odor information across the olfactory circuit. As both abilities depend on circuit size, manipulating size provides evolution with a way to adapt a species to its niche without designing developmental programs de novo. These principles might apply to other distributed circuits like the hippocampus. RESULTS The olfactory circuit (Figures 1A and 1B, reviewed in [11]) is a promising candidate for exploring whether distributed circuits have common organizational principles, because its function, connectivity, and response patterns are conserved across phyla [11–15]. To test scaling, we examined olfactory

circuits in 6 mammals: mice, rats, guinea pigs, ferrets, cats, and opossums. The species represent breadth in terms of brain size (compare mice versus cats, 0.3 cm3 versus 33 cm3 [16]), coverage of animals from within one clade to observe clade-specific trends (mice, rats, guinea pigs), and evolutionary diversity (covering 2 mammalian infraclasses: eutheria or placental mammals versus metatheria or marsupials). Number of Glomeruli Increases with Bigger Bulbs Studies have shown the activity of sister mitral cells to be correlated [17]. Therefore, we use their collective activity, represented by a glomerulus, as the functional unit of odor activity. To estimate glomerular number, we measured glomerular layer volumes (Figure 1D; Method Details: OB procedures) and glomerular densities (Figure 1E) in each species. These two measurements showed that the number of glomeruli (g) increased with glomerular layer volumes (GV ) (Figure 1F) as 1=3

g = 1; 693GV :

(Equation 1)

Note that Equation 1 is a power-law relationship of the form Y = aX b , wherein Y is the dependent variable, X is the independent variable, a is a normalization constant, and b is the scaling exponent. Since most of the olfactory bulb (OB) input emanates from the olfactory epithelium (OE) and their sizes are correlated within suborders (Figure S1G), we wondered if OB scaled with the number of OSNs. We used the glomerular layer volume as a proxy for number of OSNs, as OSN axons terminate within glomeruli. Two studies support this assumption. At least in mice, glomerular size is proportional to OSN number [18] (flies being a notable exception), and OSN size does not significantly vary across mice, rats, and rabbits [19–21]. We found that glomerular numbers and sizes increased with glomerular layer volumes (Figures 1F, 1G, and S1D). Notably, the number of glomeruli per OSN type, which indicates the number of odor copies in the bulb, also increased with glomerular layer volume (Table S2; Figures S1E and S1F). Overall, the number of glomeruli increases with OB size and, likely, with the number of OSNs. Number of Piriform Cortex Neurons Increases with Bulb Size To determine if the number of piriform cortex (PCx) neurons scales with number of glomeruli, we measured each species’

Current Biology 29, 2533–2540, August 5, 2019 ª 2019 Published by Elsevier Ltd. 2533

Figure 1. The Number and Size of Glomeruli Increases with Larger Olfactory Bulbs (A) Schematic of the olfactory circuit in mice. Odor information detected by various types (distinguished by color) of OSNs is conveyed to their cognate glomeruli in the OB, from where it is passed on via the LOT to PCx. (B) A schematic of connections from glomeruli to PCx neurons. The circles at grid junctions denote synapses, which are made without any spatial preference. (C) Representative sections of the olfactory bulb in guinea pigs and ferrets with the glomerular layer (GL), mitral/tufted (M/T) layer, and granule cell layer (GCL) marked. Scale bar, 0.5 mm. (D–G) Scaling of olfactory bulb components. 2=3 (D) As brain volume (BV ) increases, so does the volume of the glomerular layer (GV ), described by GV = 5BV ; R2 = 0:93; CI : 0:46  0:89. 2=3 (E) The glomerular density (gd ) reduces with larger glomerular layers or olfactory bulbs according to gd = 1; 693GV , R2 = 0:97;CI :  ð0:8  0:48Þ. Triangles represent data from the literature and circles represent our measurements. 1=3 (F) The number of glomeruli increases with bigger bulbs by the relationship g = 1; 693GV , R2 = 0:9; CI : 0:19  0:51 2=3 (G) The size of an average glomerulus increases with glomerular layer volume, gsize = 0:00058GV , R2 = 0:97; CI : 0:58  0:73. OSN, olfactory sensory neuron; OE, olfactory epithelium; LOT, lateral olfactory tract; PCx, piriform cortex; OB, olfactory bulb; CI, 95% confidence interval for the exponent; R2 , coefficient of determination. See also Figures S1 and S3 and Table S2.

PCx surface area (PA in mm2 , Figures 2A and 2B, Method Details: PCx procedures) and neuronal surface area density (nd )—number of neurons under 1 square mm of cortical surface 1=4 area (Figure 2C, nd = 62; 140PA , Figure S2B). We found that number of layer 2—the main processing layer of PCx—neurons (n, Figures 2D and S3C) increased with area as 3=4

n = 62; 140PA :

(Equation 2)

From here on, when we refer to piriform neurons, we mean layer 2 neurons, although the results also apply to the whole neuronal population (Figure S3C). We next examined if elements of PCx scale with OB. PCx surface area scales with glomerular volume (Figure 3A, PA = 2=3 3:14GV ). This implies that number of PCx neurons and 2=3 glomeruli should scale as n
g3=2 because PA
GV from Figure 3A, which gives 1=3 3=4 n4=3
ðg2 Þ as GV
g and PA
n from Figures 1F (Equation 1) and 2D (Equation 2). Rearranging exponents gives n
g3=2 : Empirical estimates show that this is true (Figure 3B, n = 2:08g3=2 , Figure S3D). Notably, piriform neurons, just like glomeruli, also scale with OE input (Figures S3A and S3B). Overall, olfactory circuit components (Figures 1F and 3B)

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maintain a power law relationship across species: evidence that olfactory circuits are scalable. What might be the reason for such scaling? Studies with the visual circuit [3] suggest that such scaling might result from the necessity to maintain the precision of the neural code across the circuit. Precision measures the uncertainty of the readout. For example, the firing rate (R) of an OSN in the nose might reflect the concentration of a chemical. As neurons are stochastic, the firing rate of any single neuron is unlikely to indicate the true concentration. But, the mean response of a population will average out the variability of individual responses revealing the true concentration. The precision of the mean response is given by the standard error of thepmean (Figure 4F), which will decrease ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi with more neurons as #OSN s. The precision of OE also determines the sensitivity, i.e., the lowest signal, which can be distinguished from noise. In an optimal circuit, precision should be maintained in each successive stage: it is wasted if the downstream circuit cannot maintain it. Consider the precision of the odor code in the olfactory circuit. N OSNs of the same type converge onto gOSN glomeruli (number of glomeruli per OSN type), which in turn contact n PCx neurons. For an OSN type, each glomerulus receives N =gOSN OSN inputs, each PCx neuron receives gOSN glomerular inputs, and downstream circuits receive n PCx inputs. The precision at each stage must be proportional, i.e., N = gOSN
gOSN
n

Figure 2. Piriform Cortex Components Increase with Larger Olfactory Circuits (A) Representative sections of the piriform cortex in mice and guinea pigs. The piriform cortex contains 3 morphologically distinguishable layers. Layer 1 is superficial and abuts the LOT. It is cell sparse, comprising layer 1a, where bulbar axons make synapses with L2 and L3 cells, and layer 1b, which contains associative synapses between L2 and L3 cells. Layer 2 is distinguished by high neuron density. Layer 3 is deeper, containing an intermediate number of cells between layers 1 and 3. The middle panel shows a representative section of APCx stained with Calretinin, MAP2, and NeuN to differentiate layers 1a (MAP2 and Cal) and 1b (MAP2). As shown in [22], layer 1a occupies 70% of layer 1 in APCx. (B) The surface area (PA ) of PCx increases with bigger 1=2 brains by PA = 9BV , R2 = 0:95;CI : 0:4  0:57. (C) The surface density—number of neurons per mm2 of cortex (nd )—decreases with bigger PCx as 1=4 nd = 62;140PA , R2 = 0:84;CI :  ð0:32  0:16Þ. (D) The number of layer 2 neurons (n) increases with 3=4 bigger PCx according to n = 62; 140PA , R2 = 0:98; CI : 0:67  0:83. (E) The thickness of layer 1 increases with surface area as L1 thickness = 0:13P0:215 , R2 = 0:65; A CI : 0:1  0:32. (F) Synaptic densities across different regions of the brain from 8 species, 6 brain regions, and more than 10 labs. The average synaptic density is 0.83 billion synapses/mm3 (SEM, 0.087, also see Figure S4 and Table S1). 1=5 (G) The number of L1a synapses increases gradually with larger piriform cortices as L1a synapses = 7  107 PA , R2 = 0:65; CI : 0:1  0:32. LOT, lateral olfactory tract; L1a , layer 1a of the piriform cortex; L2/3, layer 2/3 of the piriform cortex; PCx, piriform cortex; CI, 95% confidence interval for the exponent; R2 , coefficient of determination. See also Figures S2 and S3 and Tables S1 and S3.

or gOSN
N1=2 : The relationship gOSN
N1=2 also follows if we assume optimal allocation of resources in the bulb (see Method Details: scaling theory). On consideration, the glomerular layer volume (GV ) must be proportional to the number of OSNs innervating it, i.e., N
GV (Method Details: scaling theory), or 1=2 GV
gOSN
n, which is borne out by our measurements (Figure S3B). So, 1=2 1=3 3=2 1=3 n
GV = ðGV Þ = g3=2 since g
GV from Figure 1D and Equation 1 i:e:; n
g3=2 : Thus, maintaining precision requires the circuit to scale by a three halves power law. The scaling relationship also follows from considering that information is passed from a 2-dimensional system (OB, Figures S4E–S4G) to a 3-dimensional system (PCx, Method Details: scaling theory). Olfactory Circuit Connectivity Is Conserved To understand functional consequences of scaling, we need a quantitative description of information transmitted within the olfactory circuit. Braitenburg and Schuz [23] provided a parsimonious description of information transmitted. It is the number of

synapses that a glomerulus (or its mitral cells) makes with a PCx neuron, i.e., the number of afferent bulb synapses under a mm2 of layer 1a of PCx divided by number of L2 neurons under 1mm2 and glomeruli in the bulb (as there is no spatial preference to OB-PCx synapses). Studies have shown that layer 1a occupies 70% of the width of layer 1 in anterior PCx (Figure 2A, 1=5 representative PCx section, Figure 2E, L1width = 0:13PA ). We 3 used a synaptic density of 0.83 billion synapses/mm (Figures 2F and S4; Table S1) obtained by averaging across a wide variety of brain regions (Figure S4I), species (Figure S4J), and labs (Figure S4H). The number of layer 1a synapses under 1 mm2 increases with PCx area (Figure 2G), given by L1a synapses 1=5 = L1a width  synaptic density = 0:78  107  PA : mm2 Equations 1 and 2 provide the scaling relationships for glomeruli and neurons. These can be used to calculate the number of synapses (s) between a neuron and glomerulus. It is s=

L1a synapses=mm2 wherein L1a synapses #glomeruli  #neurons=mm2 1=5

1=3

= 0:78  107  PA and #glomeruli = 1; 693GV ; . 1=3 1=2 #neurons mm2 = 62; 140P0:25 ; GV = 0:56PA : A Current Biology 29, 2533–2540, August 5, 2019 2535

proportional to the number of OB synapses, s, that it receives. g
s (Figure 3C) suggests that PCx maintains OB information. To examine the importance of the mean number of synapses (s) being 1, we simulated OB and PCx responses to odors with synapse numbers ranging from 0.01–10 for multiple trials (Method Details: numerical procedures). We found that correlations between OB and PCx were variable at 0.01 (Figure 4C) but stabilized as the number of synapses increased to 0.2 (Figures S4B and S4C) and remained constant beyond 1. Thus, evolution might have designed the circuit’s connectivity parameters to be optimal for robustly maintaining information and discriminatory ability.

Figure 3. Conserved Relationships between Olfactory Circuit Components (A) The surface area of PCx scales with glomerular layer volume according to 2=3 PA = 3:14GV , R2 = 0:96; CI : 0:59  0:8. (B) The number of neurons in the piriform is related to the number of glomeruli by the relationship, n = 2:08g3=2 , R2 = 0:93; CI : 1:15  1:75 (C) The number of OB synapses received by a layer 2 neuron is proportional to the number of glomeruli: n = 482 + 0:84g, R2 = 0:89; CI : 0:64  1:03. (D) The average number of synapses made by a glomerulus with a layer 2 neuron is 1 across species (mean = 1.03, SEM = 0.037). PCx, piriform cortex; CI, 95% confidence interval for the exponent; R2 , coefficient of determination. See also Figures S2 and S3 and Tables S1 and S3.

Thus, s = 1:3P0:05 : A The estimate of 1.3 is reflected in empirical observations (Figure 3D). Despite variations in size and ecological niches, the average number of synapses across species is 1.03 (Figure 3D, horizontal line). Theoretical explorations of connectivity in the mouse piriform cortex showed that such connectivity maintains information transmitted from the OB to PCx [22] and, thus discriminatory ability. As connectivity between glomeruli and PCx neurons follows a Poisson-Gamma distribution, each glomerulus has PCx neurons that respond preferentially to it [22]. Thus, odors preferentially activate specific combinations of glomeruli and PCx neurons (a combinatorial code), maintaining discriminatory ability. Therefore, we asked if conservation of connectivity parameters (Figure 3D) implies a similar conservation of discriminatory ability across species by using a linear firing rate model of PCx as in [22] (Figure 4A; Method Details: numerical procedures). As the amount of overlap between odors increased in the bulb, it proportionately increased in the piriform similarly across species (Figure 4B), suggesting that information and discriminatory ability are maintained in OB and PCx. Figure 3C provides additional support. The information output of OB is proportional to g; the number of glomeruli, and the input of a PCx neuron is 2536 Current Biology 29, 2533–2540, August 5, 2019

Discrimination Increases with Circuit Size If precision and discriminatory ability are maintained throughout the circuit and are dependent on circuit size, then both abilities and the animal’s ability to classify odors should increase with bigger circuits [24]. We tested this notion by using a computer classification algorithm as a proxy for the neural algorithm ([22], Method Details: numerical procedures). While the computer algorithm might be more efficient than the neural one (as neurons are stochastic computing elements), it is likely to be qualitatively similar. Figure 4D provides an illustrative example. We generated olfactory bulb representations for a set of 10 odors and their corresponding PCx representations. We assigned labels to these representations after randomly mixing them and used unsupervised classification to produce classification trees for OB and PCx representations. Odor labels from both trees matched accurately (Figure 4D). We then tested the relationship between increasing circuit size (glomeruli or neuron number: 200, 400, or 800) and classification ability. The match in classification (fraction of the tree that was identical) between OB and PCx was near perfect across species for a set of 50 odors (Figure S4D). With an increase in odors, bigger circuits maintain the classification match (Figures 4E and S4E), and their classification degrades less (Figure S4F). Thus, evolution might have increased circuit size among more olfaction-dependent species in order to classify and discriminate more odors. DISCUSSION Scaling of the Primary Olfactory Circuit Scaling, which has been observed in myriad biological contexts [25], reveals design constraints imposed by evolution. Olfactory circuits have two essential properties of scalable systems: a feature invariant to system size, and the number of (circuit) components increases with bigger (brains) systems as a (mostly) power-law relationship [25]. First, the average number of synapses between a glomerulus and piriform neuron is invariant across species at 1 (Figure 3D). Using theory, we show that one synapse ensures robust transmission of information from OB to PCx (Figures 4C and S4C), which might be one reason why such connectivity is conserved across species. Second, the number of piriform neurons n and bulb glomeruli g scale as n
g3=2 (Figure 3B). Theoretical explorations (Figure 4) suggest that the two properties help maintain precision and discriminatory ability in each part of the circuit. As both abilities increase with bigger circuits (Figure 4F), bigger species like cats should have better discrimination and sensitivity. Studies of other distributed circuits have

Figure 4. Model of the Olfactory Circuit Shows that Information and Discriminatory Ability of OB Is Maintained in PCx across Species (A) Schematic of the linear rate firing model from bulb to PCx. Left: glomeruli representing different OSN types (based on color) contact PCx neurons without any spatial preference (shading of PCx neurons represents glomerular input contributions). Right: representation of a simulation in which an olfactory bulb odor when multiplied by the connection matrix yields the PCx response shown on the right. Grid squares for bulb and PCx represent firing rates of glomeruli or neurons. Grid squares for the connection matrix represent synapse strengths (Method Details: numerical procedures). (B) Correlations between pairs of odors in OB and PCx across species. Correlations between odors in OB are proportional to correlations in PCx responses ðslope = 0:91; R2 = 0:99Þ identically across species. (C) Reducing the mean number of synapses between a glomerulus and piriform neuron 50-fold produces correlations that are noisy. (D) Matching of unsupervised classification trees of OB and PCx responses. OB and PCx responses were labeled, randomly mixed, and then run through an unsupervised classification algorithm. The two classification trees were then compared to determine the number of labels (odors) that matched. Classification match was perfect for 10 odors, showing that OB information is maintained in PCx. (E) Classification accuracy improves with circuit size. The plot shows the fraction of matches (y axis) that were identical in OB and PCx for a set of 550 odors and three circuit sizes (200, 400, and 800 on the x axis). (slope = 0:91; R2 = 0:99; CI : 0:06  0:19) (F) Schematic of olfactory scaling showing the improvement in sensitivity and discrimination from mice to rats while smelling an odor (cheese). Rats have more OSNs, (and bigger) glomeruli, and PCx neurons. Black triangles indicate PCx neurons responsive to the odor. Since the rat has more PCx neurons, its discriminatory ability is better [24], even though the percent responding is similar. The increase in PCx neurons improves the precision of the olfactory code: compare the standard error of the mean (SEM) between the top and bottom. The rates for PCx firing were drawn from a normal distribution to illustrate the concept of precision. See also Figure S4.

made similar predictions [26, 27]. Notably unlike these two properties, the ability to sense a wide variety of odors is not dependent on circuit size, as the number of OSN types seems to decrease with size (Table S2, with exceptions like elephants). In assessing scaling relationships, we grouped all layer 2 neurons. Studies, however, have shown several layer 2 cell types [11, 28, 29] distinguishable by connectivity and function. While these cell types are crucial for understanding higher functions such as pattern separation, evidence of odor encoding by a distributed and sparse (representation of odors by a 10%

ensemble) [7, 8] network of PCx neurons led us to consider L2 neurons as a collective population in our experiments and theory. Future studies exploring if these cell types and their proportions are conserved will help in understanding if higher olfactory function is also conserved across species. Evidence for Scaling of Olfactory Abilities Behavior studies have provided mixed results [30] of scaling of olfactory abilities because of a few factors. One is the inability to establish a set of odorants that are equally relevant to each Current Biology 29, 2533–2540, August 5, 2019 2537

of the species [31]. Another is the wide variation in the OSN composition even between individuals of the same species that arise from mechanisms that selectively increase sensitivity to frequently experienced odors [32]. Nevertheless, studies showing comparable performance between different species with similar circuit sizes are consistent with the theory [30]. More compelling evidence comes from studies of olfactory circuits during development, aging, disease, and in ecological contexts. First, in humans, olfactory bulb size and odor detection abilities are correlated [33]. Second, developmental studies have shown that as olfactory circuits become bigger, sensitivity and discrimination improve [34]. Third, alteration of OSN number and OB volume by neurodegeneration due to age and disease or by neurogenesis is correlated with alterations in olfactory abilities [35, 36]. Our work, which suggests an improvement in olfactory sensitivity and discrimination with size, is consistent with earlier studies showing correlations between OB and home range sizes [37] as well as theories suggesting a role for olfaction in navigation [38]. Implications for Olfactory Circuit Connectivity Our estimates of synaptic connectivity vary from estimates that might be drawn from previous studies, which examined bias in OB-PCx connectivity [39], and PCx responses to multi-glomerular activation [40]. Three factors might account for the variance. First, the protocols and methods are different. While glutamate uncaging and viral tracing are excellent methods for examining function and connectivity, EM-based stereology is still the preferred method for synapse estimation. Second, viral tracing methods have improved in efficiency by at least 20-fold in the past decade [41], which means that estimates based on [39] would be underestimates. Third, previously, we showed that synapses in layer 1a follow a Gamma distribution, leading each PCx neuron to be preferentially connected to a few glomeruli [22]. The activation of PCx neurons to increasing multi-glomerular activity [40] is consistent with our results and this study [22]. Finally, ours is a rough estimate of connectivity, and improved viral tracing methods [41] provide a promising avenue for resolving synaptic connectivity number. Comparing Topographic and Distributed Circuits Topographic circuits share features such as connectivity and response patterns, leading some to suggest that computations within a column of the neocortex are similar [5, 42, 43] across species. Additionally, shared quantitative features such as conserved surface neuron density (number of neurons under a mm2) [44] reflect this similarity in function. Distributed circuits, which qualitatively differ from topographic circuits, might also be quantitatively different. This study provides two quantitative differences between topographic and distributed circuits. First, PCx surface neuron density is lower than the neocortex (59,000 versus 100,000 in mice) and variable at least in mice [22]. Recent studies of the neocortex, though, have also observed variability [45]. Second, unlike the neocortex, PCx surface density decreases with circuit size (Figure 2C). Interestingly, in a previous study [22], we had shown that PPC, which differs from APC functionally [46], had a lower neuronal density, fewer OB inputs, and more associative inputs. If this morphological difference is conserved across 2538 Current Biology 29, 2533–2540, August 5, 2019

species, then it would suggest that part of the explanation for differences in APC, PPC, and neocortical function lies in their architectural differences. Evolutionary Conservation of Distributed Circuit Features The OB-PCx circuit could be a conduit for understanding other distributed circuits that share some of its features [47]. The best described one is the fly olfactory circuit, wherein highdimensional odor information is captured by OSNs and communicated to the mushroom body (PCx analog) through glomeruli in the antennal lobe (olfactory bulb analog). Here too, connectivity from glomeruli to mushroom body neurons is distributed [15] with odors represented by a sparse neuronal ensemble [48]. Second, as animals rely on smell while growing, developing olfactory systems should follow similar organizational relationships. Third, sparse and distributed ensemble coding is also a feature of the cerebellum and the hippocampus [49]. Finally, recent work has shown that even visual regions, like the inferotemporal cortex in primates, use the kind of combinatorial coding [50–52] found in distributed circuits. If future studies show that these regions have distributed connectivity, olfactory scaling principles might apply to them too. STAR+METHODS Detailed methods are provided in the online version of this paper and include the following: d d d d

d d

KEY RESOURCES TABLE LEAD CONTACT AND MATERIALS AVAILABILITY EXPERIMENTAL MODEL AND SUBJECT DETAILS B Animal details METHOD DETAILS B Histological Procedures B Thionin Staining B Volumetric estimates B Stereological methods B Olfactory Bulb procedures B Piriform Cortex procedures B Numerical methods B Scaling theory QUANTIFICATION AND STATISTICAL ANALYSIS B Summary of the statistics DATA AND CODE AVAILABILITY

SUPPLEMENTAL INFORMATION Supplemental Information can be found online at https://doi.org/10.1016/j. cub.2019.06.046. ACKNOWLEDGMENTS We would like to thank Saket Navlakha, Joseph Zak, and Terry Sejnowski for valuable feedback on the manuscript and Edward Callaway for helpful discussions. We are grateful to Leah Krubitzer, James Dooley, and Andrew Halley for opossum brains and E.J. Chichilnisky, Edward Callaway, Clare Hulse, Kristina Nielson, and Fumitaka Okasada for Guinea pig, rat, and ferret brains. We also appreciate the computational assistance provided by Jorge Aldana and Terry Sejnowski. Finally, we thank the Kavli Institute for Brain and Mind at UCSD, NSF-1444273, and NIH DC017695 for supporting this work.

AUTHOR CONTRIBUTIONS S.S. and C.F.S. conceived the project and designed the experiments; S.S. performed the experiments and modeling; S.S. wrote and revised the paper with feedback from C.F.S. DECLARATION OF INTERESTS The authors declare no competing interests Received: February 7, 2018 Revised: March 21, 2019 Accepted: June 17, 2019 Published: July 18, 2019 REFERENCES 1. Finlay, B.L., and Darlington, R.B. (1995). Linked regularities in the development and evolution of mammalian brains. Science 268, 1578–1584. 2. Baron, G., Stephan, H., and Frahm, H.D. (1987). Comparison of brain structure volumes in Insectivora and primates. VI. Paleocortical components. J. Hirnforsch. 28, 463–477. 3. Stevens, C.F. (2001). An evolutionary scaling law for the primate visual system and its basis in cortical function. Nature 411, 193–195. 4. Srinivasan, S., Carlo, C.N., and Stevens, C.F. (2015). Predicting visual acuity from the structure of visual cortex. Proc. Natl. Acad. Sci. USA 112, 7815–7820. 5. Hubel, D.H., and Wiesel, T.N. (1962). Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J. Physiol. 160, 106–154. 6. Seabrook, T.A., Burbridge, T.J., Crair, M.C., and Huberman, A.D. (2017). Architecture, function, and assembly of the mouse visual system. Annu. Rev. Neurosci. 40, 499–538. 7. Stettler, D.D., and Axel, R. (2009). Representations of odor in the piriform cortex. Neuron 63, 854–864. 8. Illig, K.R., and Haberly, L.B. (2003). Odor-evoked activity is spatially distributed in piriform cortex. J. Comp. Neurol. 457, 361–373. 9. Rennaker, R.L., Chen, C.-F.F., Ruyle, A.M., Sloan, A.M., and Wilson, D.A. (2007). Spatial and temporal distribution of odorant-evoked activity in the piriform cortex. J. Neurosci. 27, 1534–1542. 10. Poo, C., and Isaacson, J.S. (2009). Odor representations in olfactory cortex: ‘‘sparse’’ coding, global inhibition, and oscillations. Neuron 62, 850–861.

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STAR+METHODS KEY RESOURCES TABLE

REAGENT or RESOURCE

SOURCE

IDENTIFIER

Rabbit polyclonal anti-MAP2

Invitrogen

cat # PA5-17646, RRID: AB_11006358

Goat polyclonal anti-Calretinin

Millipore

cat # AB 1550, RRID: AB_90764

Mouse monoclonal anti-NeuN

Millipore

cat # MAB377, RRID: AB_2298772

Cy3 AffiniPure Donkey polyclonal anti-Rabbit IgG

Jackson ImmunoResearch Labs

cat # 711-165-152, RRID: AB_2307443

Alexa Flour 488-AffiniPure Donkey polyclonal anti-goat IgG

Jackson ImmunoResearch Labs

cat # 705-545-147, RRID: AB_2336933

Alexa Flour 647 Donkey polyclonal anti-mouse IgG

Jackson ImmunoResearch Labs

cat # 715-605-151, RRID: AB_2340863

Mouse piriform cortex

This lab

N/A

Rat piriform cortex

Gift from Chichilnisky and Callaway Labs

N/A

Guinea pig piriform cortex

Gift from Chichilnisky and Callaway Labs

N/A

Cat piriform cortex

This lab

N/A

Opossum piriform cortex

Gift from the Krubitzer lab

N/A

Ferret piriform cortex

Gift from Callaway Lab

N/A

This paper

http://dx.doi.org/10.17632/d5p6gfbdmp.1

[53]

https://cran.r-project.org/web/packages/ dendextend/vignettes/introduction.html

Antibodies

Biological Samples

Deposited Data Neuron density counts of Anterior Piriform Cortex Software and Algorithms Dendextend

LEAD CONTACT AND MATERIALS AVAILABILITY Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Shyam Srinivasan ([email protected]). EXPERIMENTAL MODEL AND SUBJECT DETAILS Animal details Animals were obtained from other laboratories, who used them in the course of their own experiments but did not make use of the olfactory brain regions. These animals were treated in accordance with the institutional care guidelines for animals. Since we had to use brains that were made available to us from other labs, we could not control for gender. The brains used here contain a mix of males and females. Although gender differences are likely to exist, our results which concern the total number of glomeruli and neurons should not be significantly affected by gender. Previous estimates in ferrets showed that although there are differences in male and female olfactory bulbs, the number of glomeruli per section is not significantly different between males and females [54]. Moreover, the differences between the genders is significantly smaller compared to the differences that exist between species. As far as age is concerned, a recent study in mice demonstrated that olfactory bulbs attain their adult morphological characteristics by 2 months of age [55]. We made use of animals that were of a somewhat equivalent age or higher. The details of animals used are given in Table S4. METHOD DETAILS This section contains a description of the experimental procedures used for collecting data in the olfactory bulb and piriform cortex. We used stereological techniques for counting glomeruli in the bulb and neurons in the piriform cortex. Since glomeruli and neurons vary so much in terms of size, the methods for doing stereology had to be modified to adapt to this difference. Therefore, we elaborate on data collection unique to glomeruli and neurons in separate sections. First, we describe procedures common to both regions. Current Biology 29, 2533–2540.e1–e7, August 5, 2019 e1

Histological Procedures Brain tissues from mice, rats, opossums, guinea pigs, ferrets, and cats were analyzed. Animal care protocols were approved by the Salk Institute Animal and Use Committee and conform to US Department of Agriculture regulations and National Institutes of Health guidelines for humane care and use of laboratory animals. Each specimen was perfused with aldehyde fixative agents and stored long-term in 10% formalin. In preparation for cutting, all brains were submerged in solutions of 10% (wt/vol) glycerol and 10% formalin until the brain sank, and then moved into 20% glycerol and 10% formalin until the brain sank again; the average time in each solution was 3 to 10 d. These cryoprotected brains were then cut coronally on a freezing microtome at a thickness of 40 or 50 mm. Every 6th section was stained with thionin for visualization of Nissl bodies. For the bulb, to make sure we did not miss smaller glomeruli, we cut sections at a thickness of 30 mm, and we collected all sections through the length of the bulb. For marking Layers 1a and 1b in the mouse anterior piriform cortex in the representative section shown in Figure 3D, we used the same method as [22], and similar to [56]. We stained for MAP2 (1:100, anti-Rabbit, Invitrogen cat # PA5-17646, RRID: AB_11006358) and Calretinin (1:1000, anti-Goat, Millipore cat # AB 1550, RRID: AB_90764), and identified layer 1a by the expression of Calretinin and MAP2, layer 1b by the expression of MAP2, and layer 2 by the expression of NeuN (1:250, anti-mouse, Millipore cat # MAB377, RRID: AB_2298772). As a control for Calretinin, we also observed its expression in a small fraction of cells within layer 2 as shown by previous studies. The antibody staining included the following procedure. The mouse brain was cut with a Leica Vibratome, while immersed in cold (Phosphate Buffered Saline) PBS, at a thickness of 50 m. Cut sections were then washed in TBS or Tris Buffered Saline (see below for preparation of TBS and TBS++) thrice for 30 min each, followed by a wash in TBS++ for 1 hour. They were then immersed in a solution of TBS++ and primary antibody (at the indicated concentrations) solution for 48-72 hours at 4 degrees. After primary antibody incubation they were washed in TBS twice for 15 min, and TBS++ thrice for 30 min. This was followed by immersion in a solution of TBS++ and secondary antibody (1:250, Jackson ImmunoResearch Labs, anti-Rabbit cy3 cat # 711-165-152, RRID: AB_2307443, anti-Goat 488 cat # 705-545-147, RRID: AB_2336933, anti-mouse cy5 cat # 715-605-151, RRID: AB_2340863) for 60120 min at room temperature. Finally, they were washed again in TBS thrice for 15 min, counterstained with DAPI (at a concentration of 1:5000) for 5 min and then mounted and coverslipped. TBS was prepared by mixing 52.88 g of Trizma Hydrochoride, 7.76 g of Trizma Base, and 36 h of Sodium Choride to 4L of DI H20. TBS++ was prepared by adding 3 mL of normal Horse Serum to 0.25 mL of Triton X-100 and filling up to a volume of 100 mL by adding TBS. The sections were imaged on an LSM 880 Inverted Zeiss confocal microscope equipped with 10x and 20x objective lenses. Thionin Staining The tissue was defatted with 100% Ethanol: Chloroform (1:1) overnight, rehydrated in a decreasing alcohol (with DI H2O) series (100%, 95, 70, 50), then treated with DI H2O, Thionin stain, followed by DI H2O, an increasing alcohol series (50%, 70, 95, 95, 100, 100), Xylenes I, Xylenes II, and then coverslipped. The tissue was dipped 4-5 times in each of the solutions for 1 min except for the thionin stain (1-2 min), and Xylenes II (1 hour). The Thionin stain was prepared by first gently heating 1428 mL DI H2O, 54 mL of 1M NaOH, 18 mL of glacial acetic acid until the solution was steaming. Then, 3.75 g of Thionin was added and the solution was boiled gently for 45 min, cooled, filtered and used for staining. Volumetric estimates The methods we used for obtaining volumetric estimates were similar for glomeruli and neurons. We explain the methods that we used by illustrating their use for estimating piriform cortex volumes. The three piriform layers were outlined in every sixth coronal section across the rostral-caudal extent with the help of Neurolucida (version 10.53; MBF Bioscience, Wilmington, VA) at low magnification (2X and 4X objectives). The piriform cortex and its layers were identified using standard atlases and primary literature for mouse, rat, guinea pig, opossum, and cat brains [57–60]. For each section in a species, we identified the corresponding section in the atlas. Using the atlas as a yardstick, we marked the layers based on the layer and region delineations within the atlas section. For each species except one of the guinea pigs and the opossum, we used the presence of the LOT to distinguish between the anterior and posterior PCx. For the two exceptions, we used other landmarks in the surrounding brain regions: the APC approximated to around half the length of the entire PCx. We used two measures for marking the lateral olfactory tract (LOT). First, it was the region with a distinctive lighter Nissl stain on the surface of the cortex. Second, the widths that we obtained for it matched those of the atlases. Additionally, we confirmed these two methods in our previous study [22] and this one (Figure 3D) for the mouse, when we stained for Calretinin and MAP2 to demarcate layers 1a and 1b. It also delineated the LOT, and the area of the LOT from this method was similar to our measurements from Nissl stains. We marked layer 1 as the layer in between LOT and layer 2 that was distinguishable by its extreme cell density. We marked the edge of this cell dense region as the deeper border of layer 2. Immediately adjacent on the deep side of the cell dense region was a region of lower cell density, and we delineated this as layer 3. We estimated the inner or deeper boundary of PC layer 3 from anatomical studies and atlases [57–60]. We assumed that the width of layer 3 is similar to the widths depicted in the atlas and the article. Note that the density of neurons in this layer is much lower than that of layer 2 as shown in cats [61]. As a result, an over- or under-estimate will not adversely affect the total count. Once layers from each individual section were outlined, all sections were aligned for subsequent three dimensional reconstructions with Neurolucida explorer. Alignment was done by starting with the second section, and aligning each section to the previous one. Surface areas and volumes for the anterior, posterior, and entire piriform cortex were then obtained from three dimensional reconstructions. For estimations of bulb volumes, we traced every alternate section and used the same method.

e2 Current Biology 29, 2533–2540.e1–e7, August 5, 2019

In addition, in our previous study [22] we used a method outlined by [56] to measure the widths of layers1a and 1b in PCx. We found that Layer 1a occupied close to 70% of Layer 1 in APCx. Given that the total fractions of Layers 1 and 2 were relatively conserved across species (Figure S2A), we assumed that the widths of Layers 1a and 1b might be similarly conserved. Stereological methods We illustrate the stereological methods that we used for estimating glomerular and neuronal densities by using our measurements of neuronal densities in the anterior piriform cortex as an example. For each species, neurons were counted within 15-30 columns, perpendicular to the pial surface of PCx, extending down to the deeper boundary of layer 3. Each column was 10-20 m wide. The layers and column boundaries were delineated with the Neurolucida contours option. All sections were 40 m thick (except guinea pig and opossums and one ferret, which were 50 m). We chose one out of every 6th section for Nissl staining. Sections for counting neurons were chosen to ensure uniform coverage across the rostral-caudal axis. This process also ensured equal coverage of APC. For obtaining surface area density counts, three measures were used: the width of the column, the thickness of the section, and the number of neurons in this column. Within sections, columns were randomly placed while ensuring that they fulfilled two constraints: 1) there was equal coverage of the dorsal PC - part of PC above the LOT - and ventral PC across APC, and 2) they were close to perpendicular to our coronal cut and the surface of the brain. Neurons were counted with standard unbiased stereology techniques in Nissl-stained sections at 100X oil magnification (Figure A1d of [22]). The counting column functioned as a typical dissector whereby neurons and glia were marked as they come into focus given that they also fell within the acceptance lines of the dissector. Neurons were differentiated from glia on the basis of size (bigger) and morphology (distinctive shape and processes extending out) of the cell, and by the presence of a nucleolus: glia were also more punctate. A few cells (around 5%) were hard to distinguish and were labeled as unknown and not included in the counts. Approximately 50 to 100 objects of interest were counted in each 3D column. We counted all the neurons in our column from the pial surface to the white matter without the use of guard zones. A detailed discussion of guard zone use as it pertains to stereological methods and data collection for frozen sections is reported in [62]. This brings up an issue of over-counting. We were careful to avoid over-counting by marking only nucleoli. They typically have a radius of 1.5-2 m, and in 40 m sections, that reduces the margin of error to less than 5% [63, 64]. We also took care to mark a single nucleolus in those few neurons that had multiple nucleoli [63]. The validation for these counts is presented in Figure S1A for glomeruli and Figure S2C for neurons. Olfactory Bulb procedures We measured the number of glomeruli and olfactory bulb volumes summarized in Table S2. For each of the bulbs that we measured, we also provide an analysis of our counts in Figure S1A. Figures S1B–S1F show the relationships among OB parameters such as volume, number of glomeruli, and glomerular volume. Figure S1G shows the relationship between OE area and OB volume measurements from previous studies [37, 65]. Figures S1H and S1I show that the differences in the average size of the glomerulus is not significantly dependent on position. We use the glomerulus as the functional unit in the bulb. Our reasoning is based on studies that have suggested that the Mitral/ tufted cells associated with a particular glomerulus behave as a coordinated unit [17]. These studies have also been complemented by functional studies showing that glomeruli associated with a certain behavior are conserved across behaviors (see pg. 24 of Olfaction: A Model System for Computational Neuroscience by Davis and Eichenbaum for a more in-depth discussion [66]) or even [67] and [68] for related discussions in insects and computational analysis. Additionally, we chose to examine glomeruli instead of mitral cells as studies have shown that with bigger olfactory circuits, while the size of the bulb, glomerular layer and number of glomeruli increases, mitral cells do not [69]. As we wanted to study scaling, we chose glomeruli which increase with bulb size. It is likely that the number of mitral cell sizes might increase, but that is beyond the scope of this study. We also used our glomerular measurements to decipher the size of OE. Two sets of studies support the assumption that glomeruli can serve as a proxy for OE input. First, a study showed that the size of a glomerulus changes with the number of OSNs innervating that glomerulus [18]. Previous studies have shown that OSN sizes in mice, rats, and rabbits show no obvious differences [19–21], suggesting that contribution to glomerular size by OSN synapses might be similar across species. A parallel study showed that the number of OSNs of any particular type is environment-dependent because OSN-types that are activated more often, live longer, and occupy a greater fraction of the population of OSNs over time [32]. Thus, as the number of OSNs of any particular type are dynamic, glomerular sizes should not be significantly different across different parts of the bulb. Studies in mice, rats, and rabbits show no obvious spatial bias in glomerular size [69, 70]. This is reflected in our observations (Figures S1H and S1I) of glomerular sizes in guinea pigs and ferrets showing no spatial bias in size. Thus, the average glomerular volume devoted to an OSN type should be a reasonable indicator of the number of OSNs in the OE. For obtaining glomerular density estimates, we chose a portion of the glomerular layer that extended across 3 to 5 sections. We designated one of the end sections as the top section and marked all the glomeruli within the chosen region in that section. We then compared these glomeruli with those in the second section. Those glomeruli that extended into the next section were marked with the same glomerular symbol and new glomeruli were assigned new symbols. We then repeated the procedure by comparing the second and third sections. The number of glomeruli within the selected region of the glomerular layer was the number of symbols (glomeruli) which were not present in the top section (to mimic the classical counting box used in stereology). To average out errors, we followed a similar procedure from the bottom end to obtain a second count of the same portion. The average of these two counts was taken as Current Biology 29, 2533–2540.e1–e7, August 5, 2019 e3

an estimate of the number of glomeruli in the marked portion of the tissue. We then used Neuroexplorer 10.53 (MBF Bioscience, Wilmington, VA) to estimate the outer surface area of this portion of the glomerular layer. From these two estimates, we were able to obtain surface area densities for glomeruli in various parts of the tissue. Next, we provide specifics for each animal’s olfactory bulb estimates. Mouse The mouse olfactory bulb has been studied by three separate groups. The first two studies were carried out in 1988 and 1990 [70, 71] and used stereology methods to estimate the number of glomeruli in Nissl-stained coronal sections of a mouse bulb. The third, more recent study [55], used a slightly different stereological method and a VGLUT2 stain to estimate glomerular number. In this study, however, we use the earlier estimate of 2,000 [70, 71], because we want to relate olfactory circuits across species. Anatomical studies sometimes provide different results when they employ different methods. Therefore, we did not include the newer count in our study as we needed to use the same method and stain to make fair comparisons across different species. It is quite likely that the newer staining methods will yield an equivalent increase in the number of glomeruli in species other than mice. In the Nissl studies, the number of glomeruli was around 2,000 [70, 71]. The studies showed that the olfactory bulb had a volume of 8.45 mm3, and the glomerular layer occupied a volume of 1.74 mm3. Rat Three groups have recorded the number of glomeruli in rat olfactory bulbs, all using cryo-stained Nissl stains. Although they used the same strain they obtained a count of 3,400, 3,300, and 4,200 [69, 72, 73]. We took the average of
3,600. One of the groups also provided detailed volumetric estimates, and the olfactory bulb had a volume of 33.7 mm3 [74], and the glomerular layer occupied a volume of 5.5 mm3 [72]. Guinea Pig We estimated the number of glomeruli in a guinea pig by analyzing olfactory bulbs from two different animals. On average, the olfactory bulb had a volume of 55 mm3 (51.9 and 58.1), and the glomerular layer occupied a volume of 18.28 mm3. The average number of glomeruli was 4,000. Ferret We estimated the number of glomeruli in a ferret by analyzing the olfactory bulb of one ferret. The olfactory bulb had a volume of 62 mm3, and the glomerular layer occupied a volume of 19.64 mm3. The average number of glomeruli was 4,300. We also verified our count with estimates from the literature. In [54], the authors measured the glomerular area per glomeruli and the number of glomeruli in sections along the rostral caudal extent of the bulb. Using these numbers, it is possible to estimate the number of glomeruli by integrating over the sections, and their counts yield numbers between 4,000 and 4,600, which is consistent with our counts. We outline how we calculated these estimates. Figure 3 of [54] shows glomerular density per section. In Figure 4 of the study, they show the mean glomerular area along the rostro-caudal axis. From this figure, it is possible to estimate that the diameter lies somewhere in between 125 mm and 150 mm. Which means that the glomerular density per section can be reasonably assumed to extend for 125-150 mm. In every 1,000 mm of rostral-caudal length, therefore, one would expect somewhere around 7-8 times the number of glomeruli in one section. We took the average values of glomerular densities every 1,000 mm and calculated the total number of glomeruli for the five 1,000 mm intervals along the axis = (150 + 175 + 190 + 125 + 40) 3 7 (or 8) = 580 7 (or 8) = 4,060 or 4,640. What we have described is a procedure for integrating the curve shown in Figure 3 of [54]. Cat We obtained an estimate for the cat extrapolating two observations of our data and existing data on olfactory bulbs. The first observation was made by Gittleman [37] that estimating the volume of the bulb by approximating it to an ellipsoid and measuring the linear parameters of height, width, and length yields close approximations of measured volumes. Our data of measurements of guinea pig, ferret, and opossum bulbs support this study’s observations (Figure S1B). The second is that the number of glomeruli in an olfactory bulb can be predicted by volume as shown in Figure S1C: the number of glomeruli is proportional to glomerular volume and fits the equation: y = 45  x + 1,600 ðR2 = 0:98Þ. Hirano and colleagues examined more than 20 cats in [75] and found the volume of the cat olfactory bulb to be around 134 mm3 (estimated from measurements of the height, width, and length of the cat olfactory bulb as an ellipsoid). Since our linear volume were overestimates on average by about 4%, most likely because at the caudal end, glomeruli only occupy the ventral extent of the bulb (Figure S1B), we followed a similar scheme in the cat. Based on this volume estimate, the number of glomeruli in a cat is likely around 7,500 (Figure S1C). Opossum We obtained an estimate of the opossum from Nissl-stains of the coronal sections of the bulb of one animal. We used methods similar to the ones that we used for the ferret and the guinea pig (refer to the STAR Methods section above). The olfactory bulb had a volume of 31 mm3, and the glomerular layer occupied a volume of 7 mm3. The total estimated glomeruli came to 3,570. Piriform Cortex procedures In this study, we estimated the number of neurons in the anterior piriform cortex. Here, and in the main text when we refer to the piriform cortex we mean the anterior piriform cortex unless we explicitly state otherwise. We measured the number of neurons in all 3 layers as shown in Figure S2 and Table S3. In Figure S2, we also provide an individual breakup for each animal species. Figure S2B provides an analysis of the neuronal density of each of the species. Figure S2A provides an analysis of the volumetric estimates for each of the species.

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Numerical methods We used a linear rate coding model to examine odor representations in the anterior piriform cortex. We made use of the same model as [22]. In this linear rate model, activity of neurons is in spikes/second. The model simulates 3 olfactory circuit elements: activity in the olfactory bulb, the connection matrix between the Olfactory bulb (OB) and anterior piriform cortex (APC), and the activity in APC. We describe each element of the model in turn, and start with activity in the OB. Modeling activity in the bulb Here, odors are represented by the activity of mitral cells that belong to each glomerulus. Since studies [17] have shown that activity of sister mitral cells belonging to the same glomerulus are correlated, we treated either all sister mitral cells (glomerulus) as a computational unit. To simulate glomerular and mitral cell activity we used a binary model distribution. Each glomerulus (or mitral cells associated with the glomerulus) is either on or off with a fixed firing rate R = 50 spikes/s, and odors are represented by the unique of combination of glomeruli that are activated: 10% of the population. As we showed in [22], a model with an exponential distribution (parameter 0.1) gave similar results, i.e., it showed the same trends even though absolute activity and correlation levels were different. Connectivity matrix and piriform responses The next element of the model was the connection matrix between glomeruli or mitral cells belonging to it and the odor processing neurons of the piriform cortex in layer 2. Studies have shown that the axons of mitral cells make connections with layer 2 neurons throughout the PC without any discernible pattern [39, 76, 77]. As [23] showed, the most parsimonious way to describe such connection networks is by specifying the average number of synapses between all the axons emanating from the mitral cells belonging to one glomerulus and one layer 2 neuron. As we showed, this number comes out to about 1.03 (Figure 3D). Since there is no spatial preference, the distribution of number of synapses between any glomerulus and all layer 2 neurons will follow a Poisson distribution with a mean of 1. A similar argument for a Poisson distribution in the fly olfactory system has been experimentally validated [78]. An earlier study showed that the bouton volumes (as a proxy for synaptic strength) in layer 1a of APC follow a Gamma distribution (Figure 3 of [79] fit to a Gamma distribution with shape and scale factors of 1.15 and 0.16 in Figure 3C of), recapitulating studies from the hippocampus [80] which had also shown such Gamma distributions being prevalent: shape and scale factors of 2 and 11. The activity of each layer 2 neuron (represented pictorially in Figure 4A right panel) is the weighted sum of mitral cell activity where the synaptic P MI  SI or P = OB  Conn where OB is a vector of the strengths determine the weights. This is best captured by the equation PI = activity rates of all glomeruli and Conn is a vector of synapse strengths between each glomerulus and layer 2 neuron. For the purposes of simplifying computation, we modeled the effect of 1/10th the population of glomeruli on an equal number of PCx neurons. As shown in [22], an equal number of PCx neurons capture all the information of the bulb. Also, although not shown here, our simulations with higher numbers of glomeruli and PCx neurons yielded similar results (e.g., in [22] a model with 2,000 glomeruli and 4,000 PCx neurons gave the same result as those with fewer numbers). The results that we present in Figures 4 and S4 show the same trends for larger populations of glomeruli and piriform cortex neurons. Numerical procedures used in individual figures Figure 4. To test odor correlations, we used the following procedure. For odor representations in OB, we used a binary model, wherein only 10% of glomeruli (or the mitral cells belonging to it) were active at a fixed firing rate of 50 spikes/s ([81], the results that we show are independent of the absolute value of firing rates). We then generated their corresponding piriform responses. We did this for pairs of odors with varying levels of overlap (from 0 to 90%), i.e., percentage of glomeruli that had the same firing rate. For each decade (0-10, 10-20, etc.), we ran more than a 100 trials, and circles in Figure 4B show the mean for each decade, wherein the x axis values are OB correlations for the odor pair, and y axis the corresponding PC correlations. The points were fit to a line, and the coefficient of determination was 0.99. For Figure 4C, we repeated the procedures for Figure 4B, except this time we reduced the mean number of synapses between a neuron and glomerulus to 0.01 and added noise to the activation of glomeruli as well as synaptic communication. The number of trials was 3. Noise levels were 50%, and are described in more detail in the description of Figure S4 below. For the classification tests (Figures 4D and 4E), we generated OB representations of odors sets of different sizes, and their corresponding PC responses. We then used the dendextend package from R [53] to obtain the cluster classification trees for OB and PC representations, and then compared the two trees to examine how closely the classification trees matched on a scale of 0 to 1, with 1 being a perfect match. Figure 4D shows the results of a classification for a group of 10 odor trials. We labeled the odor representations from 1 to 10 for both OB and PC, scrambled the order, and used R to generate the cluster classification trees. We then fed the classification trees to the dendextend package to compare the similarity of the two trees. As shown in Figure 4D, the labels between the two trees were exactly matched showing that OB and PC produce identical trees or classifications. For Figure 4E, we tested three circuit sizes 200, 400, and 800 corresponding to roughly 1/10th the size of the cat, guinea pig, and mouse bulbs. In the figure we show the classification accuracy (the fraction of PCx odor entries that were accurately identified and matched to their bulb counterparts) for these three circuit sizes for a set of 550 odors. Figure S4. In Figure S4A, for calculations with noise, both synaptic and glomerular, the following procedure was used. Consider that a piriform neuron’s firing is a function of all the glomerular firing rates weighted by the synaptic strengths from each glomeruli. Thus, if P sij  gi . Synthe glomerular firing rate is gi and synapse strength between glomerulus gi and neuron Pj is sij , the firing rate is Pj = P P sij ½1 + Nð0; ss Þ  gi and glomerular noise took the form, Pj = sij  gi ½1 + Nð0; sg Þ where sij = Poisaptic noise took the form, Pj = son-Gamma(mean = 1,shape = 1.15,scale = 0.16), and Nð0; ss Þ, and Nð0; sg Þ are Gaussian distributions describing the noise components. To give a specific example, consider Nð0; ss Þ, the synaptic connection noise. The standard deviation ss captures the Current Biology 29, 2533–2540.e1–e7, August 5, 2019 e5

percentage of noise in the system. For instance, ss = 0:1 means that for 67% of the synapses the amount of noise would be between ± 0.1, and on average, the amount of noise would be around 7.5%. To get 10% of noise on average, ss = 0.125. The amount of noise used in the figure was 50%. For Figures S4B and S4C, we used the same procedure as Figure 4C, except we tested for a range of mean number of synapses between a glomerulus and PCx neuron: 0.01, 0.1, 1, and 10. The colored circles in the figure stand for simulations where the mean number of synapses is 0.1, 1, and 10. The case with 0.01 synapses is shown in black. For Figure S4D, we used the same procedure as Figure 4E except we used an odor set size of 50. In Figure S4E, we used a range of odor set sizes shown in different colors from 50 (top black line) to 550 (bottom pink line). In Figure S4F, we show the same results but this time plotted by circuit size in different colors, blue (800) and black (200). Scaling theory Number of glomeruli per OSN-type The number of glomeruli per OSN-type increases with bigger species. We also make another observation that although the number of glomeruli changes by almost 4-fold from mice to cats, the number of OSN-types changes much more gradually from 1,000 in mice to 700 in cats [82, 83]. Due to this reason, we make the assumption that N =gOSN is proportional to N (Figure S3A) in our argument explaining how the conservation of precision across the olfactory circuit leads to n
g3=2 . The relationship gOSN
N1=2 also follows if we assume optimal allocation of resources in the bulb. If the precision of the OB readout ðgOSN Þ were to increase, it would reduce the precision of the OE readout N =gOSN . The optimal scenario occurs when ðgOSN Þ
N=gOSN or gOSN
N1=2 . Dimensional argument for scaling theory The second reason for the scaling relationship that we observed follows from mapping the 2-dimensional (length and glomerular density) bulb system to the 3-dimensional (length, width, and density) PCx system. The olfactory bulb is a 2-dimensional system as one linear dimension and glomerular density can be used to compute the total number of glomeruli: treating the olfactory bulb as an ellipse, measurements across species show that there is a high correlation between length, width, and height (R2 = 0:79, 0.84, and 0.89 in Figures S3E–S3G, data from [37]). So, knowing one linear parameter can lead to an estimate of the other two. Similarly, the piriform cortex is a 3-dimensional system with the rostral-caudal length, the medialdorsal width, and the neuronal density varying between species, and being enough to calculate the number of neurons. All three quantities change across species and thus are treated as dimensions. If the output of a 2-dimensional system is to become the input of a 3-dimensional system while maintaining the same precision, the 2-dimensional system should grow faster by 3/2 times, i.e., g3=2
n. QUANTIFICATION AND STATISTICAL ANALYSIS To assess the number of entities of interest (either glomeruli or neurons), we first got a volume or surface density estimate, and then estimated the volume or surface area of the whole region. Using these two estimates, the total number of glomeruli or neurons was volume or surface density times the volume (or surface area). In the piriform cortex, the neuronal surface area density was estimated by counting the number of neurons within a 10-20 mm wide column in 40 or 50 mm thick section. We applied the same procedure in estimating glomerular and neuronal densities as shown in Figures S1A and S2C, except for glomeruli we used 30 mm wide sections and used counting boxes that covered, on average, a quarter of the bulb section and 3-4 bulb sections. Due to random fluctuations, there will be differences in the surface density counts obtained from each column. If the source of the fluctuations is really noise, then measurements should vary around a true mean according to a random process. Without knowing the source of the noise, it is reasonable to assume that the noise will follow a Gaussian distribution because of the central limit theorem. In order to verify that the differences in measurement are due to noise, and the mean density is the true density, we compared the cumulative frequency histogram of surface density column measurements of each animal to a best-fit cumulative frequency Gaussian shown in Figures S1A and S2C, and described previously in [44]. As observed in Figures S1 and S2, a visual inspection of the cumulative frequency fits show that the density measurements approximate a normal distribution. We verified these fits with a Shapiro Wilks test (W > 0.05). Furthermore, we also estimated the standard error of the mean (SEM) for the APC and bulb regions of each specimen (see Figure S2B for neuronal densities). All s.e.ms were less than 10% of the mean surface density. The Cumulative Gaussians for the mouse piriform cortex are presented in [22]. All statistical tests were done with the statistical programming language R version 2.34 [84]. Summary of the statistics In Figure S2 we provide a description of our piriform measurements which include the variability across species in neuronal densities (all layers together and each layer separately). The plots show that the variability in neuronal densities within PCx is low within a species (Figure S2C). We also show the variability in the widths of layers 1, 2, and 3. The variability in the width of layers 1 and 2 across species is lower than the variability of layer 3. This is because there is no clear boundary for demarcating the end of layer 3. We used atlases and previous publications in finding this boundary but as there is some variability in atlases across species, it was reflected in our measurements too. As layer 3 is relatively sparse it affected the neuron counts negligibly.

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In Figure S3, we show the variability in the estimates of synaptic densities across regions, animals, and different labs. We show that the population means (shown with confidence intervals) are not significantly different within these categories serving as the basis of our assumption to use the mean synaptic density across species. For the allometric or power-law relations in the rest of the figures, we provide the relationship, the coefficient of determination, and the confidence interval. DATA AND CODE AVAILABILITY The Neurolucida files for PCx measurements are available online. Software, written in R, for modeling and statistical analysis is available on request.

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