Scaling Principles of Distributed Circuits

Srinivasan, S.; Stevens, Charles F.

doi:10.1016/j.cub.2019.06.046

Cited by 16 publications

(16 citation statements)

References 79 publications

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“…Our results show that odors of natural complexity can be encoded in, and decoded from, signals of a relatively small number of receptor types each binding to 5-15% of odorants. Perhaps this observation has a bearing on why all animals express ~ 300 receptor types, give or take an O(1) factor, although receptor diversity does increase in larger animals [40] along with the number of neurons in each olfactory structure, the latter scaling with body size [66]. Even at the extremes, the fruitfly and the billion-fold heavier African elephant have 57 ~300 / 6 [4] and 1948 ~ 300 ×6 [67] receptor types respectively.…”

Section: Discussionmentioning

confidence: 99%

What the odor is not: Estimation by elimination

Singh

Tchernookov

Balasubramanian

2019

Preprint

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The olfactory system uses the responses of a small number of broadly sensitive receptors to combinatorially encode a vast number of odors. Here, we propose a method for decoding such a distributed representation. Our main idea is that a receptor that does not respond to an odor carries more information than a receptor that does, because a typical receptor binds to many odorants. So a response below threshold signals the absence of all such odorants. As a result, it is easier to identify what the odor is not, rather than what the odor is. We demonstrate that, for biologically realistic numbers of receptors, response functions, and odor mixture complexity, this remarkably simple method of elimination turns an underdetermined decoding problem into an overdetermined one, allowing accurate determination of the odorants in a mixture and their concentrations. We give a simple neural network realization of our algorithm which resembles the known circuit architecture of the piriform cortex.Olfaction | Receptors | Odor DecodingThe olfactory system enables animals to sense, perceive, and respond to mixtures of volatile molecules that carry messages about the world. There are many monomolecular odorants, perhaps 10 4 or more (1-3), far more than the number of receptor types available to animals (∼ 50 in fly, ∼ 300 in human, ∼ 1000 in rat, mouse and dog (4-7)). The problem of representing such a high-dimensional chemical space in such a low-dimensional response space may be solved by the presence of many receptors that bind to numerous odorants (8-14), leading to a distributed, combinatorial representation of odors (see, e.g., (12,(15)(16)(17)(18)(19)(20)(21)(22)(23)).We focus on the inverse problem: the estimation of odor composition from the response of olfactory receptors. We use a realistic competitive binding model of odor encoding by receptors (24)(25)(26)(27), and propose a scheme to decode odor composition from such responses. The scheme works over a large range of biologically relevant parameters, does not require any special constraints on receptor-odorant interactions, and works for systems with few receptors, suggesting why the relatively small olfactory receptor repertoires of most organisms are sufficient for detecting complex natural odors.Our main idea is that a receptor that does not respond to an odor carries a lot more information about the odor than a receptor that does respond to it. This is because a receptor that does not respond to an odor signals that none of the odorants (individual chemicals) that could bind to this receptor are present in the odor. With just a few such non-responding receptors, most of the odorants that are not present can be identified and eliminated. Thus, it is easier to identify what the mixture is not, rather than what the mixture is. For a large range of biologically relevant parameters, this elimination turns the estimation of odor concentration from an underdetermined problem to an overdetermined one. Thus, the concentration of the rest of the odorants can be estimated from...

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Section: Discussionmentioning

confidence: 99%

What the odor is not: Estimation by elimination

Singh

Tchernookov

Balasubramanian

2019

Preprint

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“…Because neuronal populations have a tendency to project stereotypically, variation in subpopulation of neuron numbers can be used to make inferences about variation in connectivity patterns across species. 14,17,[100][101][102][103] Neuronal populations can be quantified with stereological methods as well as from sequencing of RNA, methylation, or open chromatin regions at the single cell level. [104][105][106][107][108][109][110] The use of classical stereological approaches coupled with RNA or DNA sequencing can provide rigorous approaches to compare cell populations across species.…”

Section: Evolution Of Cortical Connectionsmentioning

confidence: 99%

Closing the gap from transcription to the structural connectome enhances the study of connections in the human brain

Charvet

2020

Developmental Dynamics

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The brain is composed of a complex web of networks but we have yet to map the structural connections of the human brain in detail. Diffusion MR imaging is a high‐throughput method that relies on the principle of diffusion to reconstruct tracts (ie, pathways) across the brain. Although diffusion MR tractography is an exciting method to explore the structural connectivity of the brain in development and across species, the tractography has at times led to questionable interpretations. There are at present few if any alternative methods to trace structural pathways in the human brain. Given these limitations and the potential of diffusion MR imaging to map the human connectome, it is imperative that we develop new approaches to validate neuroimaging techniques. I discuss our recent studies integrating neuroimaging with transcriptional and anatomical variation across humans and other species over the course of development and in adulthood. Developing a novel framework to harness the potential of diffusion MR tractography provides new and exciting opportunities to study the evolution of developmental mechanisms generating variation in connections and bridge the gap between model systems to humans.

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“…That question was chosen partly because its answer provides insight into learning principles in general, and partly because it was recently addressed experimentally: Srinivasan and Stevens found, based on six mammalian species, a very tight relationship between the number of glomeruli and the number of neurons in layer two of piriform cortex ( Fig. 1A; data taken from [18]). More precisely, using L x to denote the input layer size (the number of glomeruli), and L h to denote the hidden layer size (the number of neurons in layer 2 of piriform cortex), they found the approximate scaling law…”

Section: Introductionmentioning

confidence: 99%

“…While these models provided insight into circuit structure, none were able to provide a quantitative explanation for the population sizes of circuits across different species. Srinivasan and Stevens, on the other hand, offered several explanations, based on coding efficiency and geometry, for the scaling in mammals [18]. While those explanations are reasonable candidate hypotheses, they are more abstract than mechanistic, and do not explain the scaling seen in invertebrates.…”

Section: Introductionmentioning

confidence: 99%

Developmental and evolutionary constraints on olfactory circuit selection

Hiratani

Latham

2020

Preprint

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Across species, neural circuits show remarkable regularity, suggesting that their structure has been driven by underlying optimality principles. Here, we ask whether we can predict the neural circuitry of diverse species by optimizing the neural architecture to make learning as efficient as possible. We focus on the olfactory system, primarily because it has a relatively simple evolutionarily conserved structure, and because its input and intermediate layer sizes exhibits a tight allometric scaling. In mammals, it has been shown that the number of neurons in layer 2 of piriform cortex scales as the number of glomeruli (the input units) to the 3/2 power; in invertebrates, we show that the number of mushroom body Kenyon cells scales as the number of glomeruli to the 7/2 power. To understand these scaling laws, we model the olfactory system as a three layered nonlinear neural network, and analytically optimize the intermediate layer size for efficient learning from a limited number of samples. We find that the 3/2 scaling observed in mammals emerges naturally, both in full batch optimization and under stochastic gradient learning. We extended the framework to the case where a fraction of the olfactory circuit is genetically specified, not learned. We show numerically that this makes the scaling law steeper when the number of glomeruli is small, and we are able to recover the 7/2 scaling law observed in invertebrates. This study paves the way for a deeper understanding of the organization of brain circuits from an evolutionary perspective.

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Scaling Principles of Distributed Circuits

Cited by 16 publications

References 79 publications

What the odor is not: Estimation by elimination

What the odor is not: Estimation by elimination

Closing the gap from transcription to the structural connectome enhances the study of connections in the human brain

Developmental and evolutionary constraints on olfactory circuit selection

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