The findings are likely representative of many olfactory receptors, Ruta says. Materials provided by Rockefeller University. Note: Content may be edited for style and length. Science News. Holistic recognition Olfactory receptors were discovered 30 years ago. Story Source: Materials provided by Rockefeller University. Yedlin, Vanessa Ruta. The structural basis of odorant recognition in insect olfactory receptors. Nature , ; DOI: ScienceDaily, 4 August Rockefeller University.
Study reveals how smell receptors work. Retrieved November 11, from www. However, the olfactory receptor that contributes decisively to this sensory impression was unknown until now. Keywords: Anosmia; G protein-coupled receptors; Odorant perception; Odorant receptor; Olfactory bulb; Olfactory epithelium; Olfactory sensory neuron. Abstract Olfaction plays a critical role in several aspects of life.
Publication types Review. Mathematically, this is because the diagonal elements of Q - 1 are functions of all the variances and covariances in the overlap matrix Q. This dependence of each abundance on the full covariance translates to a complex context-dependence whereby changing the same ligand in different background environments can lead to very different adapted distributions of receptors.
In Appendix 6 we show that the correlation with the inverse overlap matrix has an intuitive interpretation: receptors which either do not fluctuate much or whose values can be guessed based on the responses of other receptors should have low abundances. To investigate how the structure of the optimal receptor repertoire varies with the olfactory environment, we first constructed a background in which the concentrations of odorants were distributed according to a Gaussian with a randomly chosen covariance matrix e.
From this base, we generated two different environments by adding a large variance to 10 odorants in environment 1, and to 10 different odorants in environment 2 Figure 4b. We then considered the optimal distribution in these environments for a repertoire of 24 receptor types with odor affinities inferred from Hallem and Carlson, We found that when the number of olfactory sensory neurons K tot is large, and thus the signal-to-noise ratio is high, the change in odor statistics has little effect on the distribution of receptors Figure 4c.
This is because at high SNR, all the receptors are expressed nearly uniformly as discussed above, and this is true in any environment. When the number of neurons is smaller or, equivalently, the signal-to-noise ratio is in a low or intermediate regime , the change in environment has a significant effect on the receptor distribution, with some receptor types becoming more abundant, others becoming less abundant, and yet others not changing much between the environments see Figure 4d.
This mimics the kinds of complex effects seen in experiments in mammals Schwob et al. The variances are drawn from a lognormal distribution. The two covariance matrices are obtained by adding a large variance to two different sets of 10 odorants out of in the matrix from a.
The altered odorants are identified by yellow crosses; their variances go above the color scale on the plots by a factor of more than The blue diamonds on the left correspond to the optimal OSN fractions per receptor type in the first environment, while the orange diamonds on the right correspond to the second environment.
In this high-SNR regime, the effect of the environment is small, because in both environments the optimal receptor distribution is close to uniform.
In the comparison above, the two environment covariance matrices differed by a large amount for a small number of odors. We next compared environments with two different randomly generated covariance matrices, each generated in the same way as the background environment in Figure 4a. The resulting covariance matrices Figure 5a , top are very different in detail the correlation coefficient between their entries is close to zero; distribution of changes in Figure 5b , red line , although they look similar by eye.
Despite the large change in the detailed structure of the olfactory environment, the corresponding change in optimal receptor distribution is typically small, with a small fraction of receptor types experiencing large changes in abundance red curve in Figure 5c. Larger changes also occurred, but very rarely: about 0.
The environments on the top span a similar set of odors, while those on the bottom contain largely non-overlapping sets of odors. The histograms in solid red and blue are obtained by pooling the samples of pairs of environment matrices from each group. The plot also shows, in lighter colors, the histograms for each individual pair.
The non-overlapping scenario has an increased occurrence of both large changes in the OSN abundances, and small changes the spike near the y -axis. The tuning width for each receptor, measuring the fraction of odorants that produce a significant activation of that receptor see Appendix 1 , was chosen uniformly between 0. The receptors from all the 50 trials were pooled together, sorted by their tuning width, and split into three tuning bins. This probability was determined by a kernel density estimate.
The boxes show the median and interquartile range for each bin. If we instead engineer two environments that are almost non-overlapping so that each odorant is either common in environment 1, or in environment 2, but not in both Figure 5a , bottom; see Appendix 4 for how this was done , the changes in optimal receptor abundances between environments shift away from mid-range values towards higher values blue curve in Figure 5c.
It seems intuitive that animals that experience very different kinds of odors should have more striking differences in their receptor repertoires than those that merely experience the same odors with different frequencies. Intriguingly, however, our simulations suggest that the situation may be reversed at the very low end: the fraction of receptors for which the predicted abundance change is below 0. Thus, changing between non-overlapping environments emphasizes the more extreme changes in receptor abundances, either the ones that are close to zero or the ones that are large.
In contrast, a generic change in the environment leads to a more uniform distribution of abundance changes. Put differently, the particular way in which the environment changes, and not only the magnitude of the change, can affect the receptor distribution in unexpected ways.
The magnitude of the effect of environmental changes on the optimal olfactory receptor distribution is partly controlled by the tuning of the olfactory receptors Figure 5d. If receptors are narrowly tuned, with each type responding to a small number of odorants, changes in the environment tend to have more drastic effects on the receptor distribution than when the receptors are broadly tuned Figure 5d , an effect that could be experimentally tested.
Our study opens the exciting possibility of a causal test of the hypothesis of efficient coding in sensory systems, where a perturbation in the odor environment could lead to predictable adaptations of the olfactory receptor distribution during the lifetime of an individual. This does not happen in insects, but it can happen in mammals, since their receptor neurons regularly undergo apoptosis and are replaced. A recent study demonstrated reproducible changes in olfactory receptor distributions of the sort that we predict in mice Ibarra-Soria et al.
These authors raised two groups of mice in similar conditions, exposing one group to a mixture of four odorants acetophenone, eugenol, heptanal, and R-carvone either continuously or intermittently by adding the mixture to their water supply. Continuous exposure to the odorants had no effect on the receptor distribution, in agreement with the predictions of our model.
In contrast, intermittent exposure did lead to systematic changes Figure 6a. The error bars show standard deviation across six individuals. Compared to Figure 5B in Ibarra-Soria et al. The error bars show the range of variation found in the optimal receptor distribution when slightly perturbing the two environments see the text. The simulation includes 59 receptor types for which response curves were measured Saito et al. We used our model to run an experiment similar to that of Ibarra-Soria et al.
Using a sensing matrix based on odor response curves for mouse and human receptors data for 59 receptors from Saito et al. We ran the simulations 24 times, modifying the odor environments each time by adding a small amount of Gaussian random noise to the square roots of these covariance matrices to model small perturbations details in Appendix 4; range bars in Figure 6b. The results show that the abundances of already numerous receptors do not change much, while there is more change for less numerous receptors.
The frequencies of rare receptors can change dramatically, but are also more sensitive to perturbations of the environment large range bars in Figure 6b.
These results qualitatively match experiment Figure 6a , where we see the same pattern of the largest reproducible changes occurring for receptors with intermediate abundances. In our model, the distinction between receptor numbers and OSN numbers is immaterial because a change in the number of receptors expressed per neuron has the same effect as a change in neuron numbers. In general, additional experiments are needed to measure both the number of receptors per neuron and the number of neurons for each receptor type.
Given detailed information regarding the affinities of olfactory receptors, the statistics of the odor environment, and the size of the olfactory epithelium through the total number of neurons K tot , our model makes fully quantitative predictions for the abundances of each OSN type.
Existing experiments e. Ibarra-Soria et al. However, such data can be collected using available experimental techniques. Given the huge number of possible odorants Yu et al. One might worry that this poses a challenge for our modeling framework. One approach might be to use low-dimensional representations of olfactory space e. Koulakov et al. For now, we can ask how the predictions of our model change upon subsampling: if we only know the responses of a subset of receptors to a subset of odorants, can we still accurately predict the OSN numbers for the receptor types that we do have data for?
Figure 7a and b show that such partial data do lead to robust statistical predictions of overall receptor abundances. Robustness in the prediction is measured as the Pearson correlation between the predicted OSN numbers with complete information, and after subsampling.
First, the optimization problem from Equation 7 was solved including all the OSN types and an environment with a random covariance matrix see Figure 5. Then a second optimization problem was run in which a fraction of the OSN types were removed. The shaded area in the plot shows the range between the 20th and 80th percentiles for the correlation values obtained in 10 trials, while the red curve is the mean.
A new subset of receptors to be removed and a new environment covariance matrix were generated for each sample. We have explored the structure of olfactory receptor distributions that code odors efficiently, that is are adapted to maximize the amount of information that the brain gets about odors. The distribution of olfactory receptors in the mammalian epithelium, however, must arise dynamically from the pattern of apoptosis and neurogenesis Calof et al. At a qualitative level, in the efficient coding paradigm that we propose, the receptor distribution is related to the statistics of natural odors, so that the life cycle of neurons would have to depend dynamically on olfactory experience.
Such modulation of OSN lifetime by exposure to odors has been observed experimentally Santoro and Dulac, ; Zhao et al. This gives. Because of the last term in Equation 9 , the death rate in our model is influenced by olfactory experience in a receptor-dependent way. In contrast, the birth rate is not experience-dependent and is the same for all OSN types. Indeed, in experiments, the odor environment is seen to have little effect on receptor choice, but does modulate the rate of apoptosis in the olfactory epithelium Santoro and Dulac, Our results suggest that, if olfactory sensory neuron lifetimes are appropriately anti-correlated with the inverse response covariance matrix, then the receptor distribution in the epithelium can converge to achieve optimal information transfer to the brain.
Performing the inverse necessary for our model is more intricate. The computations could perhaps be done by circuits in the bulb and then fed back to the epithelium through known mechanisms Schwob et al. Within our model, Figure 8a shows an example of receptor numbers converging to the optimum from random initial values.
The sensing matrix used here is based on mammalian data Saito et al. The environment covariance matrix is generated using the random procedure described earlier details in Appendix 4. We see that some receptor types take longer than others to converge the time axis is logarithmic, which helps visualize the whole range of convergence behaviors. For the same reason, OSN populations that start at a very low level also take a long time to converge.
Note that the time axis is logarithmic. A small, random deviation from the optimal receptor abundance in the initial environment was added see text. In Figure 8b , we show convergence to the same final state, but this time starting from a distribution that is not random but was optimized for a different environment. The initial and final environments are the same as the two environments used in the previous section to compare the simulations to experimental findings Figure 6b.
Interestingly, many receptor types actually take longer to converge in this case compared to the random starting point, perhaps because there are local optima in the landscape of receptor distributions. Given such local minima, stochastic fluctuations will allow the dynamics to reach the global optimum more easily. In realistic situations, there are many sources of such variability, for example, sampling noise due to the fact that the response covariance matrix R must be estimated through stochastic odor encounters and noisy receptor readings.
We built a model for the distribution of receptor types in the olfactory epithelium that is based on efficient coding, and assumes that the abundances of different receptor types are adapted to the statistics of natural odors in a way that maximizes the amount of information conveyed to the brain by glomerular responses. This model predicts a non-uniform distribution of receptor types in the olfactory epithelium, as well as reproducible changes in the receptor distribution after perturbations to the odor environment.
In contrast to other applications of efficient coding, our model operates in a regime in which there are significant correlations between sensors because the adaptation of OSN abundances occurs upstream of the brain circuitry that can decorrelate olfactory responses.
In this regime, OSN abundances depend on the full correlation structure of the inputs, leading to predictions that are context-dependent in the sense that whether the abundance of a specific receptor type goes up or down due to a shift in the environment depends on the global context of the responses of all the other receptors. All these striking phenomena have been observed in recent experiments and had not been explained prior to this study. In our framework, the sensitivity of the receptor distribution to changes in odor statistics is affected by the tuning of the olfactory receptors, with narrowly tuned receptors being more readily affected by such changes than broadly tuned ones.
The model also predicts that environments that differ in the identity of the odors that are present will lead to greater deviations in the optimal receptor distribution than environments that differ only in the statistics with which these odors are encountered. Likewise, the model broadly predicts a monotonic relationship between the number of receptor types found in the epithelium and the total number of olfactory sensory neurons, all else being equal.
A detailed test of our model requires more comprehensive measurements of olfactory environments than are currently available. Our hope is that studies such as ours will spur interest in measuring the natural statistics of odors, opening the door for a variety of theoretical advances in olfaction, similar to what was done for vision and audition.
Such measurements could for instance be performed by using mass spectrometry to measure the chemical composition of typical odor scenes. For mammals, controlled changes in environments similar to those in Ibarra-Soria et al.
To our knowledge, this is the first time that efficient coding ideas have been used to explain the pattern of usage of receptors in the olfactory epithelium. Our work can be extended in several ways. OSN responses can manifest complex, nonlinear responses to odor mixtures.
Accurate models for how neurons in the olfactory epithelium respond to complex mixtures of odorants are just starting to be developed e. Singh et al. For example, the distribution of odorants could be modeled using a Gaussian mixture, rather than the normal distribution used in this paper to enable analytic calculations.
Each Gaussian in the mixture would model a different odor object in the environment, more closely approximating the sparse nature of olfactory scenes discussed in, for example, Krishnamurthy et al. Of course, the goal of the olfactory system is not simply to encode odors in a way that is optimal for decoding the concentrations of volatile molecules in the environment, but rather to provide an encoding that is most useful for guiding future behavior.
This means that the value of different odors might be an important component shaping the neural circuits of the olfactory system. In applications of efficient coding to vision and audition, maximizing mutual information, as we did, has proved effective even in the absence of a treatment of value Laughlin, ; Atick and Redlich, ; van Hateren, a ; Olshausen and Field, ; Simoncelli and Olshausen, ; Fairhall et al.
However, in general, understanding the role of value in shaping neural circuits is an important experimental and theoretical problem. To extend our model in this direction, we would replace the mutual information between odorant concentrations and glomerular responses by a different function that takes into account value assignments see, e. Rivoire and Leibler, It could be argued, though, that such specialization to the most behaviorally relevant stimuli might be unnecessary or even counterproductive close to the sensory periphery.
Indeed, a highly specialized olfactory system might be better at reacting to known stimuli, but would be vulnerable to adversarial attacks in which other organisms take advantage of blind spots in coverage. Because of this, and because precise information regarding how different animals assign value to different odors is scarce, we leave these considerations for future work.
One exciting possibility suggested by our model is a way to perform a first causal test of the efficient coding hypothesis for sensory coding. Given sufficiently detailed information regarding receptor affinities and natural odor statistics, experiments could be designed that perturb the environment in specified ways, and then measure the change in olfactory receptor distributions.
Comparing the results to the changes predicted by our theory would provide a strong test of efficient coding by early sensory systems in the brain. We used three types of sensing matrices in this study.
Two were based on experimental data, one using fly receptors Hallem and Carlson, , and one using mouse and human receptors Saito et al. Some of our simulations used a sensing matrix based on Drosophila receptor affinities, as measured by Hallem and Carlson Hallem and Carlson, This includes the responses of 24 of the 60 receptor types in the fly against a panel of odorants, measured using single-unit electrophysiology in a mutant antennal neuron.
We used the values from Table S1 in Hallem and Carlson, for the sensing matrix elements. To estimate receptor noise, we used the standard deviation measured for the background firing rates for each receptor data obtained from the authors. The fly data has the advantage of being more complete than equivalent datasets in mammals. When comparing our model to experimental findings from Ibarra-Soria et al. This was measured using heterologous expression of olfactory genes, and tested in total mouse and human receptor types against 93 different odorants.
However, only 49 mouse receptors and 10 human receptors exhibited detectable responses against any of the odorants, while only 63 odorants activated any receptors. In this paper, we used the values obtained for the highest concentration 3 mM. The color scaling is arbitrary, with red representing positive values and blue negative values.
We started by treating the column i. We normalized the index to a coordinate x running from 0 to 1. To obtain a bell-like response profile for the receptors while preserving the periodicity of the odor coordinate we chose, we defined the response affinity to odorant x by.
This is simply a convenient choice for treating odor space in a way that eliminates artifacts at the edges of the sensing matrix, and we do not assign any significance to the particular coordinate system that we used. The overall scale of the sensing matrices was set by multiplying all the affinities by , which yielded values comparable to the measured firing rates in fly olfactory neurons Hallem and Carlson, Our qualitative results are robust across a variety of different choices for the sensing matrix Appendix 1—figure 1.
Similarly, the general effect that environment change has on optimal OSN numbers, with less abundant receptor types changing more than more abundant ones, is generic across different choices of sensing matrices Appendix 1—figure 3.
The labels refer to the sensing matrices from Appendix 1—figure 1. The labels refer to the sensing matrices from Appendix 1—figure 1 , whose scales were adjusted to ensure that the simulations are in a low SNR regime. The blue orange diamonds on the left right side of each plot represent the optimal OSN abundances in environment 1 environment 2. In the main text we assume a Gaussian distribution for odorant concentrations and approximate receptor responses as linear with additive Gaussian noise, Equation 2.
Thus it follows that the marginal distribution of receptor responses is also Gaussian. We get:. The mutual information between responses and odors is then given by see below for a derivation :. This recovers the result quoted in the main text, Equation 4. This is simply the covariance matrix of responses in which each response was normalized by the noise variance of the corresponding receptor. First, note that. Thus, taking the determinant of Equation 21 , we get the desired identity.
As a first step, let us calculate the KL divergence between two multivariate normals in n dimensions:. Using also the definition of the mean and of the covariance matrix, we have. Plugging this into Equation 26 , we get. The covariance matrix for the product distribution is. In order to find the optimal distribution of olfactory receptors, we must maximize the mutual information from Equation 4 in the main text, subject to constraints. Let us first calculate the gradient of the mutual information with respect to the receptor numbers:.
The cyclic property of the trace allows us to use the usual rules to differentiate under the trace operator, so we get. We now have to address the constraints. At the optimum, we must have:. Combined with Equation 34 , this yields. Suppose we are in the regime in which the total number of neurons is large, and in particular, each of the abundances K a is large. Then we can perform an expansion of the expression appearing in the KKT equations from Equation 37 :. With the notation.
This quadratic equation has only one large solution, and it is given approximately by. This leads to. Thus, in general, the information when only receptor type x is activated is given by.
Another way to think of this result is by employing the usual expression for the capacity of a single Gaussian channel, and then finding the channel that maximizes this capacity. The joint probability distribution for the new variables is related to the joint distribution of the original variables through the Jacobian determinants,. We can now calculate the mutual information between the new variables:.
In mammals, the axons from neurons expressing a given receptor type can project to anywhere from 2 to 16 different glomeruli. The result goes a long way toward confirming how animals identify and discriminate among astronomical numbers of smells. It also sheds light on key principles of receptor activity that might have far-reaching implications — for the evolution of chemical perception, for our understanding of how other neurological systems and processes work, and for practical applications like the development of targeted drugs and insect repellents.
Several hypotheses have competed to explain how olfactory receptors achieve the necessary flexibility. Some scientists proposed that receptors respond to a single feature of odor molecules, such as shape or size; the brain might then identify an odor from some combination of those inputs. Other researchers posited that each receptor has multiple binding sites, enabling different kinds of compounds to dock. The Rockefeller team turned to receptor interactions in the jumping bristletail, an ancestral ground-dwelling insect that has a particularly simple olfactory receptor system.
In insects, olfactory receptors are ion channels that activate when an odor molecule binds to them. And so they must carefully balance generality against specificity, staying flexible enough to detect an enormous number of potential odors while being selective enough to reliably recognize the important ones, which could differ considerably from one species or environment to another.
What was the mechanism that allowed them to navigate that fine line, and to evolve that way? But recent technological advances, most notably an imaging technique called cryo-electron microscopy, made it possible for Ruta and her colleagues to try. They looked at the structure of a jumping bristletail olfactory receptor in three different configurations: by itself, and bound to either a common odor molecule called eugenol which smells like clove to humans or the insect repellant DEET.
They then compared those structures, down to their individual atoms, to understand how odor binding opened the ion channel, and how a single receptor could detect chemicals of very different shapes and sizes. That turned out to be a deep, geometrically simple pocket, lined with many amino acids that facilitate loose, weak interactions; eugenol and DEET took advantage of different interactions to lodge within it.
Further computational modeling showed that each molecule was able to bind in many different orientations — and that many other kinds of odor compounds, though not all, could bind to the receptor in a similar way.
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