As these currents enter the complex network of the brain, it can quickly sometimes within just two or three synapses, in a tenth of a second recognize the odor. How many odors can the human brain discriminate? Until recently, most scientists would have said something like 10,; however, new research suggests a far greater number—perhaps a trillion. The computation begins as signals are received and sorted out in the olfactory bulb, a structure on the underside of the front of the brain.
The olfactory bulb also connects directly to the limbic system, the brain area that regulates emotion. A network of connections with other parts of the brain give scents a matchless power to evoke detailed, emotionally charged memories and such complex mental states as nostalgia and longing. Pheromones are airborne chemicals emitted by individuals that elicit a physiological response in other members of the same species, via the olfactory system.
In other animals, pheromones carry messages of alarm and aggression, and they play an essential role in sexual attraction and reproduction. Whether pheromones work similarly in humans is controversial. Some research suggests so: airborne molecules of sex hormones seem to alter hormone secretion in the opposite sex. For example, the scent of female tears apparently dampens male sexual desire.
However, the extent to which pheromones actually influence our actions remains uncertain. The other primary chemical sense, taste technically, the gustatory system , responds to molecules dissolved in liquid.
These molecules enter the system via taste buds: pear-shaped structures in which receptor-bearing cells surround a central pore. There are millions of receptors onsome 10, taste buds. Most are found in the familiar bumps called papillae that cover the surface of the tongue, but some line the roof of the mouth and the back of the throat. When a molecule of the appropriate taste binds to a receptor, the process changes the electrical charge in the receptor cell, triggering release of a neurotransmitter.
This messenger chemical initiates an electrical impulse in a nearby neuron, which carries the signal to the brain. It used to be thought that receptors for each taste were limited to one section of the tongue the tip of the tongue for sweet, the sides for salt and sour, the back for bitter , but now we know that receptor types are more widely distributed a single taste bud, in fact, may contain receptors for several tastes. There is no clear organization of taste receptors on the tongue.
Taste signals go from the mouth, via cranial nerves, to the medulla oblongata in the brainstem, then up to the thalamus and on to the cortex, where the sensation becomes a perception. You thus become aware of what you taste and can respond appropriately, swallowing food and spitting out possibly harmful substances. Connections from the lower brain allow taste to influence digestive processes directly.
When we chew food or sip wine, chemicals are vaporized into air passages that connect the mouth and the back of the nose, stimulating olfactory receptors and allowing us to realize the subtleties of flavor. Other aspects of the taste experience, such as food texture and temperature, engage additional senses. Experimentally, increased exposure to odorants leads variously, but reproducibly, to increased, decreased, or unchanged abundances of different activated receptors. We demonstrate that this diversity of effects is required for efficient coding when sensors are broadly correlated, and provide an algorithm for predicting which olfactory receptors should increase or decrease in abundance following specific environmental changes.
Finally, we give simple dynamical rules for neural birth and death processes that might underlie this adaptation. Each odorant activates many different receptor types. And each receptor type responds to many different odorants.
To identify a smell, the brain must therefore consider the overall pattern of activation across all receptor types. Individual receptor neurons in the mammalian nose live for about 30 days, before new cells replace them.
The entire population of odorant receptor neurons turns over every few weeks, even in adults. Studies have shown that some types of these receptor neurons are used more often than others, depending on the species, and are therefore much more abundant.
Moreover, the usage patterns of different receptor types can also change when individual animals are exposed to different smells. The results revealed that the nose adjusts its odorant receptor neurons to provide the brain with as much information as possible about typical smells in the environment.
Because each smell consists of multiple odorants, each odorant is more likely to occur alongside certain others. For example, the odorants that make up the scent of a flower are more likely to occur together than alongside the odorants in diesel. The nose takes advantage of these relationships by adjusting the abundance of the receptor types in line with them. The number of odorant receptor neurons in the human nose decreases with time. The current findings could help scientists understand how these changes affect our sense of smell as we age.
This will require collaboration between experimental and theoretical scientists to measure the odors typical of our environments, and work out how our odorant receptor neurons detect them. The sensory periphery acts as a gateway between the outside world and the brain, shaping what an organism can learn about its environment. This gateway has a limited capacity Barlow, , restricting the amount of information that can be extracted to support behavior.
On the other hand, signals in the natural world typically contain many correlations that limit the unique information that is actually present in different signals. The efficient-coding hypothesis, a key normative theory of neural circuit organization, puts these two facts together, suggesting that the brain mitigates the issue of limited sensory capacity by eliminating redundancies implicit in the correlated structure of natural stimuli Barlow, ; van Hateren, a.
This idea has led to elegant explanations of functional and circuit structure in the early visual and auditory systems see, e. These classic studies lacked a way to test causality by predicting how changes in the environment lead to adaptive changes in circuit composition or architecture. We propose that the olfactory system provides an avenue for such a causal test because receptor neuron populations in the mammalian nasal epithelium are regularly replaced, leading to the possibility that their abundances might adapt efficiently to the statistics of the environment.
The olfactory epithelium in mammals and the antennae in insects are populated by large numbers of olfactory sensory neurons OSNs , each of which expresses a single kind of olfactory receptor. Each type of receptor binds to many different odorants, and each odorant activates many different receptors, leading to a complex encoding of olfactory scenes Malnic et al. Independently evolved large olfactory receptor families can also be found in insects Missbach et al. Surprisingly, although animals possess diverse repertoires of olfactory receptors, their expression is actually highly non-uniform, with some receptors occurring much more commonly than others Rospars and Chambille, ; Ibarra-Soria et al.
In addition, in mammals, the olfactory epithelium experiences neural degeneration and neurogenesis, resulting in replacement of the OSNs every few weeks Graziadei and Graziadei, The distribution of receptors resulting from this replacement has been found to have a mysterious dependence on olfactory experience Schwob et al. Here, we show that these puzzling observations are predicted if the receptor distribution in the olfactory epithelium is organized to present a maximally informative picture of the odor environment.
Specifically, we propose a model for the quantitative distribution of olfactory sensory neurons by receptor type. The model predicts that in a noisy odor environment: a the distribution of receptor types will be highly non-uniform, but reproducible given fixed receptor affinities and odor statistics; and b an adapting receptor neuron repertoire should reproducibly reflect changes in the olfactory environment; in a sense it should become what it smells.
Precisely such findings are reported in experiments Schwob et al. In contrast to previous work applying efficient-coding ideas to the olfactory system Keller and Vosshall, ; McBride et al. Instead, we focus on the complementary question of the optimal way in which the olfactory system can use the available receptor genes.
This allows us to focus on phenomena that occur on faster timescales, such as the reorganization of the receptor repertoire as a result of neurogenesis in the mammalian epithelium. Because of the combinatorial nature of the olfactory code Malnic et al. In the absence of such correlations, efficient coding predicts that output power will be equalized across all channels if transmission limitations dominate Srinivasan et al.
Here, we show that the optimal solution is very different when the system of sensors is highly correlated: the adaptive change in the abundance of a particular receptor type depends critically on the global context of the correlated responses of all the receptor types in the population—we refer to this as context-dependent adaptation. Correlations between the responses of olfactory receptor neurons are inevitable not only because the same odorant binds to many different receptors, but also because odors in the environment are typically composed of many different molecules, leading to correlations between the concentrations with which these odorants are encountered.
Furthermore, there is no way for neural circuitry to remove these correlations in the sensory epithelium because the candidate lateral inhibition occurs downstream, in the olfactory bulb. As a result of these constraints, for an adapting receptor neuron population, our model predicts that increased activation of a given receptor type may lead to more, fewer or unchanged numbers of the receptor, but that this apparently sporadic effect will actually be reproducible between replicates.
This counter-intuitive prediction matches experimental observations Santoro and Dulac, ; Zhao et al. In vertebrates, axons from olfactory neurons converge in the olfactory bulb on compact structures called glomeruli, where they form synapses with dendrites of downstream neurons Hildebrand and Shepherd, ; see Figure 1a.
To good approximation, each glomerulus receives axons from only one type of OSN, and all OSNs expressing the same receptor type converge onto a small number of glomeruli, on average about two in mice to about 16 in humans Maresh et al. Similar architectures can be found in insects Vosshall et al. The architecture is similar in insects, with the OSNs and the glomeruli located in the antennae and antennal lobes, respectively.
Different receptor types are represented by different colors in the diagram. Glomerular responses bar plot on top right result from mixtures of odorants in the environment bar plot on bottom left. The response noise, shown by black error bars, depends on the number of receptor neurons of each type, illustrated in the figure by the size of the corresponding glomerulus.
Glomeruli receiving input from a small number of OSNs have higher variability due to receptor noise e. Response magnitudes depend also on the odorants present in the medium and the affinity profile of the receptors. K a are the numbers of OSNs of each type. The anatomy shows that in insects and vertebrates, olfactory information passed to the brain can be summarized by activity in the glomeruli. We treat this activity in a firing-rate approximation, which allows us to use available receptor affinity data Hallem and Carlson, ; Saito et al.
This approximation neglects individual spike times, which can contain important information for odor discrimination in mammals and insects Resulaj and Rinberg, ; DasGupta and Waddell, ; Wehr and Laurent, ; Huston et al. Given data relating spike timing and odor exposure for different odorants and receptors, we could use the time from respiratory onset to the first elicited spike in each receptor as an indicator of activity in our model.
Alternatively, we could use both the timing and the firing rate information together. Such data is not yet available for large panels of odors and receptors, and so we leave the inclusion of timing effects for future work. A challenge specific to the study of the olfactory system as compared to other senses is the limited knowledge we have of the space of odors.
It is difficult to identify common features shared by odorants that activate a given receptor type Rossiter, ; Malnic et al. We are neglecting temporal correlations in olfactory cues because we are focusing on odor identity rather than olfactory search where timing of cues will be especially important.
This simplifies our model, and also reduces the number of olfactory scene parameters needed as inputs. Similar static approximations of natural images have been employed powerfully along with the efficient coding hypothesis to explain diverse aspects of early vision e. This can be thought of as a maximum-entropy approximation of the true distribution of odorant concentrations, constrained by the environmental means and covariances.
This simple environmental model misses some sparse structure that is typical in olfactory scenes Yu et al. Nevertheless, approximating natural distributions with Gaussians is common in the efficient-coding literature, and often captures enough detail to be predictive van Hateren, a ; van Hateren, b ; Van Hateren, ; Hermundstad et al.
This may be because early sensory systems in animals are able to adapt more effectively to low-order statistics which are easily represented by neurons in their mean activity and pairwise correlations.
The number N of odorants that we use to represent an environment need not be as large as the total number of possible volatile molecules. We can instead focus on only those odorants that are likely to be encountered at meaningful concentrations by the organism that we study, leading to a much smaller value for N.
In practice, however, we are limited by the available receptor affinity data. Our quantitative analyses are generally based on data measured using panels of odorants in fly Hallem and Carlson, and 63 in mammals Saito et al. We next build a model for how the activity at the glomeruli depends on the olfactory environment. We work in an approximation in which the responses depend linearly on the concentration values:. The approximation we are using can be seen as linearizing the responses of olfactory sensory neurons around an operating point.
This has been shown to accurately capture the response of olfactory receptors to odor mixtures in certain concentration ranges Singh et al.
While odor concentrations in natural scenes span many orders of magnitude and are unlikely to always stay within the linear regime, the effect of the nonlinearities on the information maximization procedure that we implement below is less strong see Appendix 3 for a comparison between our linear approximation and a nonlinear, competitive binding model in a toy example. One advantage of employing the linear approximation is that it requires a minimal set of parameters the sensing matrix coefficients S a i , while nonlinear models in general require additional information such as a Hill coefficient and a maximum activation for each receptor-odorant pair for a competitive binding model; see Appendix 3.
Given our assumptions, all these distributions are Gaussian, and the integral can be evaluated analytically see Appendix 2. The result is. Thus, it is a measure of the strength of the usable olfactory signal. In the linear approximation that we are using, the information transmitted through the system is the same whether all OSNs with the same receptor type converge to one or multiple glomeruli see Appendix 2.
Because of this, for convenience we take all neurons of a given type to converge onto a single glomerulus Figure 1a. The OSN numbers K a cannot grow without bound; they are constrained by the total number of neurons in the olfactory epithelium.
Throughout the paper, we treat the OSN abundances K a as real numbers instead of integers, which is a good approximation as long as they are not very small. The optimization can be performed analytically using the Karush-Kuhn-Tucker KKT conditions Boyd and Vandenberghe, see Appendix 2 , but in practice it is more convenient to use numerical optimization. Note that in contrast to other work that has used information maximization to study the olfactory system e.
Zwicker et al. Below we analyze how the optimal distribution of receptor types depends on receptor affinities, odor statistics, and the size of the olfactory epithelium. In our model, receptor noise is reduced by averaging over the responses from many sensory neurons. When this happens, the optimization with respect to OSN numbers K a can be solved analytically see Appendix 2 , and we find that the optimal receptor distribution is given by.
When K tot is sufficiently large, the constant first term dominates, meaning that the receptor distribution is essentially uniform, with each receptor type being expressed in a roughly equal fraction of the total population of sensory neurons. In this limit, the receptor distribution is as even and as diverse as possible given the genetically encoded receptor types.
Put another way, when the OSN numbers K a are very large, the glomerular responses are effectively noiseless, and the number of receptors of each type has little effect on the reliability of the responses. This scenario applies as long as the OSN abundances K a are much larger than the elements of the inverse overlap matrix A. In panels a—c the receptor sensing matrix is based on Drosophila Hallem and Carlson, and includes 24 receptors responding to odorants.
In panels d—e , the total number of OSNs K tot is fixed at In all panels, environmental odor statistics follow a random correlation matrix see Appendix 4.
Qualitative aspects are robust to variations in these choices see Appendix 1. Here, the odor environments and the receptor affinities are held fixed as the OSN population size is increased. For every position along the x -axis, sensing matrices with a fixed receptor tuning width were generated from a random ensemble, where the tuning width indicates what fraction of all odorants elicit a strong response for the receptors see Appendix 1. When each receptor responds strongly to only a small number of odorants, response variance is a good predictor of abundance, while this is no longer true for wide tuning.
In panels d—e , the red line is the mean obtained from 24 simulations, each performed using a different sensing matrix, and the light gray area shows the interval between the 20th and 80th percentiles of results. We use this as a proxy for the number of neurons in the olfactory epithelium. Dashed line is a least-squares fit. Number of intact OR genes from Niimura et al. When the number of neurons is very small, receptor noise can overwhelm the response to the environment.
In this case, the best strategy is to focus all the available neurons on a single receptor type, thus reducing noise by summation as much as possible Figure 2b. This is reminiscent of a result in vision where the variance of a stimulus predicted its perceptual salience Hermundstad et al. As the total number of neurons increases, the added benefit of summing to lower noise for a single receptor type diminishes, and at some critical value it is more useful to populate a second receptor type that provides unique information not available in responses of the first type Figure 2b.
This process continues as the number of neurons increases, so that in an intermediate SNR range, where noise is significant but does not overwhelm the olfactory signal, our model leads to a highly non-uniform distribution of receptor types see the trend in Figure 2b as the number of OSNs increases. Indeed, an inhomogeneous distribution of this kind is seen in mammals Ibarra-Soria et al.
Broadly, this is consistent with the idea that living systems conserve resources to the extent possible, and thus the number of OSNs and therefore the SNR will be selected to be in an intermediate range in which there are just enough to make all the available receptors useful. Our model predicts that, all else being equal, the number of receptor types that are expressed should increase monotonically with the total number of sensory neurons, in a series of step transitions see Figure 2c.
Keeping in mind that these conditions are not usually met by distinct species, we can nevertheless ask whether, broadly speaking, there is a relation between the number of functional receptor genes and the size of the olfactory epithelium in various species. To this end, we looked at several mammals for which the number of OR genes and the size of the olfactory epithelium were measured Figure 2f.
We focused on the intact OR genes Niimura et al. There is a known allometric scaling relation stating that the number of neurons per unit mass for a species decreases as the 0. We applied this relation to epithelial areas using the typical mass of several species Rousseeuw and Leroy, ; FCI, ; Gross et al.
The trend is consistent with expectations from our model Figure 2f , keeping in mind uncertainties due to species differences in olfactory environments, receptor affinities, and behavior e. A direct comparison is more complicated in insects, where even closely related species can vary widely in degree of specialization and thus can experience very different olfactory environments Dekker et al. We tested the effect of changing the variance of a single odorant, and found that the effect on the optimal receptor abundances depends on the context of the background olfactory environment.
Increased exposure to a particular ligand can lead to increased abundance of a given receptor type in one context, but to decreased abundance in another Figure 3. In fact, patterns of this kind have been reported in recent experiments Santoro and Dulac, ; Zhao et al. To understand this context-dependence better, we analyzed the predictions of our model in various signal and noise scenarios.
Panel b zooms in on the central part of panel a. In light blue regions, the sign of the abundance change is the same in the two contexts; light pink regions indicate opposite sign changes in the two contexts.
In both figures, dark red indicates high-density regions where there are many overlapping data points. This is because it corresponds to odors that are always present and therefore offer no new information about the environment.
This is consistent with experiment Ibarra-Soria et al. The problem of maximizing the amount of information that OSN responses convey about the odor environment simplifies considerably if these responses are weakly correlated. In this case, standard efficient coding theory says that receptors whose activities fluctuate more extensively in response to the olfactory environment provide more information to brain, while receptors that are active at a constant rate or are very noisy provide less information.
In this circumstance, neurons expressing receptors with large signal-to-noise ratio SNR, i. Responses are less correlated if receptors are narrowly tuned, and we find indeed that if each receptor type responds to only a small number of odorants, the abundances of OSNs of each type correlate well with their variability in the environment narrow-tuning side of Figure 2d. The biological setting is better described in terms of widely tuned sensing matrices Hallem and Carlson, , and an intermediate SNR level in which noise is important, but does not dominate the responses of most receptors.
We therefore generated sensing matrices with varying tuning width by changing the number of odorants that elicit strong activity in each receptor as detailed in Appendix 1. We found that as receptors begin responding to a greater diversity of odorants, the correlation structure of their activity becomes important in determining the optimal receptor distribution; it is no longer sufficient to just examine the signal to noise ratios of each receptor type separately as a conventional theory suggests wide-tuning side of Figure 2d.
In other words, the optimal abundance of a receptor type depends not just on its activity level, but also on the context of the correlated activity levels of all the other receptor types. These correlations are determined by the covariance structures of the environment and of the sensing matrix. For narrow tuning widths, the overlap matrix Q is approximately diagonal because correlations between receptors are weak and so Q - 1 is simply the matrix of the inverse diagonal elements of Q.
Thus, in this limit, the correlation with Q - 1 simply follows from the correlation with Q that we discussed above. As the tuning width increases keeping the total number of OSNs K tot constant, the responses from each receptor grow stronger, increasing the SNR, even as the off-diagonal elements of the overlap matrix Q become significant.
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. Olfactory receptors were discovered 30 years ago. But scientists have not been able to actually see them up close and decipher their structural and mechanistic workings, in part because these receptors didn't lend themselves to commonly available molecular imaging methods. Complicating the matter, there seems to be no rhyme or reason to the receptors' preferences -- an individual odor receptor can respond to compounds that are both structurally and chemically different.
This technique, which involves beaming electrons at a frozen specimen, can reveal extremely small molecular constructs in 3D, down to their individual atoms.
The team turned to the jumping bristletail, a ground-dwelling insect whose genome has been recently sequenced and has only five kinds of olfactory receptors. Although the jumping bristletail's olfactory system is simple, its receptors belong to a large family of receptors with tens of millions of variants thought to exist in the hundreds of thousands of different insect species.
Despite their diversity, these receptors function the same way: They form an ion channel -- a pore through which charged particles flow -- that opens only when the receptor encounters its target odorant, ultimately activating the sensory cells that initiate the sense of smell.
The researchers chose OR5, a receptor from the jumping bristletail with broad recognition ability, responding to 60 percent of small molecules they tested.
They then examined OR5's structure alone and also bound to a chemical, either eugenol, a common odor molecule, or DEET, the insect repellent. With the structures in hand, the team looked closer to see exactly where and how the two chemically different molecules bind to the receptor. There have been two ideas about odor receptors' interactions with molecules. One is that the receptors have evolved to distinguish large swaths of molecules by responding to a partial but defining feature of a molecule, such as a part of its shape.
Other researchers have proposed that each receptor packs multiple pockets on its surface at once, allowing it to accommodate a number of different molecules. But what Ruta found fit neither of those scenarios. It turned out that both DEET and eugenol bind at the same location and fit entirely inside a simple pocket within the receptor.
And surprisingly, the amino acids lining the pocket didn't form strong, selective chemical bonds with the odorants, but only weak bonds. Whereas in most other systems, receptors and their target molecules are good chemical matches, here they seemed more like friendly acquaintances.
Rather, it's recognizing the more general chemical nature of the odorant," Ruta says.
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