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Animals smelling in the real world use a small number of receptors to sense a vast number of natural molecular mixtures, and proceed to learn arbitrary associations between odors and valences. Here, we propose how the architecture of olfactory circuits leverages disorder, diffuse sensing and redundancy in representation to meet these immense complementary challenges. First, the diffuse and disordered binding of receptors to many molecules compresses a vast but sparsely-structured odor space into a small receptor space, yielding an odor code that preserves similarity in a precise sense. Introducing any order/structure in the sensing degrades similarity preservation. Next, lateral interactions further reduce the correlation present in the low-dimensional receptor code. Finally, expansive disordered projections from the periphery to the central brain reconfigure the densely packed information into a high-dimensional representation, which contains multiple redundant subsets from which downstream neurons can learn flexible associations and valences. Moreover, introducing any order in the expansive projections degrades the ability to recall the learned associations in the presence of noise. We test our theory empirically using data from Drosophila . Our theory suggests that the neural processing of sparse but high-dimensional olfactory information differs from the other senses in its fundamental use of disorder. 

Some bacteria and archaea possess an immune system, based on the CRISPR-Cas mechanism, that confers adaptive immunity against viruses. In such species, individual prokaryotes maintain cassettes of viral DNA elements called spacers as a memory of past infections. Typically, the cassettes contain several dozen expressed spacers. Given that bacteria can have very large genomes and since having more spacers should confer a better memory, it is puzzling that so little genetic space would be devoted by prokaryotes to their adaptive immune systems. Here, assuming that CRISPR functions as a long-term memory-based defense against a diverse landscape of viral species, we identify a fundamental tradeoff between the amount of immune memory and effectiveness of response to a given threat. This tradeoff implies an optimal size for the prokaryotic immune repertoire in the observational range. 

Previously, in Hermundstad et al., 2014, we showed that when sampling is limiting, the efficient coding principle leads to a ‘variance is salience’ hypothesis, and that this hypothesis accounts for visual sensitivity to binary image statistics. Here, using extensive new psychophysical data and image analysis, we show that this hypothesis accounts for visual sensitivity to a large set of grayscale image statistics at a striking level of detail, and also identify the limits of the prediction. We define a 66-dimensional space of local grayscale light-intensity correlations, and measure the relevance of each direction to natural scenes. The ‘variance is salience’ hypothesis predicts that two-point correlations are most salient, and predicts their relative salience. We tested these predictions in a texture-segregation task using un-natural, synthetic textures. As predicted, correlations beyond second order are not salient, and predicted thresholds for over 300 second-order correlations match psychophysical thresholds closely (median fractional error <0.13). 

An adaptive agent predicting the future state of an environment must weigh trust in new observations against prior experiences. In this light, we propose a view of the adaptive immune system as a dynamic Bayesian machinery that updates its memory repertoire by balancing evidence from new pathogen encounters against past experience of infection to predict and prepare for future threats. This framework links the observed initial rapid increase of the memory pool early in life followed by a midlife plateau to the ease of learning salient features of sparse environments. We also derive a modulated memory pool update rule in agreement with current vaccine-response experiments. Our results suggest that pathogenic environments are sparse and that memory repertoires significantly decrease infection costs, even with moderate sampling. The predicted optimal update scheme maps onto commonly considered competitive dynamics for antigen receptors. 

A mouse’s nose contains over 10 million receptor neurons divided into about 1,000 different types, which detect airborne chemicals – called odorants – that make up smells. 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. Teşileanu et al. set out to develop a computer model that can explain these observations. 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. Teşileanu et al. show that exposure to odorants leads to reproducible increases or decreases in different receptor types, depending on what would provide the brain with most information. 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. 

In color vision, the quantitative rules for mixing lights to make a target color are well understood. By contrast, the rules for mixing odorants to make a target odor remain elusive. A solution to this problem in vision relied on characterizing receptor responses to different wavelengths of light and subsequently relating these responses to perception. In olfaction, experimentally measuring receptor responses to a representative set of complex mixtures is intractable due to the vast number of possibilities. To meet this challenge, we develop a biophysical model that predicts mammalian receptor responses to complex mixtures using responses to single odorants. The dominant nonlinearity in our model is competitive binding (CB): Only one odorant molecule can attach to a receptor binding site at a time. This simple framework predicts receptor responses to mixtures of up to 12 monomolecular odorants to within 15% of experimental observations and provides a powerful method for leveraging limited experimental data. Simple extensions of our model describe phenomena such as synergy, overshadowing, and inhibition. We demonstrate that the presence of such interactions can be identified via systematic deviations from the competitive-binding model.

 

In familiar environments, the firing fields of entorhinal grid cells form regular triangular lattices. However, when the geometric shape of the environment is deformed, these time-averaged grid patterns are distorted in a grid scale-dependent and local manner. We hypothesized that this distortion in part reflects dynamic anchoring of the grid code to displaced boundaries, possibly through border cell-grid cell interactions. To test this hypothesis, we first reanalyzed two existing rodent grid rescaling datasets to identify previously unrecognized boundary-tethered shifts in grid phase that contribute to the appearance of rescaling. We then demonstrated in a computational model that boundary-tethered phase shifts, as well as scale-dependent and local distortions of the time-averaged grid pattern, could emerge from border-grid interactions without altering inherent grid scale. Together, these results demonstrate that environmental deformations induce history-dependent shifts in grid phase, and implicate border-grid interactions as a potential mechanism underlying these dynamics. 

Place and grid cells in the hippocampal formation are commonly thought to support a unified and coherent cognitive map of space. This mapping mechanism faces a challenge when a navigator is placed in a familiar environment that has been deformed from its original shape. Under such circumstances, many transformations could plausibly serve to map a navigator's familiar cognitive map to the deformed space. Previous empirical results indicate that the firing fields of rodent place and grid cells stretch or compress in a manner that approximately matches the environmental deformation, and human spatial memory exhibits similar distortions. These effects have been interpreted as evidence that reshaping a familiar environment elicits an analogously reshaped cognitive map. However, recent work has suggested an alternative explanation, whereby deformation‐induced distortions of the grid code are attributable to a mechanism that dynamically anchors grid fields to the most recently experienced boundary, thus causing history‐dependent shifts in grid phase. This interpretation raises the possibility that human spatial memory will exhibit similar history‐dependent dynamics. To test this prediction, we taught participants the locations of objects in a virtual environment and then probed their memory for these locations in deformed versions of this environment. Across three experiments with variable access to visual and vestibular cues, we observed the predicted pattern, whereby the remembered locations of objects were shifted from trial to trial depending on the boundary of origin of the participant's movement trajectory. These results provide evidence for a dynamic anchoring mechanism that governs both neuronal firing and spatial memory.