Humans can discriminate more than 1 trillion olfactory stimuli.

Humans can discriminate several million different colors and almost half a million different tones, but the number of discriminable olfactory stimuli remains unknown. The lay and scientific literature typically claims that humans can discriminate 10,000 odors, but this number has never been empirically validated. We determined the resolution of the human sense of smell by testing the capacity of humans to discriminate odor mixtures with varying numbers of shared components. On the basis of the results of psychophysical testing, we calculated that humans can discriminate at least 1 trillion olfactory stimuli. This is far more than previous estimates of distinguishable olfactory stimuli. It demonstrates that the human olfactory system, with its hundreds of different olfactory receptors, far outperforms the other senses in the number of physically different stimuli it can discriminate.

Instantaneous frequency decomposition: an application to spectrally sparse sounds with fast frequency modulations.

Classical time-frequency analysis is based on the amplitude responses of bandpass filters, discarding phase information. Instantaneous frequency analysis, in contrast, is based on the derivatives of these phases. This method of frequency calculation is of interest for its high precision and for reasons of similarity to cochlear encoding of sound. This article describes a methodology for high resolution analysis of sparse sounds, based on instantaneous frequencies. In this method, a comparison between tonotopic and instantaneous frequency information is introduced to select filter positions that are well matched to the signal. Second, a cross-check that compares frequency estimates from neighboring channels is used to optimize filter bandwidth, and to signal the quality of the analysis. These cross-checks lead to an optimal time-frequency representation without requiring any prior information about the signal. When applied to a signal that is sufficiently sparse, the method decomposes the signal into separate time-frequency contours that are tracked with high precision. Alternatively, if the signal is spectrally too dense, neighboring channels generate inconsistent estimates-a feature that allows the method to assess its own validity in particular contexts. Similar optimization principles may be present in cochlear encoding.

Unsupervised learning and adaptation in a model of adult neurogenesis.

Adult neurogenesis has long been documented in the vertebrate brain and recently even in humans. Although it has been conjectured for many years that its functional role is related to the renewing of memories, no clear mechanism as to how this can be achieved has been proposed. Using the mammalian olfactory bulb as a paradigm, we present a scheme in which incorporation of new neurons proceeds at a constant rate, while their survival is activity-dependent and thus contingent on new neurons establishing suitable connections. We show that a simple mathematical model following these rules organizes its activity so as to maximize the difference between its responses and can adapt to changing environmental conditions in unsupervised fashion, in agreement with current neurophysiological data.

Evidence of a Hopf bifurcation in frog hair cells.

The membrane potential of hair cells in the low-frequency hearing organ of the bullfrog, the amphibian papilla, sinusoidally oscillates at small amplitude in the absence of acoustical input. We stimulate the cell with a series of periodic currents close to this natural frequency and observe that its current-to-voltage transfer function is compressively nonlinear, having a large gain for small stimuli and a smaller gain for larger currents. Along with the spontaneous oscillation, this implies that the cell is poised close to a dynamical instability such as a Hopf bifurcation, because distant from the instability the transfer function becomes linear. The cell's frequency selectivity is enhanced for small stimuli. Simulations show that the cell's membrane capacitance is effectively reduced due to a current gain provided by this dynamical instability. We propose that the Hopf resonance is widely used by transducer cells on the sensory periphery to achieve small-signal amplification.

Kinetic proofreading can explain the supression of supercoiling of circular DNA molecules by type-II topoisomerases.

The enzymes that pass DNA through DNA so as to remove entanglements, adenosine-triphosphate-hydrolyzing type-II topoisomerases, are able to suppress the probability of self-entanglements (knots) and mutual entanglements (links) between approximately 10 kb plasmids, well below the levels expected, given the assumption that the topoisomerases pass DNA segments at random by thermal motion. This implies that a 10-nm type-II topoisomerase can somehow sense the topology of a large DNA. We previously introduced a "kinetic proofreading" model which supposes the enzyme to require two successive collisions in order to allow exchange of DNA segments, and we showed how it could quantitatively explain the reduction in knotting and linking complexity. Here we show how the same model quantitatively explains the reduced variance of the double-helix linking number (supercoiling) distribution observed experimentally.

On a common circle: natural scenes and Gestalt rules.

To understand how the human visual system analyzes images, it is essential to know the structure of the visual environment. In particular, natural images display consistent statistical properties that distinguish them from random luminance distributions. We have studied the geometric regularities of oriented elements (edges or line segments) present in an ensemble of visual scenes, asking how much information the presence of a segment in a particular location of the visual scene carries about the presence of a second segment at different relative positions and orientations. We observed strong long-range correlations in the distribution of oriented segments that extend over the whole visual field. We further show that a very simple geometric rule, cocircularity, predicts the arrangement of segments in natural scenes, and that different geometrical arrangements show relevant differences in their scaling properties. Our results show similarities to geometric features of previous physiological and psychophysical studies. We discuss the implications of these findings for theories of early vision.

Noise-induced memory in extended excitable systems.

We describe a form of memory exhibited by extended excitable systems driven by stochastic fluctuations. Under such conditions, the system self-organizes into a state characterized by power-law correlations, thus retaining long-term memory of previous states. The exponents are robust and model independent. We discuss implications of these results for the functioning of cortical neurons as well as for networks of neurons.

Essential nonlinearities in hearing.

Our hearing organ, the cochlea, evidently poises itself at a Hopf bifurcation to maximize tuning and amplification. We show that in this condition several effects are expected to be generic: compression of the dynamic range, infinitely sharp tuning at zero input, and generation of combination tones. These effects are "essentially" nonlinear in that they become more marked the smaller the forcing: there is no audible sound soft enough not to evoke them. All the well-documented nonlinear aspects of hearing therefore appear to be consequences of the same underlying mechanism.

Noise in neurons is message dependent.

Neuronal responses are conspicuously variable. We focus on one particular aspect of that variability: the precision of action potential timing. We show that for common models of noisy spike generation, elementary considerations imply that such variability is a function of the input, and can be made arbitrarily large or small by a suitable choice of inputs. Our considerations are expected to extend to virtually any mechanism of spike generation, and we illustrate them with data from the visual pathway. Thus, a simplification usually made in the application of information theory to neural processing is violated: noise is not independent of the message. However, we also show the existence of error-correcting topologies, which can achieve better timing reliability than their components.

A kinetic proofreading mechanism for disentanglement of DNA by topoisomerases.

Cells must remove all entanglements between their replicated chromosomal DNAs to segregate them during cell division. Entanglement removal is done by ATP-driven enzymes that pass DNA strands through one another, called type II topoisomerases. In vitro, some type II topoisomerases can reduce entanglements much more than expected, given the assumption that they pass DNA segments through one another in a random way. These type II topoisomerases (of less than 10 nm in diameter) thus use ATP hydrolysis to sense and remove entanglements spread along flexible DNA strands of up to 3,000 nm long. Here we propose a mechanism for this, based on the higher rate of collisions along entangled DNA strands, relative to collision rates on disentangled DNA strands. We show theoretically that if a type II topoisomerase requires an initial 'activating' collision before a second strand-passing collision, the probability of entanglement may be reduced to experimentally observed levels. This proposed two-collision reaction is similar to 'kinetic proofreading' models of molecular recognition.

An automated system for the mapping and quantitative analysis of immunocytochemistry of an inducible nuclear protein.

We describe here an automated system that accurately maps tissue sections stained by immunocytochemistry for an inducible nuclear protein. The sections are scanned with a computer-controlled microscope setup hooked to a CCD camera. Raw images captured at high resolution are filtered using highly selective criteria for the recognition of labeled cell nuclei. The total population of recognized labeled nuclei is then divided into separate bins, according to their labeling intensities. Finally, information about both the position and labeling intensity of labeled nuclei is represented in average density maps. The system was optimized for the quantitative mapping of neuronal cells expressing the inducible gene ZENK in the brain of songbirds, in response to stimulation with song, but should be of general applicability for the mapping of inducible nuclear proteins.

A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels.

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system's behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken's cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

Toward a song code: evidence for a syllabic representation in the canary brain.

We show that presentation of individual canary song syllables results in distinct expression patterns of the immediate-early gene ZENK in the caudomedial neostriatum (NCM) of adult canaries. Information on the spatial distribution and labeling of stained cells provides for a classification of ZENK patterns that (1) accords to the organization of stimuli into families, (2) preserves the stimuli intrafamily relationships, and (3) confers salience to natural over artificial stimuli, resulting in a nonclassical tonotopic map. Moreover, complex syllable maps cannot be reduced to any linear combinations of simple syllable maps. These properties arise from the collective response of NCM neurons to auditory stimuli, rather than from the behavior of single neurons. The syllabic representation described here may constitute an important step toward deciphering the rules of birdsong auditory representation.

Periodically kicked hard oscillators.

A model of a hard oscillator with analytic solution is presented. Its behavior under periodic kicking, for which a closed form stroboscopic map can be obtained, is studied. It is shown that the general structure of such an oscillator includes four distinct regions; the outer two regions correspond to very small or very large amplitude of the external force and match the corresponding regions in soft oscillators (invertible degree one and degree zero circle maps, respectively). There are two new regions for intermediate amplitude of the forcing. Region 3 corresponds to moderate high forcing, and is intrinsic to hard oscillators; it is characterized by discontinuous circle maps with a flat segment. Region 2 (low moderate forcing) has a certain resemblance to a similar region in soft oscillators (noninvertible degree one circle maps); however, the limit set of the dynamics in this region is not a circle, but a branched manifold, obtained as the tangent union of a circle and an interval; the topological structure of this object is generated by the finite size of the repelling set, and is therefore also intrinsic to hard oscillators.