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Introduction: Recent work on bats flying over long distances has revealed that single hippocampal cells have multiple place fields of different sizes. At the network level, a multi-scale, multi-field place cell code outperforms classical single-scale, single-field place codes, yet the performance boundaries of such a code remain an open question. In particular, it is unknown how general multi- field codes compare to a highly regular grid code, in which cells form distinct modules with different scales. Methods: In this work, we address the coding properties of theoretical spatial coding models with rigorous analyses of comprehensive simulations. Starting fromamulti-scale,multi-field network, we performed evolutionary optimization. The resulting multi-field networks sometimes retained the multi-scale property at the single-cell level but most often converged to a single scale, with all place fields in a given cell having the same size. We compared the results against a single-scale single-field code and a one-dimensional grid code, focusing on two main characteristics: the performance of the code itself and the dynamics of the network generating it. Results: Our simulation experiments revealed that, under normal conditions, a regular grid code outperforms all other codes with respect to decoding accuracy, achieving a given precision with fewer neurons and fields. In contrast, multi- field codes are more robust against noise and lesions, such as random drop- out of neurons, given that the significantly higher number of fields provides redundancy. Contrary to our expectations, the network dynamics of all models, from the original multi-scale models before optimization to the multi-field models that resulted from optimization, did not maintain activity bumps at their original locations when a position-specific external input was removed. Discussion: Optimizedmulti-field codes appear to strike a compromise between a place code and a grid code that reflects a trade-off between accurate positional encoding and robustness. Surprisingly, the recurrent neural network models we implemented and optimized for either multi- or single-scale, multi-field codes did not intrinsically produce a persistent "memory" of attractor states. These models, therefore, were not continuous attractor networks. [ABSTRACT FROM AUTHOR]

Grid cells in medial entorhinal cortex are notoriously variable in their responses, despite the striking hexagonal arrangement of their spatial firing fields. Indeed, when the animal moves through a firing field, grid cells often fire much more vigorously than predicted or do not fire at all. The source of this trial‐to‐trial variability is not completely understood. By analyzing grid‐cell spike trains from mice running in open arenas and on linear tracks, we characterize the phenomenon of "missed" firing fields using the statistical theory of zero inflation. We find that one major cause of grid‐cell variability lies in the spatial representation itself: firing fields are not as strongly anchored to spatial location as the averaged grid suggests. In addition, grid fields from different cells drift together from trial to trial, regardless of whether the environment is real or virtual, or whether the animal moves in light or darkness. Spatial realignment across trials sharpens the grid representation, yielding firing fields that are more pronounced and significantly narrower. These findings indicate that ensembles of grid cells encode relative position more reliably than absolute position. [ABSTRACT FROM AUTHOR]

The pick-up technique has been employed to deposite single methanol molecules as chromophores on the surface of large Arx host clusters. At higher densities of the guest molecules in the interaction region, more than one methanol molecule are adsorbed on the host cluster and, hence, dimers or even larger complexes can be formed. The methanol complexes are carried by the Arx substrate clusters to the detector and are analyzed with a mass spectrometer. It turns out that the commonly encountered protonation reaction leading to the fragmentation of the ionized methanol complexes is appreciably quenched. The technique is then combined with molecular beam depletion experiments employing the infrared radiation of a pulsed CO2 laser. In the region between 1000 and 1100 cm-1, which covers the ν8 CO stretch and the ν7 CH3 rock monomer vibrations, absorption spectra have been measured for the methanol monomer as well as the methanol dimer, trimer, and tetramer adsorbed on large Arx substrate clusters. For the monomer, both vibrations are observed. The dimer spectrum features three peaks and resembles very much the spectrum obtained in a previous study of the free gas-phase dimer, except that all lines are shifted to the red by ∼2 cm-1. From this observation it is concluded that the methanol dimer on the Arx host cluster adopts the same structure as in the gas phase. Whereas this observation has also been made for the trimer, the tetramer spectrum is distinctly different. [ABSTRACT FROM AUTHOR]

Examines the photodissociation of the allyl radical using photofragment translational spectroscopy. Dissociation processes from the ground-state C3H5 potential energy surface; Contribution to H-atom loss channel from predissociation by an electronically excited state; Importance of cyclopropene formation in Rice-Ramsperger-Kassel-Marcus calculations.

The release of neurotransmitters from synapses obeys complex and stochastic dynamics. Depending on the recent history of synaptic activation, many synapses depress the probability of releasing more neurotransmitter, which is known as synaptic depression. Our understanding of how synaptic depression affects the information efficacy, however, is limited. Here we propose a mathematically tractable model of both synchronous spike-evoked release and asynchronous release that permits us to quantify the information conveyed by a synapse. The model transits between discrete states of a communication channel, with the present state depending on many past time steps, emulating the gradual depression and exponential recovery of the synapse. Asynchronous and spontaneous releases play a critical role in shaping the information efficacy of the synapse. We prove that depression can enhance both the information rate and the information rate per unit energy expended, provided that synchronous spike-evoked release depresses less (or recovers faster) than asynchronous release. Furthermore, we explore the theoretical implications of short-term synaptic depression adapting on longer time scales, as part of the phenomenon of metaplasticity. In particular, we show that a synapse can adjust its energy expenditure by changing the dynamics of short-term synaptic depression without affecting the net information conveyed by each successful release. Moreover, the optimal input spike rate is independent of the amplitude or time constant of synaptic depression. We analyze the information efficacy of three types of synapses for which the short-term dynamics of both synchronous and asynchronous release have been experimentally measured. In hippocampal autaptic synapses, the persistence of asynchronous release during depression cannot compensate for the reduction of synchronous release, so that the rate of information transmission declines with synaptic depression. In the calyx of Held, the information rate per release remains constant despite large variations in the measured asynchronous release rate. Lastly, we show that dopamine, by controlling asynchronous release in corticostriatal synapses, increases the synaptic information efficacy in nucleus accumbens. [ABSTRACT FROM AUTHOR]

Synapses are the communication channels for information transfer between neurons; these are the points at which pulse-like signals are converted into the stochastic release of quantized amounts of chemical neurotransmitter. At many synapses, prior neuronal activity depletes synaptic resources, depressing subsequent responses of both spontaneous and spike-evoked releases. We analytically compute the information transmission rate of a synaptic release site, which we model as a binary asymmetric channel. Short-term depression is incorporated by assigning the channel a memory of depth one. A successful release, whether spike evoked or spontaneous, decreases the probability of a subsequent release; if no release occurs on the following time step, the release probabilities recover back to their default values. We prove that synaptic depression can increase the release site's information rate if spontaneous release is more strongly depressed than spike-evoked release. When depression affects spontaneous and evoked release equally, the information rate must invariably decrease, even when the rate is normalized by the resources used for synaptic transmission. For identical depression levels, we analytically disprove the hypothesis, at least in this simplified model, that synaptic depression serves energy- and information-efficient encoding. [ABSTRACT FROM AUTHOR]

The article discusses on the higher dimensional stimulus domains in the grid cell activity patterns in mammals. The author focuses on the neuronal lattice codes that maximize spatial resolution and suggests hexagonal structure for mammals on land and face centered cubic lattice for three dimensional movement.

As a rat moves, grid cells in its entorhinal cortex (EC) discharge at multiple locations of the external world, and the firing fields of each grid cell span a hexagonal lattice. For movements on linear tracks, spikes tend to occur at successively earlier phases of the theta-band filtered local field potential during the traversal of a firing field – a phenomenon termed phase precession. The complex movement patterns observed in two-dimensional (2D) open-field environments may fundamentally alter phase precession. To study this question at the behaviorally relevant single-run level, we analyzed EC spike patterns as a function of the distance traveled by the rat along each trajectory. This analysis revealed that cells across all EC layers fire spikes that phase-precess; indeed, the rate and extent of phase precession were the same, only the correlation between spike phase and path length was weaker in EC layer III. Both slope and correlation of phase precession were surprisingly similar on linear tracks and in 2D open-field environments despite strong differences in the movement statistics, including running speed. While the phase-precession slope did not correlate with the average running speed, it did depend on specific properties of the animal's path. The longer a curving path through a grid-field in a 2D environment, the shallower was the rate of phase precession, while runs that grazed a grid field tangentially led to a steeper phase-precession slope than runs through the field center. Oscillatory interference models for grid cells do not reproduce the observed phenomena. [ABSTRACT FROM AUTHOR]

Maintaining the ability of the nervous system to perceive, remember, process, and react to the outside world requires a continuous energy supply. Yet the overall power consumption is remarkably low, which has inspired engineers to mimic nervous systems in designing artificial cochlea, retinal implants, and brain–computer interfaces (BCIs) to improve the quality of life in patients. Such neuromorphic devices are both energy efficient and increasingly able to emulate many functions of the human nervous system. We examine the energy constraints of neuronal signaling within biology, review the quantitative tradeoff between energy use and information processing, and ask whether the biophysics and design of nerve cells minimizes energy consumption. [ABSTRACT FROM PUBLISHER]

In systems biology, questions concerning the molecular and cellular makeup of an organism are of utmost importance, especially when trying to understand how unreliable components—like genetic circuits, biochemical cascades, and ion channels, among others—enable reliable and adaptive behaviour. The repertoire and speed of biological computations are limited by thermodynamic or metabolic constraints: an example can be found in neurons, where fluctuations in biophysical states limit the information they can encode—with almost 20–60% of the total energy allocated for the brain used for signalling purposes, either via action potentials or by synaptic transmission. Here, we consider the imperatives for neurons to optimise computational and metabolic efficiency, wherein benefits and costs trade-off against each other in the context of self-organised and adaptive behaviour. In particular, we try to link information theoretic (variational) and thermodynamic (Helmholtz) free-energy formulations of neuronal processing and show how they are related in a fundamental way through a complexity minimisation lemma. [ABSTRACT FROM AUTHOR]

Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolutionwhen decoding the animal's position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population.We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, usingmaximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial "tuning curves" for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons. [ABSTRACT FROM AUTHOR]

The initiation and propagation of action potentials (APs) places high demands on the energetic resources of neural tissue. Each AP forces ATP-driven ion pumps to work harder to restore the ionic concentration gradients, thus consuming more energy. Here, we ask whether the ionic currents underlying the AP can be predicted theoretically from the principle of minimum energy consumption. A long-held supposition that APs are energetically wasteful, based on theoretical analysis of the squid giant axon AP, has recently been overturned by studies that measured the currents contributing to the AP in several mammalian neurons. In the single compartment models studied here, AP energy consumption varies greatly among vertebrate and invertebrate neurons, with several mammalian neuron models using close to the capacitive minimum of energy needed. Strikingly, energy consumption can increase by more than ten-fold simply by changing the overlap of the Na+ and K+ currents during the AP without changing the APs shape. As a consequence, the height and width of the AP are poor predictors of energy consumption. In the Hodgkin-Huxley model of the squid axon, optimizing the kinetics or number of Na+ and K+ channels can whittle down the number of ATP molecules needed for each AP by a factor of four. In contrast to the squid AP, the temporal profile of the currents underlying APs of some mammalian neurons are nearly perfectly matched to the optimized properties of ionic conductances so as to minimize the ATP cost. [ABSTRACT FROM AUTHOR]

The nervous system adapts to experience by changes in synaptic strength. The mechanisms of synaptic plasticity include changes in the probability of transmitter release and in postsynaptic responsiveness. Experimental and neuropharmacological evidence points toward a third variable in synaptic efficacy: changes in presynaptic transmitter concentration. Several groups, including our own, have reported changes in the amplitude and frequency of postsynaptic (miniature) events indicating that alterations in transmitter content cause alterations in vesicular transmitter content and vesicle dynamics. It is, however, not a priori clear how transmitter metabolism will affect vesicular transmitter content and how this in turn will affect pre- and postsynaptic functions. We therefore have constructed a model of the presynaptic terminal incorporating vesicular transmitter loading and the presynaptic vesicle cycle. We hypothesize that the experimentally observed synaptic plasticity after changes in transmitter metabolism puts predictable restrictions on vesicle loading, cytoplasmic-vesicular transmitter concentration gradient, and on vesicular cycling or release. The results of our model depend on the specific mechanism linking presynaptic transmitter concentration to vesicular dynamics, that is, alteration of vesicle maturation or alteration of release. It also makes a difference whether differentially filled vesicles are detected and differentially processed within the terminal or whether vesicle filling acts back onto the terminal by presynaptic autoreceptors. Therefore, the model allows one to decide, at a given synapse, how transmitter metabolism is linked to presynaptic function and efficacy. [ABSTRACT FROM AUTHOR]

Information from the senses must be compressed into the limited range of responses that spiking neurons can generate. For optimal compression, the neuron's response should match the statistics of stimuli encountered in nature. Given a maximum firing rate, a nerve cell should learn to use each available firing rate equally often. Given a set mean firing rate, it should self-organize to respond with high firing rates only to comparatively rare events. Here we derive an unsupervised learning rule that continuously adapts membrane conductances of a Hodgkin-Huxley model neuron to optimize the representation of sensory information in the firing rate. Maximizing information transfer between the stimulus and the cell's firing rate can be interpreted as a non-Hebbian developmental mechanism. [ABSTRACT FROM AUTHOR]

Action potentials (spikes) can trigger the release of a neurotransmitter at chemical synapses between neurons. Such release is uncertain, as it occurs only with a certain probability. Moreover, synaptic release can occur independently of an action potential (asynchronous release) and depends on the history of synaptic activity. We focus here on short-term synaptic facilitation, in which a sequence of action potentials can temporarily increase the release probability of the synapse. In contrast to the phenomenon of short-term depression, quantifying the information transmission in facilitating synapses remains to be done. We find rigorous lower and upper bounds for the rate of information transmission in a model of synaptic facilitation. We treat the synapse as a two-state binary asymmetric channel, in which the arrival of an action potential shifts the synapse to a facilitated state, while in the absence of a spike, the synapse returns to its baseline state. The information bounds are functions of both the asynchronous and synchronous release parameters. If synchronous release facilitates more than asynchronous release, the mutual information rate increases. In contrast, short-term facilitation degrades information transmission when the synchronous release probability is intrinsically high. As synaptic release is energetically expensive, we exploit the information bounds to determine the energy–information trade-off in facilitating synapses. We show that unlike information rate, the energy-normalized information rate is robust with respect to variations in the strength of facilitation. [ABSTRACT FROM AUTHOR]

The article discusses a study that compares grid coding versus place coding for navigation using spiking neurons. It presents two different interpretations of the grid population code, which include an effective way of subdividing space with high resolution and modular arithmetic. It investigates that spatial resolution of both codes on a limited, one-dimensional space with a finite amount of cells and families of tuning curves.

Animals that rely on acoustic communication to find mates, such as grasshoppers, are astonishingly accurate in recognizing song patterns that are specific to their own species. This raises the question of whether they can also solve a far more complicated task that might provide a basis for mate preference and sexual selection: to distinguish individual songs by detecting slight variations around the common species-specific theme. Using spike-train discriminability to quantify the precision of neural responses from the auditory periphery of a model grasshopper species, we show that information sufficient to distinguish songs is readily available at the single-cell level when the spike trains are analyzed on a millisecond time scale. [ABSTRACT FROM AUTHOR]

Encoding information about continuous variables using noisy computational units is a challenge; nonetheless, asymptotic theory shows that combining multiple periodic scales for coding can be highly precise despite the corrupting influence of noise [Mathis, Herz, and Stemmler, Phys. Rev. Lett. 109, 018103 (2012)]. Indeed, the cortex seems to use periodic, multiscale grid codes to represent position accurately. Here we show how such codes can be read out without taking the long-term limit; even on short time scales, the precision of such codes scales exponentially in the number N of neurons. Does this finding also hold for neurons that are not firing in a statistically independent fashion? To assess the extent to which biological grid codes are subject to statistical dependences, we first analyze the noise correlations between pairs of grid code neurons in behaving rodents. We find that if the grids of two neurons align and have the same length scale, the noise correlations between the neurons can reach values as high as 0.8. For increasing mismatches between the grids of the two neurons, the noise correlations fall rapidly. Incorporating such correlations into a population coding model reveals that the correlations lessen the resolution, but the exponential scaling of resolution with N is unaffected. [ABSTRACT FROM AUTHOR]

Collective computation is typically polynomial in the number of computational elements, such as transistors or neurons, whether one considers the storage capacity of a memory device or the number of floating-point operations per second of a CPU. However, we show here that the capacity of a computational network to resolve real-valued signals of arbitrary dimensions can be exponential in N, even if the individual elements are noisy and unreliable. Nested, modular codes that achieve such high resolutions mirror the properties of grid cells in vertebrates, which underlie spatial navigation. [ABSTRACT FROM AUTHOR]