Carina Curto

A Simple Model of Cortical Dynamics Explains Variability and State Dependence of Sensory Responses in Urethane-Anesthetized Auditory Cortex

The responses of neocortical cells to sensory stimuli are variable and state dependent. It has been hypothesized that intrinsic cortical dynamics play an important role in trial-to-trial variability; the precise nature of this dependence, however, is poorly understood. We show here that in auditory cortex of urethane-anesthetized rats, population responses to click stimuli can be quantitatively predicted on a trial-by-trial basis by a simple dynamical system model estimated from spontaneous activity immediately preceding stimulus presentation. Changes in cortical state correspond consistently to changes in model dynamics, reflecting a nonlinear, self-exciting system in synchronized states and an approximately linear system in desynchronized states. We propose that the complex and state-dependent pattern of trial-to-trial variability can be explained by a simple principle: sensory responses are shaped by the same intrinsic dynamics that govern ongoing spontaneous activity.

Auroral source region: Plasma properties of the high‐latitude plasma sheet

the values for electron density can range from 0.01 to 0.5 cm � 3 with an average value around 0.1 cm � 3 on the poleward side and 0.3 cm � 3 on the equatorward side. Electron mean energy is found to have an average value near 900 eVon the equatorward side and 400 eVon the poleward side but varies from 100 eV to 4 keV. These values for density and mean energy are similar to those reported for measurements made in the equatorial plasma sheet by several previous spacecraft. The character of the electron distributions has been compared with Maxwellian and k-distributions with the result that the kdistribution with k � 10 yields an acceptable fit to the data twice as often as a Maxwellian distribution. This is similar to results found in the equatorial plasma sheet for both electrons and ions. The variation of electron density and mean energy around their average values have been compared with several solar wind parameters which have been developed to correlate solar wind variation with magnetospheric activity level. Few of these parameters are found to provide significant correlation with high-latitude plasma sheet electron density or temperature with the notable exception of solar wind density and solar wind particle flux which correlate with plasma sheet density. INDEX TERMS: 2764 Magnetospheric Physics: Plasma sheet; 2736 Magnetospheric Physics: Magnetosphere/ionosphere interactions; 2704 Magnetospheric Physics: Auroral phenomena (2407); 2784 Magnetospheric Physics: Solar wind/magnetosphere interactions;

Cell assembly sequences arising from spike threshold adaptation keep track of time in the hippocampus

Hippocampal neurons can display reliable and long-lasting sequences of transient firing patterns, even in the absence of changing external stimuli. We suggest that time-keeping is an important function of these sequences, and propose a network mechanism for their generation. We show that sequences of neuronal assemblies recorded from rat hippocampal CA1 pyramidal cells can reliably predict elapsed time (15–20 s) during wheel running with a precision of 0.5 s. In addition, we demonstrate the generation of multiple reliable, long-lasting sequences in a recurrent network model. These sequences are generated in the presence of noisy, unstructured inputs to the network, mimicking stationary sensory input. Identical initial conditions generate similar sequences, whereas different initial conditions give rise to distinct sequences. The key ingredients responsible for sequence generation in the model are threshold-adaptation and a Mexican-hat-like pattern of connectivity among pyramidal cells. This pattern may arise from recurrent systems such as the hippocampal CA3 region or the entorhinal cortex. We hypothesize that mechanisms that evolved for spatial navigation also support tracking of elapsed time in behaviorally relevant contexts.

Cell groups reveal structure of stimulus space.

An important task of the brain is to represent the outside world. It is unclear how the brain may do this, however, as it can only rely on neural responses and has no independent access to external stimuli in order to “decode” what those responses mean. We investigate what can be learned about a space of stimuli using only the action potentials (spikes) of cells with stereotyped—but unknown—receptive fields. Using hippocampal place cells as a model system, we show that one can (1) extract global features of the environment and (2) construct an accurate representation of space, up to an overall scale factor, that can be used to track the animals position. Unlike previous approaches to reconstructing position from place cell activity, this information is derived without knowing place fields or any other functions relating neural responses to position. We find that simply knowing which groups of cells fire together reveals a surprising amount of structure in the underlying stimulus space; this may enable the brain to construct its own internal representations.

Clique topology reveals intrinsic geometric structure in neural correlations

Significance Detecting structure in neural activity is critical for understanding the function of neural circuits. The coding properties of neurons are typically investigated by correlating their responses to external stimuli. It is not clear, however, if the structure of neural activity can be inferred intrinsically, without a priori knowledge of the relevant stimuli. We introduce a novel method, called clique topology, that detects intrinsic structure in neural activity that is invariant under nonlinear monotone transformations. Using pairwise correlations of neurons in the hippocampus, we demonstrate that our method is capable of detecting geometric structure from neural activity alone, without appealing to external stimuli or receptive fields. Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.

The Neural Ring: An Algebraic Tool for Analyzing the Intrinsic Structure of Neural Codes

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How does the brain do this? To address this question, it is important to determine what stimulus space features can—in principle—be extracted from neural codes. This motivates us to define the neural ring and a related neural ideal, algebraic objects that encode the full combinatorial data of a neural code. Our main finding is that these objects can be expressed in a “canonical form” that directly translates to a minimal description of the receptive field structure intrinsic to the code. We also find connections to Stanley–Reisner rings, and use ideas similar to those in the theory of monomial ideals to obtain an algorithm for computing the primary decomposition of pseudo-monomial ideals. This allows us to algorithmically extract the canonical form associated to any neural code, providing the groundwork for inferring stimulus space features from neural activity alone.

Population coding of tone stimuli in auditory cortex: Dynamic rate vector analysis

Neural representations of even temporally unstructured stimuli can show complex temporal dynamics. In many systems, neuronal population codes show ‘progressive differentiation’, whereby population responses to different stimuli grow further apart during a stimulus presentation. Here we analysed the response of auditory cortical populations in rats to extended tones. At onset (up to 300 ms), tone responses involved strong excitation of a large number of neurons; during sustained responses (after 500 ms) overall firing rate decreased, but most cells still showed statistically significant rate modulation. Population vector trajectories evoked by different tone frequencies expanded rapidly along an initially similar trajectory in the first tens of milliseconds after tone onset, later diverging to smaller amplitude fixed points corresponding to sustained responses. The angular difference between onset and sustained responses to the same tone was greater than between different tones in the same stimulus epoch. No clear orthogonalization of responses was found with time, and predictability of the stimulus from population activity also decreased during this period compared with onset. The question of whether population activity grew more or less sparse with time depended on the precise mathematical sense given to this term. We conclude that auditory cortical population responses to tones differ from those reported in many other systems, with progressive differentiation not seen for sustained stimuli. Sustained acoustic stimuli are typically not behaviorally salient: we hypothesize that the dynamics we observe may instead allow an animal to maintain a representation of such sounds, at low energetic cost.

Combinatorial neural codes from a mathematical coding theory perspective

Shannons seminal 1948 work gave rise to two distinct areas of research: information theory and mathematical coding theory. While information theory has had a strong influence on theoretical neuroscience, ideas from mathematical coding theory have received considerably less attention. Here we take a new look at combinatorial neural codes from a mathematical coding theory perspective, examining the error correction capabilities of familiar receptive field codes (RF codes). We find, perhaps surprisingly, that the high levels of redundancy present in these codes do not support accurate error correction, although the error-correcting performance of receptive field codes catches up to that of random comparison codes when a small tolerance to error is introduced. However, receptive field codes are good at reflecting distances between represented stimuli, while the random comparison codes are not. We suggest that a compromise in error-correcting capability may be a necessary price to pay for a neural code whose structure serves not only error correction, but must also reflect relationships between stimuli.

What Makes a Neural Code Convex

Neural codes allow the brain to represent, process, and store information about the world. Combinatorial codes, comprised of binary patterns of neural activity, encode information via the collective behavior of populations of neurons. A code is called convex if its codewords correspond to regions defined by an arrangement of convex open sets in Euclidean space. Convex codes have been observed experimentally in many brain areas, including sensory cortices and the hippocampus, where neurons exhibit convex receptive fields. What makes a neural code convex? That is, how can we tell from the intrinsic structure of a code if there exists a corresponding arrangement of convex open sets? In this work, we provide a complete characterization of local obstructions to convexity. This motivates us to define max intersection-complete codes, a family guaranteed to have no local obstructions. We then show how our characterization enables one to use free resolutions of Stanley-Reisner ideals in order to detect violations of convexity. Taken together, these results provide a significant advance in understanding the intrinsic combinatorial properties of convex codes.

Calmodulin enhances ribbon replenishment and shapes filtering of synaptic transmission by cone photoreceptors

Calmodulin promotes vesicle replenishment at photoreceptor ribbon synapses, enabling cones to transmit higher-frequency visual information.