Functional Diversity in the Retina Improves the Population Code.

Within a given brain region, individual neurons exhibit a wide variety of different feature selectivities. Here, we investigated the impact of this extensive functional diversity on the population neural code. Our approach was to build optimal decoders to discriminate among stimuli using the spiking output of a real, measured neural population and compare its performance against a matched, homogeneous neural population with the same number of cells and spikes. Analyzing large populations of retinal ganglion cells, we found that the real, heterogeneous population can yield a discrimination error lower than the homogeneous population by several orders of magnitude and consequently can encode much more visual information. This effect increases with population size and with graded degrees of heterogeneity. We complemented these results with an analysis of coding based on the Chernoff distance, as well as derivations of inequalities on coding in certain limits, from which we can conclude that the beneficial effect of heterogeneity occurs over a broad set of conditions. Together, our results indicate that the presence of functional diversity in neural populations can enhance their coding fidelity appreciably. A noteworthy outcome of our study is that this effect can be extremely strong and should be taken into account when investigating design principles for neural circuits.

Interpretation of correlated neural variability from models of feed-forward and recurrent circuits.

Neural populations respond to the repeated presentations of a sensory stimulus with correlated variability. These correlations have been studied in detail, with respect to their mechanistic origin, as well as their influence on stimulus discrimination and on the performance of population codes. A number of theoretical studies have endeavored to link network architecture to the nature of the correlations in neural activity. Here, we contribute to this effort: in models of circuits of stochastic neurons, we elucidate the implications of various network architectures-recurrent connections, shared feed-forward projections, and shared gain fluctuations-on the stimulus dependence in correlations. Specifically, we derive mathematical relations that specify the dependence of population-averaged covariances on firing rates, for different network architectures. In turn, these relations can be used to analyze data on population activity. We examine recordings from neural populations in mouse auditory cortex. We find that a recurrent network model with random effective connections captures the observed statistics. Furthermore, using our circuit model, we investigate the relation between network parameters, correlations, and how well different stimuli can be discriminated from one another based on the population activity. As such, our approach allows us to relate properties of the neural circuit to information processing.

Noise correlations in the human brain and their impact on pattern classification.

Multivariate decoding methods, such as multivoxel pattern analysis (MVPA), are highly effective at extracting information from brain imaging data. Yet, the precise nature of the information that MVPA draws upon remains controversial. Most current theories emphasize the enhanced sensitivity imparted by aggregating across voxels that have mixed and weak selectivity. However, beyond the selectivity of individual voxels, neural variability is correlated across voxels, and such noise correlations may contribute importantly to accurate decoding. Indeed, a recent computational theory proposed that noise correlations enhance multivariate decoding from heterogeneous neural populations. Here we extend this theory from the scale of neurons to functional magnetic resonance imaging (fMRI) and show that noise correlations between heterogeneous populations of voxels (i.e., voxels selective for different stimulus variables) contribute to the success of MVPA. Specifically, decoding performance is enhanced when voxels with high vs. low noise correlations (measured during rest or in the background of the task) are selected during classifier training. Conversely, voxels that are strongly selective for one class in a GLM or that receive high classification weights in MVPA tend to exhibit high noise correlations with voxels selective for the other class being discriminated against. Furthermore, we use simulations to show that this is a general property of fMRI data and that selectivity and noise correlations can have distinguishable influences on decoding. Taken together, our findings demonstrate that if there is signal in the data, the resulting above-chance classification accuracy is modulated by the magnitude of noise correlations.

Structures of Neural Correlation and How They Favor Coding.

The neural representation of information suffers from "noise"-the trial-to-trial variability in the response of neurons. The impact of correlated noise upon population coding has been debated, but a direct connection between theory and experiment remains tenuous. Here, we substantiate this connection and propose a refined theoretical picture. Using simultaneous recordings from a population of direction-selective retinal ganglion cells, we demonstrate that coding benefits from noise correlations. The effect is appreciable already in small populations, yet it is a collective phenomenon. Furthermore, the stimulus-dependent structure of correlation is key. We develop simple functional models that capture the stimulus-dependent statistics. We then use them to quantify the performance of population coding, which depends upon interplays of feature sensitivities and noise correlations in the population. Because favorable structures of correlation emerge robustly in circuits with noisy, nonlinear elements, they will arise and benefit coding beyond the confines of retina.

Self-assembly and plasticity of synaptic domains through a reaction-diffusion mechanism.

Signal transmission across chemical synapses relies crucially on neurotransmitter receptor molecules, concentrated in postsynaptic membrane domains along with scaffold and other postsynaptic molecules. The strength of the transmitted signal depends on the number of receptor molecules in postsynaptic domains, and activity-induced variation in the receptor number is one of the mechanisms of postsynaptic plasticity. Recent experiments have demonstrated that the reaction and diffusion properties of receptors and scaffolds at the membrane, alone, yield spontaneous formation of receptor-scaffold domains of the stable characteristic size observed in neurons. On the basis of these experiments we develop a model describing synaptic receptor domains in terms of the underlying reaction-diffusion processes. Our model predicts that the spontaneous formation of receptor-scaffold domains of the stable characteristic size observed in experiments depends on a few key reactions between receptors and scaffolds. Furthermore, our model suggests novel mechanisms for the alignment of pre- and postsynaptic domains and for short-term postsynaptic plasticity in receptor number. We predict that synaptic receptor domains localize in membrane regions with an increased receptor diffusion coefficient or a decreased scaffold diffusion coefficient. Similarly, we find that activity-dependent increases or decreases in receptor or scaffold diffusion yield a transient increase in the number of receptor molecules concentrated in postsynaptic domains. Thus, the proposed reaction-diffusion model puts forth a coherent set of biophysical mechanisms for the formation, stability, and plasticity of molecular domains on the postsynaptic membrane.

Visual coding with a population of direction-selective neurons.

The brain decodes the visual scene from the action potentials of ∼20 retinal ganglion cell types. Among the retinal ganglion cells, direction-selective ganglion cells (DSGCs) encode motion direction. Several studies have focused on the encoding or decoding of motion direction by recording multiunit activity, mainly in the visual cortex. In this study, we simultaneously recorded from all four types of ON-OFF DSGCs of the rabbit retina using a microelectronics-based high-density microelectrode array (HDMEA) and decoded their concerted activity using probabilistic and linear decoders. Furthermore, we investigated how the modification of stimulus parameters (velocity, size, angle of moving object) and the use of different tuning curve fits influenced decoding precision. Finally, we simulated ON-OFF DSGC activity, based on real data, in order to understand how tuning curve widths and the angular distribution of the cells' preferred directions influence decoding performance. We found that probabilistic decoding strategies outperformed, on average, linear methods and that decoding precision was robust to changes in stimulus parameters such as velocity. The removal of noise correlations among cells, by random shuffling trials, caused a drop in decoding precision. Moreover, we found that tuning curves are broad in order to minimize large errors at the expense of a higher average error, and that the retinal direction-selective system would not substantially benefit, on average, from having more than four types of ON-OFF DSGCs or from a perfect alignment of the cells' preferred directions.

High-fidelity coding with correlated neurons.

Positive correlations in the activity of neurons are widely observed in the brain. Previous studies have shown these correlations to be detrimental to the fidelity of population codes, or at best marginally favorable compared to independent codes. Here, we show that positive correlations can enhance coding performance by astronomical factors. Specifically, the probability of discrimination error can be suppressed by many orders of magnitude. Likewise, the number of stimuli encoded--the capacity--can be enhanced more than tenfold. These effects do not necessitate unrealistic correlation values, and can occur for populations with a few tens of neurons. We further show that both effects benefit from heterogeneity commonly seen in population activity. Error suppression and capacity enhancement rest upon a pattern of correlation. Tuning of one or several effective parameters can yield a limit of perfect coding: the corresponding pattern of positive correlation leads to a 'lock-in' of response probabilities that eliminates variability in the subspace relevant for stimulus discrimination. We discuss the nature of this pattern and we suggest experimental tests to identify it.

Rods in daylight act as relay cells for cone-driven horizontal cell-mediated surround inhibition.

Vertebrate vision relies on two types of photoreceptors, rods and cones, which signal increments in light intensity with graded hyperpolarizations. Rods operate in the lower range of light intensities while cones operate at brighter intensities. The receptive fields of both photoreceptors exhibit antagonistic center-surround organization. Here we show that at bright light levels, mouse rods act as relay cells for cone-driven horizontal cell-mediated surround inhibition. In response to large, bright stimuli that activate their surrounds, rods depolarize. Rod depolarization increases with stimulus size, and its action spectrum matches that of cones. Rod responses at high light levels are abolished in mice with nonfunctional cones and when horizontal cells are reversibly inactivated. Rod depolarization is conveyed to the inner retina via postsynaptic circuit elements, namely the rod bipolar cells. Our results show that the retinal circuitry repurposes rods, when they are not directly sensing light, to relay cone-driven surround inhibition.

Alert response to motion onset in the retina.

Previous studies have shown that motion onset is very effective at capturing attention and is more salient than smooth motion. Here, we find that this salience ranking is present already in the firing rate of retinal ganglion cells. By stimulating the retina with a bar that appears, stays still, and then starts moving, we demonstrate that a subset of salamander retinal ganglion cells, fast OFF cells, responds significantly more strongly to motion onset than to smooth motion. We refer to this phenomenon as an alert response to motion onset. We develop a computational model that predicts the time-varying firing rate of ganglion cells responding to the appearance, onset, and smooth motion of a bar. This model, termed the adaptive cascade model, consists of a ganglion cell that receives input from a layer of bipolar cells, represented by individual rectified subunits. Additionally, both the bipolar and ganglion cells have separate contrast gain control mechanisms. This model captured the responses to our different motion stimuli over a wide range of contrasts, speeds, and locations. The alert response to motion onset, together with its computational model, introduces a new mechanism of sophisticated motion processing that occurs early in the visual system.

Chemotaxis when bacteria remember: drift versus diffusion.

Escherichia coli (E. coli) bacteria govern their trajectories by switching between running and tumbling modes as a function of the nutrient concentration they experienced in the past. At short time one observes a drift of the bacterial population, while at long time one observes accumulation in high-nutrient regions. Recent work has viewed chemotaxis as a compromise between drift toward favorable regions and accumulation in favorable regions. A number of earlier studies assume that a bacterium resets its memory at tumbles - a fact not borne out by experiment - and make use of approximate coarse-grained descriptions. Here, we revisit the problem of chemotaxis without resorting to any memory resets. We find that when bacteria respond to the environment in a non-adaptive manner, chemotaxis is generally dominated by diffusion, whereas when bacteria respond in an adaptive manner, chemotaxis is dominated by a bias in the motion. In the adaptive case, favorable drift occurs together with favorable accumulation. We derive our results from detailed simulations and a variety of analytical arguments. In particular, we introduce a new coarse-grained description of chemotaxis as biased diffusion, and we discuss the way it departs from older coarse-grained descriptions.

Formation and stability of synaptic receptor domains.

Neurotransmitter receptor molecules, concentrated in postsynaptic domains along with scaffold and a number of other molecules, are key regulators of signal transmission across synapses. Combining experiment and theory, we develop a quantitative description of synaptic receptor domains in terms of a reaction-diffusion model. We show that interactions between only receptors and scaffolds, together with the rapid diffusion of receptors on the cell membrane, are sufficient for the formation and stable characteristic size of synaptic receptor domains. Our work reconciles long-term stability of synaptic receptor domains with rapid turnover and diffusion of individual receptors, and suggests novel mechanisms for a form of short-term, postsynaptic plasticity.

Approach sensitivity in the retina processed by a multifunctional neural circuit.

The detection of approaching objects, such as looming predators, is necessary for survival. Which neurons and circuits mediate this function? We combined genetic labeling of cell types, two-photon microscopy, electrophysiology and theoretical modeling to address this question. We identify an approach-sensitive ganglion cell type in the mouse retina, resolve elements of its afferent neural circuit, and describe how these confer approach sensitivity on the ganglion cell. The circuit's essential building block is a rapid inhibitory pathway: it selectively suppresses responses to non-approaching objects. This rapid inhibitory pathway, which includes AII amacrine cells connected to bipolar cells through electrical synapses, was previously described in the context of night-time vision. In the daytime conditions of our experiments, the same pathway conveys signals in the reverse direction. The dual use of a neural pathway in different physiological conditions illustrates the efficiency with which several functions can be accommodated in a single circuit.

Steady-state chemotaxis in Escherichia coli.

The bacterium E. coli maneuvers itself to regions with high chemoattractant concentrations by performing two stereotypical moves: "runs," in which it moves in near-straight lines, and "tumbles," in which it does not advance but changes direction randomly. The duration of each move is stochastic and depends upon the chemoattractant concentration experienced in the recent past. We relate this stochastic behavior to the steady-state density of a bacterium population, and we derive the latter as a function of chemoattractant concentration. In contrast to earlier treatments, here we account for the effects of temporal correlations and variable tumbling durations. A range of behaviors is obtained that depends subtly upon several aspects of the system -- memory, correlation, and tumbling stochasticity, in particular.