Stimulus-dependent maximum entropy models of neural population codes

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. To be able to infer a model for this distribution from large-scale neural recordings, we introduce a stimulus-dependent maximum entropy (SDME) model---a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. The model is able to capture the single-cell response properties as well as the correlations in neural spiking due to shared stimulus and due to effective neuron-to-neuron connections. Here we show that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. As a result, the SDME model gives a more accurate account of single cell responses and in particular outperforms uncoupled models in reproducing the distributions of codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like surprise and information transmission in a neural population.Comment: 11 pages, 7 figure

A biophysical model explains the spontaneous bursting behavior in the developing retina

During early development, waves of activity propagate across the retina and play a key role in the proper wiring of the early visual system. During the stage II these waves are triggered by a transient network of neurons, called Starburst Amacrine Cells (SACs), showing a bursting activity which disappears upon further maturation. While several models have attempted to reproduce retinal waves, none of them is able to mimic the rhythmic autonomous bursting of individual SACs and reveal how these cells change their intrinsic properties during development. Here, we introduce a mathematical model, grounded on biophysics, which enables us to reproduce the bursting activity of SACs and to propose a plausible, generic and robust, mechanism that generates it. The core parameters controlling repetitive firing are fast depolarizing $V$-gated calcium channels and hyperpolarizing $V$-gated potassium channels. The quiescent phase of bursting is controlled by a slow after hyperpolarization (sAHP), mediated by calcium-dependent potassium channels. Based on a bifurcation analysis we show how biophysical parameters, regulating calcium and potassium activity, control the spontaneously occurring fast oscillatory activity followed by long refractory periods in individual SACs. We make a testable experimental prediction on the role of voltage-dependent potassium channels on the excitability properties of SACs and on the evolution of this excitability along development. We also propose an explanation on how SACs can exhibit a large variability in their bursting periods, as observed experimentally within a SACs network as well as across different species, yet based on a simple, unique, mechanism. As we discuss, these observations at the cellular level have a deep impact on the retinal waves description.Comment: 25 pages, 13 figures, submitte

Separating intrinsic interactions from extrinsic correlations in a network of sensory neurons

Correlations in sensory neural networks have both extrinsic and intrinsic origins. Extrinsic or stimulus correlations arise from shared inputs to the network, and thus depend strongly on the stimulus ensemble. Intrinsic or noise correlations reflect biophysical mechanisms of interactions between neurons, which are expected to be robust to changes of the stimulus ensemble. Despite the importance of this distinction for understanding how sensory networks encode information collectively, no method exists to reliably separate intrinsic interactions from extrinsic correlations in neural activity data, limiting our ability to build predictive models of the network response. In this paper we introduce a general strategy to infer {population models of interacting neurons that collectively encode stimulus information}. The key to disentangling intrinsic from extrinsic correlations is to infer the {couplings between neurons} separately from the encoding model, and to combine the two using corrections calculated in a mean-field approximation. We demonstrate the effectiveness of this approach on retinal recordings. The same coupling network is inferred from responses to radically different stimulus ensembles, showing that these couplings indeed reflect stimulus-independent interactions between neurons. The inferred model predicts accurately the collective response of retinal ganglion cell populations as a function of the stimulus

Towards building a more complex view of the lateral geniculate nucleus: Recent advances in understanding its role

The lateral geniculate nucleus (LGN) has often been treated in the past as a linear filter that adds little to retinal processing of visual inputs. Here we review anatomical, neurophysiological, brain imaging, and modeling studies that have in recent years built up a much more complex view of LGN . These include effects related to nonlinear dendritic processing, cortical feedback, synchrony and oscillations across LGN populations, as well as involvement of LGN in higher level cognitive processing. Although recent studies have provided valuable insights into early visual processing including the role of LGN, a unified model of LGN responses to real-world objects has not yet been developed. In the light of recent data, we suggest that the role of LGN deserves more careful consideration in developing models of high-level visual processing

Searching for collective behavior in a network of real neurons

Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such "K-pairwise" models--being systematic extensions of the previously used pairwise Ising models--provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.Comment: 24 pages, 19 figure

Network Deficiency Exacerbates Impairment in a Mouse Model of Retinal Degeneration

Neural oscillations play an important role in normal brain activity, but also manifest during Parkinson’s disease, epilepsy, and other pathological conditions. The contribution of these aberrant oscillations to the function of the surviving brain remains unclear. In recording from retina in a mouse model of retinal degeneration (RD), we found that the incidence of oscillatory activity varied across different cell classes, evidence that some retinal networks are more affected by functional changes than others. This aberrant activity was driven by an independent inhibitory amacrine cell oscillator. By stimulating the surviving circuitry at different stages of the neurodegenerative process, we found that this dystrophic oscillator further compromises the function of the retina. These data reveal that retinal remodeling can exacerbate the visual deficit, and that aberrant synaptic activity could be targeted for RD treatment

A combined experimental and computational approach to investigate emergent network dynamics based on large-scale neuronal recordings

Sviluppo di un approccio integrato computazionale-sperimentale per lo studio di reti neuronali mediante registrazioni elettrofisiologich

Understanding object motion encoding in the mammalian retina.

Phototransduction, transmission of visual information down the optic nerve incurs delays on the order of 50 – 100ms. This implies that the neuronal representation of a moving object should lag behind the object’s actual position. However, studies have demonstrated that the visual system compensates for neuronal delays using a predictive mechanism called phase advancing, which shifts the population response toward the leading edge of a moving object’s retinal image. To understand how this compensation is achieved in the retina, I investigated cellular and synaptic mechanisms that drive phase advancing. I used three approaches, each testing phase advancing at a different organizational level within the mouse retina. First, I studied phase advancing at the level of ganglion cell populations, using two-photon imaging of visually evoked calcium responses. I found populations of phase advancing OFF-type, ON-type, ON-OFF type, and horizontally tuned directionally selective ganglion cells. Second, I measured synaptic current responses of individual ganglion cells with patch-clamp electrophysiology, and I used a computational model to compare the observed responses to simulated responses based on the ganglion cell’s spatio-temporal receptive fields. Third, I tested whether phase advancing originates presynaptic to ganglion cells, by assessing phase advancing at the level of bipolar cell glutamate release using two-photon imaging of the glutamate biosensor iGluSnFR expressed in the inner plexiform layer. Based on the results of my experiments, I conclude that bipolar and ganglion cell receptive field structure generates phase advanced responses and acts to compensate for neuronal delays within the retina