Gabriel Koch Ocker

The mechanics of state-dependent neural correlations

Simultaneous recordings from large neural populations are becoming increasingly common. An important feature of population activity is the trial-to-trial correlated fluctuation of spike train outputs from recorded neuron pairs. Similar to the firing rate of single neurons, correlated activity can be modulated by a number of factors, from changes in arousal and attentional state to learning and task engagement. However, the physiological mechanisms that underlie these changes are not fully understood. We review recent theoretical results that identify three separate mechanisms that modulate spike train correlations: changes in input correlations, internal fluctuations and the transfer function of single neurons. We first examine these mechanisms in feedforward pathways and then show how the same approach can explain the modulation of correlations in recurrent networks. Such mechanistic constraints on the modulation of population activity will be important in statistical analyses of high-dimensional neural data.

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

Attentional modulation of neuronal variability in circuit models of cortex

The circuit mechanisms behind shared neural variability (noise correlation) and its dependence on neural state are poorly understood. Visual attention is well-suited to constrain cortical models of response variability because attention both increases firing rates and their stimulus sensitivity, as well as decreases noise correlations. We provide a novel analysis of population recordings in rhesus primate visual area V4 showing that a single biophysical mechanism may underlie these diverse neural correlates of attention. We explore model cortical networks where top-down mediated increases in excitability, distributed across excitatory and inhibitory targets, capture the key neuronal correlates of attention. Our models predict that top-down signals primarily affect inhibitory neurons, whereas excitatory neurons are more sensitive to stimulus specific bottom-up inputs. Accounting for trial variability in models of state dependent modulation of neuronal activity is a critical step in building a mechanistic theory of neuronal cognition. DOI: http://dx.doi.org/10.7554/eLife.23978.001

Kv7 channels regulate pairwise spiking covariability in health and disease

Low-threshold M currents are mediated by the Kv7 family of potassium channels. Kv7 channels are important regulators of spiking activity, having a direct influence on the firing rate, spike time variability, and filter properties of neurons. How Kv7 channels affect the joint spiking activity of populations of neurons is an important and open area of study. Using a combination of computational simulations and analytic calculations, we show that the activation of Kv7 conductances reduces the covariability between spike trains of pairs of neurons driven by common inputs. This reduction is beyond that explained by the lowering of firing rates and involves an active cancellation of common fluctuations in the membrane potentials of the cell pair. Our theory shows that the excess covariance reduction is due to a Kv7-induced shift from low-pass to band-pass filtering of the single neuron spike train response. Dysfunction of Kv7 conductances is related to a number of neurological diseases characterized by both elevated firing rates and increased network-wide correlations. We show how changes in the activation or strength of Kv7 conductances give rise to excess correlations that cannot be compensated for by synaptic scaling or homeostatic modulation of passive membrane properties. In contrast, modulation of Kv7 activation parameters consistent with pharmacological treatments for certain hyperactivity disorders can restore normal firing rates and spiking correlations. Our results provide key insights into how regulation of a ubiquitous potassium channel class can control the coordination of population spiking activity.

Linking structure and activity in nonlinear spiking networks

Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks’ spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities—including those of different cell types—combine with connectivity to shape population activity and function.

From the statistics of connectivity to the statistics of spike times in neuronal networks

An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad principles underlying collective spiking activity in neural circuits. The first is that local features of network connectivity can be surprisingly effective in predicting global statistics of activity across a network. The second is that, for the important case of large networks with excitatory-inhibitory balance, correlated spiking persists or vanishes depending on the spatial scales of recurrent and feedforward connectivity. We close by showing how these ideas, together with plasticity rules, can help to close the loop between network structure and activity statistics.

A large-scale, standardized physiological survey reveals higher order coding throughout the mouse visual cortex

To understand how the brain processes sensory information to guide behavior, we must know how stimulus representations are transformed throughout the visual cortex. Here we report an open, large-scale physiological survey of neural activity in the awake mouse visual cortex: the Allen Brain Observatory Visual Coding dataset. This publicly available dataset includes cortical activity from nearly 60,000 neurons collected from 6 visual areas, 4 layers, and 12 transgenic mouse lines from 221 adult mice, in response to a systematic set of visual stimuli. Using this dataset, we reveal functional differences across these dimensions and show that visual cortical responses are sparse but correlated. Surprisingly, responses to different stimuli are largely independent, e.g. whether a neuron responds to natural scenes provides no information about whether it responds to natural movies or to gratings. We show that these phenomena cannot be explained by standard local filter-based models, but are consistent with multi-layer hierarchical computation, as found in deeper layers of standard convolutional neural networks.

Training and spontaneous reinforcement of neuronal assemblies by spike timing

The synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing–dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale simulations. A simple analytic account for how fast spike time correlations affect both micro- and macroscopic network structure is lacking. We develop a low-dimensional mean field theory for STDP in recurrent networks and show the emergence of assemblies of strongly reciprocally coupled neurons with shared stimulus preferences. After training this connectivity is actively reinforced by spike train correlations during the spontaneous dynamics. Furthermore, the stimulus coding by cell assemblies is actively maintained by these internally generated spiking correlations, suggesting a new role for noise correlations in neural coding. Assembly formation has been often associated with firing rate-based plasticity schemes; our theory provides an alternative and complementary framework, where fine temporal correlations and STDP form and actively maintain learned structure in cortical networks.

Visual physiology of the Layer 4 cortical circuit in silico

Despite advances in experimental techniques and accumulation of large datasets concerning the composition and properties of the cortex, quantitative modeling of cortical circuits under in-vivo-like conditions remains challenging. Here we report and publicly release a biophysically detailed circuit model of layer 4 in the mouse primary visual cortex, receiving thalamo-cortical visual inputs. The 45,000-neuron model was subjected to a battery of visual stimuli, and results were compared to published work and new in vivo experiments. Simulations reproduced a variety of observations, including effects of optogenetic perturbations. Critical to the agreement between responses in silico and in vivo were the rules of functional synaptic connectivity between neurons. Interestingly, after extreme simplification the model still performed satisfactorily on many measurements, although quantitative agreement with experiments suffered. These results emphasize the importance of functional rules of cortical wiring and enable a next generation of data-driven models of in vivo neural activity and computations. AUTHOR SUMMARY How can we capture the incredible complexity of brain circuits in quantitative models, and what can such models teach us about mechanisms underlying brain activity? To answer these questions, we set out to build extensive, bio-realistic models of brain circuitry employing systematic datasets on brain structure and function. Here we report the first modeling results of this project, focusing on the layer 4 of the primary visual cortex (V1) of the mouse. Our simulations reproduced a variety of experimental observations in a large battery of visual stimuli. The results elucidated circuit mechanisms determining patters of neuronal activity in layer 4 – in particular, the roles of feedforward thalamic inputs and specific patterns of intracortical connectivity in producing tuning of neuronal responses to the orientation of motion. Simplification of neuronal models led to specific deficiencies in reproducing experimental data, giving insights into how biological details contribute to various aspects of brain activity. To enable future development of more sophisticated models, we make the software code, the model, and simulation results publicly available.

Dimensionality in recurrent spiking networks: global trends in activity and local origins in connectivity

The dimensionality of a network’s collective activity is of increasing interest in neuroscience. This is because dimensionality provides a compact measure of how coordinated network-wide activity is, in terms of the number of modes (or degrees of freedom) that it can independently explore. A low number of modes suggests a compressed low dimensional neural code and reveals interpretable dynamics [1], while findings of high dimension may suggest flexible computations [2, 3]. Here, we address the fundamental question of how dimensionality is related to connectivity, in both autonomous and stimulus-driven networks. Working with a simple spiking network model, we derive three main findings. First, the dimensionality of global activity patterns can be strongly, and systematically, regulated by local connectivity structures. Second, the dimensionality is a better indicator than average correlations in determining how constrained neural activity is. Third, stimulus evoked neural activity interacts systematically with neural connectivity patterns, leading to network responses of either greater or lesser dimensionality than the stimulus. Author summary New recording technologies are producing an amazing explosion of data on neural activity. These data reveal the simultaneous activity of hundreds or even thousands of neurons. In principle, the activity of these neurons could explore a vast space of possible patterns. This is what is meant by high-dimensional activity: the number of degrees of freedom (or “modes”) of multineuron activity is large, perhaps as large as the number of neurons themselves. In practice, estimates of dimensionality differ strongly from case to case, and do so in interesting ways across experiments, species, and brain areas. The outcome is important for much more than just accurately describing neural activity: findings of low dimension have been proposed to allow data compression, denoising, and easily readable neural codes, while findings of high dimension have been proposed as signatures of powerful and general computations. So what is it about a neural circuit that leads to one case or the other? Here, we derive a set of principles that inform how the connectivity of a spiking neural network determines the dimensionality of the activity that it produces. These show that, in some cases, highly localized features of connectivity have strong control over a network’s global dimensionality—an interesting finding in the context of, e.g., learning rules that occur locally. We also show how dimension can be much different than first meets the eye with typical “pairwise” measurements, and how stimuli and intrinsic connectivity interact in shaping the overall dimension of a network’s response.