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The authors have declared that no competing interests exist.

Performed the mathematical analysis and simulations: MSK MH. Conceived and designed the experiments: MSK MD SG MH. Performed the experiments: MSK MH. Analyzed the data: MSK MH. Contributed reagents/materials/analysis tools: MSK MH. Wrote the paper: MSK MD SG MH.

The functional significance of correlations between action potentials of neurons is still a matter of vivid debate. In particular, it is presently unclear how much synchrony is caused by afferent synchronized events and how much is intrinsic due to the connectivity structure of cortex. The available analytical approaches based on the diffusion approximation do not allow to model spike synchrony, preventing a thorough analysis. Here we theoretically investigate to what extent common synaptic afferents and synchronized inputs each contribute to correlated spiking on a fine temporal scale between pairs of neurons. We employ direct simulation and extend earlier analytical methods based on the diffusion approximation to pulse-coupling, allowing us to introduce precisely timed correlations in the spiking activity of the synaptic afferents. We investigate the transmission of correlated synaptic input currents by pairs of integrate-and-fire model neurons, so that the same input covariance can be realized by common inputs or by spiking synchrony. We identify two distinct regimes: In the limit of low correlation linear perturbation theory accurately determines the correlation transmission coefficient, which is typically smaller than unity, but increases sensitively even for weakly synchronous inputs. In the limit of high input correlation, in the presence of synchrony, a qualitatively new picture arises. As the non-linear neuronal response becomes dominant, the output correlation becomes higher than the total correlation in the input. This transmission coefficient larger unity is a direct consequence of non-linear neural processing in the presence of noise, elucidating how synchrony-coded signals benefit from these generic properties present in cortical networks.

Whether spike timing conveys information in cortical networks or whether the firing rate alone is sufficient is a matter of controversial debate, touching the fundamental question of how the brain processes, stores, and conveys information. If the firing rate alone is the decisive signal used in the brain, correlations between action potentials are just an epiphenomenon of cortical connectivity, where pairs of neurons share a considerable fraction of common afferents. Due to membrane leakage, small synaptic amplitudes and the non-linear threshold, nerve cells exhibit lossy transmission of correlation originating from shared synaptic inputs. However, the membrane potential of cortical neurons often displays non-Gaussian fluctuations, caused by synchronized synaptic inputs. Moreover, synchronously active neurons have been found to reflect behavior in primates. In this work we therefore contrast the transmission of correlation due to shared afferents and due to synchronously arriving synaptic impulses for leaky neuron models. We not only find that neurons are highly sensitive to synchronous afferents, but that they can suppress noise on signals transmitted by synchrony, a computational advantage over rate signals.

Simultaneously recording the activity of multiple neurons provides a unique tool to observe the activity in the brain. The immediately arising question of the meaning of the observed correlated activity between different cells

In the other view, on the contrary, theoretical considerations

The role of correlations entails the question whether cortical neurons operate as integrators or as coincidence detectors

The pivotal role of correlations distinguishing the two opposing views and the appearance of synchrony at task-specific times

One particular measure for assessing the transmission of correlation by a pair of neurons is the transmission coefficient, i.e. the ratio of output to input correlation. When studying spiking neuron models, the synaptic input is typically modeled as Gaussian white noise, e.g. by applying the diffusion approximation to the leaky integrate-and-fire model

Understanding the influence of synchrony among the inputs on the correlation transmission requires to extend the above mentioned methods, as Gaussian fluctuating input does not allow to represent individual synaptic events, not to mention synchrony. Therefore, in this work we introduce an input model that extends the commonly investigated Gaussian white noise model. We employ the multiple interaction process (MIP)

In section

The neuronal dynamics considered in this work follows the leaky integrate-and-fire model, whose membrane potential

We investigate the correlation transmission of a pair of neurons considering the following input scenario. Each neuron receives input from

Let us now consider the case of

The output firing rates and output spike synchrony shown in

These two observations – the increase of input correlation and output firing rate induced by input synchrony – foil our objective to understand the sole impact of synchronous input events on the correlation transmission of neurons. In the following we will therefore first provide a quantitative description of the effect of finite sized presynaptic events on the membrane potential dynamics and subsequently describe a way to isolate and control this effect.

The synchronous arrival of

Again,

In order to isolate and control the effect of the synchrony parameter

In scenario 1 (

We evaluate this approach by simulating the free membrane potential of a pair of leaky integrate-and-fire neurons driven by correlated input. For different values of

In order to study the transmission of correlation by a pair of neurons, we need to ensure that the single neuron's working point does not change with the correlation structure of the input. The diffusion approximation (3) suggests, that the decisive properties of the marginal input statistics are characterized by the first (

In studies which investigate the effect of common input on the correlation transmission of neurons, the input correlation is identical to the common input fraction

For correlated inputs caused by common inputs alone (no synchrony,

In the limit of low input correlation

For Gaussian white noise input and in the limit of low input correlation, the correlation transmission is well understood

Before deriving an expression for the correlation transmission by a pair of neurons, we first need the firing rate deflection of a neuron

In order to understand how the neurons are able to achieve a correlation coefficient larger than one, we need to take a closer look at the neural dynamics in the high correlation regime. We refer to the strong pulses caused by synchronous firing of numerous afferents as MIP events.

Let us now recapitulate these last thoughts in terms of a pair of neurons: In the regime of synchronized high input correlation (e.g.

We would like to obtain a qualitative assessment of the correlation transmission in the high correlation input regime. Since the probability of output spikes caused by the disjoint sources is vanishing, the firing due to MIP events inherits the Poisson statistics of the mother process. Consequently, the auto-covariance function of each neurons' output spike train is a

So far, we have considered both neurons operating at a fixed working point, defined by the mean and variance (4). Due to the non-linearity of the neurons we expect the effect of synchronous input events on their firing to depend on the choice of this working point. We therefore performed simulations and computed (2) using four different values for the mean membrane potential

A further approximation of (15) and (16) confirms the intuitive expectation that the mean size of a synchronous event compared to the distance of the membrane potential to the threshold plays an important role for the output synchrony: if synchrony is sufficiently high, say

Measuring the integral of the output correlation over a window of

A qualitatively new behavior is observed in the intermediate range of input correlation

So far, for

Panels show simulation results using

In this work we investigate the correlation transmission by a neuron pair, using two different types of input spike correlations. One is caused solely by shared input – typically modeled as Gaussian white noise in previous studies

To model correlated spiking activity among the excitatory afferents in the input to a pair of neurons we employ the Multiple Interaction Process (MIP)

Given a fixed input correlation, the correlation transmission increases with

Hitherto existing studies argue that neurons either loose correlation when they are in the fluctuation driven regime or at most are able to preserve the input correlation in the mean driven regime

We presented a quantitative description of the increased correlation transmission by synchronous input events for the leaky integrate-and-fire model. Our analytical results explain earlier observations from a simulation study modeling synchrony by co-activation of a fixed fraction of the excitatory afferents

As for our spiking model,

The situation illustrated in

Several aspects of this study need to be taken into account when relating the results to other studies and to biological systems. The multiple interaction process as a model for correlated neural activity might seem unrealistic at first sight. However, a similar correlation structure can easily be obtained from the activity of a population of

The correlation transmission coefficient can only exceed unity if the firing of the neurons is predominantly driven by the synchronously arriving volleys and disjoint input does not contribute to firing. The threshold then acts as a noise gate, small fluctuations caused by disjoint input do not penetrate to the output side. In the mean driven regime, i.e. when

The boost of output correlation by synchronous synaptic impulses relies on fast positive transients of the membrane potential and strong departures from the stationary state: An incoming packet of synaptic impulses brings the membrane potential over the threshold within short time. Qualitatively, we therefore expect similar results for short, but non-zero rise times of the synaptic currents. For long synaptic time constants compared to the neuronal dynamics, however, the instantaneous firing intensity follows the modulation of the synaptic current adiabatically

The choice of the correlation measure is of importance when analyzing spike correlations. It has been pointed out recently that the time scale

It has been proposed that the coordinated firing of cell assemblies provides a means for the binding of coherent stimulus features

Though in the limit of weak input correlation the correlation in the output is bounded by that in the input, in agreement with previous reports

We here derive an approximation for the integral of the impulse response of the firing rate with respect to a perturbing impulse in the input. A similar derivation has been presented in

The first four moments of the binomial distribution

We thank the two anonymous reviewers for their helpful and constructive comments. All simulations were carried out with NEST (