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Conceived and designed the experiments: AB GD. Performed the experiments: AB. Analyzed the data: AB. Wrote the paper: AB.

The authors have declared that no competing interests exist.

In recent experimental work it has been shown that neuronal interactions are modulated by neuronal synchronization and that this modulation depends on phase shifts in neuronal oscillations. This result suggests that connections in a network can be shaped through synchronization. Here, we test and expand this hypothesis using a model network. We use transfer entropy, an information theoretical measure, to quantify the exchanged information. We show that transferred information depends on the phase relation of the signal, that the amount of exchanged information increases as a function of oscillations in the signal and that the speed of the information transfer increases as a function of synchronization. This implies that synchronization makes information transport more efficient. In summary, our results reinforce the hypothesis that synchronization modulates neuronal interactions and provide further evidence that gamma band synchronization has behavioral relevance.

Different brain areas are involved in any cognitive task. This implies that information has to be transmitted between different brain areas. Recent experimental results suggest that synchronization plays a crucial role in information exchange between cortical areas. They show that synchronization is capable of rendering network connections effective or ineffective. We study this hypothesis using a neurodynamical model and present results suggesting that both phase and strength of neuronal oscillations in the gamma frequency band influence amount and speed of information transport. We conclude that neuronal synchronization is crucial for information transmission and therefore might even have behavioral relevance.

Gamma band synchronization has been found in many cortical areas and in a variety of tasks. It has been studied most extensively in the visual cortex of cats and monkeys

In this study, we concentrate on the results shown by Womelsdorf et al.

While the results presented by

Here, to address these questions, we use a detailed biophysical model network with realistic spiking properties. A first advantage of using a model is that we can generate more data than in an experiment. This makes it possible to use an information theoretical measure for the mutual interaction instead of rank correlation. Many different interdependence measures such as mutual information, transfer information, nonlinear regression, phase synchronization and generalized synchronization have recently been proposed (see

The model we use in this study consists of integrate-and-fire neurons. One of two pools of excitatory neurons receives input (Poisson spike train) which it passes to a neighboring pool, connected by feedforward and feedback connections. Each pool of excitatory neurons is connected to a pool of inhibitory neurons, which generates oscillations in the gamma frequency band through a pyramidal-interneuron feedback loop

Womelsdorf et al.

The rank correlation coefficient between the two MUAs' 60 Hz power is plotted as a function of their phase relation. The solid line indicates a cosine fit. Adapted from

We use a model with leaky integrate-and-fire (IF) dynamics, following

The currents are defined as follows:

The fractions of open channels are given by:

The equations are integrated using a fourth order Runge-Kutta method with a time step of 0.02 ms. The network is organized in pools. Neurons within a specific pool have stronger recurrent connections than neurons between the pools. The intention of this work is to study cortical neural interactions not limited to a specific brain area. However, as our simulations needed to be directly comparable to

The network model consists of two parts (

The network consists of two parts. In each part, there are excitatory (S, NS) and inhibitory (I) neurons. The excitatory neurons are divided into two pools. The selective pool (S) receives the external input (

Gamma oscillations in a network with excitatory and inhibitory neurons are generated through a pyramidal-interneuron feedback loop

By adjusting the synaptic decay constants, the oscillation frequency can be shifted into the beta band. The crucial parameter is

Parameter | Value | Parameter | Value |

0.5 nF | |||

0.2 nF | |||

2.08 nS | |||

1.62 nS | 1.5 | ||

0.104 nS | 1.0 | ||

0.081 nS | 0.5 ms |
||

1.287 nS | 250 Hz | ||

1.002 nS | 2.4 kHz | ||

0.327 nS | 2 ms | ||

0.258 nS | 1.5 ms | ||

25 nS | 10 ms | ||

20 nS | 38 ms | ||

1.8 | 100 ms | ||

0.6 | 2 ms | ||

800 | 2 ms | ||

800 | 1 ms | ||

200 | 4 ms | ||

0 mV | feedback/feedforward ratio | 1/3 | |

From our spiking simulations we calculate the multi unit activity (MUA) to analyze our simulations, in order to be able to compare our results directly with the experiments. To simulate the MUA, we randomly chose 10 neurons in each of the selective pools. This point process data is converted to a time series by binning the spikes in windows of 5 ms. The binning window is shifted in steps of 1 ms. The time series is then normalized to zero mean and unit variance. We use the normalized time series to estimate power spectrum and transfer entropy. Normalization is applied to rule out the possible influence of rate changes.

We use the multitaper method

In Ref.

First we describe how the mean phase shift between pools of neurons is set by the delay in the feedforward and feedback connections. We then show that the correlation between the gamma power in the two pools depends on the phase relation in the gamma band. We demonstrate that TE has a very similar dependence on the phase shift and that TE increases as a function of gamma power. Finally, we reveal that if gamma power is high, information flow as measured by TE commences earlier.

Raster plots for 20 neurons from each neuronal pool are shown in (

Raster plot of spikes of 20 neurons from the default simulations (

The power spectrum of the MUA signal from a simulation with default parameters is shown.

The phases are widely distributed around the mean (marked with an asterix). The dark and light segments around the figures represent the phase bins into which trials were sorted. (

The phase shifts at 60 Hz between the two pools show a broad range of phases. We determine the phase shift in each time window of 500 ms. Then we calculate the correlation between the two pools for this time window by calculating the Spearman rank coefficient for the 60 Hz power in the two pools. The obtained correlation can now be sorted into different bins for the different phase shifts. We find that the correlation of the gamma band power between the two pools depends on the mean phase shift in the gamma band.

The rank correlation between the 60 Hz power in two neuronal pools is plotted as a function of the phase shift in the gamma band. A phase shift of zero represents the mean phase shift which is the point where the rank correlation is highest. The solid line indicates a cosine fit.

We apply TE to the same data as in the previous section. However, we measure the TE between the MUA in the two pools and not only the spectral power at 60 Hz, as was done in the experiment. We find that the TE depends strongly on the phase relation in the gamma band between the spiking activities of the two groups of neurons. It is highest for the mean phase between the two signals and drops as it moves away from the mean. This is consistent with our results for correlation. The phase dependence is illustrated in

The phases are aligned relative to the mean phase, i.e., a phase shift of zero represents mean phase shift. TE is highest for the mean phase shift and gets lower the more it differs from it. The solid line represents TE from neuronal pool 1 to pool 2 (forward), the dashed line from pool 2 to pool 1 (backward). Forward TE is clearly stronger than backward TE.

Differences in forward and backward TE are shown as a function of feedback/feedforward connection ratio, which is defined as

Another result we obtain is that the phase dependence of information transport is not restricted to the gamma band. We find that even in simulations with a network oscillating strongly in the beta band (around 20 Hz), the TE is again highest for the mean phase shift. In

The network oscillates strongly in one frequency band (either beta or gamma). The trials are sorted according to their phase shift either in the beta or gamma band. (

We further find that TE depends on the spectral power in the gamma band (30–85 Hz). For a fixed parameter set, we first sort all the trials according to their power in the gamma band into bins. In each of these bins, we measure the TE for the mean phase relation. The TE as a function of the power in the gamma band is plotted in

Network parameters are kept fixed. The TE increases as a function of gamma power.

In the previous section we have shown how TE depends on power in the gamma band for a fixed parameter set. Now we explicitly vary the amount of gamma power and study the TE dependence. Gamma band oscillations in a network of excitatory and inhibitory integrate-and-fire neurons appear when excitation is faster then inhibition

If the oscillations are strong in the gamma band (

We plot the TE for six different

Finally, we are interested in whether the gamma band oscillations also have an influence on the speed of information exchange, on top of the increased amount of information exchange. To do this, we measure the time required until the stimulus presentation to the first pool leads to an increase in TE towards the second pool. We find that the onset of TE increase is significantly earlier when there is a lot of power in the gamma band. While for a

Information starts flowing after stimulus onset when, consequently, TE starts rising. The plot shows the time required to reach 50% of the average TE. TE clearly rises faster for higher power in the gamma band (high

It has been hypothesized that interactions among neuronal groups depend on neuronal synchronization. Recent results show that gamma band oscillations and especially the phase relation in the gamma band can modify the strength of correlations in a network and therefore influence the effectiveness of connections in it

Our results support the CTC hypothesis. If the effective connections in a network are to be influenced by the phase lock in a specific frequency band between two areas, it is important that it not only affects the coherence between them, but also the throughput of information in a specific direction. By measuring TE instead of the Spearman rank coefficient, we extend the work of

As we are modeling results from visual cortical areas, we can assume that the neuronal clusters in the model transmit largely visual information. Several recent studies have contributed to the understanding of visual information transmission. These studies suggest that LFP power gradually increases as a function of stimulus contrast and gamma band LFP power increases differentially, that is, to a higher extent with respect to the baseline than relative to either higher or lower bands

In sum, we provide results to support the CTC hypothesis, we show evidence that CTC is a general mechanism independent of a specific frequency band and show that not only the phase but also the power is important to effectively shape the flow of information in a network.

We would like to thank Max Lungarella for his implementation of TE and Iva Ivanova for helpful comments on previous versions of this manuscript.