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. 2018 Dec 1;120(6):2730-2744.
doi: 10.1152/jn.00012.2018. Epub 2018 Sep 5.

A novel mutual information estimator to measure spike train correlations in a model thalamocortical network

Ekaterina D Gribkova  1   2 , Baher A Ibrahim  3   2 , Daniel A Llano  1   3   2
Affiliations

A novel mutual information estimator to measure spike train correlations in a model thalamocortical network

Ekaterina D Gribkova et al. J Neurophysiol. .

Abstract

The impact of thalamic state on information transmission to the cortex remains poorly understood. This limitation exists due to the rich dynamics displayed by thalamocortical networks and because of inadequate tools to characterize those dynamics. Here, we introduce a novel estimator of mutual information and use it to determine the impact of a computational model of thalamic state on information transmission. Using several criteria, this novel estimator, which uses an adaptive partition, is shown to be superior to other mutual information estimators with uniform partitions when used to analyze simulated spike train data with different mean spike rates, as well as electrophysiological data from simultaneously recorded neurons. When applied to a thalamocortical model, the estimator revealed that thalamocortical cell T-type calcium current conductance influences mutual information between the input and output from this network. In particular, a T-type calcium current conductance of ~40 nS appears to produce maximal mutual information between the input to this network (conceptualized as afferent input to the thalamocortical cell) and the output of the network at the level of a layer 4 cortical neuron. Furthermore, at particular combinations of inputs to thalamocortical and thalamic reticular nucleus cells, thalamic cell bursting correlated strongly with recovery of mutual information between thalamic afferents and layer 4 neurons. These studies suggest that the novel mutual information estimator has advantages over previous estimators and that thalamic reticular nucleus activity can enhance mutual information between thalamic afferents and thalamorecipient cells in the cortex. NEW & NOTEWORTHY In this study, a novel mutual information estimator was developed to analyze information flow in a model thalamocortical network. Our findings suggest that this estimator is a suitable tool for signal transmission analysis, particularly in neural circuits with disparate firing rates, and that the thalamic reticular nucleus can potentiate ascending sensory signals, while thalamic recipient cells in the cortex can recover mutual information in ascending sensory signals that is lost due to thalamic bursting.

Keywords: adaptive partition; bursting; mutual information; thalamic reticular nucleus; thalamus.

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Figures

Fig. 1.
Fig. 1.
Procedure for estimating MI using AIMIE. A: given two time series, the one that has a greater number of spikes is designated as X, and the other is designated as Y. A time series of interspike interval durations for Y is constructed, and a time series of spike densities of X corresponding to the interspike intervals of Y. M represents the total number of interspike intervals of Y. B: an adaptive partition is applied to the time series of interspike interval durations of Y and separately to the time series of spike densities of X. Marginal probability for each bin of the adaptive partition is calculated as the occupancy of the bin divided by the sum of occupancies of all bins of that adaptive partition. Note the roughly equal occupancy of the bins, which is due to the adaptive partition. C: a joint histogram is constructed, in which one of the horizontal axes represents the bins of the adaptive partition for Y and the other horizontal axis represents bins of the adaptive partition for X. Joint probability for each combination of bins is calculated as joint occupancy of both bins divided by the sum of all occupancies of the joint histogram. D: equation for calculating MI, in which the outer sum, from j = 1 to N, sums over the bins of the adaptive partition of Y and the inner sum, from k = 1 to N, sums over the bins of the adaptive partition of X. AIMIE, Adaptive partition using Interspike intervals MI Estimator; MI, mutual information.
Fig. 2.
Fig. 2.
Comparison of RMSE of MI estimators. MI was estimated between spike time series generated from random variables Xi and Yi (i = 1, 2, …, 10), and this estimate was compared with the exact MI between Xi and Yi. For each i = 1, 2, …, 10, the random variable Yi is a summation of Xi, a normally distributed random variable with mean and standard deviation of 5i and i (in ms), respectively, and N, another normally distributed random variable which serves as Gaussian noise with a mean of 5 ms and standard deviation of 1 ms. Ten trials were used for generating spike time series for MI estimation. For each MI estimator, the RMSE was calculated between each MI estimate and exact MI value and then averaged over all random variable pairs. The average RMSE was compared across all MI estimators. MI, mutual information; RMSE, root mean square error.
Fig. 3.
Fig. 3.
Application of AIMIE and other MI estimators to time series generated from the model thalamocortical network with variable simulation times. A: model architecture of a thalamocortical network containing only TC and L4 neurons, which are modeled using a Hodgkin-Huxley framework. Default model parameters are used for simulations (see Table 1). INTC corresponds to thalamic afferent inputs, which are generated as 10 Hz Poisson-modulated pulse trains. B: MI per output spike provided by AIMIE when it is applied to time series pairs with different simulation times. As simulation time increases, the number of output spikes increases as well, and AIMIE’s MI per output spike trends toward a horizontal asymptote of ~2×10−4 bits/spike. The black triangle marks a simulation time of 100 s, which provides an average of ~411 output spikes. Inset shows decreased fluctuations in MI per output spike on an expanded scale, particularly for simulation times above 100 s. Ten trials were used for each simulation time, to generate error bars and standard deviation. C: standard deviation of AIMIE’s estimates of MI per output spike from Fig. 3A for a range of simulation times. Note that standard deviation is significantly smaller at around 100 s of simulation time (black triangle) than at shorter simulation times. For all other estimators, MI per output spike for the same set of simulation times was calculated, as well as the standard deviation of their MI estimates, just as for B and C. For each MI estimator, the standard deviation of the MI estimate across simulation times 4-2,000 s was fitted to an exponential curve, followed by calculation of the simulation time at which the curve dropped to one-half of its initial value (D). AIMIE, Adaptive partition using Interspike intervals MI Estimator; DMIE, Direct Method MI estimator; FBWSE, fixed-bin-width spike partition; FBNSE, fixed bin-number spike partition; L4, layer 4; MI, mutual information; SQRSE, square-root spike partition; TC, thalamocortical.
Fig. 4.
Fig. 4.
Effect of scaling of interspike intervals on MI for different estimators. A: spike time plots demonstrating scaling of interspike intervals for input and output series. In this case, the second input and output pair is generated by scaling all interspike intervals of the first pair by a factor of 2. B: percent change in MI demonstrated by estimators AIMIE, DMIE, FBWSE, FBNSE, and SQRSE when they are applied to input and output time series with interspike intervals scaled by factors of 2, 4, and 8. Ten trials were used for each data point and to generate standard deviation for error bars. AIMIE, Adaptive partition using Interspike intervals MI Estimator; DMIE, Direct Method MI estimator; FBWSE, fixed-bin-width spike partition; FBNSE, fixed bin-number spike partition; MI, mutual information; SQRSE, square-root spike partition.
Fig. 5.
Fig. 5.
Application of different estimators to hypothetical input and output series of variable dependence. A: spike time plots of hypothetical constructed time series of Types 1, 2, 3, and 4, where Type 1 is an ideal (100%) response type, Type 2 is a 50% response type, Type 3 is a 25% response type, and Type 4 is a 25% burst response type. B: percent change in MI demonstrated by estimators AIMIE, FBNSE, and SQRSE when they are applied to input and output time series of Types 1, 2, 3, and 4. As before, 10 trials were used for each data point and to generate standard deviation for error bars. AIMIE, Adaptive partition using Interspike intervals MI Estimator; FBNSE, fixed bin-number spike partition; MI, mutual information; SQRSE, square-root spike partition.
Fig. 6.
Fig. 6.
Application of different estimators to dual-recorded spike time series of variable synchrony. Recordings from a total of five neuron pairs are used. For both estimators, for each paired recording sequence under different DNQX concentrations, the change in normalized MI is calculated as MI per spike at each DNQX concentration divided by the MI per spike at DNQX concentration of 0 µM. A: change in normalized MI demonstrated by AIMIE across different concentrations of DNQX. The inset is an image of electrode placement for a paired recording in auditory cortex of mouse brain slice, with C denoting caudal and D denoting dorsal orientation. The legend for paired recordings is located below in B. B: change in normalized MI demonstrated by FBNSE across different concentrations of DNQX. The legend corresponds to both A and B. AIMIE, Adaptive partition using Interspike intervals MI Estimator; DNQX, 6,7-dinitroquinoxaline-2,3-dione; MI, mutual information.
Fig. 7.
Fig. 7.
MI analysis of inputs and outputs in an open-loop thalamocortical network model at variable T-current conductances. A: model architecture of the open-loop thalamocortical network. Arrows represent excitatory inputs, while the TRN-to-TC projection represents inhibitory (GABAergic) input. All neurons are modeled using a Hodgkin-Huxley framework. INTRN corresponds to input to the TRN, which ranges from 0 to 200 Hz, while INTC corresponds to thalamic afferents, which ranges from 0.5 to 200 Hz. Both INTRN and INTC are generated as Poisson-modulated pulse trains. Note that the green bracket symbolizes information transfer from thalamic afferents to TC, and the purple bracket symbolizes information transfer from thalamic afferents to L4. B: average MI transmitted per output spike between thalamic afferents and TC and between thalamic afferents and L4, at a range of TC T-current conductances. There is a peak in MI per output spike at a TC T-current conductance of ~40 nS, which may indicate maximum potentiation of ascending input in open-loop thalamocortical network. Ten trials were used for each data point and generation of standard deviation for error bars. The average MI per output spike between the thalamic afferents and L4 is on average slightly greater than between the thalamic afferents and the TC cell. To examine the significance of this difference, each trial, consisting of MI per output spike values over all T-current conductances, was fitted to a logistic function of the form f(x)=a1+eb⋅(x−c)+d where a is the difference between the curve’s maximum and minimum values, b is steepness of the logistic curve, c is the T-current conductance midpoint of the curve, and d is the minimum value of the logistic curve. L4, layer 4; MI, mutual information; TC, thalamocortical; TRN, thalamic reticular nucleus.
Fig. 8.
Fig. 8.
Heat map plots of normalized MI in open-loop thalamocortical network model for variable T-current conductances. For each TC T-current conductance, an MI plot is generated using a range of combinations of TC and TRN stimulation rates and then normalized by the number of output spikes for each rate combination. Normalized MI plots are averaged over 10 trials. The rate combination of 207 Hz stimulation of TRN and 0.5 Hz stimulation of TC (see Fig. 9) is marked in a black box on each plot. Note that the horizontal black line between A and B denotes a minus sign, while the pair of horizontal black lines between B and C denotes an equals sign. A: plots of average normalized MI (bits per output spike) between thalamic afferents and L4 output for T-current conductances of 10 to 80 nS. B: plots of average normalized MI between thalamic afferents and TC output for T-current conductances of 10 to 80 nS. C: plots of average normalized MI between thalamic afferents and L4 output (Fig. 8A) minus average normalized MI between thalamic afferents and TC output (Fig. 8B) for T-current conductances of 10 to 80 nS. These difference plots show a recovery of information per spike at low thalamic afferent rates and high TRN stimulation rates. L4, layer 4; MI, mutual information; TC, thalamocortical; TRN, thalamic reticular nucleus.
Fig. 9.
Fig. 9.
Stimulation of TRN at 207 Hz and TC at 0.5 Hz in open-loop thalamocortical network model. This rate combination is marked as a black box on the normalized MI plots of Fig. 8. INTC refers to thalamic afferents, as shown in Fig. 8. A: MI per output spike between thalamic afferents and TC output and thalamic afferents and L4 output at a range of T-current conductances from 0 to 100 nS. The number of bursts observed at the TC is also shown alongside on the right vertical axis. Ten trials were used for each data point and for generation of standard deviation for error bars. B: difference of MI per spike of TC input to TC output and MI per spike of TC input and L4 output against the number of bursts produced by TC. The trend line is shown alongside a Pearson coefficient value of r = 0.843 (P < 0.001). L4, layer 4; MI, mutual information; TC, thalamocortical; TRN, thalamic reticular nucleus.
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References

    1. Bartlett EL, Wang X. Neural representations of temporally modulated signals in the auditory thalamus of awake primates. J Neurophysiol 97: 1005–1017, 2007. doi:10.1152/jn.00593.2006. - DOI - PubMed
    1. Borst A, Theunissen FE. Information theory and neural coding. Nat Neurosci 2: 947–957, 1999. doi:10.1038/14731. - DOI - PubMed
    1. Boudreau CE, Ferster D. Short-term depression in thalamocortical synapses of cat primary visual cortex. J Neurosci 25: 7179–7190, 2005. doi:10.1523/JNEUROSCI.1445-05.2005. - DOI - PMC - PubMed
    1. Castro-Alamancos MA. Properties of primary sensory (lemniscal) synapses in the ventrobasal thalamus and the relay of high-frequency sensory inputs. J Neurophysiol 87: 946–953, 2002. doi:10.1152/jn.00426.2001. - DOI - PubMed
    1. Cellucci CJ, Albano AM, Rapp PE. Statistical validation of mutual information calculations: comparison of alternative numerical algorithms. Phys Rev E Stat Nonlin Soft Matter Phys 71: 066208, 2005. doi:10.1103/PhysRevE.71.066208. - DOI - PubMed

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