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. 2010 Dec 9;6(12):e1001035.
doi: 10.1371/journal.pcbi.1001035.

Incremental Mutual Information: A New Method for Characterizing the Strength and Dynamics of Connections in Neuronal Circuits

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Free PMC article

Incremental Mutual Information: A New Method for Characterizing the Strength and Dynamics of Connections in Neuronal Circuits

Abhinav Singh et al. PLoS Comput Biol. .
Free PMC article

Abstract

Understanding the computations performed by neuronal circuits requires characterizing the strength and dynamics of the connections between individual neurons. This characterization is typically achieved by measuring the correlation in the activity of two neurons. We have developed a new measure for studying connectivity in neuronal circuits based on information theory, the incremental mutual information (IMI). By conditioning out the temporal dependencies in the responses of individual neurons before measuring the dependency between them, IMI improves on standard correlation-based measures in several important ways: 1) it has the potential to disambiguate statistical dependencies that reflect the connection between neurons from those caused by other sources (e.g. shared inputs or intrinsic cellular or network mechanisms) provided that the dependencies have appropriate timescales, 2) for the study of early sensory systems, it does not require responses to repeated trials of identical stimulation, and 3) it does not assume that the connection between neurons is linear. We describe the theory and implementation of IMI in detail and demonstrate its utility on experimental recordings from the primate visual system.

Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. The quantities involved in computing incremental mutual information.
The incremental mutual information (IMI) between two signals X and Y is computed by first computing the entropy of X[n] after conditioning on formula image, a vector comprised of the past and future of both signals relative to a delay δ. This entropy is then compared the entropy of X[n] after further conditioning on Y[n−δ]. The reduction in entropy due to this further conditioning is the incremental mutual information.
Figure 2
Figure 2. Incremental mutual information disambiguates temporal correlations and connection dynamics.
a) A schematic diagram showing two neurons X and Y. The two neurons are driven by independent uncorrelated noise sources and Y drives X through a strong dynamic connection. The cross correlation function C and normalized IMI formula image computed from the simulated activity of the two neurons at a range of delays are shown. b) A second pair of neurons X and Y. The two neurons are driven by independent noise sources. The source driving Y has temporal correlations while the source driving X is uncorrelated. Y drives X through a strong static connection with a delay of 4 samples. The cross correlation function C, the normalized IMI formula image, and the normalized IMI with only past activity conditioned out formula image computed from the simulated activity of the two neurons at a range of delays are shown. IMI was computed with ω = 2 for 220 samples.
Figure 3
Figure 3. Incremental mutual information unmasks weak connections.
a) A schematic diagram showing two neurons X and Y. The two neurons are driven by a shared correlated noise source and Y drives X through a weak static connection. The cross correlation function C and normalized IMI formula image computed from the simulated activity of the two neurons at a range of delays are shown. b) Results for the same simulated neurons driven by a shared uncorrelated source, presented as in panel a. IMI was computed with ω = 2 for 220 samples.
Figure 4
Figure 4. Incremental mutual information analysis of retinogeniculate pairs.
a) A schematic diagram showing two neurons X and Y. Y is a retinal ganglion cell driven by a stimulus with temporal correlations that are typical of the natural environment. X is an LGN relay cell driven by Y and an unobserved noise source. b) Histograms showing the distribution of time delays between each retinal PSP and the next LGN spike and the number of additional retinal PSPs that preceded the next LGN spike, as well as the cross correlation function C and normalized IMI formula image computed from the responses of two retinogeniculate pairs to a non-repeating stimulus at a range of delays. For the IMI, the black line indicates the actual estimate, the yellow band indicates 95% confidence intervals, and the red dashed line indicates the significance level. Confidence intervals and significance levels were generated via bootstrap procedures with random sampling as described in the Methods. Spike times were binned with a resolution of 2 ms and IMI was computed with ω = 4 for approximately 218 samples.
Figure 5
Figure 5. Signal and noise incremental mutual information.
The signal and noise cross correlation functions formula image and formula image and the normalized signal and noise IMI formula image and formula image computed from the responses of the same two retinogeniculate pairs as in figure 4b to repeated trials of an identical stimulus, presented as in figure 4b. Spike times were binned with a resolution of 2 ms and IMI was computed with ω = 4 for approximately 218 samples.

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References

    1. Perkel DH, Gerstein GL, Moore GP. Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. Biophys J. 1967;7:419–40. - PMC - PubMed
    1. Usrey WM, Reid RC. Synchronous activity in the visual system. Annu Rev Physiol. 1999;61:435–456. - PubMed
    1. Aertsen AM, Gerstein GL. Evaluation of neuronal connectivity: sensitivity of cross-correlation. Brain Res. 1985;340:341–54. - PubMed
    1. Brody CD. Correlations without synchrony. Neural Comput. 1999;11:1537–51. - PubMed
    1. Melssen WJ, Epping WJ. Detection and estimation of neural connectivity based on crosscorrelation analysis. Biol Cybern. 1987;57:403–14. - PubMed

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