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On the similarity of functional connectivity between neurons estimated across timescales.

Stevenson IH, Körding KP - PLoS ONE (2010)

Bottom Line: We address the origin of these correlations using simulation techniques and find evidence that the similarity between functional connectivity estimated across timescales is due to processes that do not depend on fast pair-wise interactions alone.Rather, it appears that connectivity on multiple timescales or common-input related to stimuli or movement drives the observed correlations.Despite this qualification, our results suggest that techniques with intermediate temporal resolution may yield good estimates of the functional connections between individual neurons.

View Article: PubMed Central - PubMed

Affiliation: Department of Physical Medicine and Rehabilitation, Rehabilitation Institute of Chicago, Chicago, Illinois, United States of America. i-stevenson@northwestern.edu

ABSTRACT
A central objective in neuroscience is to understand how neurons interact. Such functional interactions have been estimated using signals recorded with different techniques and, consequently, different temporal resolutions. For example, spike data often have sub-millisecond resolution while some imaging techniques may have a resolution of many seconds. Here we use multi-electrode spike recordings to ask how similar functional connectivity inferred from slower timescale signals is to the one inferred from fast timescale signals. We find that functional connectivity is relatively robust to low-pass filtering--dropping by about 10% when low pass filtering at 10 hz and about 50% when low pass filtering down to about 1 Hz--and that estimates are robust to high levels of additive noise. Moreover, there is a weak correlation for physiological filters such as hemodynamic or Ca2+ impulse responses and filters based on local field potentials. We address the origin of these correlations using simulation techniques and find evidence that the similarity between functional connectivity estimated across timescales is due to processes that do not depend on fast pair-wise interactions alone. Rather, it appears that connectivity on multiple timescales or common-input related to stimuli or movement drives the observed correlations. Despite this qualification, our results suggest that techniques with intermediate temporal resolution may yield good estimates of the functional connections between individual neurons.

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Simulation results using a generalized linear model.(A) shows a typical set of parameters after fitting the spike trains of a subpopulation of 10 neurons. On short timescales (<150 ms), refractory effects dominate spike behavior. However, there are small amplitude interactions between many neurons. (B) shows goodness of fit tests (KS-test on the time-rescaled inter-spike intervals) for three example neurons (bottom) and aggregate KS-statistics for an uncoupled model, a model with coupling, and a model including both coupling and hand velocity (top). Smaller KS-statistics correspond to better fits. After performing the filtering analysis on simulated data, the correlation between connectivity across timescales is robust for all datasets down to ∼5 Hz (C). Error-bars denote SEM across simulations (N = 100). (D) illustrates the differences between the power spectra of the observed and simulated neurons. The model with covariates follows the observed spectra down to ∼1 Hz. However, much of the observed power below 1 Hz is missing from the simulations.
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pone-0009206-g006: Simulation results using a generalized linear model.(A) shows a typical set of parameters after fitting the spike trains of a subpopulation of 10 neurons. On short timescales (<150 ms), refractory effects dominate spike behavior. However, there are small amplitude interactions between many neurons. (B) shows goodness of fit tests (KS-test on the time-rescaled inter-spike intervals) for three example neurons (bottom) and aggregate KS-statistics for an uncoupled model, a model with coupling, and a model including both coupling and hand velocity (top). Smaller KS-statistics correspond to better fits. After performing the filtering analysis on simulated data, the correlation between connectivity across timescales is robust for all datasets down to ∼5 Hz (C). Error-bars denote SEM across simulations (N = 100). (D) illustrates the differences between the power spectra of the observed and simulated neurons. The model with covariates follows the observed spectra down to ∼1 Hz. However, much of the observed power below 1 Hz is missing from the simulations.

Mentions: We start with a model that includes post-spike history kernels and coupling terms, both parameterized by raised-cosine basis functions (see Methods for details). These two sets of parameters allow us to model the spiking properties of individual neurons (i.e. refractoriness and burstiness) as well as the functional relationships between pairs of neurons on a certain timescale (100 ms in this case). To make the comparison between real and simulated data as accurate as possible, we fit the parameters of this model to subpopulations of 10 neurons in the original data. The simulated data thus reproduce certain characteristics of the observed spikes, such as firing rates and inter-spike intervals, while removing higher-order correlations as well as any dependence on external variables. Importantly, the GLM attempts to preserve the fast timescale connectivity from the original spike trains (Fig. 6A).


On the similarity of functional connectivity between neurons estimated across timescales.

Stevenson IH, Körding KP - PLoS ONE (2010)

Simulation results using a generalized linear model.(A) shows a typical set of parameters after fitting the spike trains of a subpopulation of 10 neurons. On short timescales (<150 ms), refractory effects dominate spike behavior. However, there are small amplitude interactions between many neurons. (B) shows goodness of fit tests (KS-test on the time-rescaled inter-spike intervals) for three example neurons (bottom) and aggregate KS-statistics for an uncoupled model, a model with coupling, and a model including both coupling and hand velocity (top). Smaller KS-statistics correspond to better fits. After performing the filtering analysis on simulated data, the correlation between connectivity across timescales is robust for all datasets down to ∼5 Hz (C). Error-bars denote SEM across simulations (N = 100). (D) illustrates the differences between the power spectra of the observed and simulated neurons. The model with covariates follows the observed spectra down to ∼1 Hz. However, much of the observed power below 1 Hz is missing from the simulations.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2823767&req=5

pone-0009206-g006: Simulation results using a generalized linear model.(A) shows a typical set of parameters after fitting the spike trains of a subpopulation of 10 neurons. On short timescales (<150 ms), refractory effects dominate spike behavior. However, there are small amplitude interactions between many neurons. (B) shows goodness of fit tests (KS-test on the time-rescaled inter-spike intervals) for three example neurons (bottom) and aggregate KS-statistics for an uncoupled model, a model with coupling, and a model including both coupling and hand velocity (top). Smaller KS-statistics correspond to better fits. After performing the filtering analysis on simulated data, the correlation between connectivity across timescales is robust for all datasets down to ∼5 Hz (C). Error-bars denote SEM across simulations (N = 100). (D) illustrates the differences between the power spectra of the observed and simulated neurons. The model with covariates follows the observed spectra down to ∼1 Hz. However, much of the observed power below 1 Hz is missing from the simulations.
Mentions: We start with a model that includes post-spike history kernels and coupling terms, both parameterized by raised-cosine basis functions (see Methods for details). These two sets of parameters allow us to model the spiking properties of individual neurons (i.e. refractoriness and burstiness) as well as the functional relationships between pairs of neurons on a certain timescale (100 ms in this case). To make the comparison between real and simulated data as accurate as possible, we fit the parameters of this model to subpopulations of 10 neurons in the original data. The simulated data thus reproduce certain characteristics of the observed spikes, such as firing rates and inter-spike intervals, while removing higher-order correlations as well as any dependence on external variables. Importantly, the GLM attempts to preserve the fast timescale connectivity from the original spike trains (Fig. 6A).

Bottom Line: We address the origin of these correlations using simulation techniques and find evidence that the similarity between functional connectivity estimated across timescales is due to processes that do not depend on fast pair-wise interactions alone.Rather, it appears that connectivity on multiple timescales or common-input related to stimuli or movement drives the observed correlations.Despite this qualification, our results suggest that techniques with intermediate temporal resolution may yield good estimates of the functional connections between individual neurons.

View Article: PubMed Central - PubMed

Affiliation: Department of Physical Medicine and Rehabilitation, Rehabilitation Institute of Chicago, Chicago, Illinois, United States of America. i-stevenson@northwestern.edu

ABSTRACT
A central objective in neuroscience is to understand how neurons interact. Such functional interactions have been estimated using signals recorded with different techniques and, consequently, different temporal resolutions. For example, spike data often have sub-millisecond resolution while some imaging techniques may have a resolution of many seconds. Here we use multi-electrode spike recordings to ask how similar functional connectivity inferred from slower timescale signals is to the one inferred from fast timescale signals. We find that functional connectivity is relatively robust to low-pass filtering--dropping by about 10% when low pass filtering at 10 hz and about 50% when low pass filtering down to about 1 Hz--and that estimates are robust to high levels of additive noise. Moreover, there is a weak correlation for physiological filters such as hemodynamic or Ca2+ impulse responses and filters based on local field potentials. We address the origin of these correlations using simulation techniques and find evidence that the similarity between functional connectivity estimated across timescales is due to processes that do not depend on fast pair-wise interactions alone. Rather, it appears that connectivity on multiple timescales or common-input related to stimuli or movement drives the observed correlations. Despite this qualification, our results suggest that techniques with intermediate temporal resolution may yield good estimates of the functional connections between individual neurons.

Show MeSH
Related in: MedlinePlus