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Multiple spike time patterns occur at bifurcation points of membrane potential dynamics.

Toups JV, Fellous JM, Thomas PJ, Sejnowski TJ, Tiesinga PH - PLoS Comput. Biol. (2012)

Bottom Line: The response of a neuron to repeated somatic fluctuating current injections in vitro can elicit a reliable and precisely timed sequence of action potentials.However, at specific values called bifurcation points, large shifts in the spike times were obtained in response to small changes in the stimulus, resulting in multiple spike patterns that were revealed using an unsupervised classification method.Furthermore, the spike times shifted earlier with increasing offset.

View Article: PubMed Central - PubMed

Affiliation: Computational Neurophysics Laboratory, Department of Physics & Astronomy, University of North Carolina, Chapel Hill, NC, USA.

ABSTRACT
The response of a neuron to repeated somatic fluctuating current injections in vitro can elicit a reliable and precisely timed sequence of action potentials. The set of responses obtained across trials can also be interpreted as the response of an ensemble of similar neurons receiving the same input, with the precise spike times representing synchronous volleys that would be effective in driving postsynaptic neurons. To study the reproducibility of the output spike times for different conditions that might occur in vivo, we somatically injected aperiodic current waveforms into cortical neurons in vitro and systematically varied the amplitude and DC offset of the fluctuations. As the amplitude of the fluctuations was increased, reliability increased and the spike times remained stable over a wide range of values. However, at specific values called bifurcation points, large shifts in the spike times were obtained in response to small changes in the stimulus, resulting in multiple spike patterns that were revealed using an unsupervised classification method. Increasing the DC offset, which mimicked an overall increase in network background activity, also revealed bifurcation points and increased the reliability. Furthermore, the spike times shifted earlier with increasing offset. Although the reliability was reduced at bifurcation points, a theoretical analysis showed that the information about the stimulus time course was increased because each of the spike time patterns contained different information about the input.

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Related in: MedlinePlus

Bifurcation points were observed in model simulations for amplitudes at which the spike count changed.We show the (A) R-reliability (sigma = 1 ms) and (B) rastergram as a function of amplitude obtained from simulations of the Wang-Buzsaki model neuron [22], [47], using the same injected current as in the recordings from neurons. The dip in reliability indicated by the black and gray arrow in (A) corresponds to the bifurcation in the black and gray circle in (B), respectively. The inset in B is the close up of the rastergram shown in the black circle. We plot (C) mean spike count and (D) standard deviation of the spike count across trials versus the amplitude. The gray curve is the R-reliability replotted from panel A, the full range for R, 0 to 1, is represented in the graph. Peaks in the reliability, indicated by the double-headed arrows, correspond to (C) plateaus in the spike count, for which (D) the trial-to-trial variability in the spike count was small.
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pcbi-1002615-g005: Bifurcation points were observed in model simulations for amplitudes at which the spike count changed.We show the (A) R-reliability (sigma = 1 ms) and (B) rastergram as a function of amplitude obtained from simulations of the Wang-Buzsaki model neuron [22], [47], using the same injected current as in the recordings from neurons. The dip in reliability indicated by the black and gray arrow in (A) corresponds to the bifurcation in the black and gray circle in (B), respectively. The inset in B is the close up of the rastergram shown in the black circle. We plot (C) mean spike count and (D) standard deviation of the spike count across trials versus the amplitude. The gray curve is the R-reliability replotted from panel A, the full range for R, 0 to 1, is represented in the graph. Peaks in the reliability, indicated by the double-headed arrows, correspond to (C) plateaus in the spike count, for which (D) the trial-to-trial variability in the spike count was small.

Mentions: Without knowing the internal state of a neuron it is difficult to draw any conclusions about dynamical mechanisms that might be responsible for the observed diversity of spike patterns. The same current inputs were used to study the Wang-Buzsaki (WB) model neuron [47] modified by including a small additive noise current as a source of independent trial-to-trial variability (see Methods). We simulated 50 trials for each of 101 different amplitudes b between 0 and 100% (the stimulus h(t) was normalized to have zero mean and unit standard deviation). Figure 5A shows the reliability curve, which was smoothed by a three-point running average, and Figure 5B shows the corresponding rastergram with matching amplitudes. For clarity we only displayed half of the trials and half of the amplitude values in the rastergram.


Multiple spike time patterns occur at bifurcation points of membrane potential dynamics.

Toups JV, Fellous JM, Thomas PJ, Sejnowski TJ, Tiesinga PH - PLoS Comput. Biol. (2012)

Bifurcation points were observed in model simulations for amplitudes at which the spike count changed.We show the (A) R-reliability (sigma = 1 ms) and (B) rastergram as a function of amplitude obtained from simulations of the Wang-Buzsaki model neuron [22], [47], using the same injected current as in the recordings from neurons. The dip in reliability indicated by the black and gray arrow in (A) corresponds to the bifurcation in the black and gray circle in (B), respectively. The inset in B is the close up of the rastergram shown in the black circle. We plot (C) mean spike count and (D) standard deviation of the spike count across trials versus the amplitude. The gray curve is the R-reliability replotted from panel A, the full range for R, 0 to 1, is represented in the graph. Peaks in the reliability, indicated by the double-headed arrows, correspond to (C) plateaus in the spike count, for which (D) the trial-to-trial variability in the spike count was small.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3475656&req=5

pcbi-1002615-g005: Bifurcation points were observed in model simulations for amplitudes at which the spike count changed.We show the (A) R-reliability (sigma = 1 ms) and (B) rastergram as a function of amplitude obtained from simulations of the Wang-Buzsaki model neuron [22], [47], using the same injected current as in the recordings from neurons. The dip in reliability indicated by the black and gray arrow in (A) corresponds to the bifurcation in the black and gray circle in (B), respectively. The inset in B is the close up of the rastergram shown in the black circle. We plot (C) mean spike count and (D) standard deviation of the spike count across trials versus the amplitude. The gray curve is the R-reliability replotted from panel A, the full range for R, 0 to 1, is represented in the graph. Peaks in the reliability, indicated by the double-headed arrows, correspond to (C) plateaus in the spike count, for which (D) the trial-to-trial variability in the spike count was small.
Mentions: Without knowing the internal state of a neuron it is difficult to draw any conclusions about dynamical mechanisms that might be responsible for the observed diversity of spike patterns. The same current inputs were used to study the Wang-Buzsaki (WB) model neuron [47] modified by including a small additive noise current as a source of independent trial-to-trial variability (see Methods). We simulated 50 trials for each of 101 different amplitudes b between 0 and 100% (the stimulus h(t) was normalized to have zero mean and unit standard deviation). Figure 5A shows the reliability curve, which was smoothed by a three-point running average, and Figure 5B shows the corresponding rastergram with matching amplitudes. For clarity we only displayed half of the trials and half of the amplitude values in the rastergram.

Bottom Line: The response of a neuron to repeated somatic fluctuating current injections in vitro can elicit a reliable and precisely timed sequence of action potentials.However, at specific values called bifurcation points, large shifts in the spike times were obtained in response to small changes in the stimulus, resulting in multiple spike patterns that were revealed using an unsupervised classification method.Furthermore, the spike times shifted earlier with increasing offset.

View Article: PubMed Central - PubMed

Affiliation: Computational Neurophysics Laboratory, Department of Physics & Astronomy, University of North Carolina, Chapel Hill, NC, USA.

ABSTRACT
The response of a neuron to repeated somatic fluctuating current injections in vitro can elicit a reliable and precisely timed sequence of action potentials. The set of responses obtained across trials can also be interpreted as the response of an ensemble of similar neurons receiving the same input, with the precise spike times representing synchronous volleys that would be effective in driving postsynaptic neurons. To study the reproducibility of the output spike times for different conditions that might occur in vivo, we somatically injected aperiodic current waveforms into cortical neurons in vitro and systematically varied the amplitude and DC offset of the fluctuations. As the amplitude of the fluctuations was increased, reliability increased and the spike times remained stable over a wide range of values. However, at specific values called bifurcation points, large shifts in the spike times were obtained in response to small changes in the stimulus, resulting in multiple spike patterns that were revealed using an unsupervised classification method. Increasing the DC offset, which mimicked an overall increase in network background activity, also revealed bifurcation points and increased the reliability. Furthermore, the spike times shifted earlier with increasing offset. Although the reliability was reduced at bifurcation points, a theoretical analysis showed that the information about the stimulus time course was increased because each of the spike time patterns contained different information about the input.

Show MeSH
Related in: MedlinePlus