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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

Spike timing in response to a fluctuating current is robust against changes in amplitude and offset.Responses of two Layer 5 pyramidal cells in a slice preparation of rat prefrontal cortex. In (A) the amplitude of the fluctuating current was varied, whereas in another cell (B) the current offset was varied. For each panel: (a) the rastergram, (b) the R-reliability (Schreiber measure with sigma = 3 ms, see Methods) versus amplitude or current offset and (c) the average spike time histogram across all values of either the amplitude or offset. In subpanel (Ab), the gray curve is the R-reliability based on only spikes in the time interval between 700 ms and 900 ms. The stimulus waveform is shown for reference at the bottom of subpanels (a) and (c). Each line in the rastergram represents a spike train obtained on a trial, with the ordinate of each tick representing a spike time. The spike trains are ordered in blocks (delineated by horizontal lines) based on the amplitude or offset of the injected current, expressed as a percentage, with the highest amplitude or offset on top. In (A) the amplitude ranges from 0% to 100% of maximum amplitude. In (B) the current offset ranges from 0.05 nA to 0.3 nA; indicated as a percentage (0.05/0.3 = 13% of maximum; 0.3/0.3 = 100% of maximum). Within each block the trials are in the order they were recorded, with the earliest trial at the bottom. The arrows in subpanels (b) indicates the dip in the R-reliability, which is related to the spike train dynamics highlighted by the corresponding gray box in subpanels (a). This behavior is related to the presence of so-called bifurcation points.
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pcbi-1002615-g002: Spike timing in response to a fluctuating current is robust against changes in amplitude and offset.Responses of two Layer 5 pyramidal cells in a slice preparation of rat prefrontal cortex. In (A) the amplitude of the fluctuating current was varied, whereas in another cell (B) the current offset was varied. For each panel: (a) the rastergram, (b) the R-reliability (Schreiber measure with sigma = 3 ms, see Methods) versus amplitude or current offset and (c) the average spike time histogram across all values of either the amplitude or offset. In subpanel (Ab), the gray curve is the R-reliability based on only spikes in the time interval between 700 ms and 900 ms. The stimulus waveform is shown for reference at the bottom of subpanels (a) and (c). Each line in the rastergram represents a spike train obtained on a trial, with the ordinate of each tick representing a spike time. The spike trains are ordered in blocks (delineated by horizontal lines) based on the amplitude or offset of the injected current, expressed as a percentage, with the highest amplitude or offset on top. In (A) the amplitude ranges from 0% to 100% of maximum amplitude. In (B) the current offset ranges from 0.05 nA to 0.3 nA; indicated as a percentage (0.05/0.3 = 13% of maximum; 0.3/0.3 = 100% of maximum). Within each block the trials are in the order they were recorded, with the earliest trial at the bottom. The arrows in subpanels (b) indicates the dip in the R-reliability, which is related to the spike train dynamics highlighted by the corresponding gray box in subpanels (a). This behavior is related to the presence of so-called bifurcation points.

Mentions: Rastergrams for one representative cell are shown in Figure 2A, in response to an injected current waveform. A spike-time histogram for all values of the current step and scaling factor are shown in the bottom panel. The rastergram consists of blocks of constant amplitude, with the highest amplitude on top. Within each block the trials are in the order they were collected, with the earliest at the bottom. In the rastergram (Figure 2Aa), events are visible as spike alignments that appear for low to intermediate amplitudes and that become sharper as the amplitude is increased. Overall this graph suggests that both the precision, the jitter in the spike times belonging to an event, and the reliability, the fraction of trials on which a spike is present in an event, improve with amplitude. The trial-to-trial variability was characterized using the R-reliability (see Methods) with a sigma value of 3 ms [43]; that is, spikes in two different trials with a time difference of less than 3 ms are considered effectively coincident. This measure does not distinguish between changes in reliability and changes in precision (as demonstrated previously [14], [34]), which would require an event-based analysis. Overall, R increased with amplitude (Figure 2Ab), but there were dips, indicated by the arrow. As will be shown below, the presence of a dip is characteristic of a bifurcation point, where a small change in the stimulus can lead to a large shift in the pattern of spikes.


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)

Spike timing in response to a fluctuating current is robust against changes in amplitude and offset.Responses of two Layer 5 pyramidal cells in a slice preparation of rat prefrontal cortex. In (A) the amplitude of the fluctuating current was varied, whereas in another cell (B) the current offset was varied. For each panel: (a) the rastergram, (b) the R-reliability (Schreiber measure with sigma = 3 ms, see Methods) versus amplitude or current offset and (c) the average spike time histogram across all values of either the amplitude or offset. In subpanel (Ab), the gray curve is the R-reliability based on only spikes in the time interval between 700 ms and 900 ms. The stimulus waveform is shown for reference at the bottom of subpanels (a) and (c). Each line in the rastergram represents a spike train obtained on a trial, with the ordinate of each tick representing a spike time. The spike trains are ordered in blocks (delineated by horizontal lines) based on the amplitude or offset of the injected current, expressed as a percentage, with the highest amplitude or offset on top. In (A) the amplitude ranges from 0% to 100% of maximum amplitude. In (B) the current offset ranges from 0.05 nA to 0.3 nA; indicated as a percentage (0.05/0.3 = 13% of maximum; 0.3/0.3 = 100% of maximum). Within each block the trials are in the order they were recorded, with the earliest trial at the bottom. The arrows in subpanels (b) indicates the dip in the R-reliability, which is related to the spike train dynamics highlighted by the corresponding gray box in subpanels (a). This behavior is related to the presence of so-called bifurcation points.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002615-g002: Spike timing in response to a fluctuating current is robust against changes in amplitude and offset.Responses of two Layer 5 pyramidal cells in a slice preparation of rat prefrontal cortex. In (A) the amplitude of the fluctuating current was varied, whereas in another cell (B) the current offset was varied. For each panel: (a) the rastergram, (b) the R-reliability (Schreiber measure with sigma = 3 ms, see Methods) versus amplitude or current offset and (c) the average spike time histogram across all values of either the amplitude or offset. In subpanel (Ab), the gray curve is the R-reliability based on only spikes in the time interval between 700 ms and 900 ms. The stimulus waveform is shown for reference at the bottom of subpanels (a) and (c). Each line in the rastergram represents a spike train obtained on a trial, with the ordinate of each tick representing a spike time. The spike trains are ordered in blocks (delineated by horizontal lines) based on the amplitude or offset of the injected current, expressed as a percentage, with the highest amplitude or offset on top. In (A) the amplitude ranges from 0% to 100% of maximum amplitude. In (B) the current offset ranges from 0.05 nA to 0.3 nA; indicated as a percentage (0.05/0.3 = 13% of maximum; 0.3/0.3 = 100% of maximum). Within each block the trials are in the order they were recorded, with the earliest trial at the bottom. The arrows in subpanels (b) indicates the dip in the R-reliability, which is related to the spike train dynamics highlighted by the corresponding gray box in subpanels (a). This behavior is related to the presence of so-called bifurcation points.
Mentions: Rastergrams for one representative cell are shown in Figure 2A, in response to an injected current waveform. A spike-time histogram for all values of the current step and scaling factor are shown in the bottom panel. The rastergram consists of blocks of constant amplitude, with the highest amplitude on top. Within each block the trials are in the order they were collected, with the earliest at the bottom. In the rastergram (Figure 2Aa), events are visible as spike alignments that appear for low to intermediate amplitudes and that become sharper as the amplitude is increased. Overall this graph suggests that both the precision, the jitter in the spike times belonging to an event, and the reliability, the fraction of trials on which a spike is present in an event, improve with amplitude. The trial-to-trial variability was characterized using the R-reliability (see Methods) with a sigma value of 3 ms [43]; that is, spikes in two different trials with a time difference of less than 3 ms are considered effectively coincident. This measure does not distinguish between changes in reliability and changes in precision (as demonstrated previously [14], [34]), which would require an event-based analysis. Overall, R increased with amplitude (Figure 2Ab), but there were dips, indicated by the arrow. As will be shown below, the presence of a dip is characteristic of a bifurcation point, where a small change in the stimulus can lead to a large shift in the pattern of spikes.

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