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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 patterns corresponded to voltage patterns.The single-amplitude data set was divided into four time segments. (A) Segment-by-segment rastergrams. In each segment trials were ordered according to the cluster membership in that segment. The clusters are separated by horizontal dashed lines, whereas segments are indicated by vertical lines. Because the trial order varied from segment to segment, spikes on the same row but in different segments are not necessarily obtained in the same trial. There was a 200 ms long constant current step (arrow), whose amplitude took eleven different values (only one is shown). (B) Rastergram with trials in each segment ordered based on their cluster membership on the fourth segment (asterisk) – each row thus represents the same trial across all the segments. At the bottom of A and B the current waveform is repeated for reference. (C–E) The analysis procedure found 3 spike patterns in the fourth segment (between 1500 ms and 1900 ms), labeled 1 (solid black curve), 2 (dotted black curve), and 3 (gray curve). In each of the panels C–E, we show (top) the voltage traces averaged across all trials expressing that pattern (the y-axis covers the range from −65 to −35 mV) and (bottom) the current waveform (gray curve) together with a rastergram where the trials were ordered based on the cluster membership in the fourth segment. The spikes were shifted to the left by 12 ms so that they were approximately aligned with an upswing in the injected current. In (C) the gray bands indicate the plus or minus two standard error range for the black curve. The arrow in (D) indicates the point where differences between the voltage traces appeared. Note that the spike patterns are clearly visible in panel E, but that they are hardly visible in panel D indicating a low correlation between patterns expressed in different segments. Trials are sorted in the same order in panels C–E.
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pcbi-1002615-g004: Spike patterns corresponded to voltage patterns.The single-amplitude data set was divided into four time segments. (A) Segment-by-segment rastergrams. In each segment trials were ordered according to the cluster membership in that segment. The clusters are separated by horizontal dashed lines, whereas segments are indicated by vertical lines. Because the trial order varied from segment to segment, spikes on the same row but in different segments are not necessarily obtained in the same trial. There was a 200 ms long constant current step (arrow), whose amplitude took eleven different values (only one is shown). (B) Rastergram with trials in each segment ordered based on their cluster membership on the fourth segment (asterisk) – each row thus represents the same trial across all the segments. At the bottom of A and B the current waveform is repeated for reference. (C–E) The analysis procedure found 3 spike patterns in the fourth segment (between 1500 ms and 1900 ms), labeled 1 (solid black curve), 2 (dotted black curve), and 3 (gray curve). In each of the panels C–E, we show (top) the voltage traces averaged across all trials expressing that pattern (the y-axis covers the range from −65 to −35 mV) and (bottom) the current waveform (gray curve) together with a rastergram where the trials were ordered based on the cluster membership in the fourth segment. The spikes were shifted to the left by 12 ms so that they were approximately aligned with an upswing in the injected current. In (C) the gray bands indicate the plus or minus two standard error range for the black curve. The arrow in (D) indicates the point where differences between the voltage traces appeared. Note that the spike patterns are clearly visible in panel E, but that they are hardly visible in panel D indicating a low correlation between patterns expressed in different segments. Trials are sorted in the same order in panels C–E.

Mentions: Spike patterns correspond to within-trial correlation between spike times. We determined how long these correlations persisted by applying the spike pattern analysis to approximately 500 ms long segments from seven of the nine available data sets from which we show one (Figure 4A). The segment length was chosen such that at least two events, and no more than six, were present. Within each segment the trials were ordered according to the pattern they expressed in that segment. This shuffles the trials differently in each of the segments and the spikes on a single row of the rastergram most likely correspond to a sequence of segments from different trials. We then determined how well the pattern expressed on a trial during one time segment predicted which pattern was expressed in a preceding or following segment, that is, the between-segment correlation of the patterns that neurons express. Strong correlation means that if in one segment a group of trials express the same pattern, they will also do so in the other segment. In Figure 4B, the trials were reordered in each segment based on the order in the last (fourth) segment (indicated by the asterisk). For this case, each row is one and the same trial on each segment in contrast to the display in panel A. This panel shows that even though a group of trials expressed the same pattern during segment 4, that same group expressed a mixture of patterns during segment 3 – indicative of a low between-segment correlation. This association between different segments is best expressed as the normalized mutual information between the pattern classification of a trial in two segments (IN, see Methods, which is primarily used here to summarize a two-dimensional array of transfer probabilities rather than to make statements about information content). The maximum value was normalized to one, which occurs if the classifications are identical. The IN (bias; std) between the classification in segment 4 and that in segments 3, 2 or 1 was 0.20 (0.01; 0.04), 0.003 (0.009; 0.012), or 0.025 (0.007; 0.020), respectively.


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 patterns corresponded to voltage patterns.The single-amplitude data set was divided into four time segments. (A) Segment-by-segment rastergrams. In each segment trials were ordered according to the cluster membership in that segment. The clusters are separated by horizontal dashed lines, whereas segments are indicated by vertical lines. Because the trial order varied from segment to segment, spikes on the same row but in different segments are not necessarily obtained in the same trial. There was a 200 ms long constant current step (arrow), whose amplitude took eleven different values (only one is shown). (B) Rastergram with trials in each segment ordered based on their cluster membership on the fourth segment (asterisk) – each row thus represents the same trial across all the segments. At the bottom of A and B the current waveform is repeated for reference. (C–E) The analysis procedure found 3 spike patterns in the fourth segment (between 1500 ms and 1900 ms), labeled 1 (solid black curve), 2 (dotted black curve), and 3 (gray curve). In each of the panels C–E, we show (top) the voltage traces averaged across all trials expressing that pattern (the y-axis covers the range from −65 to −35 mV) and (bottom) the current waveform (gray curve) together with a rastergram where the trials were ordered based on the cluster membership in the fourth segment. The spikes were shifted to the left by 12 ms so that they were approximately aligned with an upswing in the injected current. In (C) the gray bands indicate the plus or minus two standard error range for the black curve. The arrow in (D) indicates the point where differences between the voltage traces appeared. Note that the spike patterns are clearly visible in panel E, but that they are hardly visible in panel D indicating a low correlation between patterns expressed in different segments. Trials are sorted in the same order in panels C–E.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002615-g004: Spike patterns corresponded to voltage patterns.The single-amplitude data set was divided into four time segments. (A) Segment-by-segment rastergrams. In each segment trials were ordered according to the cluster membership in that segment. The clusters are separated by horizontal dashed lines, whereas segments are indicated by vertical lines. Because the trial order varied from segment to segment, spikes on the same row but in different segments are not necessarily obtained in the same trial. There was a 200 ms long constant current step (arrow), whose amplitude took eleven different values (only one is shown). (B) Rastergram with trials in each segment ordered based on their cluster membership on the fourth segment (asterisk) – each row thus represents the same trial across all the segments. At the bottom of A and B the current waveform is repeated for reference. (C–E) The analysis procedure found 3 spike patterns in the fourth segment (between 1500 ms and 1900 ms), labeled 1 (solid black curve), 2 (dotted black curve), and 3 (gray curve). In each of the panels C–E, we show (top) the voltage traces averaged across all trials expressing that pattern (the y-axis covers the range from −65 to −35 mV) and (bottom) the current waveform (gray curve) together with a rastergram where the trials were ordered based on the cluster membership in the fourth segment. The spikes were shifted to the left by 12 ms so that they were approximately aligned with an upswing in the injected current. In (C) the gray bands indicate the plus or minus two standard error range for the black curve. The arrow in (D) indicates the point where differences between the voltage traces appeared. Note that the spike patterns are clearly visible in panel E, but that they are hardly visible in panel D indicating a low correlation between patterns expressed in different segments. Trials are sorted in the same order in panels C–E.
Mentions: Spike patterns correspond to within-trial correlation between spike times. We determined how long these correlations persisted by applying the spike pattern analysis to approximately 500 ms long segments from seven of the nine available data sets from which we show one (Figure 4A). The segment length was chosen such that at least two events, and no more than six, were present. Within each segment the trials were ordered according to the pattern they expressed in that segment. This shuffles the trials differently in each of the segments and the spikes on a single row of the rastergram most likely correspond to a sequence of segments from different trials. We then determined how well the pattern expressed on a trial during one time segment predicted which pattern was expressed in a preceding or following segment, that is, the between-segment correlation of the patterns that neurons express. Strong correlation means that if in one segment a group of trials express the same pattern, they will also do so in the other segment. In Figure 4B, the trials were reordered in each segment based on the order in the last (fourth) segment (indicated by the asterisk). For this case, each row is one and the same trial on each segment in contrast to the display in panel A. This panel shows that even though a group of trials expressed the same pattern during segment 4, that same group expressed a mixture of patterns during segment 3 – indicative of a low between-segment correlation. This association between different segments is best expressed as the normalized mutual information between the pattern classification of a trial in two segments (IN, see Methods, which is primarily used here to summarize a two-dimensional array of transfer probabilities rather than to make statements about information content). The maximum value was normalized to one, which occurs if the classifications are identical. The IN (bias; std) between the classification in segment 4 and that in segments 3, 2 or 1 was 0.20 (0.01; 0.04), 0.003 (0.009; 0.012), or 0.025 (0.007; 0.020), respectively.

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