Limits...
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.

Show MeSH

Related in: MedlinePlus

Bifurcation points led to multiple spike patterns that persisted across multiple amplitudes.(A) The rastergram for the data shown in Figure 2A for amplitudes between 60% and 100% and during the time segment between 650 ms and 850 ms. (B) The analysis procedure suggested that there were four clusters, each corresponding to a spike pattern. We show the rastergram with the trials sorted according to their cluster membership. The numbers on the right side are the cluster index. The gray vertical bands show the detected events that remained after applying a procedure to merge events common to multiple clusters. We used the value tISI = 3 ms to detect the events using the interval method and the value tROC = 0.50 to find and merge common events. (C) Rastergram of the clustered data shown in panel A. Each block (separated by thick black lines) corresponds to a different amplitude, with the lowest amplitude at the bottom and the highest amplitude at the top. Within each block, the trials are ordered based on their cluster membership. The clusters are separated by thin dashed lines. Two events are highlighted: the ones in the black ellipses, whose reliability increased with amplitude and the ones in the gray ellipses, whose reliability decreased with amplitude. (D) The pattern occupation (or probability) for a given amplitude is the fraction of trials on which that pattern is obtained. We show the pattern occupation as a function of amplitude for the four patterns that were detected, as indicated by the numbers in the graph. (E) The diversity of patterns observed for a given value of the amplitude is quantified as the entropy of the pattern distribution. The entropy as a function of amplitude has a peak at 80% (arrow), indicating that the pattern diversity is largest for that amplitude. The error bars represent the standard deviation of the entropy determined using a resampling procedure (see Methods). There is no correction for the bias, which took values between 0.02 and 0.05 bits.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3475656&req=5

pcbi-1002615-g003: Bifurcation points led to multiple spike patterns that persisted across multiple amplitudes.(A) The rastergram for the data shown in Figure 2A for amplitudes between 60% and 100% and during the time segment between 650 ms and 850 ms. (B) The analysis procedure suggested that there were four clusters, each corresponding to a spike pattern. We show the rastergram with the trials sorted according to their cluster membership. The numbers on the right side are the cluster index. The gray vertical bands show the detected events that remained after applying a procedure to merge events common to multiple clusters. We used the value tISI = 3 ms to detect the events using the interval method and the value tROC = 0.50 to find and merge common events. (C) Rastergram of the clustered data shown in panel A. Each block (separated by thick black lines) corresponds to a different amplitude, with the lowest amplitude at the bottom and the highest amplitude at the top. Within each block, the trials are ordered based on their cluster membership. The clusters are separated by thin dashed lines. Two events are highlighted: the ones in the black ellipses, whose reliability increased with amplitude and the ones in the gray ellipses, whose reliability decreased with amplitude. (D) The pattern occupation (or probability) for a given amplitude is the fraction of trials on which that pattern is obtained. We show the pattern occupation as a function of amplitude for the four patterns that were detected, as indicated by the numbers in the graph. (E) The diversity of patterns observed for a given value of the amplitude is quantified as the entropy of the pattern distribution. The entropy as a function of amplitude has a peak at 80% (arrow), indicating that the pattern diversity is largest for that amplitude. The error bars represent the standard deviation of the entropy determined using a resampling procedure (see Methods). There is no correction for the bias, which took values between 0.02 and 0.05 bits.

Mentions: Identification of events in a peristimulus time histogram is essential for the analysis of stimulus encoding via spike time patterns. Because the events visible in the multi-amplitude rastergrams (Figure 2) persist across amplitudes, the precision, reliability and mean spike time of events can be compared across amplitudes (see Methods). One strategy for event-based analysis would be to find events for each amplitude and merge events common across amplitudes. In Figure 3 we show the results of an alternative strategy, in which spike train ensembles generated by the five highest amplitudes are analyzed at the same time. With this approach the underlying pattern-finding procedure (see Methods) is more robust because there are more trials in each pattern [34]. Our analysis revealed the presence of four patterns (Figure 3B), which led to 8 events, some of which were common to multiple patterns. We recall that events are temporally localized concentrations of spike time density across trials and patterns are transient multiplicity of spike response. In panel B the patterns are divided by gray horizontal lines, whereas all the spikes belonging to an event are enclosed in a gray vertical box.


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 led to multiple spike patterns that persisted across multiple amplitudes.(A) The rastergram for the data shown in Figure 2A for amplitudes between 60% and 100% and during the time segment between 650 ms and 850 ms. (B) The analysis procedure suggested that there were four clusters, each corresponding to a spike pattern. We show the rastergram with the trials sorted according to their cluster membership. The numbers on the right side are the cluster index. The gray vertical bands show the detected events that remained after applying a procedure to merge events common to multiple clusters. We used the value tISI = 3 ms to detect the events using the interval method and the value tROC = 0.50 to find and merge common events. (C) Rastergram of the clustered data shown in panel A. Each block (separated by thick black lines) corresponds to a different amplitude, with the lowest amplitude at the bottom and the highest amplitude at the top. Within each block, the trials are ordered based on their cluster membership. The clusters are separated by thin dashed lines. Two events are highlighted: the ones in the black ellipses, whose reliability increased with amplitude and the ones in the gray ellipses, whose reliability decreased with amplitude. (D) The pattern occupation (or probability) for a given amplitude is the fraction of trials on which that pattern is obtained. We show the pattern occupation as a function of amplitude for the four patterns that were detected, as indicated by the numbers in the graph. (E) The diversity of patterns observed for a given value of the amplitude is quantified as the entropy of the pattern distribution. The entropy as a function of amplitude has a peak at 80% (arrow), indicating that the pattern diversity is largest for that amplitude. The error bars represent the standard deviation of the entropy determined using a resampling procedure (see Methods). There is no correction for the bias, which took values between 0.02 and 0.05 bits.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002615-g003: Bifurcation points led to multiple spike patterns that persisted across multiple amplitudes.(A) The rastergram for the data shown in Figure 2A for amplitudes between 60% and 100% and during the time segment between 650 ms and 850 ms. (B) The analysis procedure suggested that there were four clusters, each corresponding to a spike pattern. We show the rastergram with the trials sorted according to their cluster membership. The numbers on the right side are the cluster index. The gray vertical bands show the detected events that remained after applying a procedure to merge events common to multiple clusters. We used the value tISI = 3 ms to detect the events using the interval method and the value tROC = 0.50 to find and merge common events. (C) Rastergram of the clustered data shown in panel A. Each block (separated by thick black lines) corresponds to a different amplitude, with the lowest amplitude at the bottom and the highest amplitude at the top. Within each block, the trials are ordered based on their cluster membership. The clusters are separated by thin dashed lines. Two events are highlighted: the ones in the black ellipses, whose reliability increased with amplitude and the ones in the gray ellipses, whose reliability decreased with amplitude. (D) The pattern occupation (or probability) for a given amplitude is the fraction of trials on which that pattern is obtained. We show the pattern occupation as a function of amplitude for the four patterns that were detected, as indicated by the numbers in the graph. (E) The diversity of patterns observed for a given value of the amplitude is quantified as the entropy of the pattern distribution. The entropy as a function of amplitude has a peak at 80% (arrow), indicating that the pattern diversity is largest for that amplitude. The error bars represent the standard deviation of the entropy determined using a resampling procedure (see Methods). There is no correction for the bias, which took values between 0.02 and 0.05 bits.
Mentions: Identification of events in a peristimulus time histogram is essential for the analysis of stimulus encoding via spike time patterns. Because the events visible in the multi-amplitude rastergrams (Figure 2) persist across amplitudes, the precision, reliability and mean spike time of events can be compared across amplitudes (see Methods). One strategy for event-based analysis would be to find events for each amplitude and merge events common across amplitudes. In Figure 3 we show the results of an alternative strategy, in which spike train ensembles generated by the five highest amplitudes are analyzed at the same time. With this approach the underlying pattern-finding procedure (see Methods) is more robust because there are more trials in each pattern [34]. Our analysis revealed the presence of four patterns (Figure 3B), which led to 8 events, some of which were common to multiple patterns. We recall that events are temporally localized concentrations of spike time density across trials and patterns are transient multiplicity of spike response. In panel B the patterns are divided by gray horizontal lines, whereas all the spikes belonging to an event are enclosed in a gray vertical box.

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