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Spike correlations in a songbird agree with a simple markov population model.

Weber AP, Hahnloser RH - PLoS Comput. Biol. (2007)

Bottom Line: Individual spike trains are generated by associating with each of the population states a particular firing mode, such as bursting or tonic firing.Our results suggest that song- and sleep-related firing patterns are identical on short time scales and result from random sampling of a unique underlying theme.The efficiency of our population model may apply also to other neural systems in which population hypotheses can be tested on recordings from small neuron groups.

View Article: PubMed Central - PubMed

Affiliation: Institute of Neuroinformatics UZH/ETH Zurich, Zurich, Switzerland.

ABSTRACT
The relationships between neural activity at the single-cell and the population levels are of central importance for understanding neural codes. In many sensory systems, collective behaviors in large cell groups can be described by pairwise spike correlations. Here, we test whether in a highly specialized premotor system of songbirds, pairwise spike correlations themselves can be seen as a simple corollary of an underlying random process. We test hypotheses on connectivity and network dynamics in the motor pathway of zebra finches using a high-level population model that is independent of detailed single-neuron properties. We assume that neural population activity evolves along a finite set of states during singing, and that during sleep population activity randomly switches back and forth between song states and a single resting state. Individual spike trains are generated by associating with each of the population states a particular firing mode, such as bursting or tonic firing. With an overall modification of one or two simple control parameters, the Markov model is able to reproduce observed firing statistics and spike correlations in different neuron types and behavioral states. Our results suggest that song- and sleep-related firing patterns are identical on short time scales and result from random sampling of a unique underlying theme. The efficiency of our population model may apply also to other neural systems in which population hypotheses can be tested on recordings from small neuron groups.

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Markov Model of HVC Activity during Behavior and Sleep(A) When birds are awake, but not singing, HVC activity persists in a ground state (state 0) with probability q = 1. When birds sing, groups of HVCRA neurons (numbered circles) are sequentially activated with probability p = 1 (the dashed arrows indicate song onset and offset). A single HVCRA neuron (red square) is linked with exactly one HVCRA group, and single RA and HVCI neurons (blue and green squares) are linked with random subsets of LR and LI groups, respectively.(B) During sleep, HVCRA groups are sequentially activated with probability p < 1; with probability 1 − p, HVC activity transits into the ground state. There, it persists with probability q < 1; with probability 1 − q, it transits back into a song state.(C) Bursts in different neuron types are modeled by the first few milliseconds of averaged song-related ISI pdfs pb(τ).(D) Tonic firing in RA and HVCI neurons is modeled by gamma functions pa(τ) (black curves). The diversity of waking-related ISI pdfs in these neurons is illustrated by the blue and green curves, each representing a different neuron.
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pcbi-0030249-g002: Markov Model of HVC Activity during Behavior and Sleep(A) When birds are awake, but not singing, HVC activity persists in a ground state (state 0) with probability q = 1. When birds sing, groups of HVCRA neurons (numbered circles) are sequentially activated with probability p = 1 (the dashed arrows indicate song onset and offset). A single HVCRA neuron (red square) is linked with exactly one HVCRA group, and single RA and HVCI neurons (blue and green squares) are linked with random subsets of LR and LI groups, respectively.(B) During sleep, HVCRA groups are sequentially activated with probability p < 1; with probability 1 − p, HVC activity transits into the ground state. There, it persists with probability q < 1; with probability 1 − q, it transits back into a song state.(C) Bursts in different neuron types are modeled by the first few milliseconds of averaged song-related ISI pdfs pb(τ).(D) Tonic firing in RA and HVCI neurons is modeled by gamma functions pa(τ) (black curves). The diversity of waking-related ISI pdfs in these neurons is illustrated by the blue and green curves, each representing a different neuron.

Mentions: In our model, HVC population activity is a random variable that evolves in roughly 5 ms steps and is either in the ground state, or in one of 100 song states. The number of song states is chosen such that a total song-motif duration of 500 ms results [20]. Each of the song states corresponds to activation of a virtual group of 50–150 RA-projecting HVC neurons (referred to as HVCRA neuron groups, or simply HVCRA groups). During singing, HVCRA groups are activated sequentially with probability p = 1 (Figure 2A). When birds are awake, but not singing, HVC activity remains in the ground state (state 0) with probability q = 1. During sleep, HVCRA groups are also sequentially activated, but with reduced probability p < 1, and, the persistence probability in the ground state is also reduced to q < 1 (Figure 2B). By construction, neurons remain for exponentially distributed times in song and ground states during sleep, in agreement with recent estimates [17].


Spike correlations in a songbird agree with a simple markov population model.

Weber AP, Hahnloser RH - PLoS Comput. Biol. (2007)

Markov Model of HVC Activity during Behavior and Sleep(A) When birds are awake, but not singing, HVC activity persists in a ground state (state 0) with probability q = 1. When birds sing, groups of HVCRA neurons (numbered circles) are sequentially activated with probability p = 1 (the dashed arrows indicate song onset and offset). A single HVCRA neuron (red square) is linked with exactly one HVCRA group, and single RA and HVCI neurons (blue and green squares) are linked with random subsets of LR and LI groups, respectively.(B) During sleep, HVCRA groups are sequentially activated with probability p < 1; with probability 1 − p, HVC activity transits into the ground state. There, it persists with probability q < 1; with probability 1 − q, it transits back into a song state.(C) Bursts in different neuron types are modeled by the first few milliseconds of averaged song-related ISI pdfs pb(τ).(D) Tonic firing in RA and HVCI neurons is modeled by gamma functions pa(τ) (black curves). The diversity of waking-related ISI pdfs in these neurons is illustrated by the blue and green curves, each representing a different neuron.
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getmorefigures.php?uid=PMC2230679&req=5

pcbi-0030249-g002: Markov Model of HVC Activity during Behavior and Sleep(A) When birds are awake, but not singing, HVC activity persists in a ground state (state 0) with probability q = 1. When birds sing, groups of HVCRA neurons (numbered circles) are sequentially activated with probability p = 1 (the dashed arrows indicate song onset and offset). A single HVCRA neuron (red square) is linked with exactly one HVCRA group, and single RA and HVCI neurons (blue and green squares) are linked with random subsets of LR and LI groups, respectively.(B) During sleep, HVCRA groups are sequentially activated with probability p < 1; with probability 1 − p, HVC activity transits into the ground state. There, it persists with probability q < 1; with probability 1 − q, it transits back into a song state.(C) Bursts in different neuron types are modeled by the first few milliseconds of averaged song-related ISI pdfs pb(τ).(D) Tonic firing in RA and HVCI neurons is modeled by gamma functions pa(τ) (black curves). The diversity of waking-related ISI pdfs in these neurons is illustrated by the blue and green curves, each representing a different neuron.
Mentions: In our model, HVC population activity is a random variable that evolves in roughly 5 ms steps and is either in the ground state, or in one of 100 song states. The number of song states is chosen such that a total song-motif duration of 500 ms results [20]. Each of the song states corresponds to activation of a virtual group of 50–150 RA-projecting HVC neurons (referred to as HVCRA neuron groups, or simply HVCRA groups). During singing, HVCRA groups are activated sequentially with probability p = 1 (Figure 2A). When birds are awake, but not singing, HVC activity remains in the ground state (state 0) with probability q = 1. During sleep, HVCRA groups are also sequentially activated, but with reduced probability p < 1, and, the persistence probability in the ground state is also reduced to q < 1 (Figure 2B). By construction, neurons remain for exponentially distributed times in song and ground states during sleep, in agreement with recent estimates [17].

Bottom Line: Individual spike trains are generated by associating with each of the population states a particular firing mode, such as bursting or tonic firing.Our results suggest that song- and sleep-related firing patterns are identical on short time scales and result from random sampling of a unique underlying theme.The efficiency of our population model may apply also to other neural systems in which population hypotheses can be tested on recordings from small neuron groups.

View Article: PubMed Central - PubMed

Affiliation: Institute of Neuroinformatics UZH/ETH Zurich, Zurich, Switzerland.

ABSTRACT
The relationships between neural activity at the single-cell and the population levels are of central importance for understanding neural codes. In many sensory systems, collective behaviors in large cell groups can be described by pairwise spike correlations. Here, we test whether in a highly specialized premotor system of songbirds, pairwise spike correlations themselves can be seen as a simple corollary of an underlying random process. We test hypotheses on connectivity and network dynamics in the motor pathway of zebra finches using a high-level population model that is independent of detailed single-neuron properties. We assume that neural population activity evolves along a finite set of states during singing, and that during sleep population activity randomly switches back and forth between song states and a single resting state. Individual spike trains are generated by associating with each of the population states a particular firing mode, such as bursting or tonic firing. With an overall modification of one or two simple control parameters, the Markov model is able to reproduce observed firing statistics and spike correlations in different neuron types and behavioral states. Our results suggest that song- and sleep-related firing patterns are identical on short time scales and result from random sampling of a unique underlying theme. The efficiency of our population model may apply also to other neural systems in which population hypotheses can be tested on recordings from small neuron groups.

Show MeSH