analysemethoden und kodierungsprinzipien - uni oldenburg · therelativecontributionsof t and p...

Analysemethoden und Kodierungsprinzipien

28.11.2005

http://www.uni-oldenburg.de/sinnesphysiologie/15241.html

Vorläufiges(!) Vorlesungsprogramm

17.10.05 Motivation24.10.05 Passive Eigenschaften von Neuronen31.10.05 Räumliche Struktur von Neuronen07.11.05 Aktive Eigenschaften von Neuronen14.11.05 Das Hodgkin-Huxley Modell21.11.05 Kodierung sensorischer Reize + Modellsimulation28.11.05 Analysemethoden und Kodierungsprinzipien05.12.05 Variabilität neuronaler Antworten12.12.05 Synaptische Übertragung08.01.06 Entstehung rezeptiver Felder16.01.06 Zwei Modelle retinaler Verarbeitung23.01.06 Populations- und Ensemble-Kodierung30.01.06 Künstliche Neuronale Netze06.02.06 Lernen in natürlichen und künstlichen Netzwerken

Themen:

Analysemethoden:Stimulus-Response KurvenRezeptive FelderTuningkurvenRasterplotPeri-Stimulus-Time-Histogram

Verschiedene KodierungsprinzipienBeispiel: Mechanoperzeption des Blutegels

Hausaufgabe

Wie sieht die Übertragungsfunktion zwischen physikalischem Stimulus und der Spikefrequenz aus?

Welche Fälle muss man betrachten?

Was sind die Schwierigkeiten bei der Bestimmung der Übertragungsfunktion?

Kodierung sensorischer Reize

Reichert 1990

physikalischerReiz

analoge Spannungs-

antwort

digitale Spannungs-

impulse

Kodierung

Um-kodierung

Auch eher eineSigmoidfunktion!

Das Nervensystem des Blutegels

21 sehr ähnliche Körpersegmente

In jedem Ganglion ca. 400 individuell bekannte Neurone

Überschaubare Neuronennetze steuern Verhalten

Weisblatt & Kristan 1985

Bestimmung von Stimulus-Response Kurven

Variation der Reiz-stärkeAndere Reizpara-meter bleiben konstantWiederholte gleiche Reizung Mittelwert und Standardabweichung der AP-Anzahl für jede Reizstärke

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Wiederholte gleiche Reizung führt zu unterschiedlichen Antworten!

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TOUCH REPRESENTATION BY LEECH SENSORY NEURONS 2589

a greater extent and produce other behavioral responses.] Byusing the same set of stimuli in a different group of fiveanimals, we found that the mean tension response increaseswith stimulus intensity in a manner similar to P-cell activa-tion but quite different from that of T-cell activation. TheT-cell spike count saturated at stimulus intensities ú1 mN;at this intensity, the behavioral response was only 25% ofthe response produced by the 37-mN stimulus. In agreementwith a previous study with a different approach (Kristan1982), this result suggests that P cells provide the majorinput for controlling the magnitude of the local bend re-sponse.However, it is still possible that the T cells provide spatial

FIG. 6. Mechanosensory neuron and behavioral tuning to stimulus inten- information, but their influence is gated by the P cells ( i.e.,sity. Stimuli of different intensities were delivered at S Å 45!. Normalized the information is not manifest in the behavior unless the Presponses (mean { SE; 5 animals) are plotted vs. stimulus intensity. Re-

cells are sufficiently active) . To test this possibility, wesponses of the T and P cells were measured by the normalized spike count,attempted to bias the tension response (measured at 45!)and the behavioral response was measured by normalized peak body wall

tension. evoked by a mechanical stimulus (S Å 45!; 22 mN) withsimultaneous intracellular stimulation of the TV cell (ú20Hz, 1-s trains) . If the T cells provide spatial information,extent to which their tuning curves overlap. In another study,the evoked tension should be diminished by TV stimulationwe characterized the local bend response as a function ofcaused by an effective shift in the bend direction to a morestimulus location (Lewis and Kristan 1998a). The RMSventral location (toward the preferred location of the TVdifference between stimulus location and the direction of thecell) . If the T cells provide nonspecific amplification to theevoked bend (i.e., behavioral error) was 8% and is shownlocal bend response, the tension response should increase.in Fig. 5B for comparison. With the stimulus encoding byWe found that TV stimulation had no effect on the tensionthe sensory neurons more than twice as accurate as the be-response measured at 45! (P ú 0.05, 2 animals, 8 trials) ,havior, it is clear that a neural code for stimulus locationindicating that the T cells play no detectable role in thisinvolving only the spike count contains more than enoughresponse. In similar experiments, intracellular P-cell stimula-information to account for the behavior.tion produced a significant and predictable effect on thebehavior (Lewis and Kristan 1998b). From these and previ-Relative importance of T and P cellsous results, we conclude that the P cells are the major carriersof spatial information to the local bend network.Because both T and P cells independently encode stimulus

location with an accuracy greater than the behavioral accu-racy, we tested whether the encoded information from each Varying encoding timecell type is actually used by the local bend networks.The thresholds and specific modalities differ for each of In Fig. 5 we showed that the decoding error with P-cell

spike trains wasÇ3%. These estimates were made for spikesthese cell types; T cells have a low threshold and are mostsensitive to the velocity of indentation of the body wall by occurring for an entire 700-ms interval after stimulus onset.

The latency for a behavioral response (muscle tension) ismechanical stimulation (Carlton and McVean 1995),whereas P cells have a higher threshold and respond best to typically Ç200 ms. How much information is available at

this short latency? To address this question, we calculatedchanges in the magnitude of body wall indentation. To testthe relative contributions of T and P cells to local bending, the mean decoding error for different encoding times (i.e.,

time since stimulus onset) . An encoding time of 700 mswe quantified the behavioral output and response of the sen-sory cells to mechanical stimuli of different intensities. We corresponds with the control condition (Fig. 5) . We mea-

sured the tuning curves and spike count variability again butlimited our studies to one stimulation site and one body walltension measurement site (45! for both) . At this stimulus only considered spikes that occurred in the time window

corresponding to a particular encoding time. For all encodinglocation, one P cell (right PD) and two T cells ( the right TDand TL) are activated to ú70% of their maximum level, and times tested, the tuning curves, normalized to maximum re-

sponse, were not significantly different from the controla third T cell ( the left TD) is activated to Ç25% of itsmaximum (see Fig. 5A) . The remaining cells are not acti- (Pú 0.05). In addition, the variability in the normalized

spike count for the different integration times was not sig-vated.Figure 6 shows the normalized spike count of the PD and nificantly different from control (P ú 0.05). This means

that the tuning curves in all cases differ only by a scalingTD (mean { SE, 5 animals) . For stimulus intensities ú1mN, the TD-cell spike count does not change significantly. factor ( i.e., the total number of spikes; see Fig. 7A) ; for

longer encoding times, more spikes are available to contrib-The PD-cell spike count increases substantially over the rangeof 1–37 mN (Fig. 6) . [A third type of mechanosensory ute information.

Again, with the tuning curves and the variability of theneuron, the high-threshold N (nociceptive) cell, never pro-duced more than one spike for the largest stimulus intensity responses, we estimated the decoding error for different encod-

ing times (Fig. 7B). At 100 ms, the error decreases belowshown here. We did not investigate stimulus intensitiesgreater than these because the N cells would be activated to that found in the behavior, and interestingly counting spikes

J131-8/ 9k2e$$no30 10-26-98 22:35:29 neupa LP-Neurophys

Lewis & Kristan 1998

J. E. LEWIS AND W. B. KRISTAN2586

stimulus location around the body perimeter. Figure 2 showstuning curves of normalized spike count versus stimuluslocation for the right T and P cells. These curves representthe averages over six different animals. Both T and P cellsexhibit broad and overlapping tuning curves, with peaksdistributed around the body perimeter. By using the commonconvention, we refer to the stimulus location that producesthe maximum response for a given cell as that cell’s pre-ferred location. The preferred locations serve to identify thedifferent cells; TD and PD are activated most by dorsal stim-uli, TV and PV by ventral stimuli, and TL by lateral stimuli.The shapes of these tuning curves, along with the periodic

nature of the dependent variable (i.e., stimulus location, S ,on the body perimeter varies between 0180 and /180!) ,suggest that a cosine function might be an appropriate sum-

FIG. 1. Typical mechanosensory spike trains. Intracellular recordings mary of the data from both cell types. We fit the means forfrom the T and P mechanosensory neurons during a 500-ms mechanical each cell from each individual animal to the cosine functionstimulus to the body wall (22 mN). The T cell exhibits rapidly adapting

in Eq. 2responses at both stimulus onset and offset, whereas the P cell shows acomparatively tonic response.

f(S) Å Rmax

1 0 A{cos (S 0 So) 0 A} (2)

in the population of sensory neurons. Theunissen and Miller deriveThis formulation was used previously (e.g., Miller et al.

an expression that describes the transinformation, T , as a function1991) and is convenient because Rmax is the maximum re-of the RMS error, e (see Eq. 1 following, and Eq. 11 in Theunissen

and Miller 1991)

T Å log2 !!2p

e " 0 1

2 ln (2)(1)

The wind-sensitive interneurons in the cricket cercal system de-scribed by Theunissen and Miller are completely analogous to themechanosensory neurons described in this study. Here we use Eq.1 to provide a quantitative measure of the information content inthe population responses of the sensory neurons and thus providean additional interpretation of the encoding error.

R E S U L T S

A mechanical stimulus that elicits the local bend behavioractivates two types of mechanosensory neurons, T cells andP cells (Kristan et al. 1982). In a single segment there aresix T cells and four P cells. Figure 1 shows typical spiketrains produced by the mechanical stimulus used in ourstudy. The T cell adapted rapidly and fired at the onset andoffset of the stimulus. Recently, Carlton and McVean (1995)proposed that the T cells encode the velocity of skin indenta-tion. The T-cell firing dynamics are similar to those shownby rapidly adapting (RA) afferents in humans (Vallbo andJohansson 1984; Wheat et al. 1995). The P-cell spike trainshowed a slowly adapting (SA) response to a mechanicalstimulus, which is similar to responses of the human SAafferents (Vallbo and Johansson 1984; Wheat et al. 1995).To quantify the responses of the T and P neurons, we simplycounted the number of spikes occurring in the 700-ms periodafter onset of a 500-ms stimulus (unless otherwise noted).In doing this, we ignore the temporal pattern of the neuralresponses.

Spatial tuning: response as a function of stimulus locationFIG. 2. Mechanosensory neuron tuning curves to stimulus location.

Mean normalized spike count is plotted for different stimulus locations forTo assess the ability of the T and P cells to encode the

the (A) 3 types of T cells and (B) 2 types of P cells (mean { SE, 6location of a mechanical stimulus on the skin, we first char- animals) . The mean spike counts at the tuning curve peaks were 15.1 (T

cells) and 7.2 (P cells) .acterized their average response properties as a function of

J131-8/ 9k2e$$no30 10-26-98 22:35:29 neupa LP-Neurophys

Variation der Reiz-position Andere Reizpara-meter bleiben konstantWiederholte gleiche Reizung Mittelwert und Standardabweichung der AP-Anzahl für jede Position

Bestimmung rezeptiver Felder

Allgemeines Verfahren:Bestimmung von Tuningkurven

Variation einer Reiz-eigenschaft Andere Reizpara-meter bleiben konstantWiederholte gleiche Reizung Mittelwert und Standardabweichung der AP-Anzahl für jede Eigenschaft

nachHubel &Wiesel

Sensorische Reize können viele Dimensionen haben. Z.B. im visuellen System

Vieldimensionale Parameterräume

Position Räumliche StrukturHelligkeit Zeitliche StrukturKontrast BewegungsrichtungWellenlänge Bewegungsgeschwindigkeit...

Programm

Arbeitsweise von Sensorzellen - Kodierung sensorischer Reize durch elektrische Signale

Stimulus-Response Kurven

Wie modelliert man Sensorzellen?

Integrate and Fire Modell

Neuronenmodelle im Vergleich

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Kombination der variierten Parameter: Mehrdimensionale Tuningkurven

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Achtung! Stolpersteine!

1. Antworten sind variabel2. Antworten hängen evtl. nicht nur

vom Reiz ab3. Antworten können mehrere

relevante Zeitskalen haben

Warum ist das Bild zu einfach, dass Stimulus-Response-Kurven, Rezeptive Felder und Tuningkurven neuronale Antworten komplett beschreiben?

Spikeraten sind nicht die einzige Kodierungsart!

Variabilität tritt nicht nur bei sensorischen Reizen, sondern auch bei Strom-injektion auf.Allerdings in geringerem Umfang.

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Um etwas über Zellantworten aussagen zu können, braucht man mehrere Reizpräsentationen und statistische Auswertung.

1. Variabilität!

2. Fehlende Stationarität!

Zellantworten sagen nicht nur etwas über den Reiz aus, sondern auch über den Zu-stand der Zelle, des Netzwerks und der Ableitqualität.Dynamische Änderungen der Antwort können auf interessante Effekte hinweisen (z.B. LTP)

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Meiste statistische Analysen sind strenggenommen nur unter stationären Bedingungen zulässig!

3. Mehrere Zeitskalen!

Manche Zellen antworten selbst auf einfache Reize mit komplexen AP-MusternDie Antwort kann aus mehreren “Events” bestehenDie Antwort kann deutlich länger dauern als der StimulusBesonders kompliziert bei zeitlichen Reizänderungen

Beispiel:Antwort einer retinalenGanglienzelle (ON/OFF)auf einen 200ms langenLichtblitz

Spikeraten können auf verschiedenen Zeitskalen betrachtet werden und zu unterschiedlichen Ergebinssen führen.

Methode Rasterplot

Rasterplots stellen die AP-Zeitpunkte für wiederholte Reizpräsentationen darRasterplots helfen

Variabilität und Stationarität abzuschätzenRelevante Zeitskala zu findenZeitliche Feinstruktur zu sehenZellen zu vergleichen

Methode PSTH(Peri-Stimulus-Time-Histogram)

PSTHs stellen die Zeitstruktur der Spike-Antworten auf wiederholte Reizpräsentationen relativ zum Reizbeginn darEinfachster Fall instantane Feuerrate: Alle Antworten in einem Zeitschritt aufsummieren und auf spikes/s normieren Feuerrate in einem Zeitfenster: Alle Antworten in N Zeitschritten aufsummieren und normieren

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PSTHs stellen die Zeitstruktur der Spike-Antworten auf wiederholte Reizpräsentationen relativ zum Reizbeginn darEinfachster Fall instantane Feuerrate: Alle Antworten in einem Zeitschritt aufsummieren und auf spikes/s normieren Feuerrate in einem Zeitfenster: Alle Antworten in N Zeitschritten aufsummieren und normieren

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Wichtiger Parameter beim PSTH: Wahl des IntegrationsfenstersVergleich von PSTHs verschieden-er Integrationsfenster ermöglicht Aussagen über die Zeitskala“Geschmacksache”: sliding average versus Fenster an Fenster“Detailkram”: Behandlung von Rändern“Verfeinerung”: z.B. Gaussfilter

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Besonders bei dynamischen Reizen zeigt das PSTH oft klarer als der Rasterplot, worauf die Zelle antwortet.

Im PSTH sieht man die Variabilität zwischen Antworten nicht.

154 Kretzberg, Warzecha and Egelhaaf

Figure 1. Graded and spiking response mode: A: (a) Sketch of a neuron that responds with graded membrane potential fluctuations evenin its output region and (b)–(d) example for responses of a fly HS-cell responding with graded potentials to a dynamically changing motionstimulus. (b) Stimulus velocity, (c) average membrane potential, (d) examples of individual responses. B: (e) Sketch of a spiking neuron and(f)–(g) responses of the spiking H1-cell of the fly to the same motion stimulus as in A. (f) Stimulus velocity, (g) PSTH of spike response,(h) individual spike responses (each vertical line represents the occurrence of a spike). H1- and HS-cell have opposite preferred directions.To allow better comparison of the responses, the graded responses of the HS-cell are shown inverted. Depending on the motion stimulus thegraded responses of the HS-cell sometimes are superimposed by active processes, but in this example only graded responses were recorded. Forexperimental methods, see Warzecha et al. (1998).

encoding stimuli because it contains neurons of eithermode with similar synaptic input organization (Fig. 1and Hausen, 1981, 1984; Egelhaaf and Warzecha,1999). Information transmission by graded responses

might be expected to be superior to that by spike re-sponses because a continuous signal has potentially agreater capacity to transmit information than the bi-nary signals of a spiking neuron. Nevertheless, most


Reiz:Bewegungs-

geschwindigkeit

mittlere Antwort:PSTH

Rasterplot vonEinzelantworten

im visuellen System der Fliege

Kretzberg et al 2001

Ratenkodierung ist nicht alles!

Alle bisher vorgestellten Methoden gehen von einem Ratenkode aus, “je mehr spikes in einer gegebenen Zeit, desto stärker war der Reiz”

Welche anderen Möglichkeiten gibt es?

Mehr Zellen:Mehr mögliche Ratenkodes

a. rate - time average

c. rate - population average

b. rate - identical stimulation average

d. population vector

*1*2*3*4 *1*2*3*4

9 12

e. weighted rate

Greschner 2005

Kodierung durch Spike-Zeitpunkte

Greschner 2005

1st

2nd

3rd

3rd

4th

2nd

3rd

1st

a. external latency

b. relative latency

c. phase-based

e. temporal pattern

d. temporal pattern - synchrony

Hausaufgabe:Wie wirkt sich Variabilität neuronaler Antworten auf die verschiedenen Kodierungsarten aus?

Wie kodieren Blutegel den Ort einer Berührung?

An jeder Stelle des Körpers überlappen sich die rezeptiven Felder von zwei P-Zellen.

P1 P2 P3 P4

P1

P2 P3

P4


Rate und Latenz hängen vom Ort der Berührung ab.

P1 P2 P3 P4

P2

P3


Vier Kodierungsarten zeigen eine signifikante Abhängigkeit der Antworten vom Berührungsort.

Thomson & Kristan 2005

absolute Latenz

relative Latenz

Rate einer Zelle

relative Rate

stärkste Abhängigkeit

Ein idealer Beobachter kann den Ort einer Berührung am besten aus der relativen Latenz der P-Zell-Antworten schliessen.

Um zu wissen, was der Egel tut, muss man die nachgeschalteten Zellantworten kennen.

latencybehaviorspike count


Nicht nur bei Blutegeln...

Antworten bestehen aus komplexen AP-Mustern, die länger als der Reiz dauern

Die AP-Gesamtzahl hängt nichtlinear von der Helligkeit ab

Auf feineren Zeitskalen gibt es ebenfalls nichtlineare Effekte der Rate

Die Latenz des ersten APs nimmt mit wachsender Helligkeit ab

Rei

zhel

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it /

Antworten einer retinalen Ganglienzelle auf Lichtblitze

verschiedener Stärke

Themen (revisited)

Analysemethoden:Stimulus-Response KurvenRezeptive FelderTuningkurvenRasterplotPSTH

KodierungsprinzipienBeispiel: Mechanoperzeption des Blutegels

gleich

es V

erfa

hren

{ Reizstärke

Reizort

Reizeigenschaft

Sigmoid

Gauss

Gauss

Gängigste Darstellung von Rohdaten

AP-Raten relativ zum Reiz auf verschiedenen Zeitskalen

AP-Raten vs AP-ZeitenEinzelzelle vs Ensembles

... und auch ein bisschen Retina:

Alles ist komplizierter als man denkt!

analysemethoden und kodierungsprinzipien - uni oldenburg · therelativecontributionsof t and p...

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