Do conventional measures of intrinsic properties predict a neuron's behavior in a network?Rachel Grashow, Ted Brookings and Eve Marder

Volen Center and Department of Biology, Brandeis University, 415 South Street, Waltham, MA 02454

Introduction

Conclusions

Distribution of half-centers Predicting map properties

Supported by Grant NIMH 46472 (E.M.), NS 007292 (T.B.), NS 058110 (R.G.).

Traditional measures ofintrinsic excitability

We pharmacologically isolated STG neurons by blocking neuromod-ulatory input from descending pathways as well as local glutamatergicsynaptic contacts. We measured the intrinsic properties of four types of STG neurons: dorsal gastric (DG), gastric mill (GM), lateral pyloric (LP) and pyloric dilator (PD) neurons.

Creating half-center oscillatorsin hybrid circuitsNeurons may be classified based on their morphology, gene

expression, innervation patterns, receptor expression, electrical excitability and more. Specifically, electrical excit-ability has been used to classify neurons based on the idea that these properties confer information about each neuron's functional role. It isn't clear, however, whether any or all of these electrical properties predict or correlate to a neuron's behavior in a circuit. We are therefore examining the following questions:

-To what extent do traditionally measured intrinsic propertiespredict how a neuron will behave in a network?-Can we create a more functionally relevant measure ofintrinsic excitability?

1) Resistance

3) Spike threshold

Freq

uenc

y

Injected current

2) F/I curve

4) +1nA spike frequency

Linear combinations ofintrinsic properties

177.16

Some intrinsic properties that alone could not solely predict map properties combined with other intrinsic properties to produce signif-icant predictions

LP mean gh fit with +1 nA spike frequency and spike threshold

Other single intrinsic properties could predict map properties, but the statistical significance of the prediction improved when combined with other properties.

DG burst fraction fit with resistance and spike threshold

0%

20%

40%

60%

80%

100%

g h (n

S)

LP (n = 12)

gsyn (nS)0 20 40 60 80 100

20

40

60

80

100

PD (n = 12)

gsyn (nS)0 20 40 60 80 100

20

40

60

80

100

DG (n = 12)

gh

(nS

)

0 20 40 60 80 100

20

40

60

80

100

gsyn (nS)

GM (n = 14)

0 20 40 60 80 100

20

40

60

80

100

gsyn (nS)

Resistance

0 2 4 6 8 100

2

4

6

8

10

12

Rank orderDG burst fraction

Pre

dict

ed ra

nk o

rder

Spike threshold

0 2 4 6 8 100

2

4

6

8

10

12

Rank orderDG burst fraction

Pre

dict

ed ra

nk o

rder

Resistance andspike threshold

0 2 4 6 8 100

2

4

6

8

10

12

Rank orderDG burst fraction

Pre

dict

ed ra

nk o

rder

p = 0.001R2 = 0.570

p = 0.004R2 = 0.498

p = 0.957R2 = 0

There were no significant pairwise correlations between any of theintrinsic properties whether the cells were pooled or segregated by cell type.

The distribution of the likelihood of finding a half-center at any map location was cell type specitfic.

We asked whether linear combinations of intrinsic properties could predict the rank order of any of the map properties. There were linear combin-ations of intrinsic properties that could predict some of the map properties to a statistically signif-icant degree. These pred-ictions were cell-type specific.

DG: GM:

LP: PD:

Pred

icte

d va

lue

Resistance Spikethreshold

FI slope +1 nA spike freq.

Meangsyn

Std gsyn

Burstfraction

Meangh

Std gh

Pred

icte

d va

lue

Resistance Spikethreshold

FI slope +1 nA spike freq.

Meangsyn

Std gsyn

Burstfraction

Meangh

Std gh

Pred

icte

d va

lue

Resistance Spikethreshold

FI slope +1 nA spike freq.

Meangsyn

Std gsyn

Burstfraction

Meangh

Std gh

Pred

icte

d va

lue

Resistance Spikethreshold

FI slope +1 nA spike freq.

Meangsyn

Std gsyn

Burstfraction

Meangh

Std gh

Size Key

p < 0.001

p < 0.01

p < 0.05

DG: GM:

LP: PD:

Pred

icte

d va

lue

Size Key

p < 0.001

p < 0.01

p < 0.05

Burstfraction

meangsyn

mean gh

stdgsyn

stdgh

Resistance

Spikethreshold

FI slope

+1 nA spike freq.

Burstfraction

meangsyn

mean gh

stdgsyn

stdgh

Resistance

Spikethreshold

FI slope

+1 nA spike freq.

Burstfraction

meangsyn

mean gh

stdgsyn

stdgh

Resistance

Spikethreshold

FI slope

+1 nA spike freq.

Burstfraction

meangsyn

mean gh

stdgsyn

stdgh

Resistance

Spikethreshold

FI slope

+1 nA spike freq.

Is information about intrinsic properties captured by the map? We looked for linear combinations of map properties that would predict any of the intrinsic properties.

Resistance

FI SlopeSpike frequency at +1 nA

Res

ista

nce

(MΩ

)

0

10

20

30

40

50

60

70

80

DG GM LP PD

Freq

uenc

y pe

r nA

(Hz)

0

5

10

15

20

25

DG GM LP PD

Freq

uenc

y (H

z)

0

2

4

6

8

10

12

14

DGn = 12

GMn = 14

LPn = 12

PDn = 12

Spi

ke th

resh

old

(mV

)

-58-56-54-52-50-48-46-44-42-40-38-36

DG GM LP PD

Spike threshold

Predicting network properties

LP stdev frequency, span of frequency,mean gh, span gsyn

Pre

dict

ed ra

nk o

rder

LP Spike threshold

p < 0.001R2 = 0.612

-4

-2

0

2

4

6

8

10

0 2 4 6 8 10Rank order

Pyloric LP ISI

p = 0.846R2 = 0

-4

-2

0

2

4

6

8

10

0 2 4 6 8 10Rank order

Pyloric LP ISI

Pre

dict

ed ra

nk o

rder

1 s

lvn

LP interspike interval

Intrinsic properties were unable to predict any LP network prop-erties, either singularly or in linear combinations. A linear combination drawn from 4out of 18 map properties did significantly predict the rank order of the interspike interval of the LP neuron in the pyloricnetwork.

Map quantification

Model winsBio winsHalf-center

We calculated 18 differ-ent map properties.Using a reduced Χ2 test, we id-entified the five map properties that showed high correlations with combinations of intrinsic properties. These include fraction of the map with half-center networks, mean gsyn, mean gh, and the standard deviation of the gsyn and gh values that produced a half-center.

mvn

stn

ion

son

dvn

lvn

pynpdn

OG

CoGon

dgn

alnaln

Spike threshold and+1 nA spike frequency

p < 0.0001R2 = 0.612

Spike threshold

p = 0.152R2 = 0.118

+1 nA spike frequency

p = 0.943R2 = 0

0 2 4 6 8 10

Rank orderLP mean gh

Pre

dict

ed ra

nk o

rder

0

2

4

6

8

10

12

0 2 4 6 8 10

Rank orderLP mean gh

Pre

dict

ed ra

nk o

rder

0

2

4

6

8

10

12

0 2 4 6 8 10

Rank orderLP mean gh

Pre

dict

ed ra

nk o

rder

0

2

4

6

8

10

12

We used a hybrid network to measure intrinsic excitability. This circuit-based functional assay describes neurons in terms of map properties that are related, but not identical to traditional intrinsic properties. Some map properties could be predicted by combinations of intrinsicproperties, and vice versa. However, map properties may be better at describing the activity of a cell within a real network.

We used the dynamic clamp to connect a Morris-Lecar model neuron to a DG, GM, LP or PD neuron. We added an artificial hyperpolarization-activated intrinsic conductance (gh) to the biol-ogical neuron and used reciprocally inhibitory asymmetrical synapses (gsyn). We varied the strength of the artificial conductances to create a map of the gsyn-gh paramter space.

-40mV

1 s

20 mV

Endogenously active Morris-Lecar model neuron

Morris-Lecar

DG, GM,LP, PD

artificialsynapse

(gsyn)

artificialh-conductance

(gh)

The shape of the bursting region within each map was similar acrosscell types. Here are three other LP-model circuit maps:

Freq

uenc

y (H

z)

LP gh (nS)ML to LP gsyn (n

S)0

50

100

0

50

100

0

0.1

0.2

0.3

0.4

0.5

Freq

uenc

y (H

z)

LP gh (nS)ML to LP gsyn (n

S)0

50

100

0

50

100

0

0.1

0.2

0.3

0.4

0.5

Freq

uenc

y (H

z)

LP gh (nS)ML to LP gsyn (n

S)0

50

100

0

50

100

0

0.1

0.2

0.3

0.4

0.5

Model winsGM winsHalf-centerSilent

Uncoupled

-50 mV2 s

20 mV

Model

GM

0

50

100

0

50

100

0

0.1

0.2

0.3

0.4

0.5

Freq

uenc

y (H

z)

GM gh (nS) Model to GM gsyn (nS)

GM:

PD:

Freq

uenc

y (H

z)

PD gh (nS) ML to PD gsyn (nS)

0

50

100

0

50

100

0

0.1

0.2

0.3

0.4

0.5

Model winsPD winsHalf-centerUncoupled

ML

PD

-50 mV2 s

20mV

DG:

-50 mV2 s

20 mV

ML

DG

Model winsDG winsHalf-centerUncoupled

Freq

uenc

y (H

z)

DG gh (nS)ML to DG gsyn (n

S)

0

50

100

0

50

100

0

0.1

0.2

0.3

0.4

0.5

LP #1:

Freq

uenc

y (H

z)

LP gh (nS) ML to LP gsyn (nS)0

50

100

0

50

100

0

0.1

0.2

0.3

0.4

0.5

0.6

Model winsLP winsHalf-centerUncoupled

-50 mV2 s

20mV

ML

LP

For gsyn, gh and frequency:

maximumminimumspanmeanstandard deviation

0 20 40 60 80 100 120

020

4060

80100

1200

0.2

0.4

0.6

0.8

Freq

uenc

y (H

z)

Frequency

gsyn (nS)

gh (nS)

Frequency sensitivity (average

gsyn sensitivitygh sensitivity

frequency /15 nS):

% of map that arehalf-centers