M. Ronen, G. Chandy, T. Meyer & J.E. Ferrell

Curve Feature Extraction

basal

storage

Sustained (delta/ratio)

Max amplitude (delta / ratio)Max slope

Time of max slope Time of max amp

No. of peaksTime of peaks

Decrease slope

Time (sec)

Ca

+2 (

nM

)

Estimating the feature: X is calcium level, t is time (sec)

basal level = mean(X,t=5-35)

max amplitude delta = max (X,t=60-300) - basal level

max amplitude ratio = max (X,t=60-300) / basal level

max rise-slope = max(diff(X, t=60-300))

sustained = max (X, t=240-480)- basal level

max amplitude of store = max(X,t=600-700)

peaks No. X is filtered by a low-pass filter,into Xf. dXf,the derivative of Xf is calculated. Successive groups of alternatively positive and negative groups of dXf are defined. Positive groups with sum of dXf higher than a threshold are counted as a peak.

pre-stimulation peaks No.=peaks No. at t<60

early peaks No.= peaks No. at 60<t<200

late peaks No.= .= peaks No. at 200<t<600;

(t=60 ligand addition, t=600 calcium store release)

Feature Clustering and discriminate analysis

* Cluster all data (pair of control & experiment)

* Test enrichment of each experiment group in each cluster

expected ratio of traces in cluster

enrichment =ratio of traces

in cluster

*Apply discriminate analysis between clusters of interest

using multivariate analysis of variance, the linear combination of the original variables that has the largest separation between groups, is estimated.

The separation measure is the ratio of between-group variance to within-group variance, for a certain linear combination

Feature 1Fe

atu

re 2

A

B

C

Fig. Example for cluster’s enrichment and separation. Cluster B is enriched with the blue, cluster C is enrich with the red. Both features, 1 & 2, could be used for separation

Example : UDP 100nM , control & SHIP1

Data was mixed & clustered into 4 groups using Kmeans algorithm

Features: max amplitude (ratio/delta) ,max rise-slope, peaks No., early peaks No., late peaks No., sustained , time of max amplitude, time of max rise-slope, max amplitude of store

sustained

No.

of

late

pea

ks

Max Amp. - basal

1

2

3

4

Clusters #2 and #4

are enriched by SHIP1

Clusters #1 and #3

Have ~ same

SHIP1 & control ratios

Fig. : spread of each cluster over three of the features. Clusters 1-4 in plots 1-4Each point represent a singlecell, blue= control, red= SHIP1

m

ax a

mp

litu

de

of

store

max a

mp

litu

de

rati

o

max a

mp

litu

de

delt

a

sust

ain

ed

max r

ise-s

lop

e

peaks

No.

earl

y p

eaks

No.

late

peaks

No.

tim

e o

f m

ax

am

plit

ud

e

tim

e o

f m

ax

rise

-slo

pe

Cluster 1Cluster 2 Cluster 3Cluster 4

Cluster’s centersA representation of the “average” value of each feature in the clusters (normalized units). The cells that belong to a certain cluster have the minimal distance to that cluster’s center.

Example : UDP 100nM , control & SHIP1

Example : UDP 100nM , control & SHIP1

Discriminating features: #4 higher amplitude, higher rise-slope (10% of SHIP1, 1% control)

#2 more late peaks, lower amplitude, higher sustained (35% of SHIP1, 9% control)

Time (sec)

Ca

+2 (

nM

)

Time (sec)

Ca

+2 (

nM

)

Fig. : Calcium response, samples from clusters 2, 4 and 1&3.cluster 4 : SHIP1 enriched cluster 2 : SHIP1 enrichedclusters 1,3 : Mix of Control & SHIP1

Calcium dynamics

Na/CaExchanger

R G PLC PIP2

DAG

IP3

IP3R

ER

agonist

Ca2+

Buffer

ATPase

Calciumchannel

CapacitativeCalciumentry

PKC

Calcium Model

(based on Hofer et al. ,J. Neuro.,22,4850)

R-G

PLCδ IP3

Ca2+(cyt)

PLCβ

agonist

Ca2+(ER)

IP3R

ER

outinSERCAreldt

dC

)( SERCAreldt

dS

inactreactdt

dR

deg PLCPLCdt

dI

Calcium(cyt)

IP3

IP3R

Calcium(ER)

Calcium Model - cont.

CSkIkC

ICRkk

IParel

4

3444

442

1

22

241

40r

in kI

I

Ckout 5

22

23

sSERCA kC

Ck

Rkinact 6 2

12

216

kC

kkreact

22

27

caPLC kC

C

0

08

)1(1

G

GG

PLC

Ik 9deg

Time (sec)

Ca

+2 (

uM

)

Fig. : Simulation of calcium response, increase in amplitude as a response to increase in stimulus. Simulations were carried up in Matlab, using stiff ode solver.

Positive feedback strength

Time (sec)

Ca

+2 (

uM

)

PLCδ

IP3

Ca2+(cyt)

PLCβ

Sustained level could be controlled by positive feedback of calcium on PLCδ

Hypothesis : perturbing this feedback will change the sustained level

From experimental data:UDP has higher sustained level than C5a

Time (sec)

Ca

+2 (

nM

)

UDP 10uMC5a 100nM

Cells

%

Figs: A: histogram of sustained level of UDP 10uM (blue)and C5a 100nM (red). B: sample calcium response from these experiments

A

B

Model simulations: varying different parameters indicated that Calcium-PLC positive feedback loop controls sustained level A B

Figs: A: simulated calcium response, changing the parameter v7. B: Schema of the feedback loop

Sensitivity analysis

How does the model output depend upon the input parameters ?

Keep all parameters constant but oneRun model simulationsCheck the correlation between changesin the parameter and model outcome

Figs.: change in calcium response, as a result of changing one of the parameters

K3

Kr

kIP3

k2

k3 KIP3

Sensitivity analysis

Sustained level is strongly correlated with parameters related to Ca+2 PLC feedback and IP3 degradation

Cor Coeff -0.42 P-value<0.001

sust

ain

ed

kIP3

Cor Coeff 0.31 P-value<0.001

sust

ain

ed

v7

Randomly sample the parameter spaceUsing Latin Hypercube Sampling Run model simulationsCheck the correlation between the parameters and the model outcomeCalculating correlation coefficients & p-values

Figs.: scatter plots of model parameter Vs model’s outcome

Sensitivity analysis

Basal level is strongly correlated with Flux out, Influx and Ca+2 leak

Cor Coeff. -0.66

basa

l

k5

Cor Coeff 0.47

basa

l

v40

Cor Coeff. 0.22

basa

l

k1

Figs.: scatter plots of model parameter Vs. model’s Outcome. Correlation P-value<0.001 for all.

Sensitivity analysis

Figs: changes in calcium maximal amplitude as a response to changes in A: G-protein level, B: Receptor level

G-protein level

Ca+

2 m

ax a

mp

litude

(uM

)

A

Receptor level

Ca+

2 m

ax a

mp

litude

(uM

)

G-protein level

B

There is a switch like transient between two steady states of the maximal amplitude of the calcium response.The slope of the switch and the level of the 2nd steady state depends on other system’s parameters.