1. Single cell Calcium response
analysis & modeling
Michal Ronen
Grischa Chandy
Mary Verghese Microscopy Lab
Tobias Meyer
James Ferrell Data analysis group

2. Automatic treatment of the single cell data
Outline
Automatic treatment of the single cell data
-Feature extraction
-Discriminate analysis
Model of calcium response
-model
-sensitivity analysis

3. Single cell data
Feature extraction and discriminate analysis

4. Curve Feature Extraction
Max amplitude
(delta / ratio)
Max slope
Decrease slope
storage
No. of peaks
Time of peaks
Ca+2 (nM)
Sustained (delta/ratio)
basal
Time (sec)
Time of max slope
Time of max amp
Single cell
trace

5. Discriminate analysis
Experiments sets :
dose experiments – compare to each other
perturbations – compare RNAi transfected to control
The aim –
to find, automatically, the features
that discriminate between the groups.
The method-
statistical analysis that estimates the features that have the largest separation between the groups.
A problem-
It does not capture small groups
with different characteristics
Does not handle nonlinear combinations of features.
Feature 1
Feature 2
1 cell group A
1 cell group B

6. Feature Clustering and discriminate analysis
* Cluster all data (control & experiment)
* Test enrichment of each experiment group in each cluster
*Apply discriminate analysis
between clusters of interest
expected ratio of
traces in cluster
enrichment =
ratio of traces
in cluster

7. Example : UDP 100nM , control & SHIP1 knockdown
Data was clustered into 4 groups
Clusters #2 and #4 are enriched in SHIP1 knockdown cells
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)
Ca+2 (nM)
Ca+2 (nM)
Sample cell from cluster 4
Sample cell from cluster 2
Sample cell from clusters 1&3
Time (sec)
Time (sec)

8. Automatic treatment of the single cell data
Feature extraction is fast, easy to use & flexible
All data is saved in a database (in process…)
this enables using queries to retrieve whatever we want
Automatic discrimination
seems reliable (need more tests)
takes into account all features
and features combinations
captures small groups of cells with different behavior

9. Calcium response modeling

10. Calcium dynamics Ca2+ agonist Calcium channel Buffer Capacitative
Na/Ca
Exchanger R G
PLC
PIP2
DAG
IP3
IP3R ER
agonist
Ca2+
Buffer
ATPase
Calcium
channel
Capacitative
entry
PKC

11. Calcium Model R-G PLCδ IP3 Ca2+(cyt) PLCβ agonist Ca2+(ER) IP3R ER
(based on Hofer et al. ,J. Neuro.,22,4850)

12. Calcium Model - more details
(cyt)
Calcium
(ER)
IP3R
IP3

13. Calcium Model - more details
(cyt)
Calcium
(ER)
IP3R
IP3

14. Calcium Model - more details
(cyt)
Calcium
(ER)
IP3R
IP3

15. Comparing simulations to experiments -
Calcium response to increased stimulation
Time (sec)
Ca+2 (uM)
Simulations
Ca+2 (nM)
C5a
300nM
10nM
5nM
Experiment’s single cell samples
Time (sec)
Ca+2 (nM)
C5a
10nM
Time (sec)
More samples from experiments

16. UDP has higher sustained level than C5a
Experimental data:
UDP has higher sustained level than C5a
Time (sec)
Ca+2 (nM)
Single cell samples of:
UDP 10uM
C5a 100nM

17. Sustained level could be controlled by positive feedback of calcium
strength
Time (sec)
Ca+2 (uM)
PLCδ
IP3
Ca2+(cyt)
PLCβ
Hypothesis :
perturbing this feedback
will change the sustained level

18. Hypothesis: Sustained level could be control by negative
feedback of calcium on the receptor
Add feedback loop to current model & test
Negative feedback
strength
Time (sec)
Ca+2 (uM)
Ca2+(cyt)
R-G
Only slight changes in sustained level occurred modeling
addition of calcium–receptor feedback loop

19. Sensitivity analysis How does the model output depend
upon input parameters ?
Receptor level
Ca+2 max amplitude (uM)
G-protein
level
-Keep all parameters constant but one
-Run model simulations
-Check the correlation between changes in the parameter and model outcome OR
Randomly sample the parameter space
Using Latin Hypercube Sampling

20. Sensitivity analysis Sustained level is strongly correlated
with these parameters:
Ca+2 PLC feedback
IP3 degradation
Cor Coeff
sustained
kIP3
Cor Coeff 0.31
sustained v7
o 1 cell
P-value<0.001

21. Sensitivity analysis Basal level is strongly correlated
Cor Coeff 0.47
basal
v40
Basal level is strongly correlated
with these parameters:
Influx
Flux Out
Ca+2 leak
Cor Coeff
basal k5
Cor Coeff. 0.22
basal k1
o 1 cell
P-value<0.001

22. Future work: Further Questions:
Improve the model – build a set of models
better explain the measurements
more reliable conclusions upon its analysis
Sensitivity analysis-
apply for each version of the model
Further Questions:
-Are the differences in the behavior of cells due
to deterministic or stochastic effects?