Modeling Single Cell's Calcium Response: Feature Extraction, Clustering, and Discriminate Analysis

1. Modeling single cell's Calcium response M. Ronen, G. Chandy, T. Meyer & J.E. Ferrell

2. 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 Curve Feature Extraction 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)

3. * Cluster all data (pair of control & experiment) * Test enrichment of each experiment group in each cluster expected ratio of traces in cluster ratio of traces in cluster enrichment = B A C Feature 2 Feature 1 Feature Clustering and discriminate analysis *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 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

4. 1 3 2 4 No. of late peaks sustained Max Amp. - basal Example : UDP 100nM , control & SHIP1 Data was mixed & clustered into 4 groups using Kmeans algorithm Features:maxamplitude (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 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 1-4 Each point represent a single cell, blue= control, red= SHIP1

5. Cluster 1 Cluster 2 Cluster 3 Cluster 4 sustained peaks No. max amplitude of store time of max amplitude time of max rise-slope max amplitude ratio max amplitude delta late peaks No. max rise-slope early peaks No. Example : UDP 100nM , control & SHIP1 Cluster’s centers A 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.

6. 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) Ca+2 (nM) Ca+2 (nM) Fig. : Calcium response, samples from clusters 2, 4 and 1&3. cluster 4 : SHIP1 enriched cluster 2 : SHIP1 enriched clusters 1,3 : Mix of Control & SHIP1 Time (sec) Time (sec)

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

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

9. Ca+2 (uM) Time (sec) Calcium Model - cont. 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.

10. From experimental data: UDP has higher sustained level than C5a A Positive feedback strength Cells % Ca+2 (uM) B UDP 10uM C5a 100nM PLCβ Ca+2 (nM) IP3 PLCδ Time (sec) Ca2+(cyt) Figs: A: histogram of sustained level of UDP 10uM (blue)and C5a 100nM (red). B: sample calcium response from these experiments Time (sec) Sustained level could be controlled by positive feedback of calcium on PLCδ Model simulations: varying different parameters indicated that Calcium-PLCd positive feedback loop controls sustained level A B Figs: A: simulated calcium response, changing the parameter v7. B: Schema of the feedback loop Hypothesis : perturbing this feedback will change the sustained level

11. k2 kIP3 Keep all parameters constant but one Run model simulations Check the correlation between changes in the parameter and model outcome K3 Kr k3 KIP3 Sensitivity analysis How does the model output depend upon the input parameters ? Figs.: change in calcium response, as a result of changing one of the parameters

12. Cor Coeff -0.42 P-value<0.001 Cor Coeff 0.31 P-value<0.001 sustained sustained kIP3 v7 Sensitivity analysis Randomly sample the parameter space Using Latin Hypercube Sampling Run model simulations Check the correlation between the parameters and the model outcome Calculating correlation coefficients & p-values Figs.: scatter plots of model parameter Vs model’s outcome Sustained level is strongly correlated with parameters related to Ca+2 PLC feedback and IP3 degradation

13. Cor Coeff 0.47 basal v40 Cor Coeff. -0.66 Cor Coeff. 0.22 basal basal k5 k1 Sensitivity analysis Basal level is strongly correlated with Flux out, Influx and Ca+2 leak Figs.: scatter plots of model parameter Vs. model’s Outcome. Correlation P-value<0.001 for all.

14. A B Ca+2 max amplitude (uM) Ca+2 max amplitude (uM) G-protein level G-protein level Receptor level Sensitivity analysis 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. Figs: changes in calcium maximal amplitude as a response to changes in A: G-protein level, B: Receptor level