Mathematics of genomic profiling of astrocytes Dávid Džamba

Faculty of Mathematics and Physics of the Charles University in Prague Physical institute UK, Ke Karlovu 5, Praha Specialization: Biophysics and chemical physics 2 Where do I come from Measurement of membrane potential by means of TPP electrode BACHELOR THESIS Membrane potential measurements in Saccharomyces cerevisiae mutant strains deficient in various membrane transporters DIPLOMA THESIS

2nd Faculty of Medicine, Charles University Institute of Experimental Medicine, EU Centre of Excellence, The Czech Academy of Sciences Laboratory of Cellular Neurophysiology 3 PhD studies

4 Laboratory of Cellular Neurophysiology Study of glial cells, especially astrocytes Pathophysiology of cerebral ischemia, Alzheimer’s disease and ageing Gene expression profiling in collaboration with Institute of Biotechnology, AS CR

GFAP/EGFP mice = mice with “green” astrocytes Collection of astrocytes - FACS 5 Collection of astrocytes 30 µm single-cells bulk samples ( cells) state of the art

DNA  RNA  protein PCR - The polymerase chain reaction 6 Gene expression

7 Cq value Cq value = number of cycle when threshold is reached threshold ,5 Low Cq value = high gene expression gene1 gene2 gene3 gene4 gene5 gene6 gene7 gene8 gene9 gene10 gene11 gene12 gene13 gene14 gene15 gene16 gene17 gene18 gene19

1. Bulk samples: average Cq value from all cells 2. Single-cells: 8 PCR results % of cells expressing given gene advantage of single-cells threshold

Validate PCR results obtained from single-cells by comparison with commonly used bulk samples containing thousands of cells 9 Mission

Need for collection of both bulk samples and single cells for comparison Together 84 genes tested in 12 mice  cca 1000 data points For each mouse and each gene we have: Bulk sample: Cq value Single cells: % of cells expressing given gene 10 Data

11 Theoretical dependence # of transcripts # of cells containing at least one transcript Given that we have 100 cells Cq value % of gene expressing cells Sigmoid formula: Fit: EC50 = 15 slope = -1 Precondition: transcripts are divided between the cells randomly!

12 Theoretical dependence Fit: EC50 = 14,5 slope = -1,5 Fit: EC50 = 14,5 slope = -1 Fit: EC50 = 15 slope = -1 Fit: EC50 = 15 slope = -1

13 Data

14 Data - curve fitting Fit: EC50 = 14,11 slope = -0,658

15 Least square curve fitting Least square method - most widespread Zero x-axis uncertainty precondition Total least square method (error-in-variables method or orthogonal regression method) – should be used when both x and y axis data have some uncertainty For linear regression – Deming regression

16 Problem Non-linear total least square curve fitting

17 Least square curve fitting Fit: EC50 = 14,11 slope = -0,658

18 Total least square curve fitting Fit: EC50 = 14,92 slope = -1,15

19 Problem solution

Thank you for your attention. 20 W. Edwards Deming ( ) “Without data you’re just another person with an opinion” “Learning is not compulsory… Neither is survival.”