1
Mathematics of genomic profiling of astrocytes
Dávid Džamba24.2.2015
2
• Faculty of Mathematics and Physics of
the Charles University in Prague
• Physical institute UK, Ke Karlovu 5,
Praha
• Specialization: Biophysics and chemical
physics
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
3
• 2nd Faculty of Medicine, Charles University
• Institute of Experimental Medicine, EU Centre
of Excellence, The Czech Academy of Sciences
• Laboratory of Cellular Neurophysiology
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
5
• GFAP/EGFP mice = mice with “green” astrocytes
• Collection of astrocytes - FACS
Collection of astrocytes
30 µm
single-cells bulk samples (103-104 cells)state of the art
6
• DNA RNA protein• PCR - The polymerase
chain reaction
Gene expression
7
Cq value
Cq value = number of cycle when threshold is reached
threshold
13 18 26,5Low Cq value
= high gene expression
gene1gene2gene3gene4gene5gene6gene7gene8gene9gene10gene11gene12gene13gene14gene15gene16gene17gene18gene19
8
1. Bulk samples: average Cq value from all cells
2. Single-cells:
PCR results
% of cells expressing given gene advantage of single-cells
threshold
9
Validate PCR results obtained from single-cells by comparison with commonly used bulk samples
containing thousands of cells
Mission
10
• 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
Data
11
Theoretical dependence# of transcripts 1 2 4 8 16 32 64 128 256 512 1024
# of cells containing at least one transcript 1 2 4 8 15 28 50 74 90 98 100
• Given that we have 100 cells
Cq value 21 20 19 18 17 16 15 14 13 12 11% of gene expressing cells 1 2 4 8 15 28 50 74 90 98 100
𝒚=𝟏
𝟏+𝐞𝐱𝐩 ( (𝑬𝑪𝟓𝟎−𝒙 )∗𝒔𝒍𝒐𝒑𝒆)
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
20
Thank you for your attention.
W. Edwards Deming(1900-1993)
“Without data you’re just another person with an
opinion”
“Learning is not compulsory… Neither is survival.”
Top Related