Cell Differentiation and Proliferation

In developmental biology, cellular differentiation is the process by which a less specialized cell becomes a more specialized cell type

Cell proliferation: An increase in the number of cells as a result of cellgrowth and cell division

box plot

Microarray data analysis

Transcripts whose probe sets with detection above background P-value ,0.05 in at least 2 out of 3
replicates at the 0 min time point were considered expressed
and used for subsequent analyses

### 1, extract probe level intensities
apt-cel-extract -o ./GSE21236/0000_pre/raw_probe_signal.txt ./GSE21236/RawData/*.CEL -c /Home/liang/data/Array/Affymetrix/Mouse/MoGene-1_0-st-v1.r4.clf -p /Home/liang/data/Array/Affymetrix/Mouse/MoGene-1_0-st-v1.r4.pgf  --b /Home/liang/data/Array/Affymetrix/Mouse/MoGene-1_0-st-v1.r4.bgp

### 2, calculate dabg p-value
apt-probeset-summarize -a dabg -c /Home/liang/data/Array/Affymetrix/Mouse/MoGene-1_0-st-v1.r4.clf -p /Home/liang/data/Array/Affymetrix/Mouse/MoGene-1_0-st-v1.r4.pgf -b /Home/liang/data/Array/Affymetrix/Mouse/MoGene-1_0-st-v1.r4.bgp -o ./GSE21236/0000_pre/ ./GSE21236/RawData/*.CEL

Quantile Normalization

Replicates

Biological Replicates: use different cell cultures prepared in parallel

Technical Replicates: use one cell culture, firstly processed and then split just before hybridization

Sample Replicates: use one cell culture, firstly split and then processed

Confidence Interval for nls or lm fitting

A confidence interval estimates the interval within which the real coefficient will fall with a certain probability

the confidence intervals are “tight” (not wide) and do not include zero, suggesting the parameters are significant.


For a large repetitive experiments, 95% chance of the true value lies in the region defined by CI.

Or:
If you perform nonlinear regression many times (on different data sets), you expect the confidence interval to include the true value 95% of the time, but to exclude the true value the other 5% of the time (but you won't know when this happens).

In most of cases, you will use the CI to get a sense of if your results are any good. If CI are narrow, you know the parameter precisely; otherwise, you know that you have not determined the parameters very precisely.

Normally, that 95% confidence ranges over a factor of about two (e.g. 20~40 or 80~160) is very satisfactory.

By Harvey Motulsky & Arthur Christopoulos, "Fitting Models to Biological Data Using Linear and Nonlinear Regression"




http://matlab.cheme.cmu.edu/2011/08/29/nonlinear-curve-fitting-with-parameter-confidence-intervals/

http://books.google.com/books?id=g1FO9pquF3kC&pg=PA100&lpg=PA100&dq=confidence+interval+curve+fitting&source=bl&ots=m-T6aj4y4q&sig=T1-Q37uBPAxPL5M9Li395iAlr88&hl=en&sa=X&ei=9h00UeOOIKvJ0AGf04HYBA&ved=0CFoQ6AEwBTgU#v=onepage&q=confidence%20interval%20curve%20fitting&f=false


https://www.zoology.ubc.ca/~schluter/R/fit-model/

NLS (nonlinear least square)

summary()->output

Formula: val ~ exp(-k * time)

Parameters:
   Estimate Std. Error t value Pr(>|t|)    
k 4.456e-03  3.398e-05   131.2 9.77e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.003644 on 3 degrees of freedom

Number of iterations to convergence: 4 
Achieved convergence tolerance: 3.743e-06 



Using T-Tables
We have learned the following things about a t-test:

• The t-test produces a single value, t, which grows larger as the difference between the means of two samples grows larger;
• t does not cover a fixed range such as 0 to 1 like probabilities do;
• You can convert a t-value into a probability, called a p-value;
• The p-value is always between 0 and 1 and it tells you the probability of the difference in your data being due to sampling error;
• The p-value should be lower than a chosen significance level (0.05 for example) before you can reject your null hypothesis.