1. Introduction to Molecular Biology

Question 1

Nucleus Definition

Answer 1

-an organelle that contains the genetic material of the cell

Question 2

Chromosome Definition

Answer 2

-organised structure of DNA in the cell nucleus

Question 3

DNA Definition

Answer 3

-deoxyribonucleic acid -it is a nucleic acid containing the genetic instructions used in the development and functioning of all known living organisms

Question 4

Gene Definition

Answer 4

-the DNA segments carrying this genetic information are called genes -a molecular unit of heredity in a living organism -a region of DNA that codes for mRNA.

Question 5

Transcription Definition

Answer 5

-the process of creating a complementary RNA copy of a sequence of DNA

Question 6

Translation Definition

Answer 6

-a process where messenger RNA (mRNA) produced by transcription is decoded by the ribosome to produce a specific amino acid chain, or polypeptide, that will later fold into an active protein

Question 7

What is RNA abundance used to measure?

Answer 7

-RNA abundance is a measurable indicator of gene expression -measured using microarray -simultaneous measurement of 15-30 thousand genes -number of samples 4-100s

Question 8

Gene Expression and Microarray Data

Answer 8

-comparison between e.g. Control/Treatment, Normal/Disease -we want to identify differently expressed genes between the two groups

Question 9

Microarray Data and Linear Regression

Answer 9

-linear regression is not possible since there are so many more variables (genes) than observations

Question 10

Microarray Definition

Answer 10

-a technology where DNA sequences (from 1000s of genes) are pre-printed onto its surface (primers) -isolate human mRNA from samples in the lab -label the mRNA with coloured dye -mix with the microarray, hybridisation occurs, RNA binds to complementary primers -quantification, scan intensity of pixels on the array

Question 11

What are the two types of microarray?

Answer 11

-single colour (Affymetrix arrays) -two-colour (cDNA arrays)

Question 12

Two Colour Microarray

Answer 12

-microarray is hybridised with cDNA from two different samples each labelled in a different colour, usually red and green -they are mixed and hybridised to a single array -the relative intensities of each colour indicate the relative expression of a particular gene in each sample -generally only able to measure relative expression not an absolute measurement

Question 13

One Colour Microarray

Answer 13

-e.g. Affymetrix gene chip -RNA from a single sample so provides intensity data for each gene from one sample -there are batch effects that have to be accounted for in comparison between different arrays

Question 14

How is microarray data plotted?

Answer 14

-frequency on y -log scale on x -histogram

Question 15

The Simple Linear Regression Model

Answer 15

yi = βo + β1xi + εi, i=1,…,n -yi is the response or dependent variable -βo and β1 are regression parameters -xi is the independent or explanatory variable, measured without error -and εi is iid N(0,σ²)

Question 16

Using Linear Regression for Microarray Data

Answer 16

-possible if we use y as the outcome (e.g. diseased or healthy) -and use the x variables as each gene -then βj represents the relationship between gene expression of gene j and the condition

Question 17

Linear Regression Estimation, β^

Answer 17

-derived by minimising the sum of square residuals S => β^ = (Xt X)^(-1) Xt y -where X is the matrix whose ij element is the ith observation of the jth independent variable (the genes) -Xt indicates the transpose of X -y is a vector whose ith element is the ith observation of the dependent variable (condition) -and β^ is a vector of estimators for the β parameters, βo^, β1^

Question 18

Linear Regression Estimation, σ²^

Answer 18

σ²^ = [et e]/[n-p] -where et indicates the transpose of e -p is the number of parameters, 2 for the simple model β0,β1 -and: e = y - Xβ^

Question 19

Hypothesis Testing for Microarray Data Test Statistic

Answer 19

T = β^j / se(βj^) ~ t(n-L-1) -where se means the standard error: se(βj^) = sqrt(var(βj^)) -L is the number of covariates

Question 20

Simple Linear Regression Model in Matrix Form

Answer 20

yi = βo + β1xi + εi, i=1,…,n -matrix form: y = Xβ + ε -where y is a column vector with entries y1, y2, …, yn -X is an nx2 matrix with entries: all 1s in the first column and x1,x2,…,xn in the second column -β is a column vector with entries βo,β1 -ε is a column vector with entries ε1,ε2,…,εn

Question 21

Linear Regression Variance-Covariance Matrix

Answer 21

Σ = cov(β^) = E [(β^-β) (β^-β)t] = σ² (XtX)^(-1) -the diagonal is the variance of each β^ -other entries are the corresponding covariances

Question 22

Linear Regression Standard Errors for β^

Answer 22

-the standard errors of βo^ and β1^ are given by the square root of the corresponding diagonal of Σ

Question 23

Linear Regression Hypothesis Testing Overview

Answer 23

-our main interest is to test whether any of (or any function of) the individual regression parameters is significantly different from zero -the hypotheses involved are: Ho : βj=0 H1 : βj≠0 -for any j

Question 24

Linear Regression Hypothesis Testing Test Statistic

Answer 24

tj = βj^ / SE(βj^) -under Ho:βj=0, tj follows a t-distribution with degrees of freedom n-p -at a significance level α, the decision is to reject Ho if either: ->in the two-sided case: |tj|>Tdf(α/2 %) ->or equivalently: P_Ho (|T|>tj) < α

Question 25

Linear Regression Matrix Form for Microarray Data Analysis

Answer 25

-in microarray data analysis, y will be the vector of gene expression in log scale -X will be the design matrix, in analysis X may need to be constructed beforehand (not given) -β would correspond to (possibly) many factors including differential expression