• GEO
• Entity - Relationship Models
• Accessing GEO from R
• Exercises with R
  • Desired difficulty
  • Error minimization

It is an international public repository that archives and distributes gene expression data submitted by the research community

• microarray,
• next-generation sequencing,
• and other forms of high-throughput functional genomics data

The minimum information that should be included when describing a microarray experiment.

Many journals and funding agencies require microarray data to comply with MIAME.

GEO encourage submitters to supply MIAME compliant data.

• The raw data for each hybridization
  • CEL or GPR files
• The final normalized data for the set of hybridizations
  • the gene expression data matrix used to draw the conclusions from the study
• The essential sample annotation including experimental factors and their values
  • compound and dose in a dose response experiment

Homework: Write down the new words or concepts and Google them

• The experimental design including sample data relationships
  • which raw data file relates to which sample,
  • which samples are technical/biological replicates
• Sufficient annotation of the array
  • gene identifiers, genomic coordinates,
  • probe oligonucleotide sequences
  • reference commercial array catalog number
• The essential laboratory and data processing protocols
  • what normalization method was used

• Each author submits a series that contains one or more samples
• Each sample uses a platform to investigate one or more organisms
• Each platform has several probes to represent genes

All these entities are related to each other

GEO is an example of a pattern that is important in Data Science:

Data can have a structure that help us to manage and understand it

• The most common database systems are relational databases
• They store entities and relationships between them

• Entities: objects, nouns
  • They exist independently of others
  • They may have attributes
• Relationships: verbs
  • connect two or more entities
  • They may have attributes

• Common noun: entity type, class
• proper noun: entity, instance
• verb: relationship
• adjective: attribute for entity
• adverb: Attribute for relationship

Eg. The genes of an organism have expression levels that depending on the growth medium

It is important to declare the possible number of relationships for each entity instance

For a given relationship between entities A and B

• Are all instances in A related to at least one instance of B?
• Can any instance of A be related to several instances of B?

Technical names: Surjective and Injective relationships. Check them

The genes of an organism have expression levels that depending on the growth medium

• one organism has one or more genes
• each gene belongs to one and only one organism
• each gene has only one expression level on each growth medium

Each instance of an entity should have an attribute to identify it

• Think of a “T.C. Kimlik No” of the entity
• One and only one for each instance
• Not shared with another instance
• Stable: never changes

Is “given name” a good identifier for a person?

Identify the entities and relationships on the following cases.

Draw E-R diagrams for each of them

• You as student of Istanbul University
• Human cells
• Streets of Istanbul
• Your class schedule

A Platform record is composed of a summary description of the array or sequencer and, for array-based Platforms, a data table defining the array template.

• Text description of the array or sequencer
• Text tab-delimited table of the array template

Each Platform record is assigned a unique and stable GEO accession number (GPLxxx).

A Platform may reference many Samples that have been submitted by multiple submitters.

Example Platform record »

Describe how a single sample was handled, the manipulations it underwent, and the abundance measurement of each element derived from it.

Each Sample record is assigned a unique and stable GEO accession number (GSMxxx).

A Sample entity must reference only one Platform and may be included in multiple Series.

• Text description of the biological sample and protocols to which it was subjected
• Text tab-delimited table of processed hybridization result
• Original raw data file, or processed sequence data file

Example Sample record »

A Series record links together a group of related Samples and provides a focal point and description of the whole study.

• Text description of the overall experiment
• Tar archive of original raw data files, or processed sequence data files

Series records may also contain tables describing extracted data, summary conclusions, or analyses.

Each Series record is assigned a unique and stable GEO accession number (GSExxx).

Example Series record »

• A curated collection of biologically and statistically comparable GEO Samples
• forms the basis of GEO’s suite of data display and analysis tools.
• Samples within a DataSet refer to the same Platform
  • they share a common set of array elements
• Value measurements for each Sample within a DataSet are assumed to be calculated in an equivalent manner
  • considerations such as background processing and normalization are consistent across the DataSet.
• Information reflecting experimental factors is provided through DataSet subsets.

Example DataSet record »

A Profile consists of the expression measurements for an individual gene across all Samples in a DataSet. Profiles can be searched using the GEO Profiles interface.

For more information, see About GEO Profiles page.

Example Profile records »

Ask Google

Notice that the second answer is not related to us

Remember that R can be extended with packages

• First we download (once) the files of the package
• When needed we load into the session using library(package)

Anybody can make new packages. Most of them are found in a repository

• CRAN
• Bioconductor

A set of libraries used to analyze molecular biology results

GEOquery is a package found in Bioconductor

Please follow the instructions on the webpage to install this package

• Always use destdir parameter to avoid excessive Internet usage
• use RStudio Environment pane to examine the components of the resulting object
• Read the series GSE3541
  • which are the samples?
  • which is the platform?
  • do you need to download the platform?
  • which are the genes?

Practice at home. We will need this next week

Many studies whow that doing things the easy way results in bad results

It is a good idea for manual and repetitive work

It is a very bad idea for creative and intellectual work

Remember: Thinking is like the gym

• It is hard if you don’t practice
• We are lazy and we avoid it
• We improve with practice
• Then we like it. And we look better

In statistics the word “error” does not mean “mistake”.

• Mistake is something we did wrong
• Error is the lack of precision even when we did everything right

Mistakes are about us. Errors are the difference between “models” and “reality”.

If we have a vector x and we want to find a single value y to “represent” it, how do we choose y?

Since usually all x[i] are different, there will be an error if we represent them with a single y.

The best y will be the one which has the lowest error.

How do we measure this error?

For example, let’s consider the parity values from birth.txt

> x <- birth$parity

What is x?

> summary(x)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   1.000   2.000   2.611   4.000   9.000 

This result shows that x is a vector (why?)

Now we choose any arbitrary value for y

> y <- 3

This is a single value, while x has many

> length(x)

[1] 694

> length(y)

[1] 1

What is x-y?

> summary(x-y)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 -2.000  -2.000  -1.000  -0.389   1.000   6.000 

> length(x-y)

[1] 694

So, a vector minus a number is still a vector

But the error should be a positive number. Let’s try again

What is (x-y)*(x-y)?

> summary( (x-y)*(x-y) )

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   1.000   1.000   2.703   4.000  36.000 

> length( (x-y)*(x-y) )

[1] 694

So, a vector times itself is still a vector

And now all numbers are all positives

Let’s average all the individual errors to get a mean error

> mean( (x-y)*(x-y) )

[1] 2.70317

This is the Mean Quadratic Error of y=3 respect to x

How can we generalize this for different values of y?

In Math and Informatics, a function is a “black box”

A rule to transform the input elements into an output

• e.g. logarithm of a number, length of a vector

The same input should produce always the same output

Notice that there may be more than one input element

In R functions are a type of data. We have

• vectors
• matrices
• lists
• data.frames
• formulas
• functions
• and others

To create a function we need to asign it to a variable

> newFunc <- function(input) {
+   commands
+   commands
+   return(output)
+ }

The keyword return can be omitted. The function output is the result of the last command

> my.func()

Error in my.func(): argument "a" is missing, with no default

> my.func(1,2,3,4)

Error in my.func(1, 2, 3, 4): unused arguments (3, 4)

• Write a function quadratic.error(y, x)

• The x input should be optional with default birth$parity

• Test it with different values of y

> err <- quadratic.error(1.5)

What is err?

We would like to calculate the quadratic error for several values of y

For example,

> many.y <- seq(from=min(x), to=max(x), length.out=100)

Now we do

> err <- sapply(many.y, quadratic.error)

What is err?

> min(err)

[1] 2.551838

> many.y[which.min(err)]

[1] 2.616162

> mean(x)

[1] 2.610951

One common way to write the error as \[E(y) = \frac{1}{N}\sum_{i=1}^N (x_i-y)^2\] This is the same we wrote in r language

> mean((x-y)*(x-y))

or

> sum((x-y)*(x-y))/N

How do we find the minimum?

• Which concepts are not clear?

• Show me your calendar

• Read the short story “Funes the Memorious” (by Argentine writer Jorge Luis Borges). You can find it on the web.
  • There is a PDF in Turkish language. Google “Funes ve Sonsuz Bellek” and look on pages 111-119.

• After reading it, do you want to have perfect memory? Why?

• Practice the usage of GEOquery

We will use both on next class