Finding the replication origin

In Bacteria there is only one replication origin

• The GC skew is positive in one part of chromosome
• And negative on the other, on average
• It changes sign in two places

The reason for this asymmetry is the DNA replication process

The origin of replication is in one of the sign changing places

Statistics in parts of the genome

Local statistics look only through a small window

A Window is a part of the genome, from an initial position, and with a fixed size

For example, we can analyze a region of 500 bp starting at position 3000 of the genome

Evaluate gc_skew() window by window

We traverse the genome with several windows of fixed size

Each window starts after the end of the previous one

In other words, the windows do not overlap

Calculate GC skew in a window

We created this function in Class 6. This is a new version

window_GC_skew <- function(position, size, dna) {
    V <- toupper(dna[seq(from=position, length.out=size)])
    count_C <- sum(V=="C")
    count_G <- sum(V=="G")
    if( (count_C+count_G) == 0) {
      return(0)
    } else {
      return( (count_G-count_C)/(count_C+count_G) )
    }
}

This new code does the same as the old one.
Can you see how does it work?

Create a vector with all window’s positions

We start at the first DNA position, until the last.
Be careful to not step out of DNA

win_pos <- seq(from=1, to=length(genome)-size, by=size)

Now we apply window_gc_skew() to each element of win_pos

skew <- sapply(win_pos, window_GC_skew, size, dna)

The result depends on window’s size

We look for the change of sign

We find two places where GC-skew changes sign

[1] 1500000 3800000

but the window size is 1E5, so the origin is somewhere between

[1] 1450000 1550000

or

[1] 3750000 3850000

Position of the maximum

The maximum value of acc_skew is

max(acc_skew)

[1] 4.9877

It is not really important

We are looking for position, not value of maximum

Position of the maximum

This is the index of the maximum in the acc_skew vector

which.max(acc_skew)

[1] 155

This is always an integer number, between 1 and length(acc_skew)

It is not the position in the genome

Position of the maximum

Since acc_skew vector has the same length as win_pos, we can find the genomic position of the maximum with this code

win_pos[which.max(acc_skew)]

[1] 1540001

win_pos contains the genome positions of each window

This code gives us the position of the window with maximum GC skew

Locating origin depends on window size

The largest GC skew is at

place_of_max <- win_pos[which.max(acc_skew)]

The replication origin is located in the interval between

• place_of_max - size/2
• place_of_max + size/2

[1] 1535000 1545000

Accumulative Sum: daily balance

The income can be positive (salary) or negative (expenses)

The balance on first day is your initial money

The balance of today is the balance of yesterday plus the income of today

balance[today] <- balance[yesterday] + income[today]

balance and income are vectors

Since they have different values every day, we represent the income on day i by income[i]

We also represent the balance on day i by balance[i]

The vector income has the values for all days

The element income[i] has the value for a single day

Balance looks like this