1. Evolutionary Change in Sequences
Lecture 2 (though L1 slightly too long ... a few slides included in beginning of L2)
Changes over long evolutionary times
e.g., mouse and human diverged 100 mya (million years ago)
Diverged = last shared a common ancestor
Study how nucleotide sequences change over time
Require (mathematical) models
Mostly based on simple probability
Have many of the ‘same’ genes, but with slightly different sequences
e.g., compare mouse myoglobin to human myoglobin

2. Jukes and Cantor one-parameter model
Simplest model of DNA sequence evolution
All substitutions occur with equal probability
Only one parameter
the rate of change of one nucleotide to another, 
3 = rate of change of nucleotide to any other

3. A G After one unit of time C T  purines    
Probability that A stays as A = 1-3
Probability that A changes to T =     
pyrimidines C T 

4. Compare number of nucleotide differences between sequences
Fewer differences = shorter time
Only four possible states (A,C,T,G)
Under this simple model, all sequences will retain 25% identity at equilibrium
After some time can no longer estimate relationships

5. Kimura’s two-parameter model
Two kinds of nucleotide
Purine: A, G
Pyrimidine: C, T
Model says that a purine is more likely to be replaced with another purine than by a pyrimidine
Transitions : replace like with like
Transversions: replace purine with pyrimidine, or vice versa
Supported by observation: transitions are more common than transversions

6. Transversion = rate of  C T
purines A G
Transition = rate of 
Transversion = rate of     
pyrimidines C T 

7. Number of substitutions between two DNA sequences
For two sequences of length N, count the number of differences n
n/N = percent identity of the sequences
BUT, there is a chance that the same position of the sequence was changed more than once
e.g., observe A at position 10 in one sequence, and T in the other
A  T
A  C  T

8. Multiple Hits 8 substitution events (arrows) Only 6 differences (dots)
Time
8 substitution events (arrows)
Only 6 differences (dots)

9. Multiple Hits When degree of divergence is high:
Observe n differences, but these are the result of >> n changes
By simply counting the differences one can greatly underestimate the amount of divergence of the sequences

10. Expected
(Molecular clock)
Number of differences
Observed
time

11. Violations of assumptions of models
Rate of substitution is not always the same for all sites
Some sites are not independent
Interacting sites may require complementary mutations (e.g., in a hairpin structure, in protein 3D structure)

12. CpG dinucleotides Susceptible to methylation
Easily deaminated to give Thymine
Results in GT mismatch
Example of particular sites with a high mutation rate
CpG = C followed by G in the 5’ – 3’ direction
This dinucleotide is particularly susceptible to methylation (addition of MH3 group) of the C
The methylated C is easily deaminated to T
Results in TG mismatch
May be corrected to CG, or to TA
5’ ...T G... 3’
3’ ...G C... 5’

13. Molecular Coevolution (Inter-protein)

14. Molecular Coevolution (Intra-protein)
Amino acids within proteins do not evolve in isolation but they rather form part of complex intra-protein evolutionary units

15. Coevolution leads to phylogenetic mirroring

16. Coevolution results from coadaptation

17. Models of coevolution
Models of molecular covariation help understand how proteins evolve and identify residues that may be functionally or structurally linked