Hidden Markov Model HMM

1
Hidden Markov Model (HMM)

• HMMs offer a more systematic approach to
  estimating model parameters
• HMMs could be compared to a kind of dynamic
  statistical profile
• Like an ordinary profile, it is built by
  analyzing the distribution of aa in a training
  set of related proteins
• The topology of a HMM can be visualized as a
  finite state machine

2
HMM multiple sequence alignment

• Assume the following sequences
• ACCG, CTG,CTG, CG
• What is the best alignment?

ACCG CTG CTG C-G
3
Hidden Markov Model (HMM)
Delete States
Insert States
A
Match States
C
C
Begin
End
G
Movement from stage n to n1 with a certain
transition probability
4
Hidden Markov Model (HMM)

• More than one path leads to the same result

Delete States
Insert States
A
Match States
C
C
Begin
End
G
Movement from stage n to n1 with a certain
transition probability
5
Hidden Markov Model (HMM)

• The probability of a given sequence is obtained
  by the sum of loge (transition probabilities)
• Hidden Markov model, as the path is hidden
• Transition probabilities are obtained by training
  on a set of sequences
• Initialization by estimated transition
  probabilities
• All possible paths generating a given sequence
  are visited proportional to the estimated
  transition probabilities
• Counting the number of times a given transition
  was visited during the above step provides
  improved transition probabilities
• Start again until the parameters do not change
  significantly
• The Viterbi algorithm is used on a trained HMM to
  determine the best path
• The Viterbi algorithm is similar to dynamic
  programming

6
Hidden Markov Model (HMM)

• HMM is a general technique that can be applied to
  many different questions
• Multiple sequence alignment
• Identification of conserved domains
• Gene prediction
• Protein secondary structure prediction

7
PAM log odds score

• PAM matrices are usually converted in log odds
  matrices
• The ratio of the hypothesis that the change
  represents an authentic evolutionary variation to
  the hypothesis that the change occurred because
  of random sequence variation (no biol.
  significance)
• Phe-gtTry
• Phe-Try score in PAM250 0.15
• Frequency of Phe in data 0.04
• Ratio 0.15/0.04 3.75
• log103.75 0.57
• Try-gtPhe log100.2/0.03 0.83
• Log odds score (0.570.83)/210 (to remove
  fractional values)

8
PAM matrices

• In the PAM 1 matrix the summed probability of
  each aa changing to another is 1
• To obtain PAM matrices for N , the PAM1 matrix
  is multiplied to itself N times
• PAM250 represents a level of 250 change
  (corresponds to 20 similarity, as some positions
  may change several times, perhaps even reverting
  to the original one))
• Computer simulations have shown that PAM250
  provides a better scoring alignment than lower
  numbered PAMs for distantly (14-27 similarity)
  proteins.