Training Problem

Another tricky problem is how to create an HMM in the first place, given a

particular set of related training sequences. It is necessary to estimate the amino

acid emission distributions in each state and all state-to-state transition

probabilities from a set of related training sequences. This is done by using the

Baum-Welch Algorithm or the Forward Backward Algorithm.

The algorithm proceeds by making an initial guess of the parameters (which may

well be entirely wrong) and then refining it by assessing its worth, and attempting

to reduce the errors it provokes when fitted to the given data. In this sense, it is

performing a form of gradient descent, looking for a minimum of an error measure.

In this section, we will delve into greater depth at specific problems in the area of

computational biology and examine the role of HMM's.

1.1. Gene finding and prediction

We introduce here the gene-prediction HMMs that can be used to predict the

structure of the gene. Our objective is to find the coding and non-coding regions of

an unlabeled string of DNA nucleotides.

The motivation behind this is to

 assist in the annotation of genomic data produced by genome sequencing

methods

 gain insight into the mechanisms involved in transcription, splicing and

other processes

1
As shown in the diagram above, a string of DNA nucleotides containing a gene will

have separate regions

 Introns – non-coding regions within a gene

 Exons – coding regions

These regions are separated by functional sites

 Start and stop codons

 Splice sites – acceptors and donors

In the process of transcription, only the exons are left to form the protein sequence

as depicted below.

2
Many problems in biological sequence analysis have a grammatical structure

. HMMs are very useful in modeling grammar. The input to such a HMM is the

genomic DNA sequence and the output, in the simplest case is a parse tree of

exons and introns on the DNA sequence.

Shown below is a simple model for unspliced genes that recognizes the start

codon, stop codon (only one of the three possible stop codons are shown) and the

coding/non-coding regions. This model has been trained with a test set of gene

data.

Having such a model, how can we predict genes in a sequence of anonymous

DNA ? We simply use the Viterbi algorithm to find the most probable path through the

model

3
4
 1.2. Protein- Profile HMMs

As we have seen earlier, protein structural similarities make it possible to create a

statistical model of a protein family which is called a profile. The idea is, given a

single amino acid target sequence of unknown structure, we want to infer the

structure of the resulting protein.

The profile HMM is built by analyzing the distribution of amino-acids in a training

set of related proteins. This HMM in a natural way can model positional dependant

gap penalties.

The basic topology of a profile HMM is shown above. Each position, or module, in

Matching
Deletion
states Insertion states
states
the model has three states. A state shown as a rectangular box is a match state

that models the distribution of letters in the corresponding column of an

alignment. A state shown by a diamond-shaped box models insertions of random

letters between two alignment positions, and a state shown by a circle models a

deletion, corresponding to a gap in an alignment. States of neighboring positions

are connected, as shown by lines. For each of these lines there is an associated

5
`transition probability', which is the probability of going from one state to the

other.

The match state represents a consensus amino acid for this position in the protein

family. The delete state is a non-emitting state, and represents skipping this

consensus position in the multiple alignment. Finally, the insert state models the

insertion of any number of residues after this consensus position.

A repository of protein profile HMMs can be found in the PFAM Database

(http://pfam.wustl.edu).

Building profiles from a family of proteins(or DNA) a profile HMM can be made for

searching a database for other members of the family. As we have seen before in

the section on HMM problems, profile HMM’s can also be used for the following

Scoring a sequence

We are calculating the probability of a sequence given a profile by simply

multiplying emmision and transition probabilities along the path.

Classifying sequences in a database

Given a HMM for a protein family and some unknown sequences, we are trying to

find a path through the model where the new sequence fits in or we are tying to

‘align’ the sequence to the model. Alignment to the model is an assignment of

states to each residue in the sequence. There are many such alignments and the

Vitterbi’s algorithm is used to give the probability of the sequence for that

alignment.

6
Creating Multiple sequence alignment

HMMs can be used to automatically create a multiple alignment from a group of

unaligned sequences. By taking a close look at the alignment, we can see the

history of evolution. One great advantage of HMMs is that they can be estimated

from sequences, without having to align the sequences first. The sequences used to

estimate or train the model are called the training sequences, and any reserved

sequences used to evaluate the model are called the test sequences. The model

estimation is done with the forward-backward algorithm, also known as the Baum-

Welch algorithm. It is an iterative algorithm that maximizes the likelihood of the

training sequences.

1.3. Prediction of protein secondary structure using HMM’s

Prediction of secondary structures is need for the prediction of protein function. As

an alternative method to direct X-ray analysis, a HMM is used to

 Analyze the amino-acid sequences of proteins

 Learn secondary structures such as helix, sheet and turn

 Predict the secondary structures of sequences

The method is to train the four HMMs of secondary structure – helix, sheet, turn

and other – by training sequences. The Baum-Welch method is used to train the

HMMs. So, the HMM of helix is able to produce helix-like sequences with high

probabilities. Now, these HMMs can be used to predict the secondary structure of

the test sequence. The forward-backward algorithm is used to compute the

probabilities of these HMMs outputting the test sequence. The sequence has the

secondary structure whose HMM showed the highest probability to output the

sequence.

7
 2. HMM implementation

These are the two publicly available HMM implementation software.

HMMER - http://hmmer.wustl.edu/

SAM system - http://www.cse.ucsc.edu/research/compbio/sam.html

3. Advantages of HMMs

 HMM’s can accommodate variable-length sequence.

Because most biological data has variable-length properties, machine learning

techniques which require a fixed-length input, such as neural networks or support

vector machines, are less successful in biological sequence analysis

 Allows position dependant gap penalties.

HMM’s treat insertions and deletions is a statistical manner that is dependant on

position.

4. Limitations of HMMs

 Linear Model

So, they are unable to capture higher order correlations among amino-acids.

 Markov Chain assumption of independent events

Probabilities of states are supposed to be independent which is not true of biology

8
 Standard Machine Learning Problems

In the training problem, we need to watch out for local maxima and so model may

not converge to a truly optimal parameter set for a given training set. Secondly,

since the model is only as good as your training set, this may lead to over-fitting.

5. Open areas for research in HMMs in biology

 Integration of structural information into profile HMMs.

Despite the almost obvious application of using structural information on a

member protein family when one exists to better the parameterization of the

HMM, this has been extremely hard to achieve in practice.

 Model architecture

The architectures of HMMs have largely been chosen to be the simplest

architectures that can fit the observed data. Is this the best architecture to use?

Can one use protein structure knowledge to make better architecture decisions, or,

in limited regions, to learn the architecture directly from the data? Will these

implied architectures have implications for our structural understanding?

 Biological mechanism

In gene prediction, the HMM’s may be getting close to replicating the same sort of

accuracy as the biological machine (the HMM’s have the additional task of finding

the gene in the genomic DNA context, which is not handled by the biological

machine that processes the RNA). What constraints does our statistical model

9
place on the biological mechanism— in particular, can we consider a biological

mechanism that could use the same information as the HMM?

6. References

1. L. R. Rabiner and B. H. Juang, An Introduction to Hidden Markov Models, IEEE

ASSP Magazine, January 1986, pp. 1-16.

2. K. Asai, S. Hayamizu and H. Handa, Prediction of protein secondary structures

by hidden Markon models, Computer Application in the Biosciences (CABIOS),

Vol 9, No 2, 1993, pp. 141-146.

3. Krogh, A., M. Brown, I.S. Mian, K. Sjolander, and D. Haussler. Hidden Markov

Models in Computational Biology: Applications to Protein Modeling, J. Mol.

Biol., Vol. 235, pp.1501-1531, 1994.

4. S. Eddy. Profile hidden Markov models. Bioinformatics, 14:755--763, 1998.

5. L. R. Rabiner, A Tutorial on Hidden Markov Models and Selected Applications

in Speech Recognition , Proceedings of the IEEE, 77 , no. 2, 257--285, February

1989.

6. Baldi, P., Chauvin, Y., Hunkapiller, T. and McClure, M.A. (1993) Hidden Markov

Models in Molecular Biology: New Algorithms and Applications, In Advances in

Neural Information Processing Systems 5, Eds. S.J. Hanson, J.D. Cowan and C.

Lee Giles, (Morgan Kaufmann) pp 747-754

7. Baldi, P., Chauvin, Y., Hunkapiller, T., and McClure, M.A. (1994) Hidden Markov

Models of Biological Primary Sequence Information, Proceedings of the

National Academy of Science, USA 91: 1059-1063.

8. David Kulp, David Haussler, Martin G. Reese, and Frank H. Eeckman, A

generalized hidden markov model for the recognition of human genes in DNA,

10
 Procedings of the Fourth International Conference on Intelligent Systems for

Molecular Biology (Menlo Park, CA), AAAI Press, 1996.

9. R. Hughey and A. Krogh. Hidden Markov models for sequence analysis:

extension and analysis of the basic method. Computer Applications in the

Biosciences, 12:95-107.1996

http://www.cse.ucsc.edu/research/compbio/html_format_papers/hughkrogh96/c

abios.html

10.Henderson,J., Salzberg,S. and Fasman,K. Finding genes in human DNA with a

hidden Markov model. Journal of Computational Biology 1997, 4, 127--141.

11.An Introduction to Hidden Markov Models for Biological Sequences by A.

Krogh. In S. L. Salzberg et al., eds., Computational Methods in Molecular

Biology, 45-63. Elsevier, 1998.

12.E Birney. Hidden Markov models in biological sequence analysis. Deep

computing for the life sciences. Volume 45, Numbers ¾ 2001.

http://www.research.ibm.com/journal/rd/453/birney.html

13.HMMer - http://hmmer.wustl.edu/

14.SAM system - http://www.cse.ucsc.edu/research/compbio/sam.html

11