# BIOLOGICAL SEQUENCE ANALYSIS PDF

Many of the most powerful sequence analysis methods are now based on Biological sequence analysis: probabilistic models of proteins and nucleic. Computational sequence analysis has been around since the rst protein sequences To a rst approximation, deciding that two biological sequences are sim-. Bioinformatics and Systems Biology - Biological Sequence Analysis - by Richard Durbin. PDF; Export citation 6 - Multiple sequence alignment methods.

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Request PDF on ResearchGate | Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids | Probablistic models are becoming. Biological Sequence Analysis 1. Martin Tompa. Technical Report # Winter Department of Computer Science and Engineering. University of. Biological sequence analysisProbabilistic models of proteins and nucleic acids (ecogenenergy.info, ecogenenergy.info, ecogenenergy.info and ecogenenergy.infoson, Cambridge. University Press.

Since presently-available DNA sequencing technologies are ill-suited for reading long sequences, large pieces of DNA such as genomes are often sequenced by 1 cutting the DNA into small pieces, 2 reading the small fragments, and 3 reconstituting the original DNA by merging the information on various fragments.

Recently, sequencing multiple species at one time is one of the top research objectives. Metagenomics is the study of microbial communities directly obtained from the environment. Different from cultured microorganisms from the lab, the wild sample usually contains dozens, sometimes even thousands of types of microorganisms from their original habitats.

Main article: Gene prediction Gene prediction or gene finding refers to the process of identifying the regions of genomic DNA that encode genes. This includes protein-coding genes as well as RNA genes , but may also include the prediction of other functional elements such as regulatory regions. Gene finding is one of the first and most important steps in understanding the genome of a species once it has been sequenced.

Identifying genes in long sequences remains a problem, especially when the number of genes is unknown. Hidden markov models can be part of the solution. Another method is to identify homologous sequences based on other known gene sequences Tools see Table 4. However, the shape feature of these molecules such as DNA and protein have also been studied and proposed to have an equivalent, if not higher, influence on the behaviors of these molecules.

## A Parallel Algorithm for Multiple Biological Sequence Alignment

The 3D structures of molecules are of great importance to their functions in nature. Since structural prediction of large molecules at an atomic level is a largely intractable problem, some biologists introduced ways to predict 3D structure at a primary sequence level.

This includes the biochemical or statistical analysis of amino acid residues in local regions and structural the inference from homologs or other potentially related proteins with known 3D structures. There have been a large number of diverse approaches to solve the structure prediction problem. In order to determine which methods were most effective, a structure prediction competition was founded called CASP Critical Assessment of Structure Prediction.

The the receiver can decode the data. Adaptive code: initialize M counters c1, c2, …, cM on the complexity under the multi-state distribution. The code thus tent regions of biological sequences so that they do not adapts in the light of successive observations vi.

Both transmitter and receiver can compute this The multi-state distribution also applies to Markov adaptive code. A it would be impossible to encode the first instance of zero-order Markov model over protein is specified by a a value.

A first-order Markov model over 3. Factorial method: first, state the number of times DNA is specified by a quartet of four-state distribu- each possible value actually occurs in v1, … vN, i. Probabilistic finite-state machines and other specify an M-way partition of N. Second, state the hidden Markov models have a multi-state distribution particular combination, i.

All such combinations are equally likely. Boulton and Wallace proved that methods 2 and 3 give exactly the same message lengths and that 4. It is The previous sections have argued that to analyze satisfying that these lengths are nearly equal because DNA or other sequences requires a good model of otherwise it would make little sense to talk about the sequences, that the best model will give the greatest information content of the data.

The slight extra cost of compression, i. Computer algorithms for sequence analysis ment of the probability values P1, …, PM. The values should also be reasonably efficient, although there is stated are close to the maximum likelihood estimate but less pressure for them to be as efficient as typical are given to an optimum and finite degree of accuracy. We estimate for P1, …, PM could in principle be used with now start to consider models that might fulfill these method 1 and the data could still be transmitted, aims.

This section recalls the LZ model of sequences, its albeit inefficiently. The small, but non-zero, probability properties and its relation to biological sequences.

The of such possibilities accounts for the slight excess cost following section describes a new model of DNA in- of 1 over 2 and 3. Alternatively, integrating over spired by it. It considers a se- asymptotically achieves the same compression as a quence to be a mixture of random characters and great variety of other models of sequences.

It can repeated substrings. To use the LZ model to encode sequences, spired a great many file-compression programs. A uniform distribution is communications and file-compression. The form of the distribution on the structure that is present. A number of workers have tried to address must be included in the total cost.

Note that if there are this discrepancy. Rivals and Dauchet searched no significant repeats, only chance ones, the model will for exact repeats but employed a heuristic to join fail to compress sequences, on average, because the neighboring repeats together.

These the characters, and their codewords are correspondingly approximate matches can contain mismatches but not longer. Several dozen weights blend the There are many ways to encode a sequence under the predictions from the approximate matches. The present LZ model and one can search for a single optimal work explicitly models the duplication and subsequent explanation.

But imagine that there were two optimal mutation of sections of a sequence. Approximate repeats be. This means their probabilities can be added, giving probability 2P for the data, i. There are of random characters and repeated substrings in either generally a great many sub-optimal ways to encode the the forward- or reverse-complementary senses; in- data. Even if each of these gives the data a probability stances of repeats may differ by change, insertion and much less than the optimal probability P, their sheer deletion.

It is quite possible to cording to the model. Starting in the base state, B, the devise a code that realizes this saving, e.

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*SEQUENCE DIAGRAM PDF*

Now, it is a legitimate question to state. The possibility of changes, insertions and if the objective is more general, e.

In probability of the data under the model or to estimate essence, states R, R2 and R3 embody a simple muta- model parameters. It has a characteristic typical of tion machine, as can be used in the sequence alignment nuisance parameters in that the number of choices in an problem Allison et al.

## Problems and Solutions in Biological Sequence Analysis

For the analysis data. If an optimal explanation really is what is wanted, of DNA, approximate reverse complementary repeats it is not a nuisance parameter, of course. Finally, the tains no such representation of characters. Instead it base state of the machine can be replaced by some contains general statistics on the relationship between other sub-model.

A first-order Markov model works parts of the sequence. The machine could be made to well here for naturally occurring DNA, giving a small match or recognize a particular family of sequences but but significant overall improvement, even when its extra only if it were given one or more examples prepended parameters are considered. To an extent, it models the The precise architecture of the machine and the process by which a sequence could be generated and it organization of states R, R2 and R3 is arbitrary to a is natural to use the term machine for this reason, and certain extent.

The current design prevents invisible also because it is common in compression, makes a repeats, i. But it is quite possible tent with earlier work Allison et al. The important points are that the current sequences from the model. The machine can also be model is simple, and that its complexity is determined used as the basis of inference algorithms to analyze a by multi-state distributions see Section 3 on the tran- given sequence.

The repeat graph Fig. More generally have gone through in generating a particular sequence, we advocate the family of such finite-state models. For here one beginning ACA… A node in the graph repre- example, linear costs for gaps indels within repeats sents the machine in some state at some position in the can be modeled by states and operations for start-insert sequence. State R3 has been collapsed into state R2 for and continue-insert etc. Note that the graph is acyclic.

There are problem Allison et al. One can even envisage a many explanations for the sequence. Another is to generate AC in the base state Note that probabilistic finite state machines, such as and then start a repeat which copies a character, A, and that above, are hidden Markov models HMM in so on.

The probability of each such explanation is the mathematical terms. However, HMM has largely come product of its individual steps. Any two explanations to mean a generalization of profiles in molecular biol- are exclusive hypotheses for the sequence so it is legiti- ogy, see Eddy for example. The latter usually mate to add all of their probabilities together. Doing so contains an explicit representation of the characters of gives the total probability of the sequence under the a type of sequence.

The machine discussed here con- model, P D H where H now represents the machine, because there is no other way in which the machine could generate it. This sum can be calculated in O n 2 time by an algorithm that scans the graph row by row, there being O n 2 nodes in the graph.

O n space is sufficient because a row of the graph can be computed given just the previous row. The algorithm also calculates the contribution of each of the paths to a node towards the probability of the sequence up to the current position, and uses this information to produce a grey-scale plot which shows the positions of repeated substrings and their fidelity.

For short sequences one can perform a second backwards pass through the repeat graph and thus calculate the probability of the true path going through each node. This is analogous to the forward— backward dynamic programming algorithm which yields alignment density plots in sequence align- ment Allison et al.

However, it requires either O n 2 space or greater time-complexity and is impracti- cal for long sequences. In practice, the plot derived from the forward pass alone gives adequate indication Fig.

Generating finite-state machine. Repeat graph. The length of a repeat is coded by stating that it probabilities of all explanations to be summed in O n 2 continues base by base until it finally ends.

This time; in effect all of the paths through a node are amounts to a unary code which corresponds to a extended simultaneously. In fact, piece-wise linear costs geometric probability distribution on lengths. The issue of repeat lengths is similar to short, probable repeats and long, less probable repeats.

So ignor- algorithm, although one with a larger constant of pro- ing the start and any mutations, the overall cost of a portionality.

If one wanted a single optimal explanation repeat is linear in its length.

## Biological Sequence Analysis (guided self study)

This is what allows the under the model it would be possible to use other 50 L. The they give concave down cost functions when the nega- node representing the final base state gives overall tive log2 is taken, by adapting the technique of Miller operation frequencies and these yield parameter esti- and Myers Miller and Myers, from alignment.

The process is stopped This would give an O n 2 or O n 2 log n algorithm when the overall message length improves by less than depending on the properties of the cost function. Convergence is guaranteed; it could be conver- gence to a local optimum but this is not a problem in 6. Parameter estimation practice.

Parameters The parameters of the model are P repeat the prob- are estimated by an expectation maximization EM ability of starting a repeat, P continue the probability process Baum and Eagon ; Baum et al. Initial parameter values are a repeat, P copy the probability of a copy, P change assumed and the algorithm makes a pass through the the probability of a change, P insert the probability of repeat graph.

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As it does so it computes the frequencies an insertion and P delete the probability of a deletion of the machine operations up to each node in the within a repeat; the last four sum to one. Test runs were graph. When two or more paths meet, the weighted performed by generating data from the model with averages of their frequency counters are formed, known parameter settings and then attempting to re- Fig.

Real vs. The single figure for compression is, as mentioned Any inference program must be able to perform well in previously, a natural way to compare competing mod- this situation.

One parameter at a time was varied els of the sequence. Table 3 gives the compressed systematically while the others were held constant. For example, Fig. Similar tests for other parameters compress, and our approximate repeat model. As noted also gave good results. While giving no detail about the 7. DNA structure of a sequence other than its complexity under models, we believe that if a single figure of merit is We can look at the compression of a DNA sequence needed then the total message length figure is the in three different ways.

First, we can calculate a num- natural one to use when comparing competing models ber for the overall compression of a DNA sequence of sequences, as was argued before. Second, we The Drosophila mastermind protein is repetitive. Not can calculate and plot the information content of the surprisingly its cDNA is also repetitive. Looking at the sequence under the model, base by base.

Yeast chro- gency. The three different representations of the com- mosome III was included as an example of a long pression of a sequence under the model, yield different sequence, and overall is less compressible than the other information and complement each other. As mentioned above, the region 25 — 29 , inverted and rearranged, and new model can be extended to allow a mixture of types corresponds to the known copy and rearrangement of of repeats.

A model distinguish- spersed repeats Rogan et al. This model gave a small readily seen on the repeat plot Fig. Repeated Alu improvement in compression, from 1. It Plotting the information content, base by base, al- is barely visible on the repeat plot, as a contributor to lows the immediate detection of repeats and areas of the second Alu at position The base by base plot low information content in the sequence.

This gene cluster contains five transcribed 62 bp. Two large areas of serves as a useful locator. Both of these Also in the grey-scale plot, the long repeat at the kinds of repeats decrease the local information content L. Regions can grow, 1. Adjusting the threshold related to show clearly on the grey-scale repeat plot of and the value of k allows the algorithm to process long the entire gene cluster.

Faster approximation algorithm long approximate repeat. Alternative methods of speed- ing up the full O n 2 algorithm are being investigated. The inference algorithm described above takes O n 2 time per EM iteration. A faster algorithm is necessary for long sequences and an approximation algorithm was The new sequence model explicitly describes approxi- created for this reason. The idea is to investigate only mate repeats.

As presented above, the true probability, thus giving an upper bound on the model does not contain any library of predefined message length, and so is a conservative approximation. This also a constant, typically in the range 6 — The region S2 S1 : If S1 and S2 are unrelated then S1 gives no remains turned on while it is contributing more than a information about S2. In this Conclusions case the repeat plot gives a non-order-preserving align- ment of S1 and S2. This could be useful for comparing Sequence analysis is carried out for a variety of S1 and S2 when the individual sequences are repetitive purposes, e.

The object is to create matches, natural variation, evolution and mutation. Only by having built up by a sequence of these block-moves. Even if this is done moves.Several dozen weights blend the There are many ways to encode a sequence under the predictions from the approximate matches. DNA bases generated from a uniform model no struc- The aim here is to use compression as a criterion for ture and analyzed under competing models of varying evaluating models, and we do not usually carry out the complexity.

The grading is based on the activity during the course. The first chapter of BSA contains an introduction to the fundamental notions of biological sequence analysis: sequence similarity, homology, sequence alignment, and the basic concepts of probabilistic modeling.

Fixed code: state the probabilities of the M possible all possible values for P1, …, PM would lead to a values, P1, P2, …, PM, and base a code on these one-part message with the same message length as 2 probabilities. Sections 1.

Note that the graph is acyclic. Durbin, S. An introduction to arithmetic coding.

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