## 2 The biological problems
### The DNA
A typical question, for instance, requires to determine the function of a newly sequenced gene by comparing it to a set of known gene sequences, looking for homologies. This is but one of a class of problems, namely _sequence analysis_. **Problem area # 1:** Sequence analysis. _Comparison of genomic sequences within individuals of a same species, or intra-species, in order to highlight their differences and similarities. Reconstruction of long sequences by assembly of shorter sequence fragments. Error correction for sequencing machines._  
The complementarity law under which DNA fragments bind to each others has been exploited in several ways. In an experiment called _hybridization_ one can label one or more DNA single-stranded sequences (_probes_) by a fluorescent dye and mix them with some target, single-stranded, longer DNA sequence. It is then possible to check if a probe binds to the target, i.e., if the complement of the probe is a subsequence of the target. This experiment can be used to determine the order of a set of probes along a target (_physical mapping_). Hybridization can also be used for sequencing (_sequencing by hybridization_), in a novel technique whose potential has not been fully exploited yet. Finally, hybridization is used for a massive parallel experiment via _DNA-chips_ (or _microarrays_). These are large bi-dimensional arrays, whose cells contain thousands of different short probes (around 10 bases each). The probes are designed by the user, and are specific for the experiment of interest. For instance, one may design \(n\) probes which bind to \(n\) different genes (each probe uniquely binds to one of the genes), and then prepare a chip in which there are \(m\) rows, one for each of \(m\) tissue cells and \(n\) columns. Each cell \((i,j)\) contains the probe for gene \(j\). The experiment reveals the levels at which each gene is expressed by each tissue. Another experiment which heavily uses hybridization is _PCR_ (Polymerase Chain Reaction). PCR is used for making a large quantity of copies of a given target DNA sequence. By PCR, a DNA sequence of any origin (e.g. bacterial, viral, or human) can be amplified hundreds of millions of times within a few hours. In order to amplify a double-stranded DNA sequence by PCR it is first necessary to obtain two short DNA fragments, called _primers_, flanking the target strands at their ends. The primers are then put in a mixture containing the four DNA bases and a specialized polymerase enzyme, capable of synthesizing a complementary sequence to a given DNA strand. The mixture is heated and the two strands separate; later the mixture is cooled and the primers hybridize to their complementary sequences on the separated strands. Finally, the polymerase builds up new full complementary strands by extending the primers. By repeating this cycle of heating and cooling, an exponential number of copies of the target DNA sequence can be readily obtained. The use of hybridization in microarrays and in other experiments defines our second problem area:  
**Problem area # 2:** Hybridization and microarrays. _Use of hybridization for sequencing. Use of microarrays for tissue identification, clustering and feature selection discriminating healthy from diseased samples. Design of optimal primers for PCR experiments. Physical mapping (ordering) of probes by hybridization experiments._