Biomedical Engineering Reference
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of the logical OR of a list of literals (the literals can be Boolean variables or
their negation), one of which needs to be satisfied. Each clause C in the formula
is processed in turn, selectively amplifying only those DNA strands whose Boo-
lean variables satisfy at least one literal of that given clause. To do so, one adds
PCR primers encoding the literals of that clause C and their Watson-Crick com-
plements. Then a series of primer-extension reactions are executed that replicate
only those DNA strands (or their Watson-Crick complements) that have subse-
quences that encode one of the literals of clause C . This process, applied as a
series of PCR cycles, thus amplifies only those DNA strands whose Boolean
variables satisfy at least one literal of that given clause, so that they vastly pre-
dominate all other strands of the Biomolecular Database. ( A technical note : on
each cycle, the amplified strands undergo loss of the material prefixing the
primer's location, but the initial step of concatenating to each DNA strand in the
database multiple copies of the strand ensure that is not a problem.) After the
process is completed for each of the clauses in turn, the output strands that sat-
isfy all the clauses would vastly predominate all other strands of the Biomolecu-
lar Database. This method for processing a logical query in the database is
exquisitely sensitive: to get a result, one requires that the initial database have no
more than 10 identical strands of DNA that satisfy the query. Again, DNA hy-
bridization array technology can be used for output of query results, providing
distinct special locations for distinct outputs.
3.9.6. Scalability
As discussed above, our query processing is executed with vast molecular-
level parallelism by a sequence of biochemical reactions requiring a time that
remains nearly invariant of the size of the database up to extremely large data-
base sizes (e.g, up to 10 15 ). This is because the key limitation is the time for
DNA hybridization, which is done in parallel for all the DNA.
3.10. Management of Errors
The logical and associative searches used to select specific molecules and
sets of molecules from Biomolecular Databases are not 100% specific or effec-
tive. There may be several different kinds of errors: false negatives (appropriate
DNA strands are present but not selected, either because of a lack of sensitivity
or depletion of the relevant sequences from the database), false positives (inap-
propriate DNA strands are selected along with desired strands), errors based on
degradation of the Biomolecular Database contents, and errors resulting from
poorly designed queries, based on incomplete understanding of complex bio-
logical parameters. These kinds of errors can affect the results of the applica-
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