Parallel and Evolutionary Approaches to Computational Biology - Parallel Computing for Bioinformatics and Computational Biology - page 12

3. Penetrance Probabilities : This is the probability of phenotypes. When geno-
types are given, they are compared with phenotypes; if they are compatible then
the penetrance probability is equal to 1, otherwise it is equal to zero.

1.1.8.2 Existing Methods Performing calculations on multi-locus data means
calculating probabilities on pedigrees using different algorithms. The traditional algo-
rithm is to choose new θ values by approximating the derivative of the likelihood
function L(θ old ) . The main disadvantage of this method, called quasi-Newton, is
that the new θ may have lower likelihood. The Expectation and Maximization (EM)
algorithm overpasses this drawback by offering a powerful general approach to obtain
maximum likelihood estimates from incomplete data. The algorithm starts by making
an initial guess of θ distribution. Then, it calculates the expected values for complete
data such as the number of recombinant and nonrecombinant meioses in each interval.
Afterward, it maximizes the likelihood estimate θ new . The algorithm keeps on repeat-
ing expectations and maximizations until the likelihood converges to a maximum. The
theoretical advantages of EM search are: less computation time per iteration, increased
likelihood on each iteration, good initial convergence properties, exact expressions
for derivatives of the likelihood, and ease of generalization.
However, the problem is also stated as the construction of multi-locus linkage
maps in humans or as a missing data problem. The efficient solutions are to deter-
mine the expected number of recombinations that occur in each interval, given the
recombination fractions θ

(θ 1 , θ 2 , ... , θ l ) and the phenotypes for all loci ( l 1 , ... , l l ).
A special case reconstruction : in this case we suppose that we can observe the
genotypes of each individual in a pedigree, including which alleles are on the pater-
nally and maternally derived chromosomes. In each interval, it is then easy to find out
by inspection if there is recombination or nonrecombination. Thus, the computational
time is proportional to the square of the number of loci.
Elston-Stewart algorithm : this is the general case of genetic reconstruction, the
algorithm is applied recursively up the family tree, with probabilities computed for
each possible genotype of each child, conditional on the genotypes of his parents, the
phenotype of the child, and the phenotypes for the child's descendents. The compu-
tation time scales with the number of alleles on each locus. This becomes impractical
if the number of loci is more than 5.
Hidden Markov algorithm : this algorithm can be applied with any number of loci
but with pedigrees of limited size. It is based on a nonhomogeneous Markov chain of
inheritance vectors v 1 , ... , v l at different loci with known transition matrices between
any two consecutive loci. An inheritance vector v i is a vector of 2 ∗ nonfounder binary
bits. A coordinate is 0 if the allele is inherited from the father; otherwise, it is 1.
Thus, the molecular biological approach to understanding the flow and expression
of genetic information involves studying the structure of macromolecules (DNA,
RNA, and protein) and the metabolic steps that mediate the flow of information from
the genome to the phenotype of the organism. With the advent of large databases
of genetic information for these macromolecules, a completely new approach to
studying gene expression and its regulation has developed. This field is known as
bioinformatics.

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