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J. Hortl. Sci.
Vol. 5 (2): 85-93, 2010

Statistical genomics and bioinformatics

Prem Narain
29278 Glen Oaks Blvd. W.

Farmington Hills, MI 48334 USA
E-mail: narainprem@hotmail.com

ABSTRACT

Some important and interesting topics in the newly emerging disciplines of Statistical genomics and bioinformatics
have been discussed briefly in relation to plants with possible references to fruit crops. This paper is therefore
divided into two parts relating to the two disciplines, respectively. In the first part, mapping of quantitative trait loci
(QTL), association mapping, mapping of gene expression transcripts (eQTL), marker-assisted selection, and a
systems approach to quantitative genetics have been dealt with. In the second part, generation of databases, annotation,
annotated sequence databases, and sequence similarity search have been described.

Key words: Statistical genomics, bioinformatics, fruit crops, eQTL, annotated sequence databases, sequence
similarity search

I. STATISTICAL GENOMICS

INTRODUCTION

Most of the traits of economic importance in plants
have an underlying genetic basis involving several genes,
and, are subject to modification by environmental factors.
Statistical considerations have been predominant in dissecting
such complex traits into estimable components (Narain,
1990). Heritability of a trait, as a proportion of the phenotypic
variation that is attributed to genetic causes, has been a
prime indicator helpful in taking decisions for genetic
improvement of economic traits. Prediction of response to
artificial selection (based on intensity and accuracy of
selection) and the existence of genetic variability have been
successful across several crop plants. However, relationship
between the phenotype and the genotype has been like a
black box where inferential approach has been the only way
to look into it. This scenario is now changing with advent of
the modern technologies of gene sequencing, microarray
experiments and the enormous advances made in attempts
to understand gene and protein expression within the cell of
an organism. In this context, information on molecular
markers has been extremely helpful in identifying regions
on chromosomes (QTL) that bring about variation in a trait,
thereby providing tools that can lead to far more accurate
selection procedures for genetic improvement. Saturated
genetic maps of markers, giving their order along a
chromosome and relative distances between them, have

been developed. Gene transcript data from microarray
experiments can be integrated with molecular marker
information to map expression traits (eQTL) that can possibly
lead to causal networks. The network approach connecting
data on genes, transcripts, proteins, metabolites, etc.
indicates emergence of a systems quantitative genetics
(Narain, 2009, 2010).

Mapping of Quantitative Trait Loci (QTL)

Genomic techniques like restriction fragment
length polymorphism (RFLP), random amplified
polymorphic DNA (RAPD), amplified fragment length
polymorphism (AFLP), variable number of tandem
repeats (VNTR) - that consist of micro satellites (short
sequences) termed as short tandem repeats (STR) or
simple sequence repeats (SSR) and mini satellites
(long sequences) - and single nucleotide polymorphisms
(SNP) have been developed that help in identification of
QTLs by correlation between a trait and its specific DNA
markers (Narain, 2000). The first problem is, therefore, to
construct a linkage map that indicates the position and relative
genetic distances between markers along the chromosomes.
Map distance is based on the total number of cross-overs
between the two markers, whereas, physical distance
between them is denoted in terms of nucleotide base pairs
(bp). A centi-Morgan (cM), corresponding to a cross-over
of 1%, may span 10 kbs to 1,000 kbs and can vary across
species.

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Since marker genotypes can be followed for their
inheritance through generations, these can serve as
molecular tags for following the QTL, provided they are
linked to the QTL. This requires detecting the marker-QTL
linkage and, if established, estimating the QTL map position
on the chromosome. However, these problems depend on
whether we have data on experimental populations obtained
from controlled crosses, as in plants, or on natural populations
like humans where controlled crosses cannot be made.

The most popular method, given by Lander and
Botstein (1989), is that of simple interval mapping (SIM).
It involves formation of intervals by pairing of adjacent
markers and treating them as a single unit of analysis for
detection and estimation purposes. It is based on joint
frequencies of a pair of adjacent markers and a putative
QTL flanked by the two markers. Suppose markers A and
B are linked with recombination fraction r and QTL Q is
located between them with r

1
recombination from A and r

from B. Then, r = r
1
+r

2
-2r

1
r

2
≅

1
+r

2
, on the assumption of

no interference and r so small that no double cross-overs
can be assumed. In the classical back-cross design with
three loci each with two alleles, A-a, B-b, and Q-q, the
expected frequencies for the eight marker-QTL genotypes
can be used to obtain conditional probabilities of the QTL
genotypes, given the marker genotypes. By setting up a
linear regression model between the trait (Y) and the
indicator variable (X) taking the value 1 if the QTL is QQ
and –1 if it is Qq, one can estimate a regression coefficient
that defines the allelic substitution effect of this QTL. In
such a model, the QTL genotype for a given individual is
unknown. X is then a random indicator variable with
conditional probabilities of obtaining QQ or Qq at the QTL.
This means the observed value is modelled as a mixture-
distribution with mixture ratios as the conditional
probabilities. We have, therefore, a situation often referred
to as a linear regression with missing data. The problem of
estimation then involves the use of EM algorithm. By
assuming that the character is normally distributed within
each of the eight marker-QTL classes with equal variance
σ2, one can set up a likelihood function in terms of unknown
parameters, and develop a log likelihood ratio ( Λ ) for testing
the hypothesis that the QTL is not located in the interval
where the log likelihoods are evaluated using the maximum
likelihood estimates of the genotypic values for the two QTL
genotypes, the variance σ2 and the recombination fraction
r

1
between marker A and the putative QTL using iterative

procedures based on EM algorithm. This statistic is
distributed as χ2 with 1 d.f. The associated lod score for the

interval mapping is then (½) (log
10

e) Λ. This statistic is
evaluated at regularly-spaced points; say 1 or 2 cm distance,
covering the interval as a function of the presumed QTL
position. Repeating this procedure for each interval along
the chromosome and plotting the lod score curve against
the interval gives a QTL likelihood map that presents
evidence for the QTL at any position in the genome.
Presence of a putative QTL is assumed if lod score exceeds
a certain threshold T and the maximum of the lod score
function in the map gives an estimate of the QTL position
and gene effects. Mapping of QTL by interval method is
widely used in practice. Analysis is done through the software
MAPMAKER/QTL.

Although SIM is the method for QTL mapping most
widely used with advantage in several practical situations,
it ignores the fact that most quantitative traits are influenced
by numerous QTLs. This is overcome either by adopting a
model of Multiple QTL Mapping (MQM) or by combining
SIM with the method of multiple linear regression, a
procedure known as composite interval mapping (CIM).
In all these methods, one uses the approach of maximum
likelihood that produces only point estimates of the
parameters such as the number of QTLs, their location, and
effects. The corresponding confidence intervals are required
to be determined separately by re-sampling methods.
Further, the correct number of QTLs is difficult to determine
using traditional methods. Their incorrect specification leads
to distortion of the estimates of locations and effects of
QTLs. To address these problems, a Bayesian approach is
often adopted wherein the joint posterior distribution of all
the unknown parameters given their prior distributions and
the observed data is computed. For details of these various
aspects, one can refer Narain (2003a, 2005).

The first application of interval mapping in plant
breeding was to an inter-specific backcross in tomato. The
parents for the back-cross were the domestic tomato
Lycopersicon esculentum (E) with fruit mass 65 g and a
wild South American green-fruited tomoto L. chmielewskii
(CL) with fruit mass 5 g. A total of 237 back-cross plants
were assayed for continuously varying characters like fruit
mass, soluble-solids concentration and pH, and, 63 RFLP
and 20 isozyme markers spaced at approximately 20 cM
intervals were selected for QTL mapping. A threshold T=2.4,
giving a probability of under 5% that even a single false-
positive will occur anywhere in the genome, was used. This
corresponds approximately to significance level for any
single test as 0.001. The resulting QTL likelihood maps
revealed multiple QTLs for each trait (6 for fruit weight, 4

J. Hortl. Sci.
Vol. 5 (2): 85-93, 2010

Prem Narain