J. Biomedical Science and Engineering, 2011, 4, 272-281 JBiSE
doi:10.4236/jbise.2011.44037 Published Online April 2011 (http://www.SciRP.org/journal/jbise/).
Published Online April 2011 in SciRes. http://www.scirp.org/journal/JBiSE
Fuzzy splicing in precursor-mRNA sequences: prediction of
aberrant splice-junctions in viral DNA context
Perambur S. Neelakanta, Sharmistha Chatterjee, Mirjana Pavlovic, Abijit Pandya, Dolores de Groff
Department of Computer and Electrical Engineering & Computer Science, Florida Atlantic University, Boca Raton, Florida, USA.
Received 31 January 2011; revised 25 March 2011; accepted 28 March 2011.
ABSTRACT
RNA splicing normally generates stable splice-junc-
tion sequences in viruses that are important in the
context of virus mimicry. Potential variability in
envelop proteins may occur with point-mutations
inducing cryptic splice-junctions, which would re-
main unrecognized by T-memory cells of higher
organisms in vaccine trials. Such aberrant splice-
junctions result from evolution-specific non-conser-
vation of actual splice-junction sites due to muta-
tions; as such, locations of splice-junctions in a test
DNA sequence could only be imprecisely specified.
Such impreciseness of splice-junction locations (or
cryptic sites) in a sequence is eva luated in this study
via “noisy” attributes (with associated stochastics)
to the mutated subspace; and, relevant fuzzy con-
siderations are invoked with membership attributes
expressed in terms of a spatial signal-to-noise ratio
(SSNR). That is, SSNR adopted as a membership
function expresses the belongingness of a site-region
to exon/intron subspaces. An illustrative example
with actual (Dengue 1 viral) DNA data is furnished
demonstrating the pursuit developed in predicting
aberrant splice-junctions at cryptic sites in the test
sequence.
Keywords: DNA; Exon/Intron; Aberrant/Cryptic
Splice-Junction; MRNA Sequence; Fuzzy Subspace;
Spatial SNR
1. INTRODUCTION
Eukaryotic genomic data encoded via spatial statistical
occurrence of the nucleotide set {A, T, C, G} eventually
translates into a protein complex through transcription
and translation processes. The effort of such correct
translation is, however, subject to the effects of muta-
tions on the evolutionary conservation. The underlying
corruptions may manifest at the so-called splice junc-
tions that separate/delineate two subsequences in a DNA
sequence, namely, the (genetic) information-bearing codon
segment (called an exon) and the non-informative “junk”
codon, also known as non-codo n or int ron. (Exons bear
necessary information towards protein-making, whereas
non-codons are non-informative and their genetic role
has not been fully elucidated. Exons and introns appear
randomly along the DNA sequence. Codons tend to be
typically no more than 200 characters long, while non-
codons could be tens of thousands of characters in length.
Thus in majority, introns prevail mostly in a typical eu-
karyotic gene).
Towards the process of protein-making, introns are
first scissored out (in the transcription stage) from the
sequence and the remaining exons are spliced together
constituting the so-called messenger RNA (mRNA), which
is rendered ready for translation into a protein complex
(at the cell interior). Should any errors have occurred
(due to mutations), they would give room to the possi-
bility of evolving wrong or cryptic splice-junctions and
lead to (imperfect) translations. That is, aberrant splice-
junctions may result from mutational spectrum [1] and
would hamper the making of correct proteins. Illustrated
in Figure 1 is the formation of mRNA via transcription
through translation steps.
Further, in Figure 1, the locations of splice-junction
shown may not so reliably be distinct. In a canonical
sense, the splice-junction consensus (Figure 1(a)) may
follow certain rules as regard to introns and exons [2].
For example, the introns almost always begin with the
residue set {gt} at 5’-end and ends with an {ag} at the
3’-end. But, inasmuch as the nucleotide sequence corre-
sponds to a set of statistically permutated elements, {A,
T, C, G}, numerous putatively occurring {gt} and {ag}
locations (other than in the introns as indicated) may
prevail and resemble such canonical patterns.
The putatively occurring {gt} and {ag} locations im-
ply that relying on such canonical details alone may not
reasonably and robustly indicate the presence of true
splice-junctions. Further, in the event of point mutations,

P. S. Neelakanta et al. / J. Biomedical Science and Engineering 4 (2011) 272-281 273
Folded
protein
5’ 3’
Intron
gt Pyrimidine tract ag
Exon Intron IntronIntron ExonExon Exon
5’ Splice site3’ Splice site
mRNA
(Post-splicing)
5’
3’ UTR
P
r
otein
Precu
r
so
r
-mRNA
Transcription
3’
Exon Intron Intron IntronExon Exon Exon 3’ UTR
Translation
DNA
5’ UTR 3’ UTR
.. (a/c)ag gt(a/g) a gt……………............(c/t)6 x (c/t) ag g(g/t)
(a)
(b)
5’ UTR
Figure 1. Transcription through translation steps: (a) Typical splice-junction consensus. (b) Illus-
tration of splice-junctions delineating exons and introns in the context of transcription through
translation phases of central dogma dictating the use of genetic information in the DNA to make the
eventual protein complex. (UTR: Untranslated region).
stemming of aberrant splice-sites is inevitable [1]. As
such, should a junction be recognized and prevailing of
possible cryptic junction sites elucidated, it is necessary
to analyze statistically, the prevailing long-range genetic
information so as to determine the extent to which sub-
sequences surrounding the splice-junctions differ from
sequence segments of adjoining spurious analogs; hence,
true versus aberrant (cryptic) splice junctions can be
distinguishably identified.
Among feasible techniques developed in ascertaining
the delineation of codon/noncodon parts, (that is, in lo-
cating the splice-junctions), indicated in [3] is an entropy
estimator method that extracts “meaningful signal” from
the exon/intron segments of a test DNA; and hence, an
entropy technique is applied to detect the underlying
splice-junctions between the segments. This is, an in-
formation-theoretic (or entropy-based) tool envisaged in
a classical setting. It demarcates introns/ exon boundary
with a fair efficacy of performance.
With the advent of newly sequenced genomes, recog-
nition of genes has, however become a challenge and
detecting relevant splice-junctions with a system (that
does not require prior training) implies inherent difficul-
ties in this endeavor warranting more novel approaches;
for example, the so-called entropic segmentation method
of [4], has shown promising results in using an algorithm
based on the so-called Jensen-Shannon (JS) contrast
measure to distinguish coding versus non-coding regions
in a DNA sequence. This JS-measure is based on condi-
tional entropy aspects of statistical divergence (SD)
specified in terms of the well-known Kullback-Liebler
measure [5]. The main driver behind the success of this
method is due to distinguishable statistical characteris-
tics of exon and intron segments. That is, a non-uniform
codon usage prevails in the exon part meaning that, spe-
cific to coding regions not all bases of {A, T, C, G} oc-
cur with the same probability; but, there are subtle dif-
ferences between the statistics of their appearance exist
depending on the position of each base in the codon
triplets. In contrast, in non-informative intron segments,
the occurrence probabilities of A, T, C and G are the
same (equal to 1/4).
Developed in [6] is another strategy that identifies the
splice-junctions between codon and non-codon regions
present in a massive stretch of a DNA chain, especially
when the delineating boundary in question is submerged

P. S. Neelakanta et al. / J. Biomedical Science and Engineering 4 (2011) 272-281 274
in a subspace where codon and non-codon parts exist as
overlapping and ambiguous/fuzzy entities. A fuzzy in-
ference engine (FIE) developed thereof uses again in-
formation-theoretic based metrics (with relevant algo-
rithms applied to symbolic as well as binary sequence
data representing the DNA) so as to score differentiating
extents of codon/non-codon populations at a given site in
the DNA sequence. The information-theoretic metrics
adopted in [6] refer to various statistical divergence
(such as KL and JS measures) as well as distance and
discriminant concepts. Further, the algorithms indicated
in [6] yield consistent results on the delineation bound-
ary sought on test subspaces that are fuzzy; and simu-
lated studies using human as well as bacteria codon-
statistics confirm the efficacy of the approach pursued.
Another approach due to Neelakanta et al. [7] uses the
concept of information redundancy in complex systems
and defines a complexity metric that is adopted to dif-
ferentiate codon/non-codon segments and specify there-
of, the intermediate splice-junction.
Notwithstanding the existence of pursuits as above in
locating splice-junctions, the computed statistical diver-
gence (SD) is extended in the present study in getting
mapped into a novel membership function that specifies
the fuzzy subspace of overlapping exon and intron seg-
ments. Relevant membership function is defined on the
basis of “error’’ feature prevailing in the overlapping
(“noisy”) segment with mutational aberrations. The un-
derlying heuristics are described below.
As indicated before, the evolutionary conservation of
splice-junctions could be hampered with inevitable phy-
logenetic-specific mutations. If such mutations are (as-
sumed) independent, any “noisy” change in the spatial
DNA pattern of the sequence (at the splice- junctions)
can be marked as a “spatial jitter” with a characteristic
parameter called spatial signal-to-noise ratio (SSNR).
Splice-junctions with a spatial jitter as above corres-
pond to fuzzy offsets of exons and introns at their junc-
tions. That is, the spatially-jittered junction corres ponds
to an overlapping mix of codon and non-codon entities
and hence constitutes a (fuzzy) universe. In other words,
the splice-junction information has a fuzzy structure that
can only be identified/specified in norms of linguistic
descriptions. Such descriptions can be characterized by a
membership (function) [5,8] of belongingness to the
attributes of exon or introns.
The thematics of the present study refers to develop-
ing an appropriate FIE that delineates fuzzy overlaps of
codon/non-codon parts so as to elucidate the underlying
cryptic (or aberrant) splice-junctions. This is done on the
basis of SSNR defined with reference to the spatial-jitter.
The SSNR is also adopted to represent the relevant
membership function. Remainder of the paper describes
the underlying considerations.
2. SPATIAL JITTER ACROSS SPLICE
JUNCTIONS
Consider a small window(-length) accommodating a fi-
nite-number (say, 100) of putatively occurring base re-
sidues along a DNA sequence. Suppose this window
traverses a splice-junction. With no a priori information
available on the accurate disposition of the splice- junc-
tion, it can be initially assumed that the reading gathered
thereof is a “blurred” information implying an overlap of
exon/intron region with a fuzzy codon /non-codon transi-
tion. That is, a spreading function is assumed to prevail
across the finite window-length. The resulting spa-
tially-varying 1-D signal so gathered from the scan of
the entire DNA sequence would resemble a set of ran-
dom telegraphic waveform train constituted by changing
statistical profiles of exons and introns (being scanned).
The task in hand is then to detect the spatial transition
sites, each delineating adjoining exon/intron (or intron/
exon) segments despite of the noisy, blurred spatial in-
formation of the transition site.
Suppose (x) represents an uncorrupted DNA se-
quence pattern metric computed along the variable x
denoting the 1-D space of the sequence length. Relevant
signal component will assumed to be corrupted in the
event of mutational changes in {A, C, T, G} had oc-
curred along the sequence are encountered. Such muta-
tion- specific effects can be modeled as a contrbution of
“noise”, m(x) on the signal part, (x). Hence, the signal
output of the window-reader can be modeled by either a
spatial-domain convolution description, namely, s(x) =
(x) × m(x) or, equivalently by a corresponding fre-
quency-domain description, S(f) = (f)M(f), where S(f),
(f) and M(f) are the Fourier transforms of s(x),(x) and
m(x) respectively.
Consider an intron-exon splice junction illustrated in
Figure 2. The upper figure (marked as (a)) is a crisp
noise-free (uncorrupted) site with a splice-junction at xo
along the DNA sequence constituted by {A, C, T, G}
residues. Should mutational corruptions have taken place,
this crisp transition-boundary xo becomes (xo  x),
where x denotes spatial jitter. Further in Figure 2, the
y-axis depicts the measure/metric of (relative) statistical
divergence of exon versus intron (or vice versa) prevail-
ing at any point, x on the sequence. (This statistical di-
vergence prevails due to the reason that exon has a dis-
tinct distribution of {A, C, T, G} constituents vis-à-vis
the corresponding distribution in the intron segment).
The effect of (mutation-specific) corruption would
make the splice-junction to become unclear or fuzzy, as
shown in Figure 2(b). In essence, x is a jitter variable
superimposed on s(x) corresponding to crisp disposition

P. S. Neelakanta et al. / J. Biomedical Science and Engineering 4 (2011) 272-281 275
x
o
x
Exon Intron
(a)
(b)
y
Nucleotide sequence
y
Figure 2. “Spatially-jittered” splice-junction mani-
festing as fuzzy exon/intron (or vice versa) tran-
sitional residues along the sequence. (a) Unal-
tered (crisp) splice-junction; (b) Fuzzy splice-
junction with a graded variation of divergence
(distance) between the statistical features of exon/
intron (or intro/exon) along the transition region
(specified as a measure on the ordinate, (y) The
abscissa (x) depicts a scale of residues along the
DNA sequence.
of the splice junction xo. The expected root-mean-
squared (RMS) jitter Jr at any splice-junction xo can be
expressed by the “noise power” imposed by the mutation
errors.
In traditional communication theory, the term sig-
nal-to-noise ratio (SNR) is defined to specify the quality
of an uncorrupted “signal (power) level” to the corrupt-
ing “noise power”. Translating this concept, suppose the
average length of intron-plus-exon is
X
, corresponding
“spatial SNR” (SSNR) with reference to the DNA se-
quence space (of Figure 2) can be defined as follows:
SSNR =

22
r
X
J.
2.1. Error Probability of Splice-Junction
Prediction
Relevant to a “noisy” intron/exon (or exon/intron) tran-
sitions, the accuracy of locating the transition site, xo is
constrained by the probability of error associated with
the estimation of xo. In this context, within the specified
blurring limits of jitter, the SSNR implicitly would pre-
dict the error probability of estimating the splice-junc-
tion.
Suppose a sequence of exon/intron (or vice versa)
transitions (0
i
x
,s) prevail at locations indexed by i = 0, 1,
2, , m. From these data, one can extract exon or intron
widths (χ) as follows: +11E or I = ()
iii
xx

 for all values
of i = 0, 1, 2,, m, where the suffix (E or I) denotes the
measurement done on an exon or an intron respectively.
In terms of the average length of consequent intron plus
exon


X
subspaces, the transition (split-junction)
locations in the presence of mutation error-induced jitter
can be expressed as follows:

Noisy = 0
= +
i
iji
j
xkXδ
X

where kj is an integer with ko being zero; and, i = 0, 1,
2,

, m; further,  is a dimensionless random variable,
which in a simple case, has zero-mean Gaussian distri-
bution with variance 
2 = (1/SSNR). (This variance is
invariant along the sequence length if the sequence sta-
tistics is assumed to be stationary). Now defining a nor-
malized variable, ii
X
 , it can be estimated as:


1
= +
iiii
kδδ 

 with (i = 0, 1, 2,, m); hence one
can specify the probability of correct decoding of the
splice-junction, Pc(m) as the probability that
κ0.5.
ii
k
Inasmuch as,

1
= +
iiii
kδδ 

, the aforesaid
probability can be restated as follows:




10
10 1
Prob
0.5, , 0.5
c
mm
Pm 
 


  (1)
With the assumed Gaussian statistics for , the cumula-
tive probability of correct decoding of the splice-junc-
tion, namely Pc(m) can be deduced as follows:
 
o
2
11
exp d
22
11
22 2
x
cx
x
Px, x
x
erf














 
 


(2)
where x with respect to an ith junction is given by ix =


1 ii
δδ
x

; and,


2
0
2exp d
u
erf uuu
. Fur-
ther, the fuzzy-space in question enclaves the universe

mdepicting an m-dimensional hypercube across the
unit interval, I  [0.5, +0.5].
Eq.2 implies that the probability of correct detection
(and hence error probability) of the splice-junction
disposition is implicitly dependent on SSNR parameter.
The plot of Eq.2 is shown in Figure 3 where Pc is
plotted as a function of


0
x
xx with respect to a
presumed, crisp splice-junction at xo posing a transi-
tional error-prone width x. This error-prone region
depicts a subspace of overlapping exon/intron sub-
spaces that smear the exact location of xo. This unspe-
cific (error-prone) subspace x is therefore, fuzzy impos-
ing an imprecision on xo. Relevantly, the generic descrip-
tion of Pc in this fuzzy subspace takes a membership at-
tribute of vagueness vis-à-vis the position vari-

P. S. Neelakanta et al. / J. Biomedical Science and Engineering 4 (2011) 272-281 276
(x
o
+ x)/x
o
(x
o
 x)/x
o
1.0
0.5
0.90
1.0
P
c
0.85 1.10 1.15
0
Increasing SSNR
Increasing SSNR
Location of crisp exon/intron crisp
transition (x
o
)
Exon subspace
I ntron subspace
Figure 3. Probability (Pc) of correct estimation of a splice-
junction versus (xo  x)/xo.
able, x. The membership here depicts the belongingness
to exon subspace or intron subspace. Hence described in
the next section are the underlying aspects of the fuzzy
subspace in question with the object of ascertaining the
splice-junction in the fuzzy subspace.
3. FUZZY SPLICE-JUNCTION
PREDICTION
Suppose a set of input values xi are taken from the se-
quence and considered as non-specific or fuzzy. By de-
noting those segment values by {ix}f, corresponding
{(Pc)i}f can be written in terms of uncertain limit-
ing-values of all the vectors in the bounding (lower and
upper) interval, x [xL, xH]. Hence it follows that
[5]:







 

ΔΔ
ΔΔ
f
cc
L
ii
ff
α-1 j-1 j
cL
if
j = 1
PxPx
+ρPxx /j!




 (3)
where 
f (.) depicts the slope equal to d(Pc)i/dxi and
 is
the number of interval-valued parameter for the range
within [xL, xH]. Further, Equation (3) denotes an alge-
braic sum of addenda computed via interval arithmetic,
which denotes the “width of the results”. In other words,
for the specified vector bounding-limits of {(Pc)i}f,
namely, x  [xL, xH], an  -set of interval-valued pa-
rameters namely, {Q}, Q = Q1, Q2, …, Q

, prevails at or
around xo with no fuzzy attributes. Then relevant crisp-
domain relation of {x} versus {Pc} can be written by a
differential equation given by [5]: d2Pc/dx2 + (dPc/
dx)2 = g(x) where g(.) is some arbitrary function of x.
In the event of overlapping fuzzy attributes existing at xo,
then the corresponding (fuzzy)-domain relation between
{x} versus {Pc} can be generalized by a stochastical
discourse of Pc versus x expressed in terms of a fuzzy
stochastical differential Equation [5]. Further, in such
exon-to-intron transition subspace (denoted as F) having
fuzzy attributes, corresponding demarcation of exon/intron
transition can be assumed to be at a centroid location (XC)
with a line-of-delineation through the centroid. This lo-
cation refers to a defuzzified elucidation based on mem-
bership-of-belongingness of the site-of-interest in the
fuzzy space. The procedure to find XC is described be-
low.
3.1. Centroid of the Fuzzy Subspace
The SSNR and Pc considerations versus (xo  x)/xo
indicated before imply inherent statistical attributes of
{A, C, T, G} population in the exon and intron regions
across the splice-junction. As said earlier, the exon-side
statistics encodes for genetic information (so as to make
necessary protein) and the intron-side statistics is
non-informative. In other words, suppose the probabili-
ties of occurrence of the elements {A, C, T, G} in the
exon are denoted by the set: {QA, QC, QT, QG} with (QA
+ QC + QT + QG = 1). Then, the associated errors for the
elements of {A, C, T, G) are decided by the inequalities,
QA  QC  QT  QG. Now, suppose the corresponding
probabilities of occurrence in the intron are: {A, C, T,
G} with (A + C + T + G = 1); then, the associated
errors for the elements of {A, C, T, G} on intron-side are
set by the condition that, A = C = T = G = 0.25.
This is because the intron-side being non-informative,
Laplacian hypothesis applies in presuming that all (four)
elements are equally-likely to occur. Hence, by virtue of
the distinction between {Q}A, C, T, G and {} A, C, T, G, rele-
vant entropy/information-theoretic (IT) distances (that is,
statistical divergence or SD values) can be computed
(for the exon and intron regions). The results would
show distinction in the profiles of SD (in exon and intron
regions) as illustrated in Figure 4. (This SD can be any
one on the divergence measure such as KL or JS men-
tioned before. Illustrative measures are presented later in
the results with reference to a real DNA structure).
Following the considerations presented in [9,10], the
expression for Pc is


12 122erf x

 and it
can be approximately written as:
 
0
qq
Lz L

where


q
Lz denotes the Bernoulli-Langevin function and the
prime sign depicts the differentiation with respect to the
argument


2zx

 . Explicitly,





  
112coth 112
12coth 12
q
Lz qqz
qqz
 

where q represents an disorder entity associated with the
statistics of the population concerned [11]. Described in

P. S. Neelakanta et al. / J. Biomedical Science and Engineering 4 (2011) 272-281 277
[11] is that the upper-bound corresponding to isotropic
disorder statistics is decided with q = 1/2 and the
lower-bound (depicting an anisotropic disorder) is speci-
fied by q →  . Inasmuch as the statistics of exon-region
would differ from that of intron-region, qE  qI. Further,
as indicated in [9], the ratio
 
0
qq
Lz L

denotes ap-
proximately the membership function q for the fuzzy
space or block, F:{xi}) of interest with its fuzzy range
(upper-to-lower) is decided by: q = 1/2 to q →  .
Hence, shown in Figure 4, is the mapping of com-
puted divergence measures (SD) of intron and exon
subspaces (across the slice-junction) into corresponding
membership values,

q(SD) (with q = 1/2 yielding up-
per-bound values and q →  giving the lower-bound
values). For example, suppose a location xa (in exon re-
gion) gives the SD-value equal to (a). Then, the value (a),
maps on to the membership-plane as the entities (aU)
and (aL) depicting respectively, the upper- and lower-
bound values. Similarly, assuming a location xb (in in-
tron region) has an SD-value (b), this value maps on to
the membership-plane as (bU) and (bL) denoting respec-
tively the upper- and lower-limits. The steps as above
can be elaborated as follows:
First, the chosen divergence measure (SD: KL or JS)
is computed for the entire fuzzy domain F at each
pointer-position within a chosen window-size. For this
purpose, two subspaces FExon and FIntron depicting re-
spectively, the exon- and intron-side of the F-space are
specified. Then, the computation of the SD-measures
with exon statistics {Q}A, C, T, G in FExon-subspace and
with intron statistics {} A, C, T, G in FIntron- subspace is
done with KL or JS algorithm.
The values of SD generated in each differential win-
dow (of FExon- and FIntron-subspaces) accounts for the
extents of codons and noncodons in the relevant fuzzy
subspace. Corresponding to window-specific pointer
positions along the sequence, the SD-score profile ob-
tained across each differential block will be distinct for
each subspace (exon or intron) in question. Next, the
values of SD obtained are translated via membership
function to provide descriptive details of belongingness
in the fuzzy domain.
The translated values gathered can be subjected to a
defuzzification process [8,12] in order to get the centroid
position (of the pointer) that delineates the boundary of
the two, fuzzy test subspaces. Relevant local search fol-
lows the principle of “search and score” procedure ap-
plied appropriately on the assigned membership values
that describe the qualitative aspects of overlapping and
ambiguous codon/non-codon locales across the fuzzy
site.
The boundary that marks the desired splice-junction
being searched corresponds to a defuzzified location
Figure 4. SD-to- 
q(SD) mapping. (I): (xo  x)/xo versus
SD curves in the intron and exon subspaces. Note the SD
profiles are distinct in each region; (II): (xo  x)/xo ver-
sus membership function, 
q(SD). (Other details given in
the text).
obtained via centroid-finding method. Towards centroid,
the fuzzy exon- and fuzzy intron-domain would con-
verge close a single membership value.
Referring to Figure 4, the SD-value (a) in the exon
subspace yields mapped values of 
q (SD): (aL and aU);
and, the SD-value, (b) in the intron subspace maps into

q(SD): (bL, bU). Suppose the set {aL, aU } in turn pro-
jects on to x-axis at xaL and xaU respectively; and, like-
wise, the set {bL, bU} projects on to x-axis at xbL and xbU
respectively. Then, the mean position of (xaL, xaU, xbL and
xbU) would correspond to the centroid being sought.
4. SIMULATION EXPERIMENTS USING
REAL DNA DATA
The efficacy of efforts and procedure described above is
illustrated with an example of real-world DNA sequence
of Dengue virus type 1 (NCBI Reference Sequence:
NC_001477.1) [13]. Its CDS stretches from nucleotide
position 95 through 10273. Using the nucleotide popula-
tion details of this virus, a moving-window based calcu-

P. S. Neelakanta et al. / J. Biomedical Science and Engineering 4 (2011) 272-281 278
lation of KL-measure is plotted in Figure 5 across the
entire sequence length.
The data available in [13] for example, shows a CDS
stretch from position 7574 through 10270 with an indi-
cation of a transition at 7574. Presented in Figure 6 is an
exclusive plot of KL-measure across this selected CDS
regime at the transition locale around 7574. While the
codon (exon)/non-codon (intron) transition is markedly
seen (via KL value change), there is however a subspace
of fuzziness, wherein an overlap of exon and intron re-
gimes prevails indistinguishably (viewed in terms of
simple KL-measure). Therefore, by assigning member-
ship attribute, the FIE algorithm (described earlier) can
be invoked to decide on the location of the splice-junc-
tion in the fuzzy region. Hence, drawn in Figure 7 is the
profile of membership values ( 
q) mapped from the
computed KL-measures (of Figure 6) across the transi-
tion region of interest. There are two profiles: (A) de-
picts 
q-values with q = 1/2 (meaning the upper-bound
on the membership); and, (B) denotes

q-values with q =
 (meaning the lower-bound on the membership).
From Figure 7, the location of the splice-junction
buried in the fuzzy domain can be ascertained. This lo-
cation corresponds to the centroid coordinate (xC). This
centroid position is featured by the upper- and lower-
bound profiles of the  -value. As discussed earlier, xC
corresponds to the mean position of xaL, xaU, xbL and xbU;
and, for the data presented in Figure 7, the computed
results show that this centroid (xC) is at 7401 as against
the crisp value indicated in [13] as 7574. (The centroid
(7401) is the mean of: [(xbL + xbU)/2 = 7401] and [(xaL +
xaU)/2 = 7401]).
5. DISCUSSIONS AND CLOSURE
Depicted in Figure 8, are base residues reported around,
for example splice-junction site, namely 7574 of [13].
The present method predicts in addition, a cryptic set of
7370 and 7419 in the vicinity of the centroid 7401 de-
termined. The selection of this set {7370, 7401} is based
on the considerations of [2] suggesting the intron’s
3’-side preferential ending being ag. That is, the values
7370 and 7401 are picked around the centroid deter-
mined such that they are in conformance with the abut-
ting of ag-residues. Further, in Figures 8(a)-8(b), the
intron-subspace ends with residue set {ag} at 7574 and
is consistent with the canonical splice-junction consen-
sus (as mentioned earlier) of [2]. Notwithstanding this
canonical pattern, the mutational influences could have
possibly induced aberrant splice-junctions.
A scan through the test DNA indicates a cluster of
sites between 7500 through 7700 exist at which the
residues a and g occur together making it ambiguous on
02000 40006000 8000 10000
N
ucleotide
p
ositions
(
DEN1 virus
)
5

3

0
0.2
0.4
KL
Figure 5. Nucleotide position versus computed KL-mea-
sure of the DNA sequence of Dengue virus type 1 (NCBI
Reference Sequence: NC_001477.1) [13].
KL
5

3

Nucleotide
positions
Fuzzy
subspace
DEN1 virus
60008000
0.2
0.4
(
a
)
(b)
Intron
subspace
Exon
subspace
Figure 6. Nucleotide position in the limited range of
5000 to 9000 versus computed KL-measure of the
DNA sequence of Dengue virus type 1 (NCBI Refe-
rence Sequence: NC_001477.1) [13].
the decision that splice-junction (such 7574 of [13])
alone can be the splice-junction of interest. However,
following the fuzzy pursuit presented here, it enables
pointing out that other cryptic splice-junctions such as
7370 and 7419 could reasonably be alternative splice-
junction sites having adjacent ag residues as illustrated,
for example in Figures 8(a)-8(b) with 7419 site.
The complete list of aberrant splice junctions evalu-
ated for the test viral DNA in the present study is pre-
sented in Table 1 and illustrated in Figure 9. Table 1
indicates the centroid values determined as well as cryp-
tic transition sites predicted on the basis of the details in
[2]. It may be noted that the data available in [13] por-
trays overlaps of CDS domains that eventually facilitate
various protein structures as listed.
The purpose of knowing correct and aberrant
splice-junctions in the context of viral DNA (such as
DEN 1 virus) is pertinent to and implicates vaccine de-
signs [14]. In general, a gene is first transcribed into
pre-mRNA, which is a copy of genomic DNA containing

P. S. Neelakanta et al. / J. Biomedical Science and Engineering 4 (2011) 272-281 279
0.8
0.9
1.0

with q = 1/2
(Upper-
bound )
(
a
)
0.9
0.9
1.0
6000 6400 6800 7200 7600
800 0
with q = 
(Lower-bound)
(
b
)
5
3

Nucleotide
p
ositions
Exon
subspace
Exon
subspace
Fuzzy centroid location of
intron/exon transition at: 7401
Intron
subspace
Intron
subspace
Fuzzy subspace
Figure 7. Membership profiles ( 
q) across the fuzzy
transition region of interest. (a)

q-values with q = 1/2
(meaning the upper-bound on the membership) versus
nucleotide positions of the test DNA; (b) q-values with
q =  (meaning the lower-bound on the membership)
versus nucleotide positions of the test DNA.
(a)
g c a c g c g g…
…g g a g a g
7574
Exon subspace
Intron subspace
CDS
5

3

Nucleotide positions
… a g
7419
Exon subspace
Intron subspace
CDS
5

3

Nucleotide positions
(b)
Figure 8. Details on nucleotides adjacent to the predicted
splice-junctions: (a) As per [13]; and (b) as per present
method. (In both cases, the intron-subspace ends with a
residue pair ag bases consistent with the canonical splice-
junction consensus. (See text).
Figure 9. Summary of results on the locations of splice junctions. Downward arrows indicate values available in [13] for
DEN 1 virus. Upward arrows indicated computed values that include details of cryptic sites in the fuzzy subspace.
exon and intron regions. Gene-splicing is an important
form of protein diversity and has also regulatory funtions
and RNA-splicing is essential so as to regulate precisely
the process that occurs after gene transcription and be-
fore mRNA translation (in which introns are removed
and exons are retained). The sequences between the
boundaries of introns (denoting regions of DNA or pre-
cursor RNA that are not represented in mature RNA, but

P. S. Neelakanta et al. / J. Biomedical Science and Engineering 4 (2011) 272-281 280
Table 1. Transition sites indicated in [13] and the predicted sites as per the present method.
Bounds of membership value
CDS range
data from
[ ]
Description Transition site
[ ] Upper-bound
(UB)*
Lower-bound
(LB)*
Centroid of UB
and LB
Cryptic transition
sites
predicted**
95 394 Capsid
protein 394 1, 401 301 352
350
354
394
94 436
Anchored
capsid
protein
436 301, 701 301, 701 501 515
710 934 Membrane
glycoprotein 710 701 701 701
437 934
Membrane
glycoprotein
precursor
934/935 701, 1101 701, 1101 901
954
935 2419 Envelope
protein 2419/2420 1801, 2501 2801 2151 2160
2420 3475 Nonstructural
protein 1 3475/3476 3301, 3801 3301, 3801 3551 3553
3476 4129 Nonstructural
protein 2a 4129/4130 4001, 4301 4001, 4301 4151 4149, 4170
4130 4519 Nonstructural
protein 2b 4519/4520 4301, 4701 4301, 4701 4501 4326, 4356 4452, 4505
4520 6376 Nonstructural
protein 3 6376 6201, 6701 6201, 6701 6451 6447, 6462
6377 6757 Nonstructural
protein 4a 6757 6701, 7001 6701, 7001 6851
6758 6826 2k protein 6826 6701, 7001 6701, 7001 6850
6833, 6857
6827 7573 Nonstructural
protein 4b 7573/74 7201, 7601 7201, 7601 7401 7370, 7419
7574 10270 Nonstructural
protein 5 10270 10001, 10401 10001, 10401 10201 10202, 10211
** The UB and LB values indicated correspond to the sites where minima of 
q-plot (map) in the fuzzy domain of interest are observed, (for example, see
Figure 7).
* The predicted site is based on locating a site in the vicinity of the centroid where the introns almost always begin with the residue set {GT} at 5’-end and
ends with an {AG} at the 3-end as illustrated in Figure 8.
reside between regions) and exons (depicting regions of
DNA or precursor RNA represented in mature RNA) are
not random. There are several splicing events that are
possible eventually resulting in: Exon-skipping, intron-
retention, cryptic splice-site usage and alternative 3- and
5’-side splice-sites [1]. Further, in RNA splicing, the
so-called splicing-variants may be formed prior to
mRNA translation due to differential inclusion or exclu-
sion of regions in the pre-mRNA structure. Also, a sys-
tematic analysis of splice-junction sequences in eu-
karyotic protein coding genes using GenBank databank
has revealed a striking similarity among the rare splice-
junctions [2] that do not contain ag at the 3’ splice site,
or gt at the 5’ splice site. As mentioned before, indistinct
splice-junctions would result from deleterious effects of
mutations that target the splice-sites causing variability
in splicing patterns.
Such deleterious effects eventually form a major
source of protein diversity leading to a considerable ex-
tent of diverse proteomic functions that stem from a
relatively small number of genes. Thus, changes in
splice-site (alternative splicing) can induce different ef-
fects on the encoded proteins, not only in humans but
also in viruses.
As regard to the viral leader sequences, there may be a
splice donor site for generation of subgenomic messages,

P. S. Neelakanta et al. / J. Biomedical Science and Engineering 4 (2011) 272-281 281
usually the Env (viral envelope) transcript. In general,
the role of RNA splicing is to generate a set of stable
splice-junctions across viral sequences so that virus
mimicry is enabled as a mechanism for potential vari-
ability in envelope proteins, (which are prone to changes
due to point-mutation and thus, avoid to be recognized
by T-memory cells of higher organisms in vaccine trials).
The present study offers a systematic way of elucidating
cryptic splice-junction sites in viral DNA structures, the
knowledge of which can be profitably used in vaccine
design efforts. The study is being extended to a variety
of viruses in order to elucidate the underlying cryptic
aspects of splice-junctions. Pertinent analytical frame-
work and computational aspects are augmented with the
details available in [15-17].
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