Data structures

A Pattern Matching Algorithm for Codon Optimization and CpG Motif-

Engineering in DNA Expression Vectors

Ravi Vijaya Satya and Amar Mukherjee

School of Engineering and Computer Science

University of Central Florida

Orlando, FL 32816

rvijaya, amar@cs.ucf.edu

Udaykumar Ranga

Jawaharlal Nehru Center for Advanced

Scientific Research

Jakkur, Bangalore, India

udaykumar@jncasr.ac.in

Abstract

Codon optimization enhances the efficiency of DNA

expression vectors used in DNA vaccination and gene

therapy by increasing protein expression. Additionally,

certain nucleotide motifs have experimentally been

shown to be immuno-stimulatory while certain others

immuno-suppressive. In this paper, we present

algorithms to locate a given set of immuno-modulatory

motifs in the DNA expression vectors corresponding to a

given amino acid sequence and maximize or minimize

the number and the context of the immuno-modulatory

motifs in the DNA expression vectors. The main

contribution is to use multiple pattern matching

algorithms to synthesize a DNA sequence for a given

amino acid sequence and a graph theoretic approach for

finding the longest weighted path in a directed graph

that will maximize or minimize certain motifs. This is

achieved using O(n 2 ) time, where n is the length of the

amino acid sequence. Based on this, we develop a

software tool.

Key Words: Codon optimization, immuno-modulatory

motifs, multiple pattern matching, longest weighted path.

1. Introduction

DNA vaccines have revolutionized the field of vaccine

technology by demonstrating the ability to induce humoral

and cellular immune responses in experimental animals

and humans [9]. Immunization of animals with plasmid

DNA encoding a protein antigen was an accidental

observation that eventually led the way to a novel strategy

of immunization. DNA vaccines, also known as "naked

DNA" or "nucleic acid" vaccines, encode the antigens of

pathogenic organisms including viruses, bacteria, fungi

and parasites [40]. The protein antigen is processed

within the cell and presented by the MHC-I and –II

pathways thereby eliciting specific immune responses

essential for controlling pathogenic infections [2].

Although DNA vaccines have been successful in

generating strong immune responses in smaller animal

model such as mouse, they have not been as efficient in

larger species such as primates and humans [23, 3, 25, 4].

Stimulating both the arms of the immune system is often

desirable for efficient control of infectious diseases

especially in the larger animals. In the case of

recombinant protein vaccines, immune-enhancers

technically known as adjuvants, such as Freund’s

adjuvants and Alum, are in use to enhance antigen

specific immune responses. However, no such adjuvants

are available for use in the context of DNA vaccines. The

lack of suitable adjuvants for DNA vaccines is one

important reason for the poor performance of the DNA

vaccines in larger animals.

Nucleotide sequence encoding a foreign protein is

directly placed under the control of a mammalian

promoter to construct a DNA vaccine. Several amino

acids are encoded by more than one triplet codon and

different organisms have variable requirement for codon

preference [13]. Cloning of a wild type gene from a

parasite into a DNA vaccine often leads to insufficient

levels of protein synthesis in the host cell as a result of

codon bias between the species. Successful immunization

with DNA vaccines requires high expression of cloned

genes to synthesize large quantities of the foreign

protein. For instance, the overall genetic content of

Human Immunodeficiency Virus-1 is AT-rich, while that

of the human beings is CG-rich. The codon frequency of

the pathogenic DNA embedded into the mammalian

expression vector may not be optimal for adequate

protein expression in the host resulting in low level

protein expression. A potential solution for the codon

bias is to optimize the codon sequences of a gene to suit

Proceedings of the Computational Systems Bioinformatics (CSB’03) 0-7695-2000-6/03 $17.00 © 2003 IEEE

the requirements of the host without altering the original

amino acid sequence of the protein [41, 16]. This

approach has been successful in eliciting strong immune

responses in several species of experimental animals [8,

28]. While immunization with synthetic genes, codon-

optimized for mammalian expression stimulated strong

immune response, immunization performed in parallel

with wild type genes generated low or moderate levels of

immune response [34, 36].

In addition to codon optimization of the synthetic

genes, a range of molecular approaches is being

evaluated to up-regulate immune responses generated by

DNA vaccines. Co-expression of cytokine genes [20], co-

stimulatory receptors [12, 35] or other

immunemodulators [33], synthetic assembly of T-helper

or CTL epitopes [6] and formulation with a variety of

chemical adjuvants [11, 24, 33, 37, 39] have been some

of the approaches reported. However, most of these

approaches may not be suitable for human application

due to toxic manifestations of the adjuvants. An ideal

agent used as an adjuvant for DNA vaccine must enhance

the immunogenicity without apparent cytotoxicity to the

host. Engineering CpG islands into DNA vaccines has

been one promising approach that showed enhanced

immune responses [19].

The well-established immune-enhancing property of

bacterial DNA has been mapped to sequence motifs

consisting of un-methylated CpG dinucleotides flanked

by base pairs in a specific context [18]. Two important

differences between the bacterial and mammalian DNA

enable the mammalian innate immune system to

recognize the former as a foreign component. CpG motifs

in bacteria are found at the expected 1:16 frequency;

however, their frequency in mammals is 4 times less than

expected. Bacterial CpG are non-methylated while those

of mammals are mostly methylated. The mammalian

immune system takes advantage of these two chemical

differences between the bacterial and mammalian DNA

to identify a bacterial infection and wage strong and

rapid anti-bacterial immune responses [29].

CpG-mediated activation of the mammalian innate

immune system has been extensively exploited in the

vaccination technology. Co-injection of CpG containing

oligonucleotides or empty vectors with protein antigens

elicited potent immune response to the antigen.

Methylation of the CpG motifs, on the other hand,

abrogated immune response to the antigens suggesting

that the CpG motifs possess adjuvant properties only

when unmethylated or hypomethylated [[5, 17]. Since the

DNA expression vectors used in genetic immunizations

are usually grown in bacteria, several CpG motifs on the

plasmids are not methylated possibly activating the

innate component of the mammalian immune system.

Presence of hypo-methylated CpG motifs is essential for

induction of immune responses to the antigens encoded

by the vectors.

While certain CpG motifs are immuno-stimulatory

(CpG-S), enhancing immune responses when the host is

vaccinated, others CpG motifs in a different nucleotide

context are immuno-inhibitory or -neutralizing (CpG-N)

abrogating antigen-specific immune response [18].

Engineering the nature and the frequency of the CpG

motifs may be critical for the design of DNA expression

vectors. DNA expression vectors are primarily used for

two different applications, expression of a foreign gene in

a host for vaccination or for correcting a genetic defect of

the host [26].

Although the basic design of these two types of vectors

is identical in several respects, their requirement for the

presence and nature of CpG motifs is diagonally

opposite. While genetic vaccines require CpG-S motifs

for efficient stimulation of the host immune system, such

a strong response must be avoided for long-term survival

of the DNA expression vector intended for gene therapy.

An ideal strategy for designing DNA vaccines must

recruit as many CpG-S motifs as possible, concomitantly

eliminating as many CpG-N motifs as possible without

altering the original protein sequence of the genes. In

contrast, design of a DNA expression vector intended for

gene therapy must eliminate as many CpG-S motifs as

possible and recruit as many CpG-N motifs as possible

for the best result. Thus, depending on the application,

some CpG motifs may be desirable, while certain others

may be undesirable.

The software tool we report here is designed to help

the researcher to engineer the composition of a gene with

respect to codon usage and CpG motifs without

modifying the original amino acid sequence of the

protein. Codon optimization is advantageous for protein

expression in a heterologous expression system such as

E.coli, Picchia, Saccharomyces, Baculo virus,

mammalian cells etc. The software could also engineer

the content and nature of the CpG motifs recruited into a

DNA expression vector in addition to optimizing the

codon usage and resolve potential conflicts arising

between these two requirements and find an optimal

nucleotide sequence.

2. Prior Work and Summary of

Contributions

Proceedings of the Computational Systems Bioinformatics (CSB’03) 0-7695-2000-6/03 $17.00 © 2003 IEEE

Objective of this algorithm is to (1) identify the best

triplet codon for codon optimization and (2) engineer the

nature and content of the CpG motifs of a gene expressed

from a genetic vector. Input for the software is the amino

acid sequence of a gene of interest or the nucleotide

sequence that needs genetic modification. The input

amino acid sequence is reverse-translated to generate

nucleotide sequence that is optimized for the codon and

CpG content. During the process of reverse-translation,

there is a one-to-many relationship between the amino

acid sequence and the DNA sequences. A given amino

acid sequence could correspond to an exponential

number of DNA sequences with respect to the length of

the given amino acid sequence. Our task here is to choose

the particular sequence that has the desirable properties

(maximum number of the desirable motifs, and the

minimum number of the undesirable motifs) from this

large number of possible DNA sequences. A brute force

search on all the possible DNA sequences will take

exponential time. The motifs (or the patterns) that need

optimization are small DNA sequences, generally not

exceeding eight nucleotides in length. If different motifs

have to be optimized simultaneously, it is possible to

have multiple motif occurrences (both desirable and

undesirable) sharing the same position in the amino acid

sequence. In such cases it may not be possible to have all

the motif occurrences in the same DNA sequence. This

problem will be explained in detail in Section 4.

McInerney[27] presented a program to perform the

codon usage analysis on a sequence or a database of

sequences. Other work in this area of bioinformatics is

mostly on finding CpG islands within the genes and

transcriptional elements that regulate gene expression.

Ponger et al [30] developed a software package to locate

CpG islands associated with the transcription start sites

of the genes. Lin et al [22] presented software for

locating non-overlapping maximum average segments in

a given sequence. These publications analyzed DNA

sequences and searched for nucleotide motifs with high

CG content.

Our emphasis in this paper is to synthesize a DNA

sequence that codes for a functional protein, with certain

characteristics and optimization parameters. The main

contribution is to use multiple pattern-matching

algorithms to synthesize a DNA sequence for a given

amino acid sequence and a graph theoretic approach for

finding the longest weighted path in a directed graph that

will maximize or minimize certain motifs as well as

guarantee certain fitness factors of codon frequency usage

for a particular species. This is achieved using O(n 2 ) time

and storage resources compared to the brute force

algorithm that might take exponential amount of

resources, where n is the length of the amino acid

sequence. The software tools developed for the purpose

will find applications in the rapid development of

vaccines and gene therapy.

In Section 3, we introduce the basic terminology. In

Section 4, we give a precise combinatorial formulation of

the problem in terms of pattern matching operations and

present the main algorithm. Section 5 gives the

complexity analysis. Section 6 gives a description of the

software and in Section 7 we present the results.

3. Terms and definitions

The alphabet of a DNA sequence is denoted as ΣN =

{A,C,G,T} 1 where A,C,G,T are the four DNA molecules

adenine, cytosine, guanine, and thymine, respectively.

The alphabet for the amino acid sequence is ΣA =

(A,R,N,D,C,Q,E,G,H,I,L,K,M,F,P,S,T,W,Y,V,stop}, each

letter indicating one of the 20 amino acids, and stop

indicating the stop codon. For example, ‘A’ indicates

Alanine, ‘R’ indicates Arginine, ‘N’ indicates

Asparagine, etc. A codon c is a triplet of the DNA

symbols in ΣN. As the size of DNA alphabet is 4, there

are 64 possible codons. In the context of amino acid

translation from mRNA, each element of ΣA gets mapped

to a maximum of 6 codons 2 . This mapping is also

referred to as the genetic code. Symbolically, the

mapping of an amino acid σ ∈ ΣA can be denoted as a set

C(σ) of n σ codons, where 1 ≤ nσ ≤ 6. The inverse-

mapping associates an amino acid σ with a codon c,

denoted by C -1

(c) = σ. The frequency of occurrence of

members of C(σ) is different for each species. This

relative difference in the frequency of occurrence for each

codon is called codon bias. The codon usage table for a

species gives the codon bias information for that species 3 .

For an amino acid σ, the codon bias (or the frequency

information) is given by the set of fractions F(σ),

corresponding to C(σ). For each fi ∈ F(σ), 1 ≤ i≤ nσ, 0 ≤

fi≤ 1, and 1 1

=∑ =

σ n

i

i f . When designing a DNA vaccine

for a species, it is often desirable to have those codons

that occur more frequently in that species. Therefore, for

each amino acid we generally choose the most frequent

1 The protein synthesis takes place from mRNA. The actual RNA

alphabet is {A,C,G,U}, in which thymine is replaced by uracil. For

simplicity of notation, we use T instead of U in this paper.

2 See http://molbio.info.nih.gov/molbio/gcode.html

3 See http://www.kazusa.or.jp/codon/ for codon usage tables for different

species.

Proceedings of the Computational Systems Bioinformatics (CSB’03) 0-7695-2000-6/03 $17.00 © 2003 IEEE

codon, henceforth referred to as the best codon. For an

amino acid σ, the index of the best codon, b σ , is defined

as b σ = {i | fi = MAX(F(σ))}. If there are more than one

values for b σ ,, we take one arbitrarily. It is also useful to

have a measure of how desirable a codon is. This

quantity is given by the fitness of the codon. The fitness

of the ith codon, ci of an amino acid σ is given by:

fitness(ci) = σ b

i

f f

, the ratio of the frequency of the ith

codon of σ to the frequency of the best codon of σ. Given

a list of codons, the average fitness of the list of codons

is defined as the arithmetic mean of the fitness values of

all codons in the list.

A motif is a short DNA sequence of length l, denoted

as M = m1m2m3……ml, mi ∈ ΣN,1≤ i ≤ l. We will

consider immuno stimulatory and immune neutralizing

(CPG-S and CPG-N) sequences as possible motifs. A

motif occurs as part of a long DNA sequence and as such

will correspond to a sequence of codons. Since the

beginning of the codon boundary could be aligned with

any one of the first, second, or third positions in the

motif, this gives rise to three possible codon encodings

for the motif. In each codon encoding, the codons that lie

completely within the motif can be translated to an amino

acid sequence. These amino acid sequences will be

referred to as amino acid search patterns (henceforth

referred to as aasp). The parts of the motif (less than

three nucleotide beginning or the end of the motif that do

not completely correspond to a codon are referred to as

the head or tail, respectively, of the motif. When l < 5,

all or some of M 1 , M

2 , M

3 may be null. The

corresponding amino acid search patterns, aasp(M 1 ),

aasp(M 2 ), aasp(M

3 ) will also be empty strings, but their

head and/or tail portions will be non-null. This implies

that, for such an aasp, every position in the amino acid

sequence is a possible occurrence of the motif. The three

possible codon encodings of a motif M and their

corresponding three amino acid search patterns are

shown in Table 1.

As an example, if M = ATCGAT, M 1 = ATCGAT,

aasp(M 1 ) = ID, head(M

1 ) = null, tail(M

1 ) = null; M

2 =

TCG, aasp(M 2 ) = S, head(M

2 ) = A, tail(M

2 ) = AT ; and

M 3 = CGA, aasp(M

3 ) = R, head(M

3 ) = AT, tail(M

3 ) =

AT. For example, searching for the motif M = ATCGAT

in the amino acid sequence …LSI…, we find S =

assp(M 2 ). head(M

2 ) = A and tail(M

2 ) = AT. L, the amino

acid that precedes S, has two codons that end with A

(head(M 2 )), and I, the amino acid that follows S, has

three codons that begin with AT (tail(M 2 )), as shown

below.

L S I

CTA

TTA

TCG ATA

ATC

ATT

Selecting any codon from the first column and any

codon from the third column will result in an occurrence

of ATCGAT. Therefore, there are 2*3 = 6 unique

combination of codons that result in the occurrence of

ATCGAT at the location in the amino acid sequence

beginning with L and ending with I. These will be

referred to as the possible occurrences of the motif. The

codons corresponding to an occurrence will be referred to

Table 1. Head and tail of amino acid search patterns

  )()(

3*3/321

1

l mmmmM LL=

aasp(M 1 ) = a1a2……  3/la ,

where a1 = C -1

(m1m2m3),etc.

nullMhead =)( 1

nullMtail =)( 1

if 03mod =l

l mMtail =)(

1 if 13mod =l

ll mmMtail

1

1 )(

−

= if 23mod =l

  )()(

13*3/)1(432

2

+− =

l mmmmM LL

aasp(M 2 ) = a1a2……  3/)1( −la ,

where a1 = C -1

(m1m2m3), etc.

1

2 )( mMhead = nullMtail =)(

2 if 13mod =l

l mMtail =)(

2 if 23mod =l

ll mmMtail

1

2 )(

−

= if 03mod =l

  )()(

23*3/)2(543

3

+− =

l mmmmM LL

aasp(M 3 ) = a1a2……  3/)2( −la ,

where a1 = C -1

(m3m4m5),etc.

21

3 )( mmMhead = nullMtail =)(

3 if 23mod =l

l mMtail =)(

3 if 03mod =l

ll mmMtail

1

3 )(

−

= if 13mod =l

Proceedings of the Computational Systems Bioinformatics (CSB’03) 0-7695-2000-6/03 $17.00 © 2003 IEEE

as constituent codons for that occurrence. We call the

collection of all possible occurrences of all motifs as the

potential occurrences, as all of these occurrences might

not be retainable in the final solution. As noted in

Section 1, some of these occurrences may be desirable

while others may be undesirable; we assign a desirability

value of +1 and –1, respectively , for these occurrences.

In general, these values could be arbitrary.

An additional step of pre-processing is required for

undesirable motifs. We want to avoid occurrence of an

undesirable motif. However, we need to make sure that

the undesirable motifs do not re-appear in the final

solution as a result of selecting the best codons for amino

acids that are not part of a desirable motif. We achieve

this by considering all alternate codon combinations of

each potential occurrence of an undesirable motif, and

treating them as potential occurrences with a desirability

value of zero. We call these alternate potential

occurrences as neutral occurrences. In the above

example, if ATCGAT were an undesirable motif, out of a

total of 6*6*3 = 108 possible encodings for the

subsequence LSI, 108-6 = 102 codon combinations do not

result in the occurrence of ATCGAT. Each one of these

102 combinations will be registered as a neutral

occurrence.

The weight of an occurrence is the sum of the

average fitness of the constituent codons and the

desirability for that motif. The total weight of a DNA

sequence is the sum of the individual weights of all the

occurrences from the given set of motifs that are part of

the DNA sequence.

4. The Algorithm

4.1 Problem Definition

Given an amino acid sequence SA = a1a2a3…………aJ,

and a list of motifs M = {M1,M2,M3, ……,Mk}, with their

corresponding desirability values, D = {D1, D2, D3, ...

..., Dk}, the problem is to find the codon sequence, SC =

c1c2c3…………cJ, where each ci ∈ C(ai), 1≤ i ≤ J, and

the DNA sequence, SD = d1d2d3…………d3*J,

corresponding one-to-one to SC, where ci = d3i-2d3i-1d3i,

such that: 1)SD has the maximum total weight possible;

and 2)Every codon ci in SC that is not part of an

occurrence (desirable, undesirable or neutral) of a motif

in M is the best codon for the corresponding amino acid

ai. In other words, we need to find the exact mapping of

the amino acid sequence into a DNA sequence that has

the maximum weighted occurrences of the motifs in M.

We find all possible occurrences of all the motifs,

including neutral occurrences for the undesirable motifs.

Out of these, if two occurrences (of the same motif or of

different motifs) extend over the same position in SA, and

require different codons for that position, then the two

occurrences have a conflict and cannot co-exist. We have

to select the largest weighted subset of these occurrences

that are mutually non-conflicting.

4.2 The Algorithm Steps

Step1: Pre-processing:

A)Form a list Lp of search patterns consisting of all

three search patterns aasp(Mi 1 ), aasp(Mi

2 ) and aasp(Mi

3 )

for each motif Mi ∈ M, 1 ≤ i ≤ k, in the list of motifs.

Also, enumerate the head and tail for all three

alignments of each motif. Each entry in Lp is an element

of a data structure having the following members:

• codon_list, the list of codons that lie entirely

within the motif.

• search_pattern, the aasp corresponding to the

codon_list.

• length, the size of the codon_list. (note: length

may be 0 for short motifs).

• head, the corresponding head – a DNA sequence

which is either null, or 1 or 2 characters in length.

• tail, the corresponding tail – a DNA sequence

which is either null or 1 or 2 characters in length.

• desirability, the desirability value for the

corresponding motif, +1 or –1.

B) Build an Aho-Corasick keyword tree [1] ACT for

all the amino acid search patterns.

• A node in the keyword tree might correspond to

multiple search patterns with different heads and

tails, henceforth referred to as the

list_of_matches, denoted by the indices into Lp.

• When the length of a motif is less than five

nucleotides, some amino acid search patterns

might be empty strings. i.e., they will have non-

empty head and/or tail, but empty search pattern.

In the keyword tree, the root itself will correspond

to such empty amino acid search patterns.

Proceedings of the Computational Systems Bioinformatics (CSB’03) 0-7695-2000-6/03 $17.00 © 2003 IEEE

Step2: Finding all potential occurrences: In this

step, we build the list of potential occurrences, P. Each

entry in P will have the following attributes:

• pBegin is the position in SA at which the match

starts.

• pEnd, the position in SA at which the match ends.

• A list of codons Lc of size pEnd-pBegin+1. The

codon at position ‘r’ in Lc indicates rth codon in

the match.

• The weight of the occurrence. We will generate

the list P in sorted order in ascending values of

pBegin; if two occurrences have same pBegin

value, they are sorted in ascending value of pEnd.

The following algorithm traverses the tree

according to the given amino acid sequence.

Algorithm 4.2.1 find_potential_occurrences

Inputs: The Aho-Corasick keyword tree ACT, the amino

acid sequence SA, list of search patterns Lp

Output: The list of potential occurrences, P, sorted.

Initialize P ← null, cur_node ← ACT.root

for q=1, until q ≤ J, traverse ACT:

if cur_node.child[aq] != null

cur_node ← cur_node.child[aq]

else

cur_node ← cur_node.failure_link

if cur_node.list_of_matches is not empty,

/*Corresponding aasp has occurred. Check if the motif

corresponding to the aasp can actually occur. The head

and tail are compared with all the codons of the amino

acids on either side aasp*/

for each entry i in the list, do the following:

a. Enumerate position p, the starting position of

Lp(i).search_pattern in SA.

b. pBegin ← p, pEnd ← q

c. if (Lp(i).head ≠ null) /* head is not null */

i. pBegin ← pBegin-1

ii. form a set of codons Chead such that

Lp(i).head is a suffix of each chead ∈

Chead, Chead ⊆ C(ap-1)

d. if (Lp(i).tail ≠ null) /* tail is not null */

i. pEnd ← pEnd+1

ii. form a set of codons Ctail such that

Lp(i).tail is a suffix of each ctail ∈ Ctail,

Chead ⊆ C(aq+1)

e. for each unique combination of chead ∈ Chead and

ctail ∈ Ctail, insert an entry to the list of potential

occurrences, P, with the entries pBegin, pEnd,

Lp(i).codon_list, and the corresponding weight

of the occurrence. Note: Chead and/or Ctail will be

empty if Lp(i).head and/or Lp(i).tail are null.

if a non-zero number of occurrences were added in

the above step, and if Lp(i).desirability < 0, insert an

entry in P for each unique combination of codons

selecting one codon each from the sets

C(SA(pBegin)), ……, C(SA(pEnd)). i.e, insert all

neutral occurrences corresponding to the current

undesirable occurrence into P.

Example: Let us assume we are trying to maximize the

number of occurrences of the motif ATCGAT in the

amino acid sequence MEPRVID. The three amino acid

search patterns, aasp(M 1 ), aasp(M

2 ) and aasp(M

3 ) are

ID, S, and R, respectively. Searching for them, we find R

at position 4, and ID at positions 6-7. R is aasp(M 3 ),

head(M 3 ) is AT, tail(M

3 ) is T, therefore we have to see if

any codons ending with AT can occur at position 3 in

MEPRVID, and if any codons beginning with T can occur

at position 5. The amino acid at position 3 is P, which

has the codons [AGA, AGG, CGA, CGC, CGG and

CGT], none of which end with AT, therefore it is not

possible for ATCGAT to occur from positions 3-5.

Coming to the next match, ID at positions 6-7, ID

=aasp(M 1 ). head(M

1 ) = null, tail(M

1 ) is null, therefore

ID at positions 6-7 can be added to the list of matches.

The corresponding entry in P will be: pBegin ← 6, pEnd

← 7, list of codons, LC ← ATC,GAT.

Step3: Mapping to a directed acyclic graph: In this

step, we find a non-conflicting subset of the occurrences

in P that has the maximum over-all weight. This can be

done by mapping the problem to that of finding the

critical path in a directed acyclic graph and finding the

nodes in the critical path, as follows:

1. Each occurrence in P is represented by a node v

in a weighted directed acyclic graph G = (V,E), where V

and E denote the vertex and the directed edge set of G.

The node weight wi of a node vi, is given by the weight of

the corresponding occurrence, P(i). i.e, wi ← P(i).weight,

1 ≤ i ≤ |P|, wi ∈ W, where W is the weight vector

corresponding to P.

2. Start with an empty edge list E. For each i, 1≤ i

≤ |P|, and j, i < j ≤ |P|, if P(i).pEnd < P(j).pBegin or if

P(i) and P(j) have the same codon encodings for all

positions r, P(j).pBegin ≤ r ≤ min(P(i).pEnd, P(j).pEnd),

then vi, vj will have an edge between them. i.e., E ← E∪

(vi,vj).

Now, we can solve for the longest weighted path

(critical path) in G, and insert the nodes in the longest

path in a list Lv. The longest weighted path can be found

by the critical path algorithm [7].

Proceedings of the Computational Systems Bioinformatics (CSB’03) 0-7695-2000-6/03 $17.00 © 2003 IEEE

4.3 Translation of the amino acid sequence to a

DNA sequence

Once we have a set of occurrences of motifs that do

not conflict with each other, the next step is to do the

actual mapping from the amino acid sequence to a codon

(or DNA) sequence. At each position in SA that is not part

of any occurrence, we select the best codon for the

corresponding amino acid. At positions in SA that are

part of an occurrence, we select the codon that is required

for the occurrence.

Let Lv be the final list of occurrences.

1. for each ai ∈ SA, 1 ≤ i ≤ J,

ci ← best codon (C(ai))

2. for all i, 1 ≤ i ≤ |Lv|,

for all j, Lv(i).pBegin ≤ j ≤ Lv(i).pEnd, /* j is

between pBegin and pEnd for the occurrence Lv(i) */

cj ← Lv(i). c

L [j-pBegin] /*the codon sequence

for the occurrence of Lv(i) */

At the end of the second step, we will have the output

codon sequence, SC = c1c2c3……cJ. This can be converted

into the output DNA sequence SD by replacing each

codon with the corresponding DNA triplet.

5. Complexity Analysis

Step1-Pre-processing: Enumerating the amino acid

search patterns takes constant time for each motif

(assuming that the upper bound for the length of each

motif is a constant). There are k motifs, therefore, this

step takes O(k) time. Building the search tree is linear,

therefore takes O(k) time.

Step2- Enumeration of all potential occurrences:

Finding the potential occurrences O(L+3k+|P|),

according to the Aho-Corasick Algorithm. The actual

number of matches considered is greater than |P|, but still

in O(|P|). As the length of each motif is bound by a

constant, so is the number of all possible codon

combinations for each motif. Therefore, |P| is in O(L).

Inserting an entry into P takes log|P| time, as P is a

sorted list. Therefore, the overall complexity for this step

is |P|log|P|.

Step3-Mapping P to a directed acyclic graph (DAG):

a. Constructing the graph – involves checking the

upper triangle of the adjacency matrix of the graph -

takes O(|P| .(|P| -1)/2) ~ O(|P| 2 ) time.

b. Finding the critical path takes O(|V| + |E|) time.

Here, |V| ← |P|. The graph is expected to be dense in

general, therefore, |E| ← |P| 2 . Therefore, this part

takes O(|P| 2 ) time.

As the number of potential occurrences found, |P|, is

in O(J), the overall complexity of the algorithm is O(J 2 ).

6. Software

The software is available both as a console program,

and as a windows application with a GUI. The program

requires four input files: a file containing the input amino

acid sequence, a file containing the codon bias

information, and a file each for the desirable and

undesirable motifs. The desirability values can be

supplied in the input files. If desirability values are not

supplied in the input files, a default value of +1 is

assigned for desirable motifs, and –1 for undesirable

motifs. Additionally, it is made sure that each

occurrence of an undesirable motif has a weight less than

zero, by setting it to a small –ve value if it is zero. The

amino acid sequence file should be in the FASTA format,

containing a single sequence. The output is in ASCII text

format, listing different solutions with varying degrees of

codon optimization. The GUI writes the formatted results

to an html file. The sample out put of the program is

shown in figure-3.

7. Results

We tested the validity of the program on different

proteins. The results are shown in Table 2. These test

cases were run with list of 33 desirable motifs and 5

undesirable motifs. Each motif was any where between 3

to 8 nucleotides long. In the sequences that were tested,

all the occurrences of undesirable motifs could be

eliminated. However, in some cases, it might be

impossible to eliminate all occurrences of undesirable

motifs.

Table 2. Results - CpG-S and CpG-N motifs

Amino

acid

sequence

(length)

CpG-S

motfs

found

CpG-S

motfs

retained

CpG-N

motifs

found

CpG-N

motifs

eliminate

d

Tat

(72)

80 7 66 66

C3d

(302)

224 30 273 273

M23809

(226)

164 24 209 209

Proceedings of the Computational Systems Bioinformatics (CSB’03) 0-7695-2000-6/03 $17.00 © 2003 IEEE

Table 3 shows the average codon fitness, which is a

measure of the degree of codon optimization. It can be

observed that the average fitness could be improved by

approximately 30% for all amino acid sequences tested.

Table 3. Results – average fitness

Amino

acid

sequence

(length)

Wild

type

Maximizin

g CpG-S

motifs

Minimizin

g CpG-N

motifs

Both

max.

and

min.

Tat

(72)

0.671 0.948 0.981 0.930

C3d

(302)

0.672 0.935 0.985 0.922

M23809

(226)

0.654 0.950 0.980 0.937

The analysis of one of these proteins, a 72 amino acid

regulatory protein, Tat, of the Human Immunodeficiency

Virus type-1 (HIV-1), is presented here. The Tat protein

of HIV-1 plays critical role in regulating viral gene

expression [15]. Additionally, Tat also modulated several

functions of the host and a wide range of pathogenic

properties has been ascribed to this viral protein.

Considering the pathogenic significance of Tat, this viral

antigen is being used as an important component of the

viral vaccines, to elicit cell-mediated and humoral

immune responses [31].

One important limitation of using the wild type Tat

gene directly as a vaccine component without any

modification is the sub-optimal codon content of the viral

gene for mammalian immunization. Selective use of

specific codons for protein translation is a characteristic

feature of several species, a phenomenon called codon

bias. Recent approaches of enhancing the immune

responses against antigens have laid emphasis on protein

translation efficiency, which is a function of the base

composition of the pathogen. Codon usage of the Tat

protein of HIV-1 is strikingly different from that of the

human genes. The AT content of HIV-1 Tat is

approximately 54% while that of the host human genome

is about 35%, relatively low in AT content. Sub-optimal

codon use could result in compromised protein

translation efficiency in a mammalian context and may

reflect in the generation of a poor immune response

against the AT-rich gene.

The characteristic features of codon use of the Tat

gene in the virus are depicted in figure-2. The 72 amino

acids encoding Tat exon-1 consisting of 219 bp represent

the consensus sequence of the HIV-1 subtype-C strains.

We used the 72 amino acid sequence (and the stop

codon) as an input for optimizing the nucleotide

sequence for mammalian expression. Alternatively, it is

also possible to use the wild type nucleotide sequence of

the gene directly obtained from the virus as the input.

The results (the occurrences of desirable and undesirable

motifs) were manually verified.

Using the software, we identified a total of 37 codons

that could be replaced by the corresponding best codons

to optimize the codon content of this gene to match that

of the mammalian genome. Of note, optimization of the

codons is fairly a simple task, provided the objective is

only to replace the sub-optimal codons with the best ones,

as is the case with several of the substitutions. For

instance, serine at the position 16 in the viral gene is

encoded by the codon AGT that has a fitness value of

only 0.62, the lowest of all the 6 codons available for this

amino acid (Figure 2). Substituting AGT at this position

with AGC (fitness value 1.0) is likely to improve the

average fitness of the viral gene for mammalian protein

expression.

The algorithm identified seven potential motifs where

CpG-S motifs could be engineered into the gene. One of

these motifs, comprising of the amino acid residues S57

and A58 (AGC GCT), is naturally present in the viral

gene (Figure 2). However, a possible conflict was

identified between the possible codon optimization of

these amino acid residues and not disrupting the CpG-S

motif in this sequence. The codon GCT (fitness 0.67)

encoding for alanine could have been substituted by the

best codon GCC (fitness 1.0) for improved average

fitness of the gene. Importantly, use of GCT in the gene

design allowed recruiting a potential CpG-S island that

could have far more beneficial effect on immunization

potential of the DNA vaccine. The average fitness of this

codon combination (AGC GCT) 0.835 ((1.0 + 0.67) / 2),

as opposed to that of best codon combination 1.0, may

not significantly modulate the protein translation

efficiency.

The algorithm also identified a second site (L35 and

V36) in the viral gene where substituting the original

viral codons CTA GTT (average fitness 0.275) with the

best codons CTG GTG (average fitness 1.0) would

improve the overall fitness of the gene. In contrast,

replacing the original codons with others, CTC GTA

(fitness 0.36), would permit recruiting a putative CpG-S

motif into the gene, though at the expense of average

fitness of the gene (Figure 2). At the moment, it is not

clear how to resolve a conflict that may arise between

optimizing the codon content of a gene and recruiting

CpG-S motifs into the sequence. Most often, the codons

useful in CpG motif design are not the ones with the

highest fitness value thus leading to a potential

Proceedings of the Computational Systems Bioinformatics (CSB’03) 0-7695-2000-6/03 $17.00 © 2003 IEEE

disagreement between the diagonally juxtaposed

requirements.

Optimization of Tat sequence finally resulted in a

nucleotide sequence that was modified in a total of 37

codons (Figure 2). The AT content of the gene changed

from 54% of the wildtype gene to 43% in the codon-

optimized version thus resembling closely that of the

mammalian context. The overall fitness value of the

codon-optimized gene also improved from 0.67 to 0.93

suggesting a possible improvement at the level of protein

translation.

Using the algorithm, we designed several variants of

the Tat gene that differed from one another in the

number of CpG islands engineered and the extent of

codon content optimized. Experiments are presently

underway to evaluate the antigenic potential of these Tat

expression vectors in different mouse strains.

Acknowledgements

U. R. acknowledges financial support from the

Department of Biotechnology, Government of India.

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Proceedings of the Computational Systems Bioinformatics (CSB’03) 0-7695-2000-6/03 $17.00 © 2003 IEEE

M 1

E 2

P 3

V 4

D 5

P 6

N 7

L 8

E 9

P 10

W 11

N 12

wt ATG GAG CCA GTA GAT CCT AAC CTA GAG CCC TGG CAT

co - - - - - - - - - - - - - - - - - - - - - - - G - - - - - - - - - - - -

H 13

P 14

G 15

S 16

Q 17

P 18

K 719

T 10

A 21

C 22

N 23

N 24

wt CAT CCA GGA AGT CAG CCT AAA ACT GCT TGC AAC AAC

co - - C - - C - - -C - - -C - - - - - C - - G - - C - - C - - - - - - - - -

C 25

Y 26

C 27

K 28

H 29

C 30

S 31

Y 32

H 33

C 34

L 35

V 36

wt TGT TAT TGT AAA CAC TGT AGC TAC CAT TGT CTA GTT

co - - C - - C - - C - - G - - - - - C - - - - - - - - C - - C - - G - - G

C 37

F 38

Q 39

T 40

K 41

G 42

L 43

G 44

I 45

S 46

Y 47

G 48

wt TGC TTT CAG ACA AAA GGC TTA GGC ATT TCC TAT GGC

co - - - - - C - - - - - C - - G - - - C-G - - - - - C AG - - - C - - -

R 49

K 50

K 51

R 52

R 53

Q 54

R 55

R 56

S 57

A 58

P 59

P 60

wt AGG AAG AAG CGG AGA CAG CGA CGA AGC GCT CCT CCA

co - - A - - - - - - A-A - - - - - - A - - A - - - - - - - - - - - - - -

S 61

S 62

E 63

D 64

H 65

Q 66

N 67

L 68

I 69

S 70

K 71

Q 72

wt AGT AGT GAG GAT CAT CAA AAT CTT ATA TCG AAG CAA

co - - C - - C - - - - - C - - C - - - - - - - - - - - - - - S - - - - - G

Figure 1. The wild type Tat amino acid sequence

A

B

C

Proceedings of the Computational Systems Bioinformatics (CSB’03) 0-7695-2000-6/03 $17.00 © 2003 IEEE

A B C

Codon H 13

P 14

G 15

S 16

L 35

V 36

S 57

A 58

Wt CAT

(0.70)

CCA

(0.83)

GGA

(0.72)

AGT

(0.62)

CTA

(0.17)

GTT

(0.38)

AGC

(1.0)

GCT

(0.67)

Best CAC

(1.0)

CCC

(1.0)

GGC

(1.0)

AGC

(1.0)

CTG

(1.0)

GTG

(1.0)

AGC

(1.0)

GCC

(1.0)

CpG ----- ----- ----- ----- CTC

(0.48)

GTA

(0.24)

AGC

(1.0)

GCT

(0.67)

Figure 2. Codon optimization at three different places in the Tat amino acid sequence

Maximizing the desirable Motifs:

AT content: 50% Avg Fitness: 0.967748%

CAC TTG ATT GTT ACC CCA TCG GGC TGC GGC GAA CAA AAT ATG ATT GGC ATG ACC CCA ACC

GTT ATT GCA GTT CAC TAT CTC GAC GAA ACC GAA CAA TGG GAA AAA TTC GGC TTG GAA AAA

CGC CAA GGG GCG TTG GAA TTG ATT AAA AAA GGC TAT ACC CAA CAA TTG GCG TTC CGC CAA

CCA TCG TCG GCG TTC GCA GCG TTC

Minimizing the Undesirable Motifs:

AT content: 55% Avg Fitness: 0.96046%

CAC TTG ATT GTT ACC CCA TCA GGC TGC GGC GAA CAA AAT ATG ATT GGC ATG ACC CCA ACT

GTT ATT GCA GTT CAC TAT TTG GAC GAA ACT GAA CAA TGG GAA AAA TTT GGC TTG GAA AAA

CGC CAA GGC GCA TTG GAA TTG ATT AAA AAA GGC TAT ACC CAA CAA TTG GCA TTC CGT CAA

CCA TCG AGC GCA TTC GCA GCA TTC

Maximizing Desirable and Minimizing Undesirable Motifs:

AT content: 53% Avg Fitness: 0.94195%

CAC TTG ATT GTT ACC CCA TCA GGC TGC GGC GAA CAA AAT ATG ATT GGC ATG ACC CCA ACT

GTT ATT GCA GTT CAC TAT CTC GAC GAA ACT GAA CAA TGG GAA AAA TTT GGC TTG GAA AAA

CGC CAA GGC GCA TTG GAA TTG ATT AAA AAA GGC TAT ACC CAA CAA TTG GCG TTC CGT CAA

CCA TCG TCG GCG TTC GCA GCG TTC

Figure 3. Sample output of the program for a part of C3d sequence (desirable occurrences are shown in bold and

neutral occurrences are shown in italics)

Proceedings of the Computational Systems Bioinformatics (CSB’03) 0-7695-2000-6/03 $17.00 © 2003 IEEE

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