Figure 2. Immunogenicity of Gag DNA vaccines in mouse. The two different versions of Gag were made into DNA vaccines and injected into Balb/C mice with 25 mg/dose, then boosted at four weeks. Anti-Gag antibody levels were measured by ELISA at the four week and six week time points. The results are expressed as the geometric mean antibody titers (6SD) of each group. RK-Gag, induced an immune response that was five times larger than the codon optimized version at four weeks, which increased to a factor of 6 difference after six weeks. doi:10.1371/journal.pone.0003214.g002 Finally this study brings up the question of why the HIV DNA sequence has been selected to express poorly in primate cells, only increasing its levels with the aid of additional proteins that recognize nucleic acid sequences in the genome. Several other retroviruses and retrotransposons have similar sequence complex- ities. This may reflect an optimal way to regulate these viruses and enhance the viral titers over an extended length of infection. In any event it is becoming clear that nucleotide sequence motifs, in addition to the choice of codons, can have dramatic impacts upon gene expression, RNA processing and transport in a cell. Methods Robins-Krasnitz algorithm The first step in the algorithm is the creation of a background sequence to compare with the human genome. This background is a completely randomized version of the coding sequences from the human genome subject to the constraints of amino acid order and codon usage in each gene. We design a Monte Carlo program that randomly permutes the codons for each amino acid within each gene. Figure 3 is an illustrative example. The shuffling procedure described above yields a set of randomized sequences. From these sequences, we need to extract a probability distribution. As long as the number of occurrences of each motif found in the total set of sequences is reasonably large, we can form a probability distribution, estimating the probability of a given motif by its fraction in the set of all motifs. After the shuffling procedure we can define two distributions, the real distribution found from the actual sequence and the Maximal Entropy Distribution (MED) which we use as the surrogate for the background. We now need a method for choosing under and over-represented motifs. The standard we used is from information theory. The motif that contributes the most bits of information to the difference between the real distribution and the MED is the first motif we chose. Using information theory has the nice feature of putting all results in the same units, number of bits. This allows us to compare motifs of Recoded HIV Vaccine Figure 3. Example of shuffling procedure. The procedure to get the maximal entropy distribution (MED) involves a set of randomized iterations. The triplets of nucleotides coding for each amino acid are permuted randomly among themselves. This is an illustrative example of a mock short protein with eight amino acids. The shuffling procedure randomly permutes L1, L2, L3, and L4 and separately permutes H1, H2, and H3. Each iteration produces a new sequence. For this example, there are 12 different combinations for the leucines and three combinations for the histidines resulting in 36 unique sequences. They are weighted in the shuffling procedure so that the MED is attained in the limit of a large number of iterations. doi:10.1371/journal.pone.0003214.g003 different lengths and motifs that are either over or under- represented. The formula we employ to compute the motif contributing the most bits of information between the two distributions is the Kullback-Leibler distance or the Relative Entropy. We compute the Relative Entropy contribution for each motif and pick out the one with the largest value. Once we have found the most under- or over-represented motif in the sequence, we have to pick out the motif which is the next most under- or over-represented. However, we cannot simply take the motif which has the next largest Relative Entropy. This is because the motifs are overlapping, so under or over representa- tion of a given motif affects the distribution of all the other motifs. The example of CpG illustrates this point. In the human genome, the dinucleotide motif CG will have the largest Relative Entropy. However, all eight trimers which contain CG fall within the top 50 highest Relative Entropy motifs. This is simply an artifact of the selection against CG. We are required to first remove the contribution of CG from the MED before recalculating the Relative Entropy to find the next motif. If we call the motif w, we rescale all motifs that contain w by the same amount so that the rescaled MED had the same distribution for w as the real distribution. This forces the Relative Entropy of w to zero and, at the same time, removes the contribution of w from all other motifs. We can readily show that this choice of rescaling monotonically decreases the overall Relative Entropy between the distributions. The procedure is iterated, so that we remove the contribution of one motif at a time from the Relative Entropy through rescaling of the MED. Then, we choose the next motif. We continue to iterate the procedure, and find additional motifs, until the motif with the largest remaining Relative Entropy is not statistically significant, as determined by comparing shuffled genomes. Experimental protocols HIV-1 subtype B gag consensus sequence was obtained from the Los Alamos HIV database (www.hiv.lanl.gov). The complete sequence of parental consensus gag was codon optimized to reflect the codon characteristics of eukaryotic expression systems (AD- gag) and assembled in house using overlapping PCR.[4,6] RK-gag was synthesized by BlueHeron Biotechnology (www.blueheronbio. com). Both constructs have an identical ‘‘Kozak signal’’ located immediately upstream of the initial ATG and were cloned into NotI and XbaI cloning sites of pVAX1 (Invitrogen). Plasmid DNAs were prepared by GenElute Endotoxin-free plasmid purification system (Sigma). For valuation of gag expression in vitro, multiple batches of plasmid DNA were prepared to ensure the reproducibility of each of the independent transfection experiments. Briefly, 0.5 and 1 mg of DNA were transfected into 293 cells using the Lipofectamine reagent in a 24- well plate format according to the manufacturer’s specification PLoS ONE | www.plosone.org 3 September 2008 | Volume 3 | Issue 9 | e3214