[7]. They demonstrate that tumors could be formed in two different mouse strains (NIH Swiss, C57BL/6) that were co-injected with 12.5 μg each of two plasmids, each containing an activated oncogene (activated human H-ras and c-myc). This
value (Om) is calculated from the estimated size of the plasmid backbone (3186 bp) used in Sheng et al. [7], assuming that the oncogene inserted to the plasmid backbone has 1925 bp. Based on the total construct, the oncogene would account for 37.7% of the construct. If 12.5 μg of the plasmid is required for each oncogene of two oncogenes, as described by Sheng et al. [7], then the total oncogene portion amount to 9.4 μg (25 × 37.7% = Om). This evaluation utilizes research results from Peden et al. [8]. Using HIV as a model, they have found that PS-341 in vitro hcDNA from HIV-infected cells is infectious at 2.5 μg. In our single infective agent safety factor calculations, we make the assumptions: (1) 2.5 μg canine hcDNA is assumed to have an infectivity similar to hcDNA containing a HIV provirus; (2) the viral RAD001 genome size is 7000 bp [10], which represents a smaller retrovirus genome than HIV genome of 10,000 bp; (3) a diploid canine genome size is 4.82 × 109 as there is usually a single copy of provirus per cell [8]. To facilitate introduction of our model, we will focus on the assessment of oncogenicity. The same method,
once fully developed, can be directly applied to the infectivity risk evaluation. For the rest of the paper, we use Φ, Ω and however c to denote the host cell genome, oncogene DNA sequence residing in the host genome and phosphate ester bond between two nucleotides, respectively. We further express Φ and Ω as equation(2) Φ=B1cB2c…cBM, Ω=BlcBl+1c…cBl+m−1,Φ=B1cB2c…cBM, Ω=BlcBl+1c…cBl+m−1,where M and m represent haploid size of host genome and oncogene size, respectively, and l ≥ 1, m > 1 and l + m − 1 < M. We refer the bond c's within Ω as c1, c2 … cm−1. Define Xi as random variables that can take value either
0 or 1, with P[Xi = 1] = P[ci is disrupted by the enzyme] = 1 − P[Xi = 0] = p. The probability p represents the cutting efficiency of the enzyme. It is reasonable to assume that all Xi are independent. Therefore these m − 1 variables Xi are independently identically Modulators distributed (i.i.d.) according to a Bernoulli distribution [11]. After the host cell genome Φ is enzymatically digested, for the oncogene Ω to remain intact, none of the bonds c’s within the oncogene should be cut by the enzyme. That is equation(3) X1=X2…=Xm−1=0.X1=X2…=Xm−1=0. Thus the probability for Ω not to be disrupted is equation(4) Pr[X1=X2…=Xm−1=0]=(1−p)m−1. Now assume that the host cell genome Φ contains I0 oncogenes of size mi. equation(5) Ωi=BlicBli+1c…cBli+mi−1, 1≤i≤I0Ωi=BlicBli+1c…cBli+mi−1, 1≤i≤I0 By (4), the probability for Ωi to be uncut by enzyme is given by equation(6) pi=(1−p)mi−1.pi=(1−p)mi−1.