(1) is a special case of Eq. (12) when there are no DNA inactivation steps. After enzyme digestion, any DNA segment takes the form: equation(14) Br+1cBr+2c…cBr+XBr+1cBr+2c…cBr+Xwhere r is an integer and X, representing the length of the DNA segment, is a random variable. Let p denote the probability for enzyme to cleave bond c, as defined in Section 2.1. Note that the length of the

above DNA segment is the same as the number CDK inhibition of failed attempts made by the enzyme at cutting through the bonds c’s before it successfully disrupts the bond c right after nucleotide Br + X. The length X, in essence, can be described by a geometric distribution with parameter p [11]. In other words: equation(15) Pr[X=k]=(1−p)k−1p,k=1,2, …, M−1.Pr[X=k]=(1−p)k−1p,k=1,2, …, M−1. The theoretical median of X is given by equation(16) median=−log 2log(1−p). If the residual DNA size distribution can be quantified, the median can be empirically estimated. Using Eq. (16), we could estimate the enzyme cutting

RG7204 order efficiency p, which in turn can be used to estimate the safety factor in Eq. (12). In clinical research laboratories, various analytical methods such as agarose, polyacrylamide and capillary electrophoresis are used to measure the size distribution of residual DNA in biological products. These methodologies resolve purified DNA in a suitable matrix where the DNA length can be estimated relative to known DNA size markers. After the distribution of residual DNA is quantified, parameters of the distribution such as mean and median can readily be obtained. many Let Med0 denote the median size of residual DNA, determined by one of the aforesaid methods. Equating Med0 to the theoretical median in Eq. (16) gives rise to an estimate of enzyme efficiency p: equation(17) pˆ=1−2−1/Med0 The relationship between

enzyme efficiency and median size of residual DNA is depicted in Fig. 1. It is evident that the more efficient the enzyme is, the smaller the median size of residual DNA is. Combining Eq. (12) and (17), we establish the following relationship between the safety factor and other characteristics of the manufacture process: equation(18) SF=Om∑i=1I02−(mi−1)/Med0miME[U]. Since the safety factor is a decreasing factor of the median size Med0 of residual DNA, the smaller the size of residual DNA is, the larger the safety factor is. A similar formula can be derived for safety factor concerning infectivity. It is given as follows: equation(19) SF1=Qm∑i=1J02−(ni−1)/Med0niNE[U]where Qm, J0 and ni are viral genome amount required to induce an infection, total number of proviruses contained in MDCK cell genome and their sizes ni, respectively, and N is the diploid size of the host cell genome. The safety factor for oncogenicity is calculated based on Eq. (18). As discussed in Section 2, the observational and experimental data suggest: (a) Om = 9.