Table 1.

List of parameter values

ParameterValueUnitsSource
λ n 1.3713Per day 11, 19a
β0 1.4017Per day 11 b
b 0 0.22 × 10−3 μM Bcl-xL per cell 11, 19 b
ν1.7404Dimensionless 11, 19 b
α0 1.9762Per day 11 b
C 0 60μM carboplatin 11 b
ρ0 3.79 × 10−3 Per day per μM carboplatin 11 b
ρ1 99Per day per μM carboplatin 11 b
bl 0.1494 × 10−3 μM Bcl-xL per cell 11 b
κ1,700Dimensionless 11 b
0.01Days 11 b
a 0 1.4Days 11 b
θ 3.4486Dimensionless 11 b
bs 0.15 × 10−3 μM Bcl-xL per cell 27, 28, 29, 30 c
λ c 0.1676Per day 31
λb 1.0397Per day 32, 33 c
γ0 0.31 × 10−3 μM Bcl-xL per cell per day d
k 1 86.4Per μM protein per day 27 e
k −1 86.4Per day 12, 34 f
λ x 0.4632Per day 35 g
ar 2Days 11
  • aIn the absence of values in the literature, biologically realistic values for these parameters were chosen so that the solution profiles best fit experimental observation as described in refs. 11 and 19.

  • bIn the absence of data, intracellular expression of Bcl-xL was taken to be similar to that of Bcl-2 (IGROV-1 cells are known to express only Bcl-xL and not Bcl-2; ref. 11). Typical expression of Bcl-2 in cells is ∼75 nmol/L (28). However, much of this is sequestered by the proapoptotic members of the Bcl family such as Bax and Bid. Typical expression levels of these are in the range of 200 to 600 nmol/L Bax (29) and 25 nmol/L Bid (28), respectively. Furthermore, the dissociation constant for Bcl-2 binding with proapoptotic proteins in the Bcl family can be as low as 0.6 nmol/L (30). Using reaction rates for Bcl-2 binding to Bax taken from ref. 27, we get that free Bcl-2 concentrations can range from 0.008 to 0.3 nmol/L per cell. Therefore, a value of 0.15 nmol/L lying between these two limits was chosen to represent the free Bcl-xL expression levels in IGROV-1 cells.

  • cThe half-life of Bcl-xL was assumed to be similar to that of Bcl-2. This has a reported value of between 12 and 20 hours; therefore, a mean value of 16 hours is chosen.

  • dThe rate of Bcl-xL production is chosen so that all cells constitutively express bS amount of free Bcl-xL. This gives Embedded Image.

  • eIt was assumed that the rate of forward reaction of ABT-737 with Bcl-xL was similar to that of Bax binding to Bcl-2 because of their comparable binding affinities.

  • fThe binding affinity of ABT-737 with Bcl-xL is ∼1 nmol/L.

  • gThe half-life of ABT-737 in culture medium is taken to be the same as that of 072RB, another small molecule inhibitor of the Bcl-family. It should be noted that the range of half-lives of other small molecule inhibitors such as sHA-14-I and Su5416 also has similar reported values.