Figure 4. Fractional synthesis rate (FSR) and fractional clearance rate (FCR) for compartmental models with multiple pathways.

(A) A simple model of a single precursor with constant labeling fraction during the labeling phase, which produces two products. (B) The labeling kinetics of each product show that variation of the production rate constants (k₁ & k₂) have no effect on labeling kinetics. Variation of the clearance rate constants (v₁ & v₂) has the only impact on labeling kinetics, and FSR and FCR are both provide good estimates of v₁ or v₂. (C) A two-step model in which precursor A is maintained at constant concentration during the labeling phase, but produces a precursor B, which then produces two products. (D) With v₁ & v₂ given the same value, the values of k₁ & k₂ were set to different values, however, their sum remained constant. Regardless of the individual values of k₁ & k₂ the labeling curves for both products overlapped. FCR was close to but slightly lower than v₁ & v₂, while FSR was difficult to associate with any of the parameters. (E) The values of k₁ & k₂ were set to different values, however, their sum remained constant. The value of v₁ was set to twice that of v₂. Regardless of the individual values of k₁ & k₂ the labeling curves for each product overlapped. FCR was a close to but slightly lower than v₁ or v₂. FSR was 47% higher when the clearance rate constant was twice as large. (F) Production rate contants k₁ & k₂ were set equal to each other, but their sum was varied while setting v₁ & v₂ equal to each other. Changes in k₁ + k₂ led to distinct labeling curves. FCR approached the value of v₁ & v₂ when k₁ + k₂ became larger, but was much lower than v₁ & v₂ when k₁ + k₂ was lower. FSR increased by 28% when k₁ + k₂was doubled.