Beyond the Michaelis–Menten: Evaluation of a <scp>tQSSA</scp> ‐Based <scp>IVIVE</scp> Approach for Predicting In Vivo Intrinsic Clearance From Hepatocyte Assays

The classical Michaelis-Menten model, under the standard quasi-steady-state approximation (sQSSA), is widely used in in vitro-in vivo extrapolation (IVIVE) studies using hepatocyte or human liver microsomal (HLM) assays to predict intrinsic hepatic clearance ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>Cl</mml:mi> <mml:mrow><mml:mi>int</mml:mi> <mml:mo>,</mml:mo> <mml:mtext>vitro</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\mathrm{Cl}}_{\operatorname{int},\mathrm{vitro}} $$</mml:annotation></mml:semantics> </mml:math> ). However, the approximation that enzyme concentration ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>E</mml:mi> <mml:mi>T</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {E}_T $$</mml:annotation></mml:semantics> </mml:math> ) is much lower than the Michaelis constant ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>K</mml:mi> <mml:mi>M</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {K}_M $$</mml:annotation></mml:semantics> </mml:math> ) does not always hold true, especially for low <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>K</mml:mi> <mml:mi>M</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {K}_M $$</mml:annotation></mml:semantics> </mml:math> compounds or enzyme induction scenarios, leading to inaccurate predictions. To improve the accuracy of IVIVE predictions, the total quasi-steady-state approximation (tQSSA) which accounts for enzyme saturation when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>E</mml:mi> <mml:mi>T</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {E}_T $$</mml:annotation></mml:semantics> </mml:math> is not negligible relative to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>K</mml:mi> <mml:mi>M</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {K}_M $$</mml:annotation></mml:semantics> </mml:math> was first applied to HLM data and confirmed that it improved clearance prediction compared with the sQSSA. Building on this, we further evaluated the performance of tQSSA using hepatocyte data. The in vivo intrinsic hepatic clearance was predicted using both the sQSSA and tQSSA with the well-stirred and parallel tube models. Predictions were evaluated across three scenarios: (1) using both the unbound fraction in blood ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>f</mml:mi> <mml:mrow><mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {f}_{u,b} $$</mml:annotation></mml:semantics> </mml:math> ) and the in vitro hepatocyte incubation system ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>f</mml:mi> <mml:mrow><mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>inc</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {f}_{u,\mathrm{inc}} $$</mml:annotation></mml:semantics> </mml:math> ), (2) using only <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>f</mml:mi> <mml:mrow><mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {f}_{u,b} $$</mml:annotation></mml:semantics> </mml:math> , and (3) without correction. Results showed that the sQSSA tended to overpredict clearance when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>E</mml:mi> <mml:mi>T</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {E}_T $$</mml:annotation></mml:semantics> </mml:math> ≥ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>K</mml:mi> <mml:mi>M</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {K}_M $$</mml:annotation></mml:semantics> </mml:math> . In the 77-compound dataset, the tQSSA yielded slightly better agreement, particularly when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>f</mml:mi> <mml:mrow><mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {f}_{u,b} $$</mml:annotation></mml:semantics> </mml:math> = <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>f</mml:mi> <mml:mrow><mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>inc</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {f}_{u,\mathrm{inc}} $$</mml:annotation></mml:semantics> </mml:math> = 1, whereas with mechanistic binding corrections both models performed similarly. For the 11-compound subset with known <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>K</mml:mi> <mml:mi>M</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {K}_M $$</mml:annotation></mml:semantics> </mml:math> values, the proportion within 2-fold error improved by about 1.5-fold compared with sQSSA. Overall, tQSSA appears promising but requires further validation for IVIVE applications.