Koichiro Yoneyama 1, Tatsuhiko Tachibana 1, Tomohisa Saito 1
1 Chugai Pharmaceutical Co., Ltd. (Tokyo, Japan)
INTRODUCTION:
In biochemistry and its applied sciences such as pharmacology, first-order rate constants (FORCs) are used in kinetic models to characterize a reaction system as a function of time. By contrast, in statistics, an FORC can be regarded as a hazard in a survival function for event occurrence (i.e., elimination rate constant of the survival probability) [1] and, if the event can occur repeatedly, it corresponds to the Poisson mean of the number of event occurrences [2]. Integrating these two disciplines, an FORC in a kinetic model of a recurring biochemical reaction should be associated with the number of reaction occurrences in theory.
OBJECTIVES:
To elucidate how the biochemical and statistical perspectives on an FORC are linked.
METHODS:
A simulation study was performed on a two-state reversible reaction system (States 1 and 2) for a reacting substance, which can be described by either a kinetic model or a continuous-time Markov model (CTMM), with the reaction of each direction (state transition) modeled by an FORC. Using a CTMM, many Bernoulli trials were performed for a single molecule of the substance to encounter a transition of either direction over many short time intervals in a long duration, with the transition probabilities described by survival functions incorporating the FORCs as the hazards. The following endpoints were compared between the model-based simulated values and FORC-based theoretical values: the number of transitions of each direction per unit time spent in the pretransition state, which should theoretically correspond to the FORC and Poisson mean, following the associated Poisson distribution, for the transition of each direction; and the proportion of time spent in each state, which should theoretically correspond to the steady-state fraction of each state derived as a ratio of the FORCs in the context of kinetic model. In addition, defining the turnover of a recurring reaction system as a return to the initial state (State 1) after reaching the terminal state (State 2), the theoretical value of the number of turnovers per unit time was derived using the FORCs and compared with the model-based simulated values. Primary CTMM simulations were performed using NONMEM version 7.4.3, and secondary Poisson regressions were performed using SAS version 9.4.
Investigation was expanded with a four-state cyclic reversible reaction system, in which State 1 is the initial state, State 4 is the terminal state, and States 2 and 3 are the intermediate states between States 1 and 4 in the separate pathways. The theoretical values of the number of transitions from States 2 or 3 to State 4 per unit time (mean terminal reaction rate) and number of returns to State 1 after reaching State 4 per unit time (mean overall turnover rate) were derived using the FORCs and compared with the model-based simulated values.
RESULTS:
With the two-state system, the model-based simulated values of the defined endpoints were well consistent with the FORC-based theoretical values, and the model-based simulated distributions of the number of transitions of each direction per unit time and number of turnovers per unit time were well consistent with the FORC-based theoretical Poisson distributions. When varying the FORC values in parallel, the number of turnovers per unit time changed in parallel with the FORCs despite the unchanged proportion of time spent in each state, revealing a comprehensive difference in the efficiency of a recurring reaction system due to different FORC values.
With the four-state system, the model-based simulated values of the defined endpoints were well consistent with the FORC-based theoretical values. When varying some opposing paired FORC values in parallel, the mean overall turnover rate changed despite the unchanged proportion of time spent in each state, but the mean terminal reaction rate did not necessarily change. Even when both metrics changed, their changes were not necessarily parallel.
CONCLUSIONS:
An FORC in a kinetic model of a recurring biochemical reaction corresponds to the Poisson mean of the number of reaction occurrences per unit time per molecule of a reacting substance. Turnover dynamics of a recurring reaction system can be quantified by FORCs, which may provide additional insights into the pharmacokinetic behaviors and pharmacological actions of drugs. Further investigations are needed to elucidate the physiological, pharmacological, or clinical relevance of the proposed dynamic metrics with case studies.
References:
REFERENCES:
[1] Holford N. CPT Pharmacometrics Syst Pharmacol 2013;2:e43.
[2] Plan EL. CPT Pharmacometrics Syst Pharmacol 2014;3:e129.
Reference: PAGE 34 (2026) Abstr 12020 [www.page-meeting.org/?abstract=12020]
Poster: Methodology - Other topics