Kühl Peter W, Jobmann Manfred
Institute of Theoretical Biology, Münchenstein, BL, Switzerland.
J Recept Signal Transduct Res. 2006;26(1-2):1-34. doi: 10.1080/10799890500391279.
Service-theoretic concepts and methods, widely used in other fields (e.g., telecommunication and operations research), are useful also in a biochemical setting because the treatment of biocatalysts (enzymes, receptors) as servers and their ligands as customers, based on the established formal methods of service or queuing theory, may lead to insights and results unobtainable by conventional, mass-action-law-based theories. In this article, we apply the service-theoretic approach to receptor-agonist systems and show how by changing the stochastic time pattern of "operationally relevant" point events (e.g., instants of agonist arrival, instants of post-climax agonist departure) a great variety of dose-response curves may be generated, even in very simple reaction schemes, which, according to mass action kinetics, invariably lead to hyperbolic r(A) curves (r and A stand for response and agonist concentration, respectively). The molecular timing inherent to a hyperbolic response system is not optimal: for instance, at the agonist concentration A(50), half of the agonist molecules are rejected ("lost") because of unfortunate timing of the arrival events. The fraction of lost arrivers can be diminished considerably if the arrivals are better timed: "sub-Poisson" arrivals improve the timing and, thus, convert hyperbolic r(A) curves into "lifted" nonhyperbolic ones. Conversely, "super-Poisson" arrivals make the non-optimal timing in hyperbolic response systems even worse and, thus, convert hyperbolic r(A) curves into "depressed" nonhyperbolic ones. Furthermore, under special timing conditions, nonhyperbolic r(A) curves can be generated, which are partly lifted, partly depressed relative to the reference hyperbola, and which resemble in shape well-known nonhyperbolic forms of enzyme and receptor kinetics (negatively cooperative, positively cooperative, and sigmoidal kinetics). In addition unusual (undulatory and sawtooth-like) r(A) curves can be generated solely by changing the temporal pattern of arrival and service completion instants. Virtually any shape of dose-response curves may be obtained by allowing for probability distributions whose characteristic shape varies with their mean; we call such distributions "variomorphic" and apply them to the arrival process of agonist molecules.
服务理论概念和方法在其他领域（如电信和运筹学）广泛应用，在生化环境中也很有用，因为基于已确立的服务或排队理论形式方法，将生物催化剂（酶、受体）视为服务器，其配体视为客户，可能会带来传统基于质量作用定律的理论无法获得的见解和结果。在本文中，我们将服务理论方法应用于受体 - 激动剂系统，并展示如何通过改变“操作相关”点事件的随机时间模式（例如，激动剂到达时刻、高潮后激动剂离开时刻），即使在非常简单的反应方案中，也能生成各种各样的剂量 - 反应曲线，而根据质量作用动力学，这些反应方案总是会导致双曲线型的r(A)曲线（r和A分别代表反应和激动剂浓度）。双曲线反应系统固有的分子时间安排并非最优：例如，在激动剂浓度A(50)时，由于到达事件的时间安排不佳，一半的激动剂分子被拒绝（“损失”）。如果到达时间安排得更好，损失的到达者比例可以大幅降低：“亚泊松”到达改善了时间安排，从而将双曲线型r(A)曲线转变为“提升”的非双曲线型曲线。相反，“超泊松”到达使双曲线反应系统中原本就不佳的时间安排变得更糟，从而将双曲线型r(A)曲线转变为“压低”的非双曲线型曲线。此外，在特殊的时间条件下，可以生成非双曲线型r(A)曲线，相对于参考双曲线，它们部分提升、部分压低，并且在形状上类似于酶和受体动力学中众所周知的非双曲线形式（负协同、正协同和S型动力学）。此外，仅通过改变到达和服务完成时刻的时间模式，就可以生成不寻常的（波动状和锯齿状）r(A)曲线。通过允许特征形状随均值变化的概率分布，几乎可以获得任何形状的剂量 - 反应曲线；我们将这种分布称为“变形态”，并将其应用于激动剂分子的到达过程。
