Rice John Jeremy, Tu Yuhai, Poggesi Corrado, De Tombe Pieter P
IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA.
Pac Symp Biocomput. 2008:366-77.
In the field of cardiac modeling, calcium- (Ca-) based activation is often described by sets of ordinary differential equations that do not explicitly represent spatial interactions of regulatory proteins or crossbridge attachment. These spatially compressed models are most often mean-field representations as opposed to methods that explicitly compute the surrounding field (or equivalently, the surrounding environment) of individual regulatory units and crossbridges. Instead, a mean value is used to represent the whole population. Almost universally, the mean-field approach assumes developed force produces positive feedback to globally increase the mean binding affinity of the regulatory proteins. We show that this approach produces hysteresis in the steady-state Force-Ca responses when developed force increases Ca-affinity troponin to the degree that is observed in real muscle. Specifically, multiple stable solutions exist as a function of Ca level that could be alternatively reached depending on stimulus history. The resulting hysteresis is quite pronounced and disagrees with experimental characterizations in cardiac muscle that generally show little if any hysteresis. Moreover, we provide data showing that hysteresis does not occur in carefully controlled myofibril preparations. Hence, we suggest that the most widely used methods to produce multiscale models of cardiac force generation show bistability and hysteresis effects that are not seen in real muscle responses
在心脏建模领域，基于钙（Ca）的激活通常由常微分方程组来描述，这些方程组并未明确表示调节蛋白或横桥附着的空间相互作用。与明确计算单个调节单元和横桥周围场（或等效地，周围环境）的方法相反，这些空间压缩模型大多是平均场表示。取而代之的是，用一个平均值来代表整个群体。几乎无一例外，平均场方法假定产生的力会产生正反馈，以全局增加调节蛋白的平均结合亲和力。我们表明，当产生的力将钙亲和力肌钙蛋白增加到在真实肌肉中观察到的程度时，这种方法会在稳态力 - 钙反应中产生滞后现象。具体而言，根据钙水平存在多个稳定解，这取决于刺激历史，可能会交替达到这些解。由此产生的滞后现象非常明显，与心肌的实验特征不符，心肌的实验特征通常显示几乎没有滞后现象。此外，我们提供的数据表明，在精心控制的肌原纤维制剂中不会出现滞后现象。因此，我们认为，用于生成心脏力产生多尺度模型的最广泛使用的方法显示出双稳态和滞后效应，而这些效应在真实肌肉反应中并未出现。
