Broad Institute of MIT and Harvard, Cambridge, MA, USA.
Department of Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, MA, USA.
Adv Exp Med Biol. 2020;1131:771-797. doi: 10.1007/978-3-030-12457-1_31.
In this article, we present an overview of simulation strategies in the context of subcellular domains where calcium-dependent signaling plays an important role. The presentation follows the spatial and temporal scales involved and represented by each algorithm. As an exemplary cell type, we will mainly cite work done on striated muscle cells, i.e. skeletal and cardiac muscle. For these cells, a wealth of ultrastructural, biophysical and electrophysiological data is at hand. Moreover, these cells also express ubiquitous signaling pathways as they are found in many other cell types and thus, the generalization of the methods and results presented here is straightforward.The models considered comprise the basic calcium signaling machinery as found in most excitable cell types including Ca ions, diffusible and stationary buffer systems, and calcium regulated calcium release channels. Simulation strategies can be differentiated in stochastic and deterministic algorithms. Historically, deterministic approaches based on the macroscopic reaction rate equations were the first models considered. As experimental methods elucidated highly localized Ca signaling events occurring in femtoliter volumes, stochastic methods were increasingly considered. However, detailed simulations of single molecule trajectories are rarely performed as the computational cost implied is too large. On the mesoscopic level, Gillespie's algorithm is extensively used in the systems biology community and with increasing frequency also in models of microdomain calcium signaling. To increase computational speed, fast approximations were derived from Gillespie's exact algorithm, most notably the chemical Langevin equation and the τ-leap algorithm. Finally, in order to integrate deterministic and stochastic effects in multiscale simulations, hybrid algorithms are increasingly used. These include stochastic models of ion channels combined with deterministic descriptions of the calcium buffering and diffusion system on the one hand, and algorithms that switch between deterministic and stochastic simulation steps in a context-dependent manner on the other. The basic assumptions of the listed methods as well as implementation schemes are given in the text. We conclude with a perspective on possible future developments of the field.
本文概述了在钙依赖性信号发挥重要作用的亚细胞域中使用的模拟策略。呈现方式遵循每种算法所涉及的空间和时间尺度。作为一个示例细胞类型，我们主要引用在横纹肌细胞（即骨骼肌和心肌）上完成的工作。对于这些细胞，有大量的超微结构、生物物理和电生理数据。此外，这些细胞还表达普遍存在的信号通路，因为它们存在于许多其他细胞类型中，因此，这里呈现的方法和结果的推广是直接的。所考虑的模型包括大多数可兴奋细胞类型中发现的基本钙信号机制，包括 Ca 离子、可扩散和固定缓冲系统以及钙调节钙释放通道。模拟策略可以分为随机和确定性算法。从历史上看，基于宏观反应速率方程的确定性方法是首先考虑的模型。随着实验方法阐明了在飞升体积中发生的高度局部化的 Ca 信号事件，随机方法越来越被考虑。然而，由于所涉及的计算成本太大，很少进行单个分子轨迹的详细模拟。在介观水平上，Gillespie 算法在系统生物学领域得到广泛应用，并且在微域钙信号模型中也越来越频繁地使用。为了提高计算速度，从 Gillespie 的精确算法推导出了快速逼近算法，最著名的是化学 Langevin 方程和 τ-跳跃算法。最后，为了在多尺度模拟中整合确定性和随机性效应，越来越多地使用混合算法。这些算法包括一方面将离子通道的随机模型与钙缓冲和扩散系统的确定性描述相结合，另一方面根据上下文在确定性和随机模拟步骤之间切换的算法。本文给出了列出方法的基本假设和实施方案。最后，我们对该领域未来的可能发展进行了展望。
