Lecca Paola, Bagagiolo Fabio, Scarpa Marina
Department of Mathematics, University of Trento, via Sommarive 14, Trento, Italy.
Department of Physics, University of Trento, via Sommarive 14, Trento, Italy.
Mol Biosyst. 2017 Nov 21;13(12):2672-2686. doi: 10.1039/c7mb00426e.
In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by complex networks of chemical reactions involving genes, proteins, and enzymes. Accurate computational models are indispensable means for understanding the mechanisms behind the evolution of a complex system, not always explored with wet lab experiments. To serve their purpose, computational models, however, should be able to describe and simulate the complexity of a biological system in many of its aspects. Moreover, it should be implemented by efficient algorithms requiring the shortest possible execution time, to avoid enlarging excessively the time elapsing between data analysis and any subsequent experiment. Besides the features of their topological structure, the complexity of biological networks also refers to their dynamics, that is often non-linear and stiff. The stiffness is due to the presence of molecular species whose abundance fluctuates by many orders of magnitude. A fully stochastic simulation of a stiff system is computationally time-expensive. On the other hand, continuous models are less costly, but they fail to capture the stochastic behaviour of small populations of molecular species. We introduce a new efficient hybrid stochastic-deterministic computational model and the software tool MoBioS (MOlecular Biology Simulator) implementing it. The mathematical model of MoBioS uses continuous differential equations to describe the deterministic reactions and a Gillespie-like algorithm to describe the stochastic ones. Unlike the majority of current hybrid methods, the MoBioS algorithm divides the reactions' set into fast reactions, moderate reactions, and slow reactions and implements a hysteresis switching between the stochastic model and the deterministic model. Fast reactions are approximated as continuous-deterministic processes and modelled by deterministic rate equations. Moderate reactions are those whose reaction waiting time is greater than the fast reaction waiting time but smaller than the slow reaction waiting time. A moderate reaction is approximated as a stochastic (deterministic) process if it was classified as a stochastic (deterministic) process at the time at which it crosses the threshold of low (high) waiting time. A Gillespie First Reaction Method is implemented to select and execute the slow reactions. The performances of MoBios were tested on a typical example of hybrid dynamics: that is the DNA transcription regulation. The simulated dynamic profile of the reagents' abundance and the estimate of the error introduced by the fully deterministic approach were used to evaluate the consistency of the computational model and that of the software tool.
在生物细胞中，细胞功能和遗传调控机制是由涉及基因、蛋白质和酶的复杂化学反应网络来实现和控制的。精确的计算模型是理解复杂系统进化背后机制的不可或缺的手段，而湿实验室实验并不总能探索这些机制。然而，为了达到其目的，计算模型应该能够在许多方面描述和模拟生物系统的复杂性。此外，它应该由需要尽可能短执行时间的高效算法来实现，以避免过度延长数据分析与任何后续实验之间的时间间隔。除了其拓扑结构的特征外，生物网络的复杂性还涉及其动力学，而动力学通常是非线性且刚性的。刚性是由于存在其丰度波动达多个数量级的分子物种。对刚性系统进行完全随机模拟在计算上是耗时的。另一方面，连续模型成本较低，但它们无法捕捉少量分子物种的随机行为。我们引入了一种新的高效混合随机 - 确定性计算模型以及实现该模型的软件工具MoBioS（分子生物学模拟器）。MoBioS的数学模型使用连续微分方程来描述确定性反应，并使用类似 Gillespie 的算法来描述随机反应。与大多数当前的混合方法不同，MoBioS算法将反应集分为快速反应、中等反应和慢速反应，并在随机模型和确定性模型之间实现滞后切换。快速反应被近似为连续确定性过程，并由确定性速率方程建模。中等反应是指其反应等待时间大于快速反应等待时间但小于慢速反应等待时间的反应。如果中等反应在跨越低（高）等待时间阈值时被分类为随机（确定性）过程，则将其近似为随机（确定性）过程。采用 Gillespie 首次反应方法来选择和执行慢速反应。在混合动力学的一个典型示例（即DNA转录调控）上测试了MoBios的性能。使用试剂丰度的模拟动态曲线以及完全确定性方法引入的误差估计来评估计算模型和软件工具的一致性。
