The recent success of biological engineering is due to a tremendous amount of research effort and the increasing number of market opportunities. Indeed, this has been partially possible due to the contribution of advanced mathematical tools and the application of engineering principles in genetic-circuit development. In this work, we use a rationally designed genetic circuit to show how models can support research and motivate students to apply mathematics in their future careers. A genetic four-state machine is analyzed using three frameworks: deterministic and stochastic modeling through differential and master equations, and a spatial approach via a cellular automaton. Each theoretical framework sheds light on the problem in a complementary way. It helps in understanding basic concepts of modeling and engineering, such as noise, robustness, and reaction–diffusion systems. The designed automaton could be part of a more complex system of modules conforming future bio-computers and it is a paradigmatic example of how models can assist teachers in multidisciplinary education.

中文翻译：

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遗传有限状态机的合理设计：结合生物学，工程学和数学进行生物计算机研究

生物工程的最新成功是由于大量的研究工作和越来越多的市场机会。确实，由于先进的数学工具的贡献以及工程原理在遗传电路开发中的应用，这在某种程度上已经成为可能。在这项工作中，我们使用合理设计的遗传电路来展示模型如何支持研究并激励学生在未来的职业中应用数学。遗传四状态机使用三个框架进行分析：通过微分方程和主方程进行确定性和随机建模，以及通过元胞自动机进行空间方法。每个理论框架都以互补的方式阐明了这个问题。它有助于理解建模和工程学的基本概念，例如噪声，鲁棒性，和反应扩散系统。设计的自动机可能是符合未来生物计算机的更复杂的模块系统的一部分，并且是模型如何协助多学科教育的范例。