Synthetic biology is an interdisciplinary field that uses well-established engineering principles for performing the analysis of the biological systems, such as biological circuits, pathways, controllers and enzymes. Conventionally, the analysis of these biological systems is performed using paper-and-pencil proofs and computer simulation methods. However, these methods cannot ensure accurate results due to their inherent limitations. Higher-order-logic (HOL) theorem proving is proposed and used as a complementary approach for analysing linear biological systems, which is based on developing a mathematical model of the genetic circuits and the bio-controllers used in synthetic biology based on HOL and analysing it using deductive reasoning in an interactive theorem prover. The involvement of the logic, mathematics and the deductive reasoning in this method ensures the accuracy of the analysis. It is proposed to model the continuous dynamics of the genetic circuits and their associated controllers using differential equations and perform their transfer function-based analysis using the Laplace transform in a theorem prover. For illustration, the genetic circuits of activated and repressed expressions and autoactivation of protein, and phase lag and lead controllers, which are widely used in cancer-cell identifiers and multi-input receptors for precise disease detection, are formally analyzed.

中文翻译：

---

使用高阶逻辑定理证明对合成生物学进行形式推理


合成生物学是一个跨学科领域，它使用完善的工程原理来执行生物系统的分析，例如生物回路、途径、控制器和酶。传统上，对这些生物系统的分析是使用纸笔校样和计算机模拟方法进行的。然而，这些方法由于其固有的局限性而无法确保准确的结果。高阶逻辑 (HOL) 定理证明被提出并用作分析线性生物系统的补充方法，其基础是开发基于 HOL 的遗传电路和合成生物学中使用的生物控制器的数学模型，并分析它在交互式定理证明中使用演绎推理。该方法涉及逻辑、数学和演绎推理，保证了分析的准确性。建议使用微分方程对遗传电路及其相关控制器的连续动态进行建模，并在定理证明器中使用拉普拉斯变换进行基于传递函数的分析。为了说明这一点，对激活和抑制表达以及蛋白质自动激活的遗传电路以及相位滞后和超前控制器进行了正式分析，这些控制器广泛用于癌细胞识别器和用于精确疾病检测的多输入受体。