Exploring the nonlinear dynamic behaviour of synthetic biological systems using nonlinear feedback control

合成生物学旨在重新设计生物体，使其产生有用的物质（药物）或获得新的功能（开关，振荡）。数学建模在合成生物学的设计周期中被广泛使用，以指示存在所需行为的参数空间区域。然而，生物化学模型的推导可能是具有挑战性的，无论是在模型结构（这取决于基本假设），和参数识别。实验数据通常是以特定的方式生成的，不完整且（非常）嘈杂。由此产生的模型的不确定性不可避免地导致误导性的结论之间的关系的物理参数的变化和关键的非线性现象（分叉），创造所需的生物功能。因此，合成生物化学电路的设计，如预期的表现是非常困难的，需要大量的设计-构建-测试iteration. Control-为基础的延续（CBC）是一个通用的和系统的测试方法，可以规避这些问题，并有可能深刻改变的方法，合成生物学的电路设计。不需要模型，CBC使用传感器和执行器来智能地探测物理系统。结合反馈控制和数值算法，CBC针对感兴趣的动态响应，跟踪其演变为可控参数的变化，并在实验测试过程中直接检测定性不同类型的行为（分叉）之间的边界。因此，CBC可以用来收集更多的信息数据，从而改善生化系统的模型，甚至可以用来调整输入和参数，以优化细胞的行为和功能。虽然CBC显示出很大的前景，并已被应用于广泛的非生命（即机电）系统，它目前不能应用于生物体。CBC中目前使用的反馈控制算法不能处理生化反应中通常存在的噪声和不同的时间尺度，并且由于CBC中使用的控制和数值方法之间存在的密切相互作用，不能直接使用控制文献中可用的传统算法。这个博士项目的目标是开发必要的控制算法，应用CBC活细胞系统。该项目将着眼于控制算法的开发，这些算法可以利用基本的数学模型（模型预测控制），但也对建模不准确具有鲁棒性。噪声的重要性将需要使用随机控制理论和复杂的滤波器（如自适应粒子滤波器）。生物化学实验经常考虑许多细胞，它们可以单独地沉降到不同的状态（双稳态）并形成不同的群体。严格的分析和探索的动态行为，这样的系统将需要我们扩展CBC人口比例的控制。

Synthetic Biology aims at redesigning living organisms so that they produce a useful substance (medicine) or gain a new functionality (switching, oscillations). Mathematical modelling is widely used within Synthetic Biology's design cycle to indicate the region of parameter space where the desired behaviours are present. The derivation of biochemical models can however be challenging, both in terms of model structure (which depend on underlying hypothesis), and parameter identification. Experimental data is often generated in an ad hoc manner, incomplete and (very) noisy. Resulting model uncertainties inevitably lead to misleading conclusions regarding the relationship between physical parameters variations and the key nonlinear phenomena (bifurcations) that create the desired biological functions. Consequently, the design of synthetic biochemical circuits that perform as intended is extremely difficult and requires numerous design-build-test iterations.Control-based Continuation (CBC) is a general and systematic testing method that can circumvent these issues and has the potential to profoundly change the approach to circuit design in synthetic biology. Without the need for a model, CBC uses sensors and actuators to intelligently probe physical systems. Combining feedback control and numerical algorithms, CBC targets the dynamic responses of interest, tracks their evolution as controllable parameters are changed and detects boundaries between qualitatively different types of behaviours (bifurcations) directly during experimental tests. CBC could therefore be exploited to collect more informative data, thereby improving models of biochemical systems, or even used to adjust inputs and parameters to optimize cell behaviour and function directly during tests. While CBC shows great promises and has been applied to a wide range of non-living (i.e. electro-mechanical) systems, it cannot currently be applied to living organisms. The feedback control algorithms currently used in CBC cannot deal with the noise and different time scales typically present in biochemical reactions, and traditional algorithms available in the control literature cannot be used directly due to the close interactions that exist between the control and the numerical methods used in CBC. The objective of this PhD project is to develop the control algorithms necessary to apply CBC to living cell systems. The project will look at the development of control algorithms that can exploit basic mathematical models (Model-predictive-control) but that are also robust to modelling inaccuracies. The importance of noise will require the use of stochastic control theory and sophisticated filters (such as adaptive particle filters). Biochemical experiments often consider many cells which can individually settle to different states (bistability) and form different populations. The rigorous analysis and exploration of the dynamic behaviour of such systems will require us to extend CBC to the control of population ratios.