In biological systems, nonlinear kinetic relationships between metabolites of interest are modeled for various purposes. Usually, little a priori knowledge is available in such models. Identifying the unknown kinetics is, therefore, a critical step which can be very challenging due to the problems of (i) model selection and (ii) nonlinear parameter estimation. In this paper, we aim to address these problems systematically in a framework based on multilinear Gaussian processes using a family of kernels tailored to typical behaviours of modulation effects such as activation and inhibition or combinations thereof. Using one such process as a model for each modulation effect leads to a much more flexible model than conventional parametric models, e.g., the Monod model. The resulting models of the modulation effects can also be used as a starting point for estimating parametric kinetic models. As each modulation effect is modeled separately, this task is greatly simplified compared to the conventional approach where the parameters in all modulation functions have to be estimated simultaneously. We also show how the type of modulation effect can be selected automatically by way of regularization, thus by-passing the model selection problem. The resulting parameter estimates can be used as initial estimates in the conventional approach where the full model is estimated. Numerical experiments, including fed-batch simulations, are conducted to demonstrate our methods.

在生物系统中，为各种目的对目标代谢物之间的非线性动力学关系进行了建模。通常，一点先验在此类模型中可获得知识。因此，由于（i）模型选择和（ii）非线性参数估计的问题，识别未知的动力学是至关重要的步骤。在本文中，我们的目标是在基于多线性高斯过程的框架中系统地解决这些问题，该过程使用一系列针对调制效应（例如激活和抑制或其组合）的典型行为量身定制的内核。使用一种这样的过程作为针对每种调制效果的模型会导致比传统的参数模型（例如Monod模型）更加灵活的模型。调制效果的结果模型也可以用作估计参数动力学模型的起点。由于每种调制效果都是单独建模的，与必须同时估计所有调制函数中的参数的常规方法相比，此任务大大简化了。我们还展示了如何通过正则化自动选择调制效果的类型，从而绕过模型选择问题。所得参数估计值可以用作常规方法中的初始估计值，在常规方法中，可以估算整个模型。进行数值实验，包括补料分批模拟，以证明我们的方法。所得参数估计值可以用作常规方法中的初始估计值，在常规方法中，可以估算整个模型。进行了数值实验，包括补料分批模拟，以证明我们的方法。所得的参数估计值可以用作常规方法中的初始估计值，在常规方法中，可以估算整个模型。进行了数值实验，包括补料分批模拟，以证明我们的方法。