Optimal Experimental Design for a Bistable Gene Regulatory Network

A Continuation Technique for Maximum Likelihood Estimators in Biological Models

Estimating model parameters is a crucial step in mathematical modelling and typically involves minimizing the disagreement between model predictions and experimental data. This calibration data can change throughout a study, particularly if modelling is performed simultaneously with the calibration experiments, or during an on-going public health crisis as in the case of the COVID-19 pandemic. Consequently, the optimal parameter set, or maximal likelihood estimator (MLE), is a function of the experimental data set. Here, we develop a numerical technique to predict the evolution of the MLE as a function of the experimental data. We show that, when considering perturbations from an initial data set, our approach is significantly more computationally efficient that re-fitting model parameters while producing acceptable model fits to the updated data. We use the continuation technique to develop an explicit functional relationship between fit model parameters and experimental data that can be used to measure the sensitivity of the MLE to experimental data. We then leverage this technique to select between model fits with similar information criteria, a priori determine the experimental measurements to which the MLE is most sensitive, and suggest additional experiment measurements that can resolve parameter uncertainty.

Deep reinforcement learning for optimal experimental design in biology

The field of optimal experimental design uses mathematical techniques to determine experiments that are maximally informative from a given experimental setup. Here we apply a technique from artificial intelligence-reinforcement learning-to the optimal experimental design task of maximizing confidence in estimates of model parameter values. We show that a reinforcement learning approach performs favourably in comparison with a one-step ahead optimisation algorithm and a model predictive controller for the inference of bacterial growth parameters in a simulated chemostat. Further, we demonstrate the ability of reinforcement learning to train over a distribution of parameters, indicating that this approach is robust to parametric uncertainty.

Statistical Design of Experiments for Synthetic Biology

The design and optimization of biological systems is an inherently complex undertaking that requires careful balancing of myriad synergistic and antagonistic variables. However, despite this complexity, much synthetic biology research is predicated on One Factor at A Time (OFAT) experimentation; the genetic and environmental variables affecting the activity of a system of interest are sequentially altered while all other variables are held constant. Beyond being time and resource intensive, OFAT experimentation crucially ignores the effect of interactions between factors. Given the ubiquity of interacting genetic and environmental factors in biology this failure to account for interaction effects in OFAT experimentation can result in the development of suboptimal systems. To address these limitations, an increasing number of studies have turned to Design of Experiments (DoE), a suite of methods that enable efficient, systematic exploration and exploitation of complex design spaces. This review provides an overview of DoE for synthetic biologists. Key concepts and commonly used experimental designs are introduced, and we discuss the advantages of DoE as compared to OFAT experimentation. We dissect the applicability of DoE in the context of synthetic biology and review studies which have successfully employed these methods, illustrating the potential of statistical experimental design to guide the design, characterization, and optimization of biological protocols, pathways, and processes.

An experimental design tool to optimize inference precision in data-driven mathematical models of bacterial infections in vivo

The management of bacterial diseases calls for a detailed knowledge about the dynamic changes in host-bacteria interactions. Biological insights are gained by integrating experimental data with mechanistic mathematical models to infer experimentally unobservable quantities. This inter-disciplinary field would benefit from experiments with maximal information content yielding high-precision inference. Here, we present a computationally efficient tool for optimizing experimental design in terms of parameter inference in studies using isogenic-tagged strains. We study the effect of three experimental design factors: number of biological replicates, sampling timepoint selection and number of copies per tagged strain. We conduct a simulation study to establish the relationship between our optimality criterion and the size of parameter estimate confidence intervals, and showcase its application in a range of biological scenarios reflecting different dynamics patterns observed in experimental infections. We show that in low-variance systems with low killing and replication rates, predicting high-precision experimental designs is consistently achieved; higher replicate sizes and strategic timepoint selection yield more precise estimates. Finally, we address the question of resource allocation under constraints; given a fixed number of host animals and a constraint on total inoculum size per host, infections with fewer strains at higher copies per strain lead to higher-precision inference.