Optimal Objective-Based Experimental Design for Uncertain Dynamical Gene Networks with Experimental Error

Plant Synthetic Biology: Quantifying the "Known Unknowns" and Discovering the "Unknown Unknowns"

Biosensors, advanced microscopy, and single- cell transcriptomics are advancing plant synthetic biology.

An experimental design framework for Markovian gene regulatory networks under stationary control policy

BACKGROUND

A fundamental problem for translational genomics is to find optimal therapies based on gene regulatory intervention. Dynamic intervention involves a control policy that optimally reduces a cost function based on phenotype by externally altering the state of the network over time. When a gene regulatory network (GRN) model is fully known, the problem is addressed using classical dynamic programming based on the Markov chain associated with the network. When the network is uncertain, a Bayesian framework can be applied, where policy optimality is with respect to both the dynamical objective and the uncertainty, as characterized by a prior distribution. In the presence of uncertainty, it is of great practical interest to develop an experimental design strategy and thereby select experiments that optimally reduce a measure of uncertainty.

RESULTS

In this paper, we employ mean objective cost of uncertainty (MOCU), which quantifies uncertainty based on the degree to which uncertainty degrades the operational objective, that being the cost owing to undesirable phenotypes. We assume that a number of conditional probabilities characterizing regulatory relationships among genes are unknown in the Markovian GRN. In sum, there is a prior distribution which can be updated to a posterior distribution by observing a regulatory trajectory, and an optimal control policy, known as an "intrinsically Bayesian robust" (IBR) policy. To obtain a better IBR policy, we select an experiment that minimizes the MOCU remaining after applying its output to the network. At this point, we can either stop and find the resulting IBR policy or proceed to determine more unknown conditional probabilities via regulatory observation and find the IBR policy from the resulting posterior distribution. For sequential experimental design this entire process is iterated. Owing to the computational complexity of experimental design, which requires computation of many potential IBR policies, we implement an approximate method utilizing mean first passage times (MFPTs) - but only in experimental design, the final policy being an IBR policy.

CONCLUSIONS

Comprehensive performance analysis based on extensive simulations on synthetic and real GRNs demonstrate the efficacy of the proposed method, including the accuracy and computational advantage of the approximate MFPT-based design.

Sequential Experimental Design for Optimal Structural Intervention in Gene Regulatory Networks Based on the Mean Objective Cost of Uncertainty

Scientists are attempting to use models of ever-increasing complexity, especially in medicine, where gene-based diseases such as cancer require better modeling of cell regulation. Complex models suffer from uncertainty and experiments are needed to reduce this uncertainty. Because experiments can be costly and time-consuming, it is desirable to determine experiments providing the most useful information. If a sequence of experiments is to be performed, experimental design is needed to determine the order. A classical approach is to maximally reduce the overall uncertainty in the model, meaning maximal entropy reduction. A recently proposed method takes into account both model uncertainty and the translational objective, for instance, optimal structural intervention in gene regulatory networks, where the aim is to alter the regulatory logic to maximally reduce the long-run likelihood of being in a cancerous state. The mean objective cost of uncertainty (MOCU) quantifies uncertainty based on the degree to which model uncertainty affects the objective. Experimental design involves choosing the experiment that yields the greatest reduction in MOCU. This article introduces finite-horizon dynamic programming for MOCU-based sequential experimental design and compares it with the greedy approach, which selects one experiment at a time without consideration of the full horizon of experiments. A salient aspect of the article is that it demonstrates the advantage of MOCU-based design over the widely used entropy-based design for both greedy and dynamic programming strategies and investigates the effect of model conditions on the comparative performances.