Efficient experimental design for uncertainty reduction in gene regulatory networks

Knowledge-driven learning, optimization, and experimental design under uncertainty for materials discovery

Significant acceleration of the future discovery of novel functional materials requires a fundamental shift from the current materials discovery practice, which is heavily dependent on trial-and-error campaigns and high-throughput screening, to one that builds on knowledge-driven advanced informatics techniques enabled by the latest advances in signal processing and machine learning. In this review, we discuss the major research issues that need to be addressed to expedite this transformation along with the salient challenges involved. We especially focus on Bayesian signal processing and machine learning schemes that are uncertainty aware and physics informed for knowledge-driven learning, robust optimization, and efficient objective-driven experimental design.

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

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

Prediction of Optimal Drug Schedules for Controlling Autophagy

The effects of molecularly targeted drug perturbations on cellular activities and fates are difficult to predict using intuition alone because of the complex behaviors of cellular regulatory networks. An approach to overcoming this problem is to develop mathematical models for predicting drug effects. Such an approach beckons for co-development of computational methods for extracting insights useful for guiding therapy selection and optimizing drug scheduling. Here, we present and evaluate a generalizable strategy for identifying drug dosing schedules that minimize the amount of drug needed to achieve sustained suppression or elevation of an important cellular activity/process, the recycling of cytoplasmic contents through (macro)autophagy. Therapeutic targeting of autophagy is currently being evaluated in diverse clinical trials but without the benefit of a control engineering perspective. Using a nonlinear ordinary differential equation (ODE) model that accounts for activating and inhibiting influences among protein and lipid kinases that regulate autophagy (MTORC1, ULK1, AMPK and VPS34) and methods guaranteed to find locally optimal control strategies, we find optimal drug dosing schedules (open-loop controllers) for each of six classes of drugs and drug pairs. Our approach is generalizable to designing monotherapy and multi therapy drug schedules that affect different cell signaling networks of interest.

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.

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

In systems biology, network models are often used to study interactions among cellular components, a salient aim being to develop drugs and therapeutic mechanisms to change the dynamical behavior of the network to avoid undesirable phenotypes. Owing to limited knowledge, model uncertainty is commonplace and network dynamics can be updated in different ways, thereby giving multiple dynamic trajectories, that is, dynamics uncertainty. In this manuscript, we propose an experimental design method that can effectively reduce the dynamics uncertainty and improve performance in an interaction-based network. Both dynamics uncertainty and experimental error are quantified with respect to the modeling objective, herein, therapeutic intervention. The aim of experimental design is to select among a set of candidate experiments the experiment whose outcome, when applied to the network model, maximally reduces the dynamics uncertainty pertinent to the intervention objective.

Evaluation and improvement of the regulatory inference for large co-expression networks with limited sample size

BACKGROUND

Co-expression has been widely used to identify novel regulatory relationships using high throughput measurements, such as microarray and RNA-seq data. Evaluation studies on co-expression network analysis methods mostly focus on networks of small or medium size of up to a few hundred nodes. For large networks, simulated expression data usually consist of hundreds or thousands of profiles with different perturbations or knock-outs, which is uncommon in real experiments due to their cost and the amount of work required. Thus, the performances of co-expression network analysis methods on large co-expression networks consisting of a few thousand nodes, with only a small number of profiles with a single perturbation, which more accurately reflect normal experimental conditions, are generally uncharacterized and unknown.

METHODS

We proposed a novel network inference methods based on Relevance Low order Partial Correlation (RLowPC). RLowPC method uses a two-step approach to select on the high-confidence edges first by reducing the search space by only picking the top ranked genes from an intial partial correlation analysis and, then computes the partial correlations in the confined search space by only removing the linear dependencies from the shared neighbours, largely ignoring the genes showing lower association.

RESULTS

We selected six co-expression-based methods with good performance in evaluation studies from the literature: Partial correlation, PCIT, ARACNE, MRNET, MRNETB and CLR. The evaluation of these methods was carried out on simulated time-series data with various network sizes ranging from 100 to 3000 nodes. Simulation results show low precision and recall for all of the above methods for large networks with a small number of expression profiles. We improved the inference significantly by refinement of the top weighted edges in the pre-inferred partial correlation networks using RLowPC. We found improved performance by partitioning large networks into smaller co-expressed modules when assessing the method performance within these modules.

CONCLUSIONS

The evaluation results show that current methods suffer from low precision and recall for large co-expression networks where only a small number of profiles are available. The proposed RLowPC method effectively reduces the indirect edges predicted as regulatory relationships and increases the precision of top ranked predictions. Partitioning large networks into smaller highly co-expressed modules also helps to improve the performance of network inference methods. The RLowPC R package for network construction, refinement and evaluation is available at GitHub: https://github.com/wyguo/RLowPC .