Likelihood-free nested sampling for parameter inference of biochemical reaction networks

Predictive power of non-identifiable models

Resolving practical non-identifiability of computational models typically requires either additional data or non-algorithmic model reduction, which frequently results in models containing parameters lacking direct interpretation. Here, instead of reducing models, we explore an alternative, Bayesian approach, and quantify the predictive power of non-identifiable models. We considered an example biochemical signalling cascade model as well as its mechanical analogue. For these models, we demonstrated that by measuring a single variable in response to a properly chosen stimulation protocol, the dimensionality of the parameter space is reduced, which allows for predicting the measured variable's trajectory in response to different stimulation protocols even if all model parameters remain unidentified. Moreover, one can predict how such a trajectory will transform in the case of a multiplicative change of an arbitrary model parameter. Successive measurements of remaining variables further reduce the dimensionality of the parameter space and enable new predictions. We analysed potential pitfalls of the proposed approach that can arise when the investigated model is oversimplified, incorrect, or when the training protocol is inadequate. The main advantage of the suggested iterative approach is that the predictive power of the model can be assessed and practically utilised at each step.

Optogenetic actuator - ERK biosensor circuits identify MAPK network nodes that shape ERK dynamics

Combining single-cell measurements of ERK activity dynamics with perturbations provides insights into the MAPK network topology. We built circuits consisting of an optogenetic actuator to activate MAPK signaling and an ERK biosensor to measure single-cell ERK dynamics. This allowed us to conduct RNAi screens to investigate the role of 50 MAPK proteins in ERK dynamics. We found that the MAPK network is robust against most node perturbations. We observed that the ERK-RAF and the ERK-RSK2-SOS negative feedback operate simultaneously to regulate ERK dynamics. Bypassing the RSK2-mediated feedback, either by direct optogenetic activation of RAS, or by RSK2 perturbation, sensitized ERK dynamics to further perturbations. Similarly, targeting this feedback in a human ErbB2-dependent oncogenic signaling model increased the efficiency of a MEK inhibitor. The RSK2-mediated feedback is thus important for the ability of the MAPK network to produce consistent ERK outputs, and its perturbation can enhance the efficiency of MAPK inhibitors.

MECHANISTIC AND DATA-DRIVEN MODELS OF CELL SIGNALING: TOOLS FOR FUNDAMENTAL DISCOVERY AND RATIONAL DESIGN OF THERAPY

A full understanding of cell signaling processes requires knowledge of protein structure/function relationships, protein-protein interactions, and the abilities of pathways to control phenotypes. Computational models offer a valuable framework for integrating that knowledge to predict the effects of system perturbations and interventions in health and disease. Whereas mechanistic models are well suited for understanding the biophysical basis for signal transduction and principles of therapeutic design, data-driven models are particularly suited to distill complex signaling relationships among samples and between multivariate signaling changes and phenotypes. Both approaches have limitations and provide incomplete representations of signaling biology, but their careful implementation and integration can provide new understanding for how manipulating system variables impacts cellular decisions.