An algorithmic-information calculus for reprogramming biological networks

Despite extensive attempts to characterize systems and networks based upon metrics drawn from traditional statistics, Shannon entropy, and graph theory to understand systems and networks to reveal their causal mechanisms without making too many unjustified assumptions remains still as one of the greatest challenges in complexity science and science in general, specially beyond traditional statistics and so-called machine learning. Knowing the causal mechanisms that govern a system allows not only the prediction of the system's behavior but the manipulation and controlled reprogramming of the system. Here we introduce a formal interventional calculus based upon universal principles drawn from the theory of computability and algorithmic probability, thereby enabling better approaches to the question of causal discovery. By performing sequences of fully controlled perturbations, changes in the algorithmic content of a system can be classified into the effects they have according to their shift towards or away from algorithmic randomness, thereby inducing a ranking of system's elements. This spectral dimension unmasks an algorithmic separation between components conditioned upon the perturbations and endowing us with a suite of powerful parameter-free algorithms to reprogram the system's underlying program. The predictive and explanatory power of these novel conceptual tools are introduced and numerical experiments are illustrated on various types of networks. We show how the algorithmic content of a network is connected to its possible dynamics and how the instant variation of the sensitivity, depth, and the number of attractors in a network is accessible by an analysis of its algorithmic information landscape. The results demonstrate how to unveil causal mechanisms to infer essential properties, including the dynamics of evolving networks. We introduce measures and methods for system reprogrammability even with no, or limited, access to the system kinetic equations or probability distributions. We expect this interventional calculus to be broadly applicable for predictive causal interventions and we anticipate it to be instrumental in the challenge of causality discovery in science from complex data.