Emergence of informative higher scales in biological systems: a computational toolkit for optimal prediction and control

Third, natural selection requires variability within a population. This has led to the proposal that the degeneracy observed in biological systems is critical for evolution to proceed [65]. This is because degeneracy provides a pool of variability for evolution to act on. However, at the same time, organisms need to be predictably consistent in their phenotypes, behavior, and structure to survive. As discussed, they need to have deterministic outcomes from noisy inputs. Therefore, having functions operate at macro-scales, whether those macro-scales arise from degeneracy or indeterminism, allows for both deterministic operation while preserving a pool of variability at the micro-scale. This may preserve population diversity while maintaining certainty over outcomes.

We have shown how information theory offers tools for objective analysis of the value of macro-scale models of biological systems, focusing on biological networks such as GRNs. Specifically, we made use of the effective information (EI) to assess the informativeness of a causal model, and then showed how EI can increase at macro-scales in both a GRN that plays an important role in mammalian cardiac development and also the largest component of the GRN of Saccharomyces cerevisiae.

While the formal tools outlined herein have undergone significant development since their first proposal [47,52] their applications in biological systems are just beginning. Although some have been skeptical about the use of information-based concepts in biology and whether it plays a key role in biological organization [66], recent advances have definitively shown how these can be rigorously applied; and indeed, software is now available to assist developmental biologists in calculating important information-theory metrics of genetic, physiological, and other data [67,68].

The techniques we’ve demonstrated apply not only to gene-regulatory and physiological circuits in development and regeneration [44,69], but also to important phenomena such as cancer [70]. However, note that the origin of data must be taken into account, as well as what a model network represents, in order for the analysis advanced here to be appropriately interpreted. In the case of inaccurate data, for instance, noise in the collection process may increase the apparent noise in the networks themselves, leading to an overestimation of causal emergence. Yet ultimately which subgraphs are good candidates for macro-nodes is a local phenomenon to those subgraphs, and EI scales with the growth of a network in a very patterned way [48]. So even in cases where the model used is incomplete or parts of it unknown, unless the unknowns directly change the connectivity of candidate subgraphs, which subgraphs are good candidates or group into macro-nodes with high EI should not be affected. However, in general, we recommend these procedures for well-studied biological networks or for large datasets wherein noise is averaged out. Applying these formalisms in continuous systems beyond discrete networks is a future area of research.

Given the advantages that multi-scale structures possess, which include error-correction, increased robustness, plasticity, and evolvability/learnability, we expect causal emergence to be common across nature. The increased informativeness of such higher scales are due to biology’s near-universal indeterminism and degeneracy and the ability of higher-level relationships to create certainty out of this uncertainty. If we are correct there should therefore be cross-species evidence that evolution selects specifically for multi-scale structure due to these advantages. This can be investigated by observing the evolutionary history of gene regulatory networks or protein interactomes, which is a significant direction for future research [61].

A further critical step will be the identification of high-information intervention targets in model systems and organisms. This is likely to first occur in simulations, including multi-scale models of development [71,72], regeneration [73–75], cancer [76,77], and physiology [78–80]. Ideally, this can provide proof that macro-scale interventions can not only control systems, but actually lead to more reliable downstream effects than their micro-scale alternatives, and therefore that biologists should adapt their scale of modeling and intervention to the system under investigation rather than taking a one-size-fits-all approach.

Many types of models in biology, from protein networks to physiological ones, can now benefit from a quantitative analysis of their causal structure, revealing the “drivers” of specific system-wide states and thus suggesting new strategies for rational interventions. Moving beyond traditional definitions of information [81] to analyzes of causation in networks across scales [82, Mayner, 83] can help drive new experimental work and applications in regenerative medicine, developmental biology, evolutionary cell biology, neuroscience, and synthetic bioengineering.

This research was supported by the Allen Discovery Center program through The Paul G. Allen Frontiers Group (12171). This publication was made possible through the support of a grant from Templeton World Charity Foundation, Inc. (TWCFG0273). The opinions expressed in this publication are those of the author(s) and do not necessarily reflect the views of Templeton World Charity Foundation, Inc. Author credits: ML and EH conceived of and wrote the paper; EH performed the analysis. Thanks to: Brennan Klein for his help with analysis of Saccharomyces cerevisiae.

This work was supported by the Paul G. Allen Frontiers Group [12171]; Templeton World Charity Foundation [TWCFG0273].