(188di) Networks, Oscillations and Evolution: A Computational Approach

Oscillations are ubiquitous in mammalian systems. Regular oscillatory patterns of varying characteristics are encountered at multiple length scales from cells to tissues, to organs, to organisms, to the environment that surrounds the living host. These oscillations are likely the result of the evolutionary adaptation of the host to rhythmic environmental conditions, including light, temperature or seasons. As such, living systems, such as plants and animals, have developed intricate networks of self-sustained oscillators working in tandem. These rhythmic characteristics satisfy mutual relationships to enable the host to anticipate properly imminent environmental changes. It is well established that loss of rhythmicity, and by extension loss of the regulatory controls of those systems, leads to a multitude of pathologies¹.

Even though the constitutive elements (motifs) of the regulatory structures that produce self-sustained, robust and entrainable oscillations have been well characterized, it is interesting to better understand the type of evolutionary pressure that leads to the emergence of specific structures (motifs) leading to oscillatory dynamics². To address this question, we developed computational models to evolve random synchronous and asynchronous Boolean networks by preferentially selecting for structures that develop oscillations of specific characteristics, robust with respect to environmental conditions. Using genetic algorithms to simulate the evolution of connectivity of the regulatory elements, as well as the nature of Boolean rules, we aimed to characterize the emerging regulatory motifs and tested the hypothesis that the evolutionary trajectories preferentially lead to robust oscillatory systems. Furthermore, we explore the dynamic, evolutionary characteristics of entrainable oscillatory structures and assess both their robustness characteristics.

In this work we demonstrate how specific features, such as certain types of feed-forward and feed-back loops, emerge in these oscillatory as a way of filtering transient signals while allowing more robust exogenous signals to have an impact on the system³. We further identify motifs serving as time delays in the transfer of information through a network⁴. Understanding the way information evolves and is transmitted through these motifs is important, as their context within the network will also influence their function^5,6.

Despite the apparent complexity of the evolved networks, we determine that a core feedback group consistently emerges, in line with current research on indicating the presence of a core pacemaker mechanism in the genetic regulation of circadian rhythms in mammals⁷. The nature of this mechanism depends on the size of the network as well as the target oscillatory characteristics. We further hypothesize that the presence of the multitude of secondary motifs which emerge help regulate the timing of the core mechanism and protect it from transient perturbations.

Our work aims at advancing our understanding of the evolutionary nature of emergence of functional motifs in oscillatory networks, especially in understanding why certain features may be more likely to be present in biological networks than random networks.

1 Rao, R. T., Pierre, K. K., Schlesinger, N. & Androulakis, I. P. The Potential of Circadian Realignment in Rheumatoid Arthritis. Crit Rev Biomed Eng 44, 177-191, doi:10.1615/CritRevBiomedEng.2016018812 (2016).

2 Mavroudis, P. D., Scheff, J. D., Calvano, S. E. & Androulakis, I. P. Systems biology of circadian-immune interactions. J Innate Immun 5, 153-162, doi:10.1159/000342427 (2013).

3 Mangan, S. & Alon, U. Structure and function of the feed-forward loop network motif. Proceedings of the National Academy of Sciences 100, 11980-11985 (2003).

4 Mangan, S., Zaslaver, A. & Alon, U. The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks. Journal of molecular biology 334, 197-204 (2003).

5 Lipshtat, A., Purushothaman, S. P., Iyengar, R. & Ma’ayan, A. Functions of bifans in context of multiple regulatory motifs in signaling networks. Biophysical journal 94, 2566-2579 (2008).

6 Ingram, P. J., Stumpf, M. P. & Stark, J. Network motifs: structure does not determine function. BMC genomics 7, 108 (2006).

7 Pett, J. P., Korenčič, A., Wesener, F., Kramer, A. & Herzel, H. Feedback loops of the mammalian circadian clock constitute repressilator. PLoS computational biology 12, e1005266 (2016).