Minimum complexity drives regulatory logic in Boolean models of living systems

Abstract

The properties of random Boolean networks as models of gene regulation have been investigated extensively by the statistical physics community. In the past two decades, there has been a dramatic increase in the reconstruction and analysis of Boolean models of biological networks. In such models, neither network topology nor Boolean functions (or logical update rules) should be expected to be random. In this contribution, we focus on biologically meaningful types of Boolean functions, and perform a systematic study of their preponderance in gene regulatory networks. By applying the k[P] classification based on number of inputs k and bias P of functions, we find that most Boolean functions astonishingly have odd bias in a reference biological dataset of 2687 functions compiled from published models. Subsequently, we are able to explain this observation along with the enrichment of read-once functions (RoFs) and its subset, nested canalyzing functions (NCFs), in the reference dataset in terms of two complexity measures: Boolean complexity based on string lengths in formal logic which is yet unexplored in the biological context, and the average sensitivity. Minimizing the Boolean complexity naturally sifts out a subset of odd-biased Boolean functions which happen to be the RoFs. Finally, we provide an analytical proof that NCFs minimize not only the Boolean complexity, but also the average sensitivity in their k[P] set.

Semiconducting Polymers for Neural Applications

“…However, despite the relatively lower mechanical modulus for organic materials, it is still high compared to most neural tissuePEDOT:PSS has been reported in the range of several GPa, 69 while brain tissue is in the several hundred Pa to low kPa range 70 typical metals used for electrodes, such as platinum or titanium, range in the hundreds of GPa. As such, conductive polymers with mechanical properties similar to PEDOT:PSS tend to be sufficiently soft to reduce trauma, due to an implant's micromotion in the brain, 71 but are still stiffer than the surrounding tissue, potentially triggering a foreignbody reaction. 66 The mechanical properties of conductive polymers are a consequence of their typically long, rigid, conjugated polymer backbones, themselves dictated by electronic requirements.…”

Advancements in Biological Neural Interfaces Using Conducting Polymers: A Review

“…The mismatch between tissue and silicon has been found to be a major factor in instigating foreign body reaction. 39,40 Polymer electrodes having properties similar to natural cell can be produced and it is assumed that such a soft polymer electrode coating could act as a mechanical buffer between the soft tissue and stiff probes. 41 Moreover, the strain resulting from micromotion also decreases, because of tight integration between the implant and the tissue.…”