Noncommutative biology as Sequential logic over combinatorial logic, a Ph.D. thesis for new synthetic biology field

  A different approach, called sequential logic, uses noncommutative sequences of a small set of regulators to drive networks to a large number of novel configurations. If certain targets are first protected, then even promiscuous regulators can activate specific subsets of lineage-specific targets. In this paper we show how sequential logic outperforms combinatorial logic, and argue that noncommutative sequences underlie a number of cases of biological regulation, e.g. how a small number of signaling pathways generates a large diversity of cell types in development. In addition to explaining biological networks, sequential logic may be a general experimental design strategy in synthetic and single-cell biology.

https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005089 

 https://thesis.library.caltech.edu/10966/

 . It is shown using time sequences of noncommutative controllers that targets which otherwise would have been activated together can be regulated independently. We derive scaling laws for two noncommutative models of regulation, motivated by phosphorylation/neural networks and chromosome folding, respectively, and show that they scale super-exponentially in the number of regulators. It is also shown that specificity in control is robust to loss of a regulator. Consequently, sequential logic overcomes the information bottleneck in complex problems and enables novel solutions through roundabout strategies. The theoretical results are connected to real biological networks demonstrating specificity in the context of promiscuity.

 In conclusion, regulation in the tangent space of gene expression resolves the paradox that development has a unique solution specified in the DNA of the egg which cannot be determined with certainty until completion of the adult. Noncommutative sequential logic generates complexity that cannot be realized at the start, while interdependent cells (and strings) require time to ensure that each fate is at the same potential difference from a common ancestor. This fundamental reimagining of the Waddington framework can be tested using new multiplexed mRNA imaging technologies that preserve the spatial context of cells in developing tissue.