GHZ States as Tripartite PR Boxes: Classical Limit and Retrocausality.

We review an argument that bipartite "PR-box" correlations, though designed to respect relativistic causality, in fact violate relativistic causality in the classical limit. As a test of this argument, we consider Greenberger-Horne-Zeilinger (GHZ) correlations as a tripartite version of PR-box correlations, and ask whether the argument extends to GHZ correlations. If it does-i.e., if it shows that GHZ correlations violate relativistic causality in the classical limit-then the argument must be incorrect (since GHZ correlations do respect relativistic causality in the classical limit.) However, we find that the argument does not extend to GHZ correlations. We also show that both PR-box correlations and GHZ correlations can be retrocausal, but the retrocausality of PR-box correlations leads to self-contradictory causal loops, while the retrocausality of GHZ correlations does not.

Regulation of gene expression by small non-coding RNAs: a quantitative view.

The importance of post-transcriptional regulation by small non-coding RNAs has recently been recognized in both pro- and eukaryotes. Small RNAs (sRNAs) regulate gene expression post-transcriptionally by base pairing with the mRNA. Here we use dynamical simulations to characterize this regulation mode in comparison to transcriptional regulation mediated by protein-DNA interaction and to post-translational regulation achieved by protein-protein interaction. We show quantitatively that regulation by sRNA is advantageous when fast responses to external signals are needed, consistent with experimental data about its involvement in stress responses. Our analysis indicates that the half-life of the sRNA-mRNA complex and the ratio of their production rates determine the steady-state level of the target protein, suggesting that regulation by sRNA may provide fine-tuning of gene expression. We also describe the network of regulation by sRNA in Escherichia coli, and integrate it with the transcription regulation network, uncovering mixed regulatory circuits, such as mixed feed-forward loops. The integration of sRNAs in feed-forward loops provides tight repression, guaranteed by the combination of transcriptional and post-transcriptional regulations.