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Conformational cooperativity is a universal molecular effect mechanism and plays a critical role in signaling pathways. However, it remains a challenge to develop artificial molecular networks regulated by conformational cooperativity, due to the difficulties in programming and controlling multiple structural interactions. Herein, we develop a cooperative strategy by programming multiple conformational signals, rather than chemical signals, to regulate protein-oligonucleotide signal transduction, taking advantage of the programmability of allosteric DNA constructs. We generate a cooperative regulation mechanism, by which increasing the loop lengths at two different structural modules induced the opposite effects manifesting as down- and up-regulation. We implement allosteric logic operations by using two different proteins. Further, in cell culture we demonstrate the feasibility of this strategy to cooperatively regulate gene expression of PLK1 to inhibit tumor cell proliferation, responding to orthogonal protein-signal stimulation. This programmable conformational cooperativity paradigm has potential applications in the related fields. Conformational cooperativity is a universal molecular effect mechanism and plays a critical role in signalling pathways. Here the authors present a programmable conformational cooperativity strategy to construct the oligo-protein signal transduction platform for logic operations and gene regulations which can be cooperatively regulated by conformational signals. [ABSTRACT FROM AUTHOR]

We show that if the one-loop partition function of a modular invariant conformal field theory can be expressed as a finite sum of holomorphically factorized terms then c and all values of h are rational. [ABSTRACT FROM AUTHOR]