Using three-dimensional microfluidic networks for solving computationally hard problems

This paper describes the design of a parallel algorithm that uses moving fluids in a three-dimensional microfluidic system to solve a nondeterministically polynomial complete problem (the maximal clique problem) in polynomial time. This algorithm relies on (i) parallel fabrication of the microfluidic system, (ii) parallel searching of all potential solutions by using fluid flow, and (iii) parallel optical readout of all solutions. This algorithm was implemented to solve the maximal clique problem for a simple graph with six vertices. The successful implementation of this algorithm to compute solutions for small-size graphs with fluids in microchannels is not useful, per se, but does suggest broader application for microfluidics in computation and control.

A positivity result in the theory of Macdonald polynomials

We outline here a proof that a certain rational function Cn(q, t), which has come to be known as the “q, t-Catalan,” is in fact a polynomial with positive integer coefficients. This has been an open problem since 1994. Because Cn(q, t) evaluates to the Catalan number at t = q = 1, it has also been an open problem to find a pair of statistics a, b on the collection

SoxR, a [2Fe-2S] transcription factor, is active only in its oxidized form.

SoxR protein is known to function both as a sensor and as a transcriptional activator for a superoxide response regulon in Escherichia coli. The activity of SoxR was tested by its ability to enable the transcription of its target gene, soxS, in vitro. The activity of the oxidized form was lost when its [2Fe-2S] clusters were reduced by dithionite under anaerobic conditions, and it was rapidly restored by autooxidation. This result is consistent with the hypothesis that induction of the regulon is effected by the univalent oxidation of the Fe-S centers of SoxR. In vivo, this oxidation may be caused by an alteration of the redox balance of electron chain intermediates that normally maintains soxR in an inactive, reduced state. Oxidized SoxR was about twice as effective as reduced SoxR in protecting the soxS operator from endonucleolytic cleavage. However, this difference could not account for a greater than 50-fold difference in their activities and therefore could not support a model in which oxidation activates SoxR by enabling it to bind to DNA. NADPH, ferredoxin, flavodoxin, or ferredoxin (flavodoxin):NADP+ reductase could not reduce SoxR directly in vitro at a measurable rate. The midpoint potential for SoxR was measured at -283 mV.