This paper introduces the class of strongly endotactic networks, a subclass of the endotactic networks introduced by Craciun, Nazarov, and Pantea. The main result states that the global attractor conjecture holds for complex-balanced systems that are strongly endotactic: every trajectory with positive initial condition converges to the unique positive equilibrium allowed by conservation laws. This extends a recent result by Anderson for systems where the reaction diagram has only one linkage class (connected component). The results here are proved using differential inclusions, a setting that includes power-law systems. The key ideas include a perspective on reaction kinetics in terms of combinatorial geometry of reaction diagrams, a projection argument that enables analysis of a given system in terms of systems with lower dimension, and an extension of Birch's theorem, a well-known result about intersections of affine subspaces with manifolds parameterized by monomials.

We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potential of the stationary distribution of stochastically modeled complex balanced systems. We extend this result to general birth-death models and demonstrate via example that similar scaling limits can yield Lyapunov functions even for models that are not complex or detailed balanced, and may even have multiple equilibria.

We have designed and constructed DNA complexes in the form of triangles. We have created hexagonal planar tilings from these triangles via self-assembly. Unlike previously reported structures self-assembled from DNA, our structures appear to involve bending of double helices. Bending helices may be a useful design option in the creation of self-assembled DNA structures. It has been suggested that DNA self-assembly may lead to novel materials and efficient computational devices.

The COVID-19 pandemic has strained testing capabilities worldwide. There is an urgent need to find economical and scalable ways to test more people. We present Tapestry, a novel quantitative nonadaptive pooling scheme to test many samples using only a few tests. The underlying molecular diagnostic test is any real-time RT-PCR diagnostic panel approved for the detection of the SARS-CoV-2 virus. In cases where most samples are negative for the virus, Tapestry accurately identifies the status of each individual sample with a single round of testing in fewer tests than simple two-round pooling. We also present a companion Android application BYOM Smart Testing which guides users through the pipetting steps required to perform the combinatorial pooling. The results of the pooled tests can be fed into the application to recover the status and estimated viral load for each individual sample. NOTE: This protocol has been validated with in vitro experiments that used synthetic RNA and DNA fragments and additionally, its expected behavior has been confirmed using computer simulations. Validation with clinical samples is ongoing. We are looking for clinical collaborators with access to patient samples. Please contact the corresponding author if you wish to validate this protocol on clinical samples.

We define catalytic networks as chemical reaction networks with an essentially catalytic reaction pathway: one which is "on" in the presence of certain catalysts and "off" in their absence. We show that examples of catalytic networks include synthetic DNA molecular circuits that have been shown to perform signal amplification and molecular logic. Recall that a critical siphon is a subset of the species in a chemical reaction network whose absence is forward invariant and stoichiometrically compatible with a positive point. Our main theorem is that all weakly-reversible networks with critical siphons are catalytic. Consequently, we obtain new proofs for the persistence of atomic event-systems of Adleman et al., and normal networks of Gnacadja. We define autocatalytic networks, and conjecture that a weakly-reversible reaction network has critical siphons if and only if it is autocatalytic.