Combinatorial optimization problems in self-assembly

Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to efficient self-assembly of shapes in the Tile Assembly Model of self-assembly proposed by Rothemund and Winfree [18]. The first is the Minimum Tile Set Problem, where the goal is to find the smallest tile system that uniquely produces a given shape. The second is the Tile Concentrations Problem, where the goal is to decide on the relative concentrations of different types of tiles so that a tile system assembles as quickly as possible. The first problem is akin to finding optimum program size, and the second to finding optimum running time for a "program" to assemble the shape.Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to efficient self-assembly of shapes in the Tile Assembly Model of self-assembly proposed by Rothemund and Winfree [18]. The first is the Minimum Tile Set Problem, where the goal is to find the smallest tile system that uniquely produces a given shape. The second is the Tile Concentrations Problem, where the goal is to decide on the relative concentrations of different types of tiles so that a tile system assembles as quickly as possible. The first problem is akin to finding optimum program size, and the second to finding optimum running time for a "program" to assemble the shape. We prove that the first problem is NP-complete in general, and polynomial time solvable on trees and squares. In order to prove that the problem is in NP, we present a polynomial time algorithm to verify whether a given tile system uniquely produces a given shape. This algorithm is analogous to a program verifier for traditional computational systems, and may well be of independent interest. For the second problem, we present a polynomial time $O(\log n)$-approximation algorithm that works for a large class of tile systems that we call partial order systems

A DNA and restriction enzyme implementation of Turing Machines.

Bacteria employ restriction enzymes to cut or restrict DNA at or near specific words in a unique way. Many restriction enzymes cut the two strands of double-stranded DNA at different positions leaving overhangs of single-stranded DNA. Two pieces of DNA may be rejoined or ligated if their terminal overhangs are complementary. Using these operations fragments of DNA, or oligonucleotides, may be inserted and deleted from a circular piece of plasmid DNA. We propose an encoding for the transition table of a Turing machine in DNA oligonucleotides and a corresponding series of restrictions and ligations of those oligonucleotides that, when performed on circular DNA encoding an instantaneous description of a Turing machine, simulate the operation of the Turing machine encoded in those oligonucleotides. DNA based Turing machines have been proposed by Charles Bennett but they invoke imaginary enzymes to perform the state-symbol transitions. Our approach differs in that every operation can be pe..

DNA nanoparticles for ophthalmic drug delivery

Nucleic acids represent very appealing building blocks for the construction of nano-scaled objects with great potential applications in the field of drug delivery where multifunctional nanoparticles (NPs) play a pivotal role. One opportunity for DNA nanotechnology lies in the treatment of ophthalmic diseases as the efficacy of eye drops is impaired by the short survival time of the drug on the eye surface. As a consequence, topical administration of ocular therapeutics requires high drug doses and frequent administration, still rarely providing high bioavailability. To overcome these shortcomings we introduce a novel and general carrier system that is based on DNA nanotechnology. Non-toxic, lipid-modified DNA strands (12mers with 4 lipid modified thymines at the 5' end) form uniform NPs (micelles), which adhere to the corneal surface for extended periods of time. In a single self-assembly step they can be equipped with different drugs by hybridization with an aptamer. The long survival times of DNA NPs can be translated into improved efficacy. Their functionality was demonstrated in several ex-vivo experiments and in an in-vivo animal model. Finally, the NPs were confirmed to be applicable even for human tissue. (C) 2017 Elsevier Ltd. All rights reserved

Rare-earth metalation of calix[4]pyrrole/calix[4]arene free of alkali-metal companions

The redox transmetalation/protolysis (RTP) reactions of ytterbium or neodymium metal with calix[4]H4 (5,11,17,23-tetra-tert-butylcalix[4]arene-25,26,27,28-tetrol) in the presence of bis(pentafluorophenyl)mercury under ultrasonication yielded [LnIII(calix[4]H)(thf)]2 (1, Ln = Yb; 2, Ln = Nd). The characterization of both 1 and 2, including an X-ray single-crystal structural determination for 2, suggests triple deprotonation of the macrocyclic ligand on metalation. The related RTP reaction of H4N4Et8 (meso-octaethylcalix[4]pyrrole) with ytterbium metal and Hg(C6F5)2 at ambient temperature, however, resulted in quadruple deprotonation and afforded the ytterbium(II) calix[4]pyrrolide complex [Yb2(N4Et8)(thf)4] (3) in good yield. Subsequent oxidation of 3 by dioxygen generated the novel tetranuclear ytterbium(III) complex [Yb4(μ-O)2(N4Et8)2(thf)2] (4). The structures of the ytterbium(II) complex 3 and the ytterbium(III) complex 4 incorporate endo (3) and endo/exo (4) pyrrolide sandwich and half-sandwich units, respectively, with metal centers η1 bound by nitrogen and η5 bonded by pyrrolide rings. The RTP reaction of lanthanum metal using diphenylmercury in place of bis(pentafluorophenyl)mercury gave the triply deprotonated and N-confused pyrrolide (with an alkyl substituent of one pyrrolide ring migrated to a β-position) macrocyclic complex [La2(HN3N′Et8)2] (5). The triple deprotonation of the macrocyclic ligand H4N4Et8 was also achieved through its reaction with 3 molar equiv of potassium metal, giving colorless crystals of [{K3(HN4Et8)(thf)(PhMe)2}n] (6). However, an attempt to isolate the corresponding partially deprotonated calix[4]pyrrolide ytterbium(III) complex through the metathesis reaction of potassium precursor 6 with ytterbium triiodide was unsuccessful