Alkene–Tetrazine Ligation for Imaging Cellular DNA

5‐Vinyl‐2′‐deoxyuridine (VdU) is the first reported metabolic probe for cellular DNA synthesis that can be visualized by using an inverse electron demand Diels–Alder reaction with a fluorescent tetrazine. VdU is incorporated by endogenous enzymes into the genomes of replicating cells, where it exhibits reduced genotoxicity compared to 5‐ethynyl‐2′‐deoxyuridine (EdU). The VdU–tetrazine ligation reaction is rapid (k≈0.02 M ^?1 s^?1) and chemically orthogonal to the alkyne–azide “click” reaction of EdU‐modified DNA. Alkene–tetrazine ligation reactions provide the first alternative to azide–alkyne click reactions for the bioorthogonal chemical labeling of nucleic acids in cells and facilitate time‐resolved, multicolor labeling of DNA synthesis.     

Linearization-based algorithms for mixed-integer nonlinear programs with convex continuous relaxation

We present two linearization-based algorithms for mixed-integer nonlinear programs (MINLPs) having a convex continuous relaxation. The key feature of these algorithms is that, in contrast to most existing linearization-based algorithms for convex MINLPs, they do not require the continuous relaxation to be defined by convex nonlinear functions. For example, these algorithms can solve to global optimality MINLPs with constraints defined by quasiconvex functions. The first algorithm is a slightly modified version of the LP/NLP-based branch-and-bouund \((\text{ LP/NLP-BB })\) algorithm of Quesada and Grossmann, and is closely related to an algorithm recently proposed by Bonami et al. (Math Program 119:331–352, 2009). The second algorithm is a hybrid between this algorithm and nonlinear programming based branch-and-bound. Computational experiments indicate that the modified LP/NLP-BB method has comparable performance to LP/NLP-BB on instances defined by convex functions. Thus, this algorithm has the potential to solve a wider class of MINLP instances without sacrificing performance.     

Label-free detection of nucleic acids by turn-on and turn-off G-quadruplex-mediated fluorescence

In this study we have used two fluorescent probes, tetrakis(diisopropylguanidino)-zinc-phthalocyanine (Zn-DIGP) and N-methylmesoporphyrin IX (NMM), to monitor the reassembly of “split” G-quadruplex probes on hybridization with an arbitrary “target” DNA. According to this approach, each split probe is designed to contain half of a G-quadruplex-forming sequence fused to a variable sequence that is complementary to the target DNA. Upon mixing the individual components, both base-pairing interactions and G-quadruplex fragment reassembly result in a duplex–quadruplex three-way junction that can bind to fluorescent dyes in a G-quadruplex-specific way. The overall fluorescence intensities of the resulting complexes were dependent on the formation of proper base-pairing interactions in the duplex regions, and on the exact identity of the fluorescent probe. Compared with samples lacking any “target” DNA, the fluorescence intensities of Zn-DIGP-containing samples were lower, and the fluorescence intensities of NMM-containing samples were higher on addition of the target DNA. The resulting biosensors based on Zn-DIGP are therefore termed “turn-off” whereas the biosensors containing NMM are defined as “turn-on”. Both of these biosensors can detect target DNAs with a limit of detection in the nanomolar range, and can discriminate mismatched from perfectly matched target DNAs. In contrast with previous biosensors based on the peroxidase activity of heme-bound split G-quadruplex probes, the use of fluorescent dyes eliminates the need for unstable sensing components (H₂O₂, hemin, and ABTS). Our approach is direct, easy to conduct, and fully compatible with the detection of specific DNA sequences in biological fluids. Having two different types of probe was highly valuable in the context of applied studies, because Zn-DIGP was found to be compatible with samples containing both serum and urine whereas NMM was compatible with urine, but not with serum-containing samples.     

Dynamics of tip-substrate interactions in atomic force microscopy

Dynamical interactions between a scanning tip and a silicon substrate are investigated using molecular dynamics simulations of both the constant-height and constant-force scan modes. Localized temporary and permanent modifications of the substrate occur, depending on tip-substrate-strate separation and scan geometry. Implications for resolving structural and force characteristics in scanning tip spectroscopies, employing atomically sharp as well as large ordered of disordered tips are discussed.     

Two-stage linear decision rules for multi-stage stochastic programming

Multi-stage stochastic linear programs (MSLPs) are notoriously hard to solve in general. Linear decision rules (LDRs) yield an approximation of an MSLP by restricting the decisions at each stage to be an affine function of the observed uncertain parameters. Finding an optimal LDR is a static optimization problem that provides an upper bound on the optimal value of the MSLP, and, under certain assumptions, can be formulated as an explicit linear program. Similarly, as proposed by Kuhn et al. (Math Program 130(1):177–209, 2011) a lower bound for an MSLP can be obtained by restricting decisions in the dual of the MSLP to follow an LDR. We propose a new approximation approach for MSLPs, two-stage LDRs. The idea is to require only the state variables in an MSLP to follow an LDR, which is sufficient to obtain an approximation of an MSLP that is a two-stage stochastic linear program (2SLP). We similarly propose to apply LDR only to a subset of the variables in the dual of the MSLP, which yields a 2SLP approximation of the dual that provides a lower bound on the optimal value of the MSLP. Although solving the corresponding 2SLP approximations exactly is intractable in general, we investigate how approximate solution approaches that have been developed for solving 2SLP can be applied to solve these approximation problems, and derive statistical upper and lower bounds on the optimal value of the MSLP. In addition to potentially yielding better policies and bounds, this approach requires many fewer assumptions than are required to obtain an explicit reformulation when using the standard static LDR approach. A computational study on two example problems demonstrates that using a two-stage LDR can yield significantly better primal policies and modestly better dual policies than using policies based on a static LDR.

     

Exact algorithms for the chance-constrained vehicle routing problem

We study the chance-constrained vehicle routing problem (CCVRP), a version of the vehicle routing problem (VRP) with stochastic demands, where a limit is imposed on the probability that each vehicle’s capacity is exceeded. A distinguishing feature of our proposed methodologies is that they allow correlation between random demands, whereas nearly all existing exact methods for the VRP with stochastic demands require independent demands. We first study an edge-based formulation for the CCVRP, in particular addressing the challenge of how to determine a lower bound on the number of vehicles required to serve a subset of customers. We then investigate the use of a branch-and-cut-and-price (BCP) algorithm. While BCP algorithms have been considered the state of the art in solving the deterministic VRP, few attempts have been made to extend this framework to the VRP with stochastic demands. In contrast to the deterministic VRP, we find that the pricing problem for the CCVRP problem is strongly \(\mathcal {NP}\)-hard, even when the routes being priced are allowed to have cycles. We therefore propose a further relaxation of the routes that enables pricing via dynamic programming. We also demonstrate how our proposed methodologies can be adapted to solve a distributionally robust CCVRP problem. Numerical results indicate that the proposed methods can solve instances of CCVRP having up to 55 vertices.