No abstract

No abstract

As we aim towards enhancing our knowledge of complex cell behaviors and developing intricate cell-based devices and improved therapeutics, it becomes imperative that we be able to control and manipulate the spatial localization of cells. Here we have developed a novel strategy to pattern cells using a hyaluronic acid hydrogel material and photocaged RGDS (Arg-Gly-Asp-Ser) peptides. In this report, we discuss the chemical synthesis and photoactive properties of the caged peptides as well as the subsequent binding of these peptides to our hydrogel base. We further demonstrate the ability of this modified hydrogel material to pattern fibroblast cells on the micron scale using near-UV light exposure through a patterned photomask to selectively switch areas of the hydrogel surface from cell non-adhesive to cell adhesive. The cells are found to adhere and proliferate along the developed line patterns for at least 2.5 days, demonstrating significantly enhanced pattern longevity in comparison with previously reported studies.

No abstract

No abstract

Techniques to pattern cells on biocompatible hydrogels allow for the creation of highly controlled cell microenvironments within materials that mimic the physicochemical properties of native tissues. Such technology has the potential to further enhance our knowledge of cell biology and to play a role in the development of novel tissue engineering devices. Light is an ideal stimulus to catalyze pattern formation since it can be controlled spatially as well as temporally. Herein, we have developed and enhanced a hydrogel cell patterning strategy. It is based on photoactive caged RGDS peptides incorporated into a hyaluronic acid (HA) hydrogel, which can be subsequently activated with near-UV light to create cell-adhesive regions within an otherwise non-adhesive hydrogel. With this strategy, we have been able to pattern multiple cell populations-either in contact with one another or held apart-on an underlying chemically patterned HA hydrogel. Furthermore, the hydrogel cell pattern could be altered with time, even 2 weeks after initial seeding, to create additional adhesive regions to regulate the direction of cell growth and migration. These dynamic hydrogel cell patterns, created with a standard fluorescence microscope, were shown to be robust and lasted at least 3 weeks in vitro.

The Wiener index is maximized over the set of trees with the given vertex weight and degree sequences. This model covers the traditional "unweighed" Wiener index, the terminal Wiener index, and the vertex distance index. It is shown that there exists an optimal caterpillar. If weights of internal vertices increase in their degrees, then an optimal caterpillar exists with weights of internal vertices on its backbone monotonously increasing from some central point to the ends of the backbone, and the same is true for pendent vertices. A tight upper bound of the Wiener index value is proposed and an efficient greedy heuristics is developed that approximates well the optimal index value. Finally, a branch and bound algorithm is built and tested for the exact solution of this NP-complete problem.Keywords: Wiener index for graph with weighted vertices, upper-bound estimate, greedy algorithm, optimal caterpillar 2010 MSC: 05C05, 05C12, 05C22, 05C35, 90C09, 90C35, 90C57 NomenclatureThis section introduces the basic graph-theoretic notation. The vertex set and the edge set of a simple connected undirected graph G are denoted with V (G) and E(G) respectively, and the degree (i.e., the number of incident edges) of vertex v ∈ V (G) in graph G is denoted with d G (v). Let W (G) be the set of pendent vertices (those having degree one) of graph G, and let $

The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, structure identification from data, etc. For the case of connecting trees with the given sequence of vertex degrees the cost of the optimal tree is shown to be bounded from below by the solution of a semidefinite optimization program with bilinear matrix constraints, which is reduced to the solution of a series of convex programs with linear matrix inequality constraints. The proposed lower bound estimate is used to construct several heuristic algorithms and to evaluate their quality on a variety of generated and real-life data sets. Optimal communication network, generalized Wiener index, origin-destination matrix, semidefinite programming, quadratic matrix inequality.