Materials in nature have fascinating properties that serve as a continuous source of inspiration for materials scientists. Accordingly, bio-mimetic and bio-inspired approaches have yielded remarkable structural and functional materials for a plethora of applications. Despite these advances, many properties of natural materials remain challenging or yet impossible to incorporate into synthetic materials. Natural materials are produced by living cells, which sense and process environmental cues and conditions by means of signaling and genetic programs, thereby controlling the biosynthesis, remodeling, functionalization, or degradation of the natural material. In this context, synthetic biology offers unique opportunities in materials sciences by providing direct access to the rational engineering of how a cell senses and processes environmental information and translates them into the properties and functions of materials. Here, we identify and review two main directions by which synthetic biology can be harnessed to provide new impulses for the biologization of the materials sciences: first, the engineering of cells to produce precursors for the subsequent synthesis of materials. This includes materials that are otherwise produced from petrochemical resources, but also materials where the bio-produced substances contribute unique properties and functions not existing in traditional materials. Second, engineered living materials that are formed or assembled by cells or in which cells contribute specific functions while remaining an integral part of the living composite material. We finally provide a perspective of future scientific directions of this promising area of research and discuss science policy that would be required to support research and development in this field.
The quantum algebra of observables of closed bosonic strings moving in 1 3±dimensional Minkowski space is constructed up to degree five. All independent relations of degree four are computed; they involve three as yet undetermined parameters. Definitions and symbols are used as introduced in the above-mentioned article.
Statistical models defined on 2-dimensional graphs are classified which are invariant under flip moves, i.e., certain local changes of the adjacency structure of the graphs. The special case of regular graphs of degree 3—which are duals of 2-dimensional triangulations—corresponds to topological models and the classification leads to metrized, associative algebras. As a novel feature flip invariant models on regular graphs of degree 4 are classified by Z2-graded metrized associative algebras. They give rise to invariants for checkered graphs. Moreover, the general case of graphs with vertices of arbitrary degree (where degree 3 does occur) is discussed. Using structure theorems for (graded,) metrized, associative algebras we prove that only the simple ideals contribute to the partition function of such models. The partition functions are computed explicitly and reveal the invariant structures of the graph under the flip moves.
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