SAT-assembly: A new approach for designing self-assembling systems

We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as building blocks, where the different units bind at specific interaction sites (the patches), and we exploit the possibility of having mixtures with several components. The interaction rules between the patches is determined by transforming the combinatorial problem into a Boolean satisfiability problem (SAT) which searches for solutions where all bonds are formed in the target structure. Additional conditions, such as the non-satisfiability of competing structures (e.g. metastable states) can be imposed, allowing to effectively design the assembly path in order to avoid kinetic traps. We demonstrate this approach by designing and numerically simulating a cubic diamond structure from four particle species that assembles without competition from other polymorphs, including the hexagonal structure.Comment: 12 pages, 4 figure

The PATS Problem : Search Methods and Reliability

This work studies an NP-hard combinatorial optimisation problem, the Pattern self-Assembly Tile set Synthesis (PATS) problem, which stems from the field of DNA self-assembly. In this problem, we are given a coloured rectangular pattern as input, and the task is to find a minimal set of unit square tiles that self-assemble that pattern in the abstract Tile Assembly Model (aTAM). We present two new search methods for the PATS problem: a heuristic algorithm that conducts a search in the lattice of partitions of the input grid, and a declarative approach that uses the Answer Set Programming (ASP) paradigm. The former is based on a previous algorithm by Göös and Orponen (DNA 2010), and performs better in finding relatively small solutions even for quite large input patterns. The latter proves to find the optimal solution quickly in cases where it is small. In addition to the search procedures, we develop a method for estimating the reliability of solutions to the PATS problem from a stochastic point of view. It turns out that tile sets found by our procedures, as well as small tile sets in general, have a higher probability of error-free assembly compared to those that can be found by previous methods

Towards the Design of Heuristics by Means of Self-Assembly

The current investigations on hyper-heuristics design have sprung up in two different flavours: heuristics that choose heuristics and heuristics that generate heuristics. In the latter, the goal is to develop a problem-domain independent strategy to automatically generate a good performing heuristic for the problem at hand. This can be done, for example, by automatically selecting and combining different low-level heuristics into a problem specific and effective strategy. Hyper-heuristics raise the level of generality on automated problem solving by attempting to select and/or generate tailored heuristics for the problem at hand. Some approaches like genetic programming have been proposed for this. In this paper, we explore an elegant nature-inspired alternative based on self-assembly construction processes, in which structures emerge out of local interactions between autonomous components. This idea arises from previous works in which computational models of self-assembly were subject to evolutionary design in order to perform the automatic construction of user-defined structures. Then, the aim of this paper is to present a novel methodology for the automated design of heuristics by means of self-assembly

DNA Computing by Self-Assembly

Information and algorithms appear to be central to biological organization and processes, from the storage and reproduction of genetic information to the control of developmental processes to the sophisticated computations performed by the nervous system. Much as human technology uses electronic microprocessors to control electromechanical devices, biological organisms use biochemical circuits to control molecular and chemical events. The engineering and programming of biochemical circuits, in vivo and in vitro, would transform industries that use chemical and nanostructured materials. Although the construction of biochemical circuits has been explored theoretically since the birth of molecular biology, our practical experience with the capabilities and possible programming of biochemical algorithms is still very young

Self-Assembly of Geometric Space from Random Graphs

We present a Euclidean quantum gravity model in which random graphs dynamically self-assemble into discrete manifold structures. Concretely, we consider a statistical model driven by a discretisation of the Euclidean Einstein-Hilbert action; contrary to previous approaches based on simplicial complexes and Regge calculus our discretisation is based on the Ollivier curvature, a coarse analogue of the manifold Ricci curvature defined for generic graphs. The Ollivier curvature is generally difficult to evaluate due to its definition in terms of optimal transport theory, but we present a new exact expression for the Ollivier curvature in a wide class of relevant graphs purely in terms of the numbers of short cycles at an edge. This result should be of independent intrinsic interest to network theorists. Action minimising configurations prove to be cubic complexes up to defects; there are indications that such defects are dynamically suppressed in the macroscopic limit. Closer examination of a defect free model shows that certain classical configurations have a geometric interpretation and discretely approximate vacuum solutions to the Euclidean Einstein-Hilbert action. Working in a configuration space where the geometric configurations are stable vacua of the theory, we obtain direct numerical evidence for the existence of a continuous phase transition; this makes the model a UV completion of Euclidean Einstein gravity. Notably, this phase transition implies an area-law for the entropy of emerging geometric space. Certain vacua of the theory can be interpreted as baby universes; we find that these configurations appear as stable vacua in a mean field approximation of our model, but are excluded dynamically whenever the action is exact indicating the dynamical stability of geometric space. The model is intended as a setting for subsequent studies of emergent time mechanisms.Comment: 26 pages, 9 figures, 2 appendice