Nondeterministic self-assembly with asymmetric interactions

Tesoro, Salvatore; Göpfrich, Kerstin; Kartanas, Tadas; Keyser, Ulrich F.; Ahnert, Sebastian E.

doi:10.1103/physreve.94.022404

Cited by 5 publications

(6 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Varying the assembly rules and parameters enables us to explore a broad range of structures, compared to the laboratory experiments and the potential limits of the aggregation process, and understand the emergence of new features 24 – 27 . A particular anisotropy of the interaction and spatial constraints can lead to some interesting low-dimensional assemblies, for example, chains 28 and patterns obtained by tiling or recognition-binding on a two-dimensional lattice 24 , and self-assembly of loops under the planar graph rules 23 . By contrast, self-assembly of geometric objects without spatial embedding can lead to complex, hierarchically organized networks.…”

Section: Introductionmentioning

confidence: 99%

Hidden geometries in networks arising from cooperative self-assembly

Šuvakov

Andjelković

Tadić

2018

Sci Rep

View full text Add to dashboard Cite

Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and compatibility of the building blocks are decisive factors. Therefore, a comprehensive understanding of these processes is essential for the design of assemblies of desired properties. Here, we introduce a computational model for cooperative self-assembly with the simultaneous attachment of structured groups of particles, which can be described by simplexes (connected pairs, triangles, tetrahedrons and higher order cliques) to a growing network. The model incorporates geometric rules that provide suitable nesting spaces for the new group and the chemical affinity of the system to accept excess particles. For varying chemical affinity, we grow different classes of assemblies by binding the cliques of distributed sizes. Furthermore, we characterize the emergent structures by metrics of graph theory and algebraic topology of graphs, and 4-point test for the intrinsic hyperbolicity of the networks. Our results show that higher Q-connectedness of the appearing simplicial complexes can arise due to only geometric factors and that it can be efficiently modulated by changing the chemical potential and the polydispersity of the binding simplexes.

show abstract

Section: Introductionmentioning

confidence: 99%

Hidden geometries in networks arising from cooperative self-assembly

Šuvakov

Andjelković

Tadić

2018

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Steric nondeterminism can prompt novel behavior in self-limiting cluster growth. In previous experimental work [17], single-seed and multi-seed self-assembly were compared, observing that complementary pair interactions can limit growth in multi-seed assembly through local steric effects. Such phenomenon is beyond the scope of this framework currently, but remains an topic for further analysis.…”

Section: A Steric Effectsmentioning

confidence: 99%

“…For example, the sickle-cell mutation of hemoglobin that leads to unbound protein aggregation can be modelled using polyominoes [15]. Furthermore, experimental implementations of the polyomino model have been realized using DNA tiles [17].…”

Section: Introductionmentioning

confidence: 99%

Determinism and boundedness of self-assembling structures

2018

Self Cite

View full text Add to dashboard Cite

Self-assembly processes are widespread in nature and lie at the heart of many biological and physical phenomena. The characteristics of self-assembly building blocks determine the structures that they form. Two crucial properties are the determinism and boundedness of the self-assembly. The former tells us whether the same set of building blocks always generates the same structure, and the latter whether it grows indefinitely. These properties are highly relevant in the context of protein structures, as the difference between deterministic protein self-assembly and nondeterministic protein aggregation is central to a number of diseases. Here we introduce a graph theoretical approach that can determine the determinism and boundedness for several geometries and dimensionalities of self-assembly more accurately and quickly than conventional methods. We apply this methodology to a previously studied lattice self-assembly model and discuss generalizations to a wide range of other self-assembling systems.

show abstract

“…Some recent investigations show how the use of topology can open new ways for designing materials inspired by mathematics 15,21 . On the other hand, the research of growing complex networks has recently been extended to explore the attachment of objects (loops, simplexes) under geometric rules and control parameters [22][23][24][25] . In this regard, the self-assembly can be understood as a language that can describe the complex architecture of these networks.…”

Section: Introductionmentioning

confidence: 99%

“…In this regard, the self-assembly can be understood as a language that can describe the complex architecture of these networks. Varying the assembly rules and parameters enables us to explore a broad range of structures, compared to the laboratory experiments and the potential limits of the aggregation process, and understand the emergence of new features [23][24][25][26] . A particular anisotropy of the interaction and spatial constraints can lead to some interesting low-dimensional assemblies, for example, chains 27 and patterns obtained by tiling or recognition-binding on a two-dimensional lattice 23 , and self-assembly of loops under the planar graph rules 22 .…”

Section: Introductionmentioning

confidence: 99%

Hidden geometries in networks arising from cooperative self-assembly

Šuvakov¹,

Andjelković²,

Tadić³

2017

Preprint

View full text Add to dashboard Cite

Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and compatibility of the building blocks are decisive factors in each phase of growth. Therefore, a comprehensive understanding of these processes is essential for the design of large assemblies of desired properties. Here, we introduce a computational model for cooperative self-assembly with simultaneous attachment of structured groups of particles, which can be described by simplexes (connected pairs, triangles, tetrahedrons and higher order cliques) to a growing network, starting from a small seed. The model incorporates geometric rules that provide suitable nesting spaces for the new group and the chemical affinity ν of the system to acceping an excess number of particles. For varying chemical affinity, we grow different classes of assemblies by binding the cliques of distributed sizes. Furthermore, to characterise the emergent large-scale structures, we use the metrics of graph theory and algebraic topology of graphs, and 4-point test for the intrinsic hyperbolicity of the networks. Our results show that higher Q-connectedness of the appearing simplicial complexes can arise due to only geometrical factors, i.e., for ν = 0, and that it can be effectively modulated by changing the chemical potential and the polydispersity of the size of binding simplexes. For certain parameters in the model we obtain networks of mono-dispersed clicks, triangles and tetrahedrons, which represent the geometrical descriptors that are relevant in quantum physics and frequently occurring chemical clusters.

show abstract

Nondeterministic self-assembly with asymmetric interactions

Cited by 5 publications

References 27 publications

Hidden geometries in networks arising from cooperative self-assembly

Hidden geometries in networks arising from cooperative self-assembly

Determinism and boundedness of self-assembling structures

Hidden geometries in networks arising from cooperative self-assembly

Contact Info

Product

Resources

About