The determinism and boundedness of self-assembling structures
Authors:
S. Tesoro,
S. E. Ahnert,
A. S. Leonard
Abstract:
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…
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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
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Submitted 8 September, 2018; v1 submitted 20 October, 2016;
originally announced October 2016.
A 1-dimensional statistical mechanics model for nucleosome positioning on genomic DNA
Authors:
S. Tesoro,
I. Ali,
A. N. Morozov,
N. Sulaiman,
D. Marenduzzo
Abstract:
The first level of folding of DNA in eukaryotes is provided by the so called '10 nm chromatin fibre', where DNA wraps around histone proteins (approx. 10 nm in size) to form nucleosomes, which go on to create a zig zagging bead on a string structure. In this work we present a 1 dimensional statistical mechanics model to study nucleosome positioning within one such 10 nm fibre. We focus on the case…
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The first level of folding of DNA in eukaryotes is provided by the so called '10 nm chromatin fibre', where DNA wraps around histone proteins (approx. 10 nm in size) to form nucleosomes, which go on to create a zig zagging bead on a string structure. In this work we present a 1 dimensional statistical mechanics model to study nucleosome positioning within one such 10 nm fibre. We focus on the case of genomic sheep DNA, and we start from effective potentials valid at infinite dilution and determined from high resolution in vitro salt dialysis experiments. We study positioning within a polynucleosome chain, and compare the results for genomic DNA to that obtained in the simplest case of homogeneous DNA, where the problem can be mapped to a Tonks gas. First, we consider the simple, analytically solvable, case where nucleosomes are assumed to be point like. Then, we perform numerical simulations to gauge the effect of their finite size on the nucleosomal distribution probabilities. Finally we compare nucleosome distributions and simulated nuclease digestion patterns for the two cases (homogeneous and sheep DNA), thereby providing testable predictions of the effect of sequence on experimentally observable quantities in experiments on polynucleosome chromatin fibres reconstituted in vitro.
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Submitted 20 January, 2016; v1 submitted 25 October, 2015;
originally announced October 2015.