Nondeterministic self-assembly of two tile types on a lattice

Area of Science:

• * Computational modeling
• * Biophysics
• * Materials science

Background:

• * Self-assembly is fundamental in biology, driving protein quaternary structure formation and disease-related protein aggregation.
• * Deterministic self-assembly forms functional cellular structures, while nondeterministic aggregation is linked to diseases.

Purpose of the Study:

• * To investigate nondeterministic self-assembly using a simplified lattice model.
• * To explore the behavior of single tiles and mixtures of two tiles at varying concentrations.
• * To characterize the concentration-dependent assembly behaviors and resulting structures.

Main Methods:

• * Development and application of a lattice model for self-assembly.
• * Simulation of single lattice tiles and mixtures of two tiles.
• * Analysis of concentration-dependent assembly transitions and structural properties.

Main Results:

• * Observed a wide range of concentration-dependent behaviors in two-tile mixtures.
• * Identified critical behaviors with sharp transitions from bound to unbound structures.
• * Cataloged monotonic, nonmonotonic, and concentration-independent assembly patterns.
• * Demonstrated fractal structures with two distinct fractal dimensions.

Conclusions:

• * Nondeterministic self-assembly exhibits complex, concentration-driven behaviors.
• * The lattice model effectively predicts critical assembly concentrations for certain tile sets.
• * Resulting structures possess fractal characteristics, offering insights into self-assembling systems.