There were several matters that needed to be simulated, among them, the simulation was limited to the control of self-assembly. As a result, the simulation showed that it self-assembles.
The purpose of the simulation is as follows. "To investigate the size distribution of the assembled molecular robots in a situation where they are randomly floating in a liquid, and they repeatedly tentatively bind to each other based on their DNA strand.”
For the simulation, a 100*100 grid was prepared and the following assumptions were made.
•Each molecular robot or a set of molecular robots occupies one square equally.
•Each molecular robot moves randomly in one of the four directions at each timestep. When a molecular robot moves from one end to the other, it moves to the opposite square.
•The movement of the molecular robot is equally probable in all four directions.
•When squares overlap, it is regarded as a collision.
•Whenever a collision occurs, a set is assumed to occur.
•Deviation occurs in the form that for an assembly of two or more molecular robots, only one of them deviates from it.
•In the actual scheme, self-assembly is attempted using two types of mof complexes, one with a single-stranded mof complex A and the other with a complementary single-stranded mof complex B. In this simulation, however, for simplicity, it is assumed that all mof complexes have the same single strand and that they are mutually attached.
First, as a simulation for the experiment, we considered the self-assembly of a DNA strand with a length of 15 nt, a particle size of 10 nm, and a concentration of 4.75 nM.
From the analysis in Nupack, the temperature dependence in DNA binding is shown in the figure below. From this, we defined the rate of divergence as follows.
$q(t) = \frac{1}{1+exp((-0.5)*(T-65))}$
**T means Temperature.