In this design, we focus on two essential problems: 1. Is our design able to load cargo? 2. Is 8-17 DNAzyme still capable of multiple turnover in our new design? We subsequently answered the questions in the experiment.
Experiment & Results
- The staple strands and M13MP18 were annealed in PCR, and formed the origami container.
- We verified the multiple turnover of 8-17 in the logic gate. In the solution, we added 5μM substrate and 1μM 8-17. From Figure 29., we could notice that more than 1 uM substrate was cleaved, which represents the multiple turnover character.
Molecule Diffusion Process Modeling
We use modeling to simulate the diffusion of DNAzyme molecule. Because the diffusion is within an origami whose size is only several nanometers, we are not sure whether the diffusion process can be described accurately by the macroscopic law. As a result, we our model is based on the general random collision theory of molecule.
- The movement of DNAzyme molecule is primarily result from the random collision of molecule.
- Assume after each time interval of Δt，the DNAzyme will move forward or backward on each direction of x, y, z axis with the distance of Δl.
- The probability of moving backward and forward are all 0.5.
- The movement of the molecule in the three directions are independent
- Origami is rigid, and the molecule will be rebound if impinging on the wall of origami
- The total volume of the origami and outer space is the volume of the solution
- When the DNAzyme molecule moved to the boundary of the outer space, it will be rebound. (Since in each outer space of any origami, there are many other outer space closely aligned with it. The possibility of other molecule moved to the space is the same as the molecule in this space moved to the adjacent space.)
Symbols and Nomenclature
- NA: Avogadro's constant;
- Vout space: The volume of the space out of the origami;
- Vorigami: The volume of space of the origami;
- N: the number of origami volume in the outer space volume.
Model Estimation and Calculation
The calculation of the number of origami fills the outer space We have designed and synthetize origami with the length, width, height 36nm, 36nm and 42n. In a breaker of 500ml, there is 1μmol origami uniformly distributed in the breaker.
The volume of each origami can be calculated as follows
The number of out space contain the time of origami volume
So we suppose the initial location of the DNAzyme is in the center of the origami, in the following steps, the DNAzyme molecule will go randomly within the space, in each time interval Δt the molecule will move Δl forward or backward in X, Y, Z directions and the corresponding possibilities are all 0.5.
After a short while, we can distinguish the molecule within the origami from those outside the one and measure the probability of the molecule within the origami through a C++ program. You can also refer to the webpage of program illustration and download the C++ program.
Finally, the probability of the DNAzyme molecule going out of the origami is the same as that going into the origami, which means the concentration of origami out of the origami is the same as those within it. We can call the concentration of the final state the equilibrium concentration.
Result and Discussion
We can see from Figure 30. that the probability of the DNAzyme within the origami will decrease rapidly at the beginning. Finally, the value of the probability will approach to an equilibrium value. The time when reaching the equilibrium concentration is very minute (several microsecond).
There is a program used to describe the whole process, using which we can also change the geometry size of the origami and the outer space and study how the diffusion curves change.
This program is compiled with C++ language. Figure 32. is the screenshot of the program. When running the program, you need to enter the size of the bigger box (outer space) and the size of the origami. You need also enter the collision distance (step size) and the number of Δt. The program can be download here.