Model

For nCDA1Δ198-BE3, two strands of DNA can be edited. We assume that AGTAGTACG is an data editing unit (Figure 1a). The sequence state is represented by x. There are four values of x (Figure 1).rated our project.

Now we have a fixed sequence-editing unit composite sequence and an operation method f(x) that defines the sequence. How to use these to achieve data editing? Considering the limited number of editing units for each fixed sequence, the values that can be represented by such a composite sequence must be limited. In such a limited number of values changes is our goal. Considering the group in the mathematical definition, we can think that the finite number constitutes a group, and the process of editing corresponds to the closed binary operation of the group. Arbitrary editing is similar to error correction. The wrong value of the data is the element of the group, and it is an error correction process to modify the element into the correct one. Since the error value may be arbitrary, error correction editing is the editing algorithm we need. Therefore, we associate the principle of Reed Solomon coding. For Figure 2b, group G can be built:

• C : The value of fixed sequence;
• f(x_n) : The value of edit unit Xn. Each unit has four values;
• n : edit units in total;
• F : Final value of composite sequence

For a composite sequence with 8 states, G is a Galois field GF[2³]. At present, C can be assigned any value artificially. If C ∈ {0,1,2,3,4,5,6,7}, n=2, f(x₁,x₂) ∈ {0,1,2,3,4,5,6,7}, Defined under binary F = G⊕ f(x₁,x₂) It can be proved that F ∈ {0,1,2,3,4,5,6,7}, table 1 lists all cases.

For a C major within an octave, it contains eight values (C, D, E, F, G, A, B). Assigning each note of the C major scale a positive integer from 0 to 7 (the value of C) in turn, we can modify the pitch arbitrarily through a composite sequence of n=2. When it comes to Sharp,Flat, Staccato,Pizz and so on, we just need to increase the value of n and give meaning to the resulting F. For instance, n=3, f(x₃) =0 means ground state; f(x₃) =1 means sharp; f(x₃) =2 means ornaments; n=4, f(x₄)=0 means ground state; f(x₄)=1 means up an octive; f(x₄)=2 means down an octive.

This coding method has two sides.

Advantages:
• 1.This kind of coding has infinite potential. As long as there are enough editing units, the original information can be modified into any information.
• 2.The idea of Galois field is used in coding, which can ensure sufficient redundancy and self correction capability

Disadvantages:
• 1.The potential of coding is acquired at the expense of information density. In the above example, supposing that each unit needs 20 bp and the fixed sequence needs 10 bp, then a note needs to occupy at least 50 bp for storage. Such information density is unacceptable.
• 2.If the editing information is very complex, a lot of editing cells need to be reserved. This will lead to a substantial increase in the cost of DNA synthesis and a decrease in the efficiency of DNA utilization.

Based on the above problems, we try to maintain a balance between coding potential and information density. The second generation refers to Midi file format for music coding. This is an important engineering iteration of our project, which will be described in detail below.

Recalling the previous article, a large number of bases and their corresponding numbers are generated in multiple data units, while the actual information part is mainly the region after the <Rhythm type>. We can think of the actual information as stored values. The data in the edit window of matrix B is changed, which is similar to the pointer type in C language.

Let's suppose that a pointer was originally created to point to the original vector B. However, when data unit B is modified by foreign vector D, B changes and a new B ` is generated. So the original B data is abandoned, but our pointer does not point to the new data B `, but to the space left by the original B. At this time, in order to prevent errors, there are two methods: one is to clean up the pointer directly, so that the data unit will disappear forever, and the other is to create a new data unit to fill the original vacancy. You only need to create a new data unit at the position of the original vector B, and it can be considered that the unit has been completely changed. The original data is' invisible ', and we can no longer identify it. Although it remains in DNA, it can no longer be observed because there is no pointer to it.

When establishing a data structure, it is necessary to record the value D of each vector B. When the data structure needs to be changed, modify the position to be modified, as shown in the following figure:

Finally, when we need to read, we just need to read the value F (a) of B in order from small to large to get the complete data.
This has three main advantages:
1 The density of data has been greatly improved, and more modifications can be made in a single edit.
2 A chunk like data structure is adopted, which greatly ensures the independence of each module.
3 It has its own identification sequence, and its resolution has no great influence on the position of the DNA chain.

Disadvantages:
1 CRISPR editing technology itself may also edit bases outside the editing window, which may lead to data structure damage.
2 During modification, new DNA fragments need to be synthesized and linked to the original fragments. If a small amount of modification is made, the cost will be too high. Therefore, it is more suitable for use after a large number of modifications.

We first needed to transform the image Microvenus[5] into DNA sequence, in a way that can be edited by base editor. We used one 35bp base sequence to encode one pixel. In the 35bp sequence, “TAG” located on 1-3, “TGA” located on 10-12 and “NGG” located on 33-35 were the positioning sequences of information. When they were recognized by our decoding program from the sequencing results, the program regarded this DNA fragment to contain image information, then it proceeded to decode. The bases located on 4-5 represented the default color for this pixel, considering that our base editor might convert C to T or G to A on non-modifying sections, we set the rule when these two bases are both pyrimidines or purines, the pixel showed up as white; when one of them is pyrimidine and the other purine, the pixel showed up as black. Follow-up base sequences on 6-7 and 8-9 represented the row and column values of the pixel, this was designed to assure our encoding system can be used to store information on the genome scale: We were able to correctly locate each pixel encoded by each base sequence, even under the circumstance where a large number of gene rearrangements happen. Sequence on 13-32 was where gRNAs targeted on and our modifications took place, the modifying site consisted of 5bp and at least one C, we coded that for each one of the C edited, the color changed once. Last three bases on 33-35 functioned as the positioning sequence and the PAM locus, necessity for base editor to take effect.

After all the editing sites were successfully edited, we got the first image - "microvenus"

[1]C.E. Shannon. A mathematical theory of communication Bell Syst. Tech. J.,1948, 27, 379-423
[2]Heckel, R.; Mikutis, G.; Grass, R. N. A Characterization of the DNA Data Storage Channel. Sci Rep 2019, 9 (1), 9663. DOI: 10.1038/s41598-019-45832-6
[3]Organick, L.; Chen, Y. J.; Dumas Ang, S.; Lopez, R.; Liu, X.; Strauss, K.; Ceze, L. Probing the physical limits of reliable DNA data retrieval. Nat Commun 2020, 11 (1), 616. DOI: 10.1038/s41467-020-14319-8
[4]Church, G. M.; Gao, Y.; Kosuri, S. Next-generation digital information storage in DNA. Science 2012, 337 (6102), 1628. DOI: 10.1126/science.1226355
[5]Davis, Joe. Contemporary Art and the Genetic Code. Art Journal, vol. 55, no. 1,1996, pp. 70-74.