Sequencing information of coding gene and application thereof

Abstract

A computer-implemented method of representing a sequence of selected RNA and / or DNA nucleotides and / or nucleotide analogs, comprising the steps of: (a) defining a cube using nucleotide bases wherein each of the eight vertices of the cube is assigned to a nitrogenous base in a subset [A (adenine), C (cytosine), G (guanine), T (thymine)], wherein the nitrogen-containing bases T (thymine) and U (uracil) are understood here as equivalent and thus interchangeable, and wherein each vertex of the cube is assigned to a nucleotide base in the subset such that, for each vertex, the assigned base is directly linked by an edge to each other base type of the subset; (b) distributing the first nucleotide base of the selected nucleotide sequence to the vertex of the cube with the distributed nucleotide nitrogen-containing base type, and sequentially distributing each subsequent nucleotide of the selected nucleotide sequence to the corresponding vertex in the cube or the tetrahedron, the distributed vertex is directly connected with the vertex of the previous nucleotide base through the edge of the cube; wherein under the condition that the nucleotide basic group is the same as the previous nucleotide basic group, the nucleotide basic group is distributed to the vertex of the cube, which is the same as the vertex to which the previous nucleotide basic group is distributed; and wherein the sequence of the selected nucleotide and / or nucleotide analogue comprises a nitrogen-containing base selected from A (adenine), C (cytosine), G (guanine), T (thymine) and / or U (uracil).

Description

Technical Field

[0001] The present invention belongs to the field of bioinformatics, in particular to the field of genome information processing.

[0002] The present disclosure relates to novel methods for representing nucleotide sequences and uses of these representations. More specifically, the present disclosure relates to methods for representing nucleotide sequences in the form of cubes or tetrahedrons or in the form of matrices representing such cubes or tetrahedrons, methods for labeling sequences using such representations, methods for determining sequence variations, and methods for defining one or more markers in a nucleotide sequence, the markers being characterized by symmetry invariance. Background Art

[0003] Many fundamental laws of nature, such as conservation of energy, conservation of momentum, or the structure of spacetime in general relativity, are derived from the concept of symmetry (https: / / www.pnas.org / doi / pdf / 10.1073 / pnas.93.25.14256). Symmetric patterns were known to the Egyptians, but the mathematical structures behind the study of symmetries, a branch of abstract algebra known as group theory, were not discovered until the 19th century by Abel, Galois, and Lie. Since then, group theory has revolutionized the understanding of many scientific disciplines such as physics, chemistry, cryptography, information theory, and many others.

[0004] The use of symbolic representations (strings of characters) to describe biological sequences has helped us understand genes and genomes. However, the lack of a "grammar" associated with these symbols has hindered rigorous mathematical analysis of genetic information.

[0005] Therefore, there is a need for better representation of biological sequences to enable mathematical analysis of genetic information, including exploitation of symmetries. Summary of the invention

[0006] A first aspect of the present invention relates to a computer-implemented method for representing a nucleotide sequence. The method comprises the steps of:

[0007] a) defining a cube or tetrahedron using nucleotide bases, wherein each vertex of the cube or tetrahedron is assigned a nucleotide base, wherein each vertex is assigned a nucleotide base such that for each vertex, the assigned base is directly connected to every other base type by an edge,

[0008] b) from a selected nucleotide sequence, the nucleotide sequence comprising nucleotides from one of the nucleotide subsets [A, C, G, T] or [A, C, G, U], assigning a first nucleotide base of the selected nucleotide sequence to a vertex to which the nucleotide base type has been assigned, and sequentially assigning each subsequent nucleotide of the selected nucleotide sequence to a corresponding vertex in a cube or tetrahedron, such that the assigned vertex is either directly connected to the vertex of the previous nucleotide base through an edge of the cube or tetrahedron, respectively, or, in the case where the nucleotide base is the same as the previous nucleotide base, the nucleotide base is assigned to the same vertex as the vertex to which the previous nucleotide base is assigned; and

[0009] c) determining, for each vertex of the cube or tetrahedron, the number of nucleotides assigned to the vertex of the cube or tetrahedron, respectively.

[0010] In a preferred embodiment, the first nucleotide is assigned to its corresponding vertex in a predetermined initial face of a cube or tetrahedron.

[0011] In a more preferred embodiment in which the nucleotide sequence is represented in the form of a cube, the predetermined initial face is a face comprising the nucleotide bases in the order of GATC or GAUC in a clockwise direction.

[0012] In a more preferred embodiment, the nucleotide sequence is further represented in the form of a matrix. The method also includes:

[0013] d) assigning each vertex of the cube or tetrahedron to an element of a matrix having at least as many elements as there are vertices of the cube or tetrahedron; and

[0014] e) Assigning the total number of nucleotide bases assigned to each vertex of the cube or tetrahedron as the value of the assigned element of the matrix.

[0015] In a preferred embodiment of the matrix representation embodiment, the matrix is ​​a square matrix, and preferably wherein the vertices of a cube or tetrahedron are represented by elements on the matrix diagonal. More preferably, when the nucleotide sequence is represented in the form of a cube, the square matrix is ​​preferably a 4×4 matrix.

[0016] In a preferred embodiment of the matrix representation embodiment, the nucleotide sequence is represented in the form of a cube, and wherein the vertices of the cube are assigned to the matrix by a three-dimensional projection of the cube onto a two-dimensional Euclidean plane, thereby defining internal nucleotide base sets and external nucleotide base sets, each nucleotide base set representing an opposite face of the cube, preferably wherein the projection axis is an axis perpendicular to the predetermined initial face.

[0017] In a preferred embodiment of any embodiment of the first aspect of the present invention, the received nucleotide sequence further comprises information indicating the 5' end and the 3' end of the sequence, and wherein the nucleotides are sequentially assigned to bases in a cube or tetrahedron in the 5'→3' direction.

[0018] A second aspect of the present invention relates to a computer-implemented method for labeling a nucleotide sequence by encoding the nucleotide sequence in the form of a matrix by any matrix representation method embodiment according to the first aspect of the present invention.

[0019] A third aspect of the present invention relates to a computer-implemented method for determining a nucleotide sequence modification. The method comprises the steps of:

[0020] a) calculating a matrix representation of the sequence according to any matrix representation method embodiment of the first aspect of the invention from at least one selected nucleotide sequence representing the template sequence and at least one selected nucleotide sequence representing at least one nucleotide sequence to be varied,

[0021] b) individually comparing identical matrix elements of the matrix representation of at least one template sequence with at least one sequence for which variation is to be determined, and

[0022] c) When any of the identical matrix elements are not equal, it is determined that a change occurs between at least one template sequence and at least one sequence to be determined to be changed.

[0023] Alternatively, the method comprises the steps of:

[0024] a) calculating a matrix representation of the first sequence and the second sequence from at least one selected nucleotide sequence representing the template sequence and at least one selected sequence representing the nucleotide sequence of at least one variation to be determined, according to any matrix representation method embodiment of the first aspect of the invention, wherein the matrix is ​​a square matrix,

[0025] b) computing the determinant of the matrix representation of the sequence in step a),

[0026] c) comparing the determinants of the matrix representations of at least one template sequence and at least one sequence for which a change is to be determined, and

[0027] d) When the determinants of step c) are not equal, determining that a change has occurred between at least one template sequence and at least one sequence to be determined to be changed.

[0028] In a preferred embodiment, the change is one or more of a SNP, a nucleotide insertion, a nucleotide deletion or a nucleotide transposition.

[0029] In a more preferred embodiment of any embodiment of the third aspect of the present invention, the method further comprises determining that the integrity of the biological sequence is disrupted when a change is determined to exist in the sequence.

[0030] A fourth aspect of the invention relates to a computer-implemented method for defining one or more markers in a nucleotide sequence, the markers being characterized by symmetry invariance, the method comprising the steps of:

[0031] a) receiving a nucleotide sequence;

[0032] b) Select a portion of the sequence to be analyzed, whose base length is an integer square n 2 ;

[0033] c) Set the base length to n 2 The sequence is split into n segments of length n;

[0034] d) assembling the sequences into an n×n matrix;

[0035] e) computing several transformations of the matrix using one or more symmetries until all feasible transformations for each selected symmetry are exhausted;

[0036] f) determining the matrix elements that are invariant under all transformations for each selected symmetry; and

[0037] g) designating the invariant elements of the matrix as invariant markers;

[0038] h) Repeating steps a) to g) using another portion of the sequence, preferably by sliding the start of the sequence to be analyzed by one or more nucleotides, until all of the sequence has been analyzed.

[0039] In a preferred embodiment, the one or more symmetries include rotational symmetry and / or mirror symmetry.

[0040] In another preferred embodiment, n is an odd number, preferably a prime number, and more preferably greater than or equal to 5.

[0041] A fifth aspect of the present invention relates to a computer program product comprising instructions which, when executed by a processor, cause the computer to perform the steps of any method according to the first, second, third and / or fourth aspects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to better understand the present disclosure and explain how to put it into practice, reference is now made to the attached schematic diagram by way of example only, in which:

[0043] Figure 1Shown are list representations, triangle representations, square representations, and matrix representations of nucleotide sequences according to one or more embodiments, along with the strand orientation of each representation.

[0044] Figure 2 A shows a non-redundant tetranucleotide substitution of the GATC alphabet.

[0045] Figure 2 B shows non-redundant trinucleotide substitutions of the GATC alphabet.

[0046] Figure 3 Shown is how six copies represented by squares form a nucleotide cube according to one or more embodiments.

[0047] Figure 4 It is shown how four copies represented by triangles form a nucleotide tetrahedron according to one or more embodiments.

[0048] Figure 5 A shows a cube of nucleotide bases according to one or more embodiments.

[0049] Figure 5 B shows a schematic diagram of a Figure 5 The square of A's cube represents the expansion.

[0050] Figure 5 C shows the Figure 5 The square of B represents the expanded nucleotide rhombicuboctahedron.

[0051] Figure 6 The relationship of a cube to an octahedron through a rhombicuboctahedron is shown in accordance with one or more implementations.

[0052] Figure 7 A shows a perspective view of a gene cube according to one or more embodiments.

[0053] Figure 7 B shows a plan view of a gene cube according to one or more embodiments.

[0054] Figure 7 C shows another plan view of a gene cube distinguishing between internal and external nucleotide sets according to one or more embodiments.

[0055] Figure 8 A shows an example of a nucleotide sequence according to one or more embodiments.

[0056] Figure 8 B shows an example of a cube definition using nucleotide bases and the Figure 8 Example of the assignment of the nucleotide sequence of A to the vertices of a cube.

[0057] Figure 8 C shows an isometric three-dimensional projection of a cube according to one or more embodiments and Figure 8 Sequential assignment of B's ​​cube.

[0058] Figure 8 D shows Figure 8 A series and Figure 8 Matrix representation of the cube representation of B and 8C.

[0059] Fig. 9 An example of a matrix encoding of a larger nucleotide sequence is shown in accordance with one or more embodiments.

[0060] Fig.10 An example of the sensitivity of matrix encoding to small changes is shown in accordance with one or more embodiments.

[0061] Fig.11 A schematic diagram illustrating a process for determining invariant markers in a nucleotide sequence according to one or more embodiments is shown.

[0062] Fig.12 An example of a process for determining invariant markers in a nucleotide sequence according to one or more embodiments is shown.

[0063] Fig.13 A schematic diagram of a computer-implemented product according to one or more embodiments is shown.

[0064] Fig.14 A schematic diagram of the use of a TISA deconvolution matrix (TDM) according to one or more embodiments is shown.

[0065] Fig.15 A schematic diagram showing an example of how a TISA deconvolution matrix (TDM) may be constructed in accordance with one or more implementations.

[0066] Fig.16 A diagram showing an example of how to decode a TISA deconvolution matrix (TDM) according to one or more embodiments. DETAILED DESCRIPTION

[0067] definition

[0068] The term "symmetric group" refers to a group whose elements are bijections from a set to itself and whose group operations are combinations of functions. In the specific case of the present invention, the finite symmetric group S4 defined on a finite set of 4 symbols consists of permutations that can be performed on 4 symbols. Since there are n! (n factorial) such permutation operations, the order (number of elements) of the symmetric group S4 is 4! = 24.

[0069] The term "dihedral group" refers to the group formed by different rotational and reflection symmetries of regular polygons with n sides. There are n rotational symmetries and n reflection symmetries. The dihedral group D4 is the symmetry group of the square.

[0070] The term "alternating group" refers to the group of even permutations of a finite set. The alternating group on a set of n elements is called the n-ary alternating group, or the alternating group on n letters, denoted An or Alt(n).

[0071] The term "genocube" refers to a cube in which each nucleotide is represented twice, at diagonally opposite vertices of the cube.

[0072] describe

[0073] In this work, we explore whether biological sequences encoded by genes and genomes contain symmetries that can be resolved using the mathematical power of abstract algebra and group theory. It is hypothesized that the apparent opposition between symmetric and evolutionary transformations may actually represent two different manifestations of the same phenomenon. It is first noted that changes in nucleotide sequences (i.e. mutations) can be simulated by mathematical rearrangements (i.e. permutations) of ordered sets of nucleotides.

[0074] Although this work focused on the four letters used in DNA, the findings and methods described here can be easily extended to any 4-letter nucleotide alphabet, such as the RNA alphabet or other 4-letter alphabets of varying nucleotides. Figure 1 As shown, the four letters of DNA can be represented in several different ways, such as linear (A), circular (B and C), and tabular (D). These representations are equivalent in terms of information, as any polynucleotide can be represented in these three models, but their symmetries vary. However, when examined under the prism of symmetry, representations B, C, and D exhibit some unique properties. The "tabular representation" contains no a priori symmetry (except for repetitive sequences, monotonic sequences, and / or palindromic sequences). The "equilateral triangle representation" exhibits 6th-order dihedral symmetry. Both the "square representation" and the "matrix representation" exhibit 8th-order dihedral symmetry, but show different chain orientations (antiparallel vs. parallel).

[0075] Since biological sequences (including gene sequences) are linear polymers of consecutive nucleotides, the substitution of GATC was studied. Figure 2 As shown, by systematically analyzing n-permutations (n ​​is 2 to 12), we surprisingly find that the permutation groups generated by 3- and 4-permutations of GATC contain the same number of elements (24). This observation can be explained by the so-called symmetry group S nThe existence of a universal mathematical structure of , which describes the number of possible permutations associated with a set of n elements, namely n! . In the example in this article, the number of non-redundant 4-permutations of GATC is obtained by calculating 4! = 4 × 3 × 2 × 1 = 24. Similarly, the number of non-redundant 3-permutations of GATC is obtained by the probability formula 4 × 3 × 2 = 24. These two sets have a bijective relationship with the symmetry group S4 and are therefore isomorphic to this group. Since group S4 is isomorphic to the symmetry group of the cube, this result establishes a one-to-one and surjective correspondence between the 3-nucleotide permutation group and the 4-nucleotide permutation group and the symmetry group of the cube. If we number the vertices of the cube from 1 to 4, and the opposite vertices are given the same number, the permutation corresponding to the symmetry can be read from one of the faces.

[0076] Also of interest is that the S4 group can be decomposed into three finite subgroups: (i) the dihedral group D3, which is isomorphic to the symmetry group of the triangle, (ii) the dihedral group D4, which is isomorphic to the symmetry group of the square, and the alternation group (A4), which is isomorphic to the symmetry group of the regular tetrahedron. From a biological perspective, the existence of these group isomorphisms means that any nucleotide sequence consisting of 3-permutations and 4-permutations of the {G,A,T,C} alphabet can be represented as a unique path through the vertices of a tetrahedron or cube.

[0077] refer to Figure 3 , it can be seen that when described using the "square representation", the 24 non-redundant tetranucleotide substitutions of the GATC alphabet are divided into three subsets of 8 different substitutions. Each subset contains 8 dihedral symmetries corresponding to the symmetry group D4. This group has 8 elements, namely: an identity element (ID), three rotational symmetries (R1 to R3), and three mirror symmetries (M1 to M4). More interestingly, when represented twice, these 48 substitutions form a cube (called a gene cube), in which each nucleotide is represented twice at opposite vertices of the gene cube. This representation is advantageous because any nucleotide sequence can be represented on such a gene cube. The resulting group (two copies of S4) is isomorphic to the 48-order octahedral symmetry group (O h ), the group consists of permutations (S4) and cycles Combination of subgroups )composition.

[0078] The same reasoning is carried out for the set of 3-permutations. Figure 4As shown, the 24 non-redundant 3-permutations of GATC can be represented by placing a single nucleotide at each vertex of an equilateral triangle, i.e., the “triangle representation”. The resulting action classifies all 3-permutations into 4 subsets (6×4=24) of 6 different permutations, each corresponding to the symmetry of the dihedral group D3 that represents the symmetry group of equilateral triangles. This group has 6 elements, namely: an identity element (ID), two rotational symmetries (R1 to R2), and three reflection mirror symmetries (M1 to M3). This discovery allows us to assemble the resulting equilateral triangles into regular tetrahedrons, which, as observed in the gene cube, have the property of representing any nucleotide sequence (DNA, RNA, or a sequence including modified nucleotides) at its vertices.

[0079] The GATC's 24 non-redundant permutations only cover the types of words that can be replaced with redundant 3-letter codes (4 3 = 24 of 64 possible characters) or a 4-letter code (4 4 = 24 of the 256 possible characters). We note that this obstacle can be overcome because the geometry of the cube (see Figure 5 A and Figure 5 B) Create a multiplicity of the original nucleotide at each vertex (see Figure 5 Example of a triplet of A and T shown in C). Therefore, by simply expanding the faces of the gene cube, the 24 non-redundant 3-permutations and 4-permutations of the GATC alphabet can be expanded to cover any redundant permutations (e.g. AAA, GAA, TTT, AAAA, GAAA, ATTT, etc.). This leads to the generation of three copies of the letters present in each vertex of each square. Once connected, this transforms the cube into a new shape, intermediate between a cube and an octahedron, called a rhombicuboctahedron. This rhombicuboctahedron can represent any of the 64 triplets that make up the genetic code. This observation is supported by the mathematical property of "duality", which transforms the cube topologically into a regular octahedron by expanding triangles at each vertex of the cube. As Figure 6 As shown, a rhombicuboctahedron can be converted to a regular octahedron by eliminating the squares at each vertex of the triangles. Conversely, an octahedron can be converted to a rhombicuboctahedron by blowing out squares at each of its vertices. It should be noted that the regular octahedron has 24 rotational (or orientation preserving) symmetries, for a total of 48 symmetries. These symmetries include transformations that combine reflections and rotations. The cube has the same set of symmetries, as it is the dual polyhedron of the octahedron.

[0080] Using this dual model, it is possible to represent non-redundant permutations on a cube and / or tetrahedron and locally / temporarily extend this geometry to represent the remaining redundant permutations. In summary, we hypothesize that this new representation will have a profound impact on the general understanding of the nature, structure, and evolution of the genetic code and genetic information.

[0081] Therefore, we describe here a new method to compactly represent nucleotide sequences as unique virtual paths along the vertices of a cube or tetrahedron.

[0082] A first aspect of the present invention relates to a computer-implemented method for representing a nucleotide sequence. The method comprises the following steps:

[0083] a) Define a cube or tetrahedron using nucleotide bases so that each vertex of the cube or tetrahedron is assigned a nucleotide base. Each vertex is assigned a nucleotide base so that for each vertex, the assigned base is directly connected to each other base type through an edge. Therefore, when deciding which nucleotide base to assign to a vertex, the base of the vertex directly connected to the vertex through an edge must be considered and a different nucleotide base from the directly connected vertices is assigned. Since each vertex is directly connected to three other vertices through an edge, after the cube or tetrahedron definition is completed, any vertex of interest will be directly connected to three vertices through an edge, wherein these three vertices have different bases assigned to them and are connected to the base assigned to the vertex of interest.

[0084] It should be noted that when a nucleotide sequence is represented in the form of a cube, each nucleotide base type is represented twice, at diagonally opposite vertices of the cube. Advantageously, this allows any nucleotide sequence to be represented on such a cube, since in all cases each subsequent nucleotide base can be assigned to the same vertex as the vertex to which the previous nucleotide base was assigned, or to a vertex directly connected to the vertex to which the previous nucleotide base was assigned, since each vertex is directly connected to each of the other base types via edges.

[0085] b) from a selected nucleotide sequence comprising nucleotides from one of the nucleotide subsets [A, C, G, T] or [A, C, G, U], assigning a first nucleotide base of the selected nucleotide sequence to a vertex to which the nucleotide base type has been assigned, and sequentially assigning each subsequent nucleotide of the selected nucleotide sequence to a corresponding vertex in a cube or tetrahedron, such that the assigned vertex is either directly connected to the vertex of the previous nucleotide base through an edge of the cube or tetrahedron, respectively, or, in the case where the nucleotide base is the same as the previous nucleotide base, the nucleotide base is assigned to the same vertex as the vertex to which the previous nucleotide base has been assigned.

[0086] It is important to note that thus, DNA, RNA, or any sequence of the set of four modified nucleotides can be represented. It is also important to note that a tetrahedron has only four vertices, so each vertex is assigned a different nucleotide base. Therefore, the first nucleotide is assigned to the only vertex that has that nucleotide base type assigned. However, in the case of a cube, there are 8 vertices, so for each nucleotide base, there are two vertices that have that nucleotide base type assigned. Therefore, the first nucleotide base of a nucleotide sequence can be assigned to either of the two vertices that have that nucleotide base type assigned.

[0087] c) determining for each vertex of the cube or tetrahedron, respectively, the number of nucleotides assigned to the vertex of the cube or tetrahedron. Thus, a cubic or tetrahedral representation of the nucleotide sequence is obtained, wherein each vertex of the cube or tetrahedron has a determined value.

[0088] According to a preferred embodiment in which the nucleotide sequence is represented in the form of a cube or a tetrahedron, the first nucleotide is assigned to its corresponding vertex in the predetermined initial face of the cube or tetrahedron. Advantageously, having a predetermined initial face in the cube solves the redundancy problem of the number of vertices for distributing nucleotide base types. By setting up a predetermined face, a consistent representation of any sequence in the form of a cube can be achieved. It should be noted that this will not occur on a tetrahedron because a tetrahedron has only one vertex to distribute the first nucleotide base, so there is no redundancy.

[0089] In another preferred embodiment, when the nucleotide sequence is represented in the form of a cube, the predetermined initial face is a face comprising nucleotide bases in the order of GATC or GAUC in a clockwise direction. Advantageously, this provides a consistent selection of the predetermined initial face.

[0090] In order to further utilize the characteristics of this encoding, a matrix representation of the gene cube can be designed. In a preferred embodiment of any of the aforementioned embodiments, the nucleotide sequence is further represented in the form of a matrix. Advantageously, representing the nucleotide sequence in the form of a matrix enables the use of different matrix tools in the representation of the nucleotide sequence. Therefore, preferably, the method further comprises the steps of:

[0091] d) assigning each vertex of the cube or tetrahedron to an element of a matrix having at least as many elements as the vertices of the cube or tetrahedron. In the case where the nucleotide sequence is represented in the form of a tetrahedron, each vertex of the tetrahedron is assigned to an element of a matrix having at least 4 elements. In the case where the nucleotide sequence is represented in the form of a cube, each vertex of the tetrahedron is assigned to an element of a matrix having at least 8 elements.

[0092] e) assigning the total number of nucleotide bases assigned to each vertex of the cube or tetrahedron as the value of the assigned element of the matrix. Thus, a matrix representing the nucleotide sequence is obtained, which contains at least the number of nucleotides at each vertex of the cube or tetrahedron.

[0093] From here on, the matrix representing the vertices of the gene cube may be referred to as TISA (Topologically Invariant Sequence Array). It should be noted that in the context of the present invention, the expression topologically invariant means that the sequence identity remains unchanged through various transformations and / or representations, i.e. the matrix is ​​just another representation of the amino acid sequence.

[0094] It should be noted that several designs can be foreseen when assigning the vertices of a cube or tetrahedron to a matrix, because multiple choices can be made when deciding how to assign the vertices to each element in the matrix representing the vertices. For example, in the case where the nucleotide sequence is represented in the form of a tetrahedron, a matrix containing at least 4 elements can be shaped as at least (column-binned) a 4×1, 2×2 or 1×4 matrix. In the case where the nucleotide sequence is represented in the form of a cube, the number of matrix sizes can be expanded. In addition, multiple matrix designs can meet the requirement of containing at least as many elements as the vertices of the cube or tetrahedron. Therefore, in the case where the nucleotide sequence is represented in the form of a cube, a 4×4 matrix can be used to represent the sequence, wherein half of the elements (8) of the matrix are assigned to the cube vertices, while the other half of the elements (8) are not assigned to the cube vertices.

[0095] In a more preferred embodiment, the matrix is ​​a square matrix. Advantageously, a square matrix has further properties, such as the determinant can be calculated.

[0096] In a more preferred embodiment, when the nucleotide sequence is represented in the form of a cube, the sequence is represented by a 4×4 matrix. In an even more preferred embodiment, the vertices of the cube or tetrahedron are represented on the elements on the diagonal of the matrix. Advantageously, this ensures that the matrix determinant will not be 0 whenever the sequence wraps around all the vertices of the cube at least once. In another even more preferred embodiment, when the nucleotide sequence is represented in the form of a cube, the cube vertices are assigned to a 4×4 square matrix, wherein the vertex values ​​are assigned to its diagonal elements.

[0097] like Figure 7 A cube can be represented using an isometric three-dimensional projection, or as Figure 7 B, projected onto the 2D Euclidean plane. Of interest, the 2D projection transforms the cube into a planar graph that defines the external and internal nucleotide base sets (e.g. Figure 7 C), where the outer set of nucleotides is highlighted. This property is interesting because it mimics the inherent polarity of polynucleotide sequences.

[0098] In a more preferred embodiment of any of the foregoing preferred embodiments in which the nucleotide sequence is represented in the form of a cube, the vertices of the cube are assigned to the matrix by a three-dimensional projection of the cube onto a two-dimensional Euclidean plane, thereby defining an internal set of nucleotide bases and an external set of nucleotide bases, each representing an opposite face of the cube. Advantageously, this allows the cube to be consistently represented in the form of a 4×4 square matrix, wherein the vertex values ​​are assigned to the diagonal elements of the square matrix, such as Figure 8 D. More preferably, the projection axis is a projection axis perpendicular to a predetermined initial surface.

[0099] In each nucleotide sequence, a 5' end and a 3' end can be defined. In another preferred embodiment of any of the aforementioned embodiments, the received nucleotide sequence also includes information indicating the 5' end and the 3' end of the sequence, and wherein the nucleotides are sequentially assigned to the bases in a cube or tetrahedron in a 5'→3' direction. Advantageously, this further prevents the possibility of obtaining two different representations of the same sequence when the starting end is not considered. It should be noted that, alternatively, the nucleotides can be sequentially assigned to the bases in a cube or tetrahedron in a 5'→3' direction.

[0100] Given a specific nucleotide sequence, the nucleotide sequence can be marked so that it can be easily identified in other sequences. The representation method described herein by a matrix can be used as a way to mark a sequence. Therefore, a second aspect of the present invention relates to a computer-implemented method for using a matrix to represent a marked sequence by encoding the nucleotide sequence in the form of a matrix according to any method described in the first aspect of the present invention.

[0101] A third aspect of the present invention relates to a computer-implemented method for determining nucleotide sequence variations. Deep sequencing, human genome polymorphism or pan-genome studies are activities that require processing of large amounts of nucleotide sequences. In the process of processing, exchanging or storing this information, errors may occur and threaten the quality of the conclusions extracted from this data. Fig.10 As shown in Example 2, the TISA matrix is ​​extremely sensitive to sequence changes. In fact, any change, even a small change (SNP), will change the winding path of the sequence under consideration, and will therefore change the structure of the TISA matrix and the results of its determinant. Similarly, TISA can be used to represent and score genetic mutations between related or unrelated sequences.

[0102] The computer-implemented method for determining nucleotide sequence changes comprises the following steps:

[0103] a) calculating a matrix representation of the sequence according to any method of the first aspect of the invention from at least one selected nucleotide sequence representing a template sequence and at least one selected sequence representing at least one nucleotide sequence for which a change is to be determined, wherein the nucleotide sequence is represented in the form of a matrix. Preferably, the template sequence is the expected sequence of the sequence for which a change is to be determined.

[0104] b) individually comparing identical matrix elements of the matrix representations of at least one template sequence and at least one sequence to be determined for variation. Identical matrix elements of each matrix are elements located at the same position (ie, column and row) of the represented matrix.

[0105] c) When any of the identical matrix elements are not equal, it is determined that a change occurs between at least one template sequence and at least one sequence to be determined to be changed.

[0106] It is important to note that although a perfect palindrome and a sequence with the same 5->3' and 3'-5' composition will have the same TISA signature, there must be a change between the first and second sequences as long as any of the identical matrix elements are not equal.

[0107] Alternatively, the computer-implemented method for determining nucleotide sequence variations comprises the following steps:

[0108] a) calculating a matrix representation of the sequence according to any method of the first aspect of the present invention from at least one selected nucleotide sequence representing a template sequence and at least one selected sequence representing at least one nucleotide sequence for which a change is to be determined, wherein the nucleotide sequence is represented in the form of a square matrix. Preferably, the template sequence is the expected sequence of the sequence for which a change is to be determined.

[0109] b) Compute the determinant of the matrix representation of the sequence.

[0110] c) comparing the determinants of the matrix representations of at least one template sequence and at least one sequence for which a change is to be determined.

[0111] d) When the determinants of step c) are not equal, determining that a change has occurred between at least one template sequence and at least one sequence to be determined to be changed.

[0112] Similarly, it is important to point out that although perfect palindromes and sequences with the same 5->3' and 3'-5' composition will have the same TISA signature, and it is extremely unlikely that two completely different matrices will have the same determinant, there will definitely be changes between the first and second sequences as long as the determinants are not equal.

[0113] Advantageously, using determinants instead of equivalent elements of the TISA matrix further simplifies the comparison process and can further compress relevant information by assigning only a determinant to each sequence.

[0114] In a preferred embodiment of any embodiment of the third aspect of the present invention, the change is one or more of SNP, nucleotide insertion, nucleotide deletion or nucleotide transposition. As shown in Example 2, in the process of storing / recovering or exchanging nucleotide sequences through the network, nucleotide insertion, nucleotide deletion or nucleotide transposition will produce different TISA matrices.

[0115] Therefore, in another preferred embodiment of any embodiment of the third aspect of the present invention, the method further comprises the step of determining that the integrity of the biological sequence is compromised when a change is present in the determined sequence. As also shown in Example 2, the TISA matrix representation is a good checksum system because any change caused by information loss, noise, or error will produce a different TISA matrix, so when the biological sequence is compromised, it can be determined by comparing the current TISA matrix with the previous matrix or the current determinant with the previous determinant.

[0116] After discovering the symmetry laws in the DNA alphabet, the existence of nucleotides or sequences that remain unchanged in symmetry transformations was analyzed. For this purpose, the RIP, MIP, and RMIP methods were designed, which stand for the invariant pattern (IP) of rotation (R), mirror image (M), or rotation + mirror image (RM), respectively. Fig.12 The principles of all these methods are illustrated using RIP, but MIP and RMIP are similar (the only change is the nature of the symmetry applied).

[0117] A fourth aspect of the present invention relates to a computer-implemented method for defining one or more markers in a nucleotide sequence, the markers being characterized by symmetry invariance. The method comprises the following steps:

[0118] a) receiving a nucleotide sequence comprising nucleotides from one of the nucleotide subsets [A, C, G, T] or [A, C, G, U]. It should be noted that any sequence of DNA, RNA or the set of four modified nucleotides can be represented.

[0119] b) Select a part of the sequence as the window to be analyzed, whose base length is an integer square n 2 It should be noted that the base length of the nucleotide sequence must be at least n 2 This can be done in Fig.11 as seen in step 1.

[0120] c) Set the base length to n 2 The sequence is split into n fragments of length n. It should be noted that the sequence is split into n fragments so that the first nucleotide of each fragment is a consecutive nucleotide of the last nucleotide of the previous fragment.

[0121] d) Assembling the sequences into an n×n matrix. The matrix is ​​preferably assembled by placing each sequence fragment as a row of the matrix and placing consecutive fragments in consecutive rows. However, it should be noted that other obvious assembly strategies can be used, such as placing the fragments as columns or using other distributions of the fragments. This can be done in Fig.11 as shown in step 2.

[0122] e) Computing several transformations of the matrix using one or more symmetries until all feasible transformations for each chosen symmetry are exhausted, which can be done in Fig.11 as shown in step 3.

[0123] f) Determine the matrix elements that are invariant in all transformations for each selected symmetry. To this end, compare identical matrix elements in each matrix symmetry and thus determine the elements that are invariant in all transformations. This can be done in Fig.11 as seen in steps 4 and 5.

[0124] g) Designate the invariant elements of the matrix as invariant markers.

[0125] h) repeating steps a) to g) using another portion of the sequence, preferably by sliding the start of the sequence to be analyzed by one or more nucleotides, until all of the sequence has been analyzed. Fig.11 as shown in step 6.

[0126] The RIP method and its derivative variants (MIP and RMIP) are advantageous because they can identify and distinguish markers and genetic markers in a single nucleotide sequence in the absence of any polymorphism. Therefore, the RIP, MIP and RMIP methods are suitable tools for studying the structure, function and evolution of genes and genomes.

[0127] In another preferred embodiment, one or more symmetries are any one of rotational symmetry and / or mirror symmetry. As shown in Example 3, the square matrix has several rotational symmetries and mirror symmetries. It should be noted that for the square matrix having three rotational symmetries (see Fig.11 ) and four types of mirror symmetry (across each diagonal and across the middle rows and columns), and any combination of rotational symmetry and / or mirror symmetry can be applied.

[0128] Interestingly, the number of invariant markers is a multiple of the number of transformations applied, and optionally there is also an invariant marker corresponding to the center of rotation. Fig.12 In RIP, the number of invariant markers is a multiple of 4, because of the 3 rotations + the identity element (rotation center).

[0129] In a preferred embodiment of any embodiment of the fourth aspect of the present invention, n is preferably an odd number n, more preferably a prime number, and more preferably greater than or equal to 5. It should be noted that when n is an odd number, the matrix will be centered on the nucleotide, so an invariant element will always be found in the central element (n / 2, n / 2) of the matrix. This element should not be regarded as a marker.

[0130] Since RIP, MIP and RMIP can process any biological sequence (nucleotides, proteins, epigenetic markers, sugars, etc.), they are an option for studying genotypes, phenotypes and biological traits. In fact, like previously described markers (e.g. SNPs, RFLPs, mass spectrometry features, etc.), they can be used to establish the association between the presence or absence of a given invariant marker and a given biological trait related to health prevention, disease detection, breeding, population studies, etc.

[0131] The presence or absence of invariant markers and patterns of invariant markers may be associated with a physiological condition. In addition, there may be a correlation between the presence or absence of one or more potential biomarkers on one or more n×n matrices and the expression of a given genotype, phenotype, or biological trait. Therefore, if a strong correlation is found, the invariant markers can be used to indicate a physiological condition and / or the expression of a given genotype, phenotype, or biological trait.

[0132] The computer-implemented method of any of the foregoing embodiments of the first, second, third and / or fourth aspects of the invention may be performed on any suitable computing system comprising one or more processing units, such as a microprocessor, a GPU, a CPU, a multi-core processor or the like, a server or a distributed computing system such as a cloud.

[0133] A fifth aspect of the present invention relates to a computer program product comprising instructions which, when executed by a processor, cause a computer to perform the steps of any method according to the first, second, third and / or fourth aspects of the present invention. The computer program product may be implemented in hardware and / or software.

[0134] Fig.13 A computer program product 100 for implementing the method disclosed in this document is shown, which can be implemented in software, hardware, or a combination of the two. The module can be stored in the memory of the system, or can be stored remotely, such as in a remote server or distributed computing system that is communicatively connected to the system. The memory can include one or more of the following: a volatile or non-volatile memory device (such as DRAM, SRAM), flash memory, read-only memory, ferroelectric RAM, hard drive, floppy disk, tape, optical disk, or the like.

[0135] In some embodiments, the module may include a representation module 110 configured to represent the nucleotide sequence as a cube or a tetrahedron, optionally as a matrix according to any embodiment of the first aspect of the present invention.

[0136] In some embodiments, the module may include a labeling module 120 for assigning a matrix to a nucleotide sequence by receiving a matrix representing a nucleotide sequence from a representation module 110 according to the second aspect of the invention and assigning it to the nucleotide sequence.

[0137] In some embodiments, the module may include a variation determination module 130 configured to determine a variation in a nucleotide sequence by comparing the nucleotide sequence to a template sequence according to any embodiment of the third aspect of the present invention.

[0138] In some embodiments, the module may include a transformation module 140 configured to obtain a matrix resulting from performing a symmetric transformation on a square matrix.

[0139] In some embodiments, the module may include an invariance determination module 150 configured to superimpose the original matrix and the transformed matrix from the transformation module and calculate the matrix elements (same row and same column) that are equal in all matrices.

[0140] On the other hand, Fig.14 As shown in the example in , TISA matrices are particularly beneficial for supporting the exchange and analysis of large amounts of genomic information between two remote locations. They provide a fast, powerful, flexible, and lightweight data structure that can be easily exchanged over telecommunication networks such as the Internet, wide area networks (WANs), local area networks (LANs), satellite networks, mobile phone networks, etc. The TISA matrix is ​​a compact and convolutional representation of genomic information that carries only a small fraction of the weight of the transmitted information (in bits, typically well below 1% of the original weight). When considered together with a secondary matrix called the TISA deconvolution matrix (TDM), the TISA matrix can be easily decoded to extract the original genomic information in a lossless manner. This communication scheme does not violate the Shannon Information Theorem, as the amount of information contained in the sum of the TISA+TDM matrices is greater than or equal to the calculated Shannon entropy.

[0141] Fig.15 An example is given to illustrate how to construct a TDM matrix.

[0142] on the other hand, Fig.15D represents a typical deconvolution TDM matrix. In this configuration, the position and location of each nucleotide of the original sequence can be retrieved by dividing each TDM individual number (Gf, Af, Tf, Cf, Gb, Ab, Tb, Cb) by its corresponding prime number. Only one of the 8 possible numbers (Gf, Af, Tf, Cf, Gb, Ab, Tb, Cb) is divisible by this prime number, indicating its position on the gene cube.

[0143] Therefore, a sixth aspect of the present invention relates to a computer-implemented method for representing a sequence of selected RNA nucleotides and / or DNA nucleotides and / or nucleotide analogs, comprising the following steps:

[0144] a) defining a cube using nucleotide bases, wherein each of the eight vertices of the cube is assigned to a nitrogenous base from the subset [A (adenine), C (cytosine), G (guanine), T (thymine)], wherein the nitrogenous bases T (thymine) and U (uracil) are understood herein to be equivalent and therefore interchangeable, and wherein each vertex of the cube is assigned to a nucleotide base from the subset such that for each vertex the assigned base is directly connected to every other base type of the subset via an edge,

[0145] b) assigning the first nucleotide base of the selected nucleotide sequence to a vertex of a cube to which the nucleotide nitrogenous base type has been assigned, and sequentially assigning each subsequent nucleotide of the selected nucleotide sequence to a corresponding vertex in a cube or tetrahedron such that the assigned vertex is directly connected to the vertex of the previous nucleotide base through an edge of the cube;

[0146] wherein, when the nucleotide base is the same as the previous nucleotide base, the nucleotide base is assigned to the same vertex of the cube as the vertex to which the previous nucleotide base is assigned; and

[0147] Therein, the sequence of selected nucleotides and / or nucleotide analogs includes nitrogenous bases selected from A (adenine), C (cytosine), G (guanine), T (thymine) and / or U (uracil).

[0148] In a preferred embodiment of the sixth aspect of the present invention, the method further comprises the following steps:

[0149] c) assigning a prime number to each consecutive nucleotide position over the total length of the selected sequence, wherein each position of the selected sequence is assigned a different prime number unless there is a pattern of one type of nitrogenous base (A (adenine), C (cytosine), G (guanine), T (thymine), or U (uracil)) repeating and the repeats of two or more of the same type of nitrogenous bases are directly adjacent to each other, in which case each position in the pattern is assigned the same prime number; and

[0150] d) identifying all nucleotide positions assigned to each vertex of the cube and calculating the product of all prime numbers assigned to each of said nucleotide positions, including duplicate prime numbers (if any) for each vertex of the cube.

[0151] In a preferred embodiment of the sixth aspect of the invention, prime numbers are assigned to each consecutive nucleotide position over the total length of the selected sequence according to any of the following: in ascending order from the 5′ end of the selected nucleotide sequence to the 3′ end of the selected nucleotide sequence;

[0152] ● In descending order from the 5' end of the selected nucleotide sequence to the 3' end of the selected nucleotide sequence;

[0153] ● Randomly;

[0154] ● starting from assigning the prime number 2 to the first nucleotide of the selected nucleotide sequence located at the 5' end of the selected nucleotide sequence, in ascending order from the 5' to the 3' direction of the selected nucleotide sequence; or

[0155] ●Starting from assigning the prime number 2 to the first nucleotide of the selected nucleotide sequence located at the 3' end of the selected nucleotide sequence, in ascending order from the 3' to 5' direction of the selected nucleotide sequence.

[0156] In the present invention, preferably, starting from assigning prime number 2 to the first nucleotide of the selected nucleotide sequence at the 5' end of the selected nucleotide sequence, prime numbers are assigned to each continuous nucleotide position on the total length of the selected sequence in ascending order from the 5' to 3' direction of the selected nucleotide sequence.

[0157] In another preferred embodiment of the sixth aspect of the present invention, the selected nucleotide sequence is further represented in the form of a matrix, in particular in the form of a TISA deconvolution matrix (TDM), wherein the method further comprises the following steps:

[0158] e) assigning each vertex of the cube to an element or component of a matrix having at least as many elements or components as there are vertices of the cube, and

[0159] f) for each element or component of the matrix representing the vertices of the cube, assigning the corresponding calculated product to said vertex calculated in step d) of the sixth aspect of the invention.

[0160] In yet another preferred embodiment of the sixth aspect of the present invention, the selected nucleotide sequence is represented as a TISA deconvolution matrix (TDM) in the form of a cube, preferably a 4×4 matrix.

[0161] In another preferred embodiment of the sixth aspect of the present invention, the selected nucleotide sequence is represented in the form of a cube, wherein the vertices of the cube are assigned to the matrix by a three-dimensional projection of the cube on a two-dimensional Euclidean plane, thereby defining an internal nucleotide base set and an external nucleotide base set, each nucleotide base set representing an opposite face of the cube, preferably wherein the projection axis is an axis perpendicular to the predetermined initial face.

[0162] In yet another preferred embodiment of the sixth aspect of the present invention, the selected nucleotide sequence further comprises information indicating the 5' end and the 3' end of the selected nucleotide sequence, and wherein the nucleotides are sequentially assigned to the bases in the cube in the 5'→3' direction.

[0163] The seventh aspect of the present invention relates to a computer-implemented method for labeling a nucleotide sequence, by encoding the nucleotide sequence in the form of a matrix according to any method according to the sixth aspect of the present invention.

[0164] An eighth aspect of the present invention relates to a computer-implemented method for decoding a nucleotide sequence in the form of a TISA deconvolution matrix (TDM) as defined in the sixth aspect of the present invention, wherein the method comprises the following steps:

[0165] ●Integer factorization of each element or component of the matrix representing the position of different vertices of the cube (corresponding to Gf, Af, Tf, Cf, Gb, Ab, Tb, Cb) to calculate its prime factors;

[0166] ●Assign all the obtained prime factors and their corresponding nitrogenous bases to positions in the selected nucleotide sequence, where each prime number is located at a predetermined position in the selected sequence.

[0167] In a preferred embodiment of the eighth aspect of the present invention, starting from assigning prime number 2 to the first nucleotide of the selected nucleotide sequence located at the 5' end of the selected nucleotide sequence, prime numbers are assigned to each continuous nucleotide position on the total length of the selected sequence from the 5' to 3' direction of the selected nucleotide sequence in ascending order; and according to the ascending position of each prime number in the selected sequence, each prime factor obtained and its corresponding nitrogenous base are attributed to the position in the selected nucleotide sequence.

[0168] In another preferred embodiment of the eighth aspect of the present invention, prime numbers are randomly assigned to each continuous nucleotide position on the total length of the selected sequence; and wherein each prime factor obtained and its corresponding nitrogenous base are attributed to the position in the selected nucleotide sequence according to the predetermined position of each of the prime numbers in the selected sequence.

[0169] The following examples are only used to illustrate the present invention but not to limit the present invention.

[0170] Example

[0171] Example 1: Example of sequence matrix encoding

[0172] As a first embodiment, encoding the nucleotide sequence into a matrix is ​​performed according to a step-by-step process, such as Figure 8 As shown in A to 8D.

[0173] The initial nucleotide sequence in the 5'→3' direction is: GATTGCCTACCT, e.g. Figure 8 A. Then, Figure 8 A cube is defined in B, where each base is connected to every other base type by an edge. Then, the front face of the cube is defined as the predetermined initial face, and the sequence is wrapped around the vertices so that the assigned base is connected to the base of the previous nucleotide by an edge of the cube. Then, in Figure 8 C shows the three-dimensional projection of the cube onto the two-dimensional Euclidean plane defining the interior and exterior squares, and how the sequence winding looks from this perspective. Figure 8 In D, the number of nucleotides assigned to each base of the cube is assigned to the vertices of the cube respectively, and the nucleotide sequence is encoded in the form of a square matrix, where the vertices are represented on the elements on the diagonal of the matrix. This square matrix is ​​a topologically invariant sequence array (TISA).

[0174] It should be noted that the TISA matrix preserves the topology of the gene cube. When the sequence to be encoded contains consecutively repeated nucleotide segments (such as TT or CC in Example A), redundancy is captured by calculating 2 units of the corresponding vertices. The sum of all positions in the TISA matrix is ​​the same as the length of the encoded nucleotide sequence (here 12 nucleotides).

[0175] also, Fig. 9 The TISA matrix of a more complex nucleotide sequence is shown, i.e. a partial sequence of the 16S ribosomal RNA of E. coli strain U 5 / 41 (accession number NR_024570.1). The final TISA matrix is ​​a 4×4 square matrix, with the vertices of the cube represented on the elements on the matrix diagonal. The TISA wrapping of a real DNA sequence around a gene cube (cube) illustrates the compression and compactness achieved by this method.

[0176] This suggests that a nucleotide sequence can be encoded by a matrix while preserving the topological information of the wound nucleotide fragments in the form of a cube. It should be noted that the same applies to the winding of tetrahedra, which will result in a simple matrix.

[0177] Example 2: Example of matrix encoding sensitivity to changes

[0178] The second example is intended to demonstrate the high sensitivity of matrix coding to small sequence changes according to one or more embodiments.

[0179] like Fig.10 As shown, from Fig. 9 The elements of the TISA matrix for the sequence introduced in (partial sequence of Escherichia coli strain U 5 / 41 16S ribosomal RNA (Accession No. NR_024570.1)) change significantly when changes (even small changes) are made.

[0180] First, two compensatory changes are made by replacing the positions of two bases so that the percentage of each base present in the sequence is the same. It can be noted that all elements of the matrix representing the vertices have changed.

[0181] Second, smaller changes were tested. Single nucleotide polymorphisms (i.e., changing one nucleotide to another with a different base) were tested. Again, all elements of the matrix representing the vertices were changed.

[0182] While the changes in the TISA matrices are evident, they can be further noted when calculating the determinant of each TISA matrix. For the compensatory changes, the determinant decreased by more than 11 million, while for the SNPs, the determinant increased by more than 8 million.

[0183] It can therefore be seen that the unique ID obtained (TISA matrix or its determinant) can be used to check the integrity of the nucleotide sequence during storage / recovery or exchange over a network. Any changes due to information loss, noise, errors will produce a different TISA matrix. Since the TISA matrix retains the topological information of the intertwined nucleotide fragments, it can be used as a compact representation of the coding sequence / gene / genome. Therefore, TISA encoding can be used as a way to label sequences. In addition, this further shows that TISA encoding can be used to study the effects of mutations on nucleotide sequences by representing and scoring genetic mutations between related or unrelated sequences.

[0184] Example 3: Example of determining invariant markers in nucleotide sequences by rotational symmetry (RIP)

[0185] Finally, a fourth embodiment showing different rotational invariant patterns (RIPs) in two randomly generated nucleotide sequences is shown.

[0186] According to one or more embodiments, in a given sequence, the window length n has been preselected to be 17. Therefore, Fig.13A 17×17 matrix is ​​initially given in (Step 2). After implementing several rotational symmetries, the symmetry invariant elements are identified, from which position information (i.e. the position of the symmetry invariant element in the matrix) and qualitative values ​​(i.e. the nature of the element (base type)) can be obtained.

[0187] It should be noted that, since n is an odd number, the center of the matrix remains unchanged (rotation center). Since this element itself does not provide any information, it is necessary to discard it. If a smaller n is selected, an alternative matrix can be constructed and different symmetry invariant elements can be located. Similarly, in longer sequences, further RIPs can be calculated by moving the initial nucleotides. It should be noted that this embodiment relates to RIP, but the same considerations can be applied to other variants, such as mirror image invariant mode (MIP) and rotation mirror image invariant mode (RMIP).

[0188] The RIP, MIP and RMIP methods may be suitable tools for studying the structure, function and evolution of genes and genomes.

[0189] Example 4 - Convolution of TDM Matrix

[0190] like Fig.14 As shown, TISA matrices are particularly advantageous for supporting the exchange and analysis of large amounts of genomic information between two remote locations. They provide a fast, robust, flexible, and lightweight data structure that can be easily exchanged over telecommunication networks such as the Internet, wide area networks (WANs), local area networks (LANs), satellite networks, mobile phone networks, etc. The TISA matrix is ​​a compact and convolutional representation of genomic information that carries only a small fraction of the weight of the transmitted information (in bits, typically well below 1% of the original weight). When considered together with a secondary matrix called the TISA deconvolution matrix (TDM), the TISA matrix can be easily decoded to extract the original genomic information in a lossless manner. This communication scheme does not violate the Shannon information theory principle, as the amount of information contained in the sum of the TISA+TDM matrices is greater than or equal to the calculated Shannon entropy.

[0191] Fig.15 The following is an example of how the TDM matrix is ​​constructed. The first 40 DNA nucleotides that make up the esaX gene of Mycobacterium tuberculosis (encoding the ESAT-6 immunogenic protein) Fig.15 A) TISA encoding is performed using the following scheme ( Fig.15 B) and TDM coding ( Fig.15 D). TISA encoding has been performed as shown in the previous embodiment. The encoding of TDM is as follows Fig.15 C, using the following three consecutive steps:

[0192] Step #1 - The gene sequence corresponding to the esaX gene (40 nucleotides long) is presented in a table, where:

[0193] o The first row contains the nucleotides of the sequence considered in 4 to 4 orientation.

[0194] o The second row contains prime numbers, starting with the number 2, assigned to each nucleotide. In the case of consecutive redundant nucleotides such as GG, AA, TTT, GG and CC in this example, the same prime number is assigned multiple times.

[0195] Step #2 - The third row of the table contains the position of each nucleotide / prime number pair that was once represented on the gene cube. The gene cube is selected here to display the GATC sequence in a clockwise direction on the front of the cube. The corresponding nucleotide sequence and the associated prime number are given specific symbols depending on whether they are located at the front corner of the gene cube (Gf, Af, Tf, Cf) or the back corner (Gb, Ab, Tb, Cb).

[0196] Step #3 - Multiply the prime numbers corresponding to each of the 8 corners of the cube (labeled Gf, Af, Tf, Cf, Gb, Ab, Tb, Cb) and report the corresponding products in the TDM matrix ( Fig.15 D).

[0197] Example 5 - Deconvolution of TDM Matrix

[0198] Fig.15 D represents a typical convolutional TDM matrix. In this configuration, the position and location of each nucleotide of the original sequence can be retrieved by dividing each TDM individual number (Gf, Af, Tf, Cf, Gb, Ab, Tb, Cb) by its corresponding prime number. Only one of the 8 possible numbers (Gf, Af, Tf, Cf, Gb, Ab, Tb, Cb) is divisible by this prime number, indicating its position on the gene cube.

[0199] For example, the start of the esaX sequence (A from ATG) can be identified at the Af position, since it is the only position divisible by 2. In general, the position of the first nucleotide in a sequence is at an even-parity position, since 2 is the only even prime number.

[0200] To reconstruct the original nucleotide sequences encoded in the TISA and TDM matrices, the following two-step approach can be used:

[0201] Step #1- Integer factorize each of the positions (Gf, Af, Tf, Cf, Gb, Ab, Tb, Cb) to get their prime factors.

[0202] Step #2 - Collect all the prime factors obtained into a list and arrange them in ascending order. For each prime number, assign its corresponding nucleotide value, which is inferred from its position in the TDM matrix.

[0203] Fig.16 A and Fig.16 B shows examples of steps 1 and 2, respectively. It is important to note that the value at each position in the TISA matrix corresponds to the number of factors of the corresponding number in the TDM matrix. For example, the number 14 found at position Gb of the TISA matrix calculates the number of prime factors (14) of the number 2389558903510844901830255 (5, 17, 23, 47, 59, 59, 73, 83, 83, 83, 107, 113, 113, 131).

Claims

1. A computer-implemented method for representing a sequence of selected RNA nucleotides and / or DNA nucleotides and / or nucleotide analogs, comprising the steps of: g) defining a cube using nucleotide bases, wherein each of the eight vertices of the cube is assigned to a nitrogenous base from the subset [A (adenine), C (cytosine), G (guanine), T (thymine)], wherein the nitrogenous bases T (thymine) and U (uracil) are understood herein to be equivalent and therefore interchangeable, and wherein each vertex of the cube is assigned to a nucleotide base from the subset such that for each vertex the assigned base is directly connected to every other base type of the subset via an edge, h) assigning the first nucleotide base of the selected nucleotide sequence to a vertex of a cube to which the nucleotide nitrogenous base type has been assigned, and sequentially assigning each subsequent nucleotide of the selected nucleotide sequence to a corresponding vertex in a cube or tetrahedron such that the assigned vertex is directly connected to the vertex of the previous nucleotide base through an edge of the cube; wherein, in the case where the nucleotide base is the same as the previous nucleotide base, the nucleotide base is assigned to the same vertex of the cube as the vertex to which the previous nucleotide base is assigned; and The sequence of selected nucleotides and / or nucleotide analogs includes a nitrogenous base selected from A (adenine), C (cytosine), G (guanine), T (thymine) and / or U (uracil).

2. The method according to claim 1, further comprising the steps of: i) assigning a prime number to each consecutive nucleotide position over the total length of a selected sequence, wherein each position of the selected sequence is assigned a different prime number unless there is a pattern of one type of nitrogenous base (A (adenine), C (cytosine), G (guanine), T (thymine), or U (uracil)) repeating and the repeats of two or more of the same type of nitrogenous bases are directly adjacent to each other, in which case each position in the pattern is assigned the same prime number; as well as j) identifying all nucleotide positions assigned to each vertex of said cube and calculating the product of all prime numbers assigned to each of said nucleotide positions, including repeated prime numbers, if any, for each vertex of said cube.

3. method according to claim 2, wherein each continuous nucleotide position on the total length of the selected sequence is assigned a prime number according to any of the following: a. from the 5' end of the selected nucleotide sequence to the 3' end of the selected nucleotide sequence in ascending order; b. from the 5' end of the selected nucleotide sequence to the 3' end of the selected nucleotide sequence in descending order; c. Randomly; d. starting from assigning the prime number 2 to the first nucleotide of the selected nucleotide sequence located at the 5' end of the selected nucleotide sequence, in ascending order from the 5' to 3' direction of the selected nucleotide sequence; or e. Starting from assigning the prime number 2 to the first nucleotide of the selected nucleotide sequence located at the 3' end of the selected nucleotide sequence, in ascending order from the 3' to 5' direction of the selected nucleotide sequence.

4. The method according to any one of claims 2 or 3, wherein the selected nucleotide sequence is further represented in the form of a matrix, wherein the method further comprises the following steps: k) assigning each vertex of the cube to an element or component of a matrix having at least as many elements or components as there are vertices of the cube, and 1) for each element or component of the matrix representing a vertex of the cube, assigning the corresponding calculated product to the vertex calculated in step d) according to claim 2. The method of claim 4 , wherein the matrix is ​​a square matrix.

6. The method according to claim 5, wherein the selected nucleotide sequence is represented in the form of a cube, preferably a 4×4 matrix.

7. A method according to claim 6, wherein the selected nucleotide sequence is represented in the form of a cube, and wherein the vertices of the cube are assigned to the matrix by a three-dimensional projection of the cube on a two-dimensional Euclidean plane, thereby defining an internal nucleotide base set and an external nucleotide base set, each nucleotide base set representing an opposite face of the cube, preferably wherein the projection axis is an axis perpendicular to the predetermined initial face.

8. The method according to any one of the preceding claims, wherein the selected nucleotide sequence further comprises information indicating the 5' end and the 3' end of the selected nucleotide sequence, and wherein the nucleotides are assigned to the bases in the cube sequentially in the 5'→3' direction.

9. A computer-implemented method for labeling a nucleotide sequence, encoding the nucleotide sequence in the form of a matrix according to any one of claims 4 to 8.

10. A computer-implemented method for decoding a nucleotide sequence in matrix form according to claim 9, wherein the method comprises the steps of: a. performing integer factorization on each element or component of the matrix representing different vertex positions of the cube to calculate its prime factors; b. assigning all prime factors obtained and their corresponding nitrogenous bases to positions in the selected nucleotide sequence, wherein each prime number is located at a predetermined position of the selected sequence.

11. computer-implemented method according to claim 10, wherein starting from the first nucleotide of the selected nucleotide sequence that prime number 2 is assigned to the 5' end of the selected nucleotide sequence, prime numbers are assigned to each continuous nucleotide position on the total length of the selected sequence in ascending order from the 5' to 3' direction of the selected nucleotide sequence; and wherein according to the ascending position of each prime number in the selected sequence, each prime factor that obtains and its corresponding nitrogenous base are attributed to the position in the selected nucleotide sequence.

12. computer-implemented method according to claim 10, wherein prime number is randomly assigned to each continuous nucleotide position on the total length of described selected sequence; And wherein according to the predetermined position of each described prime number in described selected sequence, each prime factor that obtains and its corresponding nitrogenous base are attributed to the position in described selected nucleotide sequence.

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