Patent Description:
With digital data being generated at an exponential rate, storage of digital data becomes particularly important to the growth of information technology. These digital data are represented by bits of <NUM> and <NUM> and stored in media, such as hard drives and magnetic tapes. Many of rarely accessed data have been archived on reels of magnetic tapes. The physical limitations in the thickness of tapes and the size of magnetic domains pose a limitation to the maximum data density, which is expected to reach a plateau soon. In order to store the huge amount of data generated, huge storage space in specially built data centres is needed. Furthermore, the magnetic tapes are rated to last for several decades only, and copying data from old tapes into new tapes from time to time is required, which is both time-consuming and expensive.

One of the emerging technologies to fulfil this need is storing digital data in DNA, where the set of monomers (nucleotides) with different side chains represents the different combinations of <NUM> and <NUM> in digital data. To retrieve the data, the DNA strands are sequenced, and the sequence information of the monomers is converted back to combinations of <NUM> and <NUM>. However, DNA has only <NUM> natural nucleotides, and unnatural nucleotides may not be used for data storage since they cannot be recognized by the enzymes for DNA sequencing. In addition, DNA is prone to degradation which makes it challenging for long-term data storage.

It is desirable to have a technique for storing and retrieving digital data that seeks to address one or more of the above-mentioned problems. In designing such technique, retrieval of data stored in a molecule such as a DNA is accomplished by sequencing the molecule. It is desirable and advantageous to reduce errors in sequencing the molecule.

<CIT> discloses methods for controlled segregation of blocks of information encoded in a sequence of a biopolymer, such as nucleic acids and polypeptides, with rapid retrieval based on multiply addressing nanostructured data. Data-encoded biopolymers of any length or form are used to form sequence controlled polymer memory objects for storing data. These memory objects include sequence address labels used to associate or select memory objects for sequencing read-out, enabling rapid and efficient organization and access of distinct memory objects or subsets of memory objects using Boolean logic to thereby increase efficiency in data retrieval. Furthermore, it is claimed that errors in sequencing the biopolymer sequence can be eliminated by reading multiple copies of memory objects and using consensus sequence mapping. Reading multiple copies of memory objects, however, is a form of repetition coding and is generally not efficient in resource utilization.

<CIT> discloses systems and methods for polynucleotide sequencing where detection and correction of base calling errors can be achieved without reliance on a reference sequence. Redundant information is introduced during measurement so as to allow such detection of errors. Such redundant information and measurements can be facilitated by encoding of nucleotide sequence being measured. Consider adding redundancy to K nucleotides, where each nucleotide yields measurements of one or more of M detectable characteristics. Redundancy may be achieved by having a quantity NM greater than a quantity LK, with each of the K nucleotides being one of L types, and with each of the M detectable characteristics being one of N types. In particular, the quantity M can be represented as M = KxS/P where S represents a number of unique hybridization, pairing, matching, interrogation, or probing steps and P represents a number of variable factors associated with one of more of these steps. Redundancy can be achieved by selecting the quantity S and/or by selecting the quantity P. However, the polynucleotide sequencing technique disclosed by <CIT> is not simple to implement.

<CIT> discloses methods of storing information using oligomers. In particular, <CIT> provides a method of retrieving a format of information from a plurality of synthesized oligonucleotide sequences encoding bit sequences of the format of information. The method comprises amplifying the plurality of oligonucleotide sequences, sequencing the amplified oligonucleotide sequences, converting the oligonucleotide sequences to bit sequences, and converting the bit sequences to the format of information, where amplification includes the production of copies of a nucleic acid molecule via repeated rounds of primed enzymatic synthesis such as polymerase chain reaction. The oligonucleotide sequences may include one or more or all of a data block sequence, an address sequence specifying the location of the data block in the bit stream, or flanking common sequences at each end of the oligonucleotide for amplification and sequencing. In addition, <CIT> discloses that the effect of sequencing error may be reduced by joining overlapping paired-end reads of data-encoded oligomers. However, this arrangement is in some sense similar to repetition coding, which is generally not efficient in resource utilization.

<CIT> discloses a polypeptide comprising a polypeptide character string for storing secure information. However, aspects on sequencing the polypeptide are not provided.

There is a need in the art for the above-mentioned technique that also provides an improved performance in sequencing.

According to a first aspect, there is provided a method of storing digital data into peptides.

The method of storing digital data into peptides comprises: encoding the digital data into a digital code; translating the digital code into the peptide sequences; and synthesizing the translated peptide sequences. An individual peptide sequence comprises a sequence of amino acids corresponding to a part of the digital code such that the part of the digital code is carried in the individual peptide sequence. An individual amino acid in the sequence of amino acids represents a pattern of bits or symbols. In particular, the encoding of the digital data into the digital code comprises adding one or more order-checking bits into the part of the digital code. The one or more order-checking bits are used for protecting the order of selected bits or symbols in the part of the digital code and are generated based on one or more orders of the selected bits or symbols. The selected bits or symbols consist of first and second sequences of patterns of bits or symbols. The first sequence of patterns of bits or symbols being located at one end of the individual peptide sequence while the second sequence of patterns of bits or symbols is located at another end thereof. Each peptide is generated from one translated peptide sequence such that a respective peptide synthesized from the individual peptide sequence carries the one or more order-checking bits. Advantageously, the one or more order-checking bits in the respective peptide assists selection of a single candidate sequence to be the individual peptide sequence among plural candidate sequences each having a length of the individual peptide sequence and each obtained from a two-stage sequencing method used in tandem mass spectrometry (MS/MS) analysis when the respective peptide is sequenced during retrieving the digital data from the peptides.

In one embodiment, the translating of the digital code into peptide sequences comprises mapping a bit pattern or a symbol pattern into one or more amino acids such that the digital code is represented by a sequence of amino acids in the peptide sequences.

In one embodiment, the method of storing digital data into peptides further comprises adding one or more error-correction codes into the digital code, wherein the one or more error-correction codes comprises any one or combination of repetition code, convolutional code, turbo code, fountain code, low-density parity-check (LDPC) code, Reed-Solomon (RS) code, Hadamard code, and Hamming code.

In one embodiment, the one or more error-correction codes are generated based on the digital code, or both the digital code and the one or more order-checking bits added into the digital code.

In one embodiment, the peptide sequences comprise distinct functional groups, isotope labels or affinity labels.

In one embodiment, the peptide sequences comprise digital data bearing amino acids and non-digital data bearing amino acids.

According to a second aspect, there is provided a method of retrieving digital data from peptides.

The method of retrieving digital data from peptides comprises: sequencing the peptides by MS/MS to determine an order of the peptide sequences; converting the peptide sequences with the determined order into a digital code; and decoding the digital data from the digital code. An individual peptide sequence is obtained by sequencing a respective peptide. The individual peptide sequence comprises a sequence of amino acids corresponding to a part of the digital code such that the part of the digital code is carried in the individual peptide sequence, an individual amino acid in the sequence of amino acids representing a pattern of bits or symbols. In particular, the part of the digital code comprises one or more order-checking bits. The one or more order-checking bits are used for protecting the order of selected bits or symbols in the part of the digital code and are generated based on one or more orders of the selected bits or symbols. The selected bits or symbols consist of first and second sequences of patterns of bits or symbols. The first sequence of patterns of bits or symbols is located at one end of the individual peptide sequence while the second sequence of patterns of bits or symbols is located at another end thereof. The one or more order-checking bits in the respective peptide assist selection of a single candidate sequence to be the individual peptide sequence among plural candidate sequences each having a length of the individual peptide sequence and each obtained from a two-stage sequencing method used in MS/MS analysis when the respective peptide is sequenced during retrieving the digital data from the peptides. The method further comprises: encoding the order of the selected bits or symbols in the digital code by using pre-defined rules to thereby generate one or more generated order-checking bits; comparing the one or more order-checking bits with the one or more generated order-checking bits; and indicating a detected error if the one or more order-checking bits do not match the one or more generated order-checking bits.

In one embodiment, the converting of the peptide sequences with the determined order into the digital code comprises mapping one or more amino acids in the peptide sequences into a bit pattern or a symbol pattern such that the digital code is obtained from a sequence of amino acids in the peptide sequences with the determined order.

In one embodiment, the digital code comprises one or more error-correction codes, wherein the one or more error-correction codes comprises any one or combination of repetition code, convolutional code, turbo code, fountain code, LDPC code, RS code, Hadamard code, and Hamming code.

In one embodiment, decoding the digital data from digital code uses algorithms comprising belief-propagation algorithm, message-passing algorithm, and sum-product algorithm, and bit-flipping algorithm.

Embodiments of the present disclosure provide an efficient data storage method and system using peptides. The storage of digital data is performed by mapping a pattern of bits/symbols of the digital data in one or more amino acids of the peptide sequences. Firstly, peptides can offer a much higher data density than DNA. In addition to the <NUM> natural amino acids, unnatural amino acids can be also incorporated for data storage since the peptide sequencing can be performed using MS/MS with no enzyme recognition involved. The increased set of possible monomers, together with the lower masses of amino acids than those of nucleotides, could endow peptides a much higher data density than DNA. Secondly, peptides are typically less prone to degradation than DNA and can be still detectable even after millions of years when DNA would have already degraded. Furthermore, the peptide synthesis industry has been well developed, and various peptides can be easily obtained at a reasonable price. With the development of proteomics, the hardware and software for separation, detection and sequencing of peptides have been well established. Sequencing thousands of peptides in a mixture at a very small amount has become routine and can be completed within a short time of period.

Embodiments of the disclosure will be better understood and readily apparent to one of ordinary skill in the art from the following written description, by way of example only, and in conjunction with the drawings, in which:.

Skilled artisans will appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been depicted to scale. For example, the dimensions of some of the elements in the illustrations, block diagrams or flowcharts may be exaggerated in respect to other elements to help to improve understanding of the present embodiments.

Embodiments of the present disclosure will be described, by way of example only, with reference to the drawings. Like reference numerals and characters in the drawings refer to like elements or equivalents.

Some portions of the description which follows are explicitly or implicitly presented in terms of algorithms and functional or symbolic representations of operations on data within a computer memory. These algorithms and functional or symbolic representations are the means used by those skilled in the data processing arts to convey most effectively the substance of their work to others skilled in the art. An algorithm is here, and generally, conceived to be a self-consistent sequence of steps leading to a desired result. The steps are those requiring physical manipulations of physical quantities, such as electrical, magnetic or optical signals capable of being stored, transferred, combined, compared, and otherwise manipulated.

The present specification also discloses apparatus for performing the operations of the methods. Such apparatus may be specially constructed for the required purposes, or may include a computer or other computing device selectively activated or reconfigured by a computer program stored therein. Various machines may be used with programs in accordance with the teachings herein. Alternatively, the construction of more specialized apparatus to perform the required method steps may be appropriate. The structure of a computer will appear from the description below.

In addition, the present specification also implicitly discloses a computer program, in that it would be apparent to the person skilled in the art that the individual steps of the method described herein may be put into effect by computer code. The computer program is not intended to be limited to any particular programming language and implementation thereof. It will be appreciated that a variety of programming languages and coding thereof may be used to implement the teachings of the disclosure contained herein. Moreover, the computer program is not intended to be limited to any particular control flow. There are many other variants of the computer program, which can use different control flows without departing from the spirit or scope of the disclosure.

Furthermore, one or more of the steps of the computer program may be performed in parallel rather than sequentially. Such a computer program may be stored on any computer readable medium. The computer readable medium may include storage devices such as magnetic or optical disks, memory chips, or other storage devices suitable for interfacing with a computer. The computer readable medium may also include a hard-wired medium such as exemplified in the Internet system, or wireless medium such as exemplified in the GSM mobile telephone system. The computer program when loaded and executed on a computer effectively results in an apparatus that implements the steps of the preferred method.

As used herein, the terms "peptide" and "peptide sequence" refer to a string of the amino acid residues, wherein the order of the assembly of the amino acid is the peptide sequence in the peptide. As used herein, the term "amino acid" refers to an organic compound that comprises an amine group (-NH<NUM>) and a carboxyl group (-COOH). Amino acids can be natural, unusual, unnatural or synthetic, wherein examples include, but are not limited to, D or L optical isomers, and amino acid analogs and peptidomimetics. Further examples of naturally occurring amino acids can be, but are not limited to, alanine, arginine, asparagine, aspartic acid, asparagine (or aspartic acid), cysteine, glutamic acid, glutamine, glycine, histidine, isoleucine, leucine, lysine, methionine, phenylalanine, proline, serine, threonine, tryptophan, tyrosine or valine. In another example, groups of unnatural amino acids can be, but are not limited to, beta-homo-amino acids, N-methyl amino acids, alpha-methyl amino acids. Further examples of unnatural, unusual occurring or synthetic amino acids include, but are not limited to, citrulline, hydroxyproline, norleucine, <NUM>-nitrotyrosine, nitroarginine, ornithine, naphtylalanine, methionine sulfoxide, methionine sulfone, cyclohexylalanine, ring-substituted phenylalanine, tyrosine or tryptophan derivatives (including but not limited to, for example, cyano-phenylalanine, o. tyrosine, m. tyrosine, hydroxy-tryptophan, methoxy-tryptophan), or halogen-labelled amino acids derivatives (including but not limited to, for example, fluoro/chloro/bromo/iodo-phenylalanine, fluoro-tryptophan, fluoro/chloro/bromo/iodo-alanine).

As used herein, the term "peptide" refers to a polymer of <NUM> or more amino acids, amino acid analogs, peptidomimetics, or any combinations thereof. The subunits can be linked by peptide bonds. In another example, the subunits may be linked by other bonds such as, but not limiting to ester or ether bonds. Peptides also have a structure, wherein the structure can be generally understood to be linear or cyclic. In one example, a peptide can be, but is not limited to, dipeptides, tripeptides, oligopeptides or polypeptides. In another example, the peptide can be about <NUM> to <NUM> amino acids in length. In yet another example, the peptide can be about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length, about <NUM> to about <NUM> amino acids in length. In yet another example, the peptide can be <NUM> amino acids in length. Shorter peptides are cheaper to synthesize, and easier to be sequenced with reduced missed fragmentation, while longer peptides can store more data per peptide, reduce the number of peptides required for analysis, and reduce the address and error correction overhead.

As used herein, one or more amino acids in a peptide sequence represents a pattern of bits/symbols. A sequence of amino acids in a peptide sequence therefore represents a string of bits/symbols, which in turn represents part of the digital data. Therefore, the representation of digital data by peptide sequences is referred to herein as the digital data being stored in peptide sequences for simplicity sake. Since the digital data is expressed in a different form or system, the representation of digital data by peptide sequences can also be described as the digital data being encoded in peptide sequences. Therefore, the storing of digital data in peptide sequences is the same as the encoding of digital data in peptide sequences.

In the present disclosure, it is defined that.

Referring to <FIG>, a schematic diagram of a system <NUM> configured to store digital data into peptide sequences is depicted. The system <NUM> includes a synthesizer <NUM> configured to synthesize peptide sequences, a processor <NUM> in communication with the synthesizer <NUM>, and a memory <NUM> including computer program code. The memory <NUM> is in communication with the processor <NUM> such that the processor <NUM> can read the computer program code stored in the memory <NUM>. The processor <NUM> can then execute the computer program code to encode digital data into peptide sequences. The processor <NUM> then transmits the peptide sequences to the synthesizer <NUM>, so that the synthesizer <NUM> can synthesize the transmitted peptide sequences. These components can be integrated in one location or distributed among different locations, and the communications can be performed in real-time, in near-real-time, or in batches.

A synthesizer can be used to assemble amino acids into a peptide in a desired sequence. The synthesizer <NUM> can include, but not limited to, equipment / device for liquid-phase peptide synthesis, solid-phase peptide synthesis or microwave-assisted peptide synthesis. The synthesizer <NUM> can also be configured to include equipment / device for peptide purification methods, such as, but not limited to, reverse-phase chromatography, size-exclusion chromatography, ion exchange chromatography, partition chromatography, high-performance liquid chromatography, or any combinations thereof. The synthesizer <NUM> may be a single equipment / device or a series of equipment / devices in combination configured to synthesize the peptide sequences and/or form a mixture of peptides.

The system <NUM> can be used to implement method <NUM> for storing digital data into peptide sequences as depicted in <FIG>. The processor <NUM> and the memory <NUM> including computer program code in the system <NUM> can be parts of a general purpose computing device as depicted in <FIG>, in which the processor <NUM> corresponds to processor <NUM>, and the memory <NUM> corresponds to memory <NUM>. The method <NUM> broadly includes:.

At step <NUM>, digital data can be encoded into a digital code by the processor <NUM>. The digital data may be retrieved from the memory <NUM> or received from an external device (e.g., an external hard drive, an optical disc, etc.). The digital data may be in the form of video, image, audio, text, computer program, and the like. The digital data is then encoded in a digital code, for example, in a collection of bits (<NUM> and <NUM>) or symbols (e.g. numbers, letters). The collection of digital code may be presented in, but not limited to, forms of strings, arrays, vectors, matrices, data blocks, and the like. In practical applications, the encoding schemes can be user-defined, and additional codes can be added during the encoding process for various purposes, such as labelling, address indication, accuracy enhancement, redundancy, and error correcting.

For data security purposes, the digital data can be scrambled or encrypted or ciphered before being encoded in a digital code, which at step <NUM> is translated to one or more amino acids in one or more peptides. Examples of encryption systems include Rivest-Shamir-Adleman (RSA), Elliptic Curve Cryptography (ECC), Advanced Encryption Standard (AES) and Data Encryption Standard (DES). The digital data and/or the encrypted data and/or the encoded digital code can be interleaved before being mapped to amino acids in part of a peptide, or one or more peptides.

At step <NUM>, the digital code obtained at step <NUM> is translated into peptide sequences. In embodiments of the present disclosure, one or more amino acids represent a bit pattern or a symbol pattern in the digital code. For example, the amino acid serine ("S") may represent a bit pattern of <NUM>, the amino acid threonine ("T") may represent a bit pattern of <NUM>. A sequence of amino acids in a peptide therefore corresponds to a part of the digital code and carries part of the information of the digital data. Examples of mapping methods between amino acid(s) and bit/symbol patterns are listed below, with alanine ("A"), threonine ("T"), leucine ("L"), valine ("V"), glutamic acid ("E"), histidine ("H"), tyrosine ("Y"), phenylalanine ("F"), aspartic acid ("D"), lysine ("K"), arginine ("R"), proline ("P"), tryptophan ("W"), cysteine ("C"), glycine ("G"), serine ("S"), asparagine ("N"), and glutamine ("Q") as amino acid example representations. <FIG> shows examples of the mapping between bit(s)/symbol(s) to amino acid(s).

It is to be appreciated that there can be other variations for the mapping methods, and a combination of mapping methods can be used for mapping the digital code to amino acids. It is also to be appreciated that there can be other translation methods, other than mapping, to translate the digital code to peptide sequences.

At step <NUM>, the translated peptide sequences are synthesized into peptides. As the peptide sequences are translated from the digital code, the synthesized peptides bear digital data. In embodiments of the present disclosure, the digital data bearing peptides can be mixed to form a mixture of peptides as less space is required in comparison to storing the discrete peptides. Peptides can be synthesized by methods including, but not limited to, liquid-phase peptide synthesis, solid-phase peptide synthesis or microwave-assisted peptide synthesis. Peptides can also undergo peptide purification such that the peptides obtained are not in a mixture, wherein the peptide purification methods include, but are not limited to, reverse-phase chromatography, size-exclusion chromatography, ion exchange chromatography, partition chromatography, high-performance liquid chromatography, or any combinations thereof.

The synthesized peptides and mixtures of peptides can be stored in different conditions. It would generally be understood that storage conditions are dependent on the properties of the peptides to be stored. In one example, the conditions can comprise, but not limited to, temperature or phases. In another example, peptides can be stored in the solid or liquid phase. In another example, the mixture of peptides can be kept in the dry room in a powder form or in a solution form and stored between -<NUM> and -<NUM>.

When performing step <NUM> of method <NUM>, the digital data can be advantageously encoded to a digital code with error-correction codes. In one arrangement, the digital data is encoded in a digital code. Error-correction codes are then added to the digital code. Therefore, the error-correction codes are in addition to the digital code. Suitable error-correction methods provide the capability of recovering the original digital data when errors occur in the data storage and retrieval processes. Hereinafter, the term "starting digital code" is used to refer to the digital code generated from the original digital data. The starting digital code is a digital code without any error-correction codes.

<FIG> shows an example of an error-correction method. The example error-correction method adds two redundant bits to each bit in the starting digital code. Therefore, the error-correction method adds redundancy to the starting digital code. For example, bit <NUM> in the starting digital code is added with additional <NUM> bits, while bit <NUM> in the starting digital code is added with addition <NUM> bits. The digital code with the error-correction code in this example is transformed as (<NUM>, <NUM>) → (<NUM>, <NUM>). As used herein, the term "redundancy" refers to extra data that is generated for repetition of information or inclusion of additional information during the data storage / retrieval / transfer. By adding redundancy, error correction and detection can be advantageously achieved. In the example in <FIG>, the error-correction method allows an error in any of the triplet of bits to be corrected by "majority vote" as demonstrated in the decoding table. The error-correction method also allows up to <NUM> bits of triplet omitted (not presented in the figure). It is worth noting that, although simple to implement, this triple modular redundancy is a relatively inefficient error-correction method. In the present disclosure, a more efficient error-correction method based on order-checking bits, and one or more LDPC codes or one or more RS codes is designed to correct errors during the synthesis, detection and sequencing of the peptides.

<FIG> shows a flowchart illustrating a method <NUM> of encoding digital data in a digital code, the digital code including order-checking bits and one or more LDPC codes. The order-checking bits and the one or more LDPC codes form an error-correction method. In one example, a digital code representing information of the digital data is provided as the starting digital code. At step <NUM>, order-checking bits are generated based on one or more orders of bits/symbols, or segments of bits/symbols in the starting digital code. Order-checking bits have the function of protecting the correct order of bits/symbols in the starting digital code when the digital code is being processed during the data storage / retrieval / transfer.

In one arrangement, the order-checking bits are added into the starting digital code as redundant bits, which can contain information of the correct order of certain bits/symbols in the starting digital code. The value of the order-checking bits can be determined according to user-defined rules, for example, the order-checking bit of "<NUM>" is added to a symbol if the subsequent symbol has a lesser value. For example, a starting digital code has symbols of <NUM>. An order-checking bit is then added according to the above example user-defined rules. As the first symbol has a greater value (i.e., "<NUM>" representing <NUM> bits "<NUM>") than the second symbol (i.e., "<NUM>" representing <NUM> bits "<NUM>"), a redundant bit "<NUM>" is added as an order-checking bit. The same process can be repeated for the second symbol to add an order-checking bit. Therefore, there can be one or more order-checking bits generated from the starting digital code. In one example, the generated order-checking bits can be added to the starting digital code and become part of the digital code before performing step <NUM>.

At step <NUM>, one or more LDPC codes are generated based on the digital code obtained from step <NUM>. The digital code of step <NUM> includes the starting digital code and the order-checking bits. As such, the one or more LDPC codes are capable of correcting the starting digital code and the order-checking bits. LDPC code is a linear error-correction code constructed using a sparse bipartite graph. The encoding of LDPC codes into the digital code comprises: (<NUM>) constructing a sparse parity-check matrix, and (<NUM>) generating codewords with the matrix. A codeword contains information bits and parity bits, in which the parity bits are the redundant bits appended to the information bits. A parity bit is set to either <NUM> or <NUM> depending on the total number of the <NUM>-bits in some of the information bits either even or odd, which can advantageously be used to detect and/or correct errors in the information bits. In alternative embodiments, error-correction codes can include any one or combination of repetition code, convolutional code, turbo code, fountain code, LDPC code, RS code, Hadamard code, and Hamming code.

At step <NUM>, a block of bits or symbols is built using the information of the starting digital code (representing the original digital data), the order-checking bits (generated at step <NUM>) and the one or more LDPC codes (generated at step <NUM>). Although it is described that the digital data is encoded in a digital code having a block of bits or symbols, it is to be appreciated that the encoded digital code can be in any form determined by the user.

As an illustrative example of method <NUM>, digital data is encoded in a starting digital code with <NUM> information bits, b = {b<NUM>, b<NUM>,. , b<NUM>}, The starting digital code is to be processed using error-correction methods and then stored into <NUM><NUM>-mer peptide sequences. In other words, a starting digital code of <NUM> information bits together with its error-correction codes is to be translated to <NUM> peptide sequences, each sequence having <NUM> amino acids. In one arrangement, the starting digital code is encoded to <NUM> sequences of symbols (i.e., Seq #<NUM>, Seq #<NUM>,. , Seq #<NUM>), each peptide sequence having <NUM> symbols (i.e., S<NUM>, S<NUM>,. , S<NUM>) and each symbol represents a <NUM>-bit pattern. Each symbol corresponds to an amino acid in the synthesized peptide sequence, and each sequence of symbols corresponds to a peptide sequence.

The starting digital code may be arranged in another format before adding error-correction codes. In this example, the starting digital code is reformatted into a matrix of sequences before adding the error-correction codes. Table <NUM> shows the sequences of symbols of this example. As shown in Table <NUM>, each sequence (i.e., Seq #<NUM>, Seq #<NUM>,. , Seq #<NUM>) includes <NUM> symbols where <NUM> of the <NUM> symbols are used as an address pair (i.e., {Ai,<NUM>, Ai,<NUM>}, i = <NUM>, <NUM>,. , <NUM>), where i is the sequence number. In Table <NUM>, the address pair occupies the first <NUM> symbols of each peptide sequence. In another arrangement, the address pair may occupy any <NUM> symbols of each peptide sequence.

The address pair of a peptide sequence (e.g., Seq #<NUM>) is used to indicate the position of the peptide sequence (e.g., Seq #<NUM>) in the order of the peptide sequences (e.g., Seq #<NUM>, Seq #<NUM>, etc.). For example, a peptide sequence Seq #j may have an address pair value of A<NUM>,<NUM>, of <NUM> and A<NUM>,<NUM> of <NUM>, which is combined to provide an address value of <NUM>. Further, the peptide sequence Seq #k may have an address pair value of A<NUM>,<NUM> of <NUM> and A<NUM>,<NUM> of <NUM>, which is combined to provide an address value of <NUM>. Therefore, based on the address value, the peptide sequences of Table <NUM> commence with Seq #k followed by Seq #j. As such, when retrieving the data from the synthesized peptide by sequencing, the address pairs of the peptide sequences indicate the correct order of the peptide sequences, and in turn allow the digital code (inclusive of any error-correction codes) to be reconstructed based on order indicated by the address pairs. The addressing of the peptide sequences may also use more or less than <NUM> symbols of a peptide sequence.

Due to the <NUM>-symbol address pairs, <NUM> symbols in a <NUM>-mer peptide sequence are available to represent the information bits. Therefore, a total of <NUM> symbols are available in the <NUM> peptide sequences to represent the <NUM> information bits. In one arrangement, the information bits b are filled in the data block according to the following arrangements:.

As can be seen in Table <NUM>, there are also order-checking bits Q and redundant bits Pi(j), i = <NUM>, <NUM>,. , β, j = <NUM>, <NUM> and <NUM>, of LDPC codes in the peptide sequences. The order-checking bits Q are added at step <NUM> and the redundant bits Pi(j) of LDPC codes are added at step <NUM>.

Starting at step <NUM>, order-checking bits are generated based on the digital code arranged in Table <NUM>. For each of the <NUM> peptide sequences, two order-checking bits are generated to protect the order of (i) S<NUM> and S<NUM>, and (ii) S<NUM> and S<NUM>, respectively. The order of S<NUM> and S<NUM> is protected by symbol S<NUM> and the order of S<NUM> and S<NUM> is protected by symbol S<NUM>. In one arrangement, the first bit of symbol S<NUM> (Q<NUM>,<NUM>) is an order-checking bit that protects the order of S<NUM> and S<NUM>. The order of S<NUM> and S<NUM> is protected by an order-checking bit in the first bit of symbol S<NUM> (Q<NUM>,<NUM>). In other arrangements, the second or third bit in the <NUM>-bit symbol S<NUM> or S<NUM> may be used as the order-checking bit.

Therefore, in this example, the first bit of S<NUM> (Q<NUM>,<NUM>) checks the order of symbols S<NUM> and S<NUM>, and the first bit of S<NUM> (Q<NUM>,<NUM>) checks the order of symbols S<NUM> and S<NUM>. In this example, the user-defined rule which determines the value of an order-checking bit is:.

For example, if S<NUM> = <NUM> and S<NUM> = <NUM>, the value of the order-checking bit (Q<NUM>,<NUM>) in symbol S<NUM> is "<NUM>" according to the rule. Also, if S<NUM> = <NUM> and S<NUM> = <NUM>, the value of the order- checking bit (Q<NUM>,<NUM>) in symbol S<NUM> is "<NUM>" according to the rule. It is possible to generate the order-checking bits based on other user-defined rules that are not presented here. It is also possible to use different user-defined rules to generate different order-checking bits in the same digital code.

At step <NUM>, one or more LDPC codes are generated based on the starting digital code and the order-checking bits. Three LDPC codes are used in the example shown in Table <NUM>. In this example, symbols S<NUM> to S<NUM> (in peptide sequences Seq #<NUM> to Seq #<NUM>) and symbol S<NUM> (in peptide sequences Seq #<NUM> to Seq #<NUM>) are filled with the parity bits generated by the LDPC codes. The number of parity bits in the peptide sequences of Table <NUM> is <NUM>, and the total number of bits to be encoded is <NUM> (inclusive of <NUM> information bits b, <NUM> bits of zero bits, and <NUM> bits of order-checking bits). In this embodiment, the address pairs are not included in the <NUM> bits for LDPC encoding purpose, which allows more amino acids to be used for storing digital data. In other words, the number of information bits/symbols corresponding to the digital data is increased in the <NUM> × <NUM> data block. During the decoding process, the address pairs are assumed to be correct, based on which the peptide sequences can be arranged. In some other embodiments, the address pairs can be included in the information bits and considered for LDPC encoding, or other error-correction codes. In particular, if the length of each peptide is much longer (e.g. <NUM>-mer), it is more efficient to encode each peptide separately to protect its address and the digital data stored in the peptide. For this example with <NUM> bits to be encoded by LDPC, if one LDPC code is generated, the LDPC code should have a codeword comprising <NUM> bits, represented as (<NUM>, <NUM>). Since there is a total of <NUM> information bits, the overall code rate R is R = <NUM>/<NUM> = <NUM>. In a preferred method, since there are <NUM> bits for each symbol, three (<NUM>, <NUM>) LDPC codes are generated instead of one (<NUM>, <NUM>) LDPC code, and the code rate of the LDPC code RLDPC is RLDPC = <NUM>/<NUM> = <NUM>. In an alternative embodiment, since the bits of the <NUM>-bit symbols can be divided into <NUM> sets, it is possible to use <NUM> different error-correction codes which may have dissimilar error-correcting capabilities, thereby in combination providing a more robust and efficient error-correction performance. In other words, the jth (j = <NUM>, <NUM> and <NUM>) bits of all the symbols after step <NUM> (all <NUM> sequences of Symbols S<NUM>- S<NUM> and S<NUM>- S<NUM> and the last <NUM> sequences of S<NUM>) are passed to the jth LDPC code as the information bits. The three (<NUM>, <NUM>) LDPC codes are generated based on the encoding process below.

Given a M' × N'parity-check matrix H for the LDPC code of length N'. In theory, the information bits (d ) are encoded by using <MAT> where the superscript T is the transpose operator, c = [d p ] = [d<NUM> , d<NUM> ,. , dK', p<NUM> , p<NUM> ,. , PM'] represents a codeword, d = [d<NUM> , d<NUM>,. , dK'] is the vector of the information bits with K' = N' - M', and p = [p<NUM>, p<NUM> ,. , pM'] is the vector of the parity bits. G is the generator matrix and <NUM> is the all-zero matrix. Then the information bits can be decoded by <MAT> Based on Eq. (<NUM>), it can be obtained that <MAT> where hi, j represents the element in the ith row and the jth column of matrix H. Generally, the generator matrix G is difficult to be obtained when the code length is long. Hence, the structured code is used for easy encoding purpose. A simple example for the code with the dual-diagonal structure is shown in Table <NUM>, the <NUM> × <NUM> parity-check matrix represents a LDPC code with length of <NUM>. Then there are <NUM> information bits (i.e., d<NUM>, d<NUM>,. , d<NUM> ) and <NUM> parity bits (i.e., p<NUM>, p<NUM> ,. , p<NUM> ). The parity bits can be evaluated by using the information bits as follows <MAT> <MAT> <MAT> <MAT> <MAT> <MAT> Thus the codeword is formed by a set of <NUM> bits {d<NUM> , d<NUM>,. , d<NUM> , p<NUM>, p<NUM> ,. The decoding is performed such that all information bits can fulfill all of the above equations. Suppose that the information bit d<NUM> is missing in the received sequence. Then d<NUM> can be estimated by applying Eq. (<NUM>) or (<NUM>) <MAT> <MAT> Usually, the LDPC code can be decoded by using the iterative message-passing algorithms to find a codeword c such that cH T = <NUM> (<NPL>).

Proceeding to step <NUM>, <NUM> parity bits of the three (<NUM>, <NUM>) LDPC codes are filled in the available bits of the <NUM> × <NUM> data block. In a preferred embodiment, due to the dual-diagonal structure of parity check matrix and the peptide error pattern, a random interleaver can be added to the output of each LDPC code to disturb the orders of the parity bits before inputting the LDPC code into the peptide sequences. Interleaving is a process of arranging data in a non-contiguous manner. It is common that errors occur to a number of bits/symbols in a digital code during the data storage / retrieval / transfer. When interleaving is applied, the errors affect bits/symbols that are not in fact next to one another when the digital code was created. As a result, when the data is de-interleaved, the errors are spread throughout the digital code rather than being focused in a particular spot, which makes it easier for error detection and correction. As an example, at step <NUM> of the method <NUM> (see <FIG> and associated discussion below), if the orders of the estimated symbols do not match with the first bits of the estimated symbols S<NUM> and S<NUM> (the order-checking bits), the corresponding symbol sequences in the data block are erased. When this happens, the LDPC decoding process is needed to retrieve these erased bits/symbols. By using an interleaver, it can advantageously ensure that these erased bits/symbols are not consecutive bits/symbols of an LDPC code. Instead, the erased bits/symbols are uniformly or randomly distributed in the LDPC code, which makes the recovery process easier.

In this example, the output parity-bit set of the jth LDPC code is defined as <MAT> (j = <NUM>, <NUM> and <NUM>), and the interleaved parity-bit set for the jth LDPC code is defined as <MAT> (j = <NUM>, <NUM> and <NUM>). The set P(j) corresponds to set P(j) (j = <NUM>, <NUM> and <NUM>). The set P(j) (j = <NUM>, <NUM> and <NUM>) is arranged in the jth bits of Symbols S<NUM>, S<NUM>, S<NUM>, S<NUM> and S<NUM> for all sequences, and Symbol S<NUM> of the first <NUM> sequences. In the end, the output <NUM> × <NUM> data block has <NUM> × <NUM> × <NUM> = <NUM> bit positions, with <NUM> information bits, <NUM> bits of zero bits, <NUM> bits of address pairs, <NUM> bits of order-checking bits and <NUM> parity bits in the LDPC code.

Reed-Soloman (RS) code can alternatively be used for the error-correction method for step <NUM>. Assume that the requirements for the coding scheme are:.

The error-correction method includes: (i) three order-checking bits for each peptide sequence with the first order-checking bit to protect the order of the first two symbols, the second order-checking bit to protect the order of the second and the third symbols, and the third order-checking bit to protect the order of the last two symbols in each sequence; and (ii) four RS codes to recover the original data even when any arbitrary <NUM>% <NUM>-symbol sequences {S<NUM>S<NUM>S<NUM>}, any arbitrary <NUM>% <NUM>-symbol sequences {S<NUM>S<NUM>S<NUM>}, any arbitrary <NUM>% <NUM>-symbol sequences {S<NUM>S<NUM>S<NUM>}, and any arbitrary <NUM>% <NUM>-symbol sequences {S<NUM>S<NUM>S<NUM>}, cannot be recovered correctly.

Assuming the digital code is stored into <NUM> peptide sequences of length of <NUM> amino acids. Accordingly, a <NUM> × <NUM> block of symbols is constructed (Table <NUM>), which comprises <NUM> × <NUM> × <NUM> = <NUM> bits. The <NUM>-symbol sets {Ai,<NUM>, Ai,<NUM>, Ai,<NUM>), i= <NUM>, <NUM>,. , <NUM> are used for addressing, with Symbols S<NUM> to S<NUM> having the values of {<NUM><NUM><NUM>}, {<NUM><NUM><NUM>}, {<NUM><NUM><NUM>},. , {<NUM><NUM><NUM>}, {<NUM><NUM><NUM>}. The three bits of Symbol S<NUM> are the three order-checking bits used to protect the order of Symbols S<NUM> and S<NUM>, the order of Symbols S<NUM> and S<NUM>, and the order of Symbols S<NUM> and S<NUM>, respectively. Then there are <NUM> × <NUM> × <NUM> = <NUM> bit positions in Symbols S<NUM> to S<NUM> of the block to store the information and parity bits for the RS codes.

Due to different protection requirements for partial sequences {S<NUM>S<NUM>S<NUM>S<NUM>S<NUM>S<NUM>} and {S<NUM>S<NUM>S<NUM>S<NUM>S<NUM>S<NUM>}, two (<NUM>, <NUM>) RS codes are used for partial sequences {S<NUM>S<NUM>S<NUM>} and {S<NUM>S<NUM>S<NUM>}, another two (<NUM>, <NUM>) RS codes are used for partial sequences {S<NUM>S<NUM>S<NUM>} and {S<NUM>S<NUM>S<NUM>}. Each symbol in RS code comprises <NUM> bits. The first <NUM> rows of {S<NUM>S<NUM>S<NUM>S<NUM>S<NUM>S<NUM>} and the first <NUM> rows of {S<NUM><NUM>S<NUM><NUM>S<NUM><NUM>S<NUM>S<NUM>S<NUM>} are used to record the parity symbols of the (<NUM>, <NUM>) and (<NUM>, <NUM>) RS codes, respectively. For example, the <NUM> bits p<NUM>(j), p<NUM>(j),. , p<NUM>(j), (j = <NUM>, <NUM>, <NUM> and <NUM>) of Sequence <NUM> represent the first parity symbol in the jth RS code. The remaining rows are used to store the information bits. For example, the <NUM> bits b<NUM>, b<NUM>,. , b<NUM> in {S<NUM>S<NUM>S<NUM>} of Sequence <NUM>, and the <NUM> bits b<NUM>, b<NUM>,. , b<NUM> in {S<NUM>S<NUM>S<NUM>} of Sequence <NUM>, are convert to two symbols of the first RS code. Similarly, the <NUM> bits b<NUM>, b<NUM>,. , b<NUM> in {S<NUM>S<NUM>S<NUM>} of Sequence <NUM>, and the <NUM> bits b<NUM>, b<NUM>,. , b<NUM> in {S<NUM>S<NUM>S<NUM>} of Sequence <NUM>, form two symbols of the second RS code. The (<NUM>, <NUM>) RS and (<NUM>, <NUM>) RS codes can correct up to <NUM> and <NUM><NUM>-bit symbol errors, respectively. The code rates RRS of the (<NUM>, <NUM>) and (<NUM>, <NUM>) RS codes are given by RRS = <NUM> / <NUM> = <NUM>, and RRS = <NUM> / <NUM> = <NUM>, respectively. Moreover, the numbers of total information bits and total parity bits of all four RS codes are given by (<NUM> + <NUM>) × <NUM> × <NUM> = <NUM> and (<NUM> + <NUM>) × <NUM> × <NUM> = <NUM>, respectively. Then the maximum overall code rate R of the block can be calculated by R = <NUM> / <NUM> = <NUM>.

Assuming that there are two sets of information data, <NUM> information bits in Set b and <NUM> information bits in Set b'. Then the overall code rate R of the block is given by R = <NUM> / <NUM> = <NUM>. All <NUM> information bits are filled in Symbols {S<NUM>S<NUM>S<NUM>S<NUM>S<NUM>S<NUM>} of Sequences <NUM> to <NUM> and Symbols {S<NUM>S<NUM><NUM>S<NUM>S<NUM>S<NUM>S<NUM>} of Sequences <NUM> to <NUM>. The information set b' is arranged in the last <NUM> sequences. The remaining <NUM> - <NUM> = <NUM> information bit positions in the block are set to zeros because no more information needs to be sent. These zero-bit positions are located at the first bits in S<NUM> of Sequences <NUM> to <NUM>, the first bits in S<NUM> of Sequences <NUM> to <NUM>, and the <NUM> bits in Symbol S<NUM> of Sequences <NUM> to <NUM>.

Referring to <FIG>, an illustration <NUM> of storing digital data into peptide sequences in accordance with embodiments of the disclosure is depicted. Performing step <NUM> of method <NUM>, the <NUM> bits long text symbol for "The Hong Kong Polytechnic University, 80th anniversary. " in both Chinese and English and the motto of The Hong Kong Polytechnic University (PolyU) in Chinese, in BIG5 encoding, is encoded in a digital code having <NUM> lines of <NUM> triplets of bits. An error-correction method with LDPC code as described in method <NUM> is used at the encoding step <NUM>. Performing step <NUM> of method <NUM>, order-checking bits are added. The order-checking bits are generated to protect the order of the first and second symbols and the order of the first and second last symbols in a peptide sequence. Performing step <NUM> of method <NUM>, <NUM> LDPC codes are used to encode the <NUM> bits long text symbol and the order-checking bits to <NUM> lines of data, each line with <NUM> triplets of bits. The LDPC codes are designed with the aim to recover the raw digital data when any arbitrary <NUM>% of peptides cannot be retrieved, in case of insufficient signals in MS/MS spectra.

Performing step <NUM> of method <NUM>, the digital code are then translated into <NUM><NUM>-mer peptide sequences using an independent and fixed bits-to-amino-acid mapping. As discussed in the present disclosure, amino acid in the peptide sequence can be digital data bearing or non-digital data bearing. The peptides in the example are of the format of F-[<NUM> residues]-R, in which: (i) there are <NUM> amino acids in each peptide; (ii) the amino acids at the N-terminal and C-terminal of each peptide are known (F and R) and do not carry any information (non-digital data bearing), and only <NUM> amino acids are taken into account for each peptide in the coding scheme; and (iii) <NUM> different amino acids (S, T, E, Y, A, V, L, and F) are used for translating the digital code (<NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, and <NUM>). Performing step <NUM> of method <NUM>, the <NUM> translated peptide sequences are synthesized into peptide sequences by the synthesizer <NUM>, mixed into a mixture of peptides, and stored in a suitable condition.

As described above, by adopting error-correction methods for encoding or by using non-digital data bearing amino acids for synthesis purpose, the amount of amino acids in the peptides that can carry digital data is reduced. It is desirable to have efficient error-correction methods that enable a minimal amount of redundancy but still can protect the integrity of the digital data stored in the peptide sequences. One or more amino acids in a peptide sequence can be used to represent the identity (e.g. the address and version) of the peptide, and one or more amino acids in a peptide sequence can be used for identifying errors and/or checking the integrity of the peptide.

In consideration of the various factors such as cost of synthesis, the amino acids are selected and length of the peptides is optimized to minimize the sequencing error while maximizing data storage. Shorter peptides are cheaper to synthesize and easier to be sequenced with reduced missed cleavage, but longer peptides can store more data per peptide, reduce the number of peptides required for analysis, and reduce the address and error correction overhead. In an embodiment, <NUM> natural amino acids are selected, and the length of peptide is <NUM> amino acids long. In alternative embodiments, the length of the peptide can be varied, the set of amino acids can be expanded by incorporating unnatural amino acids, and distinct functional groups, or affinity labels, together with enrichment strategy or selection strategy during MS/MS (such as precursor ion scan or neutral loss scan), can be incorporated to allow selective retrieval of specific peptides to increase signal-to-noise ratios.

For detection and identification purposes, peptides can be labelled. In one example, the label can be at the N- or C-terminal of the peptide. In yet another example, the label can be, but is not limited to, amino acids, affinity labels, solubilisation labels, chromatography labels, epitope labels, fluorescence labels, radioisotope labels, or combinations thereof. In yet another example, the label can be bromine or chlorine labelled amino acids attached to either N-terminal or C-terminal of peptides such that the digital data bearing peptides can be identified in MS spectra and the direction of peptides can be identified in MS/MS spectra. The bromine or chlorine may also be labelled to an unnatural amino acid. In yet another example, the label can be an isotope labelled molecule bound to the N-terminal or side-chain of the peptide, such that when the digital data bearing peptides are fragmented, the appearance of the specific peaks related to the labelled molecule on MS/MS spectra indicates the presence of digital data bearing peptides. In yet another example, the label can be non-digital data bearing amino acids.

In the present disclosure, the peptide sequence determines the physicochemical properties of the peptide, which can be critical to achieve optimal peptide structures to store digital data and to retrieve digital data by sequencing. In one example, the physicochemical property can be, but is not limited to, physical, chemical and molecular properties. In another example, the physicochemical property comprises, but is not limited to, hydrophobicity, solubility, charge, stability, <NUM>-dimensional peptide structure, signal strength, mass, polarizability, freezing point, boiling point, melting point, infrared spectrum, viscosity, density or combinations thereof.

The physicochemical property of the peptide can be influenced by amino acids in the peptide, wherein properties such as, but not limited to, length, type, order, or any combinations thereof, of the amino acids can be critical to achieve an optimal peptide structure to store digital data. In one example, a peptide that is <NUM> amino acids in length is critical to achieve an optimal peptide structure to store digital data. In another example, a hydrophilic peptide, which includes more hydrophilic amino acids in the peptide sequence, is critical to achieve an optimal peptide structure to store digital data. As used herein, the term "hydrophilic amino acids" refers to amino acids having a hydrophilic side chain; such side chain may be uncharged, positively (cationic) or negatively charged (anionic) under normal physiological conditions, in particular at about pH <NUM>. Uncharged hydrophilic amino acids can include, but are not limited to, asparagine and glutamine; positively charged hydrophilic amino acids can be, but are not limited to, arginine, histidine and lysine, and the unnaturally occurring amino acid ornithine; negatively charged amino acids include aspartic acid and glutamic acid. In another example, a hydrophobic peptide, which includes more hydrophobic amino acids in the peptide sequence, is critical to achieve an optimal peptide structure to store digital data. "Hydrophobic amino acids" refers to naturally occurring amino acids having a hydrophobic and/or aromatic side chain, such as, but not limited to, alanine, valine, leucine, isoleucine, and the aromatic amino acids phenylalanine, tyrosine and tryptophan. Further included are unnaturally occurring amino acids such as, but not limited to, cyclohexylalanine. In yet another example, the amino acids at the N- or C-terminal of the peptide can affect the optimal peptide structure. In yet another example, the N-terminal of the peptide can be phenylalanine or the C-terminal of the peptide can be arginine.

Referring to <FIG>, a schematic diagram of a system <NUM> configured to retrieve digital data from peptide sequences is depicted. The system <NUM> includes a sequencer <NUM> configured to sequence and determine an order of the peptide sequences, a processor <NUM> in communication with the sequencer <NUM>, and a memory <NUM> including computer program code. The memory <NUM> is in communication with the processor <NUM> such that the processor <NUM> can read the computer program code stored in the memory <NUM>. The processor <NUM> can then execute the computer program code to decode peptide sequences received from the sequencer <NUM> to digital data. The processor <NUM> receives the peptide sequences from the sequencer <NUM>, which determines stored peptide sequences. These components can be integrated in one location or distributed among different locations, and the communications can be performed in real-time, in near-real-time, or in batches.

The sequencer <NUM> can include equipment / device such as, but not limited to, gel electrophoresis apparatus, high performance liquid chromatography (HPLC) machine, capillary electrophoresis apparatus, ionizer, and mass spectrometer. The sequencer <NUM> may be single equipment / device or a series of equipment / devices in combination configured to sequence and determine an order of the peptide sequences and/or separate peptide sequences from a mixture of peptides. Peptide sequencing is expected to be continuously performed for research purposes, as peptides are important for all living organisms. Consequently, equipment / devices and methods to retrieve digital data from digital data bearing peptides will be available. This can be advantageous over storage devices such as optical disks, in which case, once they became obsolete, it is very difficult to find the drives to retrieve data from these media, similar to the fate of obsolete lomega Zip and floppy disks.

The system <NUM> can be used to implement method <NUM> for retrieving digital data from peptide sequences as depicted in <FIG>. The processor <NUM> and the memory <NUM> including computer program code in the system <NUM> can be parts of a general purpose computing device as depicted in <FIG>, in which the processor <NUM> corresponds to processor <NUM>, and the memory <NUM> corresponds to memory <NUM>. The processor <NUM> and the memory <NUM> in the system <NUM> can be the same as or different from the processor <NUM> and the memory <NUM> used in the system <NUM>. The method <NUM> broadly includes:.

At step <NUM>, the digital data bearing peptides are sequenced and an order of the peptide sequences is determined by the sequencer <NUM>. The sequencing can be based on enzymatic digestion, mass spectrometry (MS), Edman Degradation, nanopore sequencing, or any combinations thereof. Sequencing comprises multiple steps including, but are not limited to, peptide separation, ionization, ion selection, fragmentation, sequencing, or any combinations thereof. In one example, individual peptides can be separated from a mixture of peptides using methods such as, but are not limited to, electrophoresis, liquid chromatography (LC), ion mobility, cationic exchange (SCX), high performance liquid chromatography (HPLC), ultrahigh pressure liquid chromatography (UPLC), nano-liquid chromatography or any combinations thereof. In yet another example, peptides can be sequenced using methods such as, but not limited to, mass spectrometry (MS), tandem mass spectrometry (MS/MS), matrix-assisted laser desorption/ionization (MALDI) spectrometry, Matrix-Assisted Laser Desorption/lonization Time-of-Flight (MALDI-TOF) spectrometry, or any combinations thereof. In another example, peptides are converted to charged ions using ionization methods such as, but not limited to, electrospray ionization, matrix-assisted laser desorption/ionization, surface-assisted laser desorption/ionization, atmospheric-pressure ionization, direct ionization, or any combinations thereof for mass spectrometry analysis. In yet another example, peptides that are ionized can undergo ion selection using methods such as, but are not limited to, data-independent-acquisition (DIA), data-dependent-acquisition (DDA), non-targeted, targeted, or any combinations thereof, for MS/MS analysis. In another example, peptides that are ionized can be fragmented based on methods such as, but are not limited to, collision-induced dissociation (CID), high-energy collisional dissociation (HCD), electron-capture dissociation (ECD), electron-transfer dissociation (ETD), or any combinations thereof to elucidate the amino acid sequences. The conditions of the sequencer <NUM> can optimized for separation, detection and sequencing of peptides in the mixtures. In an embodiment of the present disclosure, a LC-MS/MS protocol has been developed and successfully applied to analysis of a mixture containing <NUM> data-bearing <NUM>-mer peptides, each with two fixed amino acids at the two ends.

Analysis of the peptide sequence can be accomplished by methods including, but not limited to, database search or de novo sequencing. "Database search" refers to a simple version wherein the mass spectral data of the unknown peptide is submitted and checked against the mass spectral data in the database to find a match with a known peptide sequence, with the drawback that database searching cannot identify novel proteins and modified proteins which are not contained in the database. For digital data storage, the peptides are used to carry random information bits with "<NUM>"s and "<NUM>"s. The peptides are therefore unnatural peptides and no database is available for searching and identifying these peptides. In contrast to database search method, de novo sequencing method expands the search space to all combinations of the amino acids.

"De novo sequencing" refers to the process of assigning fragment ions directly from a mass spectrum, wherein different parameters and algorithms can be selected and used for interpretation, without referring to established databases. As such, the determination of the peptide sequence requires a computational method that is able to utilize the readout generated by the sequencing step, for example from a mass spectrum, and to identify the order of the amino acids based on the sequencing method disclosed herein. A number of algorithms have been developed by use of the graph theory model together with the dynamic programming algorithms, including, but are not limited to, Lutefisk, Sherenga algorithm, PepNovo, MSNovo, pNovo, UniNovo, NovoHCD, and Novor.

A constraint for the dynamic algorithm is that no training spectra are provided for the sequencing of the digital data bearing peptides. Accordingly, de novo sequencing based on the graph model is utilized for determining the peptide sequences. In the graph model, the MS/MS spectrum is represented by a directed acyclic graph (DAG), called spectrum graph. The peaks of the spectrum can be taken as vertices, while an edge is added between two vertices when the mass gap between two peaks is equal to the mass of an amino acid. The objective of the dynamic programming is to find the longest path (or best path) in the graph starting from the head vertex to the tail vertex. An alternative approach to identify the sequence is to start with the middle part of the MS/MS spectrum. For example, the sequence tagging method first infers a partial sequence called tag, and then finds the whole sequence that can match the tag. In the tag-based method, the tags are first found from the MS/MS spectrum based on some scoring schemes. The inference of the sequence then relies on peptide comparison using the database search method or on extending the valid path of the tag in the middle position of the path using the de novo sequencing.

The peptide sequencing problem is outlined in Table <NUM>, with knowledge of the information of the amino acids used, the spectrum S, the mass of the whole sequence, and the head and tail amino acids. The sequencing problem is to find the peptide P, whose theoretical spectrum T(P) best matches the experimental spectrum S. In some embodiments, it is assumed that the length N of the peptide sequence is fixed and known. Thus, the candidate peptides without length N are discarded. Two sequencing methods, namely two-stage sequencing method and highest-intensity-tag based sequencing method, are proposed. For both methods, the sequences are estimated in a manner that first infers a partial sequence with a small amount of reliable information and then finds the missing part of the sequence with less reliable data or the raw data. The purpose is to improve the speed of sequencing by generating fewer candidates. Moreover, due to the introduction of the tag, the highest-intensity-tag based sequencing method is more effective in rejecting the unlikely candidates.

<FIG> shows a flowchart illustrating a method <NUM> of two-stage sequencing. Four steps are involved in the two-stage sequencing method <NUM>: (<NUM>) preprocessing, (<NUM>) candidate sequence generation, (<NUM>) sequence selection, and (<NUM>) candidate refining. As shown in <FIG>, Steps <NUM>-<NUM> belong to the first stage (Stage <NUM>), while Step <NUM> is processed in the second stage (Stage <NUM>). In Stage <NUM> of the two-stage sequencing method <NUM>, partial sequence is inferred using the preprocessed data after Step <NUM>. In Stage <NUM>, the remaining part of the sequence is determined using the raw data.

At Step <NUM>, preprocessing is performed. The goal of the preprocessing is twofold. Firstly, the goal is to remove some uninterpretable masses caused by noise and uncertainty. Secondly, the goal is to convert the mass/charge ratio set (m/z) to the corresponding mass sets m'b and m'y. Given a set of mass/charge (m/z) ratios, these ratios are grouped into ρ subsets G<NUM>, G<NUM>,. , Gρ, where in each subset Gi, i = <NUM>, <NUM>,. , p, all (m/z) ratios are isotopes of a particular fragment, with a charge of value <NUM>, <NUM>, or <NUM> equaling the inverse of difference between consecutive (m/z) ratios in this subset. For each subset Gi, a monoisotopic mass m'i is calculated by m'i = (m/z)i,<NUM> z'i,<NUM> - mH z'i',<NUM>, i = <NUM>, <NUM>,. , ρ, where (m/z)i,<NUM> is the lowest value in this subset, and z'i,<NUM> is the corresponding charge for (m/z)i,<NUM>. These m'i values are then distributed among the mass sets m'b and m'y. In some embodiments, one of the criteria of distribution is based on the intensities corresponding to the m'i values. In some embodiments, one of the criteria of distribution is the isotopic pattern of the (m/z) ratios in Gi. In some embodiments, one of the criteria of distribution is based on the fact that if m'i is in m'b,i, then there is a corresponding m'j in m'y,j, where m'j = M - m'i. In some embodiments, the distribution is determined real-time in Step <NUM> as described later in paragraphs [<NUM>]-[<NUM>]. In some embodiments of the preprocessing, only those with typical property of charges are reserved as the preprocessed data such that the preprocessed data may be more reliable than the raw data. However, in the event of the incomplete or ambiguous data (e.g., data lacking charge property), some useful mass values may be discarded in the preprocessing based on the abovementioned criteria. Hence, in the case when missing/uncertain elements of the sequence exist in Stage <NUM>, the raw data may be considered in Stage <NUM>.

At Step <NUM>, the preprocessed data from step <NUM> is used to find the valid paths (sequences), and the number n of candidate sequences is counted. In <FIG>, suppose that mNgroup = mH and mCgroup = mOH. The graph theory model is used to find the candidate paths (valid paths) which start with head mass mhead and end with mass M - mH - MCgroup - mtail in a directed acyclic graph (DAG). Since the masses obtained by mass/charge ratio set (m/z) are likely created by b-ion, y-ion, or both b-ion and y-ion. The mass set m'b,i, m'y,i or both sets m'b,i and m'y,i can be considered in the path finding algorithm. In the graph model, the mass of the fragment ion can be represented by a vertex. If the mass gap between two fragment ions equals the mass of any amino acid, then an edge is added between these two vertices. As shown in <FIG>, the tree can be expanded edge by edge. If the set of vertices is complete for the correct path, the sequencing problem can be reduced to finding the longest path in the graph. The path should include both the head and the tail vertices. Moreover, only those paths ending with mass M are taken as the candidates. For the example shown in <FIG>, only Path <NUM> and Path <NUM> are the candidate paths.

Due to the imperfect fragmentation in MS/MS characterizations, two and three missing ions are often observed in a sequence. In the model disclosed herein, in order to ensure that the paths from the head can be extended to the tail, the number of missing amino acids is considered to be up to <NUM> in Stage <NUM>. Starting from the mass with mb,<NUM> = <NUM>, firstly, attempt is made to find the mass of the head amino acid, mb,<NUM> = mhead + Δ<NUM>. Next, the mass mb,i+<NUM> is found by using the preprocessed data such that the mass gap between the current and the next vertices is approximate to mass si or mass summation <MAT> of up to <NUM> amino acids with mass sv ∈ g (v= <NUM>, <NUM>,. , N), i.e., mb,i+<NUM> = mb,i + (si +Δi) for two consecutive vertices i and (i + <NUM>), or <MAT> (where Δi,i+l e [-lδ, +lδ] for a length-l tag from Vertex i to Vertex (i + /). As shown in <FIG>, suppose that Path <NUM> is the correct path but with experimental masses, mb,<NUM> = <NUM>, mb,i+<NUM> = Mb,i + (mi +Δi) for two consecutive vertices, or mb,i+l = <MAT> for a length-l tag. If Path <NUM> is the correct path with theoretical masses, then mb,i+l = Mb,i + mi with mb,<NUM> = (mNgroup - mH), mb,<NUM> = (mNgroup - mH) + mhead,. , mb,N = M - mH - mCgroup - mtail, mb,N+<NUM> = M- mH - mCgroup, mb,N+<NUM> = M. Referring to <FIG>, if the mass gap between two vertices equals the mass of an amino acid, then a solid edge is added. On the other hand, if the mass gap equals the mass summation of two or more amino acids, then the dashed edges are added with hollow circles representing the missing vertices.

At Step <NUM>, the effects of the following five factors are jointly considered when arriving at the score of a sequence candidate from Step <NUM> to Step <NUM>: length of consecutive amino acids retrieved, number of amino acids retrieved, match error, average intensity of amino acids retrieved, and number of occurrences for different ion types with different offsets. The sequences with the longest length of consecutive amino acids retrieved are first selected (Step <NUM>). Among the selected sequences, the sequences with the largest number of amino acids retrieved are then selected (Step <NUM>). For the sequences with equal length of consecutive amino acids retrieved together with equal number of amino acids retrieved, the match error is evaluated, which is the mean square error between the observed mass values for the amino acids retrieved from the experimental spectrum and the actual mass values of the amino acids (Step <NUM>). If there is more than one sequence with identical match errors, the average intensity of amino acids retrieved is further calculated and a higher score is given to a sequence with a larger average intensity value (Step <NUM>). In addition, multiple ion types are usually considered as the important factors in inferring an amino acid, which means that a mass value may correspond to different types of ions in the spectrum. Generally, the more the number of occurrences for different ion-types of an amino acid is, the more likely the amino acid is correct. Therefore, for the sequences with equal score after the aforementioned evaluations of Steps <NUM>-<NUM>, the number of occurrences for different ion-types is counted to determine the sequence (Step <NUM>). The mass offset sets for the N-terminal a-ion, b-ion and c-ion type sets, i.e., {a, a-H<NUM>O, a-NH<NUM>, a-NH<NUM>-H<NUM>O}, {b, b-H<NUM>O, b-H<NUM>O-H<NUM>O, b-NH<NUM>, b-NH<NUM>-H<NUM>O}, and {c, c-H<NUM>O, c-H<NUM>O-H<NUM>O, c-NH<NUM>, c-NH<NUM>-H<NUM>O} are {-<NUM>, -<NUM>, -<NUM>, -<NUM>}, {+<NUM>, -<NUM>, -<NUM>, -<NUM>, -<NUM>}, and {+<NUM>, <NUM>, -<NUM>, +<NUM>, -<NUM>}, respectively. The mass offset sets for the C-terminal x-ion and y-ion type sets can be calculated by shifting the masses of the c-ion and b-ion type sets by +<NUM> and +<NUM>, respectively. According to the fragmentation method and the property of the data, all or some of the above ion types can be used flexibly.

Since the candidate sequences obtained at Step <NUM> are found by using the preprocessed data, which aim to provide more reliable information to generate the partial sequence, amino acid combinations (AACs) may present in the sequence due to insufficient data provided by preprocessing. At Step <NUM>, if selected sequences with missing mass values exist, which means that the corresponding mass gaps are equal to the summation of at least two amino acids, the raw data may be used to find as many vertices as possible for the path in Stage <NUM>. For the raw data, suppose that all (m/z) ratios have opportunity to be created by the singly, doubly or triply charged ions. Then the set with q mass/charge ratios (m/z)i (i = <NUM>, <NUM>,. , q) can be converted to the mass set m'b of putative b-ion and the equivalent b-ion mass set m'y of putative y-ion, each of sets m'b and m'y has <NUM>q elements. Although the number of mass values increases, only the range between the head mass and the tail mass of the AAC is considered, which is relatively smaller when compared to that for the whole sequence. As shown in <FIG>, a gap being the mass summation of <NUM> amino acids is shown in Path <NUM>. With more information provided by the raw data, the following cases can be found for the gap: (a) composition of amino acid and AAC, (b) composition of two AACs, (c) composition of tag and AAC, and (d) one tag. Note that a gap being the mass summation of more amino acids is effective to ensure that the valid paths can be formed. However, more candidate sequences may be generated and thus longer time is required for the sequencing.

As shown in <FIG>, after finding the missing amino acids of AACs at Step <NUM>, the sequences with the longest length of consecutive amino acids retrieved in AACs are selected as candidate sequences (Step <NUM>). If there still remain at least two candidate sequences after selection, a final decision is made based on the match error of the amino acids retrieved in AACs for each sequence (Step <NUM>).

The mass/charge (m/z) ratio corresponding to the first or second highest intensity is first recognized to further infer the tag or the path. In highest-intensity-tag based sequencing method, short tags with three amino acids are used in the tag-based methods, such as GutenTag, DirecTag, and NovoHCD. Although tags with shorter length can avoid introducing the wrong amino acids, the number of candidate tags is relatively larger and sometimes it is hard to infer the sequences due to insufficient information provided by the tag. As disclosed herein, the length of the tag is not fixed and can be up to the length of the peptide if the data is complete, which helps to reduce the search space. When a tag contains wrong amino acids, usually, it cannot be extended with valid prefix and suffix parts. In this case, the length of the tag is shortened by adaptively reducing the number of the higher-intensity data points used for the tag-finding algorithm. In addition, the vertex with the highest intensity may not definitely present in the correct path due to the uncertainty of the data. When valid paths cannot be found, it may be possible to infer the tag with the second highest intensity.

<FIG> shows a flowchart illustrating a method <NUM> of highest-intensity-tag based sequencing. The method <NUM> commences at step <NUM> for preprocessing of the raw data. Step <NUM> is the same as step <NUM> of the two-stage sequencing method <NUM>. The method <NUM> then proceeds from step <NUM> to steps <NUM>, <NUM>, and <NUM>.

At steps <NUM>, <NUM> and <NUM>, the intensities of the preprocessed data are sorted from the largest to the smallest and values with J denoting the ranking of intensity. The mass/charge ratio with the highest intensity is then identified and the mass/charge ratio is converted to the corresponding mass of a b-ion. As a start, it is set as J = <NUM> and i = <NUM>, and using only W = wi (N ≥ w<NUM> > w<NUM> >. > wV) masses with the higher ranking in the tag-finding processing.

The method <NUM> then proceeds to step <NUM> to find the highest-intensity-based tag. Starting from the mass m'B,J of the b-ion or m'Y,J of the y-ion with the highest intensity, the highest-intensity-based tag is found by simultaneously connecting the vertices in the forward direction pointing to the tail vertex of the path, and connecting the vertices in the backward direction pointing to the head vertex of the path, where the vertices have mass gap being the mass gk (k = <NUM>, <NUM>, ···, K) of any amino acid and preferably the length of the tag is as long as possible (see <FIG>). The tags containing the amino acid with the highest intensity are obtained subsequently, which are called highest-intensity-based tags. With knowledge of the masses of the head and the tail amino acids of a highest-intensity-based tag, the method proceeds to step <NUM> to find the prefixes that can connect the head of the path to the head of the tags in the forward direction by using the method described at Step <NUM> of the two-stage sequencing method <NUM>. For the tags with valid prefixes, at step <NUM>, the suffix parts of the sequences can be further found by linking the tail of the tags to the tail of the path in the forward direction using the similar method.

At step <NUM>, the candidate paths can be constructed by combining the three parts: prefix, tag, and suffix. At step <NUM>, one can follow Steps <NUM> and <NUM> of the two-stage sequencing method <NUM> to select and refine the sequences. Note that a larger value for W sometimes introduces one or more wrong amino acids in the head and/or tail parts of a tag, while a smaller value for W may give more reliable tag but the length of the tag may be limited. Therefore, at steps <NUM> and <NUM>, if no valid candidate can be found, one may attempt to reduce the value of W with W = wi by increasing i by <NUM>, i.e., i = i + <NUM>, and repeat the tag-prefix-suffix finding procedure until the candidate sequence can be found or i = V.

At steps <NUM> and <NUM>, for the special case when the experimental mass with the highest intensity gives an unreliable message due to noise and uncertainty, a highest-intensity-based tag or a valid path with the highest-intensity-based tag cannot be found. In this case, the mass with the second highest intensity is used by setting J = <NUM> and i = <NUM> to find the second highest-intensity-based tag and the candidates.

The computational method for the rapid and correct assignment of peptide sequences from the large number of MS/MS spectra presented in this disclosure has the following features: (i) assigning the peptide sequences based on the length, amino acids and sequence format that are determined at step <NUM>; (ii) following the general rules of fragmentation of peptide ions for the sequence assignment; (iii) distinguishing isotope labels, so that if such labels, e.g. chlorine or bromine, are incorporated in the peptides, the method could identify the isotopic pattern and assign the correct ion type; and (iv) assigning the gaps when some of the b or y ion peaks in the MS/MS spectra are of low abundances or missing. In an embodiment, the method implemented in a software is developed. The method gives scores to sequence candidates based on the following five factors: the length of consecutive amino acids retrieved, the number of amino acids retrieved, match error, intensity, and the number of occurrences for different ion types with difference offsets. The higher the score is, the more likely that the sequence is correct. The computational method implemented in the software can be further optimized for better and faster sequence assignment.

Referring to the example in <FIG>, a mixture of peptides are synthesized from <NUM> peptide sequences. In one embodiment, a set of <NUM> spectra is obtained for the <NUM> peptide sequences after MS/MS analysis, each with different mass M of the whole sequences. If the data is sufficient for estimating the peptide sequences, one or more candidate sequences for each spectrum can be obtained using the peptide sequencing methods <NUM> and/or <NUM>. Moreover, there are about <NUM> spectra per peptide sequence on average after ignoring the failed spectra, which means that two or more candidate sequences may correspond to one address pair. Thus, it is necessary to further select only one sequence for each address pair, which can involve the steps of: (<NUM>) finding and selecting the sequences based on Steps <NUM>-<NUM>, <NUM>-<NUM> of the two-stage sequencing method <NUM>; (<NUM>) checking the length of the candidate sequences and discarding those without length of (N - <NUM>); (<NUM>) for the remaining candidate sequences, checking the order of Symbols S<NUM> and S<NUM>, and the order of Symbols S<NUM> and S<NUM> according to the first bits of Symbols S<NUM> and S<NUM>, respectively; and (<NUM>) removing the duplicate candidate sequences in each spectrum.

As a result, a set of candidate sequences regardless of the generating spectra can be obtained. The candidate sequences are then grouped according to <NUM> address pairs {Ai,<NUM>, Ai,<NUM>}, i = <NUM>, <NUM>,. For each group, there are following cases possible:.

For Case <NUM>, the only sequence can be assigned for the group. For Case 2a, the result with two or more sequences is selected. For Case 2b, the results with two or more sequences can be selected as candidate sequences. Among the candidate sequences, the sequence with the highest score according to Steps <NUM>-<NUM>, <NUM>, and <NUM> of method <NUM> can be further selected. For Case 3a, the sequence with the highest score according to Steps <NUM> and <NUM> of method <NUM> can be selected. For Case 3b, the sequences obtained by Steps <NUM>, <NUM>, and <NUM> of method <NUM> are examined for duplicate sequences. If there are duplicate sequences, the output is the result with duplicate sequences. If not, the sequence with the highest score according to Steps <NUM>-<NUM>, <NUM>, and <NUM> of method <NUM> is selected. For Case 3c, the sequence with the highest score according to Steps <NUM>-<NUM>, <NUM>, and <NUM> of method <NUM> is selected. To reduce the number of candidates more efficiently, it is possible to first find the groups belonging to Cases <NUM> and <NUM> and record the spectra of sequences in these groups. Subsequently, find the sequences created by these spectra but presented in other groups, and mark them as the presented sequences. For Case <NUM>, the presented sequences in the grouping can be discarded.

Upon performing peptide sequencing and/or sequence grouping using the computational methods described above, at step <NUM> of the method <NUM>, the obtained peptide sequences with the determined order can be converted into a digital code by the processor <NUM>. The peptide sequences with the determined order are obtained by sequencing the peptides or the mixture of peptides at step <NUM>. The methods for converting the peptide sequences into the digital code should correspond to the methods for translating the digital code into peptide sequences in the data storage process (step <NUM> of method <NUM>). In embodiments of the present disclosure, each peptide sequence is formed by amino acids. One or more amino acids are used to represent a bit pattern or symbol pattern in the data storage process. Therefore, in order to convert the peptide sequence into a digital code, one or more amino acids in the peptide sequence are represented by the corresponding bit pattern or symbol pattern. For example, when one symbol in a digital code is mapped to three amino acids to form a peptide sequence at step <NUM>, three amino acids in the peptide sequence shall be reversely mapped to the one symbol to convert the peptide sequences into the digital code at step <NUM>.

At step <NUM>, the digital data can be decoded from the digital code by the processor <NUM>. When error-correction method is used for encoding the digital data, one or more error-correction technique(s) is/are applied to recover the starting digital code. In an example, when a LDPC code is used for encoding the digital data into a digital code, the converted digital code obtained from step <NUM> is decoded based on LDPC code. The converted digital code contains estimated information bits and estimated parity bits. The estimated parity bits are used to detect and correct errors in the estimated information bits. The correct information bits can therefore be retrieved from the converted digital code. In another example, when order-checking bits are used for encoding the digital data into a digital code, the converted digital code obtained from step <NUM> is decoded based on the pre-defined rules of generating the order-checking bits. The converted digital code contains redundancy of order-checking bits. The order-checking bits are used to check if certain bit(s)/symbol(s) are in the right order, therefore correcting the wrong orders of bit(s)/symbol(s) to retrieve the correct digital data from the converted digital code. Decoding the digital data from the digital code can use algorithms such as belief-propagation algorithm, message-passing algorithm, sum-product algorithm and bit-flipping algorithm.

In the case when the digital data is encrypted or ciphered before being stored, one or more decryption technique(s) is/are applied to the reverse-mapped bits/symbols to recover the original digital data. In the case when the digital data and/or the encrypted data and/or the encoded digital code are interleaved before being stored, one or more deinterleaved technique(s) is/are applied to the reverse-mapped bits/symbols to recover the original digital data.

<FIG> shows a flowchart illustrating a method <NUM> for decoding digital data from a digital code used at step <NUM>. The digital code includes order-checking bits and one or more LDPC codes. After performing step <NUM> and <NUM>, the system <NUM> obtains a digital code converted from an order of estimated peptide sequences. At step <NUM>, the system <NUM> creates a n × <NUM> block of symbols based on the estimated sequences. In some embodiments, the converted digital code contains bit(s)/symbol(s) that indicate the addresses or positions of the estimated peptide sequences in the block of symbols. The information relating to the addresses or positions of the estimated peptide sequences is used to arrange the estimated peptide sequences in a right order in the block of symbols. The <NUM> symbols in each sequence are denoted as S<NUM>, S<NUM>,. At step <NUM>, according to the orders of the estimated symbol pairs {S<NUM>, S<NUM>} and {S<NUM>, S<NUM>}, the order-checking bits are generated based on pre-defined rules. At step <NUM>, the order-checking bits are compared against the corresponding first bits of the estimated symbols S<NUM> and S<NUM> to see if they are identical. As an example, if there is no error in the orders of S<NUM> and S<NUM>, the generated order-checking bit for {S<NUM>, S<NUM>} should match the first bit of the estimated symbol S<NUM>. If the generated order-checking bits do not match the first bit of S<NUM> and/or S<NUM> in an estimated sequence, the estimated sequence in the block should be erased.

On the condition that the generated order-checking bits match the first bits of the estimated symbols S<NUM> and S<NUM>, method <NUM> proceeds from step <NUM> to step <NUM>. At step <NUM>, the bits in the estimated symbols S<NUM>-S<NUM> of the block are passed to the decoders of the LDPC codes to perform decoding of LDPC code. At step <NUM>, the system <NUM> outputs a <NUM> × <NUM> block of symbols using the decoded bits of the LDPC codes. Similarly to step <NUM>, order-checking bits are generated based on pre-defined rules at step <NUM> according to the decoded symbols pairs {S<NUM>, S<NUM>} and {S<NUM>, S<NUM>}. At step <NUM>, the order-checking bits are compared against the corresponding first bits of the decoded symbol S<NUM> and S<NUM> to see if they are identical. If not, the system <NUM> reports a detected error and indicates that the decoding fails. If yes, the system <NUM> outputs the decoded sequences.

Referring to <FIG> and <FIG>, illustrations <NUM> and <NUM> of retrieving digital data from peptide sequences in accordance with embodiments of the disclosure is depicted. Performing step <NUM> of method <NUM>, the stored mixture is first analyzed by LC-MS/MS. A <NUM> C18 column is used for ultrahigh pressure liquid chromatography (UPLC) separation, with the elution gradient changed from <NUM>% solution A (<NUM>% formic acid in water) to <NUM>% solution B (<NUM>% formic acid in acetonitrile). The MS analysis is performed on an orbitrap mass spectrometer coupled with the UPLC. A non-target strategy with m/z limits of <NUM>-<NUM> and peptide isotopic pattern recognition are used to select ions for MS/MS analysis. High-energy collisional dissociation (HCD) and electron-capture dissociation (ECD) are performed in parallel to produce MS/MS spectra. A total of <NUM> spectra are produced.

In one embodiment (<FIG>), when two-stage sequencing method <NUM> is used, among <NUM> spectra, there are <NUM> spectra without output sequences and another <NUM> spectra without length of <NUM>, which are discarded in the sequence grouping. The sequences have length of <NUM> because the head and tail amino acids are excluded for simplicity. Excluding duplicate sequences, there are <NUM> distinct sequences with length of <NUM>. After grouping based on the scores, <NUM> sequences are obtained corresponding to <NUM> groups with address pairs of {<NUM><NUM>}, {<NUM><NUM>}, {<NUM><NUM>},. , {<NUM><NUM>}, {<NUM><NUM>}. Performing step <NUM> of method <NUM>, these peptide sequences are converted into a digital code or equivalent symbols. The reverse-mapping method used is amino-acid-to-bits reverse mapping, in which an amino acid is reversely mapped to a triplet of bits. Because the amino acid F at the N-terminal and the amino acid R at the C-terminal do not carry any information, only the <NUM> amino acids in the <NUM>-mer peptide sequences are converted to digital code or equivalent symbols. The digital code is decoded by performing step <NUM> of method <NUM> and method <NUM>. In method <NUM>, the order of the first two amino acids and the order of the last two amino acids are checked using the first bits of S<NUM> and S<NUM>, respectively, in accordance with the encoding rules of the order-checking bits. If the bits generated according to the order-checking rules using the first two amino acids and the last two amino acids do not match the first bits of S<NUM> or S<NUM> respectively, then the corresponding sequence will be erased. Finally, a <NUM> × <NUM> block of symbols can be constructed. The error-correction method confirms the correct sequence assignment of <NUM> peptides, corrected <NUM> peptides, and excluded <NUM> impurity peptides. These corrected codes are further decoded to original data, with <NUM>% retrieval. The data density of peptides for data storage in this preliminary study is ~<NUM><NUM> bits/g, estimated from the injection volume of <NUM> and peptide concentration of about <NUM>.

In another embodiment (<FIG>), the highest-intensity-tag based sequencing method <NUM> is used. Among the <NUM> spectra, <NUM> spectra cannot produce any valid sequence, <NUM> spectra produce valid sequences of length not equal to <NUM>, and the remaining <NUM> spectra produce a total of <NUM> valid sequences. Thus, some of the groups have multiple sequences generated by the same or different spectra. Excluding duplicate sequences, there are <NUM> distinct sequences with length of <NUM>. The sequence grouping method described in paragraphs [<NUM>]-[<NUM>] is used to obtain <NUM> groups, each with only one sequence. Step <NUM> of method <NUM> is performed to decode. Performing method <NUM> or step <NUM> of method <NUM>, the correctness of all <NUM> sequences are confirmed, showing that all sequences in the group are correct even without performing order-checking and error-correction processes of steps <NUM>-<NUM>, leading to <NUM>% retrieval of the original data.

The data density may be further improved significantly since MS/MS sequencing of peptides with much smaller amounts, e.g., sub-attomole, could be achieved. At this detection limit, it is estimated at least <NUM><NUM> bits/g could be achieved with the same setup.

<FIG> depicts an exemplary computing device <NUM>, hereinafter interchangeably referred to as a computer system <NUM>, where one or more such computing devices <NUM> may be used to execute the methods <NUM>, <NUM>, <NUM> and <NUM> of <FIG>, <FIG>. One or more components of the exemplary computing device <NUM> can also be used to implement the systems <NUM>, <NUM> as well as the synthesizer <NUM> and the sequencer <NUM>. The following description of the computing device <NUM> is provided by way of example only and is not intended to be limiting.

As shown in <FIG>, the example computing device <NUM> includes a processor <NUM> for executing software routines. Although a single processor is shown for the sake of clarity, the computing device <NUM> may also include a multi-processor system. The processor <NUM> is connected to a communication infrastructure <NUM> for communication with other components of the computing device <NUM>. The communication infrastructure <NUM> may include, for example, a communications bus, cross-bar, or network.

The computing device <NUM> further includes a main memory <NUM>, such as a random access memory (RAM), and a secondary memory <NUM>. The secondary memory <NUM> may include, for example, a storage drive <NUM>, which may be a hard disk drive, a solid state drive or a hybrid drive and/or a removable storage drive <NUM>, which may include a magnetic tape drive, an optical disk drive, a solid state storage drive (such as a USB flash drive, a flash memory device, a solid state drive or a memory card), or the like. The removable storage drive <NUM> reads from and/or writes to a removable storage medium <NUM> in a well-known manner. The removable storage medium <NUM> may include magnetic tape, optical disk, non-volatile memory storage medium, or the like, which is read by and written to by removable storage drive <NUM>. As will be appreciated by persons skilled in the relevant art(s), the removable storage medium <NUM> includes a computer readable storage medium having stored therein computer executable program code instructions and/or data.

In an alternative implementation, the secondary memory <NUM> may additionally or alternatively include other similar means for allowing computer programs or other instructions to be loaded into the computing device <NUM>. Such means can include, for example, a removable storage unit <NUM> and an interface <NUM>. Examples of a removable storage unit <NUM> and interface <NUM> include a program cartridge and cartridge interface (such as that found in video game console devices), a removable memory chip (such as an EPROM or PROM) and associated socket, a removable solid state storage drive (such as a USB flash drive, a flash memory device, a solid state drive or a memory card), and other removable storage units <NUM> and interfaces <NUM> which allow software and data to be transferred from the removable storage unit <NUM> to the computer system <NUM>.

The computing device <NUM> also includes at least one communication interface <NUM>. The communication interface <NUM> allows software and data to be transferred between computing device <NUM> and external devices via a communication path <NUM>. In various embodiments of the disclosure, the communication interface <NUM> permits data to be transferred between the computing device <NUM> and a data communication network, such as a public data or private data communication network. The communication interface <NUM> may be used to exchange data between different computing devices <NUM> which such computing devices <NUM> form part an interconnected computer network. Examples of a communication interface <NUM> can include a modem, a network interface (such as an Ethernet card), a communication port (such as a serial, parallel, printer, GPIB, IEEE <NUM>, RJ45, USB), an antenna with associated circuitry and the like. The communication interface <NUM> may be wired or may be wireless. Software and data transferred via the communication interface <NUM> are in the form of signals which can be electronic, electromagnetic, optical or other signals capable of being received by communication interface <NUM>. These signals are provided to the communication interface via the communication path <NUM>.

As used herein, the term "computer program product" may refer, in part, to removable storage medium <NUM>, removable storage unit <NUM>, a hard disk installed in storage drive <NUM>, or a carrier wave carrying software over communication path <NUM> (wireless link or cable) to communication interface <NUM>. Computer readable storage media refers to any non-transitory, non-volatile tangible storage medium that provides recorded instructions and/or data to the computing device <NUM> for execution and/or processing. Examples of such storage media include magnetic tape, CD-ROM, DVD, Blu-ray™ Disc, a hard disk drive, a ROM or integrated circuit, a solid state storage drive (such as a USB flash drive, a flash memory device, a solid state drive or a memory card), a hybrid drive, a magneto-optical disk, or a computer readable card such as a PCMCIA card and the like, whether or not such devices are internal or external of the computing device <NUM>. Examples of transitory or non-tangible computer readable transmission media that may also participate in the provision of software, application programs, instructions and/or data to the computing device <NUM> include radio or infra-red transmission channels as well as a network connection to another computer or networked device, and the Internet or Intranets including e-mail transmissions and information recorded on Websites and the like.

The computer programs (also called computer program code) are stored in main memory <NUM> and/or secondary memory <NUM>. Computer programs can also be received via the communication interface <NUM>. Such computer programs, when executed, enable the computing device <NUM> to perform one or more features of embodiments discussed herein. In various embodiments, the computer programs, when executed, enable the processor <NUM> to perform features of the above-described embodiments. Accordingly, such computer programs represent controllers of the computer system <NUM>.

Software may be stored in a computer program product and loaded into the computing device <NUM> using the removable storage drive <NUM>, the storage drive <NUM>, or the interface <NUM>. The computer program product may be a non-transitory computer readable medium. Alternatively, the computer program product may be downloaded to the computer system <NUM> over the communication path <NUM>. The software, when executed by the processor <NUM>, causes the computing device <NUM> to perform the necessary operations to execute the methods <NUM>, <NUM>, <NUM>, and <NUM> as shown in <FIG>, <FIG>.

It is to be understood that the embodiment of <FIG> is presented merely by way of example to explain the operation and structure of the system <NUM>. Therefore, in some embodiments one or more features of the computing device <NUM> may be omitted. Also, in some embodiments, one or more features of the computing device <NUM> may be combined together. Additionally, in some embodiments, one or more features of the computing device <NUM> may be split into one or more component parts.

It will be appreciated that the elements illustrated in <FIG> function to provide means for performing the various functions and operations of the system as described in the above embodiments.

Claim 1:
A method of storing digital data into peptides comprising:
encoding (<NUM>) the digital data into a digital code;
translating (<NUM>) the digital code into the peptide sequences, wherein an individual peptide sequence comprises a sequence of amino acids corresponding to a part of the digital code such that the part of the digital code is carried in the individual peptide sequence, an individual amino acid in the sequence of amino acids representing a pattern of bits or symbols; and
synthesizing (<NUM>) the translated peptide sequences into the peptides;
characterised in that:
the encoding (<NUM>) of the digital data into the digital code comprises adding one or more order-checking bits into the part of the digital code, the one or more order-checking bits being used for protecting the order of selected bits or symbols in the part of the digital code and being generated based on one or more orders of the selected bits or symbols, the selected bits or symbols consisting of first and second sequences of patterns of bits or symbols, the first sequence of patterns of bits or symbols being located at one end of the individual peptide sequence while the second sequence of patterns of bits or symbols is located at another end thereof; and
each peptide is generated from one translated peptide sequence such that a respective peptide synthesized from the individual peptide sequence carries the one or more order-checking bits, the one or more order-checking bits in the respective peptide assisting selection of a single candidate sequence to be the individual peptide sequence among plural candidate sequences each having a length of the individual peptide sequence and each obtained from a peptide sequencing method used in tandem mass spectrometry analysis when the respective peptide is sequenced during retrieving the digital data from the peptides.