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The title says it all. I'm just curious. I read that scientists mapped the genome for Malus Domestica, but I can't find a sequence anywhere.If this is a stupid question, I would appreciate if you tell me where I'm wrong in this!
You can see the data in the URL above. The details are described in this article.
As others said, NCBI seems useful. Go to this site. Chose chromosome you want to see and click genebank or refsequence corresponding to the chromosome in the table (Assembly Unit: Primary Assembly). You can see overview of the sequence. Find FASTA in the page showing the overview and click FASTA. Then the sequence data will be downloaded.
Here is the apple genome on NCBI.
by Allison Baker
figures by Lillian Horin
The Arctic apple is the juiciest newcomer to produce aisles. It has the special ability to resist browning after being cut (Figure 1), which protects its flavor and nutritional value. Browning also contributes to food waste by causing unappealing bruising on perfectly edible apples. Food waste, especially for fruits and vegetables, is a major problem worldwide nearly half of the produce that’s grown in the United States is thrown away, and the UK supermarket Tesco estimates that consumer behavior significantly contributes to the 40% of its apples that are wasted. Therefore, Arctic apples not only make convenient snacks, but they also might be able to mitigate a major source of food waste.
Figure 1: Traditional Golden Delicious apple (left) versus the Arctic variety (right). After slicing into the apples, the traditional Golden Delicious apple is turning brown as expected. On the other hand, the Arctic Golden doesn’t become discolored at all. (Image credit: Okanagan Specialty Fruits Inc.)
While a non-browning apple sounds great, how exactly was this achieved? Arctic apples are genetically engineered (GE) to prevent browning. This means that the genetic material that dictates how the apple tree grows and develops was altered using biotechnology tools. But before learning about the modern science used to make Arctic apples, let’s explore how traditional apple varieties are grown.
Brief Introduction on Three Generations of Genome Sequencing Technology
It has been over 30 years since the first generation of DNA sequencing technology was developed in 1977. During this period, sequencing technology has made considerable progress. From the first generation to the third generation and even the fourth generation, sequencing technology has experienced the read length from long to short, and short to long. Although the second generation—short-read sequencing technology still dominates the current global sequencing market, the third and fourth generation of sequencing technologies are rapidly evolving over the course of the two-year period. Every transformation of sequencing technology results in a huge role in promoting genome research, disease medical research, drug development, breeding and other fields. This blog is mainly focusing on the current genome sequencing technologies and their sequencing principles.
The Development of Sequencing Technology
In 1952, Hershey and Chase completed the famous T2 phage infection of bacteria experiment, which effectively proved that DNA is a genetic material. In 1953, Crick and Watson showed their DNA model in the British magazine–Nature. After a thorough study at Cambridge University, they described DNA model with “double helix”. In 1958, Francis Crick proposed the genetic central dogma, which was reiterated in Nature in 1970. Genetic code, also known as codons, genetic codons or triple codes, determines the nucleotide sequence of the amino acid sequence in the protein, which are consist of three consecutive nucleotides. In 1966, Hola announced that the genetic code had been deciphered. In 1974, Szibalski, Polish geneticist, proposed genetic recombination technology was synthetic biology concept. DNA recombinant technology, also known as genetic engineering, aims to recombine DNA molecules in vitro, proliferating in the appropriate cells. In 1983, PCR (polymerase chain reaction) was developed by Dr. Kary B.Mullis. It is a molecular biology technique and used to amplify specific DNA fragments, which can be regarded as the special DNA replication in vitro.
In 1977, A.M. Maxam and W. Gilbert firstly established a DNA fragment sequence determination method, which is also called Maxam-Gilbert chemical degradation method. Currently, this chemical degradation method and enzymatic method (dideoxy chain termination method) proposed by Sanger are rapid sequencing techniques. In 1986, the first automated sequencer—abi prism 310 gene analyzer was developed by an American company—Pe Abi. And then Hood and Smith utilized fluorescently labeled dNTP for electrophoresis technology. Therefore, the first commercial automatic sequencer was born. After that, the capillary electrophoresis sequencer was developed in 1996 and 3700 type automated sequencer was developed in 1998.
In 2008, Quake group designed and developed HeliScope sequencer, which is also a loop chip sequencing equipment. In the same year, nanopore sequencing was developed based on the electrophoresis technology. In the next year, SMRT was developed. In 2010, ion PGM and GeXP were put into use.
In 2005, Roche company designed 454 technology–genome sequencer 20 system—an ultra high throughput genome sequencing system, which was praised as a milestone in the development of sequencing technology by Nature. In 2006, illumina sequencer was developed and it is suitable for DNA libraries prepared by various methods. In 2007, Solid System was developed.
First generation of sequencing technology
The first generation of sequencing technology is based on the chain termination method developed by Sanger and Coulson in 1975 or the chemical method (chain degradation) invented by Maxam and Gulbert during 1976 and 1977. And Sanger in 1977 judged the first genome sequence belonging to Phage X174 with the whole length of 5375 bases. Since then, human beings have aquired the ability to snoop the nature of the genetic difference of life, and also it is a beginning of the genomic era. Researchers continue to improve the Sanger method during performance. In 2001, it was based on the improved Sanger method that the first human genome map was completed. The core principle of Sanger method is that ddNTP cannot form phosphodiester bond during the synthesis of DNA, due to the lack of hydroxyl in its 2 ‘and 3’. So it can be used to interrupt the DNA synthesis reaction. Add a certain proportion of ddNTP with radioactive isotope label, including ddATP, ddCTP, ddGTP and ddTTP, into four DNA synthesis reaction systems respectively. After gel electrophoresis and autoradiography, the DNA sequences of the samples can be determined according to the position of the electrophoretic band.
In addition to Sanger method, it is worth noting that during the period of sequencing technology development, there are many other sequencing technologies emerging, such as pyrophosphate sequencing method, ligation enzyme method and so on. Among these, pyrophosphate sequencing method was later used by Roche company for 454 technique, while the ligation enzyme method was used for SOLID technique by ABI company. The common core method shared by both of them was to use dNTP which can interrupt DNA synthesis, similar to ddNTP in Sanger method.
All in all, the first generation of sequencing technology has the read-length ability of 1000bp with the 99.999% accuracy, which are the main feature. However, its high cost, low throughput and other disadvantages result in a serious impact on its real large-scale application. Therefore, the first generation of sequencing technology is not the most ideal sequencing method. Undergoing development and improvement, the second generation of sequencing technology was born symbolized by Roche’s 454 technology, Illumina’s Solexa, Hiseq technology, and ABI’s Solid technology. The second generation of sequencing technology cannot only greatly reduce sequencing cost, but also dramatically increase the speed of sequencing, maintaining high accuracy. The turn-around time of the second generation sequencing technology to complete a human genome project can just be one week, while that using the first generation sequencing technology to achieve the same goal is three years. However, the read length of the second generation of sequencing technology is much shorter than that of the first generation.
In the next blog chapter, we will continue to introduce the second generation of sequencing technology.
Computer Security and Privacy in DNA Sequencing
There has been rapid improvement in the cost and time necessary to sequence and analyze DNA. In the past decade, the cost to sequence a human genome has decreased 100,000 fold or more. This rapid improvement was made possible by faster, massively parallel processing. Modern sequencing techniques can sequence hundreds of millions of DNA strands simultaneously, resulting in a proliferation of new applications in domains ranging from personalized medicine, ancestry, and even the study of the microorganisms that live in your gut.
Computers are needed to process, analyze, and store the billions of DNA bases that can be sequenced from a single DNA sample. Even the sequencing machines themselves run on computers. New and unexpected interactions may be possible at this boundary between electronic and biological systems. As a multi-disciplinary group of researchers who study both computer security and DNA manipulation, we wanted to understand what new computer security risks are possible in the interaction between biomolecular information and the computer systems that analyze it.
Here we highlight two key examples of our research below: (1) the failure of DNA sequencers to follow best practices in computer security and (2) the possibility to encode malware in DNA sequences. See our paper for more detailed information on our findings. This paper will appear at the peer-reviewed USENIX Security Symposium in August 2017.
Computer Security Analysis of DNA Sequencing Programs
After DNA is sequenced, it is usually processed and analyzed by a number of computer programs through what is called the DNA data processing pipeline. We analyzed the computer security practices of commonly used, open-source programs in this pipeline and found that they did not follow computer security best practices. Many were written in programming languages known to routinely contain security problems, and we found early indicators of security problems and vulnerable code. This basic security analysis implies that the security of the sequencing data processing pipeline is not sufficient if or when attackers target the pipeline.
DNA Encoded Malware
DNA stores standard nucleotides—the basic structural units of DNA—as letters such as A, C, G, and T. After sequencing, this DNA data is processed and analyzed using many computer programs. It is well known in computer security that any data used as input into a program may contain code designed to compromise a computer. This lead us to question whether it is possible to produce DNA strands containing malicious computer code that, if sequenced and analyzed, could compromise a computer.
To assess whether this is theoretically possible, we included a known security vulnerability in a DNA processing program that is similar to what we found in our earlier security analysis. We then designed and created a synthetic DNA strand that contained malicious computer code encoded in the bases of the DNA strand. When this physical strand was sequenced and processed by the vulnerable program it gave remote control of the computer doing the processing. That is, we were able to remotely exploit and gain full control over a computer using adversarial synthetic DNA.
No Reason for Concern
Note that there is not present cause for alarm about present-day threats. We have no evidence to believe that the security of DNA sequencing or DNA data in general is currently under attack. Instead, we view these results as a first step toward thinking about computer security in the DNA sequencing ecosystem. One theme from computer security research is that it is better to consider security threats early in emerging technologies, before the technology matures, since security issues are much easier to fix before real attacks manifest.
We again stress that there is no cause for people to be alarmed today, but we also encourage the DNA sequencing community to proactively address computer security risks before any adversaries manifest. That said, it is time to improve the state of DNA security.
We encourage the DNA sequencing community to follow secure software best practices when coding bioinformatics software, especially if it is used for commercial or sensitive purposes. Also, it is important to consider threats from all sources, including the DNA strands being sequenced, as a vector for computer attacks. See our research paper for a more detailed discussion of threats to the DNA sequencing pipeline and potential defenses.
Is it possible to exploit a computer program with synthesized DNA?
The results from our study show that it is theoretically possible to produce synthetic DNA that is capable of compromising a computer system. For now, these attacks are difficult in practice because it is challenging to synthesize malicious DNA strands and to find relevant vulnerabilities in DNA processing programs. Thus, while scientifically interesting, we stress that people today should not necessarily be alarmed, as we discuss both above and below.
What are your findings, regarding leading open-source computational biology software packages?
We analyzed open-source bioinformatics tools that are commonly used by researchers to analyze DNA data. Many of these are written in languages like C and C++ that are known to contain security vulnerabilities unless programs are carefully written. In this case the programs did not follow computer security best practices. For example, most had little input sanitization and used insecure functions. Others had static buffers that could overflow. The lack of input sanitization, the use of insecure functions, and the use of overflowable buffers can make a program vulnerable to attackers modern computer security best practices are to avoid or cautiously use these programmatic constructs whenever possible.
Is there any reason for immediate concern?
No. We have no reason to believe that there have been any attacks against DNA sequencing or analysis programs. A primary goal of this study was to better understand the feasibility of DNA-based code injection attacks. Our DNA-based exploit is hypothetical, compromising a program that we intentionally modified to include a vulnerability. We also know of no efforts by adversaries to compromise computational biology programs.
However, since DNA sequencing technologies are maturing and becoming more ubiquitous, we do believe that these types of issues could pose a growing problem into the future, if unaddressed. We therefore believe that now is the right time to begin hardening the computational biology ecosystem to cyber attacks.
Are there any risks to people with DNA-based exploits? Will this infect my genome?
The answers to both questions are no. Your genome is untouched. Our exploit shows that specifically designed DNA can be used to affect computer programs, not living organisms themselves. Said another way, our exploit is designed to compromise a computer program involved in the DNA sequencing pipeline (and a program intentionally modified to include a vulnerability). The DNA sequence we designed for this paper does not have any biological significance. We further stress that researchers often synthesize DNA with non-biological functions, e.g., when using DNA for digital data storage.
Are you helping the bad guys?
As computer security researchers, we are interested in understanding the security risks of emerging technologies, with the goal of helping improve the security of future versions of those technologies.
The security research community has found that evaluating the security risks of a new technology while it is being developed makes it much easier to confront and address security problems before adversarial pressure manifests. One example has been the modern automobile and another the modern wireless implantable medical device. In both cases, the government and industry responded to security research uncovering potential risks, and as a result both the modern automotive industry and the medical device industry have significantly increased their computer security protections. We encourage the computational biology community to do the same.
What is the DNA data processing pipeline?
DNA sequencing is a complicated process that begins with physical DNA samples that are prepared in a laboratory. These prepared samples are then run through a machine that produces raw DNA sequence output. To make this data useful, it is manipulated and analyzed through a number of different programs that process the data in stages. These programs constitute the DNA data processing pipeline.
Do you have any advice for governments?
The government is currently involved in regulating the production of synthetic DNA products that may be used to generate dangerous compounds (e.g., infectious diseases, toxins, etc.) and federal law requires adequate security in connection to some types of health information. At this point, we are not in a position to propose any specific additional regulations. However, we intend to analyze the law and policy ramifications of this work in partnership with the UW Tech Policy Lab and encourage regulators to consider this area moving into the future.
Do you have any advice for biology researchers and the computational biology community?
The DNA sequencing community, and especially the programmers of bioinformatics tools, should consider computer security when developing software. In particular, we encourage the wide adoption of security best practices like the use of memory safe languages or bounds checking at buffers, input sanitization, and regular security audits.
Another issue to consider is how to best maintain and patch bioinformatics software. Much of it is written and maintained by many entities, which makes it difficult to patch and has led to a high prevalence of out-of-date software.
Please see the research paper for a detailed threat analysis and additional security recommendations.
Do you have recommendations for the computer security community?
DNA synthesis and sequencing are very important tools in molecular and synthetic biology, and over time, we expect that they will increase in prevalence, especially as they move into new commercial domains. This study is just a first attempt to consider the security risks of this field. Given the importance of these technologies and their close connection to computers it is important that the security community consider the broad threats to this ecosystem.
Should I avoid genetic testing because of these findings?
No, not at all. Genetic sequencing and testing has many important benefits, and the risks we describe in this study are far from practice.
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Some of the services provided by the DNASC include:
- Custom PacBio sequencing on 2 Sequel II instruments. We offer a range of services for these instruments including HiFi library construction and sequencing, CLR library construction and sequencing, Iso-Seq library preparation and sequencing.
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The DNASC is supported by Brigham Young University through the Department of Biology under the direction of Dr. Michael F. Whiting and managed by Dr. Edward Wilcox.
- all variants should be described at the most basic level, the DNA level. Descriptions at the RNA and/or protein level may be given in addition.
- descriptions should make clear whether the change was experimentally determined or theoretically deduced by giving predicted consequences in parentheses
- descriptions at RNA/protein level should describe the changes observed on that level (RNA/protein) and not try to incorporate any knowledge regarding the change at DNA-level (see Questions below)
- the reference sequence file used should be public and clearly described, e.g. NC_000023.10, LRG_199, NG_012232.1, NM_004006.2, LRG-199t1, NR_002196.1, NP_003997.1, etc. (see Reference Sequences)
- when variants are not reported in relation to a genomic reference sequence from a recent genome build, the preferred reference sequence is a Locus Reference Genomic sequence (LRG)
- when no LRG is available, one should be requested (see Reference Sequences).
- the reference sequence used must contain the residue(s) described to be changed.
- “c.” for a coding DNA reference sequence
- “g.” for a linear genomic reference sequence
- “m.” for a mitochondrial DNA reference sequence
- “n.” for a non-coding DNA reference sequence
- “o.” for a circular genomic reference sequence
- “p.” for a protein reference sequence
- “r.” for an RNA reference sequence (transcript)
- exception: two variants separated by one nucleotide, together affecting one amino acid, should be described as a “delins” NOTE: the SVD-WG is preparing a proposal to modify this recommendation. To apply the current rule one needs to know whether the two variants are in a coding sequence and affecting one amino acid. Recommendations should be general. The new recommendation will be: two variants separated by less then two nucleotides should be described as a “delins”
- the 3’rule also applies for changes in single residue stretches and tandem repeats (nucleotide or amino acid)
- the 3’rule applies to ALL descriptions (genome, gene, transcript and protein) of a given variant
- exception: deletion/duplication around exon/exon junctions using c., r. or n. reference sequences (see Numbering)
- DNA-level 123456A>T (see Details): number(s) referring to the nucleotide(s) affected, nucleotides in CAPITALS using IUPAC-IUBMB assigned nucleotide symbols
- RNA-level 76a>u (see Details): number(s) referring to the nucleotide(s) affected, nucleotides in lower case using IUPAC-IUBMB assigned nucleotide symbols
- protein level Lys76Asn (see Details): the amino acid(s) affected in three- or one-letter code followed by a number IUPAC-IUBMB assigned amino acid symbols
- three-letter amino acid code is preferred (see Standards)
- the “*“ can be used to indicate the translation stop codon in both one- and three-letter amino acid code descriptions
- when a variant can be described as a duplication or an insertion, prioritisation determines it should be described as a duplication
- descriptions removing part of a reference sequence replacing it with part of the same sequence are not allowed (e.g. NM_004006.2:c.[762_768del767_774dup])
In HGVS nomenclature some characters have a specific meaning
- “ + ” (plus) is used in nucleotide numbering c.123+45A>G
- “ - ” (minus) is used in nucleotide numbering c.124-56C>T
- “ * ” (asterisk) is used in nucleotide numbering and to indicate a translation termination (stop) codon (see Standards) c.*32G>A and P.Trp41*
- “ _ ” (underscore) is used to indicate a range g.12345_12678del
- “ [ ] ” (square brackets) are used for alleles (see DNA, RNA, protein), which includes multiple inserted sequences at one position and insertions from a second reference sequence
- “ ” (semi colon) is used to separate variants and alleles g.[123456A>G345678G>C] or g.[123456A>G][345678G>C]
- “ , ” (comma) is used to separate different transcripts/proteins derived from one allele r.[123a>u, 122_154del]
Abbreviations in variant descriptions
Specific abbreviations are used to describe different variant types.
- “ > ” (greater then) indicates a substitution (DNA and RNA level) g.123456G>A, r.123c>u (see DNA, RNA)
- a substitution at the protein level is described as p.Ser321Arg (see protein)
- duplicating insertions are described as duplications, not as insertions
“ ext ” indicates an extension p.Met1 ext -5 (see Extension)
- “ cen ” indicates the centromere of a chromosome
- “ chr ” indicates a chromosome chr11:g.12345611G>A (NC_000011.9)
- “ pter indicates the first nucleotide of a chromosome
- “ qter ” indicates the last nucleotide of a chromosome
- “ sup ” indicates an supernumary chromosome (marker chromosome)
- “ gom ” indicates a gain of methylation g.12345678_12345901 |gom
- “ lom ” indicates a loss of methylation g.12345678_12345901 |lom
- “ met ” indicates a methylation g.12345678_12345901 |met=
Scientists sequence Norway spruce DNA. The tree’s genome is LONG
Researchers reported Wednesday that they had sequenced the genome of the Norway spruce, a giant evergreen native to Europe that has also been planted widely in parts of North America.
Published in the journal Nature, the catalog of the tree’s DNA was notable for its length. The human genome is made up of about 3 billion pairs of DNA base letters, which store all the genetic information needed to make a person. The Norway spruce genome was nearly seven times longer, at 20 billion base pairs. Putting its DNA in the right order was a technical challenge because the genome includes so many repetitive segments.
The research revealed that despite its jumbo-sized genome, spruces seem to have a similar number of protein-encoding genes as humans: on the order of 30,000. Why the Norway spruce has so very much other DNA, and whether that DNA plays an ongoing role in conifer biology, is a question scientists will explore further, the researchers wrote.
Conifers, like spruce, fir and pine trees, are members of a sub-group of seed-producing plants known as gymnosperms, which all have very long genomes. Another super-long conifer genome, that of the white spruce, was also described this week, in the journal Bioinformatics.
University of British Columbia plant biochemist Joerg Bohlmann, a coauthor on both studies, said in a statement that the newly assembled genome sequences would let researchers perfect the way foresters breed trees, focusing in on challenges such as “insect resistance, wood quality, growth rates and adaptation to changing climate.”
Understanding more about the Norway spruce could also, indirectly, help scientists who are working to develop longer-lasting, more appealing Christmas trees, said Washington State University plant pathologist Gary Chastagner.
In December, the Los Angeles Times profiled Chastagner’s work, which focuses on finding what genetic changes might help create trees that won’t shed all their needles between Thanksgiving and New Year’s. At the time, Chastagner said his lab was just beginning to incorporate DNA findings into his analysis of fir trees.
Chastagner doesn’t focus on spruce trees in his research. But he said in an email Wednesday that the new genome sequences had the potential to aid his work if they illuminated how genes influence needle retention in spruce trees.
“It may allow us to determine if the same mechanism controls needle loss in other species, such as the true firs we are working with,” he wrote.
Want to learn more about gymnosperms? Nature included a News & Views article with the Norway spruce genome study (subscription required for full text) in which North Carolina State University researcher Ronald Sederoff explains more about why scientists are interested in the conifer genomes.
And for a different type of appreciation of the mighty spruce, music fans can check out “C is for Conifer,” this 2005 song by They Might be Giants:
Managing apple maggots with insecticides
Apple maggot adult female. Photo by Joseph Berger, Bugwood.org.
Moderate levels of apple maggot adult emergence have been detected at the Michigan State University Trevor Nichols Research Center in Fennville, Michigan, following rainfall events. Controlling apple maggots has been traditionally achieved with organophosphate insecticides, like Imidan. Synthetic pyrethroid compounds, like Asana, Warrior, Danitol, Battalion, Mustang Max and Baythroid, are also toxic to adult fruit flies, but are generally viewed to be moderately effective because they have a shorter field residual. There are several reduced-risk and organophosphate-replacement insecticide products that include apple maggot on their labels.
The neonicotinoids Belay, Admire and Assail are labeled for apple maggot control. They have limited lethal action on adult apple maggots, but provide strong curative activity on eggs and larvae. The METI compound, Apta, is toxic to adult fruit flies as a contact insecticide. The Spinosyn compounds Delegate and Entrust are active on apple maggots when ingested, but have shown to be only fair control materials in field trials with high pest pressure, thus are labeled for apple maggot suppression only.
The Diamide compound Exirel and premix Minecto Pro (diamide plus avermectin) are active on apple maggots and labeled for population suppression. Leverage, Voliam Flexi and Endigo are pre-mix compounds that are labeled for apple maggot control.
What is a hidden Markov model?
Statistical models called hidden Markov models are a recurring theme in computational biology. What are hidden Markov models, and why are they so useful for so many different problems?
Often, biological sequence analysis is just a matter of putting the right label on each residue. In gene identification, we want to label nucleotides as exons, introns, or intergenic sequence. In sequence alignment, we want to associate residues in a query sequence with homologous residues in a target database sequence. We can always write an ad hoc program for any given problem, but the same frustrating issues will always recur. One is that we want to incorporate heterogeneous sources of information. A genefinder, for instance, ought to combine splice-site consensus, codon bias, exon/ intron length preferences and open reading frame analysis into one scoring system. How should these parameters be set? How should different kinds of information be weighted? A second issue is to interpret results probabilistically. Finding a best scoring answer is one thing, but what does the score mean, and how confident are we that the best scoring answer is correct? A third issue is extensibility. The moment we perfect our ad hoc genefinder, we wish we had also modeled translational initiation consensus, alternative splicing and a polyadenylation signal. Too often, piling more reality onto a fragile ad hoc program makes it collapse under its own weight.
Hidden Markov models (HMMs) are a formal foundation for making probabilistic models of linear sequence 'labeling' problems 1,2 . They provide a conceptual toolkit for building complex models just by drawing an intuitive picture. They are at the heart of a diverse range of programs, including genefinding, profile searches, multiple sequence alignment and regulatory site identification. HMMs are the Legos of computational sequence analysis.
A toy HMM: 5′ splice site recognition
As a simple example, imagine the following caricature of a 5′ splice-site recognition problem. Assume we are given a DNA sequence that begins in an exon, contains one 5′ splice site and ends in an intron. The problem is to identify where the switch from exon to intron occurred—where the 5′ splice site (5′SS) is.
For us to guess intelligently, the sequences of exons, splice sites and introns must have different statistical properties. Let's imagine some simple differences: say that exons have a uniform base composition on average (25% each base), introns are A/T rich (say, 40% each for A/T, 10% each for C/G), and the 5′SS consensus nucleotide is almost always a G (say, 95% G and 5% A).
Starting from this information, we can draw an HMM (Fig. 1). The HMM invokes three states, one for each of the three labels we might assign to a nucleotide: E (exon), 5 (5′SS) and I (intron). Each state has its own emission probabilities (shown above the states), which model the base composition of exons, introns and the consensus G at the 5′SS. Each state also has transition probabilities (arrows), the probabilities of moving from this state to a new state. The transition probabilities describe the linear order in which we expect the states to occur: one or more Es, one 5, one or more Is.
It's useful to imagine an HMM generating a sequence. When we visit a state, we emit a residue from the state's emission probability distribution. Then, we choose which state to visit next according to the state's transition probability distribution. The model thus generates two strings of information. One is the underlying state path (the labels), as we transition from state to state. The other is the observed sequence (the DNA), each residue being emitted from one state in the state path.
The state path is a Markov chain, meaning that what state we go to next depends only on what state we're in. Since we're only given the observed sequence, this underlying state path is hidden—these are the residue labels that we'd like to infer. The state path is a hidden Markov chain.
The probability P(S,π|HMM,θ) that an HMM with parameters θ generates a state path π and an observed sequence S is the product of all the emission probabilities and transition probabilities that were used. For example, consider the 26-nucleotide sequence and state path in the middle of Figure 1, where there are 27 transitions and 26 emissions to tote up. Multiply all 53 probabilities together (and take the log, since these are small numbers) and you'll calculate log P(S,π|HMM,θ) = −41.22.
An HMM is a full probabilistic model—the model parameters and the overall sequence 'scores' are all probabilities. Therefore, we can use Bayesian probability theory to manipulate these numbers in standard, powerful ways, including optimizing parameters and interpreting the significance of scores.
Finding the best state path
In an analysis problem, we're given a sequence, and we want to infer the hidden state path. There are potentially many state paths that could generate the same sequence. We want to find the one with the highest probability.
For example, if we were given the HMM and the 26-nucleotide sequence in Figure 1, there are 14 possible paths that have non-zero probability, since the 5′SS must fall on one of 14 internal As or Gs. Figure 1 enumerates the six highest-scoring paths (those with G at the 5′SS). The best one has a log probability of −41.22, which infers that the most likely 5′SS position is at the fifth G.
For most problems, there are so many possible state sequences that we could not afford to enumerate them. The efficient Viterbi algorithm is guaranteed to find the most probable state path given a sequence and an HMM. The Viterbi algorithm is a dynamic programming algorithm quite similar to those used for standard sequence alignment.
Beyond best scoring alignments
Figure 1 shows that one alternative state path differs only slightly in score from putting the 5′SS at the fifth G (log probabilities of −41.71 versus −41.22). How confident are we that the fifth G is the right choice?
This is an example of an advantage of probabilistic modeling: we can calculate our confidence directly. The probability that residue i was emitted by state k is the sum of the probabilities of all the state paths that use state k to generate residue i (that is, πi = k in the state path π), normalized by the sum over all possible state paths. In our toy model, this is just one state path in the numerator and a sum over 14 state paths in the denominator. We get a probability of 46% that the best-scoring fifth G is correct and 28% that the sixth G position is correct (Fig. 1, bottom). This is called posterior decoding. For larger problems, posterior decoding uses two dynamic programming algorithms called Forward and Backward, which are essentially like Viterbi, but they sum over possible paths instead of choosing the best.
Making more realistic models
Making an HMM means specifying four things: (i) the symbol alphabet, K different symbols (e.g., ACGT, K = 4) (ii) the number of states in the model, M (iii) emission probabilities ei(x) for each state i, that sum to one over K symbols x, Σxei(x) = 1 and (iv) transition probabilities ti(j) for each state i going to any other state j (including itself) that sum to one over the M states j, Σjti(j) = 1. Any model that has these properties is an HMM.
This means that one can make a new HMM just by drawing a picture corresponding to the problem at hand, like Figure 1. This graphical simplicity lets one focus clearly on the biological definition of a problem.
For example, in our toy splice-site model, maybe we're not happy with our discrimination power maybe we want to add a more realistic six-nucleotide consensus GTRAGT at the 5′ splice site. We can put a row of six HMM states in place of '5' state, to model a six-base ungapped consensus motif, parameterizing the emission probabilities on known 5′ splice sites. And maybe we want to model a complete intron, including a 3′ splice site we just add a row of states for the 3′SS consensus, and add a 3′ exon state to let the observed sequence end in an exon instead of an intron. Then maybe we want to build a complete gene model. whatever we add, it's just a matter of drawing what we want.
HMMs don't deal well with correlations between residues, because they assume that each residue depends only on one underlying state. An example where HMMs are usually inappropriate is RNA secondary structure analysis. Conserved RNA base pairs induce long-range pairwise correlations one position might be any residue, but the base-paired partner must be complementary. An HMM state path has no way of 'remembering' what a distant state generated.
Sometimes, one can bend the rules of HMMs without breaking the algorithms. For instance, in genefinding, one wants to emit a correlated triplet codon instead of three independent residues HMM algorithms can readily be extended to triplet-emitting states. However, the basic HMM toolkit can only be stretched so far. Beyond HMMs, there are more powerful (though less efficient) classes of probabilistic models for sequence analysis.
A Vision of the Future
Moving forward, the potential for DNA-based storage is nearly limitless. Finkelstein presents a vision of the future wherein DNA, encoded with data, can be incorporated inside other materials.
In one example, he says, researchers impregnated a piece of 3D-printed plastic with strands of DNA that contained the object files for the plastic object being printed. As the plastic passes through the printer, it can release the DNA to recreate the file in a circular process.
Or, you could use DNA-based data storage as a way to make forensic discoveries about inanimate objects that don't have their own genetic material. Say you coat an airplane with a material that contains DNA, with the full instructions for building that particular portion of the plane. If something goes awry, and the plane ends up in the sea, the DNA contained in the coating will degrade to some degree due to the sun's ultraviolet rays.
But put another way, that degradation is just a way to record information about what has happened to the plane. If even one piece of the wreckage is recovered, scientists can analyze the stored DNA&ndashand the degradation&mdashto see how long it has been lost at sea.
Even with the breakthroughs that Finkelstein's team has made, DNA-based digital storage is still some time away. "I think that niche applications are probably close to being on the horizon," he says, "but I don&rsquot think it&rsquos going to be a mass market product for a decade or more."
It's been nearly 60 years since magnetic tape overcame punch cards as the primary mode for data storage, bringing about a revolution in personal computing. Since then, disk drives have only gotten smaller and smaller. So a future where the storage medium of choice is so small that you can hardly even see it actually makes sense.
When we reach that reality, DNA-based storage will be the most impressive leap yet.
Watch the video: Γρήγορη Νηστίσιμη Μηλόπιτα. Άκης Πετρετζίκης (May 2022).