Intelligent DNA Chips: Logical Operation of Gene Expression Profiles on DNA Computers

Transcription

1 Genome Informatics 11: (2000) 33 Intelligent DNA Chips: Logical Operation of Gene Expression Profiles on DNA Computers Yasubumi Sakakibara 1 Akira Suyama 2 yasu@j.dendai.ac.jp suyama@dna.c.u-tokyo.ac.jp 1 Department of Information Sciences, Tokyo Denki University, Hatoyama, Hiki-gun, Saitama , Japan 2 Institute of Physics and Department of Life Sciences, Graduate School of Arts and Sciences, University of Tokyo, Komaba, Meguro, Tokyo , Japan Abstract We propose a new type of DNA chips with logical operations executable. In DNA computing researches, some methods have been developed to represent and evaluate Boolean functions on DNA strands. By employing the evaluation methods, we are able to deal with logical operations such as logical- and and logical- or for gene expressions. By combining with the DNA Coded Number method, we implement universal DNA chips which not only detect gene expressions but also find logical formulae of gene expressions. An important advantage of our intelligent DNA chip is that the intensity of the fluorescence at each element is not only proportional to the expression level of the genes in the sample but also proportional to the satisfiability level of the Boolean formula at the element with the gene expression pattern. These features of the intelligent DNA chip and the DCN method allow us more quantitative analyses of gene expression profiles and the logical operations. Keywords: DNA chip, DNA coded number, logical operation, DNA computing 1 Introduction Recently, DNA chip [3] or Microarray [2, 6, 10] technologies have been developed and considered as an important tool for detecting the gene expression levels. A most fascinating feature of DNA chip is the massive parallelism to enable to simultaneously detect the expressions for a large number of genes. This is done by using a simple technology of the hybridizations to complementary DNA strands bonded to a glass surface in an array format. Nevertheless, DNA chip technology has a much potential for various applications including gene discovery and disease diagnosis. In DNA computing researches, some methods have been developed to represent and evaluate Boolean functions on DNA strands. Specifically, Sakakibara [5] has recently proposed new methods to encode any DNF Boolean formula to a DNA strand, evaluate the encoded DNF formula for a truthvalue assignment by using hybridization and primer extension with DNA polymerase. By employing this evaluation methods, we are able to deal with logical operations such as logical- and and logical- or for gene expressions on DNA strands. Sakakibara [5] has applied the representation and evaluation methods for Boolean formulae to solving a learning problem of Boolean formulae (that is known as computationally intractable) using DNA-based massively parallel search. On the other hand, Suyama et al. [7] have developed the DNA Coded Number (DCN) method with the purpose to apply DNA based computers to genome information processing. In the DCN method, genome information is first converted into data expressions in DCNs using a conversion table written with DNA molecules. DCNs are numbers represented by orthonormal DNA base sequences. The orthonormal sequences have uniform melting temperature and no mishybridization or folding potential to minimize computational error in DNA computing. DCN-encoded genome information is

2 34 Sakakibara and Suyama A B C D... (A^B)_:C B_(C^D) (A^C)_(D^E)... An usual DNA chip A DNA chip with logical operations executable Figure 1: (left:) An usual DNA chip and (right:) a DNA chip with logical operations executable. then analyzed with a power of the massive parallelism of DNA computing. The results of the analysis are finally obtained by reading out a sequence of DCNs. The DCN method was applied to gene expression analysis, which determine the concentration distribution of mrna transcripts of expressed genes [7]. Gene expression profiling based on DNA chips usually requires the use of target-dependent high-density DNA chips, definitely causing undesirable restrictions on extensive application of DNA chips to gene expression profiling. On the contrary, the DCN method for gene expression profiling does not require the use of target-dependent DNA chips but requires the use of a universal DNA chip with a small number of orthonormal DNA probes, whose sequences are optimized for accurate and quantitative hybridization. In addition, gene expression profiling by the DCN method allows us more quantitative analysis of gene expression profiles. In this paper, we propose a new kind of DNA chips, called intelligent DNA chip, by combining DNA chips with the DNA-computing method for representing and evaluating Boolean functions and the DCN method. We implement universal DNA chips which not only detect gene expressions but also find logical formulae of gene expressions. In this sense, the intelligent DNA chip is a kind of DNA chip with information processing abilities. The intelligent DNA chip is also considered as a natural extension of the usual DNA chips. This is because in the case that every probe on DNA chip consists of only one Boolean variable (attribute) for representing one gene expression, the intelligent DNA chip is exactly an usual DNA chip. We illustrate DNA chips with logical operations executable in Figure 1. For example, a Boolean formula (A B) C in the figure means that if the gene A is expressed and the gene B is expressed or if the gene C is not expressed, the formula is satisfied. This kind of ability has a significant potential for various applications. For example, the detection of disease-specific genes using two different samples, which is solved by differential expression analyses using two-color fluorescence labeling in the usual microarray, is more easily and precisely realized by using DNA chips with logical operations and DCNs. To detect specific genes using two different samples (such as a sample in a disease state and a sample in the normal state), we first prepare two DCNs which represent two Boolean variables, say A and B, for a gene expression in the target sample and the same gene expression in the other sample, and implement DNA chip with a probe for the Boolean formula (A B). Second, by applying those samples, if the Boolean formula is found satisfied, we conclude the gene is expressed in the target sample and not expressed in the other sample, and hence the gene is specific to the target sample. We have already verified the biological feasibilities for the evaluation method of Boolean formulae [8] and the DCN method [7]. In this sense, our proposal of intelligent DNA chips is very practical. We also consider two applications of intelligent DNA chips to medical diagnoses and Boolean genetic networks.

3 Intelligent DNA Chips 35 biotin a i A i E D D C i N SD ta rg e t train sc rip t SD E D SA m agnetic beads E D D C i N SD expressed genes unexpressed genes D C ê k ND C k N expressed genes D C i N D C N k ê D C N k * D C N k D C * k N unexpressed genes Figure 2: Generation of DCN strands, DCN i and DCN i, corresponding to expressed and unexpressed genes, respectively. 2 DNA Coded Number DNA coded numbers (DCNs) are molecular arithmetic numbers represented by DNA base sequences chosen from a set of orthonormal DNA base sequences, which have uniform melting temperature and no mishybridization or folding potential. A set of over 200 orthonormal sequences of length 25 nt has been designed using a greedy algorithm [9]. This set is sufficient to uniquely represent the truth-value assignments of 100 and distinct genes in 1-digit and 2-digit DCNs, respectively. DCNs associated with expressed or unexpressed genes are generated using DNA molecular reaction as shown in Figure 2. First, an expressed gene transcript is converted into a corresponding DCN with a partially double-stranded DNA adapter molecule A and a single-stranded DNA anchor molecule a. The adapter contains a single-stranded region, which is the right half of a unique sequence of target transcript, and a double-stranded region encoding a unique DCN with flanking common sequences SD and ED. The anchor has a single-stranded region, which is the left half of a unique sequence of target transcript, and a biotin molecule at the 5 end. The sequence of cdna complementary to a unique sequence of expressed gene transcript facilitates ligation of adapter A to anchor a with Taq DNA ligase. This operation is identical to the append operation, which has been used to solve an instance of 3-SAT problems on DNA-computers [9]. All adapter molecules ligated to biotinylated anchors are captured on streptavidin (SA) magnetic beads and are then melted into single strands to obtain a set of single-stranded DNA molecules representing DCNs corresponding to expressed genes. DNA single strands representing DCNs are then amplified by PCR with a primer pair of SD and ED. The use of the common primer pair SD and ED and the orthonormality of base sequences representing DCN facilitate the uniform amplification, which is needed for quantitative gene expression profiling. Amplified DCNs with flanking SD and ED sequences are captured on SA magnetic beads through biotin at the 5 -end of SD primer. They are then melted into single strands to serve as probes for the get operation to extract DCNs corresponding to expressed genes. The get operation starts with addition of the magnetic beads with single-stranded SD-DCN-ED sequences to a solution mixture of DCN single strands of all target genes. After hybridization and washing, only DCN single strands of expressed genes are extracted. Part of the extracted DCN solution is used to generate DCNs of unexpressed genes. DCN strands of expressed genes are annealed to 5 -biotinylated single strands of DCN -DCN sequences, and then

4 36 Sakakibara and Suyama subjected to primer extension with DNA polymerase. DCN -DCN single strands corresponding to expressed genes are converted into double strands while those strands corresponding to unexpressed genes remain single-stranded. Double-stranded and single-stranded DCN -DCN sequences are separated with hydroxyapatite beads, which have different affinity to single- and double-stranded DNA. Single-stranded DCN -DCN sequences are then used for the get operation to extract DCN sequences of unexpressed genes, i. e., DCNs corresponding to unexpressed genes, from a mixture of DCN strands of all target genes. 3 How to Evaluate Boolean Formulae on DNA Strands The Boolean function is a mathematical function defined on attributes (Boolean variables) which is often used to define gene regulation rules for gene regulation networks. A Boolean formula is a representation for Boolean functions and consists of attributes, logical- and, logical- or and negation. More formally, there are n Boolean variables (or attributes) and we denote the set of such variables as X n = {x 1,x 2,...,x n }.Atruth-value assignment a =(b 1,b 2,...,b n ) is a mapping from X n to the set {0, 1} or a binary string of length n where b i {0, 1} for 1 i n. Note that the Boolean variables correspond to the gene expressions (that is, the expression for a gene to be ON or OFF ) and the assignments correspond to the gene expression patterns. When a gene is expressed, the truth-value of a Boolean variable which corresponds to the gene becomes 1 and when the gene is unexpressed, the truth-value of the Boolean variable becomes 0. A Boolean function is defined to be a mapping from {0, 1} n to {0, 1}. Boolean formulae are useful representations for Boolean functions. The simplest Boolean formula is just a single variable. Each variable x i (1 i n) is associated with two literals: x i itself and its negation x i.aterm is a conjunction of literals. A Boolean formula is in disjunctive normal form (DNF, for short) if it is a disjunction of terms. Every Boolean function can be represented by a DNF Boolean formula. For any constant k, a k-term DNF formula is a DNF Boolean formula with at most k terms. We denote the truth value of a Boolean formula β for an assignment a {0, 1} n by β(a). We implement an evaluation algorithm for DNF Boolean formulae using DNA strands and biological operations. First, we encode a k-term DNF formula β into a DNA single-strand as follows: Let β = t 1 t 2 t k be a k-term DNF formula. (1) For each term t = l 1 l 2 l j in the DNF formula β where l i (1 i j) is a literal, we use the DNA single strand of the form: 5 stopper marker seqlit 1 seqlit j 3 where seqlit i (1 i j) is the encoded sequence for a literal l i. The stopper is a stopper sequence for the polymerization stop that is a technique developed by Hagiya et al. [4]. The marker is a special sequence for a extraction used later at the evaluation step. (2) We concatenate all of these sequences encoding terms t j (1 j k) inβ. Let denote the concatenated sequence encoding β by e(β). For example, the 2-term DNF formula (x 1 x 2 ) ( x 3 x 4 ) on four variables X 4 = {x 1,x 2,x 3,x 4 } is encoded as follows and illustrated in Figure 3: 5 marker x 1 x 2 stopper marker x 3 x 4 3 Second, we put the DNA strand e(β) encoding the DNF formula β into the test tube and do the following biological operations to evaluate β for the truth-value assignment a =(b 1,b 2,...,b n ).

5 Intelligent DNA Chips 37 Figure 3: The DNA strand encoding the DNF formula (x 1 x 2 ) ( x 3 x 4 ). Algorithm B(T,a): (1) Let the test tube T contain the DNA single-strand e(β) for the DNF formula β. (2) Let a =(b 1,b 2,...,b n ) be the truth-value assignment. For each b i (1 i n), if b i =0 then put the Watson-Crick complement x i of the DNA substrand encoding x i into the test tube T, and if b i = 1 then put the complement x i of x i into T. (3) Cool down the test tube T for annealing these complements to complementary substrands in e(β). (4) Apply the primer extension with DNA polymerase to the test tube T with these annealed complements as the primers. As a result, if the substrand for a term t j in β contains a literal lit i and the bit b i assigns 0 to lit i (that is, if b i is 0 then the truth-value of lit i equal to x i becomes 0, and if b i is 1 then the truth-value of lit i equal to x i becomes 0), then the complement seqlit i of the substrand seqlit i has been put at Step (2) and is annealed to seqlit i. The primer extension with DNA polymerase extends the primer seqlit i and the subsequence for the marker in the term t j becomes double-stranded, and the extension stops at the stopper sequence. Otherwise, the subsequence for the marker remains singlestranded. This means that the truth-value of the term t j is 1 for the assignment a. (5) Extract the DNA (partially double-stranded) sequences that contains single-stranded subsequences for markers. These DNA sequences represent the DNF formulae β whose truth-value is 1 for the assignment a. The figure 4 illustrates the behavior of the algorithm B for β =(x 1 x 2 ) ( x 3 x 4 ) and a truth-value assignment a = (0000) on X 4 = {x 1,x 2,x 3,x 4 }, and the figure 5 illustrates for β and a truth-value assignment a = (1011). The truth-value of β is 0 for the assignment a = (0000) and 1 for the assignment a = (1011). We call the algorithm B(T,a) the logical evaluation operation for a DNA strand encoding a DNF formula. We have already verified the biological feasibilities for the evaluation method of Boolean formulae [8]. Yamamoto et al. [8] have done the following biological experiments to confirm the effects of the evaluation algorithm B(T,a) for DNF Boolean formulae: 1. for a simple 2-term DNF Boolean formula on three variables, we have generated DNA sequences encoding the DNF formula by using DNA ligase in the test tube, 2. the DNA sequences are amplified by PCR, 3. for a truth-value assignment, we have put the Watson-Crick complements of DNA substrands encoding the assignment, applied the primer extension with DNA polymerase, and confirmed the primer extension and the polymerization stop at the stopper sequences, 4. we have extracted the DNA sequences encoding the DNF formula with magnetic beads through biotin at the 5 -end of primer and washing. 4 Intelligent DNA Chips with Logical Operations We combine the DNA-computing method for representing and evaluating Boolean functions with the DCN method, and implement DNA chips with logical operations executable. Such implemented DNA

6 38 Sakakibara and Suyama + x 1 x 2 x 3 x 4 (for the assignment ( )) Annealing: x 1 x 4 Primer extension with DNA polymerase: x 1 x 4 Figure 4: (upper:) For the assignment (0000), the Watson-Crick complements x 1, x 2, x 3 and x 4 of the encodings for x 1, x 2, x 3 and x 4 respectively are put to the test tube and (middle:) x 1 and x 4 are annealed to the DNA strand encoding the formula (x 1 x 2 ) ( x 3 x 4 ). (lower:) Primer extension with DNA polymerase extends the primers x 1 and x 4 and both markers become double-stranded. Annealing: x 3 Primer extension with DNA polymerase: x 3 Figure 5: (upper:) For the assignment (1011), the complements x 1, x 2, x 3 and x 4 of the encodings for x 1, x 2, x 3 and x 4 are put to the test tube and x 3 is annealed to the DNA strand for (x 1 x 2 ) ( x 3 x 4 ). (lower:) Primer extension with DNA polymerase extends the primer x 3, and the right marker becomes double-stranded and the left marker remains single-stranded.

7 Intelligent DNA Chips 39 chips are intelligent in the sense that the DNA chips not only detect gene expressions but also find logical formulae of gene expressions, and universal in the sense that by simply changing the DCNs, we will be able to deal with any class of gene expressions with a fixed DNA chip. First, we build the DNA chip (microarray) in an usual way. We prepare a set of probes (complementary DNA strands) that encode a set of DNF Boolean formulae as shown in Section 3. Those probes are bonded to a glass surface in an array format with each DNF Boolean formula occupying a unique location. Next, the operations on the so-built DNA chip proceed as follows: 1. The messenger RNA (mrna) is extracted from the sample, and a complementary DNA (cdna) sequence is generated. The target sequences (transcripts) represent all of the genes expressed in the reference sample. 2. (Case 1: expressed genes) For an expressed gene, the truth-value of a Boolean variable for the gene becomes 1. Therefore, those cdna sequences generated at Step 1 are translated into DCN sequences such that each gene expression is translated into an unique DCN sequence encoding the negation of a Boolean variable representing the gene. 3. (Case 2: unexpressed genes) For an unexpressed gene, the truth-value of a Boolean variable for the gene becomes 0. Therefore, for each unexpressed gene, an unique DCN sequence which encodes a Boolean variable representing the gene is generated. 4. Those DCN sequences are simultaneously applied to a DNA chip with DNA strands encoding Boolean formulae, and the logical evaluation operation is executed for the DNA chip. 5. The complementary marker sequences fluorescently tagged are applied to the DNA chip after the logical evaluation operation and annealed to marker subsequences in the DNA chip which remain single-stranded. 6. If the DNA-chip element shows a color, it indicates that the truth-value of the Boolean formula at the element is 1 and hence the Boolean formula at the element is satisfied with the gene expressions. If an element shows no color, it indicates that the truth-value of the Boolean formula at the element is 0. We illustrate our intelligent DNA chip in Figure 6. The intensity of the fluorescence at each element is not only proportional to the expression level of the genes in the sample but also proportional to the satisfiability level of the Boolean formula at the element with the gene expression pattern. Precisely, when the DNF Boolean formula encoded at the element is not satisfied with the gene expression pattern, all marker subsequences in the formula become double-stranded. In this case, the element shows no color. When the Boolean formula is satisfied with the expression pattern, some (at least one) of marker subsequences in the formula remain single-stranded. In this case, the complementary marker sequences fluorescently tagged are annealed to the single-stranded marker subsequences and the element shows the fluorescent color. If more marker subsequences in the formula remain single-stranded, that is, there exist more terms which are satisfied with the expression pattern, more complementary marker sequences fluorescently tagged are annealed and the element shows the fluorescent color with greater level. This feature is a significant advantage of our intelligent DNA chip compared with other methods executing logical operations on the silicon computers. Figure 7 illustrates these operations for the intelligent DNA chip.

8 40 Sakakibara and Suyama Expressed Gene 1 DCN ":A" Gene 2 Gene 3 UNexpressed Gene 11 Gene DCN ":B" DCN ":C" DCN "D" DCN "E" (A^B)_:C B_(C^D) (A^C)_(D^E)... Gene 13 DCN "F".. Encoding to DNA Coded Numbers A DNA chip with logical operations executable An intelligent DNA chip Figure 6: An intelligent DNA chip. 5 Applications Clinical conditions or disease states are often diagnosed by using logical rules in the expert systems. These diagnoses are a promising application of DNA chips. Our intelligent DNA chip will be able to provide logical inference for such diagnoses based on detected gene expression patterns. For example, differential expression analyses using two-color fluorescence labeling are often used in microarraybased methods to detect disease-related genes. Instead of differential expression analyses, this kind of logical inference is more easily and precisely realized by using our intelligent DNA chips. To detect disease-specific genes using two different samples (such as a sample in a disease state and a sample in the normal state), we first prepare two DCNs, one for the target sample of a disease state and the other for the normal state, and a target gene expression in the disease state is translated into a DCN for representing a Boolean variable, say A, and the same gene expression in the normal state is translated into the other (different) DCN, say B, for a different Boolean variable. We also implement DNA chip with a probe for the Boolean formula (A B). Second, by applying two different samples and putting DCNs in those samples together into the DNA chip, if the Boolean formula is found satisfied with the gene expression pattern, we conclude that the target gene is expressed in the disease state and not expressed in the normal state, and hence the gene is specific to the disease state. Recently, the Boolean network has been often used to model gene regulation networks [1]. The Boolean network uses a Boolean function to define a gene regulation rule. Most studies employ the silicon computers to identify these Boolean networks from the data of gene expression patterns. However, the problems of identifying Boolean functions (and hence Boolean networks) from the data is computationally hard problems (most of them are known as NP-hard). By applying the DNA-based evaluation methods for Boolean formulae and DNA-based massively parallel exhaustive search, we will be able to efficiently solve the identification problem of the genetic network on our intelligent DNA chips.

9 Intelligent DNA Chips 41 Assume the genes encoded to "A", "B" and "C" are expressed and "D", "E", and "F" are unexpressed "(D_E_F) is 0" m D s m E s m F F E D "(:A_:B_C) is 1" m :A s m:b s m C :B :A "(A_B_C) is 1" m A s m B s m C :A :B :C D F E complementary ":A", ":B", and ":C" and "D", "E", and "F"... no color color greater color level "m" represents "marker" : fluorescently tagged "s" represents "stopper" ":A", ":B", ":C", "D", "E", "F" are DCN sequences Figure 7: (upper:) the gene expressions generated from mrna in the sample are translated to DCNs which are Watson-Crick complementary sequences encoding A, B and C, and the unexpressed genes D, E and F are translated to DCNs encoding them respectively. (middle:) the complementary D, E and F are annealed to the DNA single strands encoding DNF Boolean formulae on the DNA chip and the primer extension with DNA polymerase is applied with the primers. As a result, all marker subsequences in the formula (D E F) become double-stranded, which means the truth-value of the formula is 0, and the element shows no color. Two marker subsequences in the formula ( A B C) become double-stranded and one marker subsequence remains singlestranded, which means the truth-value of the formula is 1, and the complementary marker sequences fluorescently tagged are annealed to the single-stranded marker subsequence and the element shows a fluorescent color. All marker subsequences in the formula (A B C) remain single-stranded, which means all terms are satisfied with the expression pattern, and three complementary marker sequences fluorescently tagged are annealed and the element shows a fluorescent color with greater level.

10 42 Sakakibara and Suyama 6 Conclusions We have proposed a new type of DNA chips with logical operations, called intelligent DNA chip, by combining DNA chips with the DNA-computing method for representing and evaluating Boolean functions and the DCN method. We have modeled in theory that the intelligent DNA chips not only detect gene expressions but also find logical formulae of gene expressions and hence the intelligent DNA chip is considered as a kind of DNA chip with information processing abilities. We have also shown that the intelligent DNA chip has a significant potential for various applications such as disease diagnosis and Boolean network. Once again, significant advantages of our intelligent DNA chip compared with those software programs executing logical operations on the silicon computers are the massive parallelism of DNA computing and the quantitative analyses of gene expression profiles using the intensity of the fluorescence at each element. While the biological feasibilities for the evaluation method of Boolean formulae [8] and the DCN method [7] have already been verified, a practical implementation and the test of the intelligent DNA chip will be significantly important for a convincing argument. Acknowledgments This work is supported in part by Research for the Future Program No. JSPS-RFTF 96I00101 from the Japan Society for the Promotion of Science. References [1] Akutsu, T., Miyano, S., and Kuhara, S., Identification of genetic networks from a small number of gene expression patterns under the Boolean network model, Proc. Pacific Symp. Biocomputing 99, World Scientific, 17 28, [2] DeRisi, J.L., Lyer, V.R., and Brown, P.O., Exploring the metabolic and genetic control of gene expression on a genomic scale, Science, 278: , [3] Fodor, S.P.A., Massively parallel genomics, Science, 277: , [4] Hagiya, M., Arita, M., Kiga, D., Sakamoto, K., and Yokoyama, S., Towards parallel evaluation and learning of Boolean µ-formulas with molecules, Proc. Third Annual Meeting on DNA Based Computers, , [5] Sakakibara, Y., Solving computational learning problems of Boolean formulae on DNA computers, Proc. 6th International Meeting on DNA Based Computers, , [6] Schena, M., Shalon, D., Heller, R., Chai, A., Brown, P.O., and Davis, R.W., Parallel human genome analysis: Microarray-based expression monitoring of 1000 genes, Proc. Natl. Acad. Sci., 93(20): , [7] Suyama, A., Nishida, N., Kurata, K., and Omagari, K., Gene expression analysis by DNA computing, Currents in Computational Molecular Biology (S. Miyano, R. Shamir, T. Takagi eds.), University Academy Press, 20 21, [8] Yamamoto, Y., Komiya, S., Sakakibara, Y., and Husimi, Y., Application of 3SR reaction to DNA computer, Seibutu-Buturi, 40(S198), [9] Yoshida, H. and Suyama, A., Solution to 3-SAT by breadth first search, DNA Based Computers V (E. Winfree, D. K. Gifford eds.), American Mathematical Society, 9 20, [10]