Article pubs.acs.org/ac
Boolean Logic Tree of Graphene-Based Chemical System for Molecular Computation and Intelligent Molecular Search Query Wei Tao Huang, Hong Qun Luo,* and Nian Bing Li* Key Laboratory of Eco-environments in Three Gorges Reservoir Region (Ministry of Education), School of Chemistry and Chemical Engineering, Southwest University, Tiansheng Road, BeiBei District, Chongqing 400715, PR China S Supporting Information *
ABSTRACT: The most serious, and yet unsolved, problem of constructing molecular computing devices consists in connecting all of these molecular events into a usable device. This report demonstrates the use of Boolean logic tree for analyzing the chemical event network based on graphene, organic dye, thrombin aptamer, and Fenton reaction, organizing and connecting these basic chemical events. And this chemical event network can be utilized to implement fluorescent combinatorial logic (including basic logic gates and complex integrated logic circuits) and fuzzy logic computing. On the basis of the Boolean logic tree analysis and logic computing, these basic chemical events can be considered as programmable “words” and chemical interactions as “syntax” logic rules to construct molecular search engine for performing intelligent molecular search query. Our approach is helpful in developing the advanced logic program based on molecules for application in biosensing, nanotechnology, and drug delivery. switch.38c And using the fluorescence emission wavelength shift as the output, the graphene-based Ag+/cysteine-driven dualoutput fluorescent DNA INHIBIT logic gate has also been designed.38e In fact, much more combinations based on interactions between versatile DNA and nanomaterials provide excellent background for artificial computing devices application and development.39 Because these biochemical processes can emulate Boolean logic, they can be used as “digital” biochemical sensors with multiple analytes inputs,40 for example, in biomedical applications (diagnosis of disease or injury),41 environmental monitoring, and multicomponent analysis. However, for real conditions the logic values 0 and 1 of concentrations (or possibly ranges of concentrations) should correspond to normal and abnormal states of the organism or environment, respectively. In most cases the difference between the inputs at the logic 0 and 1 is comparable with the level of natural noise, making the discrimination of the 0 and 1 output signals difficult unless careful optimization of the signal processing systems is performed.42 Privman and co-workers have done a lot of pioneering work in biochemical computing43 and Boolean logic-based biomedical analysis.44 For improving performance of the logic gates, scalability in biochemical computing, and separation of output signals, they developed biochemical “filter”26,45 to successfully achieve noise reduction and control.46
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ngoing efforts within information technology have been directed toward the building and designing of novel artificial computing devices, such as molecular computers1,2 and biocomputers,3−5 using biochemical molecules1,2,6−8 and engineered biological units3−5,9 as building blocks. Following highly influential papers by de Silva,10 there have been many reported examples of individual molecular logic gates.11 And molecular equivalents of even more complex digital designs were presented in recent years, such as half adders,12 halfsubtractors,13 multiplexers−demultiplexers,14 encoders−decoders,15 “tic-tac-toe” gaming systems,16 and molecular ID tags,17 molecule-based parity generator/checker.18 Molecular logic has also been extending in many directions, including sequential logic,19 reversible logic,19b,20 fuzzy logic,21 and allphotonic logic.18,19b,d,22 Furthermore, biomolecular systems or biological phenomena in complex reaction networks8 and biological processes3−5,23 have been abstracted and simplified for the development of enzymatic logic gates and networks,24 amplifiers,25 signal-converters,25 filters,26 memory system (flipflop,27 associative memory systems28 ), neural network computation,29 and artificial intelligence systems.1,30−35 In recent years, an intense interest has grown in applications of nanomaterials with exceptional physical, optical, and electrical properties.36 An example of such a unique ability for aromatic compounds adsorbing as well as its super fluorescence quenching capacity with wide energy transfer range has shown graphene to be robust artificial nanomaterials.37 Recently, we reported the applications of graphene for detection of G-quadruplex DNA, hydroxyl radicals (HO•), heavy metal ions, cysteine, and hemin.38 We designed the INHIBIT logic gate using Hg2+ and cysteine as the two inputs that operate the fluorescence of dye-graphene-based nano© 2014 American Chemical Society
Received: January 28, 2014 Accepted: April 4, 2014 Published: April 16, 2014 4494
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Microscopy. Tapping mode atomic force microscopy (AFM) measurements were performed on a Multimode microscope (Veeco, U.S.A.) with a Nanoscope IIIa controller, equipped with a Nanoscope Quadrex in tapping mode using a TESP7 Veeco AFM tip. Gel Electrophoresis. Electrophoresis analysis was performed by putting the samples on a 4% agarose gel in a 1 × TAE buffer (40 mM Tris acetate, 1 mM EDTA, pH 8.5) followed by electrophoresis for 50 min at 80 V. After ethidium bromide staining, the gel was imaged using a Gel Doc 2000 system (BIO-RAD, U.S.A.).
However, (bio)molecular Boolean logic and computing is suffering from several well-identified problems. On the one hand, most reported classical (bio)molecular devices10 are based on (bio)chemical reactions or processes: binding of an appropriate combination of analytes to specially designed receptors offer simple logic operations11 and arithmetic calculations.12,13 However, the most serious, and yet unsolved, problem consists in connecting all of these molecular fragments into a usable device.43a,47 On the other hand, the analogue region of the nonlinear response in (bio)chemical processes is not a distinct two-state (high/low) but fuzzy. The inexact natures considered as error in conventional hard computing often hinder the development of artificial computers and “digital” biochemical sensing. Here, the logic evolution tree of complex chemical systems is demonstrated and applied for organizing and connecting chemical events. Solution-based reactions between DNA, nanomaterials, organic dye, and metal ions is programmed33,48 for implementing multilogic gate operations, constructing complex logic evolution network, and developing the intelligent search engine based on hybrid Boolean and fuzzy logic.21 Our approach will help to combine the merits of nanotechnology, Boolean logic, and fuzzy logic. Thus, these (bio)chemical processes can emulate Boolean logic and fuzzy logic and thus can be used as “intelligent and linguistic” biochemical sensors38a with multiple analytes inputs for multicomponent analysis and combinatorial analysis. This combination will open new opportunities for the development and design of intelligent molecular engineering and sensing applications, such as biosensing, environmental monitoring systems, medical diagnosis, and chemical processes.
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RESULTS AND DISCUSSION Logic Tree Analysis and Logic Computation of Chemical System. Because of the π−π stacking interaction,37a reduced graphene oxide (G) self-assembled with acridine orange (AO) dye to form AO−G complex, resulting in the fluorescent quenching of AO (Scheme 1a, Supporting Scheme 1. Boolean Logic Tree Analysis of a Solution-Based Chemical System Based on Interactions among AO, G, TBA, Cations, and Fenton Reactiona
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EXPERIMENTAL SECTION Oligonucleotides. The 15-base linear thrombin aptamer (TBA:5′-GGTTGGTGTGGTTGG-3′), 15-base linear random DNA sequence (R15:5′-AGTAGCTGGTGGCGT-3′), 20-base linear poly(dT) DNA sequence (T20:5′-TTTTTTTTTTTTTTTTTTTT-3′), and 20-base linear poly(dA) DNA sequence (A20:5′-AAAAAAAAAAAAAAAAAAAA-3′) were purchased from Songon Inc. (Shanghai, China) and purified by high performance liquid chromatography. Fabrication of Graphene Oxide and Reduced Graphene Oxide. Graphene oxide was synthesized from graphite (spectral pure, Sinopharm Chemical Reagent Co., Ltd., China) by the Hummers method, and dried for 2 weeks over phosphorus pentoxide in a vacuum desiccator. Reduced graphene oxide (G) was prepared by hydrazine reduction. Fluorescence Measurements. All spectral studies were performed in 20 mM Tris-HAc buffer (pH 7.4). The DNA solutions were prepared in the 20 mM Tris-HAc buffer solution (pH 7.4) with and without 20 μM K+ or Pb2+. HO• was chemically generated through the Fenton reaction (Fe2+/H2O2 1:6 mol mol −1 ). All fluorescence measurements were performed on a Hitachi F-2700 fluorescence spectrophotometer (Hitachi Ltd., Japan). The operation conditions are described as follows: PMT voltage: 400 V, excitation wavelength: 490 nm, slit: 10 nm. Fuzzy Logic Analysis. Fuzzy analysis was implemented with Fuzzy Logic Toolbox in Matlab 7.1 (Mathworks, U.S.A.). The fuzzy logic system (FLS) is implemented by the Mamdani’s method with the centroid defuzzification (details of the defuzzifier and defuzzy process are added in Supporting Information).
a
The orange glow represents fluorescence emission.
Information Figure S1).38a,c,f When mixed with G-quadruplex (G4) thrombin aptamer (G4TBA) induced by K+ or Pb2+ (Scheme 1b, c),49 the resulting AO−G complex was broken because of a specifically competitive binding of AO with G4TBA, and a more stable AO−G4TBA complex than AO−G complex was formed,38f resulting in restoration of dye fluorescence (Scheme 1d, Supporting Information Figure S2). In the presence of HO•-generating Fenton reagent (Fe2+/Fe and H2O2/H) (Scheme 1e), G4TBA was broken into fragments,38b which disturbs competitive binding of the dye with G4, resulting in fluorescence requenching of the AO dye (Scheme 1f, Supporting Information Figure S3). The aforementioned processes in Scheme 1 show that DNA, nanomaterials, organic dye, metal ions, and Fenton reaction in solution phase can self-assemble, compete, and connect with each other. Because learning and using the language of other 4495
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Figure 1. (A) AO ANDNOT G gate. (B) TBA AND K+ gate. (C) K+ OR Pb2+ gate. (D) Fe NAND H gate which consists of Fe AND H gate and HO•-input NOT gate. (E) Symbol (left) and processing performance (right) of 6-input compound logic circuits with six chemical inputs and oneoutput fluorescence (blue points represent logic output 1). AO, 2 μM; G, 5 μg mL−1; K+/Pb2+, 20 μM; TBA, 400 nM; Fe, 2 mM; H, 12 mM. The data represent the mean and standard deviation of three independent experiments. a.u., arbitrary units.
disciplines is a way of taking chemical ideas to nonchemist hearts and minds,50 we utilize fault-like tree analysis to study the logic evolution of chemical events in aforementioned processes. Fault tree analysis51 is a deductive failure analysis in which an undesired state of a system is analyzed using Boolean logic to combine a series of lower-level events. There are two types of symbols which appear in the fault tree structure: gates and events. Typical examples of event symbols used in the fault tree structure are illustrated in green box of Scheme 1. The events in the fault tree are linked using “gate” symbols. Common gates are shown in red box of Scheme 1. The three fundamental logic gates are “AND”, “OR” and “NOT”. For an AND gate the output event occurrence requires the simultaneous existence of all of the input events. The output (higher level event of an OR gate) will result from the occurrence of at least one of the input (lower level) events. The output to a NOT gate happens as long as the input event does
not. G (basic event) self-assembled with AO (basic event) to form AND-gate nanocomplex (intermediate event) (Scheme 1a). TBA (basic event) was folded to form AND-gate G4TBA (intermediate event) in the presence of K+ or Pb2+ (basic event) (Scheme 1c). Because G4TBA can be induced by K+ or Pb2+, the basic events K+ and Pb2+ perform OR logic function (Scheme 1b). G4TBA (intermediate event) and the AO−G complex (intermediate event) through superimposed AND gates interacted and exchanged AO molecules to produce two outputs: AO−G4TBA (top event) and G (Scheme 1d). The AO−G complex and G4TBA exchanged AO molecules which can be considered as a messenger to carry information and communicate with one another. Fe and H (basic events) implement AND gate operation and exports HO• (Scheme 1e). HO• is highly reactive, consequently short-lived, and to easily degrade and “reset” G4TBA into fragments, corresponding to the inverted IMPLY (N-IMPLY) gateAO−G4TBA AND4496
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NOT HO• gate (Scheme 1f). Thus, we can represent the whole cascade reactions as ((AO AND G) AND ((K+ OR Pb2+) AND TBA)) ANDNOT (Fe AND H). We use the fluorescence change in the different combinations of these aforementioned chemical events for implementing multifunctional logic computation. Logical outputs are defined when fluorescence (F) < 15 (a.u.) for logical 0 and >20 (a.u.) for logical 1, respectively. Self-assembly of AO and G functions as N-IMPLY fluorescence gate. By combining the two input signals AO and G in accordance with the truth table, the fluorescence output is produced exclusively in the presence of AO and not G as shown by fluorescence analysis (Figure 1A). By combining the two input signals TBA and K+ in accordance with the truth table, the substrate AO−G complex gave the fluorescence signal only when (TBA AND K+)-induced G4TBA was added, corresponding to AND and YES fluorescence gate functions (Figure 1B). Similarly, by combining the two input signals Pb2+ and K+ in accordance with the truth table, only if one of Pb2+ and K+ is present, the substrate TBA was induced to produce the same output G4TBA, resulting in fluorescence turn-on of the AO−G system (Figure 1C). HO•-switched AO−G4TBA system really functions as a NOT fluorescence gate, because fluorescence turn-off happened as long as the input HO• is present. By regarding HO• as Fe AND H, we also fabricated NAND gate (Figure 1D, Supporting Information Figure S3). These chemical events (AO, G, K+, TBA, Fe, H) not only can be connected to form complex logic evolution networks, but also use the fluorescence signal as output for computing AO·(G̅ + K+·TBA)·(Fe·H) (Figure 1E). Fuzzy Logic Operation and Intelligent Molecular Search Query. In the (bio)chemical process, there is usually the nonlinear (sigmoidal) response because of mass action of molecule populations. The extremes of the response possess two plateaux which arise from two discrete states of a molecule (target-bound/free) and are the basis of molecular binary logic computation.50 However, the analogue region of the sigmoidal response is not a distinct two-state (high/low) but fuzzy. The inexact natures considered as error in conventional hard computing (binary logic) often hinder the development of artificial computers and “digital” biochemical sensing. But it can be developed into fuzzy logic operation.21 Based on the fuzzy nature of chemical reactions, we can deal with uncertain information in the analogue region to implement soft computation through the formulation of FLS. FLS is a nonlinear mapping of an input crisp data vector (x)̅ into a scalar crisp output (y) and this mapping can be expressed 52 quantitatively as y = f (x). FLS consists of four basic elements: ̅ fuzzifier, rules, inference engine, and defuzzifier (more information in Supporting Information). A fuzzy set S for the variable X, is characterized by a membership function, μS(x), which associates a real number, included in the interval [0, 1], to each element of X. A fuzzy variable is a variable that takes on fuzzy sets as values. They are usually referred to as linguistic variables, such as concentration C and fluorescence F. To handle the variable in the absence of exact values, we estimate the variable in terms of a few linguistic values such as low, medium, or high. Outputs and inputs are modeled as fuzzy variables. As shown in Figure 2 green box, the fluorescence of AO has quasi- negated-translated sigmoidal response to G. The CG input variable and the F output variable are defined by the fuzzy sets as illustrated in Figure 2. The inference rules can be
Figure 2. Scheme of fuzzy relation based on fuzzy inference rules mapping input CG to output F. Green box: Fluorescence intensity of AO (2 μM) as a function of CG used for titration. Fuzzy variable is decomposed in three fuzzy sets. CG: (1) Low (zmf μlow, [1.5 2]); (2) medium (trimf μmedium, [1.5 2 3]); (3) high (smf μhigh, [2.5 3.5]). F: (1) Low (zmf μlow, [8.5 22.5]); (2) medium (trimf μmedium, [8.5 60 120]); (3) high (smf μhigh, [60 120]).
extracted from Figure 2 green box. They are expressed as a collection of IF-THEN statements, for example ‘‘IF CG is low, THEN F is high” (Figure 2). The IF-part is called the antecedent, and the THEN-part is called the consequence. The inference engine of the FLS maps input fuzzy sets into output fuzzy sets (Figure 2). The defuzzifier maps output fuzzy sets into crisp numbers. The output crisp number can correspond to a prediction of a variable, like F. By using Boolean and fuzzy logic, we can construct molecular search engine for querying target molecular events (such as TBA and Fe AND H) in the molecular library. According to the aforementioned logic tree analysis, our chemical system can be represented as ((AO AND G) AND ((K+ OR Pb2+) AND TBA)) ANDNOT (Fe AND H) for the top event AO− G4TBA. This Boolean logic tree can provide an effective approach and a powerful programming language for organizing chemical events as programmable “words” and connect them through chemical interactions as “syntax” logic rules. For search query for TBA, the basic event K+ (20 μM) was first typed into the solution-based library for forming AND-gate G4TBA. Then the programmed AND-gate AO−G was added to construct the self-organizing compiler (?TBA AND K+) AND (AO AND G) for exporting the top event AO−G4TBA and to compute AO· (G̅ + K+·?TBA) for producing the fluorescence reporter output. The self-organizing compiler can perform Boolean logic function to determine whether TBA is present in the solution-based library. If TBA is present, the AO−G4TBA is produced, resulting in the fluorescence turn-on. Otherwise, the fluorescence is still quenched. According to the fluorescence responses of the AO−G complex to TBA (when 20 μM K+ is present), we can construct a FLS and perform fluorescence FLS 4497
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Figure 3. (A) Scheme of fuzzy relation based on fuzzy inference rules mapping input F to output correlation (Co) to search for TBA. Green box: The fluorescence responses of the AO−G complex to TBA (when 20 μM K+ is present). Fuzzy variable is decomposed in three fuzzy sets. F: (1) Low (zmf μlow, [12.5 25]); (2) medium (trimf μmedium, [12.5 25 37.5]); (3) high (smf μhigh, [25 37.5]). CTBA: (1) Low (zmf μlow, [100 200]); (2) medium (trimf μmedium, [100 200 300]); (3) high (smf μhigh, [200 300]). Co: (1) Low (zmf μlow, [25% 50%]); (2) medium (trimf μmedium, [25% 50% 75%]); (3) high (smf μhigh, [50% 75%]). (B) Scheme of fuzzy relation based on fuzzy inference rules mapping input F to output Co to search for Fe AND H. Green box: The fluorescence responses of the AO−G4TBA to Fe AND H (CFe AND H = CFe, Fe/H = 1:6). Fuzzy variable is decomposed in three fuzzy sets. F: (1) Low (zmf μlow, [10 15]); (2) medium (trimf μmedium, [10 16 22]); (3) high (smf μhigh, [20 22]). CFe AND H: (1) Low (zmf μlow, [20 100]); (2) medium (trimf μmedium, [25 250 750]); (3) high (smf μhigh, [400 750]). Co: (1) Low (zmf μlow, [25% 50%]); (2) medium (trimf μmedium, [25% 50% 75%]); (3) high (smf μhigh, [50% 75%]).
103 nM. Then the crisp CTBA was imported into the next FLS. Finally, Co of TBA was 19.7%. If F was 37.5, then the crisp CTBA was 350 nM. Finally, Co of TBA was 81.2%. Different concentrations of TBA in solution library can obtain different crisp F values, which can export different outputs of Co (see Figure 4A). If there were no TBA in solution libraries, these Cos were low; whereas high concentrations of TBA in solution libraries had higher Co. Because the AO−G can specifically screen the G-quadruplex DNA, the coexisting other linear DNA sequences R15, A20, and T20 did not interfere with molecular search results (see Figure 4A). Obviously, by comparing with binary expression (such as “present” and “absent”), this analytical method based on fuzzy logic can reason and provide
analysis to intelligently search for TBA (Figure 3A). The fluorescence signal is usually distorted by complexity of samples and the presence of interferents, resulting in inaccuracy of the detection results. Thus, we use correlation (Co) to represent the search results of molecules. For example, if the monitored crisp F was 10, we obtained the membership value 1.0 to which the F was low (μlow(F) = 1.0). According to Figure 3A, CTBA was low (μlow(CTBA) = 1.0) and the crisp value was 75.2 nM (defuzzy process in Supporting Information). Then the crisp CTBA was imported into the next FLS. Thus, Co was low (μlow(Co) = 1.0). Through defuzzifier, Co of TBA was 18.8%. Similarly, if F was 15.63, μlow(F) was 0.25, and μmedium(F) was 0.75. Through defuzzifier, CTBA was 4498
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CONCLUSIONS In summary, Boolean logic tree which was utilized to organize and connect “plug and play” chemical events for developing the multifunctional and self-organized logic programmable “languages” can generate logic evolution system and intelligent search engine. The versatility of Boolean logic tree could expand gate connectivity with molecular-based systems and give a favorable opportunity to develop large-scale integration. Moreover, fuzzy logic computing may be an attractive alternative to utilize vague nature of chemical reactions for modeling the imprecise modes of reasoning and sensing, which are very important in artificial intelligence. Furthermore, molecular program based on Boolean logic tree and FLS will provide more opportunities for biomedical nanotechnology, intelligent sensing and control, and artificial life.
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ASSOCIATED CONTENT
S Supporting Information *
AFM images, gel electrophoresis, fluorescence spectral data, and details of the operation of fuzzy logic system. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Authors
*Tel: +86 23 68253237. Fax: +86 23 68253237. E-mail: [email protected]. *Tel: +86 23 68253237. Fax: +86 23 68253237. E-mail: linb@ swu.edu.cn. Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.
Figure 4. Processing performance of intelligent molecular searching for TBA (A) and Fe AND H (B) in different solution libraries containing different coexisting matter combinations. −, +, and ++ represent absence, presence, and 2-fold concentration of +, respectively. 2-fold concentrations of A20, T20, R15, and TBA were all 400 nM. Concentrations of Na+ and Al3+ were 5 mM. 1-fold concentrations of Fe and H were 1 and 6 mM, respectively. The Taiji symbol means fuzzy implication.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (No. 20975083 and 21273174), the Municipal Science Foundation of Chongqing City (No. CSTC2013jjB00002), the Fundamental Research Funds for the Central Universities (No. XDJK2013D006), and the Innovation and Technology Foundation of Southwest University for Excellent Doctoral Student (kb2011010).
more precise and abundant quantitative information on molecules. Boolean web searches usually use operators to perform more specific queries. Using AND, OR, and NOT operators allow people to refine the search by adding or removing specific terms. Similarly, for restricting the search terms for Fe AND H, the basic molecular events (400 nM TBA, 20 μM K+, 2 μM AO, and 5 μg mL−1 G) self-assembled to form AND-gate molecular connector and were typed in solution library to form molecular self-programming compiler ((AO AND G) AND (K+ AND TBA)) ANDNOT ?(Fe AND H) and to compute AO·(G̅ + K+· TBA)·?(Fe·H) for producing the fluorescence reporter output. According to the fluorescence responses of the AO−G4TBA to Fenton reagent (Fe AND H) and the constructed FLS in Figure 3B, the molecular search engine can search for the different Cos of Fe AND H and the coexisting other cations did not almost interfere with molecular search results (see Figure 4B). From a sensing viewpoint, the above molecular search processes are only general analytical procedures. However, from a computing viewpoint, they are one kind of molecular programmable computing.
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Boolean Logic Tree of Graphene-Based Chemical System for Molecular Computation and Intelligent Molecular Search Query Wei Tao Huang, Hong Qun Luo,* and Nian Bing Li* Key Laboratory of Eco-environments in Three Gorges Reservoir Region (Ministry of Education), School of Chemistry and Chemical Engineering, Southwest University, Tiansheng Road, BeiBei District, Chongqing 400715, PR China S Supporting Information *
ABSTRACT: The most serious, and yet unsolved, problem of constructing molecular computing devices consists in connecting all of these molecular events into a usable device. This report demonstrates the use of Boolean logic tree for analyzing the chemical event network based on graphene, organic dye, thrombin aptamer, and Fenton reaction, organizing and connecting these basic chemical events. And this chemical event network can be utilized to implement fluorescent combinatorial logic (including basic logic gates and complex integrated logic circuits) and fuzzy logic computing. On the basis of the Boolean logic tree analysis and logic computing, these basic chemical events can be considered as programmable “words” and chemical interactions as “syntax” logic rules to construct molecular search engine for performing intelligent molecular search query. Our approach is helpful in developing the advanced logic program based on molecules for application in biosensing, nanotechnology, and drug delivery. switch.38c And using the fluorescence emission wavelength shift as the output, the graphene-based Ag+/cysteine-driven dualoutput fluorescent DNA INHIBIT logic gate has also been designed.38e In fact, much more combinations based on interactions between versatile DNA and nanomaterials provide excellent background for artificial computing devices application and development.39 Because these biochemical processes can emulate Boolean logic, they can be used as “digital” biochemical sensors with multiple analytes inputs,40 for example, in biomedical applications (diagnosis of disease or injury),41 environmental monitoring, and multicomponent analysis. However, for real conditions the logic values 0 and 1 of concentrations (or possibly ranges of concentrations) should correspond to normal and abnormal states of the organism or environment, respectively. In most cases the difference between the inputs at the logic 0 and 1 is comparable with the level of natural noise, making the discrimination of the 0 and 1 output signals difficult unless careful optimization of the signal processing systems is performed.42 Privman and co-workers have done a lot of pioneering work in biochemical computing43 and Boolean logic-based biomedical analysis.44 For improving performance of the logic gates, scalability in biochemical computing, and separation of output signals, they developed biochemical “filter”26,45 to successfully achieve noise reduction and control.46
O
ngoing efforts within information technology have been directed toward the building and designing of novel artificial computing devices, such as molecular computers1,2 and biocomputers,3−5 using biochemical molecules1,2,6−8 and engineered biological units3−5,9 as building blocks. Following highly influential papers by de Silva,10 there have been many reported examples of individual molecular logic gates.11 And molecular equivalents of even more complex digital designs were presented in recent years, such as half adders,12 halfsubtractors,13 multiplexers−demultiplexers,14 encoders−decoders,15 “tic-tac-toe” gaming systems,16 and molecular ID tags,17 molecule-based parity generator/checker.18 Molecular logic has also been extending in many directions, including sequential logic,19 reversible logic,19b,20 fuzzy logic,21 and allphotonic logic.18,19b,d,22 Furthermore, biomolecular systems or biological phenomena in complex reaction networks8 and biological processes3−5,23 have been abstracted and simplified for the development of enzymatic logic gates and networks,24 amplifiers,25 signal-converters,25 filters,26 memory system (flipflop,27 associative memory systems28 ), neural network computation,29 and artificial intelligence systems.1,30−35 In recent years, an intense interest has grown in applications of nanomaterials with exceptional physical, optical, and electrical properties.36 An example of such a unique ability for aromatic compounds adsorbing as well as its super fluorescence quenching capacity with wide energy transfer range has shown graphene to be robust artificial nanomaterials.37 Recently, we reported the applications of graphene for detection of G-quadruplex DNA, hydroxyl radicals (HO•), heavy metal ions, cysteine, and hemin.38 We designed the INHIBIT logic gate using Hg2+ and cysteine as the two inputs that operate the fluorescence of dye-graphene-based nano© 2014 American Chemical Society
Received: January 28, 2014 Accepted: April 4, 2014 Published: April 16, 2014 4494
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Microscopy. Tapping mode atomic force microscopy (AFM) measurements were performed on a Multimode microscope (Veeco, U.S.A.) with a Nanoscope IIIa controller, equipped with a Nanoscope Quadrex in tapping mode using a TESP7 Veeco AFM tip. Gel Electrophoresis. Electrophoresis analysis was performed by putting the samples on a 4% agarose gel in a 1 × TAE buffer (40 mM Tris acetate, 1 mM EDTA, pH 8.5) followed by electrophoresis for 50 min at 80 V. After ethidium bromide staining, the gel was imaged using a Gel Doc 2000 system (BIO-RAD, U.S.A.).
However, (bio)molecular Boolean logic and computing is suffering from several well-identified problems. On the one hand, most reported classical (bio)molecular devices10 are based on (bio)chemical reactions or processes: binding of an appropriate combination of analytes to specially designed receptors offer simple logic operations11 and arithmetic calculations.12,13 However, the most serious, and yet unsolved, problem consists in connecting all of these molecular fragments into a usable device.43a,47 On the other hand, the analogue region of the nonlinear response in (bio)chemical processes is not a distinct two-state (high/low) but fuzzy. The inexact natures considered as error in conventional hard computing often hinder the development of artificial computers and “digital” biochemical sensing. Here, the logic evolution tree of complex chemical systems is demonstrated and applied for organizing and connecting chemical events. Solution-based reactions between DNA, nanomaterials, organic dye, and metal ions is programmed33,48 for implementing multilogic gate operations, constructing complex logic evolution network, and developing the intelligent search engine based on hybrid Boolean and fuzzy logic.21 Our approach will help to combine the merits of nanotechnology, Boolean logic, and fuzzy logic. Thus, these (bio)chemical processes can emulate Boolean logic and fuzzy logic and thus can be used as “intelligent and linguistic” biochemical sensors38a with multiple analytes inputs for multicomponent analysis and combinatorial analysis. This combination will open new opportunities for the development and design of intelligent molecular engineering and sensing applications, such as biosensing, environmental monitoring systems, medical diagnosis, and chemical processes.
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RESULTS AND DISCUSSION Logic Tree Analysis and Logic Computation of Chemical System. Because of the π−π stacking interaction,37a reduced graphene oxide (G) self-assembled with acridine orange (AO) dye to form AO−G complex, resulting in the fluorescent quenching of AO (Scheme 1a, Supporting Scheme 1. Boolean Logic Tree Analysis of a Solution-Based Chemical System Based on Interactions among AO, G, TBA, Cations, and Fenton Reactiona
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EXPERIMENTAL SECTION Oligonucleotides. The 15-base linear thrombin aptamer (TBA:5′-GGTTGGTGTGGTTGG-3′), 15-base linear random DNA sequence (R15:5′-AGTAGCTGGTGGCGT-3′), 20-base linear poly(dT) DNA sequence (T20:5′-TTTTTTTTTTTTTTTTTTTT-3′), and 20-base linear poly(dA) DNA sequence (A20:5′-AAAAAAAAAAAAAAAAAAAA-3′) were purchased from Songon Inc. (Shanghai, China) and purified by high performance liquid chromatography. Fabrication of Graphene Oxide and Reduced Graphene Oxide. Graphene oxide was synthesized from graphite (spectral pure, Sinopharm Chemical Reagent Co., Ltd., China) by the Hummers method, and dried for 2 weeks over phosphorus pentoxide in a vacuum desiccator. Reduced graphene oxide (G) was prepared by hydrazine reduction. Fluorescence Measurements. All spectral studies were performed in 20 mM Tris-HAc buffer (pH 7.4). The DNA solutions were prepared in the 20 mM Tris-HAc buffer solution (pH 7.4) with and without 20 μM K+ or Pb2+. HO• was chemically generated through the Fenton reaction (Fe2+/H2O2 1:6 mol mol −1 ). All fluorescence measurements were performed on a Hitachi F-2700 fluorescence spectrophotometer (Hitachi Ltd., Japan). The operation conditions are described as follows: PMT voltage: 400 V, excitation wavelength: 490 nm, slit: 10 nm. Fuzzy Logic Analysis. Fuzzy analysis was implemented with Fuzzy Logic Toolbox in Matlab 7.1 (Mathworks, U.S.A.). The fuzzy logic system (FLS) is implemented by the Mamdani’s method with the centroid defuzzification (details of the defuzzifier and defuzzy process are added in Supporting Information).
a
The orange glow represents fluorescence emission.
Information Figure S1).38a,c,f When mixed with G-quadruplex (G4) thrombin aptamer (G4TBA) induced by K+ or Pb2+ (Scheme 1b, c),49 the resulting AO−G complex was broken because of a specifically competitive binding of AO with G4TBA, and a more stable AO−G4TBA complex than AO−G complex was formed,38f resulting in restoration of dye fluorescence (Scheme 1d, Supporting Information Figure S2). In the presence of HO•-generating Fenton reagent (Fe2+/Fe and H2O2/H) (Scheme 1e), G4TBA was broken into fragments,38b which disturbs competitive binding of the dye with G4, resulting in fluorescence requenching of the AO dye (Scheme 1f, Supporting Information Figure S3). The aforementioned processes in Scheme 1 show that DNA, nanomaterials, organic dye, metal ions, and Fenton reaction in solution phase can self-assemble, compete, and connect with each other. Because learning and using the language of other 4495
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Figure 1. (A) AO ANDNOT G gate. (B) TBA AND K+ gate. (C) K+ OR Pb2+ gate. (D) Fe NAND H gate which consists of Fe AND H gate and HO•-input NOT gate. (E) Symbol (left) and processing performance (right) of 6-input compound logic circuits with six chemical inputs and oneoutput fluorescence (blue points represent logic output 1). AO, 2 μM; G, 5 μg mL−1; K+/Pb2+, 20 μM; TBA, 400 nM; Fe, 2 mM; H, 12 mM. The data represent the mean and standard deviation of three independent experiments. a.u., arbitrary units.
disciplines is a way of taking chemical ideas to nonchemist hearts and minds,50 we utilize fault-like tree analysis to study the logic evolution of chemical events in aforementioned processes. Fault tree analysis51 is a deductive failure analysis in which an undesired state of a system is analyzed using Boolean logic to combine a series of lower-level events. There are two types of symbols which appear in the fault tree structure: gates and events. Typical examples of event symbols used in the fault tree structure are illustrated in green box of Scheme 1. The events in the fault tree are linked using “gate” symbols. Common gates are shown in red box of Scheme 1. The three fundamental logic gates are “AND”, “OR” and “NOT”. For an AND gate the output event occurrence requires the simultaneous existence of all of the input events. The output (higher level event of an OR gate) will result from the occurrence of at least one of the input (lower level) events. The output to a NOT gate happens as long as the input event does
not. G (basic event) self-assembled with AO (basic event) to form AND-gate nanocomplex (intermediate event) (Scheme 1a). TBA (basic event) was folded to form AND-gate G4TBA (intermediate event) in the presence of K+ or Pb2+ (basic event) (Scheme 1c). Because G4TBA can be induced by K+ or Pb2+, the basic events K+ and Pb2+ perform OR logic function (Scheme 1b). G4TBA (intermediate event) and the AO−G complex (intermediate event) through superimposed AND gates interacted and exchanged AO molecules to produce two outputs: AO−G4TBA (top event) and G (Scheme 1d). The AO−G complex and G4TBA exchanged AO molecules which can be considered as a messenger to carry information and communicate with one another. Fe and H (basic events) implement AND gate operation and exports HO• (Scheme 1e). HO• is highly reactive, consequently short-lived, and to easily degrade and “reset” G4TBA into fragments, corresponding to the inverted IMPLY (N-IMPLY) gateAO−G4TBA AND4496
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NOT HO• gate (Scheme 1f). Thus, we can represent the whole cascade reactions as ((AO AND G) AND ((K+ OR Pb2+) AND TBA)) ANDNOT (Fe AND H). We use the fluorescence change in the different combinations of these aforementioned chemical events for implementing multifunctional logic computation. Logical outputs are defined when fluorescence (F) < 15 (a.u.) for logical 0 and >20 (a.u.) for logical 1, respectively. Self-assembly of AO and G functions as N-IMPLY fluorescence gate. By combining the two input signals AO and G in accordance with the truth table, the fluorescence output is produced exclusively in the presence of AO and not G as shown by fluorescence analysis (Figure 1A). By combining the two input signals TBA and K+ in accordance with the truth table, the substrate AO−G complex gave the fluorescence signal only when (TBA AND K+)-induced G4TBA was added, corresponding to AND and YES fluorescence gate functions (Figure 1B). Similarly, by combining the two input signals Pb2+ and K+ in accordance with the truth table, only if one of Pb2+ and K+ is present, the substrate TBA was induced to produce the same output G4TBA, resulting in fluorescence turn-on of the AO−G system (Figure 1C). HO•-switched AO−G4TBA system really functions as a NOT fluorescence gate, because fluorescence turn-off happened as long as the input HO• is present. By regarding HO• as Fe AND H, we also fabricated NAND gate (Figure 1D, Supporting Information Figure S3). These chemical events (AO, G, K+, TBA, Fe, H) not only can be connected to form complex logic evolution networks, but also use the fluorescence signal as output for computing AO·(G̅ + K+·TBA)·(Fe·H) (Figure 1E). Fuzzy Logic Operation and Intelligent Molecular Search Query. In the (bio)chemical process, there is usually the nonlinear (sigmoidal) response because of mass action of molecule populations. The extremes of the response possess two plateaux which arise from two discrete states of a molecule (target-bound/free) and are the basis of molecular binary logic computation.50 However, the analogue region of the sigmoidal response is not a distinct two-state (high/low) but fuzzy. The inexact natures considered as error in conventional hard computing (binary logic) often hinder the development of artificial computers and “digital” biochemical sensing. But it can be developed into fuzzy logic operation.21 Based on the fuzzy nature of chemical reactions, we can deal with uncertain information in the analogue region to implement soft computation through the formulation of FLS. FLS is a nonlinear mapping of an input crisp data vector (x)̅ into a scalar crisp output (y) and this mapping can be expressed 52 quantitatively as y = f (x). FLS consists of four basic elements: ̅ fuzzifier, rules, inference engine, and defuzzifier (more information in Supporting Information). A fuzzy set S for the variable X, is characterized by a membership function, μS(x), which associates a real number, included in the interval [0, 1], to each element of X. A fuzzy variable is a variable that takes on fuzzy sets as values. They are usually referred to as linguistic variables, such as concentration C and fluorescence F. To handle the variable in the absence of exact values, we estimate the variable in terms of a few linguistic values such as low, medium, or high. Outputs and inputs are modeled as fuzzy variables. As shown in Figure 2 green box, the fluorescence of AO has quasi- negated-translated sigmoidal response to G. The CG input variable and the F output variable are defined by the fuzzy sets as illustrated in Figure 2. The inference rules can be
Figure 2. Scheme of fuzzy relation based on fuzzy inference rules mapping input CG to output F. Green box: Fluorescence intensity of AO (2 μM) as a function of CG used for titration. Fuzzy variable is decomposed in three fuzzy sets. CG: (1) Low (zmf μlow, [1.5 2]); (2) medium (trimf μmedium, [1.5 2 3]); (3) high (smf μhigh, [2.5 3.5]). F: (1) Low (zmf μlow, [8.5 22.5]); (2) medium (trimf μmedium, [8.5 60 120]); (3) high (smf μhigh, [60 120]).
extracted from Figure 2 green box. They are expressed as a collection of IF-THEN statements, for example ‘‘IF CG is low, THEN F is high” (Figure 2). The IF-part is called the antecedent, and the THEN-part is called the consequence. The inference engine of the FLS maps input fuzzy sets into output fuzzy sets (Figure 2). The defuzzifier maps output fuzzy sets into crisp numbers. The output crisp number can correspond to a prediction of a variable, like F. By using Boolean and fuzzy logic, we can construct molecular search engine for querying target molecular events (such as TBA and Fe AND H) in the molecular library. According to the aforementioned logic tree analysis, our chemical system can be represented as ((AO AND G) AND ((K+ OR Pb2+) AND TBA)) ANDNOT (Fe AND H) for the top event AO− G4TBA. This Boolean logic tree can provide an effective approach and a powerful programming language for organizing chemical events as programmable “words” and connect them through chemical interactions as “syntax” logic rules. For search query for TBA, the basic event K+ (20 μM) was first typed into the solution-based library for forming AND-gate G4TBA. Then the programmed AND-gate AO−G was added to construct the self-organizing compiler (?TBA AND K+) AND (AO AND G) for exporting the top event AO−G4TBA and to compute AO· (G̅ + K+·?TBA) for producing the fluorescence reporter output. The self-organizing compiler can perform Boolean logic function to determine whether TBA is present in the solution-based library. If TBA is present, the AO−G4TBA is produced, resulting in the fluorescence turn-on. Otherwise, the fluorescence is still quenched. According to the fluorescence responses of the AO−G complex to TBA (when 20 μM K+ is present), we can construct a FLS and perform fluorescence FLS 4497
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Figure 3. (A) Scheme of fuzzy relation based on fuzzy inference rules mapping input F to output correlation (Co) to search for TBA. Green box: The fluorescence responses of the AO−G complex to TBA (when 20 μM K+ is present). Fuzzy variable is decomposed in three fuzzy sets. F: (1) Low (zmf μlow, [12.5 25]); (2) medium (trimf μmedium, [12.5 25 37.5]); (3) high (smf μhigh, [25 37.5]). CTBA: (1) Low (zmf μlow, [100 200]); (2) medium (trimf μmedium, [100 200 300]); (3) high (smf μhigh, [200 300]). Co: (1) Low (zmf μlow, [25% 50%]); (2) medium (trimf μmedium, [25% 50% 75%]); (3) high (smf μhigh, [50% 75%]). (B) Scheme of fuzzy relation based on fuzzy inference rules mapping input F to output Co to search for Fe AND H. Green box: The fluorescence responses of the AO−G4TBA to Fe AND H (CFe AND H = CFe, Fe/H = 1:6). Fuzzy variable is decomposed in three fuzzy sets. F: (1) Low (zmf μlow, [10 15]); (2) medium (trimf μmedium, [10 16 22]); (3) high (smf μhigh, [20 22]). CFe AND H: (1) Low (zmf μlow, [20 100]); (2) medium (trimf μmedium, [25 250 750]); (3) high (smf μhigh, [400 750]). Co: (1) Low (zmf μlow, [25% 50%]); (2) medium (trimf μmedium, [25% 50% 75%]); (3) high (smf μhigh, [50% 75%]).
103 nM. Then the crisp CTBA was imported into the next FLS. Finally, Co of TBA was 19.7%. If F was 37.5, then the crisp CTBA was 350 nM. Finally, Co of TBA was 81.2%. Different concentrations of TBA in solution library can obtain different crisp F values, which can export different outputs of Co (see Figure 4A). If there were no TBA in solution libraries, these Cos were low; whereas high concentrations of TBA in solution libraries had higher Co. Because the AO−G can specifically screen the G-quadruplex DNA, the coexisting other linear DNA sequences R15, A20, and T20 did not interfere with molecular search results (see Figure 4A). Obviously, by comparing with binary expression (such as “present” and “absent”), this analytical method based on fuzzy logic can reason and provide
analysis to intelligently search for TBA (Figure 3A). The fluorescence signal is usually distorted by complexity of samples and the presence of interferents, resulting in inaccuracy of the detection results. Thus, we use correlation (Co) to represent the search results of molecules. For example, if the monitored crisp F was 10, we obtained the membership value 1.0 to which the F was low (μlow(F) = 1.0). According to Figure 3A, CTBA was low (μlow(CTBA) = 1.0) and the crisp value was 75.2 nM (defuzzy process in Supporting Information). Then the crisp CTBA was imported into the next FLS. Thus, Co was low (μlow(Co) = 1.0). Through defuzzifier, Co of TBA was 18.8%. Similarly, if F was 15.63, μlow(F) was 0.25, and μmedium(F) was 0.75. Through defuzzifier, CTBA was 4498
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CONCLUSIONS In summary, Boolean logic tree which was utilized to organize and connect “plug and play” chemical events for developing the multifunctional and self-organized logic programmable “languages” can generate logic evolution system and intelligent search engine. The versatility of Boolean logic tree could expand gate connectivity with molecular-based systems and give a favorable opportunity to develop large-scale integration. Moreover, fuzzy logic computing may be an attractive alternative to utilize vague nature of chemical reactions for modeling the imprecise modes of reasoning and sensing, which are very important in artificial intelligence. Furthermore, molecular program based on Boolean logic tree and FLS will provide more opportunities for biomedical nanotechnology, intelligent sensing and control, and artificial life.
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ASSOCIATED CONTENT
S Supporting Information *
AFM images, gel electrophoresis, fluorescence spectral data, and details of the operation of fuzzy logic system. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Authors
*Tel: +86 23 68253237. Fax: +86 23 68253237. E-mail: [email protected]. *Tel: +86 23 68253237. Fax: +86 23 68253237. E-mail: linb@ swu.edu.cn. Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.
Figure 4. Processing performance of intelligent molecular searching for TBA (A) and Fe AND H (B) in different solution libraries containing different coexisting matter combinations. −, +, and ++ represent absence, presence, and 2-fold concentration of +, respectively. 2-fold concentrations of A20, T20, R15, and TBA were all 400 nM. Concentrations of Na+ and Al3+ were 5 mM. 1-fold concentrations of Fe and H were 1 and 6 mM, respectively. The Taiji symbol means fuzzy implication.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (No. 20975083 and 21273174), the Municipal Science Foundation of Chongqing City (No. CSTC2013jjB00002), the Fundamental Research Funds for the Central Universities (No. XDJK2013D006), and the Innovation and Technology Foundation of Southwest University for Excellent Doctoral Student (kb2011010).
more precise and abundant quantitative information on molecules. Boolean web searches usually use operators to perform more specific queries. Using AND, OR, and NOT operators allow people to refine the search by adding or removing specific terms. Similarly, for restricting the search terms for Fe AND H, the basic molecular events (400 nM TBA, 20 μM K+, 2 μM AO, and 5 μg mL−1 G) self-assembled to form AND-gate molecular connector and were typed in solution library to form molecular self-programming compiler ((AO AND G) AND (K+ AND TBA)) ANDNOT ?(Fe AND H) and to compute AO·(G̅ + K+· TBA)·?(Fe·H) for producing the fluorescence reporter output. According to the fluorescence responses of the AO−G4TBA to Fenton reagent (Fe AND H) and the constructed FLS in Figure 3B, the molecular search engine can search for the different Cos of Fe AND H and the coexisting other cations did not almost interfere with molecular search results (see Figure 4B). From a sensing viewpoint, the above molecular search processes are only general analytical procedures. However, from a computing viewpoint, they are one kind of molecular programmable computing.
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