Enzyme-Based Biomolecular Computing

This research project is conducted in a close collaboration with Prof. Vladimir Privman






PI: Evgeny Katz, Co-PI: Vladimir Privman

Molecular and biomolecular logic gates and their networks processing chemical input signals similarly to computers received high attention and were rapidly developed in the last decade. Being a subarea of unconventional computing, they can process chemical information mimicking Boolean logic operations using binary definitions (1,0; YES/NO) for concentrations of reacting species. Using this approach, chemical reactions could be reformulated as information processing steps with built-in logic operations. Then, the chemical processes could be programmed similar to computer programming yielding networks performing several logic operations.

As a network that processes information becomes large, and the information is processed in greater quantities and at higher complexity, noise inevitably builds up and can ultimately degrade the useful “signal” which is the intended result of the computation. One then has to develop approaches to achieve what is known as “fault-tolerant” information processing that involves noise control and suppression. One notable example is the “robustness” of many complex processes in cell functions.

Presently, we are aware of three primary fault-tolerant information processing paradigms. The first is the analog/digital electronics paradigm of the Si-chip technology in modern computers. We know how to design such devices and they have been successfully built. Living organisms are the second paradigm: While we obviously know that this paradigm leads to scalability, we do not yet fully understand it, though significant strides have been made in Systems Biology to explore the structure and functioning of biological “networks.” The third, recent paradigm, involves massive parallelism: quantum (quantum computing) or ensemble (variants of DNA computing), both in the preliminary research stages.

Biochemical computing — in our case based on enzymatic reactions^1-3 — attempts to process information with biomolecules and biological objects.^4-13 However, the information processing paradigm assumed, has, in most cases, been that of the ordinary electronics. Indeed, most biochemical computing studies attempt to realize and, most recently, network “gates” that mimic Boolean digital logic.^14,15

Networks with computational steps that solely involve biochemical processes,^16,17 are being researched for new technological capabilities: multi-input biosensors with new functionalities,^18-20 as well as approaches that allow removing the batteries from, and generally reducing the need for inorganic leads and electrical power supply for those stages of information processing that occur during biomedical testing, implantable devices, and other fast decision making steps in applications. Futuristic ideas for applications of biochemical logic include more direct brain-computer and body-computer interfacing for both reading out and inputting information, and generally erasing the barrier between the inorganic and organic information processing in computer device functioning.

The primary present challenge in the field of biochemical computing can be summarized as follows. Recent studies took the field somewhat beyond the earlier set of works that have realized simple gates mimicking two-input, one-output Boolean functions. Specifically, few-gate networking has been accomplished,^16,17 first steps in the analysis of network scalability have been reported very recently,²¹ and first attempts at “smart” interfacing with ordinary electronics have been initiated.^22-25 In these studies, biocomputing based on enzymatic reactions has emerged as an appealing approach for information processing due to the specificity and other useful chemical-kinetics properties of enzyme reactions.

However, these advances have also set the stage for new challenges. In particular, it has been realized that large-scale networking and fault-tolerance cannot be achieved without the development of a “toolbox” of new network elements, specifically, filters, signal splitters (copying), signal balancers, resetting functions, etc. These non-Boolean network elements for biochemical computing might not follow too closely the analogy with ordinary electronic devices. In fact, concepts borrowed from Nature, including the delayed identity — part of the feed-forward network motif,²⁶ or “memory” properties²⁷ have recently received attention in information processing network studies. The present research program attempts to address these challenges, building on the earlier works in the fields of chemical and biochemical computing.

At present there are chemical-computing studies that have used molecular or supra-molecular systems^28‑44 to mimic processes typical for electronic computing devices such as simple Boolean logic operations AND, OR, XOR, etc.,^45-63 as well as more complex systems including molecular comparator, digital demultiplexer, encoder-decoder, keypad lock, write-read-erase memory units, half-adder/half-subtractor or full-adder/full-subtractor,^64-86 etc. Chemical systems are, in principle, capable of performing computations at the level of a single molecule⁸⁷ resulting in nano-scaling of the computing units⁸⁸ and allowing parallel computation performed by molecules involved in various chemical reactions.⁸⁹ However, one of the most important challenges in the chemical computing is networking and fault-tolerance.^1,15 Complex multi-component chemical logic systems usually require ingenious molecular assemblies to allow compatibility between information processing sub-units^28,77 and perform rather simple functions despite their extreme synthetic complexity.⁹⁰

Biomolecular systems, on the other hand, offer the advantage of specificity (of being very selective) in their chemical functions and therefore being more usable in complex “chemical soup” environments. As a result, complex enzyme-based information processing units could be more easily scaled up giving rise to artificial biocomputing networks performing various logic functions and mimicking natural biochemical pathways.^{16,17,21,42,91} An added advantage of biomolecular computing systems is the capability to process biochemical information received in the form of chemical signals directly from biological systems and the ability to operate in a biological environment.⁹² This is important for interfacing of the resulting biochemical-logic “devices” with processes in living organisms,⁹³ for potential biomedical applications.

Recent experimental advances in enzyme-based biocomputing have included not just experimental demonstrations of several single Boolean gates, such as AND, OR, XOR, Inhibit, etc.,^1-4 but also networking of several, up to 3-5 presently, gates.^{14,16,17,21,24} Similar logic operations were also realized using non-biological chemical systems.^64-85 However, the biochemical systems offered relative simplicity of the assembled logic schemes. Still, ultimately the increasing complexity of enzyme-based logic networks will require exploration of noise suppression approaches in biochemical logic-gates networks. Fault tolerance within the analog/digital information processing paradigm is accomplished by gate optimization for suppression of the “analog” noise amplification^1,94 as well as by network design and/or network topology.²¹ For larger networks, another, “digital” mechanism⁹⁵ of noise amplification emerges. It is combated by redundancy in network design and requires truly digital information processing with appropriate network elements for filtering, signal splitting, etc.

The present sizes of the biochemical computing networks have already allowed exploration of aspects of design and optimization issues related to suppression of the “analog” noise amplification. The work on this topic was initiated in our recent publications.^1,21,94,95 The field is presently wide open for research developments. The following brief description of our recent results attempts to summarize the group activity in the project.

Boolean Logic Gates Using Enzymes as Input Signals Biochemical systems demonstrating Boolean logic operations AND, OR, XOR and InhibA were developed using soluble compounds representing the chemical “devices” and enzymes glucose oxidase (GOx), glucose dehydrogenase (GDH), alcohol dehydrogenase (AlcDH) and microperoxidase-11 (MP-11) operating as the input signals that activate the logic gates. The enzymes were used as soluble materials and as immobilized biocatalysts. The studied systems were suggested as one step forward to the construction of “smart” signal responsive materials with the built-in Boolean logic. G. Strack, M. Pita, M. Ornatska,E. Katz, Boolean logic gates using enzymes as input signals. ChemBioChem, 2008, 9, 1260-1266.

Enzyme-based NAND and NOR logic gates with modular design The logic gates NAND / NOR were mimicked by enzyme biocatalyzed reactions activated by sucrose, maltose and phosphate. The sub-units performing AND / OR Boolean logic operations were designed using maltose phosphorylase and cooperative work of invertase/amyloglucosidase, respectively. Glucose produced as the output signal from the AND / OR sub-units was applied as the input signal for the INVERTER gate composed of alcohol dehydrogenase, glucose oxidase, microperoxidase-11, ethanol and NAD+, which generated the final output in the form of NADH inverting the logic signal from 0 to 1 or from 1 to 0. The final output signal was amplified by a self-promoting biocatalytic system. In order to fulfill the Boolean properties of associativity and commutativity in logic networks, the final NADH output signal was converted to the initial signals of maltose and phosphate, thus allowing assembling of the same standard units in concatenated sequences. The designed modular approach, signal amplification and conversion processes open the way towards complex logic networks composed of standard elements resembling electronic integrated circuitries. J. Zhou, M.A. Arugula, J. Halámek, M. Pita, E. Katz, Enzyme-based NAND and NOR logic gates with modular design. J. Phys. Chem. B 2009, 113, 16065-16070.

Analog Noise Reduction in Enzymatic Logic Gates In this work we demonstrate both experimentally and theoretically that the analog noise generation by a single enzymatic logic gate can be dramatically reduced to yield gate operation with virtually no input noise amplification. We demonstrate that when a co-substrate with a much smaller affinity than the primary substrate is used, a negligible increase in the noise output from the logic gate is obtained as compared to the input noise level. Our general theoretical conclusions were confirmed by experimental realizations of the AND logic gate based on the enzyme horseradish peroxidase using hydrogen peroxide as the substrate, with 2,2'‑azino‑bis(3-ethylbenzthiazoline-6-sulphonic acid) (ABTS) or ferrocyanide as co‑substrates with vastly different rate constants. D. Melnikov, Strack, M. Pita, V. Privman, E. Katz, Analog noise reduction in enzymatic logic gates. J. Phys. Chem. B 2009, 113, 10472-10479.

Realization and Properties of Biochemical-Computing Biocatalytic XOR Gate Based on Signal Change We consider a realization of the XOR logic gate in a system involving two competing biocatalytic reactions, for which the logic-1 output is defined by these two processes causing a change in the optically detected signal. A model is developed for describing such systems in an approach suitable for evaluation of the analog noise amplification properties of the gate and optimization of its functioning. The initial data are fitted for gate quality evaluation within the developed model, and then modifications are proposed and experimentally realized for improving the gate functioning. V. Privman, J. Zhou, J. Halámek, E. Katz, Realization and properties of biochemical-computing biocatalytic XOR gate based on signal change. J. Phys. Chem. B 2010, 114, 13601-13608.

Biochemical Filter with Sigmoidal Response: Increasing the Complexity of Biomolecular Logic The first realization of a designed, rather than natural, biochemical filter process is reported and analyzed as a promising network component for increasing the complexity of biomolecular logic systems. Key challenge in biochemical logic research has been achieving scalability for complex network designs. Various logic gates have been realized, but a "toolbox" of analog elements for interconnectivity and signal processing has remained elusive. Filters are important as network elements that allow control of noise in signal transmission and conversion. We report a versatile biochemical filtering mechanism designed to have sigmoidal response in combination with signal-conversion process. Horseradish peroxidase-catalyzed oxidation of chromogenic electron donor by H2O2, was altered by adding ascorbate, allowing to selectively suppress the output signal, modifying the response from convex to sigmoidal. A kinetic model was developed for evaluation of the quality of filtering. The results offer improved capabilities for design of scalable biomolecular information processing systems. V. Privman, J. Halámek, M.A. Arugula, D. Melnikov, V. Bocharova, E. Katz, Biochemical filter with sigmoidal response: Increasing the complexity of biomolecular logic. J. Phys. Chem. B 2010, 114, 14103-14109.

Towards Biochemical Filter with Sigmoidal Response to pH Changes We realize a biochemical filtering process based on the introduction of a buffer in a biocatalytic signal-transduction logic system based on the function of an enzyme, esterase. The input, ethyl butyrate, is converted into butyric acid—the output signal, which in turn is measured by the drop in the pH value. The developed approach offers a versatile "network element" for increasing the complexity of biochemical information processing systems. Evaluation of an optimal regime for quality filtering is accomplished in the framework of a kinetic rate-equation model. The reaction biocatalyzed by an enzyme, here esterase, results in the hydrolysis of ethyl butyrate (the logic Input) to yield butyric acid which releases H+ ions upon dissociation. A limited quantity of a buffer, here HEPES, if introduced, consumes most of the biocatalytically produced H+ ions when the input is applied at a low concentration. The pH change (the logic Output, measured by the pH drop, as indicated by an arrow) sets in when the biocatalytically produced H+ ions overwhelm the buffer. The biocatalytic process and buffering combined, yield a sigmoidal dependence of the pH change as a function of the input concentration. The inset illustrates the onset of the sigmoidal response in our experimental system. The solid curves show the output, y, vs. the input, x, properly redefined/rescaled to vary in the "binary-logic ranges" from 0 to 1, as explained in the text. Experimental data were fitted by using rate equations appropriate for the processes involved, and the results are shown, here for the reaction time 120 min, for increasing buffer (HEPES) concentrations. The top (red) curve corresponds to [HEPES] = 0; middle (blue): [HEPES] = 50 mM, bottom (green): [HEPES] = 100 mM. The dashed black curve does not correspond to experimental data but rather illustrates a desirable, "ideal" filter response with small slopes at both binary logic points 0 and 1, and with a steep, symmetrically positioned inflection region in the middle. M. Pita, V. Privman, M.A. Arugula, D. Melnikov, V. Bocharova, E. Katz, Towards biochemical filter with sigmoidal response to pH changes: Buffered biocatalytic signal transduction. PhysChemChemPhys 2011, in press (DOI: 10.1039/c0cp02524k).

1.     V. Privman, G. Strack, D. Solenov, M. Pita, E. Katz, Optimization of enzymatic biochemical logic for noise reduction and scalability: How many biocomputing gates can be interconnected in a circuit? J. Phys. Chem. B 2008, 112, 11777-11784.

  2.   G. Strack, M. Pita, M. Ornatska, E. Katz, Boolean logic gates using enzymes as input signals, ChemBioChem 2008, 9, 1260-1266.

  3.   R. Baron, O. Lioubashevski, E. Katz, T. Niazov, I. Willner, Two coupled enzymes perform in parallel the “AND” and “InhibAND” logic gates operations, Org. Biomol. Chem. 2006, 4, 989-991; R. Baron, O. Lioubashevski, E. Katz, T. Niazov, I. Willner, Logic gates and elementary computing by enzymes, J. Phys. Chem. A 2006, 110, 8548-8553.

  4.   S. Sivan, N. Lotan, A biochemical logic gate using an enzyme and its inhibitor. Part I: The inhibitor as switching element, Biotechnol. Prog. 1999, 15, 964-970; S. Sivan, S. Tuchman, N. Lotan, A biochemical logic gate using an enzyme and its inhibitor, Biosystems 2003, 70, 21-33.

  5.   A.S. Deonarine, S.M. Clark, L. Konermann, Implementation of a multifunctional logic gate based on folding/unfolding transitions of a protein, Future Generation Comp. Syst. 2003, 19, 87-97.

  6.   G. Ashkenazi, D.R. Ripoll, N. Lotan, H.A. Scheraga, A molecular switch for biochemical logic gates: Conformational studies, Biosens. Bioelectron. 1997, 12, 85-95.

  7.   R. Unger, J. Moult, Towards computing with proteins, Proteins 2006, 63, 53-64.

  8.   M.N. Stojanovic, D. Stefanovic, T. LaBean, H. Yan, Computing with nucleic acids, in: Bioelectronics: From Theory to Applications, I. Willner, E. Katz (Eds.), Wiley-VCH, Weinheim, 2005, pp. 427-455.

  9.   A. Saghatelian, N.H. Volcker, K.M. Guckian, V.S.Y. Lin, M.R. Ghadiri, DNA-based photonic logic gates: AND, NAND, and INHIBIT, J. Am. Chem. Soc. 2003, 125, 346-347.

10.   G. Ashkenasy, M.R. Ghadiri, Boolean logic functions of a synthetic peptide network, J. Am. Chem. Soc. 2004, 126, 11140-11141.

11.   M.N. Win, C.D. Smolke, Higher-order cellular information processing with synthetic RNA devices, Science 2008, 322, 456-460.

12.   M.L. Simpson, G.S. Sayler, J.T. Fleming, B. Applegate, Whole-cell biocomputing, Trends Biotechnol. 2001, 19, 317-323.

13.   J.D. Gunton, R. Toral, C. Mirasso, M.E. Gracheva, Invited review: The role of noise in some physical and biological systems, chapter in the book Recent Research Developments in Applied Physics, Recent Res. Developm. Appl. Phys. 2003, 6, 497-514.

14.   R. Baron, O. Lioubashevski, E. Katz, T. Niazov, I. Willner, Elementary arithmetic operations by enzymes: A model for metabolic pathway based computing, Angew. Chem. Int. Ed. 2006, 45, 1572-1576.

15.   E. Katz, V. Privman, Enzyme-based logic systems for information processing, Chem. Soc. Rev. 2010, 39, 1835-1857.

16.   T. Niazov, R. Baron, E. Katz, O. Lioubashevski, I. Willner, Concatenated logic gates using four coupled biocatalysts operating in series, Proc. Natl. Acad. USA. 2006, 103, 17160-17163.

17.   G. Strack, M. Ornatska, M. Pita, E. Katz, Biocomputing security system: Concatenated enzyme-based logic gates operating as a biomolecular keypad lock, J. Am. Chem. Soc. 2008, 130, 4234-4235.

18.   E. Katz, V. Privman, J. Wang, Towards Biosensing Strategies Based on Biochemical Logic Systems, in: Proc. Conf. ICQNM 2010, IEEE Comp. Soc. Conf. Publ. Serv., Los Alamitos, California, 2010, pp. 1-9.

19.   K.M. Manesh, J. Halámek, M. Pita, J. Zhou, T.K. Tam, P. Santhosh, M.-C. Chuang, J.R. Windmiller, D. Abidin, E. Katz, J. Wang, Enzyme logic gates for the digital analysis of physiological level upon injury, Biosens. Bioelectron. 2009, 24, 3569-3574.

20.   M. Pita, J. Zhou, K.M. Manesh, J. Halámek, E. Katz, J. Wang, Enzyme logic gates for assessing physiological conditions during an injury: Towards digital sensors and actuators, Sens. Actuat. B 2009, 139, 631-636.

21.   V. Privman, M.A. Arugula, J. Halámek, M. Pita, E. Katz, Network Analysis of Biochemical Logic for Noise Reduction and Stability: A System of Three Coupled Enzymatic AND Gates, J. Phys. Chem. B 2009, 113, 5301-5310.

22.   T.K. Tam, J. Zhou, M. Pita, M. Ornatska, S. Minko, E. Katz, Biochemically controlled bioelectrocatalytic interface, J. Am. Chem. Soc. 2008, 130, 10888-10889.

23.   J. Zhou, T.K. Tam, M. Pita, M. Ornatska, S. Minko, E. Katz, Bioelectrocatylic system coupled with enzyme-based biocomputing ensembles performing Boolean logic operations: Approaching “smart” physiologically controlled biointerfaces, ACS Appl. Mater. Interfaces, 2009, 1, 144-149.

24.   M. Privman, T.K. Tam, M. Pita, E. Katz, Switchable electrode controlled by enzyme logic network system: Approaching physiologically regulated bioelectronics, J. Am. Chem. Soc. 2009, 131, 1314-1321.

25.   M. Krämer, M. Pita, J. Zhou, M. Ornatska, A. Poghossian, M. J. Schöning, E. Katz, Coupling of biocomputing systems with electronic chips: Electronic interface for transduction of biochemical information, J. Phys. Chem. B 2009, 113, 2573-2579.

26.   U. Alon, An Introduction to Systems Biology. Design Principles of Biological Circuits, Chapman & Hall/CRC Press, Boca Raton, FL, 2007.

27.   D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, The missing memristor found, Nature 2008, 453, 80-83; J.J. Yang, M.D. Pickett, X. Li, D.A.A. Ohlberg, D.R. Stewart, R.S. Williams, Memristive switching mechanism for metal/oxide/metal nanodevices, Nature Nanotechnology 2008, 3, 429-433; L.N. Cooper, Memories and memory: a physicist’s approach to the brain, Int. J. Mod. Phys. A 2000, 15, 4069-4082; T. Munakata, Fundamentals of the new artificial intelligence: Neural, evolutionary, fuzzy and more, 2^nd Ed., Springer, 2008; M. Di Ventra, Y.V. Pershin, L.O. Chua, Circuit elements with memory: memristors, memcapacitors and
meminductors, Proceedings of the IEEE 2009, 97, 1717-1724; Y.V. Pershin, S. La Fontaine, M. Di Ventra, Memristive model of amoeba's learning, Phys. Rev. E 2009, 80, Article 021926; Y.V. Pershin, M. Di Ventra, Spin memristive systems, Phys. Rev. B 2008, 78, Article 113309.

28.   A.P. de Silva, S. Uchiyama, T.P. Vance, B. Wannalerse, A supramolecular chemistry basis for molecular logic and computation, Coord. Chem. Rev. 2007, 251, 1623-1632; A.P. de Silva, S. Uchiyama, Molecular logic and computing, Nature Nanotech. 2007, 2, 399-410; K. Szacilowski, Digital information processing in molecular systems, Chem. Rev. 2008, 108, 3481-3548.

29.   P. Dittrich, Chemical computing, Lect. Notes Computer Sci. 2005, 3566, 19-32.

30.   A.N. Shipway, E. Katz, I. Willner, Molecular memory and processing devices in solution and on surfaces, in: Structure and Bonding, volume title “Molecular Machines and Motors,” J.-P. Sauvage (Ed.), Springer-Verlag, Berlin, 2001, Vol. 99, pp. 237-281.

31.   M. Suresh, A. Ghosh, A. Das, Half-subtractor operation in pH responsive N-heterocyclic amines, Tetrahedron Lett. 2007, 48, 8205-8208.

32.   S. Iwata, K. Tanaka, A novel cation “AND” anion recognition host having pyrido[1',2': 1,2]-imidazo[4,5-b]pyrazine as the fluorophore, J. Chem. Soc., Chem. Commun. 1995, 1491-1492.

33.   S.H. Lee, J.Y. Kim, S.K. Kim, J.H. Leed, J.S. Kim, Pyrene-appended calix[4]crowned logic gates involving normal and reverse PET: NOR, XNOR and INHIBIT, Tetrahedron 2004, 60, 5171-5176.

34.   D.C. Magri, G.J. Brown, G.D. McClean, A.P. de Silva, Communicating chemical congregation: A molecular AND logic gate with three chemical inputs as a ‘Lab-on-a-Molecule’ prototype, J. Am. Chem. Soc. 2006, 128, 4950-4951.

35.   F.M. Raymo, S. Giordani, All-optical processing with molecular switches, Proc. Natl. Acad. USA 2002, 99, 4941-4944.

36.   G. Nishimura, K. Ishizumi, Y. Shiraishi, T. Hirai, A triethylenetetramine with anthracene and benzophenone as a fluorescent molecular logic gate with Either-Or switchable dual logic functions, J. Phys. Chem. B 2006, 110, 21596-21602.

37.   Y. Shiraishi, Y. Tokitoh, T. Hirai, A fluorescent molecular logic gate with multiply-configurable dual outputs, Chem. Commun. 2005, 5316-5318.

38.   R. Baron, A. Onopriyenko, E. Katz, O. Lioubashevski, I. Willner, S. Wang, H. Tian, An electrochemical/photochemical information processing system using a monolayer-functionalized electrode,,Chem. Commun. 2006, 2147-2149.

39.   M. Biancardo, C. Bignozzi, H. Doyle, G. Redmond, A potential and ion switched molecular photonic logic gate, Chem. Commun. 2005, 3918-3920.

40.   J.H. Qian, Y.F. Xu, X.H. Qian, S.Y. Zhang, Molecular logic operations based on surfactant nanoaggregates, ChemPhysChem 2008, 9, 1891-1898.

41.   A.P. de Silva, Molecular computing – a layer of logic, Nature 2008, 454, 417-418.

42.   S. Nitahara, N. Terasaki, T. Akiyama, S. Yamada, Molecular logic device using mixed self-assembled monolayers, Thin Solid Films 2006, 499, 354-358.

43.   T. Gupta, M.E. van der Boom, Redox-active monolayers as a versatile platform for integrating Boolean logic gates, Angew. Chem. Int. Ed. 2008, 47, 5322-5326.

44.   A. Credi, V. Balzani, S.J. Langford, J.F. Stoddart, Logic operations at the molecular level. An XOR gate based on a molecular machine, J. Am. Chem. Soc. 1997, 119, 2679-2681.

45.   A.P. de Silva, H.Q.N. Gunaratne, C.P. McCoy, A molecular photoionic AND gate based on fluorescent signalling, Nature 1993, 364, 42-44; A.P. de Silva, H.Q.N. Gunaratne, C.P. McCoy, Molecular photoionic AND logic gates with bright fluorescence and "Off-On" digital action, J. Am. Chem. Soc. 1997, 119, 7891-7892.

46.   A.P. de Silva, H.Q.N. Gunaratne, G.E.M. Maguire, 'Off-on' fluorescent sensors for physiological levels of magnesium ions based on photoinduced electron transfer (PET), which also behave as photoionic OR logic gates, J. Chem. Soc., Chem. Commun. 1994, 1213-1214.

47.   A.P. de Silva, N.D. McClenaghan, Simultaneously multiply-configurable or superposed molecular logic systems composed of ICT (Internal Charge Transfer) chromophores and fluorophores integrated with one or two ion receptors, Chem. Eur. J. 2002, 8, 4935-4945.

48.   A.P. de Silva, I.M. Dixon, H.Q.N. Gunaratne, T. Gunnlaugsson, P.R.S. Maxwell, T.E. Rice, Integration of logic functions and sequential operation of gates at the molecular-scale, J. Am. Chem. Soc. 1999, 121, 1393-1394.

49.   S.D. Straight, P.A. Liddell, Y. Terazono, T.A. Moore, A.L. Moore, D. Gust, All-photonic molecular XOR and NOR logic gates based on photochemical control of fluorescence in a fulgimide-porphyrin-dithienylethene triad, Adv. Funct. Mater. 2007, 17, 777–785.

50.   Z. Wang, G. Zheng, P. Lu, 9-(Cycloheptatrienylidene)-fluorene derivative: Remarkable ratiometric pH sensor and computing switch with NOR logic gate, Org. Lett. 2005, 7, 3669-3672.

51.   H.T. Baytekin, E.U. Akkaya, A molecular NAND gate based on Watson-Crick base-pairing, Org. Lett. 2000, 2, 1725-1727.

52.   G. Zong, L. Xiana, G. Lua, l-Arginine bearing an anthrylmethyl group: fluorescent molecular NAND logic gate with H+ and ATP as inputs, Tetrahedron Lett. 2007, 48, 3891-3894.

53.   T. Gunnlaugsson, D.A. MacDónaill, D. Parker, Lanthanide macrocyclic quinolyl conjugates as luminescent molecular-level devices, J. Am. Chem. Soc. 2001, 123, 12866-12876; T. Gunnlaugsson, D.A. MacDónaill, D. Parker, Luminescent molecular logic gates: the two-input inhibit (INH) function, Chem. Commun. 2000, 93-94

54.   M. de Sousa, B. de Castro, S. Abad, M.A. Miranda, U. Pischel, A molecular tool kit for the variable design of logic operations (NOR, INH, EnNOR), Chem. Commun. 2006, 2051-2053.

55.   L. Li, M.-X. Yu, F.Y. Li, T. Yi, C.H. Huang, INHIBIT logic gate based on spiropyran sensitized semiconductor electrode, Colloids Surf. A 2007, 304, 49-53.

56.   V. Luxami, S. Kumar, Molecular half-subtractor based on 3,3'-bis(1H-benzimidazolyl-2-yl)[1,1']binaphthalenyl-2,2'-diol, New J. Chem. 2008, 32, 2074-2079.

57.   J.H. Qian, X.H. Qian, Y.F. Xu, S.Y. Zhang, Multiple molecular logic functions and molecular calculations facilitated by surfactants’ versatility, Chem. Commun. 2008, 4141-4143.

58.   E. Pérez-Inestrosa, J.-M. Montenegro, D. Collado, R. Suau, J. Casado, Molecules with multiple light-emissive electronic excited states as a strategy toward molecular reversible logic gates, J. Phys. Chem. C 2007, 111, 6904-6909.

59.   W. Sun, C.H. Xu, Z. Zhu, C.J. Fang, C.H. Yan, Chemical-driven reconfigurable arithmetic functionalities within a fluorescent tetrathiafulvalene derivative, J. Phys. Chem. C 2008, 112, 16973-16983; Z.-X. Li, L.-Y. Liao, W. Sun, C.-H. Xu, C. Zhang, C.-J. Fang, C.-H. Yan, Reconfigurable cascade circuit in a photo- and chemical-switchable fluorescent diarylethene derivative, J. Phys. Chem. C 2008, 112, 5190-5196.

60.   A. Coskun, E. Deniz, E.U. Akkaya, Effective PET and ICT switching of boradiazaindacene emission: A unimolecular, emission-mode, molecular half-subtractor with reconfigurable logic gates, Org. Lett. 2005, 7, 5187-5189.

61.   D. Jimenez, R. Martinez-Manez, F. Sancenon, J.V. Ros-Lis, J. Soto, A. Benito, E. Garcia-Breijo, Multi-channel receptors and their relation to guest chemosensing and reconfigurable molecular logic gates, Eur. J. Inorg. Chem. 2005, 2393-2403.

62.   W. Sun, Y.-R. Zheng, C.-H. Xu, C.-J. Fang, C.-H. Yan, Fluorescence-based reconfigurable and resettable molecular arithmetic mode, J. Phys. Chem. C 2007, 111, 11706-11711.

63.   Y. Zhou, H. Wu, L. Qu, D. Zhang, D. Zhu, A new redox-resettable molecule-based half-adder with tetrathiafulvalene, J. Phys. Chem. B 2006, 110, 15676-15679.

64.   U. Pischel, B. Heller, Molecular logic devices (half-subtractor, comparator, complementary output circuit) by controlling photoinduced charge transfer processes, New J. Chem. 2008, 32, 395-400.

65. J. Andreasson, S.D. Straight, S. Bandyopadhyay, R.H. Mitchell, T.A. Moore, A.L. Moore, D. Gust, A molecule-based 1:2 digital demultiplexer, J. Phys. Chem. C 2007, 111, 14274-14278; M. Amelia, M. Baroncini, A. Credi, A simple unimolecular multiplexer/demultiplexer, Angew. Chem. Int. Ed. 2008, 47, 6240-6243; E. Perez-Inestrosa, J.M. Montenegro, D. Collado, R. Suau, A molecular 1 : 2 demultiplexer, Chem. Commun. 2008, 1085-1087.

66.   J. Andreasson, S.D. Straight, T.A. Moore, A.L. Moore, D. Gust, Molecular all-photonic encoder−decoder, J. Am. Chem. Soc. 2008, 130, 11122-11128.

67.   D. Margulies, C.E. Felder, G. Melman, A. Shanzer, A molecular keypad lock: A photochemical device capable of authorizing password entries, J. Am. Chem. Soc. 2007, 129, 347-354; M. Suresh, A. Ghosh, A. Das, A simple chemosensor for Hg²⁺ and Cu²⁺ that works as a molecular keypad lock, Chem. Commun. 2008, 3906-3908.

68.   R. Baron, A. Onopriyenko, E. Katz, O. Lioubashevski, I. Willner, S. Wang, H. Tian, An electrochemical/photochemical information processing system using a monolayer-functionalized electrode, Chem. Commun. 2006, 2147-2149.

69.   E. Katz, I. Willner, A quinone-functionalized electrode in conjunction with hydrophobic magnetic nanoparticles acts as a “Write–Read–Erase” information storage system, Chem. Commun. 2005, 5641-5643.

70.   E. Katz, I. Willner, A bis-quinone-functionalized gold-electrode subjected to hydrophobic magnetic nanoparticles acts as a three-state "Write-Read-Erase" information storage system, Electrochem. Commun. 2006, 8, 879-882.

71.   F. Galindo, J.C. Lima, S.V. Luis, A.J. Parola, F. Pina, Write-Read-Erase molecular-switching system trapped in a polymer hydrogel matrix, Adv. Funct. Mater. 2005, 15, 541-545.

72.   A. Bandyopadhyay, A.J. Pal, Memory-switching phenomenon in acceptor-rich organic molecules: Impedance spectroscopic studies, J. Phys. Chem. B 2005, 109, 6084-6088.

73.   F. Pina, J.C. Lima, A.J. Parola, C.A.M. Afonso, Thermal and photochemical properties of 4',7-dihydroxyflavylium in water-ionic liquid biphasic systems: A Write-Read-Erase molecular switch, Angew. Chem. Int. Ed. 2004, 43, 1525-1527.

74.   G. Will, J.S.S.N. Rao, D. Fitzmaurice, Heterosupramolecular optical write–read–erase device, J. Mater. Chem. 1999, 9, 2297-2299.

75.   J. Hiller, M.F. Rubner, Reversible molecular memory and pH-switchable swelling transitions in polyelectrolyte multilayers, Macromolecules 2003, 36, 4078-4083.

76.   F. Pina, A. Roque, M.J. Melo, I. Maestri, L. Belladelli, V. Balzani, Multistate/multifunctional molecular-level systems: light and pH switching between the various forms of a synthetic flavylium salt, Chem. Eur. J. 1998, 4, 1184-1191.

77.   U. Pischel, Chemical approaches to molecular logic elements for addition and subtraction, Angew. Chem. Int. Ed. 2007, 46, 4026-4040.

78.   G.J. Brown, A.P. de Silva, S. Pagliari, Molecules that add up, Chem. Commun. 2002, 2461-2463.

79.   D.-H. Qu, Q.-C. Wang, H. Tian, A half adder based on a photochemically driven [2]rotaxane, Angew. Chem. Int. Ed. 2005, 44, 5296-5299.

80.   J. Andréasson, S.D. Straight, G. Kodis, C.-D. Park, M. Hambourger, M. Gervaldo, B. Albinsson, T. A. Moore, A.L. Moore, D. Gust, All-photonic molecular half-adder, J. Am. Chem. Soc. 2006, 128, 16259-16265; J. Andréasson, G. Kodis, Y. Terazono, P.A. Liddell, S. Bandyopadhyay, R.H. Mitchell, T.A. Moore, A.L. Moore, D. Gust, Molecule-based photonically switched half-adder, J. Am. Chem. Soc. 2004, 126, 15926-15927.

81.   M.V. Lopez, M.E. Vazquez, C. Gomez-Reino, R. Pedrido, M.R. Bermejo, A metallo-supramolecular approach to a half-subtractor, New J. Chem. 2008, 32, 1473-1477.

82.   D. Margulies, C.E. Felder, G. Melman, A. Shanzer, A molecular keypad lock: A photochemical device capable of authorizing password entries, J. Am. Chem. Soc. 2006, 128, 4865-4871.

83.   O. Kuznetz, H. Salman, N. Shakkour, Y. Eichen, S. Speiser, A novel all optical molecular scale full adder, Chem. Phys. Lett. 2008, 451, 63-67.

84.   Y. Liu, W. Jiang, H.-Y. Zhang, C.-J. Li, A multifunctional arithmetical processor model integrated inside a single molecule, J. Phys. Chem. B 2006, 110, 14231-14235.

85.   X. Guo, D. Zhang, G. Zhang, D. Zhu, Monomolecular logic: “Half-Adder” based on multistate/multifunctional photochromic spiropyrans, J. Phys. Chem. B 2004, 108, 11942-11945.

86.   F. Pina, M.J. Melo, M. Maestri, P. Passaniti, V. Balzani, Artificial chemical systems capable of mimicking some elementary properties of neurons, J. Am. Chem. Soc. 2000, 122, 4496-4498.

87.   R. Stadler, S. Ami, C. Joachim, M. Forshaw, Integrating logic functions inside a single molecule, Nanotechnology 2004, 15, S115-S121; F.M. Raymo, S. Giordani, Signal processing at the molecular level, J. Am. Chem. Soc. 2001, 123, 4651-4652.

88.   A.P. De Silva, Y. Leydet, C. Lincheneau, N.D. McClenaghan, Chemical approaches to nanometer-scale logic gates, J. Phys. Cond. Matter 2006, 18, S1847-S1872.

89.   A. Adamatzky, Computing with waves in chemical media: Massively parallel reaction-diffusion processors, IEICE Trans. Electronics 2004, E87C, 1748-1756.

90.   A.H. Flood, R.J.A. Ramirez, W.Q. Deng, R.P. Muller, W.A. Goddard, J.F. Stoddart, Meccano on the nanoscale - A blueprint for making some of the world’s tiniest machines, Austr. J. Chem. 2004, 57, 301-322.

91.   J. Xu, G.J. Tan, A review on DNA computing models, J. Comput. Theor. Nanosci. 2007, 4, 1219-1230.

92.   M. Kahan, B. Gil, R. Adar, E. Shapiro, Towards molecular computers that operate in a biological environment, Physica D 2008, 237, 1165-1172.

93.   X.-G. Shao, H.-Y. Jiang, W.-S. Cai, Advances in biomolecular computing, Prog. Chem. 2002, 14, 37-46.

94.   D. Melnikov, G. Strack, M. Pita, V. Privman, E. Katz, Analog noise reduction in enzymatic logic gates, J. Phys. Chem. B 2009, 113, 10472-10479.

95.   L. Fedichkin, E. Katz, V. Privman, Error correction and digitalization concepts in biochemical computing, J. Comput. Theor. Nanosci 2008, 5, 36-43.