Ribozymes performing logical operations and simple computations
Dr. Darko Stefanovic accepted the invitation on 12 September 2009 (self-imposed deadline: 12 March 2010).
Editing test.
assigned topic: Ribozymes performing logical operations and simple computations
It may be better to rename the article to Deoxyribozymes performing logical operations and simple computations.
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Several systems of ribozymes performing logical operations and simple computations have been reported starting in the early 2000's. Ribozymes are nucleic acid (link?) enzymes. This article focuses (for now?) on deoxyribozymes, enzymes made of DNA. The catalytic activity effected by deoxyribozymes that is used for computational purposes is the cleavage of other nucleic acid strands. Deoxyribozyme molecules can be structurally modified through the addition of binding sites that specifically bind to yet other nucleic acid strands. These modifications are designed such that the presence of the ligand nucleic acid strand strongly promotes, or strongly inhibits, the catalytic activity of the deoxyribozyme. In this fashion, logical operations and simple computations are carried out over signals represented as concentrations of oligonucleotides (link?), short single-stranded DNA molecules.
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Section a
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DNA enzymes
The switch part of a deoxyribizyme logic gate is derived from a deoxyribozyme, a nucleic acid enzyme that catalyzes DNA reactions. In this case the enzyme is a phosphodiesterase, which cleaves an oligonucleotide substrate into two shorter oligonucleotide products, or outputs.
FIGURE GOES HERE: GIF
DNA outputs and fluorescence monitoring
In order to monitor output formation, the outputs can be labeled with fluorescent dyes. In the case above, the Substrate is labeled with “red” channel TAMRA (T) dye, but its fluorescence is quenched by the Black-Hole 2 (BH2) quencher, which absorbs all of the TAMRA fluorescence. After cleavage, the TAMRA is separated from the BH2 and the fluorescence is no longer absorbed, leading to an increase in fluorescence within the mixture, which can be monitored via fluorescence spectroscopy.
FIGURE GOES HERE: GIF LogicGateOutput2.GIF
The fluorescence is merely a byproduct of the reaction for monitoring purposes. Output formation can be coupled to many different downstream events, such as the activation of downstream gates to create cascades or branched circuits, or the release of a small molecule such as a drug.
DNA inputs and stem-loop controllers
The DNA enzyme is turned into a switch that is regulated by input DNA through the addition of specific stem-loop regions, which contain oligonucleotide binding regions. If input DNA (an oligonucleotide) is added, it will hybridize to the oligonucleotide binding region, causing the stem-loop to undergo a conformational change and break apart.
FIGURE GOES HERE: GIF LogicGateInput2.GIF
DNA inputs are highly selective, and (to a first approximation) will only hybridize to their specific complementary sequence. Thus it is possible to have many inputs and stem-loop regions in the same mixture without undesirable gate activation from input cross-reactivity. The use of stem-loop controlling structures also makes the gates fully modular, such that many oligonucleotide sequences can be placed for input binding in the loop regions.
Types of Logic gates== ===YES gate=
The simplest deoxyribozyme logic gates is a repeater, the YES gate. In this gate, the DNA enzyme has been modified to include a stem-loop region that regulates the binding of substrate to the enzyme. If the stem-loop is closed, the substrate cannot bind, the enzyme is inactivated, and no outputs are formed. However, when input DNA is added, it hybridizes to the stem-loop region and alters the conformation of the gate molecule. The conformational change causes the enzyme to become active, allowing cleavage of the substrate to produce the output DNA. That is, a YESx gate is active in the presence of a single input ix (wiki formatting?) (see diagram below).
FIGURE GOES HERE: GIF LogicGateYES2.GIF
NOT gate
Another type of molecular logic gate is the NOT gate. In this case, the catalytic core of the enzyme has been modified to include a stem-loop region that regulates enzyme activity. If the stem-loop is closed, the enzyme is active. However, when an input DNA is added, it hybridizes to the stem-loop region and alters the conformation of the gate molecule. The conformational change causes the enzyme to become inactive, preventing cleavage of the substrate to produce output DNA. Thus, a NOTz gate is active unless a single input iz (wiki formatting?) is added, which inactivates the gate (see diagram below).
FIGURE GOES HERE: GIF LogicGateNOT2.GIF
AND gate
By using combinations of the modular structures described above forYES and NOT loop structures, further Boolean logic gate structures can be made. The AND gate is made by combining two activating stem-loop structures:
FIGURE GOES HERE: GIF LogicGateAND2.GIF
ANDANDNOT gates
The ANDANDNOT gate is created by combining twoactivating stem-loop structures and one inhibitory stem-loop structure. For input signals x, y, and z, it computes x AND y AND NOT z. (wiki formatting?).
FIGURE GOES HERE: GIF LogicGateANDANDNOT2.GIF
Significance of Logic gates
In deoxyribozyme logic gates the inputs and outputs are of the same kind (namely oligonucleotides). This allows the cascading of gates without any external interfaces. The inputs are compatible with sensor molecules (aptamers) that could detect cellular disease markers, and the outputs can be tied to the release of small molecules, such as drugs. Thus it may eventually be possible to make therapeutic decisions cell-by-cell according to a complex decision function based on many attributes of the cell. This is sometimes referred to as "intelligent drug delivery".
Simple computations
Arithmetic primitives
Half-adder
A molecular half-adder has been constructed that is able to calculate a sum and carry digit by adding two DNA "bits" of information, using three molecular logic gates and a two-color fluorogenic output system in a single tube.
FIGURE HERE HalfAdder_toc GIF
Full Adder
A molecular full-adder has been constructed that is able to calculate a sum and carry digit by adding three DNA "bits" of information, using 7 logic gates and a two-color fluorogenic output system in a single tube.
FIGURE HERE fulladder_toc GIF
Automata for games of strategy
Automata are self-operating machines, or robots, that are able to analyze a series of stimuli and respond to them. Deoxyribozyme logic gates have been used to build automata based on a logical abstraction to play simple games of strategy.
MAYA-I
MAYA-I was an automaton that plays a symmetry-pruned restricted game of tic-tac-toe (noughts and crosses). The automaton always goes first in the middle well of a nine-well (3 by 3) game board representation, and the human player can respond by moving in only two wells.
FIGURE HERE MAYAI_toc
MAYA-II
MAYA-II plays a non-symmetry-pruned complete game of tic-tac-toe. The automaton still always goes first in the middle well, but its human opponent may move in any remaining square. The automaton displays both human and automaton moves using a two-color fluorogenic output system.
FIGURE HERE MAYA-II_toc
Automata for learning
MAYA-III
MAYA-III goes beyond playing a fixed game strategy. It is a generic device that can be trained by example to play one of a large set of possible strategies for any possible position game on a two-by-two board.
FIGURE HERE
Subsection b
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Subsection c
Refer to figures and equations as Figure 1 and Eq. (1).
Section d
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Subsection e
Subsection f
Citing references
Groups of authors larger than 2 can be cited with "et al.".
- As proven in (Albero A, 1999).
- As Albero (2009) said.
- As proven in (Albero and Bocca, 2001)
- As proven by Albero and Bocca (2001)
- As proven by Albero et al. (2003)
- As proven by Albero, Bocca and Cuoco (2003)
- As proven by Albero et al. (2007a), confirmed by Albero et al. (2007b) and discarded by Albero et al. (2007c)
- As proven in (Albero A, 1999).
- As proven by Albero and Bocca (2001).
References
- Albero, Antony (1999). Pizza Margherita. Journal of pizza eaters 19(3): 13. arXiv:0808.000
- Albero, Antonio and Bocca, Bill (2001). Pizza Capricciosa. Journal of pizza eaters 27: 121-127. arXiv:0808.000
- Albero, Antonio; Bocca, Bill and Cuoco, C T (2003). Pizza Quattro Stagioni. Journal of pizza eaters 34(4): 12.
- Albero, Antonio; Bocca, Bill; Cuoco, C T and Dude, David B (2007a). Pizza Napoletana. Journal of pizza eaters 37: 121-127.
- Albero, Antonio; Bocca, Bill; Cuoco, C T; Dude, David and Elica, E Q (2007b). Pizza Marinara. Journal of pizza eaters 43(4): 1-13.
- Albero, Antonio et al. (2008). Pizza Piccante. Journal of pizza eaters 45(5): 1-13.
- Alto, Antony (1999). La Pizza! Mangiare bene, Volume 3. Albero and Bacca editors. Food Publishers, Genoa.
- Alto, Antony and Bocca, Bill (2000). La Pasta! Mangiare bene. Albero editor. Food Publishers, Genoa. Chapter 1.
- Alto, Antony; Bocca, Bill and Cuoco, C T (2002). Pizza: prepare it yourself. Food Publishers, Genoa. Page 22. ISBN 1-234-99929-0.
- Alto, Antony; Bocca, Bill; Cuoco, C T and Dude, David B (2005a). Italian Pizza. Food Publishers, Genoa.
- Alto, Antony; Bocca, Bill; Cuoco, C T; Dude, David B and Elica, E Q (2005b). Napolitan Pizza. Food Publishers, Genoa.
- Alto, Antony et al. (2005c). American Pizza. Food Publishers, Genoa.
Further reading
- Magro, C T (2008). Pizza: a danger for health? Food Publishers, Paris. page 22. ISBN 1-234-90929-0. This reference is unreliable in conclusions, but quite accurate in its introduction.
- Izhikevich, E M (2007). Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting The MIT Press, Cambridge, MA. ISBN 0262090430. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience.
