2. 1Introduction 2Theoretical background Biochemistry/molecular biology 3Theoretical background computer science 4History of the field 5Splicing systems 6P systems 7Hairpins 8Detection techniques 9Micro technology introduction 10Microchips and fluidics 11Self assembly 12Regulatory networks 13Molecular motors 14DNA nanowires 15Protein computers 16DNA computing - summery 17Presentation of essay and discussion Course outline

3. Membrane transport

4. www.cellsalive.com/ Cell membranes

6. At very high magnification & in color Cell membranes

7. http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/C/CellMembranes.html Membrane structure

8. Every cell is encircled by a membrane and most cells contain an extensive intracellular membrane system. Membranes fence off the cell's interior from its surroundings. Membranes let in water, certain ions and substrates and they excrete waste substances. They act to protect the cell. Without a membrane the cell contents would diffuse into the surroundings, information containing molecules would be lost and many metabolic pathways would cease to work. The cell would die! Cell membranes

9.  Surround all cells  Fluid-like composition, like soap bubbles  Composed of:  Lipids in a bilayer  Proteins embedded in lipid layer (called trans-membrane proteins)  And, Proteins floating within the lipid sea (called integral proteins)  And Proteins associated outside the lipid bi-layer (peripheral). Cell membranes

10.  Transporters are of two general classes:  carriers and channels.  These are exemplified by two ionophores (ion carriers produced by microorganisms):  valinomycin (a carrier)  gramicidin (a channel). Membrane transport

11. Valinomycin is a carrier for K +. It is a circular molecule, made up of 3 repeats of the sequence shown above. Valinomycin NCHCO H C CH CH 3 H 3 C O CN CH CH 3 H 3 C O H C CH CH 3 H 3 C COCH CH 3 C O H O H 3 L -valine D -hydroxy- D -valine L -lactic isovaleric acid acid

12. Valinomycin is highly selective for K + relative to Na +. The smaller Na + ion cannot simultaneously interact with all 6 oxygen atoms within valinomycin. Thus it is energetically less favorable for Na + to shed its water of hydration to form a complex with this ionophore. Valinomycin reversibly binds a single K + ion. The ring closely surrounds the K + ion, which interacts with 6 oxygen atoms of valinomycin. Valinomycin O OO OO Hydrophobic O K +

13. Whereas the interior of the valinomycin-K + complex is polar, the surface of the complex is hydrophobic. Valinomycin enters the lipid core of the bilayer and solubilizes K + within this hydrophobic milieu. Valinomycin O OO OO Hydrophobic O K + Crystal structureCrystal structure (at Virtual Museum of Minerals & Molecules).

14. Valinomycin is a passive carrier for K +. It can bind or release K + when it encounters the membrane surface. Valinomycin can catalyze net K + transport because it can translocated either in the complexed or uncomplexed state. The direction of net flux depends on the electrochemical K + gradient. Valinomycin Val -K + -K + K + membrane K +

15.  Proteins that act as carriers are too large to move across the membrane.  They are transmembrane proteins, with fixed topology.  Example: GLUT1 glucose carrier, found in plasma membranes of various cells, including erythrocytes.  GLUT1 is a large integral protein, predicted via hydropathy plots to include 12 transmembrane α- helices. Proteins as carrier

16. Carrier proteins cycle between conformations in which a solute binding site is accessible on one side of the membrane or the other. There may be an intermediate conformation in which a bound substrate is inaccessible to either aqueous phase. With carrier proteins, there is never an open channel all the way through the membrane. Proteins as carrier conformation change conformation change Carriermediated solute transport

17. Carriers exhibit Michaelis-Menten kinetics. The transport rate mediated by carriers is faster than in the absence of a catalyst, but slower than with channels. A carrier transports only one or few solute molecules per conformational cycle. Kinetics of transport carriers

18. Uniport (facilitated diffusion) carriers mediate transport of a single solute. Examples include GLUT1 and valinomycin. These carriers can undergo the conformational change associated with solute transfer either empty or with bound substrate. Thus they can mediate net solute transport. Classes of carrier proteins Uniport SymportAntiport AA B A B

19. Symport (cotransport) carriers bind 2 dissimilar solutes (substrates) & transport them together across a membrane. Transport of the 2 solutes is obligatorily coupled. A gradient of one substrate, usually an ion, may drive uphill (against the gradient) transport of a co-substrate. An example is the plasma membrane glucose-Na + symport. Classes of carrier proteins Uniport SymportAntiport AA B A B

20. Usually antiporters exhibit "ping pong" kinetics. One substrate is transported across a membrane and then another is carried back. Example: ADP/ATP exchanger (adenine nucleotide translocase) which catalyzes 1:1 exchange of ADP for ATP across the inner mitochondrial membrane. Antiport (exchange diffusion) carriers exchange one solute for another across a membrane. Classes of carrier proteins Uniport SymportAntiport AA B A B

21. Active transport enzymes couple net solute movement across a membrane to ATP hydrolysis. An active transport pump may be a uniporter, or it may be an antiporter that catalyzes ATP-dependent transport of 2 solutes in opposite directions. ATP-dependent ion pumps are grouped into classes, based on transport mechanism, genetic & structural homology. Active transport S 1 S 2 ATP ADP+ Pi Side 1 Side 2 Active Transport

22. P-class ion pumps are a gene family exhibiting sequence homology. They include:  Na +,K + -ATPase, in plasma membranes of most animal cells, is an antiport pump. It catalyzes ATP-dependent transport of Na + out of a cell in exchange for K + entering.  (H +, K + )-ATPase, involved in acid secretion in the stomach, is an antiport pump. It catalyzes transport of H + out of the gastric parietal cell (toward the stomach lumen) in exchange for K + entering the cell. Ion pumps

23. P-class pumps (cont):  Ca ++ -ATPases, in endoplasmic reticulum (ER) & plasma membranes catalyze transport of Ca ++ away from the cytosol, either into the ER lumen or out of the cell. There is some evidence that H + may be transported in the opposite direction. Ca ++ -ATPase pumps keep cytosolic Ca ++ low, allowing Ca ++ to serve as a signal. Ion pumps

24. The reaction mechanism for a P-class ion pump involves transient co- valent modification of the enzyme. At one stage of the reaction cycle, P i is transferred from ATP to the carboxyl of a Glu or Asp residue, forming a “high energy” anhydride linkage (~P). At a later stage in the reaction cycle, the phosphate is released by hydrolysis. Ion pumps P-Class Pumps ATP C O OPO- O- O C O OH ADP Enzyme- Enzyme- P i H 2 O

25. In this diagram of the SERCA reaction cycle, conformational changes altering accessibility of Ca ++ - binding sites to the cytosol or ER lumen are depicted as positional changes. Keep in mind that SERCA is a large protein that maintains its transmembrane orientation. The ER Ca ++ pump is called SERCA: Sarco(Endo)plasmic Reticulum Ca ++ -ATPase. Ca ++ pump E E-Ca ++ 2 2Ca ++ ER cytosol membrane lumen 2Ca ++ E ~ P-Ca ++ 2 E ~ P-Ca ++ 2 ADP P i ATP

26. Reaction cycle 12 Ca ++ bind tightly from the cytosolic side, stabilizing the conformation that allows ATP to react with an active site aspartate residue. 2Phosphorylation of the active site aspartate induces a conformational change that shifts accessibility of the 2 Ca ++ binding sites from one side of the membrane to the other, & lowers the affinity of the binding sites for Ca ++. Ca ++ pump E E-Ca ++ 2 2Ca ++ ER cytosol membrane lumen 2Ca ++ E ~ P-Ca ++ 2 E ~ P-Ca ++ 2 ADP P i ATP

27. 3Ca ++ dissociates into the ER lumen. 4Ca ++ dissociation promotes hydrolysis of P i from the enzyme Asp and the conformational change (recovery) that causes the Ca ++ binding sites to be accessible again from the cytosol. Ca ++ pump E E-Ca ++ 2 2Ca ++ ER cytosol membrane lumen 2Ca ++ E ~ P-Ca ++ 2 E ~ P-Ca ++ 2 ADP P i ATP

28. 2 Ca ++ Asp351 Muscle SERCA PDB 1EUL membrane domain cytosolic domain The structure of muscle SERCA, determined by X- ray crystallography, shows 2Ca ++ ions bound between transmembrane α-helices. These intramembrane Ca ++ binding sites are presumed to participate in Ca ++ transfer across the membrane. SERCA structure

29. 2 Ca ++ Asp351 Muscle SERCA PDB 1EUL membrane domain cytosolic domain The active site Asp351, which is transiently phosphorylated during catalysis, is in a cytosolic domain, far from the Ca ++ binding sites. The sequence adjacent to Asp351 (DKTGTLT) is in all P-class pumps. Ca ++ has been found to induce large structural changes in cytosolic and transmembrane domains of SERCA, consistent with the proposed conformational coupling between active site and membrane domains. SERCA structure

30. Observed changes in rotation and tilt of transmembrane α- helices may be involved in altering access of Ca ++ binding sites to one side of the membrane or the other, and altering the affinity of binding sites for Ca ++, at different stages of the SERCA reaction cycle. Only 2 transmembrane α-helices are represented above. AnimationAnimation of mechanism by MacLennan lab. Ca ++ transport Ca ++ enzyme phosphorylation phosphate hydrolysis SERCA Conformational Cycle

31. This transport across a cell layer depends on localization of specific plasma membrane transporters at either the apical end of each epithelial cell (facing the intestinal lumen) or the basal end (facing a blood capillary). In the example shown, 3 carrier proteins accomplish absorption of glucose & Na + in the small intestine. Trans-epithelial transport glucose Na + ATP ADP + P i K+K+ GLUT2 Na + pump glucose-Na + symport intestinal epithelial cell apical end basal end

32.  The Na + gradient drives uphill transport of glucose into the cell at the apical end, via glucose-Na + symport. [Glucose] within the cell is thus higher than outside.  Glucose flows passively out of the cell at the basal end, down its gradient, via GLUT2 (uniport related to GLUT1).  The Na + pump, at the basal end of the cell, keeps [Na + ] lower in the cell than in fluid bathing the apical surface. Trans-epithelial transport glucose Na + ATP ADP + P i K+K+ GLUT2 Na + pump glucose-Na + symport intestinal epithelial cell apical end basal end

33. Channels cycle between open & closed conformations. When open, a channel provides a continuous pathway through the bilayer. Whereas carriers transport only one or a few ions or molecules per conformational cycle, many ions flow through a channel, each time it opens. Transport rates are higher for channels than for carriers. Ion channels closed conformation change open

34. Gating (opening & closing) of a gramicidin channel is thought to involve reversible dimerization. An open channel forms when two gramicidin molecules join end to end to span the membrane. This model is consistent with the finding that at high [gramicidin] overall transport rate depends on [gramicidin] 2. Gating open closed Proposed mechanism of gramicidin gating

35. Membrane computing

36. Since the origins, Computer Scientist have looked to relationships among machines and living organisms  McCulloch and Pitts, Neural Networks, 1943  Von Neumann, Cellular Automata, 1966  Lindenmayer, L systems, 1968  Holland, Genetic Programming, 1975 A look at history

37. L-systems are a mathematical formalism proposed by the biologist Aristid Lindenmayer in 1968 as a foundation for an axiomatic theory of biological development. More recently, L-systems have found several applications in computer graphics. Two principal areas include generation of fractals and realistic modeling of plants L-systems

38. “....Theoretical arguments suggest that more efficient and adaptable modes of computing are possible, while emerging biotechnologies point out to possibilities for implementation. Their common ground is molecular computing... It is likely that molecular computing will prove more valuable outside the context of conventional Von Neumann computers. Critically important computing needs such as adaptive patterns and process control may be refractory to simple decreases in size and increases in speed. Instead of suppressing the unique properties of carbon polymers, we should consider how to harness them to fill these needs....” Michael Conrad, On Design Principles for a Molecular Computer, 1985 Molecular computing

39. ....Inheritance is a discourse, a set of instructions passed from generation to generation. It has a vocabulary - the genes themselves- a grammar, the way in which the information is arranged, and a literature, the thousands of instructions needed to make a human being...” Steve Jones, The Language of The Genes, 1993 Another quote

40.  DNA may be viewed as a double sequence of four symbols: A, T, C, G  DNA is naturally processed by duplication, recombination, etc.  Biologist and Genetists have developed so far a variety of techniques to manipulate DNA sequences (Biotechnologies)  Information stored in DNA sequences is translated into proteins by DNA Transcription  Proteins control and regulate the activity of the genes (Gene Expression) How cells process information

41.  Gh. Păun, Computing with Membranes, 1998  Membrane Computing looks at the whole cell structure and functioning as a computing device  Membranes play a fundamental role in the cell as filters and separators  Modeling the living cell is beyond the purpose of Membrane Computing Membrane computing

42. references

43.  Păun, Gh., Membrane Computing. An Introduction, Springer-Verlag, Berlin, 2002.  Păun, Gh., Rozenberg, G., Salomaa, A., Zandron, C. (eds.), Membrane Computing, LNCS, 2597, Springer-Verlag, 2003.  Cavaliere, M., Martin-Vide, C., Paun, Gh. (eds.), Brainstorming Week on Membrane Computing, Technical Report of the Research Group on Mathematical Linguistics, N. 26/03, Universitat Rovira I Virgili, Tarragona, Spain, 2003.  The P systems Web Pages, http://psystems.disco.unimib.it  Alberts, B., et al., Molecular Biology of the Cell, Garland Science, New York, 2002. references

44.  A membrane structure formed by several membranes embedded in a unique main membrane  Multi-sets of objects placed inside the regions delimited by the membranes (one per each region)  The objects are represented as symbols of a given alphabet (each symbol denotes a different object)  Sets of evolution rules associated with the regions (one per each region), which allow the system  to produce new objects starting form the existing ones  to move objects from one region to another A membrane system (or P-system)

46.  Each region contains a multi-set of objects and a set of rules. The objects are represented by symbols from a given alphabet. Typically, a evolution rule from region r is of the form ca→cb in d out d here and it says that a copy of object a in the presence of a copy of the catalyst c is replaced by a copy of the object b and 2 copies of the object d.  b has to immediately enter the inner membrane of region r labeled j, a copy of d is sent out through the membrane of region r and a copy of d remains in r.

47.  We start with an initial configuration: an initial membrane structure and some initial multi-sets of objects placed inside the regions of the system.  We apply the rules in a non-deterministic maximal parallel manner: in each step, in each region, each object that can be evolved according to some rule must do it  A computation is said successful if it halts, that is, it reaches a configuration where no rules can be applied.  The result of a successful computation may be the multi- sets formed either by the objects contained in a specific output membrane or by the objects sent out of the systems during the computation  A non-halting computation yields no result A computation in a P-system

48. An example

50. R 1 : aa → (a,here)(a,in),ab → (b,here)(a,in) R 2 : a → (a,out)(b,out)(b,in),a → (c,in) R 3 : b → (a,here)(a,out)(b,in),cb → (a,here) R 4 : Ø An other example

51.  Membrane dissolution: a special operator which can be used for dissolving a membrane Example: r: abb → (a,here)(b,in)(a,out)δ if the rule r is used inside a membrane, such a membrane is dissolved after the application of the rule r  Membrane thickness: two operators δ, τ for varying the permeability of the membranes  Priority: a partial order among the rules, which define a priority relationship In each step, if a rule with high priority is applied then no rule with a lower priority can be applied in the same step More ingredients

52.  Cooperation restricted to some special objects called catalysts ca → cv with v = (a 1,t 1 )(a 2,t 2 ) … (a n,t n ), t j ε {in,here, out} A catalyst cannot be modified by any rule and cannot be moved from one region to another  Bi-stable catalysts: catalysts with two states ca → cv Using catalysts

53. P-systems with catalysts are computationally universal Main result

54. Using catalysts and bi-stable catalysts Bi-stable catalysts

55.  P-systems are bio-inspired distributed and parallel computing devices  They operates on multi-sets of objects  The objects are located inside specific regions delimited by the Membranes  The objects evolve according to local rules associated with the Regions  The rules can modify the objects or move them through the membranes Summary 1

56.  The objects are strings over a given alphabet  The regions have associated languages instead of multi- sets of objects. The rules encode string-operations  rewriting: X → (y, tar), with tar ε {here, in, out}  replicated rewriting: X → (y 1, tar 1 )||…||(y n, tar n ), with tar 1,…, tar n ε {here, in, out}  splicing ...  More ingredients: membrane dissolution, membrane thickness, priority, distributing the rules according to an underlying state machine (Eilenberg P-sytems) P-systems with string objects

57.  Communication of objects through membranes is one of the most important ingredients of every P-system  Purely communicative systems: the objects are not changed during a computation, but they just change their place inside the system  The systems is embedded in an infinite environment, which contains an arbitrary number of copies of each object  The environment provides the objects the system needs to perform its internal computations Communicative P-systems

58. Computing by communication

59. Membrane transport of small molecules

60. (Păun, A., Păun, Gh.)  Rules encode symport/antiport mechanism and they are associated with the membranes  Generalization: (x,in), (x,out), (x,in; y,out), for x, y multi-sets of arbitrary size P-systems with symport/antiport

61. P-systems with symport/antiport are computationally universal (Păun, A., Frisco, P., Păun, Gh., 2003) (1,2) + 1Mem = T.M. (2,0) + 4Mem = T.M. (3,0) + 2Mem = T.M. (3,0) + 1Mem = T.M. (n,m) denotes the size of the rules: for each (x,in), (x,out), |x| ≤ n, and for each (x,in; y,out), max{|x|,|y|} ≤ m The power of communication

62. P-systems with boundary rules  Communication rules: xx’ [ i y’y → xy’ [ i x’y  Evolution rules: [ i y → [ i y’ Evolution- Communication P-systems  Communication rules: (x,in), (y,out), (x,in; y,out)  Evolution rules: y → y’ where x, x’, y, y’ represent multi-sets of arbitrary size EC P-systems

63. EC P systems are computationally universal The power of EC P-systems

64. The environment is reduced to some specific input objects If the system halts in a final configuration, we say the system recognizes such an input P-automata

65.  A model of communication inspired by a membrane transport mechanism for small molecules called symport/antiport  Purely communicative P-systems based on symport/antiport are computationally universal (if provided with an infinite environment)  EC P-systems, a model that combines communication controlled by symport/antiport and evolution rules for modifying the content of the Membranes  P-automata, Communicating P-systems as recognizing devices Summary 2

66.  Rules are able to perform operation for modifying the membrane structure:  membrane creation: [ i a ] i → [ j b ] j  membrane division: [ i a ] i → [ k b ] k [ j c ] j  membrane duplication: [ i a ] i → [ k b [ j c ] j ] k  membrane dissolution: [ i a ] i → a where a, b are objects and i, j, k are labels of possible membranes  Communication and Evolution rules assume the form [ i a → v ] i, [ i a ] i → [ i b ] i, [ i a ] i → [ i b ] i where a, b are objects and i, j, k are labels of possible membranes P-systems with active membranes

67.  The Hamiltonian Path Problem (HPP) can be solved in quadratic time and the SAT problem can be solved in linear time by P-systems with active membranes, by using membrane division and dissolution  HPP can be solved in linear time by using membrane creation The idea is of generating in an efficient manner all paths from a specified initial node, then checking whether or not this at least one of these paths is Hamiltonian. Trading time for space

68. Manipulating membrane structures to generate some kind of structured information  Generating in parallel all the sentential forms of a given grammar  Generating representation for strings in a language  Generating picture languages Alternative approach

69. G = {S → AC, S → AB, C → SB, A → a, B → b} with L(G) = {a n b n } All the strings of length n are produced exactly in 2n-1 steps. Such strings are present in the membrane structure at depth 2n-1 Generating the sentential forms

70. G = {S → AC, S → AB, C → SB, A → a, B → b} It is possible to provide characterizations of recursively enumerable languages Representing strings in a language

71. A picture is represented by means of a network of membranes Generating picture languages

72. Whatever you want  Energy-Controlled P-systems  P-systems with promoters/inhibitors  P-systems with carriers  P-systems with gemmation of mobile membranes  Tissue P-systems  Probabilistic P-systems  P-systems with elementary graph productions  Parallel Rewriting P-systems ... What else

73.  Membrane Computing provides computational models that abstract from the living cells structure and functioning  Such models have been proved to be computationally powerful (equiv. to T.M.) and efficient (solving NP-Complete problems)  Membrane Computing defines an abstract framework for reasoning about  distribute architectures  communication  parallel information processing  Such features are relevant both for Computer Science (Distributed Computing Models, Multi-Agent Systems) and Biology (Modeling and Simulation of Biological Systems) Conclusion

74.  Membranes systems have been developed so far as a purely generative devices in the context of Formal Languages Theory  They lack a well-defined semantics for reasoning about real systems  Non-Determinism and Maximal Parallelism are not always desirable features Conclusion

76. 1Introduction 2Theoretical background Biochemistry/molecular biology 3Theoretical background computer science 4History of the field 5Splicing systems 6P systems 7Hairpins 8Detection techniques 9Micro technology introduction 10Microchips and fluidics 11Self assembly 12Regulatory networks 13Molecular motors 14DNA nanowires 15Protein computers 16DNA computing - summery 17Presentation of essay and discussion Course outline

77. Hairpins

79.  DNA strands with self-complementary base sequences have the potential to form hairpin structures. Formed only with a single DNA (or RNA) strand.  Hairpin is a common secondary/tertiary structure in RNA. It requires complementarity between part of the strand. Hairpins

80.  G-C and A-U form hydrogen bonded base pairs and are said to be complementary.  Base pairs are approximately coplanar and are almost always stacked onto other base pairs in an RNA structure. Contiguous base pairs are called stems.  Unlike DNA, RNA is typically produced as a single stranded molecule which then folds intra- molecularly to form a number of short base-paired stems. This base-paired structure is called RNA secondary structure. RNA secondary structures

81. Hairpins

83.  Single stranded subsequences bounded by base pairs are called loops. A loop at the end of a stem is called a hairpin loop. Simple substructures consisting of a simple stem and loop are called stem loops or hairpins.  Single stranded bases within a stem are called a bulge or bulge loop if the single stranded bases are on only one side of the stem.  If single stranded bases interrupt both sides of a stem, they are called an internal (interior) loop.  There are multi-branched loops from which three or more stems radiate. RNA secondary structures

85.  Sequences variations in RNA sequences maintain base pairing patterns that give rise to double-stranded regions (secondary structures) in molecules.  Alignments of RNA sequences will show covariation at interacting base-pair positions, see figure below. RNA secondary structures

86.  In addition to secondary structural interactions in RNA, there are also tertiary interactions, illustrated in figure below. These include A pseudoknots, B kissing hairpins and C hairpin-bulge contact.  These complicated structures are usually not predictable by secondary structure prediction tools. RNA secondary structures

87.  The bending in Hairpin loops facilitates the binding of some proteins to the DNA  Short base sequences (example UUCG) which are found at the end of RNA hairpins facilitates the folding of RNA into its precise three dimensional structure Hairpins

88. Secondary Structure Of large ribosomal RNA tRNA structure

89. Another direction in sequence design is designing a sequence that folds into a given secondary structure. This problem is called inverse folding, because it is the inverse of the problem of finding the secondary structure of a sequence with the minimum free energy. The inverse folding problem is to find a sequence whose minimum energy structure coincides with the given one Inverse folding

90. 5’5’ 3’3’ TTC…GCA 3’3’ 5’5’ folding inverse folding Inverse folding

91. Multi-state machines

92.  A multi-state molecular machine makes sequential state transitions by several inputs.  Even a few kinds of inputs can lead to a lot of states of the machine by signaling iteratively.. Multi-state machine

93. input 1 input ２ input ３ ２ １ ２ ３ １ ３ ３３ １ ２ …… This machine changes its state sequentially by three kinds of inputs, and the state branches with every input. Multi-state machine

94. A conformational state machine is a multi-state machine which keeps its state as its conformation, i.e. secondary structure. Hairpin based state machine

95.  The components of this system are DNA hairpins and oligomers whose sequences appear in the hairpin stems.  The DNA oligomer can open the hairpin structure by invading the hairpin stem part by branch migration.  The hairpins are concatenated with an additional sticky end and form repeated hairpin structures of a single DNA strand.  The whole repeated hairpin structures comprise a multi-state machine, which maintains its state with its hairpin structures, and the DNA oligomers correspond to state transition signals. Hairpin based state machine

96.  The oligomer can interacts with the hairpin structure at one end of strand with a sticky end.  And if the sequences of the hairpin stem part and the oligomer agree, the oligomer invades the hairpin structure by branch migration after hybridizing with the sticky end.  Another new sticky end appears.  Therefore, the repeated hairpin structures are opened by corresponding oligomers successively from one end of the DNA strand. Hairpin based state machine

98.  The hairpin-based state machine can be improved by branching the hairpin stems as the state transition branches.  This branching hairpin-based state machine consists of three kinds of hairpin stem sequences and several kinds of hairpin loop sequences. Its state branches into two ways at every step.  This machine realizes the concept of the multi-state machine which changes its state sequentially. Branching hairpin based state machine

100. The opener consists of two parts  The part which hybridizes with the sticky end of a hairpin is called the head (green part)  The part which invades and hybridizes with the stem of a hairpin is called the tail (red part). The sticky end of a hairpin is also a part of the stem of another hairpin. Openers

101.  The sticky end and the hairpin agree with the head and the tail of the opener respectively. The hairpin will opened.  The sticky end does not agree with the head of the opener. If the ordinality is satisfied, the hairpin is not opened.  The hairpin does not agree with the tail of the opener. The hairpin should not be opened.  Neither the sticky end nor the hairpin agrees with the opener. The hairpin should not be opened. Possible configurations

103. Energy level

104. 3SAT engine

105.  Sakamoto et al., Science, May 19, 2000.  The essential part of the SAT computation is done by hairpin formation.  Autonomous Molecular Computation SAT engine

106.  The SAT Engine makes use of hairpin structures in DNA molecules.  In the SAT Engine, complementary literals are encoded by complementary nucleotide sequences in the sense of Watson and Crick.  If a single-stranded DNA molecule contains two literals that are inconsistent with each other, i.e. a variable and its negation, then the molecule forms a hairpin. This means that inconsistent assignments correspond to molecules containing a hairpin, so a SAT problem can be solved by removing hairpin molecules and checking whether consistent assignments remain. SAT engine

107. Procedure (i)Generate the literal strings according to the given formula. This step is implemented by a ligation reaction, which concatenates the literals. (ii)Allow ssDNA molecules, each representing a literal string, to form hairpins. This step performs the main logic of computation only by regulating the temperature. Even enzymes are not necessary. (iii)Remove the hairpin-forming molecules. The remaining molecules represent the satisfying literal strings, which can be identified with the solutions (value assignments) to the problem.

108. b ￢b￢b e (a ∨ b ∨ c) ∧ ( ￢ d ∨ e ∨￢ f) ∧ … ∧ ( ￢ c ∨￢ b ∨ a) ∧... b ￢b￢b digestion by restriction enzyme exclusive PCR SAT engine

111.  Digestion by Restriction Enzyme  Hairpins are cut at the restriction site inserted in each literal sequence.  Exclusive PCR  PCR is inefficient for hairpins.  In exclusive PCR, solution is diluted in each cycle to keep the difference in amplification.  The number of steps is independent of the number of variables or clauses. Selection by hairpin structure

112. 6-Variable 10-Clause Formula (a ∨ b ∨￢ c) ∧ (a ∨ c ∨ d) ∧ (a ∨￢ c ∨￢ d) ∧ ( ￢ a ∨￢ c ∨ d) ∧ (a ∨￢ c ∨ e) ∧ (a ∨ d ∨￢ f) ∧ ( ￢ a ∨ c ∨ d) ∧ (a ∨ c ∨￢ d) ∧ ( ￢ a ∨￢ c ∨￢ d) ∧ ( ￢ a ∨ c ∨￢ d) SAT engine

113. SAT engine, solution

114. Whiplash pcr

115. DNA Automaton ： State Machine by DNA  Polymerization of Hairpin  Polymerization Stop Whiplash PCR

116. DNA state machine  Transition table 5’-stopper-state’ 1 -state 1 -……-stopper-state’ n -state n -3’ stopper: stopper sequence state’ 1 -state 1 : state pair state 1 : state before transition state’ 1 :state after transition  Current state 5’-transition table-spacer-state i -3’

117. Polymerization stop  States are encoded with 3 out of the 4 possible deoxyribonucleotides (dATP, dGTP, dCTP, dTTP)  A repetition of the missing nucleotide works as a stopper sequence in polymerization  The polymerization buffer contains only the complements of these 3 deoxyribonucleotides.

118. x BAx C B a Whiplash PCR

119. x BAx C B x a

120. x BAx C B x ab

121. x BAxCB x a b

122. x BAxCB x a b

123. x BAxCB x a bc

124. Encoding

125. Each ssDNA executes a simple, autonomous computation… Whiplash PCR, problems

126. Whiplash PCR has a technical problem…back-hybridization. Whiplash PCR, problems

127. WPCR efficiency may be enhanced by re-design… Predicted result: large increase in computational efficiency. J. Rose, et al., Phys. Rev. E 65 (2002). Whiplash PCR