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Course outline. Hairpins. Hairpins. Hairpins. DNA strands with self-complementary base sequences have the potential to form hairpin structures. Formed only with a single DNA (or RNA) strand.
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Hairpins • 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.
RNA secondary structures • 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 • 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 • 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 • 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.
Hairpins • 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
tRNA structure Secondary Structure Of large ribosomal RNA
Inverse folding 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 3’ folding 5’ 3’ TTC…GCA inverse folding 5’
Multi-state machine • 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 input 1 ２ １ …… ３ ３ input ２ １ ２ input ３ …… ３ ３ １ …… ２ This machine changes its state sequentially by three kinds of inputs, and the state branches with every input.
Hairpin based state machine A conformational state machine is a multi-state machine which keeps its state as its conformation, i.e. secondary structure.
Hairpin based state machine • 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 • 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.
Branching hairpin based state machine • 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.
Openers • 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.
Possible configurations • 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.
SAT engine • Sakamoto et al., Science, May 19, 2000. • The essential part of the SAT computation is done by hairpin formation. • Autonomous Molecular Computation
SAT engine • 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.
Procedure • Generate the literal strings according to the given formula. This step is implemented by a ligation reaction, which concatenates the literals. • 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. • 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.
SAT engine (a∨b∨c)∧(￢d∨e∨￢f)∧ … ∧(￢c∨￢b∨a)∧ ... e b ￢b digestion by restriction enzyme exclusive PCR b ￢b
Selection by hairpin structure • 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.
SAT engine 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)
Whiplash PCR DNA Automaton： State Machine by DNA • Polymerization of Hairpin • Polymerization Stop
DNA state machine • Transition table 5’-stopper-state’1-state1-……-stopper-state’n-staten-3’ stopper: stopper sequence state’1-state1: state pair state1: state before transition state’1: state after transition • Current state 5’-transition table-spacer-statei-3’
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.
Whiplash PCR a B C x B A x
Whiplash PCR B x a C x B A x
Whiplash PCR B x b a C x B A x
Whiplash PCR b a x x B A x C B
Whiplash PCR a b x x B A x C B
Whiplash PCR a c b x x B A x C B
