Desired Mechanism
In this research, we designed following strands, st1,st2, st3, st3, l1, j2, j3 and j3'. We ordered these oligos to Integrated DNA Technologies, Inc.
The designed of oligos and their sequences are shown Figure d-1. 
Figure d-1. design of DNA hydrogel components and their sequences
Strands, st1~st4, form X motif which can shake their arms with another X-motif on the stickyend (sequence painted red). The X-motifs bind one after another, finally they construct huge backbones of DNA hydrogel. 
Figure d-2. X-motif DNA hydrogel structure
l1 can hybridize with st1~st4, and form dimers with itself. Therefore, l1 bridges X motifs.
Figure d-3. The expected structure of bridging DNA hydrogel stickyends by l1 dimers
In addition, l1 has a loop structure. When j2 or j3 are present, the loop opens and mesh size of X-motif becomes larger. It cause the swelling of DNA hydrogel.  Before swelling, the length of a side of a X motif mesh is 74.
The number of base pairs in l1 loop is 30. Therefore, after swelling, the length of a side of a X motif mesh becomes 134. This means, in theory, mesh size is enlarged by 1.85 times!
Figure d-4. Mechanism of swelling gel by adding j3. This reaction would be also occurred in j2.
The loop of l1 opened by j3 can be closed when j3’ are added, because j3 and j3’ has a toehold sequence(light green) and create more stable dsDNA.
When swelling, in theory,  mesh size is shorten by 0.55 times!
Figure d-5. Mechanism of shrinking DNA hydrogel by adding j3'.
The difference of sequence between j2 and j3 is the toehold (the sequence painted light green). In order to show the shrinking of DNA hydrogel, we need to peel off the strands which attach to loop of j1. Thus it is required higher free energy to peel them off. Toehold gives free energy to peel off from l1. However, there are ssDNA site in j3 after hybridization to l1. So j2-l1 would be more stable than that of j3, we prepared both of them.
j2 can be used only when swelling. 
j3 can be used both when swelling and shrinking.

Simulation
Key hybridization mentioned above, was simulated using nupack(http://www.nupack.org/).
In all cases, simulations showed desired structures of reaction of each pair we mentioned(Figure d-6).

Hybridization st1 + l1 (bridging X-motif)      http://www.nupack.org/partition/show/1620324?token=EDwCq6dbUr


Hybridization l1 + j2 (loop opening when swelling)    http://www.nupack.org/partition/show/1620302?token=p2pi0fsHAK

Hybridization l1 + j3 (loop opening when swelling)    http://www.nupack.org/partition/show/1607627?time_refresh=1.0&token=101YHENenU

Hybridization j3 + j3' (recovery of l1 loop​​​​​​​)    http://www.nupack.org/partition/show/1607629?time_refresh=1.0&token=18wFqIrflE

Figure d-6. Simulation by nupack
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