1. What contributions have the authors mentioned in the paper "Two computational primitives for algorithmic self-assembly: copying and counting" ?
Although the yield of counting crystals is low, and per-tile error rates in such crystals is roughly 10 %, this work demonstrates the potential of algorithmic self-assembly to create complex nanoscale patterns of technological interest.. This general principle, that computation has an essential role in construction tasks, was clearly expounded by von Neumann in his study of self-reproducing machines.. Here the authors show that algorithmic self-assembly can be used to create an extended patternsbinary countingsof technological relevance for molecular electronics as the layout for a demultiplexing circuit20-24 and of fundamental theoretical interest due to its appearance as a primitive for many other computation and construction tasks.. 25-27 Additionally, using a subset of these tiles the authors show that a string of binary information can be propagated along the length of a DNA tube, which is of independent interest to the study of crystal evolution and the origin of life.. 28 The binary counter pattern consists of an array in which each row represents an integer in binary, and each subsequent row represents the integer following the one below it.. Without any a priori knowledge of integer arithmetic or binary representation, this table can be generated by following simple rules based on the logic of the classical ripple-carry adder.. This can be summarized in equations as where bi n is the bit in the ith column and nth row of the binary counting array, and ci n is the carry bit provided by that position to its leftward neighbor.. As shown in Figure 1a, each tile contains four “ binding domains ” whose shape either matches information provided by the tile below and by the tile to its right ( the inputs ) or provides information to the tiles above and to its left ( the outputs ).. 31 Note that if tiles may be added only when they bind by at least two domains, which the authors call legal growth, then a finite-sized assembly can not grow beyond existing rows and columns ; for example, the assembly shown in Figure 1b will add exactly five tiles on the upper right and four tiles at the lower left.. Unlike previously considered tile sets for binary counters,25,32 for experimental simplicity the tile set and scaffold discussed here do not provide a mechanism for initiating the counter at a specific number.. It is therefore important that, when implemented molecularly, tiles attaching by a single binding domain will be rare under the physical conditions that the authors will study.. ( Although this doublecrossover motif has been shown previously to have intrinsic curvature that encourages assemblies of tiles to roll up into tubes,17,34 assemblies grown from long scaffolds in that work usually contained 5 to 15 layers of rule tiles, which the authors predicted would be sufficient for their investigations here. ). To distinguish tiles representing 0 ’ s from tiles representing 1 ’ s, the authors decorated the latter with protruding hairpin motifs that provide topographic contrast when imaged by atomic force microscopy ( AFM ).. ( Although this doublecrossover motif has been shown previously to have intrinsic curvature that encourages assemblies of tiles to roll up into tubes,17,34 assemblies grown from long scaffolds in that work usually contained 5 to 15 layers of rule tiles, which the authors predicted would be sufficient for their investigations here. ). To distinguish tiles representing 0 ’ s from tiles representing 1 ’ s, the authors decorated the latter with protruding hairpin motifs that provide topographic contrast when imaged by atomic force microscopy ( AFM ).. Furthermore, to specifically amplify the single-stranded sense strand at the end of assembly PCR ( which produces long periodic double-stranded DNA ), the entire scaffold strand sequence consists of only A, T, C ; the final stage of synthesis, therefore, is provided only those nucleotides.. In fact, the tiles here called VE-NO and SEJ-N1 are identical to the tiles VE-00 and SEs ( 1,5: h14 ) reported in ref 34 to each form single-tile tubes, frequently longer than 5 μm with a circumference typically between 4 and 12 tiles and with the tile axis parallel to the length of the tubes.. In this work, single-tile tubes are prepared by mixing each relevant strand at 200 nM in TAE/Mg2+ buffer ( 40 mM Tris acetate, 1 mM EDTA, 12. 5 mM Mg acetate, pH 8. 3 ) and annealing from 90 to 20 °C at 1 °C/min.. To investigate whether this disproportionation could be due to a difference in the binding affinities of the two tiles, the authors examined the thermal formation and melting profiles of each single-tile tube, using UV spectrophotometry.. ( These formation and melting curves reveal a number of unusual characteristics, such as the hysteresis of the tile formation and the large size of the tube formation transition, that are the subject of a separate study.. To test the full set of all four rule tiles, which is not expected to give clearly interpretable results when annealed to form tubes and assemblies, the authors first created a scaffold corresponding to the blue column in the abstract assembly diagram ( Figure 1b ).. The authors interpret the images as tile assemblies as shown in Figure 3b ; unclear imaging and lattice defects ( missing tiles as well as inserted rows and columns ) prevent unambiguous interpretation at some locations.. Given that the authors examined roughly 75 scaffold-nucleated crystals ( many at a resolution too poor to identify tiles ) with a total length of no more than 33 μm, i. e., 2400 tiles, it is exceedingly unlikely that they would have observed any counting patterns similar to those in Figure 3a if the assembly had been random ( i. e., an error rate of 50 % during assembly ).. Finally, the most striking problem in the work reported here is that the overall yield is very low: by far the majority of the material is in the form of tubes, amorphous aggregates, and illegal growth from scaffold strands.. This work provides further evidence that algorithmic selfassembly provides a general mechanism for universal construction in the sense of von Neumann.. Although the absolute temperature at which significant tube nucleation and growth occur will depend on the speed of cooling, these results suggest that during the annealing of COPY tubes, where both tiles are present in the same solution, VE-N0 single-tile tubes may nucleate and grow first, at a temperature too high for significant amounts of SEJ-N1 tiles to nucleate either as single-tile tubes or as heterogeneous COPY tubes.. Stripes frequently “ wrap around ” from one side to the other, suggesting that they formed a contiguous helical stripe on the intact closed tube, that few tiles are lost during the opening process, and that few tiles were gained by assembly while on the mica.. Searching revealed crystals that had one straight edge, suggesting the presence of the scaffold strand, and a pattern of bits along that edge that suggested pattern formation according to the binary counting algorithm.. Furthermore, initiation of the first layer of tiles at distance sites on a scaffold could result in a “ hinged ” crystal that, when it grows together, could contain many mismatch errors and lattice defects at the seam.. 52-54 Furthermore, different tile geometries and longer sticky ends can potentially increase the number of unique tiles that can be created.. Areas shown are selected from larger crystals that extend further to the left and/or right.. The authors thank the Caltech Molecular Materials Research Center for use of their AFM scanners.
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