Fig 1.
Heuristic algorithms designed in EC have great prospects for the transfer to synthetic biology and biotechnologies.
Namely, the impressive similarity between the problem of the synthesis of multidomain (multifunctional) macromolecules from scratch and the RR problem suggests that it is promising to transfer and implement these heuristics into new experimental techniques.
Fig 2.
The specific implementation of the BioRS function in the molecular biological aspect.
Aptamer is presented as a composite BB of two half-schemes, which is representative for the organization of aptamers. The inset shows the internal structure of each half-scheme of the Sassanfar–Szostak motif [85, 86]. See text for details. All the domains are assumed to be identic. (B-C) Structural details of conservative functional regions of an aptamer using Sassanfar–Szostak motif as an example: (B) 2D structure and (C) nucleotide sequence. Positions in the recognition bulge are colored according to whether they are invariant (red), two-base varying (green), or non-conserved (black). Here …xxxxx corresponds to the halves of the insulating spacer sequences, NNNNN & nnnnn are the complementary halves of the sequences of the first and second stem, ** …** is arbitrary and corresponds to the closing loop sequence. (D) 26 nucleotide core part of the Sassanfar-Szostak motif implemented in our BioRS as a consensus. Four G-nucleotides of this consensus are single-valued (red), 10 loci are defined up to nucleotide pairs (blue), while the rest are assumed arbitrary (N or n, in black).
Fig 3.
Molecular biological illustration of the idea of evolutionary search with BioRS.
(A) General idea of the battery of (identical) modules as it is formulated by Babiskin & Smolke [82]. (B) Our scheme of sequential search from scratch of a tetrameric aptamer. (C) Search scheme for a classic RS function with 4 BBs (above). Domains (BBs) separated by insulating spacers of predetermined length are searched sequentially from left to right. Delta is an increment of fitness level for each correctly found aptamer (BB). See text and legend to Fig 2 for the detailed description of an aptamer structure.
Fig 4.
General idea of alternative structures of aptamers binding the same ligand and its specific implementation scheme for the BioRS function.
(A-С) Three structures of aptamers binding to ATP that differ in their sequence and secondary–tertiary structure. The first structure (structure-I) (Sassanfar-Szostak motif) we will name as a “rod” (A). Second structure (structure-II) will be referred to as a “cloverleaf” (B) [93]. (С) One more version of an aptamer binding ATP [92]. (D) Consensus sequences of (A) and (C), critical to the recognition and binding of a ligand, in spite of their general similarity, differ to such extent that it is infeasible to transit from one to the other by a series of mutations not losing the aptamer functionality (sequences similar in both versions are framed and marked by double-headed arrows). (E) Single- and double-valued loci in our simplified version of the aptamer with alternative structures. Single-valued nucleotides, necessarily present in both structures, are given in red, those present in one of the alternative structures in black. The other positions are arbitrary. See text for details.
Fig 5.
Extended (competitive) version of BioRS, implementing alternative aptamer structures and interference.
(A-F) Evolutionary search scheme for the competitive BioRS. (A) An initial arbitrary sequence of a given length with zero fitness. (B-C) The first functional domain (aptamer) is identified by an evolutionary search. It may have one of two alternative structures: cloverleaf or rod (see Fig 4A). (D) If the cloverleaf structure is found in a certain position, this makes it impossible to find the second functional domain due to steric interactions of two neighboring domains. (E-F) In the case of a rod structure of the already found domain, it is possible to find the second functional domain in one of two alternative structures. This is only case (E) which can evolve further. (G) Schematic of the competitive BioRS illustrating its multimodality (bimodality within each epoch). See text for details.
Fig 6.
Idea of the search for a domain/motif within the range from 1 to W positions (in the window) instead of an only predetermined position.
The first position is shifted by w = 1 …W nucleotides, where W is not too large (100–200).
Table 1.
Effectiveness of SELEX tests in silico.
Fig 7.
Effectiveness of evolutionary GA search (mutations only) with (μ, λ) selection, μ/λ = 0.4, 4 domains, 6+4 defined positions out of 26, W = 220 at varying mutation rate and population size as a function of mutation rate and population size.
In inset the area of the robust algorithm work with low sensitivity to mutation rate is presented at three values of population size: P = 100, 600, and 2000. Within this area populations of low size are preferable. The mean number of fitness evaluations are computed over 100 runs per test. Standard deviations are of value comparable to the mean.
Fig 8.
RMHC: Effectiveness vs mutation rate.
Simple consensus-based BioRS (4 domains, 6+4 defined positions out of 26, W = 220). The mean number of fitness evaluations are computed over 200 runs per test. Standard deviations are shown as vertical bars. Inset is presented in logarithmic coordinates.
Fig 9.
In silico tests with parallel RMHC: Effectiveness vs number of parallel processes.
(4 domains, 6+4 defined positions out of 26, W = 220; mean mutation rate is 20 per chromosome). The mean number of fitness evaluations are computed over 100 runs per test. Standard deviations are of value comparable to the mean.
Table 2.
Effectiveness (number of evaluations) and success rate for the competitive BioRS by means of standard GA with a single-point crossover.
Table 3.
Effect of the recombination of segments.
Fig 10.
Block diagram of the experimental setup.
Block diagram of the experimental setup of the experimental setup for the implementation of parallel RMHCs in the experiment. Includes several experiments organized and running in parallel.
Fig 11.
Schemes of the RR (left) and RS (right) functions.