806 research outputs found
DNA Computing by Self-Assembly
Information and algorithms appear to be central to biological organization
and processes, from the storage and reproduction of genetic information to
the control of developmental processes to the sophisticated computations
performed by the nervous system. Much as human technology uses electronic
microprocessors to control electromechanical devices, biological
organisms use biochemical circuits to control molecular and chemical events.
The engineering and programming of biochemical circuits, in vivo and in
vitro, would transform industries that use chemical and nanostructured
materials. Although the construction of biochemical circuits has been
explored theoretically since the birth of molecular biology, our practical
experience with the capabilities and possible programming of biochemical
algorithms is still very young
Evolutionary Dynamics in a Simple Model of Self-Assembly
We investigate the evolutionary dynamics of an idealised model for the robust
self-assembly of two-dimensional structures called polyominoes. The model
includes rules that encode interactions between sets of square tiles that drive
the self-assembly process. The relationship between the model's rule set and
its resulting self-assembled structure can be viewed as a genotype-phenotype
map and incorporated into a genetic algorithm. The rule sets evolve under
selection for specified target structures. The corresponding, complex fitness
landscape generates rich evolutionary dynamics as a function of parameters such
as the population size, search space size, mutation rate, and method of
recombination. Furthermore, these systems are simple enough that in some cases
the associated model genome space can be completely characterised, shedding
light on how the evolutionary dynamics depends on the detailed structure of the
fitness landscape. Finally, we apply the model to study the emergence of the
preference for dihedral over cyclic symmetry observed for homomeric protein
tetramers
Programmable Control of Nucleation for Algorithmic Self-Assembly
Algorithmic self-assembly, a generalization of crystal growth processes, has
been proposed as a mechanism for autonomous DNA computation and for bottom-up
fabrication of complex nanostructures. A `program' for growing a desired
structure consists of a set of molecular `tiles' designed to have specific
binding interactions. A key challenge to making algorithmic self-assembly
practical is designing tile set programs that make assembly robust to errors
that occur during initiation and growth. One method for the controlled
initiation of assembly, often seen in biology, is the use of a seed or catalyst
molecule that reduces an otherwise large kinetic barrier to nucleation. Here we
show how to program algorithmic self-assembly similarly, such that seeded
assembly proceeds quickly but there is an arbitrarily large kinetic barrier to
unseeded growth. We demonstrate this technique by introducing a family of tile
sets for which we rigorously prove that, under the right physical conditions,
linearly increasing the size of the tile set exponentially reduces the rate of
spurious nucleation. Simulations of these `zig-zag' tile sets suggest that
under plausible experimental conditions, it is possible to grow large seeded
crystals in just a few hours such that less than 1 percent of crystals are
spuriously nucleated. Simulation results also suggest that zig-zag tile sets
could be used for detection of single DNA strands. Together with prior work
showing that tile sets can be made robust to errors during properly initiated
growth, this work demonstrates that growth of objects via algorithmic
self-assembly can proceed both efficiently and with an arbitrarily low error
rate, even in a model where local growth rules are probabilistic.Comment: 37 pages, 14 figure
Connected Coordinated Motion Planning with Bounded Stretch
We consider the problem of connected coordinated motion planning for a large
collective of simple, identical robots: From a given start grid configuration
of robots, we need to reach a desired target configuration via a sequence of
parallel, collision-free robot motions, such that the set of robots induces a
connected grid graph at all integer times. The objective is to minimize the
makespan of the motion schedule, i.e., to reach the new configuration in a
minimum amount of time. We show that this problem is NP-complete, even for
deciding whether a makespan of 2 can be achieved, while it is possible to check
in polynomial time whether a makespan of 1 can be achieved. On the algorithmic
side, we establish simultaneous constant-factor approximation for two
fundamental parameters, by achieving constant stretch for constant scale.
Scaled shapes (which arise by increasing all dimensions of a given object by
the same multiplicative factor) have been considered in previous seminal work
on self-assembly, often with unbounded or logarithmic scale factors; we provide
methods for a generalized scale factor, bounded by a constant. Moreover, our
algorithm achieves a constant stretch factor: If mapping the start
configuration to the target configuration requires a maximum Manhattan distance
of , then the total duration of our overall schedule is ,
which is optimal up to constant factors.Comment: 28 pages, 18 figures, full version of an extended abstract that
appeared in the proceedings of the 32nd International Symposium on Algorithms
and Computation (ISAAC 2021); revised version (more details added, and typing
errors corrected
Self-assembly: modelling, simulation, and planning
SamoskládánĂ je proces, pĹ™i kterĂ©m se kolekce neuspořádanĂ˝ch částic samovolnÄ› orientuje do uspořádanĂ©ho vzoru nebo funkÄŤnĂ struktury bez pĹŻsobenĂ vnÄ›jšà sĂly, pouze za pomoci lokálnĂch interakcĂ mezi samotnĂ˝mi částicemi. Tato teze se zaměřuje na teorii dlaĹľdicovĂ˝ch samoskládacĂch systĂ©mĹŻ a jejich syntĂ©zu. NejdĹ™Ăve je pĹ™edstavena oblast vĂ˝zkumu vÄ›nujĂcĂ se dlaĹľdiÄŤovĂ˝m samoskládacĂm systĂ©mĹŻm, a potĂ© jsou dĹŻkladnÄ› popsány základnĂ typy dlaĹľdicovĂ˝ch skládacĂch systĂ©mĹŻ, kterĂ˝mi jsou abstract Tile Assembly Model (aTAM ), kinetic Tile Assembly Model (kTAM ), a 2-Handed Assembly Model (2HAM ). PotĂ© jsou pĹ™edstaveny novÄ›jšà modely a modely se specifickĂ˝m pouĹľitĂm. Dále je zahrnut struÄŤnĂ˝ popis pĹŻvodu teorie dlaĹľdicovĂ©ho samoskládánĂ spoleÄŤnÄ› s krátkĂ˝m popisem nedávnĂ©ho vĂ˝zkumu. Dále jsou pĹ™edstaveny dva obecnĂ© otevĹ™enĂ© problĂ©my dlaĹľdicovĂ©ho samoskládánĂ s hlavnĂm zaměřenĂm na problĂ©m Pattern Self-Assembly Tile Set Synthesis (PATS), coĹľ je NP-těžká kombinatorická optimalizaÄŤnĂ Ăşloha. Nakonec je ukázán algoritmus Partition Search with Heuristics (PS-H ), kterĂ˝ se pouĹľĂvá k Ĺ™ešenĂ problĂ©mu PATS. NásledovnÄ› jsou demonstrovány dvÄ› aplikace, kterĂ© byly vyvinuty pro podporu vĂ˝zkumu abstraktnĂch dlaĹľdicovĂ˝ch skládacĂch modelĹŻ a syntĂ©zy mnoĹľin dlaĹľdic pro samoskládánĂ zadanĂ˝ch vzorĹŻ. PrvnĂ aplikace je schopná simulovat aTAM a 2HAM systĂ©my ve 2D prostoru. Druhá aplikace je Ĺ™ešiÄŤ PATS problĂ©mu, kterĂ˝ vyuĹľĂvá algoritmu PS-H. Pro obÄ› aplikace jsou popsány hlavnĂ vlastnosti a návrhová rozhodnutĂ, která Ĺ™Ădila jejich vĂ˝voj. Nakonec jsou pĹ™edloĹľeny vĂ˝sledky nÄ›kolika experimentĹŻ. Jedna skupina experimentĹŻ byla zaměřena na ověřenĂ vĂ˝poÄŤetnĂ nároÄŤnosti vyvinutĂ˝ch algoritmĹŻ pro simulátor. Druhá sada experimentĹŻ zkoumala vliv jednotlivĂ˝ch vlastnostĂ vzorĹŻ na vlastnosti dlaĹľdicovĂ˝ch systĂ©mĹŻ, kterĂ© byly zĂskány syntĂ©zou ze vzorĹŻ pomocĂ vyvinutĂ©ho Ĺ™ešiÄŤe PATS problĂ©mu. Bylo prokázáno, Ĺľe algoritmus simulujĂcĂ aTAM systĂ©m má lineárnĂ ÄŤasovou vĂ˝poÄŤetnĂ nároÄŤnost, zatĂmco algoritmus simulujĂcĂ 2HAM systĂ©m má exponenciálnĂ ÄŤasovou vĂ˝poÄŤetnĂ nároÄŤnost, která navĂc silnÄ› závisĂ na simulovanĂ©m systĂ©mu. Aplikace pro Ĺ™ešenĂ syntĂ©zy mnoĹľiny dlaĹľdic ze vzorĹŻ je schopna najĂt relativnÄ› malĂ© Ĺ™ešenĂ i pro velkĂ© zadanĂ© vzory, a to v pĹ™iměřenĂ©m ÄŤase.Self-assembly is the process in which a collection of disordered units organise themselves into ordered patterns or functional structures without any external direction, solely using local interactions among the components. This thesis focuses on the theory of tile-based self-assembly systems and their synthesis. First, an introduction to the study field of tile-based self-assembly systems are given, followed by a thorough description of common types of tile assembly systems such as abstract Tile Assembly Model (aTAM ), kinetic Tile Assembly Model (kTAM ), and 2-Handed Assembly Model (2HAM ). After that, various recently developed models and models with specific applications are listed. A brief summary of the origins of the tile-based self-assembly is also included together with a short review of recent results. Two general open problems are presented with the main focus on the Pattern Self-Assembly Tile Set Synthesis (PATS) problem, which is NP-hard combinatorial optimisation problem. Partition Search with Heuristics (PS-H ) algorithm is presented as it is used for solving the PATS problem. Next, two applications which were developed to study the abstract tile assembly models and the synthesis of tile sets for pattern self-assembly are introduced. The first application is a simulator capable of simulating aTAM and 2HAM systems in 2D. The second application is a solver of the PATS problem based around the PS-H algorithm. Main features and design decisions are described for both applications. Finally, results from several experiments are presented. One set of experiments were focused on verification of computation complexity of algorithms developed for the simulator, and the other set of experiments studied the influences of the properties of the pattern on the tile assembly system synthesised by our implementation of PATS problem solver. It was shown that the algorithm for simulating aTAM systems have linear computation time complexity, whereas the algorithm simulating 2HAM systems have exponential computation time complexity, which strongly varies based on the simulated system. The synthesiser application is capable of finding a relatively small solution even for quite large input patterns in reasonable amounts of time
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