A Molecular Algorithm for Path Self-Assembly in 3 Dimensions

A molecular algorithm is a set of molecular interactions that carry out a particular task. We describe a molecular algorithm for self-assembling a path between two stationary points when the locations of these points are not known in advance. While efficient path finding algorithms for electronic robots exist, molecules lack the centralized memory or computing power to implement them. The algorithm takes advantage of the inherent physics at the molecular scale, and unlike other biomimetic algorithms for path finding, is designed to work in an unstructured environment and does not require complex molecular components. Designed molecules self-assemble a DNA nanotube starting from a “seed” molecule attached to the start point. During growth, the DNA nanotube’s end diffuses through space, and this diffusion is harnessed as a search process: when the DNA nanotube’s end contacts the destination, it attaches to it and stops growing, forming a stable path. We use simulations and analysis to predict that paths of up 10 microns are formed with more than 99% probability if the destination is larger than 500 nanometers in diameter, making it practical. However, the probability of the DNA nanotube missing the destination is highly dependent on destination distance and size. It increases as exp ˆ

[1]  Jehoshua Bruck,et al.  Programmability of Chemical Reaction Networks , 2009, Algorithmic Bioprocesses.

[2]  M. Kirschner,et al.  Dynamic instability of microtubule growth , 1984, Nature.

[3]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[4]  I. Vernos,et al.  The Mitotic Spindle: A Self-Made Machine , 2001, Science.

[5]  E. Winfree,et al.  Design and characterization of programmable DNA nanotubes. , 2004, Journal of the American Chemical Society.

[6]  Joshua T. Jones,et al.  Efficient Chromosome Capture Requires a Bias in the ‘Search-and-Capture’ Process during Mitotic-Spindle Assembly , 2005, Current Biology.

[7]  G. Whitesides,et al.  Molecular self-assembly and nanochemistry: a chemical strategy for the synthesis of nanostructures. , 1991, Science.

[8]  E. Winfree,et al.  Algorithmic Self-Assembly of DNA Sierpinski Triangles , 2004, PLoS biology.

[9]  Yuriy Brun,et al.  Path finding in the tile assembly model , 2009, Theor. Comput. Sci..

[10]  Nadrian C. Seeman,et al.  An Overview of Structural DNA Nanotechnology , 2007, Molecular biotechnology.

[11]  Radhika Nagpal,et al.  Programmable self-assembly using biologically-inspired multiagent control , 2002, AAMAS '02.

[12]  D A Lauffenburger,et al.  Analysis of intracellular receptor/ligand sorting. Calculation of mean surface and bulk diffusion times within a sphere. , 1986, Biophysical journal.

[13]  Erik Winfree,et al.  An information-bearing seed for nucleating algorithmic self-assembly , 2009, Proceedings of the National Academy of Sciences.

[14]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[15]  Erik Winfree,et al.  On the computational power of DNA annealing and ligation , 1995, DNA Based Computers.

[16]  Ruojie Sha,et al.  A Bipedal DNA Brownian Motor with Coordinated Legs , 2009, Science.

[17]  Jacob Beal,et al.  Infrastructure for engineered emergence on sensor/actuator networks , 2006, IEEE Intelligent Systems.

[18]  W. L. Jorgensen.  Supramolecular chemistry. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[19]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[20]  R. Pecora,et al.  Rotational and translational diffusion in semidilute solutions of rigid-rod macromolecules , 1982 .

[21]  S. LaValle,et al.  Motion Planning , 2011, IEEE Robotics & Automation Magazine.

[22]  M. Magnasco.  CHEMICAL KINETICS IS TURING UNIVERSAL , 1997 .

[23]  Paul W. K. Rothemund,et al.  Rothemund, P.W.K.: Folding DNA to create nanoscale shapes and patterns. Nature 440, 297-302 , 2006 .

[24]  Erik Winfree,et al.  Molecular robots guided by prescriptive landscapes , 2010, Nature.

[25]  Axel Ekani-Nkodo,et al.  Joining and scission in the self-assembly of nanotubes from DNA tiles. , 2004, Physical review letters.

[26]  J. Herskowitz,et al.  Proceedings of the National Academy of Sciences, USA , 1996, Current Biology.

[27]  Ivan V. Markov,et al.  Crystal growth for beginners , 1995 .

[28]  G. Seelig,et al.  Enzyme-Free Nucleic Acid Logic Circuits , 2022 .

[29]  Ashish Goel,et al.  Error Free Self-assembly Using Error Prone Tiles , 2004, DNA.

[30]  Jean-Claude Latombe,et al.  Numerical potential field techniques for robot path planning , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[31]  C. S. Tung,et al.  NAMOT2 - a redesigned nucleic acid modeling tool: construction of non-canonical DNA structures , 1996, Comput. Appl. Biosci..

[32]  J. Reif,et al.  Logical computation using algorithmic self-assembly of DNA triple-crossover molecules , 2000, Nature.

[33]  Erik Winfree,et al.  Programmable Control of Nucleation for Algorithmic Self-Assembly , 2009, SIAM J. Comput..

[34]  Eric Karsenti,et al.  Gradients in the self-organization of the mitotic spindle. , 2006, Trends in cell biology.

[35]  J. Wetmur.  DNA probes: applications of the principles of nucleic acid hybridization. , 1991, Critical reviews in biochemistry and molecular biology.

[36]  S. LaValle,et al.  Motion Planning , 2008, Springer Handbook of Robotics.

[37]  E. Winfree.  Simulations of Computing by Self-Assembly , 1998 .

[38]  Jean-Marie Lehn,et al.  Supramolecular Chemistry / Science , 1999 .

[39]  Erik Winfree,et al.  The program-size complexity of self-assembled squares (extended abstract) , 2000, STOC '00.

[40]  Paul W. K. Rothemund,et al.  A DNA and restriction enzyme implementation of Turing machines , 1995, DNA Based Computers.

[41]  Leonard M. Adleman,et al.  Theory and experiments in algorithmic self-assembly , 2001 .

[42]  Hao Yan,et al.  Studies of thermal stability of multivalent DNA hybridization in a nanostructured system. , 2009, Biophysical journal.

[43]  P. Rothemund.  Folding DNA to create nanoscale shapes and patterns , 2006, Nature.

[44]  Chris Hanson,et al.  Amorphous computing , 2000, Commun. ACM.

[45]  A. Turberfield,et al.  A free-running DNA motor powered by a nicking enzyme. , 2005, Angewandte Chemie.

[46]  N. Seeman,et al.  A Proximity-Based Programmable DNA Nanoscale Assembly Line , 2010, Nature.

[47]  S. Smith,et al.  Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads. , 1992, Science.

[48]  Klaus Schulten,et al.  First passage time approach to diffusion controlled reactions , 1980 .

[49]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[50]  Erik Winfree,et al.  Complexity of Self-Assembled Shapes , 2004, SIAM J. Comput..

[51]  E. Winfree,et al.  Synthesis of crystals with a programmable kinetic barrier to nucleation , 2007, Proceedings of the National Academy of Sciences.

[52]  Shawn M. Douglas,et al.  Self-assembly of DNA into nanoscale three-dimensional shapes , 2009, Nature.