The tile assembly model is intrinsically universal David Doty, Jack - PowerPoint PPT Presentation

The tile assembly model is intrinsically universal David Doty, Jack H. Lutz, Matthew J. Patitz, Robert T. Schweller, Scott M. Summers, Damien Woods Caltech Iowa State 1 Damien Woods, FOCS 2012

Motivation • Nature computes • Engineers are building nanoscale molecular (chemical) computers Sumazin et al. Cell 147(2). 2011 Soloveichik, Seelig, Winfree. DNA Rothemund, PWK. Folding DNA to as a Universal Substrate for create nanoscale shapes and patterns. Chemical Kinetics. PNAS 2010 Nature 2006 • We need a computational theory of self assembly and molecular interactions • Perhaps more importantly (for us), we can find interesting theoretical problems: computation, geometry, asynchronousity, kinetics, thermodynamics Rothemund, Papadakis, Winfree 2004 2 Damien Woods, FOCS 2012

Abstract tile assembly model • Square units called tiles (non-rotatable) • Each side has a glue (a,b,c,d,...) • Each glue has a strength (0,1,2,3,...) • Finite set of tile types, unlimited supply of each tile type • Growth begins from a seed tile • Tiles stick to the growing assembly if their glues match, and are strong enough ( sum of strengths is at least the temperature ) • Asynchronous strength 2 strength 1 a c b d Winfree, 1998 Rothemund, Papadakis, Winfree 2004 Defn. Tile assembly system: tile set, seed tile, temperature 3 Damien Woods, FOCS 2012

Abstract tile assembly model j ? H i G E e h g j h a B F’ c C’ b c d f g b A F C c e a f f a e E Seed d D a e d Seed d i i Temperature = 2 • Square units called tiles (non-rotatable) • Each side has a glue (a,b,c,d,...) strength 2 • Each glue has a strength (0,1,2,3,...) • strength 1 Growth begins from a seed tile a • Tiles stick to the growing assembly if their glues match, and are c b strong enough ( sum of strengths is at least the temperature ) d • Finite set of tile types, unlimited supply of each tile type 4 Defn. Tile assembly system: tile set, seed tile, temperature Damien Woods, FOCS 2012 Winfree, 1998

Abstract tile assembly model j ? H i G E e h g j h a B F’ c C’ b c d f g b A F C c e a f b A f a e E a Seed d D a e d Seed d i i Temperature = 2 • Square units called tiles (non-rotatable) • Each side has a glue (a,b,c,d,...) strength 2 • Each glue has a strength (0,1,2,3,...) • strength 1 Growth begins from a seed tile a • Tiles stick to the growing assembly if their glues match, and are c b strong enough ( sum of strengths is at least the temperature ) d • Finite set of tile types, unlimited supply of each tile type 4 Defn. Tile assembly system: tile set, seed tile, temperature Damien Woods, FOCS 2012 Winfree, 1998

Abstract tile assembly model j ? H i G E e h g j h a B F’ c C’ b c d f g a b B A F c C b c e a f b A f a e E a Seed d D a e d Seed d i i Temperature = 2 • Square units called tiles (non-rotatable) • Each side has a glue (a,b,c,d,...) strength 2 • Each glue has a strength (0,1,2,3,...) • strength 1 Growth begins from a seed tile a • Tiles stick to the growing assembly if their glues match, and are c b strong enough ( sum of strengths is at least the temperature ) d • Finite set of tile types, unlimited supply of each tile type 4 Defn. Tile assembly system: tile set, seed tile, temperature Damien Woods, FOCS 2012 Winfree, 1998

Abstract tile assembly model j ? H i G E e h g j h a B F’ b c A C’ b c d f a g a b B A F c C b c e a f b A f a e E a Seed d D a e d Seed d i i Temperature = 2 • Square units called tiles (non-rotatable) • Each side has a glue (a,b,c,d,...) strength 2 • Each glue has a strength (0,1,2,3,...) • strength 1 Growth begins from a seed tile a • Tiles stick to the growing assembly if their glues match, and are c b strong enough ( sum of strengths is at least the temperature ) d • Finite set of tile types, unlimited supply of each tile type 4 Defn. Tile assembly system: tile set, seed tile, temperature Damien Woods, FOCS 2012 Winfree, 1998

Abstract tile assembly model j ? H i G E e a h g B c j b h a B F’ b c A C’ b c d f a g a b B A F c C b c e a f b A f a e E a Seed d D a e d Seed d i i Temperature = 2 • Square units called tiles (non-rotatable) • Each side has a glue (a,b,c,d,...) strength 2 • Each glue has a strength (0,1,2,3,...) • strength 1 Growth begins from a seed tile a • Tiles stick to the growing assembly if their glues match, and are c b strong enough ( sum of strengths is at least the temperature ) d • Finite set of tile types, unlimited supply of each tile type 4 Defn. Tile assembly system: tile set, seed tile, temperature Damien Woods, FOCS 2012 Winfree, 1998

Abstract tile assembly model b A j ? H a i G E e a h g B c j b h a B F’ b c A C’ b c d f a g a b B A F c C b c e a f b A f a e E a Seed d D a e d Seed d i i Temperature = 2 • Square units called tiles (non-rotatable) • Each side has a glue (a,b,c,d,...) strength 2 • Each glue has a strength (0,1,2,3,...) • strength 1 Growth begins from a seed tile a • Tiles stick to the growing assembly if their glues match, and are c b strong enough ( sum of strengths is at least the temperature ) d • Finite set of tile types, unlimited supply of each tile type 4 Defn. Tile assembly system: tile set, seed tile, temperature Damien Woods, FOCS 2012 Winfree, 1998

Abstract tile assembly model b A j ? H a i G E e a h g B c j b h a B F’ b c A C’ b c d f a g a b B A F c C b c e a f b A f a e E a Seed d D a e d D e Seed d d i i i Temperature = 2 • Square units called tiles (non-rotatable) • Each side has a glue (a,b,c,d,...) strength 2 • Each glue has a strength (0,1,2,3,...) • strength 1 Growth begins from a seed tile a • Tiles stick to the growing assembly if their glues match, and are c b strong enough ( sum of strengths is at least the temperature ) d • Finite set of tile types, unlimited supply of each tile type 4 Defn. Tile assembly system: tile set, seed tile, temperature Damien Woods, FOCS 2012 Winfree, 1998

Abstract tile assembly model b A j ? H a i G E e a h g B c j b h a B F’ b c A C’ b c d f a g a b B C A F c c e C b c e a f b A f a e E a Seed d D a e d D e Seed d d i i i Temperature = 2 • Square units called tiles (non-rotatable) • Each side has a glue (a,b,c,d,...) strength 2 • Each glue has a strength (0,1,2,3,...) • strength 1 Growth begins from a seed tile a • Tiles stick to the growing assembly if their glues match, and are c b strong enough ( sum of strengths is at least the temperature ) d • Finite set of tile types, unlimited supply of each tile type 4 Defn. Tile assembly system: tile set, seed tile, temperature Damien Woods, FOCS 2012 Winfree, 1998

Abstract tile assembly model b A j ? H a i G E e a h g B c j b h a B F’ b c A C’ b c d f a g a b B C A F c c e C b c e a f b A f a e E a Seed d D a e f d e E D e Seed d d i i i Temperature = 2 • Square units called tiles (non-rotatable) • Each side has a glue (a,b,c,d,...) strength 2 • Each glue has a strength (0,1,2,3,...) • strength 1 Growth begins from a seed tile a • Tiles stick to the growing assembly if their glues match, and are c b strong enough ( sum of strengths is at least the temperature ) d • Finite set of tile types, unlimited supply of each tile type 4 Defn. Tile assembly system: tile set, seed tile, temperature Damien Woods, FOCS 2012 Winfree, 1998

Abstract tile assembly model b A j ? H a i G E e a h g B c j b h a B F’ b c A C’ b c d f a g a b B C A F c c e C b c e a f g b A F f a e E a f Seed d D a e f d e E D e Seed d d i i i Temperature = 2 • Square units called tiles (non-rotatable) • Each side has a glue (a,b,c,d,...) strength 2 • Each glue has a strength (0,1,2,3,...) • strength 1 Growth begins from a seed tile a • Tiles stick to the growing assembly if their glues match, and are c b strong enough ( sum of strengths is at least the temperature ) d • Finite set of tile types, unlimited supply of each tile type 4 Defn. Tile assembly system: tile set, seed tile, temperature Damien Woods, FOCS 2012 Winfree, 1998

Abstract tile assembly model b A j ? H a ? i G E G e a e h g B c j g b h a B F’ b c A C’ b c d f a g a b B C A F c c e C b c e a f g b A F f a e E a f Seed d D a e f d e E D e Seed d d i i i Temperature = 2 • Square units called tiles (non-rotatable) • Each side has a glue (a,b,c,d,...) strength 2 • Each glue has a strength (0,1,2,3,...) • strength 1 Growth begins from a seed tile a • Tiles stick to the growing assembly if their glues match, and are c b strong enough ( sum of strengths is at least the temperature ) d • Finite set of tile types, unlimited supply of each tile type 4 Defn. Tile assembly system: tile set, seed tile, temperature Damien Woods, FOCS 2012 Winfree, 1998