Selected Title s i n Thi s Serie s

44 Laur a F . Landwebe r an d Eri c B . Baum , Editors , DN A Base d Computer s I I

43 Pano s Pardalos , Sangutheva r Rajasekaran , an d Jos e Rol im , Editors ,

Randomization Method s i n Algorith m Desig n

42 Ding-Zh u D u an d Fran k K . Hwang , Editors , Advance s i n Switchin g Network s

41 Davi d Aldou s an d J a m e s Propp , Editors , Microsurvey s i n Discret e Probabilit y

40 Pano s M . Pardalo s an d Dingzh u D u , Editors , Networ k Design : Connectivit y an d

Facilities Locatio n

39 Pau l W . B e a m e an d Samue l R Buss , Editors , Proo f Complexit y an d Feasibl e

Arithmetics

38 Rebecc a N . Wrigh t an d Pete r G . N e u m a n n , Editors , Networ k Threat s

37 Bori s Mirkin , F . R . McMorris , Fre d S . Roberts , an d Andre y Rzhetsky , Editors ,

Mathematical Hierarchie s an d Biolog y

36 Josep h G . Rosenste in , Debora h S . Franzblau , an d Fre d S . Roberts , Editors ,

Discrete Mathematic s i n th e School s

35 Dingzh u Du , Ju n Gu , an d Pano s M . Pardalos , Editors , Satisfiabilit y Problem :

Theory an d Application s

34 Nathanie l Dean , Editor , Africa n American s i n Mathematic s

33 Rav i B . Boppan a an d Jame s F . Lynch , Editors , Logi c an d Rando m Structure s

32 Jean-Charle s Gregoire , Gerar d J . Holzmann , an d Doro n A . Pe led , Editors , Th e

SPIN Verificatio n Syste m

31 Nei l Immerma n an d Phokio n G . Kolait is , Editors , Descriptiv e Complexit y an d

Finite Model s

30 Sandee p N . Bhat t , Editor , Paralle l Algorithms : Thir d DIMAC S Implementatio n

Challenge

29 Doro n A . Peled , Vaugha n R . Prat t , an d Gerar d J . Holzmann , Editors , Partia l

Order Method s i n Verificatio n

28 Larr y Finkelstei n an d Wil l ia m M . Kantor , Editors , Group s an d Computatio n I I

27 Richar d J . Lipto n an d Eri c B . B a u m , Editors , DN A Base d Computer s

26 Davi d S . Johnso n an d Michae l A . Trick , Editors , Cliques , Coloring , an d

Satisfiability: Secon d DIMAC S Implementatio n Challeng e

25 Gilber t Baumslag , Davi d Epste in , Rober t Gilman , Hamis h Short , an d Charle s

Sims, Editors , Geometri c an d Computationa l Perspective s o n Infinit e Group s

24 Loui s J . Billera , Curti s Greene , Rodic a Simion , an d Richar d P . Stanley , Editors , Formal Powe r Serie s an d Algebrai c Combinatorics/Serie s Formelle s e t Combinatoir e Algebrique, 1994

23 Pano s M . Pardalos , Davi d I . Shalloway , an d Guolian g Xue , Editors , Globa l Minimization o f Nonconve x Energ y Functions : Molecula r Conformatio n an d Protei n Foldin g

22 Pano s M . Pardalos , Maurici o G . C . Resende , an d K . G . Ramakrishnan , Editors ,

Parallel Processin g o f Discret e Optimizatio n Problem s

21 D . Fran k Hsu , Arnol d L . Rosenberg , an d Dominiqu e Sotteau , Editors ,

Interconnection Network s an d Mappin g an d Schedulin g Paralle l Computation s

20 Wil l ia m Cook , Laszl o Lovasz , an d Pau l Seymour , Editors , Combinatoria l

Optimization

19 Ingema r J . Cox , Pierr e Hansen , an d Bel a Julesz , Editors , Partitionin g Dat a Set s 18 Gu y E . Blelloch , K . Man i Chandy , an d Sures h Jagannathan , Editors ,

Specification o f Paralle l Algorithm s

17 Eri c Sve n Ristad , Editor , Languag e Computation s

16 Pano s M . Pardalo s an d Henr y Wolkowicz , Editors , Quadrati c Assignmen t an d Related Problem s

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DIMACS Series i n Discret e Mathematic s

and Theoretica l Compute r Scienc e

Volume 4 4

DNA Based Computer s I I DIMACS Worksho p J u n e 10-12 , 199 6

Laura F . Landwebe r Eric B . Bau m

Editors

NSF Scienc e an d Technolog y Cente r in Discret e Mathematic s an d Theoretica l Compute r Scienc e A consortiu m o f Rutger s University , Princeto n University ,

AT&T Labs , Bel l Labs , an d Bellcor e

American Mathematica l Societ y

https://doi.org/10.1090/dimacs/044

This conferenc e wa s publishe d i n October 199 8 an d carries th e proceed -ings o f a conferenc e hel d Jun e 10-12 , 1996.

This DIMAC S volum e contain s paper s fro m th e Secon d DIMAC S Worksho p o n DN A Based Computers . Th e Worksho p wa s hel d o n Jun e 10-12 , 1996 , a t Princeto n University , Princeton, N . J .

1991 Mathematics Subject Classification. Primar y 92-06 , 92B05 , 92C40 , 68Q05 .

Library o f Congres s Cataloging-in-Publicatio n D a t a

DNA base d computer s I I : DIMACS workshop , Jun e 10-12 , 199 6 / Laur a F . Landweber , Eri c B . Baum, editors .

p. cm . — (DIMAC S serie s i n discret e mathematic s an d theoretica l compute r scienc e ; v. 44 ) "NSF Scienc e an d Technolog y Cente r i n Discret e Mathematic s an d Theoretica l Compute r

Science, a consortiu m o f Rutger s University , Princeto n University , AT& T Labs , Bel l Labs , an d Bellcore."

Includes bibliographica l references . ISBN 0-8218-0756- 0 1. Molecula r computers—Congresses . I . Landweber , Laur a F . (Laur a Faye) , 1967 - .

II. Baum , Eri c B. , 1957 - . III . NS F Scienc e an d Technolog y Cente r i n Discret e Mathematic s and Theoretica l Compute r Science . IV . DIMAC S (Group ) V . Series . QA76.887.D52 199 8 511.3—dc21 98-3527 8

CIP

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Contents

Foreword vi i

Introduction i x

Acknowledgments x i

A sticke r base d mode l fo r DN A computatio n SAM ROWEIS , ERI K WINFREE , RICHAR D BURGOYNE , NICHOLA S V .

CHELYAPOV, MYRO N F . GOODMAN , PAU L W . K . ROTHEMUND ,

AND LEONAR D M . ADLEMA N 1

On applyin g molecula r computatio n t o th e dat a encryptio n standar d LEONARD M . ADLEMAN , PAU L W . K . ROTHEMUND , SA M ROWEIS ,

AND ERI K W I N F R E E 3 1

Massively paralle l DN A computation : Expansio n o f symboli c determinant s THOMAS H . LEETE , MATTHE W D . SCHWARTZ , ROBER T M . WILLIAMS ,

DAVID H . W O O D , JEROM E S . SALEM , AN D HARVE Y RUBI N 4 5

Universal DN A computin g model s base d o n th e splicin g operatio n GHEORGHE PAU N 5 9

Running dynami c programmin g algorithm s o n a DN A compute r ERIC B . BAU M AN D DA N BONE H 7 7

A molecula r computatio n o f the roa d colorin g proble m NATASA JONOSK A AN D STEPHE N A . KAR L 8 7

DNA base d molecula r computation : Template-templat e interaction s i n PC R P E T E R D . KAPLAN , GUILLERM O CECCHI , AN D ALBER T

LIBCHABER 9 7

Use o f a horizonta l chai n reacto n fo r DNA-base d additio n FRANK GUARNIER I AN D CARTE R BANCROF T 10 5

Computation wit h DNA : Matri x multiplicatio n JOHN S . OLIVE R 11 3

A surface-based approac h t o DN A computatio n QINGHUA Liu , ZHE N G U O , ZHENGDON G F E I , ANN E E . CONDON ,

ROBERT M . CORN , MA X G . LAGALLY , AN D LLOY D M . SMIT H 12 3

vi C O N T E N T S

Mesoscopic compute r engineering : Automatin g DNA-base d molecula r computing vi a traditiona l practice s o f paralle l compute r architectur e design JOHN-THONES AMENY O 13 3

Error-resistant implementatio n o f DN A computation s MARTYN AMOS , ALA N GIBBONS , AN D DAVI D HODGSO N 15 1

Making DN A computer s erro r resistan t DAN BONEH , CHRISTOPHE R DUNWORTH , RICHAR D J . LIPTON ,

AND JIR I SGAL L 16 3

Active transpor t i n biologica l computin g STUART A . KURTZ , STEPHE N R . MAHANEY , JAME S S . ROYER ,

AND JANO S SIMO N 17 1

RNA base d computing : Som e example s fro m RN A catalysi s an d RN A editing LAURA F . LANDWEBE R 18 1

Universal computatio n vi a self-assembl y o f DNA : Som e theor y an d experiments ERIK WINFREE , XIAOPIN G YANG , AN D NADRIA N C . SEEMA N 19 1

The peril s o f polynucleotides : Th e experimenta l ga p betwee n th e desig n an d assembly o f unusua l DN A structure s NADRIAN C . SEEMAN , HU I WANG , BIN G LIU , JIN G Q I , XIAOJU N

LI, XIAOPIN G YANG , FURON G LIU , WEIQION G SUN , ZHIYON G

SHEN, RUOJI E SHA , CHENGD E MAO , YINL I WANG , SIWE I ZHANG ,

Tsu-Ju Fu , SHOUMIN G DU , JOH N E . MUELLER , YUWE N ZHANG ,

AND JUNGHUE I CHE N 21 5

DNA sequence s usefu l fo r computatio n ERIC B . BAU M 23 5

A restricte d geneti c alphabe t fo r DN A computin g KALIM U . M I R 24 3

Good encoding s fo r DNA-base d solution s t o combinatoria l problem s R. DEATON , R . C . MURPHY , M . GARZON , D . R . FRANCESCHETTI ,

AND S . E . STEVENS , J R . 24 7

DNA computation s ca n hav e globa l memor y RICHARD J . LIPTO N 25 9

Exascale compute r algebr a problem s interconnec t wit h molecula r reaction s and complexit y theor y ROBERT M . WILLIAM S AN D DAVI D HARLA N W O O D 26 7

Foreword

The Secon d Annua l Worksho p o n DN A Base d Computer s wa s hel d o n Jun e 10-12, 199 6 a t Princeto n University , N . J . W e would lik e t o expres s ou r apprecia -tion t o Eri c Baum , Da n Boneh , Pete r Kaplan , Richar d Lipton , Joh n Reif , an d Nadrian Seema n fo r thei r effort s t o organiz e an d pla n thi s successfu l workshop .

The Worksho p wa s par t o f the broade r Specia l Yea r o n DN A Computing . W e extend ou r thank s t o Richar d Lipto n an d Laur a Landwebe r fo r thei r wor k ove r many month s a s Specia l Yea r organizers .

The Worksho p wa s a foru m fo r bringin g togethe r researcher s workin g o n al l areas tha t relat e directl y t o computin g wit h DNA , includin g algorithms , applica -tions, techniques , architectures , computationa l processe s i n vivo, and relevan t idea s regarding biologica l evolution .

DIMACS gratefull y acknowledge s th e generou s suppor t tha t make s thes e pro -grams possible . Th e Nationa l Scienc e Foundation , throug h it s Scienc e an d Tech -nology Cente r program , th e Ne w Jerse y Commissio n o n Scienc e an d Technology , and DIMACS ' partner s a t Rutgers , Princeton , AT& T Lab s Research , Bel l Labs , and Bellcor e generousl y supporte d th e Specia l Year .

Fred S . Robert s Director

Bernard Chazell e Co-Director fo r Princeto n

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Introduction

DNA Computin g ha s fuele d a tremendou s amoun t o f excitemen t b y offerin g a fresh paradig m fo r performin g an d viewin g computations : thi s i s biological mathe -matics, whil e als o mathematical biology . Encodin g o f data i n DN A string s couple d with th e powe r o f molecular biolog y no w allows the executio n o f computational op -erations on single strands o f DNA in the laboratory . A s a small drop of solution ca n house several quadrillion DN A molecules, DNA computers use much less energy an d space tha n traditiona l computers . Consequently , the y offe r th e tantalizin g poten -tial o f on e da y outperformin g electroni c computers . Computin g wit h DN A i s als o massively parallel , wit h billion s an d trillion s o f molecules undergoin g simultaneou s chemical reaction s an d performin g computation s almos t spontaneously .

The produc t o f a radicall y differen t marriag e o f compute r scienc e t o molec -ular biology , th e fledglin g fiel d o f DN A computer s bega n i n 1994 , whe n Leonar d Adleman surprise d th e scientifi c communit y b y usin g DN A molecules , protei n en -zymes, and chemical s t o solv e an instanc e o f a hard computationa l problem . Thes e proceedings fro m th e Secon d DIMAC S Worksho p o n DN A Base d Computer s a t Princeton Universit y - hel d onl y on e year an d a hal f afte r th e publicatio n o f Adle -man's semina l experimen t - contai n a se t o f referee d paper s tha t highligh t som e of the excitin g progres s i n thi s fiel d an d togethe r buil d a stron g foundatio n fo r th e current theor y o f molecula r computation .

This volum e introduce s suc h importan t advance s a s "mar k an d destroy " DN A algorithms an d th e us e o f surface chemistr y i n DN A computing . I t als o include s a healthy discussio n o f the myria d possibilitie s a s wel l a s potentia l pitfalls , mean s o f error correction, an d genera l practicality o f building DNA based computers. Severa l articles draw on the analog y betwee n DN A computin g an d othe r cuttin g edge field s of biology such a s directed evolution . I n principle, both type s of experiments searc h for a single or unique class of molecules in a random o r heterogeneous mixture . Suc h techniques have been enormously successfu l i n discovering biologica l molecules wit h novel capacitie s fo r performin g chemica l reactions . A s thes e molecule s ca n eve n encode th e solutio n t o a mathematica l problem , nuclei c aci d base d computer s ma y be viewe d a s a natura l extensio n o f test-tub e evolutio n experiment s tha t searc h a defined spac e o f mathematica l solutions . Indeed , the y ar e "solution s o f solutions! "

Laura F . Landweber , Princeto n Universit y

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Acknowledgements

We gratefully acknowledg e th e generou s suppor t fro m ou r sponsors : DI M ACS, NSF, an d th e NE C Researc h Institute . W e als o than k th e othe r member s o f th e program committe e - Da n Boneh , Pete r Kaplan , Richar d Lipton , Joh n Reif , an d Nadrian Seema n - fo r helpin g t o organiz e th e conference . Lastly , w e especiall y thank To m Hagedor n fo r helpin g t o produc e thi s volume .

Laura Landweber , Princeto n Universit y

Eric Baum , NE C

XI

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