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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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