MAPMEN THE TRAVELLING SALESMAN PROBLEM solutions. 2 THE TRAVELLING - PowerPoint PPT Presentation

MAPMEN �

THE TRAVELLING SALESMAN PROBLEM solutions. 2

THE TRAVELLING SALESMAN PROBLEM y is the TSP impor 3

THE TRAVELLING SALESMAN PROBLEM y is the TSP impor 3

THE TRAVELLING SALESMAN PROBLEM y is the TSP impor 3

THE TRAVELLING SALESMAN PROBLEM y is the TSP impor 3

THE TRAVELLING SALESMAN PROBLEM y is the TSP impor 3

THE TRAVELLING SALESMAN PROBLEM y is the TSP impor 3

THE TRAVELLING SALESMAN PROBLEM Number of Cities Number of Routes Brute Force Time* 4 3 1 / 3 millisecond 5 12 1 millisecond 10 181 440 18 seconds 13 239 500 800 7 hours 15 43 589 145 600 50 days 16 653 837 184 000 2 years 20 60 822 550 000 000 000 193 millennia *Assuming 10 000 routes mapped per second. 4

HAMILTONIAN GRAPH PROBLEM 4

COMPUTATION IN BIOLOGICAL TERMS solutions.

COMPUTATION IN BIOLOGICAL TERMS ApR ClrR KanR RFP GFP aCP A A C G C G K R K R B B purple/AmpR/KanR Green/AmpR/ClrR Orange/KanR/ClrR 5

COMPUTATION IN BIOLOGICAL TERMS ApR ClrR KanR RFP GFP aCP ApR ClrR ApR RFP GFP RFP Ori Ori Ori GFP aCP aCP ClrR KanR KanR 5

COMBINATORIAL PLASMID ASSEMBLY 6

COMBINATORIAL PLASMID ASSEMBLY A unique solution It’s plasmid analogue ClrR C RFP Ori R K G GFP KanR A 10-piece sequential assembly Step ClrR KanR Ori RFP GFP dT 18 dA 18 10 8 6 7 4 Kan/Chlr

COMBINATORIAL PLASMID ASSEMBLY Kan/Chlr transformation 652 complete solutions (orange colonies) 69 incomplete solutions (red +green colonies) 8

PLASMID IDENTIFICATION BY PHENOTYPE 8

PROOF OF PRINCIPLE 1 ¡ ApR ClrR KanR RFP 1 ¡ 1 ¡ GFP 1 ¡ aCP 10

PROOF OF PRINCIPLE 11

PROOF OF PRINCIPLE 12

PROOF OF PRINCIPLE 12

PROOF OF PRINCIPLE 13

PHASE II: FIFTEEN CITY PROBLEM 120 inter-city paths 43 589 145 600 unique routes The 15-city problem 14

PHASE II: FIFTEEN CITY PROBLEM T A K H C S D E R P N W Q Y F cities are represented by essential genes selected Cities are represented by A strain of E. coli that from 15 amino acid biosynthetic pathways essential genes selected Assembly step: N carries deletions for the from 15 amino acid 15 city genes. biosynthetic pathways. 15

REVISED CITY-PATH STRATEGY 16

CONSTRUCTING A COSMID LIBRARY 17

PCR ANALYSIS 18

THE BIOCOMPUTATIONAL ADVANTAGE • A complete library of solutions can be created through simultaneous in vitro manipulation of 10 9 to 10 12 DNA molecules. • Solutions can be hierarchically biased and amplified toward the best using… o Sequential gene assembly o Accurate distance-to-concentration conversion o Phage packaging o Essential genes for all cities Eliminating the cost of complexity 18

THANK YOU & ACKNOWLEDGEMENTS 23