Problem

1. Programming Bacterial Computers for Network OptimizationorUsing Punctuated Equilibrium for Network Optimization

2. Problem • Given a desired network of gene expression • Magnetosome • Enzymes in a metabolic pathway • Subunits of a protein • Other examples??? • Optimal function of network sensitive to • Levels of node components • Interactions among node components • Interactions with other genome-encoded elements • How can combinatorics be used to optimize the function of a network?

3. Expression of Problem D B C Desired Network Function A Various Network States • The graph shows the desired network function • Starting at positions A or C, the network can be improved incrementally by small changes, perhaps achieving the local maximum at B • If larger changes can be introduced into the network, the distant, higher maximum at D could be found

4. Golden Gate Combinatorial Diversity LVA LVA LVA LVA s Genes u Degradation tags n Promoters t RBS http://2011.igem.org/Team:Washington/Magnetosomes/Background

5. Too Many Combinations • The number of combinations for the network is given by: N = (n x t x u)s • Example • There are 19 promoters in the J23100 series alone • There are 5 commonly used RBSs • Consider a network that involves 6 genes • There are at least 4 degradation tags in the Registry N = (19 x 5 x 4) 6 = 3 x 1015

6. Solution • 3 x 1015 combinations is too many to search through, even with selection • Solution may be to conduct stages • Search for best combinations of promoters • Search for best RBSs • Search for best degradation tags • Repeat

7. Golden Gate Combinatorial Diversity assemble in vitro test and select in vivo isolate and sequence copy number variations via plasmids allow for random mutations and sequence genome

8. Principles • Bacteria already are computers • They take in input, manipulate data, produce output • They have existing hardware that we can exploit • We can learn how to program bacterial computers with living algorithms • Gain control of existing networks and to produce new ones • Bacteria could learn to address problems through selection of networks • Tune the network • Determine the importance of nodes

9. Starting Constructs Word1 Word2 LVA Gene 1 BsaI BsaI BsaI BsaI BsaI BsaI BsaI BsaI Word1 Word2 Gene 2 LVA Word1 Word2 Gene 3 LVA Word1 Word2 LVA Gene 4

10. Promoter Library Word1 Word2 BsaI BsaI BsaI BsaI BsaI BsaI BsaI BsaI Word1 Word2 Word1 Word2 Word1 Word2

11. First Stage Procedure • Use BsaI GGA to generate a combinatorial library of promoters connected to one type of RBS and the network genes • Select first layer of network based on output • Sequence members of population • Move on to Second Stage

12. Second Stage Procedure • Use BsmBI GGA to generate a combinatorial library of RBS elements connected to each of the network genes • Select second layer of network based on output • Sequence members of population • Move on to Third Stage

13. Second Stage Word3 Word4 LVA Gene 1 BsmBI BsmBI BsmBI sites are used to insert various RBS elements

14. Third Stage Procedure • Use BtsI GGA to generate a combinatorial library of Degradation tags connected to each of the network genes • Select third layer of network based on output • Sequence members of population • Repeat Stages 1 and 2 or • Move on to Hypermutation Stage

15. Third Stage Word3 Word4 Gene 1 LVA BtsI BtsI BtsI sites are used to insert various LVA elements

16. Hypermutation Stage • Find conditions under which hypermutation occurs in E. coli (????) • Select for clones that have increased network function • Sequence genome of interesting clones to discover mutations of various genes • Optional: perform some type of subtraction experiment to sort out mutations that several clones have in common

17. Possible math connections 6 15 13 14 2 7 3 10 4 5 1 9 8 12 11 Graph Search Algorithms – Finding local maxima

18. 6 15 13 14 2 7 3 10 4 5 1 9 8 12 11 Possible math connections Algorithm 1: (Maximal improvement) Beginning at a node, move to the adjacent node with largest improvement (in absolute size or percentage). If no such node exists, then at local max. Each node will go to exactly one local max (assuming no ties).

19. Possible math connections Algorithm 1: (Maximal improvement) Beginning at a node, move to the adjacent node with largest improvement (in absolute size or percentage). If no such node exists, then at local max. Each node will go to exactly one local max (assuming no ties). 6 15 2 13 14 7 3 10 4 5 1 9 8 12 11

20. 6 15 13 14 2 7 3 10 4 5 1 9 8 12 11 Possible math connections Algorithm 2: (Do no harm) Beginning at a node, move to an adjacent node with a larger number. If no such node exists, then at local max. Some nodes can go to only one local max, others can go to more than one. This leads to probabilistic questions. (Which ending more likely?)

21. Possible math connections Algorithm 2: (Do no harm) Beginning at a node, move to an adjacent node with a larger number. If no such node exists, then at local max. Some nodes can go to only one local max, others can go to more than one. This leads to probabilistic questions. (Which ending more likely?) 6 15 13 14 2 7 3 10 4 5 1 9 8 12 11

22. Possible math questions • How many local maxima are there? • How many starting points lead to each local max? • How many starting points lead to only one max? • What is the longest path to each local max? • If steps are restricted to k steps, what are possible ending states? • Is there a node in the graph that leads to all local max (using Algorithm 2)? • What about ties? • How many starting points would need to chosen to be confident that each local max is found for a particular graph? • What information can be gained from the unlabeled graph? • Connections to Mastermind?