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1. 4. 3. 2. 5. Living Hardware to Solve the Hamiltonian Path Problem Davidson College: Oyinade Adefuye, Will DeLoache, Jim Dickson, Andrew Martens, Amber Shoecraft, Mike Waters, Dr. A. Malcolm Campbell, Dr. Karmella Haynes, Dr. Laurie Heyer

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Living Hardware to Solve the Hamiltonian Path Problem

Davidson College: Oyinade Adefuye, Will DeLoache, Jim Dickson, Andrew Martens, Amber Shoecraft, Mike Waters,

Dr. A. Malcolm Campbell, Dr. Karmella Haynes, Dr. Laurie Heyer

Missouri Western State University: Jordan Baumgardner, Tom Crowley, Lane Heard, Nick Morton, Michelle Ritter, Jessica Treece, Matthew Unzicker, Amanda Valencia, Dr. Todd Eckdahl, Dr. Jeff Poet

Abstract

Modeling a Bacterial Computer

Bacteria Successfully Solve the Problem!

Silicon computers are powerful tools for solving mathematical problems but are inefficient parallel processors. For iGEM2007, Davidson College and Missouri Western State University have jointly developed a bacterial system capable of solving a Hamiltonian Path Problem in vivo. Our system takes advantage of E. coli’s exponential growth to address the complexity of this problem in a way that traditional computers cannot. We successfully detected solutions to a Hamiltonian Path Problem through phenotypic screening.

To determine the feasibility of our system, weimplemented mathematical models to answer to following questions:

The HPP constructs were transformed into E. coli expressing T7 RNA polymerase, and their phenotypes were observed. After about two days, they had visible color. “Unflipped” colonies exhibited uniform fluorescent phenotypes, while colonies exposed to Hin protein varied in their fluorescence. Fluorescent phenotypes were observed by eye and confirmed by fluorometer.

Does starting orientation matter?

No, after a large number of flips, all orientations converge to the same probability.

4 Nodes & 3 Edges

Probability of HPP Solution

Can we detect a solution?

Yes, for a 14-edge graph with 7 nodes, growing 1 billion bacterial computers gives a 99.9% chance of detecting a solution. We determined this using a cumulative Poisson distribution. 1 mL of culture contains 1 billion bacteria.

Number of Flips

The Hamiltonian Path Problem

The Hamiltonian Problem (HPP) asks: given a directed graph with designated starting and ending nodes, is it possible to travel through the graph visiting every node exactly once?

Cumulative Poisson Distribution

Are there too many false positives?

No, using MATLAB, we computed the ratio of true positive to total positives and found that even for a 14-edge graph, the ratio was above 0.05. Combined with PCR screening, this ratio is well within detectable limits.

Linear increases in graph complexity yield exponential increases in the number of possible paths through a graph. Due to the absence of an efficient algorithm, parallel processing is required when attempting to solve complex graphs in a limited amount of time. The exponential growth of E. coli computers provides the required processing power.

Possible Paths through the graph

Extra Edge

False Positive

PCR Fragment Length

# of Edges in Graph

True Positive

PCR Fragment Length

# of Processors

Building a Bacterial Computer

Flipping was also detected by PCR, using multiplex primers that bound to three distinct regions of the HPP-A constructs. Different edge orientations produce 8 unique PCR product lengths.

Both methods show strong evidence for flipping of DNA, and PCR shows that some of the bacteria may have solved the problem.

Cell Division

For our system to work, reporter genes must maintain functionality despite the addition of 13 amino acids. We were able to perform successful

Design Principles

Hin Hin Hin

MW ABC ACB BAC ABC ACB BAC

As a part of iGEM2006, we reconstituted a hin/hix DNA recombination mechanism as standard biobricks for use in E. coli. This system allows for rearrangement of DNA segments that are flanked by hixC sites and was implemented in our HPP computer in the following way:

hixC insertions in both GFP and RFP. We therefore designed the following HPP constructs to test our system on 2 simple graphs:

  • Represent each node as a reporter gene
  • Represent each edge as a flippable unit of DNA flanked by hixC sites
  • Flipping generates a random walk through the graph
  • A solution is screened for by phenotype

Acknowledgements

We thank The Duke Endowment, HHMI, NSF, Genome Consortium for Active Teaching, James G. Martin Genomics Program, MWSU Student Government Association, MWSU Student Excellence Fund, MWSU Foundation, and the MWSU Summer Research Institute. Team members Oyinade Adifuye and Amber Shoecraft are from North Carolina Central University and Johnson C. Smith University, respectively. Special thanks to the iGEM organizers and community. We had a great time!

hixC sites

Edge

Hin-mediated Recombination