Mutation Rates of Escherichia Coli with Different Balanced Growth Rates: a New Fluctuation Test Protocol and Phenotypic Lag Adju

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Mutation Rates of Escherichia Coli with Different Balanced Growth Rates: a New Fluctuation Test Protocol and Phenotypic Lag Adju Mutation rates of Escherichia coli with different balanced growth rates: a new fluctuation test protocol and phenotypic lag adjustments by Christian Terry Henderson Barna A thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Master of Mathematics in Applied Mathematics Waterloo, Ontario, Canada, 2020 c Christian Terry Henderson Barna 2020 Author's Declaration I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract Bacteria are the oldest, most abundant life form on the planet, and every other organ- ism's livelihood is dependent on them. The bacteria Escherichia coli (E. coli) is commonly used in microbiology as a model organism to give insight into the functions of bacteria and cells in general. Of particular interest in these studies is the methods with which bacteria grow and evolve. Growth is what propagates a bacteria's species; whereas evolution is what allows them to adapt to the ever-changing world. Evolution is made possible by mutations which change a bacterium's DNA. In 1943, Luria and Delbr¨uck developed a method, called a “fluctuation test", to estimate mutation rates from the number of mutants in a collection of parallel cultures exposed to a selecting agent after growth. The original fluctuation test methodology suffers from two major limitations. First, the bacteria are not in a re- producible, balanced state of growth throughout the test. Second, the new phenotype resulting from a mutation may not be immediately expressed (referred to as \phenotypic lag") resulting in an underestimated mutation rate. To overcome these issues, I developed a refined experimental protocol that ensures cells are in balanced growth and a suite of analysis tools that account for the effects of phenotypic lag. To test the methodology, I compared the mutation rate and phenotypic lag in fast growing E. coli (23 minutes per doubling) and slow growing E. coli (48 minutes per doubling). It is found that when not accounting for phenotypic lag, fast growing E. coli have a markedly lower mutation rate than slow growing E. coli, but when phenotypic lag is accounted for, the faster growing cells have a longer phenotypic lag, resulting in an indistinguishable mutation rate for fast and slow growing populations. The implications of mutation rate being coupled to growth rate, as well as possible explanations for why it and phenotypic lag would be growth rate dependent are discussed. Finally, possible ways to improve the experimental methodology and analysis protocols, in addition to future experiments that can be performed to further explore mutation rate - growth rate coupling are proposed. iii Acknowledgements All research for this thesis was completed on the lands of the Haudenosaunee, Anishi- naabeg, and Neutral peoples [165]. I have lived in the valley of the Ose'kow´ahne(\Grand River") [7] for the majority of my life, completing grades 1-12, a B.Sc., and now a Masters here. This means I have spent over 20 years reaping the benefits of being a white settler on stolen First Nation land, and for much of it I wasn't even aware. The entirety of Kitchener- Waterloo is situated on treaty land that was taken from the people it was promised to. In fact, all land within 6 miles of the \Grand River" was promised to the Haudenosaunee as part of the Haldimand proclamation in 1784 [111], but now they control less than 5% of this land due to manipulation and forceful displacement. From time immemorial the First Nations peoples have been caring for the land we call home, and for the last several hundred years they have been battling white supremacy and its destructive perception of land [39]. If we wish to have a healthy planet and just society, I believe that we have to give control of all land that is considered \North America" and beyond back to the indigenous peoples. It is possible to live sustainably on this land, but to do so we must de-colonise our minds and re-learn what our place on this planet is. I want to thank the earth for giving me everything I need to survive and do all this science. Doing science requires resources that come from the earth, and most are extracted in an unsustainable and unethical fashion. I can confidently say that I used more plastic during this masters degree than I normally would in a decade. This has been a source for much internal conflict and has helped shape my perception of science's role in society. I think all scientists need to look at their research and seriously question if the potential re- sults are worth the resources being consumed and the ethical implications. We desperately need a more ethical and sustainable way to do science, and if we need to take a break from actively doing science in the mean time, I think that's a fair trade. An extra big thank you to Matt Scott. Your patience and guidance over the last 3 years is appreciated beyond belief; I truly could not have asked for a better supervisor. You have taught me so much about what it means to be a good scientist, as well as a good teacher and mentor. I always looked forward to our meetings and seeing your big smile in the halls. I sincerely hope our paths cross again in the future. Thank you to Brian Ingalls for being much like a co-supervisor to me. Your guidance, insight, and general presence were incredibly appreciated. Thank you Ed Vrscay for agreeing to be on my committee and making my introduction to university level mathematics nearly 10 years ago so fun. iv Thank you to my parents, Lynne and Terry Barna, for your support over the last 28 years and in particular over the last 3 years. Raising me and allowing me to mooch off you for so long is so very appreciated. I couldn't have done this without you! Thank you to Micaela Yawney, your love and support over the last year has kept me going. I'm so happy we met and have got to spend so much time getting to know each other during my masters. Here's to our future adventures together! Thank you to my office mates. Jesse Legaspi, you are the funniest, most wonderful human who's memes and video game nights got me through. Josh Thompson, it was always nice having someone to relate to and relax with. Tim Dockhorn, thank you for lending me your brain on occasion and all the good tennis matches. Rishi Chakraborty, thank you for laughing at my jokes and always keeping an open mind. Greg Wang, thank you for your smile and giant heart. Thank you to all my lab mates. Nate Braniff, I don't think I could ever truly communi- cate how much help you were to me through this degree; you provided great conversation, great ideas, great lab help, and great friendship. Nicole Wang, Linda Chan, Sarah Odinot- ski, Yesha Patel, Leah Fulton, Max Reed, Fatima Abrar, and Cody Receno, thank you for helping and keeping me company in the lab. Extra big shout out to everyone who helped me count plates! Thank you to all my other friends in the Applied Math department. Lizz Webb, thank you for sharing all that hot goss and candy. Tom Bury, thank you for the conversations and racket sports games. Kat Fair, thank you for all the awesome conversations, especially about radical politics. Laura Chandler, Kate Clements, Stan Zonov, Saptarshi Pal, Sarah Walsh, Lindsey Daniels, Zahraa Abbas, Taylor Hanson, Maliha Ahmed, Alison Cheeseman, Andrew Grace, Maria Papageorgiou, Vivek Thampi, Brendon Phillips, Lauren Burnett, Giselle Sosa Jones, Luciana Chavez Rodriguez, and Ben Storer you all helped make this experience fun. Thank you to my Outers Club friends. Tim Hill, Claire Parrott, Evan Takefman, Nicole Sos, Elif Tuzlali, and Kanishk Goomer, you all made running Outers so rewarding and fun. Thank you to all my friends and family. Emma McKay, you are truly the best friend a person can ask for; you have taught and given me so much and for this I will forever be grateful. Shane Lawrence, your friendship and belief in me keeps me going on hard days. Seth Holland, I'm always happy when we get to chat about science and slap our hands together. Martin Bauman, I wish I got to ride on your shoulders more, but I still appreciate your friendship immensely. Rachel Barna, your support and jokes are food for my soul. Maddy MacEachern, I was gonna make an R2D2 and C3PO reference, but we're both R2D2 so that doesn't work; you get the point though. Mary Tye, you are the kindest v most wonderfulest. Alex Pearce, you are also the kindest most wonderfulest. Ilia Poichuck, you're so compassionate and fun and I am very happy we were reunited. David Paton, Will Gertler, Erin & Kyle Wagstaff, Qui Crawford, Graham Notar-Maclean, Nathan Butt, Palmer Vaughn, Saam Koukpari, Claire Leuty, Al Sachs, Ashley Beitel, Tiana Van De Veerdonk, Emily Carlson, Jackson Smith, Warren Jones, Giulia Langella, Aidan Power, Emma Raaflaub, and more, you all make being in this world so much more enjoyable. Thank you to the D&D group that gave me something to look forward to and a world to escape to most weeks. Finally, a big shout out to ice cream, peanut butter, and chocolate for helping me get through these wild times people call grad school.
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