Information Propagation In Populations by Conjugation Justyn Jaworski

Overview Motivation Model Design Preliminary Results & Interpretation Necessary Modifications for Model

Motivation Interested in a probabilistic model for identifying information propagation in a population via a transmissible plasmids. Determine the distribution of E. coli having received the information Determine the distribution of E. coli having received the information Want to determine transient response of information spreading throughout the system Want to determine transient response of information spreading throughout the system

Two Major Components to Model

Bacterial Conjugation Bacterial plasmids may contain a “fertility factor” F+ Plasmids known as F + are capable of transfer of ssDNA Cells containing F + can conjugate with other bacteria via pilus F+F+ F-F- F Pilus Formation F FF F+F+

Phases of Bacterial Growth in Batch Culture Lag Phase Acclimate to the food of their new environment Acclimate to the food of their new environment Log Phase Exponential Doubling Exponential Doubling Stationary Phase Number of bacteria stabilizes to balance competition for food Number of bacteria stabilizes to balance competition for food Death Phase Food is depleted Food is depleted Waste accumulates Waste accumulates

Basic Assumptions Growth Perfectly Mixed – No migratory considerations Perfectly Mixed – No migratory considerations No cell death (not interested in system once death phase occurs) No cell death (not interested in system once death phase occurs) Populations multiply at plasmid number dependent rate Populations multiply at plasmid number dependent rate More plasmids require a longer replication time Conjugation Only two cells can conjugate Only two cells can conjugate Conjugation is temperature independent (within reason) Conjugation is temperature independent (within reason) Transfer of only one plasmid at a time Transfer of only one plasmid at a time Transfer is always unidirectional; F+ (donor) to F- (recipient) Transfer is always unidirectional; F+ (donor) to F- (recipient) One copy always remains in the donor by rolling replication One copy always remains in the donor by rolling replication

System Parameters Conjugation Plasmid Transfer Rate = 1.2E-7 (mL/h*cell) Plasmid Transfer Rate = 1.2E-7 (mL/h*cell) Variable with concentration Variable with concentrationReplication Generation Time---- Double every 26.5 minutes Generation Time---- Double every 26.5 minutes Max concentration 10^9 cells/ml

Gillespie algorithm for modeling conjugation In this case n i is always 1 so a u is simplified to a u =c u *x D *x R a u represents the conjugation rate a u represents the conjugation rate X D represents number of donor cells X D represents number of donor cells X R represents the number of recipient cells X R represents the number of recipient cells (May already contain mobile plasmid though some systems ensure that recipient cell does not already contain a similar element.) C u represent stochastic transfer rate constant C u represent stochastic transfer rate constant C u =transfer rate * concentration

Initial Results CONSTANT FRACTION OF INFORMATION Previously thought doubling time was so fast that fraction of information in system was constant Previously thought doubling time was so fast that fraction of information in system was constant Considered a potential correction may be to slow the rate of replications since conjugation rate is constant Has shown effective in system of plate grown 25C Has shown effective in system of plate grown 25C The actual problem was that I had not yet taken into account transconjugation Plasmid transfer of F factor which allows “infected” recipient bacteria to then become a donor bacteria. Plasmid transfer of F factor which allows “infected” recipient bacteria to then become a donor bacteria. Now it becomes more like an epidemic model.

Results from Today Time constant for (10% Seed) Ci = 100 cell/ml Ci = 100 cell/ml Tc = 34.5 hrs Ci = 1000 cells/ml Ci = 1000 cells/ml Tc = 27 hrs Ci =10000 cells/ml Ci =10000 cells/ml Tc = 32.8 hrs Tc decreases for Ci increases above Tc decreases for Ci increases above : % of cells w/o information after 48 hours : % of cells w/o information after 48 hours 50% Seed Concentration % ERROR 50% Seed Concentration % ERROR 10% Seed Concentration % ERROR 10% Seed Concentration % ERROR 1% Seed Concentration % ERROR 1% Seed Concentration % ERROR Seed Percentage = Initial # Donor Cells / Total # Cells

Necessary Modifications N = Number of mobilizable plasmids in recipient cell Very rarely plasmid is incorporated in chromosome Transfer occurs but not completely for recipient to become F+ (no-transfer state) Transfer occurs but not completely for recipient to become F+ (no-transfer state) Conjugation takes longer (approx 100 minutes) Conjugation takes longer (approx 100 minutes) Account for NON-transmission of plasmid Two Potential Plasmid Transfer States Two Potential Plasmid Transfer States A transfers to B N(t+dt) = N(t) + 1 N(t+dt) = N(t) + 1 No transfer occurs N(t+dt) = N(t) Need a conjugation wait time Approx. 100 minutes during which division is halted for the conjugating pairs Approx. 100 minutes during which division is halted for the conjugating pairs

What do we want to finally get from the simulations? Transient response of information movement through the growing network Rate of error and information movement Proportion of cells with information at stationary phase Identify competition for mobilizable plasmids Wetlab Validation of Model Flow cytometry to count proportion of cells that possess the program (mobilizable plasmid)

Questions