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Lecture_5_ESM219_07

# Lecture_5_ESM219_07 - Concepts ESM 219 Lecture 4 Growth and...

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1 ESM 219 Lecture 4: Growth and Kinetics Concepts Concerned with populations of cells and population numbers and characteristics Various ways to report population sizes Unrestricted cellular division is well- understood Mass transfer-limited growth models, including on solid media, involve more terms Unrestricted Cell division = population growth X = 2 n X = number of cells n = number of division events (doublings) At the beginning, X = 2 0 = 1 2 1 = 2 2 2 = 4, etc……. Population growth, X = 2 n (cont.) Let n = (# doublings / time) * t = growth rate constant * t = μ *t where μ = “specific growth rate” Notice that equation is exponential, so can express as X = e μ t Note that starting concentration is not 1, So X = X o e μ t where X o is the initial concentration. Unrestricted cell division is a “first order” rate process Unrestricted cell division is a first order rate process. ( ) ) e X ( dt d X dt d t 0 μ = X dt dX μ = So, ….. X dt dX μ = = = = = = = t t t t t t dt X dX dt X dX 0 0 μ μ e X X X X t t t t μ μ 0 0 ln = = Now let’s go the other direction….. Separate variables. Integrate over the interval 0 to t. The result is a straight line equation…. t X X μ + = 0 ln ln And if we raised e to both sides, we’d be back where we started…

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2 During exponential phase growth, a log-linear plot produces a straight line, because t X X μ + = ) ln( ) ln( 0 Microbial Laboratory Culture Well-mixed liquid (flask or culture tube or chemostat) Solid media culture (agar or sand culture) In all cases Prepare media with nutrients, and establish conditions required for growth • Inoculate With a small amount of known cells for pure culture With an environmental sample for enrichment culture Monitor over time Quantify population size at various time points Or measure / observe beginning and end. How to measure cell concentration 1. Direct counts with a microscope How to measure cell concentration 2. Culturable counts With or without a dilution series.