1ESM 219Lecture 4: Growth and KineticsConcepts•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 termsUnrestricted Cell division = population growthX = 2nX = number of cellsn = number of division events (doublings)At the beginning, X = 20= 121= 222= 4, etc…….Population growth, X = 2n (cont.)Let n = (# doublings / time) * t= growth rate constant * t= μ*twhere μ= “specific growth rate”Notice that equation is exponential,so can express as X = eμtNote that starting concentration is not 1,So X = Xoeμtwhere Xois the initial concentration.Unrestricted cell division is a “first order” rate process•Unrestricted cell division is a first order rate process.())eX(dtdXdtdt0μ=XdtdXμ=So, …..XdtdXμ=∫∫======ttttttdtXdXdtXdX00μμeXXXXttttμμ00ln==Now let’s go the other direction…..Separate variables.Integrate over the interval 0 to t.The result is a straight line equation….tXXμ+=0lnlnAnd if we raised e to both sides, we’d beback where we started…
has intentionally blurred sections.
Sign up to view the full version.
2During exponential phase growth, a log-linear plot produces a straight line, becausetXXμ+=)ln()ln(0Microbial Laboratory CultureWell-mixed liquid(flask or culture tubeor 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 concentration1.Direct counts with a microscopeHow to measure cell concentration2.Culturable countsWith or without a dilution series.