Kinetics of Microbial Cell Growth

Nay 3.3 3.04.2023 Mathematics of growth hag Stationary . phase - - cannot dying. be process used for doubling time So only exponential phase! the organisms will double at a const interval in exponential phase in the time taken for a population the organism to double population or in number during a spenfie length of time - Generation time doubling time

20min 10min 60min 16 ( is in 2 population A can be unten 8 as 2 bacterium 'n' no.o generation No - -Imitial population Nf - -populatn at time 't' , n 4 n No of generations NE No 2n Take log on both the sides log Nt . - log No f 2log Antlogs n = lgy - log No 2 log 2 logNE - logNo 0.301 as the rate of growth in a batch culture system is given mean growth rate constant (k) expressed as gen /unit u Generation / hour K= n/t K= logNt - log No 3 0.301 t The population cull double in no. at a given length is mean gen time or doubling time (g) If the population doubles t=g = Nt = 2No double the populatn of initial populat K = log(2No) log No 0 log2 + log No - log No 0.301 g 0.301 g K 2 I K = 1 to g K 2 1/g

g is is me reciprical of mean grown rate const g-Y Nt : 109, No= 103, t= 10 hrs K= wg Nt logN. = log 10"-logio 0-301 (t) (0.301) (10) = 9 log 10 - 3 log 10 0.301110) = 9(1)-301 3 = 6/3 g - 1/k 1/2 = 2 gen/thr = 0.5 hr/gen Esomin/gent