Exercise No.5 Biotech

 

Kinetics of cell death The kinetics of cell death is an important consideration in design of sterilisation processes and in analysis of fermentations where substantial viability loss is expected. In a lethal environment, all cells in a population do not die at once. Deactivation of the culture occurs over a finite period of  time depending on the initial initial number of viable cells and the severity of the conditions imposed. imposed. Loss of cell viability can be described mathematically in the same way as enyme deactivation. The destru destructi ction on of micro! micro!or organ ganism ismss by steam steam "moist "moist heat# heat# at specif specific ic temper temperatu ature re can be de desc scri ribe bed d as a  first-order   chemical reaction provided if we considerer loss of viability not destruction.

r   $ k . %

&&'

(here, r  is  is rate of cell death,  % is number of viable cells, and k is the specific the specific death constant.

x,

If  is the cell concentration then rate of cell death can be expressed using cell concentration rather than cell number as)

 

r   $ k . *

…………2

(here, k is the specific death constant based on cell concentration and * is the concentration of viable cells. In a closed system, cell death is the only process that affecting viable cell concentration, the rate of cell death is e+ual to the rate of decrease in cell number. Therefore, from +. "'#)

 

r   $ !d%-dt $ k . %

&&&

If k is constant, then we can integrate +. "# to derive an expression for % as a function of time as )

 

!kt

%t-%/ $e

!kt

 %t  $ %/ .e

&&&...0

(here, %1 is the initial initial number of viable cells at time ero. Taking Taking natural logarithms of both sides of +. "0# we have )  

 

ln %t  $ ln%/ ! kt

 

 

ln (Nt/N0) =

-k t

………..5

2ccording to +. "3#, if first!order first!order death kinetics apply, then a plot of In  "%t-%/ # versus t gives a straight line with slope !k d.

4ig ' 5lots of the proportion of survivors and the natural logarithm of the proportion of survivors in a population of microorganisms sub6ected to a lethal temperature over a time period. The relationship displayed in 4ig. ' would be observed only with the steriliation of a pure culture in one physiological form, under ideal steriliation conditions. The value of k is not only species dependent, but dependent on the physiological form of the cell7 for example, the endospores of the genus Bacillus genus Bacillus are far more heat resistant than the vegetative cells. The relati relations onship hip of +. "3#7 "3#7 have confir confirmed med by the experi experimen mental tal measur measureme ements nts for many ve veget getat ativ ivee cell cells. s. 2s an ex exam ampl ple, e, data data for for therm thermal al de deat ath h of s sche cheri richi chiaa coli at various temperatures are shown in 4igure 8 given below.

 

4igure 8 9elationship between temperature and rate rate of thermal death for vegetative Escherichia vegetative  Escherichia coli coli cel cells. ls. "4rom :. 2iba, 2iba, 2.. 2.. ;umphr ;umphrey ey and %.4. 3,  Biochemical Engineering, 2cademic 5ress, %ew ?ork.# 2s we know know that that for any first! first!ord order er reacti reaction, on, the reacti reaction on rat ratee increa increases ses with increa increase se in temper tem peratu ature re due to an increa increase se in the reaction reaction rate constan constant. t. :imila :imilarly rly in the case of the destruction of micro!organisms, is the specific death rate (k) is same as  reaction rate constant. Theref The refore ore , k is a true constant only under constant temperature conditions. The relationship  between temperature and the reaction rate constant was demonstrated by b y 2rrhenius and may be represented by the e+uation)  d-dT .lnK $ a-9T8&&&&&&&&..>

(here a is the activation energy 9 is the gas constant T is the the absolute temperature 1n integrating e+. "># we have

k $ 2.e  @a-9T

&&&..A

 by taking natural logarithm in e+. "A# we have

lnk $ ln2!a-9T

&&&&B

 

Typical a values for thermal destruction of microorganisms are high, and will be generally 83/! 8=/ kC gmo'!'. Therefore, small increases in temperature have a significant effect on k  and   and rate of death.

4rom e+uation "B# it may be seen that a plot of Ink against the reciprocal of the absolute temperature will give a straight line. :uch a plot is termed an 2rrhenius plot which helps in the calculation of the activation energy and the prediction of the reaction rate for any temperature.

y combining together e+uations "3# and "A#, the following expression may be derived for  the heat steriliation of a pure culture at a constant temperature)  

ln %/-%t $ 2.t.e  @a-9T 

&&&&&&&.=

Deindo Dein doer erfe ferr an and d ;ump ;umphr hrey ey "'=3 "'=3=# =# us used ed the the te term rm ln(N0/Nt)  as a desig design n cr crite iterio rion n for for sterilization , which has been also called Del factor or Nabla factor and sterilization criterion represented by the term EF. Therefore we can say that the Del factor is a measure of the fractional reduction in iable organism count !roduced b" a certain heat and time regime. Therefore)

&&&&&'/ 1n rearranging, and taking natural logarithm of e+uation "'/# we have

&&&&&&&&&..'' Thus, a plot of the natural logarithm of the time re+uired to achieve a certain EF value against the reciprocal of the absolute temperature will yield a straight line, the slope of which is dependent on the activation energy, as shown in 4ig. 0 below. b elow.

 

4rom 4ig. 0 it is clear that the same degree of steriliation "EF# may be obtained over a wide range of time and temperature regimes7 that is, the same degree of steriliation may result from treatment at a high temperature for a short time as from a low temperature for a long time. This kinetic description of bacterial death give the design of procedures by giving certain value of EG factors factors for the steriliation of fermentation broths.

 

Huestiion '. The number of viable spores of a new strain Huestiion strain of acillus subtilis subtilis is measured measured as a function of time at various temperatures.

"a# Determine the activation energy for thermal death of . subtilis spores. "b# (hat is the specific death constant at '// "c# stimate the time re+uired to kill ==J of spores in a sample at '//