54 GROWTH CURVES OF BACTERIA 



slowly or not at all until a certain minimum concentration of carbon dioxide is pres- 

 ent. This would lead to the development of a definite lag phase which would be much 

 longer with small than with large seedings. Slator has shown that when very large 

 inocula of yeast are used there may be no logarithmic phase. 



EFFECT OF CONCENTRATION OF CONSTITUENTS OF SUBSTRATE 

 UPON GROWTH CURVES 



The various constituents of the culture medium may act either as accelerators or 

 inhibitors of growth. The effect upon rates of increase is in general a function of the 

 concentration. The exact relationship may be most satisfactorily evaluated usually 

 by comparison of the rates of increase per cell {k) in different concentrations during 

 the logarithmic growth phase. In chemical reactions generally it is found that the 

 velocity coefficient of the rate of the reaction varies directly as some constant power 

 of the concentration of the reactant. It is frequently advisable, as a first approxima- 

 tion, to test the hypothesis that a similar relationship holds between rate of increase 

 and concentration of a nutrient or inhibiting agent. This would give the relationship 



Integration yields 

 in which 



f^=KC^b (i8) 



In b^KCH+ln B (19) 



/ir = Constant 



C= Concentration of chemical 



«= Constant 



It is apparent that the velocity coefficient (rate of increase per cell, k) is evaluated as 



k=KC^ (20) 



A determination of the validity of this relationship with varying concentrations may 

 be made by plotting the logarithms of the velocity coefficients {k) against the log- 

 arithms of the concentrations. Since 



log ^ = w log C+log i? (21) 



a straight line should be developed with slope n. If increase in concentration increases 

 the growth rate, n will be positive; if it inhibits, n will be negative. 



EFFECT OF TEMPERATURE UPON THE FORM OF GROWTH CURVES 



The effect of temperature changes upon rates of increase is usually best evaluated 

 by comparisons of the velocity coefficients {k) during logarithmic growth. It is cus- 

 tomary to designate the ratio between the velocity constants at the higher and at the 

 lower temperature as the temperature quotient (Q). The temperature interval for 

 which determinations are usually made is 10° C. For this interxal the quotient is 

 commonly designated as ()i„. 



It is frequently desirable to determine whether temperature effects upon growth 



