Microbial Kinetics and Substrate utilization in Fermentation

Batch culture and Kinetics of Microbial growth in batch culture After inoculation the growth rate of the cells gradually increases. The cells grow at a constant, maximum, rate and this period is known as the log or exponential, phase.

Growth of a typical microbial culture in batch conditions

The rate of growth is directly proportional to cell concentration or biomass- i.e. dx/dt α X dx/dt = μX ----------1 Where, X is the concentration of microbial biomass, t is time, in hours μ is the specific growth rate, in hours -1

On integration of equation (1) from t=0 to t=t ,we have: xt = xo e μt --------- 2 Where, Xo is the original biomass concentration, Xt is the biomass concentration after the time interval, t hours, e is the base of the natural logarithm.

On taking natural logarithms of equation (2) we have : In Xt = In Xo + μt (3)

Therefore, a plot of the natural logarithm of biomass concentration against time should yield a straight line, the slope of which would equal to μ. During the exponential phase nutrients are in excess and the organism is growing at its maximum specific growth rate, ‘μmax ‘ for the prevailing conditions.

Typical values of μmax for a range of microorganisms are given below in the Table.

Effect of substrate concentration on microbial growth Whether the organism is unicellular or mycelia the growth is influenced by consumption of nutrients and the excretion of products. The cessation of growth may be due to the depletion of essential nutrient in the medium (substrate limitatioln), the accumulation of some autotoxic product of the organism in the medium (toxin limitation) or a combination of the substrate limitation and toxin limitation. The nature of the limitation of growth may be discussed by growing the organism in the presence of a range of substrate concentrations and plotting the biomass concentration at stationary phase against the initial substrate concentration is shown given below in fig 2: FIG. 2. The effect of initial substrate concentration on the biomass concentration at the onset of stationary phase, in batch culture.

From figure 2 it may be seen that over the zone A to B due to an increase in initial substrate concentration gives a proportional increase in the biomass occur at stationary phase. This relation between increase in initial substrate concentration and proportional increase in the biomass may be described by equation: X = Y(SR - s) ---------(3) Where, X -is the concentration of biomass produced, Y -is the yield factor (g biomass produced g-1 substrate consumed), SR -is the initial substrate concentration, and s -is the residual substrate concentration. Thus, equation (3) may be used to predict the production of biomass from a certain amount of substrate

In Fig. 2:- Over the zone A to B: s = 0; at the point of cessation of growth. Over the zone C to D an increase in the initial substrate concentration does give a proportional increase in biomass due to the exhaustion of another substrate or the accumulation of toxic products

Monod Equation The decrease in growth rate and the cessation of growth due to the depletion of substrate, may be described by the relationship between μ and the residual growth limiting substrate. This relationship is represented by a equation given by Monod in1942 is know as Monod equation. Based upon Michaelish-Menten kinetics. According to Monad equation- μ = μmax . S /Ks + S (4) Where, S is residual substrate concentration, Ks is substrate utilization constant, numerically equal to substrate concentration when μ is half of μmax. Ks s a measure of the affinity of the organism with substrate It tell about the relationship between specific growth rate ‘μ’ and growth limiting substrate concentration ‘S’.

Fig: 3 The effect of residual limiting substrate concentration on specific growth rate of a hypothetical bacterium. In the above figure The zone A to B is equivalent to the exponential phase in batch culture where substrate concentration is in excess and growth is at μmax . The zone C to A is equivalent to the deceleration phase of batch culture where the growth of the organism is due to the depletion of substrate to a growth-limiting concentration which will not support μmax .

Some representative values of Ks for a range of micro-organisms and substrates Typical values of K, for a range of organisms and substrates are usually very small and therefore the affinity for substrate is high.

If the organism has a very high affinity for the limiting substrate (a low Ks value) the growth rate will not be affected until the substrate concentration has declined to a very low level. Thus, the deceleration phase for such a culture would be short. However, if the organism has a low affinity for the substrate (a high Ks value) the growth rate will be deleteriously affected at a relatively high substrate concentration. Thus, the deceleration phase for such a culture would be relatively long. The biomass concentration at the end of the exponential phase is at its highest level. Therefore the decline in substrate concentration will be very rapid so that the time period during which the substrate concentration is close to Ks is very short. The stationary phase in batch culture is that point where the growth rate has declined to zero. This phase is also known as the maximum population phase.

Growth Curve Log CFU/ml Optical Density Lag

Lag phase Three causes for lag: physiological lag low initial numbers appropriate gene(s) absent growth approx. = 0 (dX/dt = 0)

Exponential phase Nutrients and conditions are not limiting growth = 2n or X = 2nX0 Where X0 = initial number of cells X = final number of cells n = number of generations 20 21 22 23 24 2n 20 21 22 23 24 2n 20 21 22 23 24 2n 20 21 22 23 24 2n 20 21 22 23 24 2n 20 21 22 23 24 2n

This is an increase is 5 orders of magnitude!! Example: An experiment was performed in a lab flask growing cells on 0.1% salicylate and starting with 2.2 x 104 cells. As the experiment below shows, at the end there were 3.8 x 109 cells. This is an increase is 5 orders of magnitude!! How many doublings or generations occurred? Cells grown on salicylate, 0.1% X = 2nX0 3.8 x 109 = 2n(2.2 x 104) 1.73 x 105 = 2n log(1.73 x 105) = nlog2 17.4 = n

Calculating growth rate during exponential growth dX/dt = uX where u = specific growth rate (h-1) Calculating growth rate during exponential growth dX/dt = uX where u = specific growth rate (h-1) Rearrange: dX/X = udt Integrate: lnX = ut + C, where C = lnX0 lnX = ut + ln X0 or X = X0eut y = mx + b (equation for a straight line) Note that u, the growth rate, is the slope of this straight line

Calculating growth rate during exponential growth dX/dt = uX where u = specific growth rate (h-1) Rearrange: dX/X = udt Integrate: lnX = ut + C, where C = lnX0 lnX = ut + ln X0 or X = X0eut y = mx + b (equation for a straight line) Note that u, the growth rate, is the slope of this straight line

Find the slope of this growth curve lnX = ut + ln X0 or u = lnX – lnX0 t – t0 u = ln 5.5 x 108 – ln 1.7 x 105 8.2 - 4.2 = 2 hr-1

What is fastest known doubling time? Slowest? Now calculate the doubling time If you know the growth rate, u, you can calculate the doubling time for the culture. lnX = ut + ln X0 For X to be doubled: X/X0 = 2 or: 2 = eut From the previous problem, u = 2 hr-1, 2 = e2(t) t = 0.34 hr = 20.4 min What is fastest known doubling time? Slowest?

How can you change the growth rate??? When under ideal, nonlimiting conditions, the growth rate can only be changed by changing the temperature (growth increases with increasing temp.). Otherwise to change the growth rate, you must obtain a different microbe or use a different substrate. In the environment (non-ideal conditions), the growth rate can be changed by figuring out what the limiting condition in that environment is. Question: Is exponential growth a frequent occurrence in the environment?

Growth Curve Stationary

Stationary phase Death phase nutrients become limiting and/or toxic waste products accumulate growth = death (dX/dt = 0) death > growth (dX/dt = -kdX) Death phase

Monod Equation The exponential growth equation describes only a part of the growth curve as shown in the graph below. The Monod equation describes the dependence of the growth rate on the substrate concentration: u = um S Ks + S . u = specific growth rate (h-1) um = maximal growth rate (h-1) S = substrate concentration (mg L-1) Ks = half saturation constant (mg L-1)

Combining the Monod equation and the exponential growth equation allows expression of an equation that describes the increase in cell mass through the lag, exponential, and stationary phases of growth: dX/dt = uX u = dX/Xdt u = um S Ks + S . Monod equation Exponential growth equation dX/dt = um S X Ks + S . Does not describe death phase!

Ks . There are two special cases for the Monod growth equation At high substrate concentration when S>>Ks, the Monod equation simplifies to: dX/dt = umX growth will occur at the maximal growth rate. Ks 2. At low substrate concentration when S<< Ks, the Monod equation simplifies to: dX/dt = um S X Ks . growth will have a first order dependence on substrate concentration (growth rate is very sensitive to S). Which of the above two cases is the norm for environmental samples?

Growth in terms of substrate loss In this case the growth equation must be expressed in terms of substrate concentration. The equations for cell increase and substrate loss can be related by the cell yield: dS/dt = -1/Y (dX/dt) where Y = cell yield Y = g cell mass produced g substrate consumed Glucose (C6H12O6) Pentachlorophenol (C6Cl5OH) Octadecane (C18H38) 0.4 0.05 1.49

Growth in terms of substrate loss dS/dt = -1/Y (dX/dt) dS/dt = -1/Y (dX/dt) Combine with: dX/dt = um S X Ks + S . Combine with: dX/dt = um S X Ks + S . . dS/dt = - um (S X) Y (Ks + S) Which parts of this curve does the equation describe?