Question

#1: Cell Culture Growth Phases For the following cell mass and substrate consumption data in Table P6.1, determine the parameters requested below (for credit, you must generate your answers by plotting the data on a cell mass vs time graph, with cell mass given on a logarithmic scale): puNET, in this particular case. k 0) a. The maximum observed growth rate, He (same as b. Yield on substrate S, Yxs c. Cell mass doubling time, T d. Monod saturation constant for the substrate, Ks Table P6.1 Batch Growth Culture/Substrate Data X (gdw/liter) 0.1 0.11 0.18 0.7 2.5 6.5 7.6 7.7 7.8 7.9 S (gr/liter) 17 16.98 16.83 15.71 11.84 3.23 0.86 0.65 0.43 0.21 0.00 0.00 Time (hrs) 0 6 9.5 10 10.5 12 8 CHEN 4311 Homework #6 Spring 2019

Answer 1

Solution:

We know the Monod model as (when k_d = 0)

μ=μmaxSKS+S

μ maxS Ks + S

Where,

µ = specific growth rate (you can write µ_NET as k_d = 0) (h^-1)

K_S = saturation constant (g/L)

S = limiting substrate concentration (g/L)

a. We can linearize the above equation by doing reciprocal of the same

1μ=KSμmax1S+1μmax

5 1 Kc 11 μ max

Plot of 1S vs 1μ results

Slope = KSμmax

Intercept = 1μmax

Again, we know

μ=1XdXdt

1 dX X dt

Where,

X = cell mass concentration (g/L)

dXdt=Xn+1-Xn-1tn+1-tn-1

dr = tnti-4.1

t (h)	X(g/L)	S(g/L)	dX/dt	µ	1/S	1/µ
0	0.1	17
1	0.11	16.98	0.04	0.363636	0.058893	2.75
2	0.18	16.83	0.196667	1.092593	0.059418	0.915254
4	0.7	15.71	0.58	0.828571	0.063654	1.206897
6	2.5	11.84	1.45	0.58	0.084459	1.724138
8	6.5	3.23	1.7	0.261538	0.309598	3.823529
9	7.6	0.86	0.8	0.105263	1.162791	9.5
9.5	7.7	0.65	0.2	0.025974	1.538462	38.5
10	7.8	0.43	0.2	0.025641	2.325581	39
10.5	7.9	0.21	0.2	0.025316	4.761905	39.5
11	8	0	0.066667	0.008333		120
12	8	0

From the plot

n,nax = 0.9794 h-1

b. We know yield

Plot of (S₀ – S) vs (X – X₀) results as a slope of Y_X/S

X(g/L)	S(g/L)	S0-S	X-X0
0.1	17	0	0
0.11	16.98	0.02	0.01
0.18	16.83	0.17	0.08
0.7	15.71	1.29	0.6
2.5	11.84	5.16	2.4
6.5	3.23	13.77	6.4
7.6	0.86	16.14	7.5
7.7	0.65	16.35	7.6
7.8	0.43	16.57	7.7
7.9	0.21	16.79	7.8
8	0	17	7.9
8	0	17	7.9

Cell mass yield y = 0.4647x R2 = 1 6 0 15 20 10 0 So-S 0

Therefore, cell mass yield = 0.4647 g/g

c. Cell mass doubling time can be calculated as

In (2) μΝΕΤ NET

For maximum growth, we can assume μNET=μmax

d. From the section a

Ks -7.875 9/L