Anal. Chem. 1994,66, 1354-1362
Noninvasive Spectroscopy for Monitoring Cell Density in a Fermentation Process Zhlhong Ge,'J Anna G. Cavlnato,* and James B. Callls Center for Process Analytical Chemistty, Department of Chemistry, B G 10, Universiw of Washington, Seattle, Washington 98 195 Short-wavelength near-infrared spectroscopy in the wavelength range 700-1100 nm is used to monitor cell density in a fermentation process vessel over a wide concentration range (1-60 g/L). The measurement is performed noninvasively through the glass walls of the vessel using a bifurcated fiberoptic bundle to both excite the sample and collect the diffusely backscattered radiation. It was found that, in regions where there was little absorption, the major changewas an exponential decrease of the logarithm of the diffusely backscattered radiation with increasing cell concentration. Various types of models were fit to the data. The newly developed multivariate method of locally weighted regression gave the best results. It allowed noninvasive determination of cell density of yeast fermentations that were being both bubbled and stirred with an average standard error of prediction of 1.6 g/L. The above results were found to be valid only if the stirring and bubbling rates remained constant during the fermentation. However, experiments with variation of these two parameters suggested correction factors for them could be readily developed. Cell mass concentration in bioreactors is an important parameter in both laboratory experiments and production control.lJ In fermentations of recombinant organisms, many process event milestones can be correlated with cell mass concentration. For example, as biomass reaches a critical point for induction, it could be used to signal addition of inducer to produce the desired product. Thus, optical yields are achieved only if the environmental conditions in the bioreactor are accurately monitored and controlled and if real-time information obtained by on-line measurements on the growth of the organisms is a ~ a i l a b l e .A~ number of procedures for estimating biomass concentration based on the measurement of a chemical response or physical property of the sample have been reported. Alternatively, indirect procedures using mathematical manipulation have been used to obtain biom a ~ s . ~Chemical ,~ methods, such as bioluminescence and chemiluminescence,require disposable reagents, aseptic sampling, and sample processing and, therefore, are not appropriate for real-time monitoring. Indirect mathematical methods, which relate cell concentration to the rate of 02 uptake and/ Merck & Co., Inc., P.O. Box 2000, R80Y-120, Rahway, N J 07065-0900. D2 Development, 1108 J Ave., LaGrande, OR 97850. (1) Sonnleitner, B. Process Control Qual. 1992, 2, 97-104. (2) Fung, D. Y.-C. In Handbook of Anaerobic Fermentations; Erickson, L. E., Fung, D. Y.-C., Eds.; Mercel Dekker: New York, 1988; pp 501-536. (3) Bishop, B. F.; Lorbert, S . J. In Sensors in Bioprocess Confrol; Twork, J., Yacyuych, A., Eds.; Marcel Dekker: New York, 1990; pp 1-17. (4) Phillips, J. A. In Compurer Control of Fermentation Processes; Omstead, D. R., Ed.; CRC Press: Boca Raton, FL, 1990; pp 15-72. (5) Kell, D. B.; Markx, G. H.; Davey, C. L.; Todd, R. W . Trends Anal. Chem. 1990, 9 (a), 190-194. f
t
1354
Analytical Chemistty, Vol. 88, No. 8, April 15, 1994
or C02 evolution as measured by mass spectrometry are, to date, the only ones implemented on-line? However, due to the indirect nature of the measurement, this method is prone to failure, particularly when environmental conditions and cell physiology change during the course of the process. Physical methods which can provide instantaneous responses on a biological time scalei show more promise for the development of a real-time cell mass probe. For example, electrochemical approaches have been described based on the dielectric properties of microbial cell suspensions. Harris showed that such properties are a unique and monotonic function of the volume fraction and that their measurement may be used to estimate microbial biomass concentration.' Optical methods have traditionally been employed in the offline estimation of cell mass concentration. Instruments have been designed for automated, on-line nephelometry and t~rbidimetry,~.~ but their on-line application is limited to a narrow working range due to nonlinearities. Thus, in these devices, the fermentation broth samples must be removed to a measurement chamber where the material is diluted to within the linear range of the spectrophotometer. The applications of a variety of spectroscopic techniques, such as fluorescence spectroscopy,IOJ1photoacoustic spectroscopy,'* and nuclear magnetic resonance spectrometry,13 have been reported. Of these, fluorescence has received by far the most attention. A number of fluorophores such as NADH, tryptophan, pyridoxine, and riboflavin naturally present in cells can be monitored and changes in their concentration can reflect various changes in cell concentration, cell activity, and environmental ~0nditions.l~ However many factors affect culture fluorescencesignals, thus limiting practical applications of this technique. Cell mass measurements based on scattered light recorded over fiber optics have also been used over a narrow concentration range.15 Another approach involvesthe addition of various fluorescence indicators directly to the (6) Armiger, W . In Comprehensive Biotechnology; Moo-Young, Ed.; Pergamon Press: New York, 1985; Vol. 1, pp 133-148. (7) Harris, C. M.; Todd, R. W.; Bungard, S. J.; Lovitt, R. W.; Morris, J. G.; Kell, D. B. Enzyme Microbiol. Technol. 1987, 9, 181-186. (8) Lee,L.; Lim, H. Biotechnol. Bioeng. 1980, 22,639-642. (9) Nielsen, J.; Nikolajsen, K.; Benthin, S.; Villadsen, J. Anal. Chim. Acta 1990, 273, 165-175. (10) Zabriskie, D. W . ; Humphrey, A. Appl. Enuiron. Microbiol. 1978, 35, 337343. (11) Junker, B. H.; Wang. D. I. C.; Hatton, T. A. Biotechnol. Bioeng. 1988, 32,
55-63. (12) Gordon, S. H.; Richard, V. G.;Shelby, N. F.; Christopher, J. Biotechnol. Appl. Biochem. 1990, 12, 1-10. (13) Gadian, D. G. Annu. Rev. Biophys. Bioeng. 1983, 12,69-81. (14) Li, J.-K.; Humphrey, A. E. Biotechnol. Bioeng. 1991, 37, 1043-1049. (1 5) Loser, R.F. Sulzer/Aquasant BiomassSensor for Cell Culture. Sulzer Biotech Systems, proposal, 1990; No. 85, 808-90.
0003-2700/94/036&1354$04.50/0
0 1994 American Chemlcal Society
fermentation broth. The area under their emission spectra can be directly related to cell density in the broth.” In this paper, the development of a noninvasive optical method to monitor biomass concentration over a wide concentration range (1-60 g/L) is illustrated. The measurement is performed in theshort-wavelength near-infrared (SWnear-IR) region of the spectrum (700-1 100nm) by collecting the diffusely reflected light with a fiber-optic bundle. A similar approach was used previously to successfully monitor the production of ethanol during a yeast fermentation.I6
THEORY In this paper, as in all previous research on the application of optical methods to biomass monitoring, it is found that the optical signal is a nonlinear function of the biomass. We propose to deal with this problem in two ways: (a) modeling the response at a single wavelength with a convenient, empirically derived nonlinear function and (b) using the multivariatetechnique of locally weighted regression to model the response at multiple wavelengths simultaneously. Since this latter technique is unfamiliar, we briefly review it in this section. Locally weighted regression (LWR)” is based on the assumption that a continuoussingle-valuednonlinear function can be locally approximated with a simple model (linear or quadratic). For example, in the case of the linear model, the estimate of the parameter of interest is obtained from the measured optical response using the following equation:
where, for our case, test is the estimate of cell mass concentration, runkis a row vector of the diffusely reflected intensities measured over the J wavelength channels of interest, and 6 is a row vector of Jcoefficients, the partial sensitivities which indicate how the optical intensity at each wavelength channel contributes to the estimated biomass. In the case of diffuse reflectance, the coefficient vector 6 is not known in advance; instead it must be estimated by the empirical procedure of calibration. For the calibration phase, one selects I representative samples. For each of these, the diffuse reflectancespectrum is measured and an independent reference method is employed to obtain the “true” value of the parameter which is to be estimated from the response vector. The calibration equation is given by
c=RbT+e,
(2)
where c is I X 1 vector of concentration values as determined by the reference method, R is an I X Jmatrix of spectral data, bT is the J X 1 vector of regression coefficients, and e,is the I X 1 vector of concentration residuals. Up to this point, L W R appears to be identical to other linear multivariate methods such as multiple linear regression. The difference is that only a small number of samples from the whole calibration set are used for estimating a new regression vector
I \a
W Independent Variable Figure 1. Schematic diagram of locally weighted regression.
b for each new unknown sample. Here, the q closest points (ri, i = 1, q) are selected and used in the regression (Figure 1). Each of these selected calibration samples is assigned a
...,
weight value dependent on its distance to runk, and the regression is performed with respect to these weighted values. The weighting is a function of the Euclidean distancesbetween the q calibration points and the unknown sample. The weighting function originally described by Cleveland and Devlin (18) is equal to
where Wi(runk)is the weight associated with the ith sample in the weighted regression for the prediction of runk,r(runk,ri)is the Euclidean distance between the unknown sample and the ith calibration sample, d(runk)is the largest r(runk,ri)over all i, and W(u) = (1 - u3)3
{o
0 Iu I1
u>l
(4)
The weight function W(u)decreases as the distance from runk to ri increases. In the calibration step, one of the chemometric methods, e.g., eq 1, can be used to build the model. The optimal value of q (orf= q/l,the fractionof all points used in each regression, also referred to as the smoothing) can be determined by crossva1idati0n.l~ Another important phase is the selection of principal components to use in the nonlinear equation. As in the conventional multivariate linear models, enough components must be used to represent the data adequately but without overfitting. Again cross-validation can be used as a guide for the selection. For an unknown sample, the prediction is given by (linear case)
but now 6 is chosen specifically for the unknown on the basis
(16) Cavinato, A. G.; Mayes, D. M.; Ge, Z.; Callis, J. B. Anal. Chem. 1990, 62,
1977-1982. (17) Naes, T.; Isaksson, T.; Kowalski, B. R. Anal. Chem. 1990,62,664-673.
(18) Cleveland, W.; Devlin, S. J. Am. Srar. Assoc. 1988,83, 596-610. (19)Stone, M.; Roy, J. Srar. Soc. B 1974.36, 111-131.
AnalytlcalChemistry, Vol. 66, No. 8, April 15, 1994
1355
Table 1. Medium for Saccharomyces cerevlslae Fermentation
component
concn (g/kg)
Bacto yeast extract ammonium sulfate potassium hydrogen phosphate magensium sulfate Pluronic antifoam
25 10 3 2 1
olychromator Tbngsten Halogen Lamp " I
p-\ Computer
\ PDA Detector
7
Fiberoptics to and from sample Fermentor
Figure 2. Schematic diagram of instrument.
of its resemblance to a limited number of samples in the calibration set. MATERIALS AND METHODS Fermentation. All data were obtained from fed-batch fermentations of Saccharomyces cereuisiae (Novo Nordisk A 1339-3) run in a 5-L Bioflow I11 reactor from New Brunswick Scientific, Inc. Stock cultures of the yeast maintainedon agar slants were resuspended in 10 mL of sterile distilled water and used to inoculate 3 L of medium (Table 1). Glucose was fed through a peristaltic pump as a carbon source. The pumping rate was varied between 0 and 30 g/h depending on the type of fermentation (aerobic or anaerobic). The culture was maintained at 30 OC and pH 4.5 by additions of ammonium hydroxide. Aeration, agitation, and nutrient feed rates were varied over the course of the experiment. Off-LineCell Mass Analysis. Cell mass concentration was determined by dry weight. Aliquots (5 mL) of unfiltered fermentation broth were withdrawn periodically over the course of the fermentation. Each sample was centrifuged and washed once with deionized water, following by drying at 110 OC for 24 h in a preweighed aluminum pan. The uncertainty in this measurement is approximately 0.2 g/L. Spectroscopy. Short-wavelength near-infrared spectra were collected with a silicon photodiode array spectrophotometer developed in-house.20 Measurementswere performed noninvasively, in diffuse reflectance mode, by placing a bifurcated fiber-optic bundle (Sterngold Corp.; 1 m in length, 6-mm outside bundle diameter, 2-mm inside bundle diameter) on the outside of the glass-wall fermentor ve~se1.l~A block diagram of the experimental setup is shown in Figure 2. As a light source, a tungsten/halogen lamp (Osram No. 64635, 150 W) with a gold-coated reflector was operated from a stable dc power supply. The reflector was designed specifically (20) Mayes, D. M.; Callis, J. B. Appl. Spectrosc. 1989, 43, 27-32.
1356 Analyfcal Chemistry, Vol. 66, No. 8, April 15, 1994
700
750
800
850
900
Si0
1000
1050
11100
Wavelength (nm)
Figure 3. Spectra of yeast/water mixtures. R, the ratio of diffusely reflectedlight from the vessel to that of the reflectance standard (Re/ Ro).
to focus near-IR light onto the fiber-optic bundle. The light from the source is guided to the fermentor by the outer fiber bundle, launched into the vessel, and scattered by the particles in the medium. The backscattered light is collected by the inner fiber bundle and focused on the entrance slit of the polychromator. Analysis of yeast/water mixtures was carried out by placing the bifurcated fiber-optic probe up to the side of a 1 X 1 X 4 cm quartz cuvette (1-cm path length) containing the sample. In order to increase the signal-to-noise ratio of the spectra, 250 were averaged together over an acquisition period of 2 min. A reference spectrum was taken by placing the probe against a ceramic plate. Care was taken to ensure that the intensity of the referencespectra was the same among the different fermentations. Thus, a calibration developed in one fermentationcan be used to predict successivefermentation processes. Data Analysis. Data were collected on an IBM PC-AT and analyzed in the 386-MATLAB (The Mathworks, Inc.) environment. For calibration and prediction of cell mass concentration, nonlinear fitting based on the MarquardtLevenburg algorithmwas used. Alternatively, locally weighted regression (LWR) based on principle component regression was ap~1ied.I~ All the programs were written as scripts in the MATLAB environment. RESULTS AND DISCUSSION Analysis of Yeast/ Water Mixtures. A series of preliminary experimentswere conductedin order to evaluate the scattering properties of the medium while varying the concentration of the yeast cells in a controlled fashion. Two sets of artificial mixtures of yeast and water were obtained from growing cultures of Saccharomyces cereuisiae. In both cases, the range of yeast cell concentration was from 1.5 to 30 g/L. A representative set of spectra obtained from the yeast/water mixtures is shown in Figure 3. These measurements were performed in a 1 X 1 X 4 cm cuvette in diffuse reflectance geometry. The prominent peak at 960 nm arises from the combination band of OH stretching of water.21 The band is particularly broad due to the presence of two or more types of hydrogen-bonded water complexes.22 We have chosen to (21) Phelan, M. K.; Barlow, C. H.; Kelly, J. J.; Jinguji, T. M.; Callis, J. B. Anal. Chem. 1989,61, 1419-1424. (22) Scherer, J. R. A d a Infrared Raman Spectrosc. 5, 149-216.
35
0.81
E
-9
25
-
0.6
20
*
0.4 -
3
15
1
0.2
t
4
I t
i
l 5o t
35
0
~
0
5
10
15
25
20
Biomass Concentration
30
5
(g/L)
10
'5
20
25
30
35
Actual Biomass Concentration (giL) 1
i
\
I -0.04
~
0
5
10
15
20
25
30
35
0
5
10
15
20
25
30
35
Biomass Concentration ( g i ~ )
Biomass Concentration (@L)
Flgure 4. Curve fitting results for yeastlwater mixtures. (a) log(1lR) vs biomass concentration at 810-nm wavelength: 0, experimental data; solid line, least squares best flt. (b) Residuals between the least squares flt and experimental data.
Figure 5. Prediction results for yeastlwater mixtures by curve fitting method. (a) Correlation plot of predicted biomass concentration vs actual concentration: solid line, 45'. (b) Residual plot.
transform the intensity of the backscattered light to the form of log (1 / R ) ,where R is the ratio of diffusely reflected light from the vessel Robsto that of a reflectance standard Ro.23The most obvious change in the spectra is a decrease in log( 1/R) baseline with increased yeast concentration. The phenomenon arises from the fact that as the concentration of scattering material increases, the relative amount of backscattered light reaching the detector also increases, causing a decrease in apparent absorbance Aob(c) calculated as log( l/R). This transformation was chosen in part because historicallyit results in good linearity with c ~ n c e n t r a t i o n .However, ~~ while this decrease is monotonic with yeast concentration, it is not linear. Figure 4a illustrates the changes of log(l/R) vs cell mass concentrationat 810nm. This wavelength waschosen because it was least affected by the water absorption in this spectral region. Other regions of low absorbance behave similarly. Given the form of this decrease, it seems reasonable to approximate it as follows:
In the calibration step, the values of the constants Ao, k, and bo at 810 nm were estimated by nonlinear curve fitting based on the Marquardt-Levenburg algorithm.25 When this procedure is applied to one of the yeast/water mixtures data sets (data set I), the following results are obtained: A, = 1.3 1, k = 0.070, bo = -0.189. In Figure 4a, the fitted curve is shown as the solid line. Clearly the exponential form is a reasonable approximation to the observed data. The major discrepancy occurs in the first few data points as shown in the residual plot (Figure 4b). In the prediction step, eq 6 was used in inverse form to predict cell mass concentration on the data set 11. The prediction equation is given by
Aob,(C) = log(l/R) = A , exp(-kc)
+ bo
(6)
where c represents cell mass concentration in grams per liter, k is the decay constant, A, is a proportionality constant, and bo is the intercept of the slope. (23) Reynolds, L.; Johnson, C.; Ishimaru, A. Appl. Opt. 1976, IS, 2059-2067. (24) Wendlandt, W. W.; Hccht, H. G. Reflectance Spectroscopy; Elvin, P. J., Kothoff, I. M., Eds.; Interscience Publishers: New York, 1968.
c =-iln(+)Aob
-
(7)
The standard error of prediction (SEP) for this model was 0.8 g/L ( R = 0.999) based upon its ability to predict the cell mass of the second independently obtained data set. Figure 5a represents a correlation plot of the actual cell mass concentration as determined by off-line dry weight measurements vs the predicted values. Figure 5b shows the residual plot. These residualsindicate two problems: (a) the previously noted inability to account for the first few data points and (b) (25) Bevington,P. R. DataReductionandErrorAnalysis forthe PhysicaISciences; McGraw-Hill: New York, 1969; Chapter 1 1 .
Analytcal Chemism, Vot. 88, No. 8, April 15, 1994
1357
Tabk 2. LWR tor Analydr of YoarVWatr MMur& f 0.2 0.3 0.4 0.5 0.6 0.7
pred(1) pred(2) pred(3)
I 703
900
SC0
$309
1100
Wavelength (nm)
700
800
900
1000
0.72
0.64 1.53
0.52 1.85
0.41 2.16 1.65
0.41 2.28 1.85
0.8
0.50 2.43 2.39
0.77 2.23 2.14
1100
The term pred indicatesprediction,the number in the parentheses indicates how many factors are used, fie the fraction of samples used in the regression, and the entries are SEP values. O4 7 Wavelenglh (nm)
32
35
1
I
Wavelength (nm)
Wavelength (nm)
Flguro 8. Loadings plots for yeastlwater mixtures. I
0.5 I
0' 0
1 1>
-3 5
20
30
40
Biomass Conc (gL)
1
'3
20
Biomass Conc (gii)
10
20
30
Lo
n
30
LO
-1
3
10
20
30
5
3
Biomass Conc (#L)
-0 5
0
-
3
10
15
20
25
30
35
Actual Biomass Concentration WL)
0.8
40
8tomass Conc i#LI
e 7. Scores plots for yeastiwater mixtures.
a marked sensitivity to thevalue chosen for the baseline. Similar results were obtained with a model constructed by curve fitting the decay of log( 1/R) at other wavelengths were the absorbance due to water was negligible. Two traditional chemometrics methods, Principle component regression (PCR) and partial least squares (PLS) were also used to analyze the data. Figures 6 and 7 show the loadings and scores plots of the yeast/water mixture data set for principal component analysis (PCA). The first latent variable is essentiallythe average spectrum. The second latent variable explains the major changes of the shape of the absorption curve in going from low to high biomass concentration. The third latent variable contains further information about the change in shape of the water band. PCR and PLS were applied by using one data set as a calibration set to predict the biomass concentration of another data set. Unfortunately, the results revealed the failure of the two factor PCR and PLS models (spectral were mean-centered) to deal with nonlinear behavior of the optical response (SEP = 1.7 g/L). As a final trial method, the nonlinear calibration method, LWR, was evaluated for its ability to treat the nonlinear data sets properly. Table 2 shows the results obtained by using yeast/water data set I to predict data set I1 when LWR is applied. The best model yielded a SEP of 0.4 g/L (R = 0.9995). Figure 8 represents a correlation (a) and residuals plot (b) of actual cell mass concentration vs LWR predicted values. These results wereobtained with a linear model based on one latent variable (spectra were mean-centered) and a fraction of the calibration set off = 0.5. 1358 Analytical Chemistry, Vol. 66,No. 8, April 15, 1994
-1
1
0
5
10
15
20
25
30
35
Biomass Concentration (g/L)
F I g m 8. Predktlon results for yeast/water mixtures data sets by LWR. (a) Conelationplotof predictedblomass concentratlonvs actual Concentration: solM line, 45". (b) Residuals plot.
Quantitative Determination of Cell Density in Fermentations. Encouraged by the results obtained on yeast/water mixtures, we next evaluated the procedure on real fermentations. In order to test whether a model developed for one fermentation could be applied to succeeding runs, four fermentations were run under constant stirring conditions (500 rpm) and airflow rate (3 L/min), but different glucose feed rates and, therefore, different growth rates. In these fermentation processes, growth of yeast cells from 0 to 60 g/L was carried out under aerobic conditions. This is a much wider concentration range than those in the yeast/water mixtures. SW-near-IR spectra were acquired at 10-min intervals over a 40-h period. Dry weight cell mass measurements were carried out for validation by withdrawing samples at 1-h intervals. A representative set of spectra recorded for a real fermentation process is shown in Figure 9. These spectra were obtained noninvasively using the instrumental setup described in Figure 2. They appear to be very similar to those recorded for yeast/water mixtures (see Figure 3). As before,
"- I
l A
I b e g i n n i n g of fermentation
I
1.2
0
e n d of fermentation
- ,
750
700
800
850
1000
950
900
1050
1100 -0 2 1
Wavelength (nm)
0
10
20
Flgure 0, Spectra of the fermentation process.
30
40
50
60
70
50
60
70
Biomass Concentration (gii)
3 08
-0.2
1
0
10
20
30
50
40
60
1
70
- __
0
10
20
30
40
Biomass Concentration (gi~)
Biomass concentration (giU
Flgure 11. Curve fitting results for a fermentation process. (a) log(l/R)vs biomessconcentratlonat810-nmwavelength: 0,experknental data: solid line, least squares best flt. (b) Residuals between W least squares ftt and experimental data. 1
Table 3. Nonllnear Fmlng Parameter8 In Four Formentatlonr expt Ao k bo
1 2 3 4
1.28 1.28 1.26 1.32
0.067 0.067 0.083 0.063
-0.0178
o.Ooo1 0.0638 -0,0118
i.
10-3
0
10
20
30
40
50
60
Biomass Concentration (giL)
Flgure 10. Comparlson of four fermentations: (0) ferml08, (+) ferml09, (*) fermll0, and (X) fermll2. (a) iog(1lR) at 810 nm vs biomass concentration. (b) Same data plotted on a logarithmic scale.
the only obvious change in the spectra is the overall decrease of log( 1/ R ) with increased time of reaction and therefore increased cell mass concentration. Figure 10a shows the reproducibility of log( 1/R) at 810 nm for four fermentation experiments, and Figure 10b shows the same data plotted on a logarithmic scale. It is clear that these measurements are reasonably reproducible among all the fermentations. Thus, it seems possible that a multivariate statistical model developed on one fermentation can be used to predict the biomass in succeeding runs. The decrease of log( 1/R) vs biomass concentration at one wavelength followsan approximately exponential curve similar to that observed in yeast/water mixtures. The data were
analyzed by nonlinear curve fitting at 810 nm using the same equation as in the yeast/water mixtures (eq 6). Figure 11 shows the least squares best fit for one fermentation. The parameters Ao, k, and bo in four fermentations are listed in Table 3. It is evident that the cell mass concentration's dependence on relative diffuse reflectance is reasonably reproducible. The parameters obtained from the first fermentation were then substituted into eq 7 to predict the other succeeding fermentations. Figure 12 shows the results. Clearly in the range 0-40 g/L, the method works quite well. However, prediction ability declines at higher concentrations. This appears to be due to the decreased sensitivity of that part of the curve to changes in cell mass concentration, which leads to increased sensitivity to the baseline offset, which in turn leads to a systematic deviation. SEPs of 4.5,4.6, and 3.6 g/L were achieved respectively in the three experiments. This represents a considerable increase in the standard error of the estimate when compared with the yeast/water mixtures. Examinationof the residual estimates in Figure 12 shows that much of the error occurs at high biomass, and here the error Analyfcal Chemlstty, Vol. 66,No. 8, Aprll 15, 1994
1350
ao
Table 4. LWR Analysis of a Fermentatlon ProceW
70
f
r
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1.68 11.54
1.50 11.21 8.61
1.19 8.63 4.14
1.19 6.45 4.59
1.60 6.07 4.92
2.36 6.33 4.67
3.34 6.47 4.67
2.86 2.80 15.98 20.19 25.45
2.67 14.04 12.61
2.65 10.73 11.92
2.92 9.51 11.32
0.96 3.09 4.27
1.17 2.88 4.37
1.53 3.03 4.48
1.57 3.65 $0
C
2c
30
43
50
SO
50
60
Actual Biomass Concentration (g/L)
1.22 3.17 5.58
4.46 3.52 8.82 8.26 11.08 10.31 2.06 3.25 4.88
3.05 3.38 4.66
"The term pred indicates prediction. The number in the parentheses indicates how many factors are used, f is the fraction of samples used in the regression, and the entries are SFP values.
l5I 10
1
-101
0
10
20
30
Biomass Concentration
40
(UL)
0
10
Figure 12. Prediction of biomass concentration by nonlinear fitting
1360
Analytical Chemistty, Vol. 66,No. 8, April 15, 1994
30
40
50
60
Actual Biomass Concentration (giL)
method during other fermentations. (a) Correlation plot: solid line, 45'; (0)second fermentation, (+) third fermentation, and (*) fourth fermentation. (b)Residuals plot: solid line,second fermentation;dashed line, third fermentation: dotted line, fourth fermentation.
is clearly in the form of a systematic deviation rather than a random one. One possible interpretation of these results is that the estimation of the baseline parameter is not sufficiently precise to be applied confidently on succeeding data sets. When one fermentation data set was used to predict other fermentations by LWR, the best result was achieved using one latent variable (spectra were mean-centered) and a fraction of the calibration set off= 0.4with linear fit in the calibration model. This optimal model is similar to that used for the artificial mixtures. The results of evaluation of different parameters for LWR using one fermentation to predict other three fermentations are listed in Table 4. Figure 13 shows the prediction of cell mass concentrations in three succeeding experiments by applying the calibration models developed by LWR. In this case, SEPs of 1.19, 2.67,and 0.96 g/L were achieved respectively, which are consistently better than those obtained by nonlinear curve fitting. These improved results may be explained by the fact that LWR more effectively models the nonlinear aspects of the data. Effects of Culture Environment,Agitation Rate, and Airflow Rate. It should be noted that the four fermentation experiments were run under different process conditions, e.g., different glucose feeding rates. Changes in glucose feeding conditions profoundly affect numerous parameters in the fermentation broth, including pH, dissolved oxygen, formation of byproducts (ethanol), etc. The results suggest that the
20
0
10
20
30
40
50
60
Biomass Concentration (g/L)
Figure 13. Predictionof biomassconcentration by LWR methodduring other fermenfations. (a) Correlation plot: solid line, 45'; (0)second fermentation, (+) third fermentation, and (*) fourth fermentation. (b) Residuals plot: solid line, second fermentation; dashed line, third fermentation; dotted line, fourth fermentation.
method for cell mass concentration determination described above is independent of the culture environment. However, it was observed over the course of a number of experiments that the relationship between the backscattered light and the cell mass concentration is affected by the agitation rate and airflow rate, thus introducing ambiguity for quantitative measurements under circumstances where these parameters change. Accordingly, a systematic study of these sources of variance were undertaken, and the results are depicted in Figures 14-17. Figure 14 shows that, for a constant biomass concentration, a higher agitation rate causes an increase in
Agitation Rate
in"
0 15
0.1 1 -
!
-
\ 1
P
-
2
1
I
\\
06-
F
s
04-
233
253
330
350
0-
45C
4CC
Xi
5CC
553
550
700
Agitation Rate (rpm) Biomass Concentration (dL)
Flgure 15. Effects of stirrlng rate at dlfferent biomass concentration (from top to bottom): (+) 200, (0)300, (*) 400, (X) 500, (+) 600, and (0)700 rpm; ilne, least squares best fit; symbol, experimental data.
the amount of backscattered light returned to the detector. The effect is particularly pronounced at lower biomass concentration (
