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## Brazilian Journal of Chemical Engineering

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*Print version* ISSN 0104-6632*On-line version* ISSN 1678-4383

### Braz. J. Chem. Eng. vol.17 n.2 São Paulo June 2000

#### http://dx.doi.org/10.1590/S0104-66322000000200011

**Developing an objective function to characterize the tradeoffs in salting out and the foam and droplet fractionation processes**

**J. Cherry, S. Ko, R.Grainger, A. Prokop, and R. D. Tanner* **Department of Chemical Engineering, Vanderbilt University,

Nashville - TN, 37235, USA

Received: August 30, 1999 ; Accepted: January 23, 2000

Abstract -There are many methods for separating and purifying proteins from dilute solutions, such as salting out/precipitation, adsorption/chromatography, foam fractionation, and droplet fractionation. In order to determine the optimal condition for a selected separation and purification process, an objective function is developed. The objective function consists of three parameters, which are the protein mass recovery, the separation ratio, and the enzymatic activity ratio. In this paper the objective function is determined as a function of the pH of the bulk solution for egg albumin, cellulase, and sporamin (for foam fractionation) and invertase ( for droplet fractionation). It is found that the optimal pH for all the systems except for cellulase is near their isoelectric point.

Keywords: protein separation, optimization, tradeoffs, foam fractionation process, droplet fractionation process.

INTRODUCTION

Many methods have been used to separate and purify proteins from dilute solutions. Two promising methods are foam fractionation and droplet fractionation because they are simple and relatively inexpensive (Eiamwat et al., 1998). In contrast, the more widely used salting out method is more expensive, requires a cleanup step to recover the salt, and is very time consuming. There are three primary parameters, which characterize the effectiveness of these processes (Loha, 1998). The first is the protein mass recovery (MR), and it is defined as the ratio of the recovered protein mass in the concentrated protein phase to the initial protein mass in the foam fractionation column. The second is the separation ratio (SR), which is defined as the ratio of the protein level in the concentrated phase to that in the residual or bulk phase. The third is the enzymatic activity ratio (AR), which is defined as the ratio of the enzymatic activity per unit protein mass in the concentrated phase to the initial enzymatic activity per unit protein mass in the initial bulk liquid.

An objective function (f ) can be determined for either the foam or droplet protein process by multiplying the three above-mentioned parameters (possibly raised to exponential powers), which provides as follows the relative weightings a , b , and d (Loha, 1998):

(1) |

In this paper we explore how the pH and, in the case of the foam fractionation process, the superficial velocity of the carrier gas contribute to the overall objective function, f . For this analysis and the sake of simplicity, we assume equal weightings for each parameter, which sets the values of a , b , and d equal to 1 (Loha, 1998). Thus, equation (1) becomes

(2) |

When the protein being studied is not an enzyme, then enzymatic activity, AR, is omitted from equation (2) and the objective function for that case is further reduced (Loha, 1998):

(3) |

In the case of the salting out process, also explored here as a means to calibrate f and compare it with the foam and droplet methods, the objective function does not contain the separation ratio, SR. Thus the objective function for the salting out process becomes

(4) |

In this paper, the objective function is analyzed for four systems. These systems characterize the three hydrophobic (foam forming) proteins, egg albumin, cellulase, and sporamin. The hydrophilic protein, invertase, is used to characterize the droplet fractionation system. Cellulase is also used as the example in the salting out process (Santana et al., 1999) and allows a direct comparison of the objective function responses for foam fractionation and salting out.

RESULTS AND DISCUSSION

Figure 1 illustrates how bulk solution pH affects the objective function, comprised of the product of MR and SR, of egg albumin at an initial protein concentration of 100 mg/L and an air superficial velocity ranging from 4 to 32 cm/min (Loha, 1998). The objective function has pH-bounded maxima at bulk solution pHs of 2 and 11 and a sharp local maximum at a pH of 4. At the pH-bounded maxima of the bulk solution, the egg albumin protein is most likely denatured, which is a condition that increases hydrophobicity and protein mass recovery. High hydrophobicity also occurs at the local maximum (pH 4), which is near the isoelectric point of egg albumin (pI = 4.5). Excluding results for pH 2 and 11 possible denaturization from the objective function shown in Figure 1 (since denatured proteins are generally not desired in commercial applications), the maximum of the objective function is at pH 4. Here both of the underlying separation criteria (SR and MR) are individually maximized (SR of 35.49 and MR of 75.83%) at pH 4 and an air superficial velocity rate of 4 cm/min.

Figure 2 illustrates the effect of bulk solution pH on the objective function of cellulase at an initial protein concentration of 130 mg/L and an air superficial velocity ranging from 4 and 32 cm/min. Unlike the egg albumin case, here the enzymatic activity ratio is included in f (equation [2]), since cellulase is an enzyme and egg albumin is not. Like egg albumin, cellulase has absolute maxima at the bulk solution pH bounds of 2 and 11 (again representing possible denaturization). However, the local maximum for this cellulase mixture is at a bulk solution pH of 9 to 10 rather than an acidic pH near its isoelectric point as it was for the egg albumin. This is apparently an unusual result since the best operating condition is usually close to the isoelectric point. This unusual result is apparently due to the combination of coalescence and drainage (Narsimhan and Uraizee, 1996). Neglecting the extreme values where there is a possibility of denaturization, the maximum protein separation and the objective function are both at an initial bulk solution of 9 to 10. The optimal separation condition is at a bulk solution pH of 9 and 10 for air superficial velocities of 32 and 24 cm/min, respectively.

Figure 3 depicts how bulk solution pH affects the objective function of sporamin (the storage protein of a sweet potato) with the air superficial velocity ranging from 1.47 to 4.28 cm/s (Ko et al., 1998). The objective function has a local maximum at a pH of 3 at 1.47 cm/s, which is at its isoelectric point (pI = 3). It is also interesting to note that other local maxima are at a basic pH of 8 for the two higher superficial velocities, which is similar to the only local maximum for cellulase at the various superficial velocities, as shown in Figure 2. Since Figure 3 (the sporamin system) does not have just single maxima within the pH range studied, like the previous two figures, it apparently offers more possible optima under different conditions.

Figure 4 illustrates an alternative to foam fractionation for enriching the protein concentration: using droplets instead of foam. Figure 4 graphs the results obtained by the sonic wave separation of invertase (Ko et al., 1999). This method used ultrasonic waves enhanced with a bubbling gas stream to increase the protein concentration in the droplets created. Although invertase is an enzyme, activity measurements were not obtained for the conditions shown on the graph. Therefore, the objective function was calculated using equation 3. The optimal separation condition was at a bulk pH of 5. This peak is also near the isoelectric point of invertase (pI = 4.5).

The isoelectric point (pI) is the point where the electrical charge on a protein is zero. At zero charge, hydrophobicity is at its maximum (Wilson and Walker, 1994). Figure 5 shows the relationship between the peak pH’s of the four systems and their respective isoelectric points. The egg albumin, sporamin, and invertase peak pH’s (pH = 4, 3, 5, respectively), are close to their isoelectric points (pI = 4.5, 3, 5) and follow a similar trend. However, the cellulase peak pH (pH = 9) is double its isoelectric point (pI = 4.5) and does not follow the trend line. This means that cellulase does not behave in the classic or expected manner and needs to be studied further to better understand its behavior in a foam fractionation column.

Salting out has different variables of interest compared to foam or droplet fractionation, but the objective function can still be used in order to find the optimal condition of operation. It is included here to show the potential of this objective function analysis as a way to calibrate the results of foam and droplet fractionation. Figure 6 shows the effect of mixing level on the objective function in keeping with the underlying data. The system that is studied is cellulase, and the variables for the process include incubation temperature, aging time, rate of salt addition, and level of mixing (Santana et al., 1999). The optimal condition for this method is at an incubation temperature of 35^{o}C, an aging time of 11 hours, a salt addition of 30 ml/min, and a mixing level of 165 rpm. Because the points were collected according to a statistical design, they could not be ordered like the other graphs at constant parametric values for plotting trajectories. The optimal MR is around 71% and the optimal AR is around 78%. For the foam fractionation of cellulase, the optimal MR is about 80% and the optimal AR is about 67%. The two methods are close in their results concentration and separation of the protein. However, for the salting out process, it took 11 hours to run the experiment, whereas the foam fractionation only took a few minutes.

CONCLUSIONS

The objective function, f , is used to quantify the optimal recovery of proteins from a dilute solution for both foam and droplet fractionation experiments. In general, the objective function, f , equals the product of MR, SR, and AR. Here, equal exponential weightings of one are employed (Loha, 1998). The optimal separation condition for each system was well represented graphically by sharply defined peaks on plots of the objective function versus bulk solution pH. Except for cellulase, the optimal conditions were located near the isoelectric point for each system. In order to test the generality of this objective function analysis on other purification methods, it was shown that it can also be applied to salting out data.

ACKNOWLEDGEMENTS

This material is based on work supported by the National Science Foundation under Grant No. CTS-9712486 and the Vanderbilt University Summer Research Program (School of Engineering).

REFERENCES

Eiamwat, J., Loha, V., Prokop, A., and Tanner, R. D. (1998). Appl. Biochem. Biotechnol. 70-72, 559-567. [ Links ]

Loha, V. (1998), Optimizing Protein Separation in a Foam Fractionation Process. Ph. D. Dissertation, Vanderbilt University, Nashville, TN. [ Links ]

Narsimhan, G. and Uraizee, F. (1996). Biotechnology and Bioengineering. 51, 384-398. [ Links ]

Ko, S., Loha, V., Prokop, A., and Tanner, R. D. (1998), Appl. Biochem. Biotechnol. 70-72, 547-548. [ Links ]

Ko, S., Loha, V., Prokop, A., and Tanner, R. D. (1999), Paper presented at The Twenty-first Symposium on Biotechnology for Fuels and Chemicals, Fort Collins, CO. [ Links ]

Wilson, K. and Walker, J. (1994), Principles and Techniques of Practical Biochemistry. 4^{th} ed. 164. [ Links ]

Santana, C. C., Miranda, E. A., Rosa, P. T. V., Azzoni, A. R., and Avelino, S. (1999), Appl. Biochem. Biotechnol. 77-79, 807-815. [ Links ]

* To whom correspondence should be adressed