Effects of Immobilized Enzymes on Industrial Bioprocesses - Research Paper Example

Determining the Effect of Process Parameters on the Size of Chitosan Microspheres Introduction The firms that need the enzyme applications offer significant considerations to the enzyme size because such elements assists in the determination of the effectiveness of separating them from the desired commodity. Huge particles have a large surface area to volume ratio, and therefore, the rate of reaction was slow. Typically, there is a prime between the reaction rate and separation. The paper analyzes the immobilized enzymes that have significance in the industrial bioprocesses particularly in pharmaceutical, food and nutritional technologies. The collection of based on how various elements influence the immobilized enzyme size. Nevertheless, the data will reveal inconsistency, even in similar test circumstances, because, the size of such particles may not be round from location of the measurement. There are four key design criteria, which are significant for the determination of particle size. There are tween 80 concentration, stirring rate, glutaraldehyde concentration, and chitosan concentration. The purpose of the study is to determine the necessary conditions for making an enzyme particle of a specific size through application of statistical methods. 2. The particle size effect To get a feel of how the particle sizes are at stirring rate of 1000rpm and 500rpm, a stem and leaf analysis was carried out. Stirring rate= 1000 rpm Stirring rate= 500 rpm Stem Leaves Stem Leaves 0.38: 6 0.38: 11138 0.39: - 0.39: 8 0.40: 134449 0.40: 14458 0.41: 77789 0.41: 0118 0.42: 5 0.42: 236 0.43: 457789 0.43: 3 0.44 - 0.44 1 0.45: 3 Fig1. Stem and leaf analysis of the stirring rate data. Fig. 1 shows that classical size of the particle value size of chitosan obtained at various stirring speed. The actual values at 1000RPM are 0.40 to 0.41 and 0.43 as the data appears as though it has many peaks. Therefore, it shows that there was a contamination of data. However, at 1000RPM, the chitosan particle diameter margin is 0.376 to 0.439. Accordingly, at 1000RPM the chitosan particle diameter ranges are 0.386 to 0.453. Consequently, the data seems to be skewed towards the smaller particle size. While at 500RPM the particle sizes range from 0.381 to 0.441. The actual values of the particle size of chitosan are 0.38, 0.40 and 0.41.For, the 500RPM the data appears to be skewed towards the smaller particle size. Analysis using Box plot Fig.2 below yields a boxplot of a similar data set. Take note first the 1000RPM stirring rate boxplot. This plot indicates that an actual value for particle size of the chitosan is 0.4175 and that much of the data, such as 75% of the data, on particle size of the chitosan ranges between 0.404 and 0.4355. The unquestionable fine data - that is the data, which is not under consideration even potentially as outliers - have values between 0.35675 and 0.48275. The data is also skewed with the median being pulled towards the lower quartile. Similarly, obe should take note of the next 500 stirring rate boxplot. The boxplot revealst that the real value for lift is 0.4065, which is less than when is the stirring rate of 1000RPM. Similarly, much of the data (75% of the data) on lift ranges between 0.3955 and 0.419. The unquestionable fine data - that is the date not under consideration even potentially as outliers - will have values between 0.36025 and 0.45425. The spreads in the data is slightly larger than when the stirring rate is 1000RPM. Nevertheless, the data does not seem to be skewed for the stirring rate of 500RPM. There are no outliers present for both 1000RPM and 500RPM. Comparing both, the stirring rates indicate there is existence of some overlaps for many particle sizes among different stirring rates. Therefore, it is clear from the box plot that through changing the stirring rates the diameter of the chitosan substance varies only to a small extent and hence, the actual nature of the connection requires a further analysis and this would be shown in the subsequent sections. The data for the 1000RPM is spread than the one at 500RPM. Fig.2.Boxplot for the different stirring rates 3. Confidence limits 3.1 Parametric test The boxplot indicated the very various 1000RPM and 500RPM stirring rates brought about distinct chitosan diameter size. Nevertheless, to be a lot conclusive concerning the statistical significance test needs to be carried out. Since the sample size is n=20(small) the central limit theorem cannot be applicable. Therefore, a supposition could suffice for the particle size from a natural distribution regardless of the stirring rates. Under the supposition, student confidence periods can be constructed for the various stirring rates. Based on speculation, a 95% confidence gap (corresponding to α=0.05) for the unknown value of the population mean diameter of stirring rate is given by: For 1000RPM: 1 xn−1, α ∕2, xn−1, α ∕2 Where x = 0.4199, s = 0.0171 and t19, 0.025 = 2.09 thus 1 0.4199 – 2.09, 0.4199 + 2.09 1 (0.4119, 0.4279) The credible values for the true mean coefficient of 1000RPM range between 0.4119 and 0.4279. Therefore, it means the results could be 95% sure that the particle size is within this range. Accordingly, there is a 5% chance to prove it wrong that the size of the particles are within this range. For 500RPM: 1 xn−1, α ∕2, xn−1, α ∕2 Where x = 0.4065, s = 0.0177 and t19, 0.025 = 2.09 thus 1 0.4065 – 2.09, 0.4065 + 2.09 1 (0.3982, 0.4148) The reliable values for the chitosan particle size at 500RPM are 0.3982 and 0.4148. In other words, one can be 95% certain that the chitosan particle size is within such range. However there is a 5% chance of being rebutted in this conclusion. At the 95% confidence intervals, the two types of stirring rates the particle diameter does overlap at some extent. 3.2 Probability Plots The supposition is has a footing on the earlier belief that normal distribution is being true. The Fig. 3 below shows a probability plot of the particle size for various stirring rates at 1000RPM and 500RPM. Accordingly, the figure indicates the empirical distribution plotted against the normal distribution. The standard and mean deviations are contingent on the sample estimates as shown in the previous calculations above. For a stirring rate of 500RPM, the normal distribution describes the data well at the lower end of the distribution but this is not the case at the upper tail. It is similar to the leaf and stem plot, which shows various skews in the data that becomes inconsistent with the normality assumption. Fig3.probability plot of both of the stirring rates 3.3 A non-parametric test The performance of a non-parametric test is significant to show whether the stirring rates affect the mean particle size. In fig 4a, Using an approximate confidence level of 95% at 1000RPM the median is (0.4040, 0.434). In fig 4b, an approximate confidence level of 95% was selected and it was seen that the median was (0.398, 0.418) at 500RPM. Therefore, it is clear that there is a slight overlap of the mean particle size at the two stirring rates. There are no assumptions for such conclusions and it substantiates the evidence for the conclusions made earlier from the t-test and box plots. Fig.4a An approximate 95% confidence interval for the average particle size at 1000RPM Fig 4b.An approximate 95% confidence interval for the average particle size at 500RPM 3. A Model for Particle size The following second order response surface model was chosen to represent the data set for the particle size at various conditions: Y = β0 + + + + ε Where Y was particle size, X1 was the stirring rate, X2 was the Tween 80 concentration, X3 was the Chitosan concentration, and X4 was the glutaraldehyde concentration ε was the prediction error or residual The β coefficient are estimated by minimizing the total squared prediction error or minimize. Where n=43 was the number of observation on Y. This was achieved using Excel’s data analysis tool pack and the results are shown in Table 1 below. Design Variable Coefficient Standard error T stat Lower 90% Upper 90% Intercept 1.15983771 0.236755521 0.40275214 0.75708557 1.562589849 X1 -0.000113288 0.000220465 0.00037504 -0.000488328 0.000261753 X2 -0.068920369 0.115407966 0.196324061 -0.26524443 0.127403692 X3 -0.510875747 0.176710631 0.300607921 -0.811483668 -0.210267826 X4 -0.111817781 0.058181763 0.098974797 -0.210792578 -0.012842984 X1X2 2.31613E-05 4.82967E-05 8.2159E-05 -5.89977E-05 0.00010532 X1X3 0.000104228 9.25004E-05 0.000157355 -5.31272E-05 0.000261583 X1X4 -4.8057E-05 2.31251E-05 3.93388E-05 -8.73959E-05 -8.7182E-06 X2X3 -0.041528517 0.048124284 0.081865708 -0.123394225 0.040337191 X2X4 0.029548796 0.012031071 0.020466427 0.009082369 0.050015223 X3X4 0.044989317 0.024520904 0.041713269 0.003276048 0.086702586 X2 1 3.0252E-08 7.94346E-08 1.35129E-07 -1.04877E-07 1.65381E-07 X2 2 -0.021693683 0.0277936 0.047280554 -0.068974236 0.025586871 X2 3 0.087344068 0.041583634 0.070739207 0.016604862 0.158083275 X2 4 0.005654504 0.007181897 0.012217346 -0.006562843 0.01787185 Table1. Estimated 2nd order response surface model. The data does not fit an X3 linear relationship and X4 does not have the zero value. Therefore, we are 90% certain that such variables are real factors. Therefore, it has the effect that the glutaraldehyde concentration and Chitosan concentration are crucial in the size of the particles. The interpretation of the data could only be in the model if the data fitted a normal distribution. Therefore, figure 5 shows a probability plot to ascertain whether such data fits a normal distribution. The figure indicates that there is a fair relationship between normal and empirical distribution. Consequently, it can be observed that the residuals are normally distributed. They appear to scatter near the regression line, which suggests that they could be normally distributed. Fig5. Probability plot for experiment 2 To better show, the data a graph was drawn up of actual size against predicted particle size. If the model was perfect then a 450 straight line can be drawn from the origin. Fig6 Actual particle size vs predicted particle size. The model above (Figure 6) was found to have a R2 value of 70.2%. The R2 value indicates how well the data fits a linear straight line. To see if the model was not under or over estimating the value a graph of particle size against residuals was drawn up. Fig7. The scatter of the residuals The graph shows random scatter for the residuals, therefore under or over estimation was not occurring. 4.2 A simplified model Using the upper and lower 90% columns from table 1, a simplified model can be drawn up. If the range of possible result for the design variable contain the value ‘ ’ then that term can be eliminated from the model. Design Variable Coefficient Standard error T stat Lower 90% Upper 90% Intercept 0.911426652 0.110557409 0.186653821 0.724772831 1.098080473 X3 -0.469896681 0.142502104 0.240585976 -0.710482658 -0.229310705 X4 -0.042215471 0.031790434 0.053671717 -0.095887187 0.011456246 X1X4 -2.2676E-05 1.13638E-05 1.91854E-05 -4.18614E-05 -3.49063E-06 X2X4 -0.01037619 0.006258663 0.010566486 -0.020942676 0.000190295 X3X4 0.044683685 0.026185332 0.044208636 0.000475049 0.08889232 X32 0.086848778 0.046187203 0.07797775 0.008871028 0.164826528 Table 2 the simplified model. To better illustrate the data a graph of simplified model with prediction and confidence bands (figure 8) was drawn. Inserted into the graph are prediction and confidence band. The decreased was 95% therefore we can say that 95% of the prediction data can be found in-between red band and 95% of the data can be found in the blue band. The value for the R2 value has decreased therefore this model was not very accurate. Fig. 8 simplified model with prediction and confidence bands. 4. Optimization The application of the model enables one to calculate the necessary condition. As Tween 80 concentration and stirring rate are not actual elements, they are fixed conditions. It was established that the particles’ size is larger with a low Tween 80 concentration and a slower stirring rate. Considering that, the larger and small particles’ conditions were estimated. Fig. 9 Predicted particle size for large particles. Figure 9 was used to show the larger particles. The set conditions for figure 9 are to have a stirring rate of 50rpm and a Tween 80 concentration of 0.5 v/v%. A large particle was a particle that was larger than 0.53mm. As it can be seen from the graph this occurs in the Green bands. The Chitosan concentration was below 0.8w/w% and above about 2.18w/w% at a glutaraldehyde concentration of 5w/w% and at a glutaraldehyde concentration of 1w/w% the Chitosan concentration was about 1 w/w% Fig. 10 Predicted particle size for small particles. Figure 10 was necessary to show smaller particles. Figure 10’s set conditions are to have a 1750rpm-stirring rate and a Tween 80 concentration of 2.5 v/v%. A small particle was a particle that was smaller than 0.25mm. It is clear that the graph occurs within limited bands. At a glutaraldehyde concentration of 5w/w% the Chitosan concentration was between about 2.2w/w% and about 0.6w/w%. At a glutaraldehyde, concentration of about 3.75w/w% the peak for the Chitosan concentration was about 1.75w/w%. 6.0 Conclusion The above analysis has revealed a number of interesting conclusions about the conditions that determine the size of particles. 1. There were some overlaps in particle sizes for different stirring rates at 500RPM and 1000RPM demonstrated in the stem and leaf diagram. 2. The stirring rate was not an actual element in the particle size. This is visible on all data analyses carried out. For the model, it was established that the Tween 80 concentration was not a real factor. 3. The building of a simplified model for the prediction of the Particle size was feasible. It was established through the model that for bigger particles in general there was a slow stirring rate with low concentrations of glutaraldehyde concentration, Chitosan concentration and Tween 80 concentration. The largest particle in the experiment range was 0.67mm and the smallest was 0.20mm. Read More