Materials & Apparatus - Penn Engineering
Calcium Content of Milk
Final Report for BE 210 – Bioengineering Lab II
Dr. Mitchell Litt
April 29, 1998
Group W8
Minhthe Luu
Sofiya Kuchuk
Anil Seetharam
Adrian Shieh
Abstract
The objectives of the experiment were to experimentally determine the calcium content in milk through atomic absorption spectrophotometry and to ascertain whether the standard method described by Perkins-Elmer Co. for calcium determination in milk using atomic absorption spectrophotometry is the most viable procedure.
The calcium content of four different types of commercially available cow’s milk was determined using a flame atomic absorption spectrophotometer. Milk was treated with one or both of two reagents, trichloroacetic acid and lanthanum chloride. The addition of lanthanum only was found to be most efficient on the basis of accuracy, speed, and cost. Using this method, the calcium content (in ppm) of whole, 2%, 1% and skim milk were found to be 1218 ( 5.21%, 1158 ( 0.79%, 1175 ( 1.53% and 1154 ( 1.53%, respectively.
Background
Milk is a complex mixture of emulsified lipids and proteins, in addition to other dissolved components such as lactose, vitamins, and minerals. Milk is known for its high calcium content. In milk, calcium exists both as an ion and as Ca9(PO4)6 bound to the protein casein (Dairy Science & Technology). Casein is the major protein in milk, and it forms spherical submicelles due to its hydrophobic nature. These submicelles clump together due to the interactions between Ca9(PO4)6 and (-casein (Figure 1). Anywhere from 75% to 90% of the calcium present in cow’s milk is bound to casein (Hurley) (Dairy Science & Technology).
Milk must undergo several different stages of processing before it can be sent to the market (Figure 2). The first stage is clarification, standardization, and separation. The milk is centrifuged to remove fat and solid impurities. Cream is reintroduced to the purified milk if necessary (to make non-skim milk). The second stage, pasteurization, is a process that eliminates most bacteria from milk by heating it over an extended period of time. The third process, homogenization, reduces the size of fat globules in milk. Finally, the milk is fortified with nutrients such as vitamins A & D, and possibly calcium if the milk is of the calcium-enriched variety (Dairy Science & Technology). It is important that, in processing the milk, there is no mechanism by which dairy producers change the calcium concentration. Except for enriched milk, the calcium present in the raw milk is essentially unchanged after processing. Therefore, the calcium concentration in milk depends on the calcium in the diet of the cows.
To determine the total calcium content in milk, it is necessary to dissociate the calcium ion from the calcium-casein complex. This is typically accomplished by acid precipitation of casein. Acid liberates calcium from casein, causing the insoluble phosphoprotein to precipitate (Laboratory of Crystallography). Precipitation of the protein also means that it can be easily removed to prevent clogging of the spectrophotometer. Another consideration is interference with calcium caused by the formation of calcium-phosphorus and calcium-sulfur compounds. These compounds cannot be easily dissociated in the flame. Lanthanum or strontium are added to compete with calcium for phosphorus, to prevent formation of Ca-P molecules (McKenzie, 174). Sodium, magnesium and potassium can also cause interference, but only at concentrations of 500 ppm or more, higher than concentrations typically found in milk (Stable Isotope Lab, U. of Ga.). Methods and theory related to the use of the atomic absorption spectrophotometer can be found in the Bioengineering Laboratory II Manual.
Figure 1: Diagram of the casein submicelle and micelle structures(Dairy Science & Technology).
Figure 2: A flow chart of the processing milk undergoes from a raw state to
packaging (Dairy Science & Technology).
Materials & Apparatus
1. Trichloroacetic acid, Sigma-Aldrich (100% w/v, 6.1N)
2. Lanthanum chloride, Sigma-Aldrich
3. Milk (Wawa brand – skim, 1% milk fat, 2% milk fat, whole)
4. Perkin-Elmer Model AA 4000 atomic absorption spectrophotometer
5. Miscellaneous glassware
6. 15 & 50 mL plastic flasks
7. Stir plate
8. International Equipment Company Model PR-7000 centrifuge
9. Digital micropipetters- P-20, P-200, P-1000
10. Pipet-Aid
Procedure
Overview
This lab required the preparation of three stock solutions to be used to calibrate the AAS. These solutions were diluted calcium stock solutions with the following reagents: (1) TCA + La, (2) La only, and (3) TCA only. In addition, twelve test milk solutions were prepared by treating each of the four milk samples with the above reagents. The following is a detailed outline of the preparation of these solutions.
Day One
The first task was preparation of the necessary solutions. The solutions and subsequent dilutions were made with deionized water. The lanthanum solution was made by taking 8.828g of LaCl3 and mixing with 100 mL of deionized water, to produce a 5% w/v solution. The lab coordinator provided a 1000 ppm Ca standard and 100% w/v TCA. Before the measurements were taken on the AAS it was configured to test for calcium. Bulb two was selected with the current at 10 mA, slit size 0.7L, and wavelength of 422.7 nm. The optimum fuel rate, after experimenting with tap water (which is calcium-rich) and different fuel-air settings, was determined to be 18 fuel to 45 air.
The first task was to prepare the different kinds of calibration solutions. The solutions made were calcium plus TCA and La solution, calcium with TCA only, and calcium with La solution only. The only solutions used the first day were the TCA plus La solutions, the rest were stored for days two and three.
1. Preparation of calibration stock
Prepared stock Ca solutions (1-6 ppm) with TCA + La/TCA/La and blanks (no Ca). For X ppm, use X * 10 (L Ca stock
a. for TCA-lanthanum: (e.g. 1ppm) 10(L Ca stock + 120(L TCA + 1mL lanthanum and diluted up to 10mL
• the blank was constructed by taking 120(L TCA + 1mL lanthanum and diluting up to 10mL
b. for TCA only: 10(L Ca stock + 120(L TCA and diluted up to 10mL
• the blank was constructed by taking 120(L TCA and diluting up to 10mL
c. for lanthanum only: 10(L Ca stock + 1mL lanthanum and diluted up to 10mL
• the blank was constructed by taking 1mL lanthanum and diluting up to 10mL
On day one, the milk samples were prepared. The milk was treated with TCA to precipitate out the proteins. After the milk was centrifuged, the supernatant was used to make three different dilutions of calcium. An equal amount of La was added to each. These samples were tested in the AAS. For the first day, only the milk samples containing both TCA and La were tested.
2. Preparation of milk sample
Milk types: Skim, 1% low fat, 2% low fat, whole
A. For sample with TCA & Lanthanum:
a. 500 μL milk + 1.2 mL TCA dilute to 10mL
b. shake at five minute intervals for 30 minutes
c. centrifuge at 8oC, 2500 RPM, 5 min.
d. transfer the supernatant into a different vial to store for future use
e. three concentrations of each milk sample were made from the supernatant
• 200μL milk stock + 500μL lanthanum and diluted up to 5mL
• 300μL milk stock + 500μL lanthanum and diluted up to 5mL
• 400μL milk stock + 500μL lanthanum and diluted up to 5mL
f. the samples were tested using AAS
The calibration stock and supernatant from the milk was saved for use on days two and three.
Day Two
On day two, using the supernatant from day one two different treatments were performed. One of them contained both TCA and La, the other contained only TCA. From the original milk stock a treatment containing La only was performed. During this treatment the milk was diluted and centrifuged as before, except no TCA was added to precipitate the proteins. From all the three treatments only one concentration was prepared. Instead of making three different concentrations, a dilution factor of 333 was used since it was found to be the most favorable concentration.
2. Preparation of milk sample (continuation from day one)
B. For sample with TCA and lanthanum:
a. using the supernatant from A, a 3ppm concentration of each milk type was made
• 300μL milk stock + 500μL lanthanum diluted up to 5mL
b. calibration curve was constructed using stock (part 1a)
c. samples were analyzed using AAS
C. For sample with TCA only:
b. using the supernatant from A. a 3ppm concentration of each milk type was made
• 300μL milk stock diluted up to 5mL
b. calibration curve was constructed using stock (part 1b)
c. samples were analyzed using AAS
D. For sample with lanthanum only:
a. 500 μL milk was diluted to 10 mL
b. centrifuge at 8oC, 2500 RPM, 5 min
c. no pellet formed, consider all as a supernatant
d. three concentrations of each milk sample were made from the supernatant
• 300μL milk stock + 500μL lanthanum and diluted up to 5mL
e. calibration curve was constructed using stock (part 1c)
f. samples were analyzed using AAS
Day Three
On day three, the focus was on two treatments only, TCA + La and La only. It was decided that further testing of TCA only samples would not be performed, since on day two the results obtained made it obvious that La was a necessary component in the solution. For the two treatments performed new milk stock was prepared for both as well a calibration stock for TCA with La. Three aliquots were taken from each milk sample to provide a larger sample size to facilitate statistical analysis of the results. Otherwise, the procedures for sections B and D from day two are unchanged.
Results
A calibration curve was constructed for each milk treatment (See Procedure for more details about stock preparation). The equation of the best-fit line of each curve was used to calculate the concentration of Ca2+ in the samples given the AAS-generated absorbance measurements. Figure 1 is an example of a calibration curve. Concentrations used to plot these curves were selected to lie within the optimum detection range of calcium for the AAS: 0.2 ppm to 7 ppm.
Figure 1: A representative calibration curve, in this case, the plot for the TCA + La treatments series, Day 3.
The following graphs give the measured mean concentrations for each milk type and treatment. A clear observation that can be made is that all experimental results are less than the expected (USDA) results. A second observation is that the measured concentrations for all samples tested with TCA alone were significantly lower than those of the other tests.
Figure 2: A comparison of measured calcium content using the three methods
described in Procedure. Note: Approximately 50% decrease in calcium
detection when using TCA only.
Figure 3: Summary of calcium content for 2% milk for three procedures tested.
Figure 4: Summary of calcium content for 1% milk for the three procedures tested.
Figure 5: Summary of calcium content for skim milk for the three procedures tested.
Statistical Analysis
Two statistical tests were used to compare the data collected in the experiment. To determine whether or not a significant difference existed between the calcium content of different types of milk, a single-factor analysis of variance (ANOVA) test was employed. This statistical test is used typically to analyze populations of data where more than two different treatments of one factor are used, e.g. four different milk types (Devore, 390). A two-sample t-test was used to compare different treatments of the sample milk type. The variances of the two samples were not assumed equal ((12 ( (22). This test is typically used to compare two distinct groups of data. In this case, the distinction between the populations is the treatment method used on the milk samples (Devore, 357).
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|Milk Type |t-stat |t-critical |
|Whole |-0.505 |1.76 |
|2% |-6.186 |1.70 |
|1% |4.381 |1.71 |
|Skim |-2.385 |1.73 |
Table 1: Two-Sample t-test with unequal variances shows there is no significant statistical difference within whole, 2% and Skim between TCA & La versus La only treatments, while for 1% there is a difference.
|ANOVA single factor: | | |
|between milk types | | |
|Treatment |F |F-critical |
|TCA & La |68.83 |2.72 |
|La |2.94 |2.81 |
|TCA |13.23 |4.07 |
Table 2: ANOVA single factor test was performed within milk treatment groups between the four milk types. The test showed a significant difference for TCA & La treatment as well as the TCA only treatment. For the La only treatment a smaller, but still significant, difference was found.
|Milk Type |Dairy Council (ppm) |USDA (ppm) |
|Whole |1230 |1194+0.41% |
|2% |1255 |1216 |
|1% |1268 |1230 |
|Skim |1276 |1234+4.02% |
Table 3: The data in the left column were quoted as Federal standards by the Dairy Council of California. The USDA standards in the right column are drawn from a nutrient database collected from different independent research groups. The database listed standard error and number of samples for the whole and skim standards. This data was used to determine the 95% confidence interval shown in the table.
The sum of the 95% confidence and propagated error data listed in Table 4 gives the percent-wise interval around the mean that is valid for each result. For example, this interval for whole milk treated with TCA + La would be ( 8.18% about the mean.
|Milk |Milk Treatments |Propagated |95% confidence |% Error, Dairy |% Error, USDA |
|Type | |Error |intervals |Council | |
|Whole |TCA & La |6.79% |1.39% |2.27% |0.67% |
| |TCA |11.74% |1.34% |46.24% |44.62% |
| |La |6.24% |5.21% |1.00% |1.98% |
|2% |TCA & La |6.98% |1.06% |11.48% |8.62% |
| |TCA |11.77% |1.55% |47.54% |45.84% |
| |La |6.35% |0.79% |7.72% |4.74% |
|1% |TCA & La |6.74% |1.10% |3.35% |0.37% |
| |TCA |11.67% |1.32% |47.24% |45.61% |
| |La |6.32% |1.53% |7.31% |4.45% |
|Skim |TCA & La |6.96% |1.10% |11.47% |8.43% |
| |TCA |12.06% |1.32% |50.65% |48.96% |
| |La |6.36% |1.53% |9.57% |6.46% |
Table 4: Summary table of error found in each milk type and treatment given with respect to the Dairy Council of California and USDA values. The propagated error was determined using the exact differential approach (See Appendix).
Discussion
The experimental results showed statistically significant differences between the calcium concentrations of the four milk types tested, in all treatment groups. The statistical analysis (using the single-factor ANOVA method) shows that calcium content does depend on the type (fat content) of milk. It does not elucidate the nature of the correlation. Literature values report a general trend of increasing calcium concentration with decreased milk fat. This is a logical conclusion since the lipids in milk do not contain calcium. As the fraction of fat by volume increases, the amount of protein and water (where the calcium resides) per unit volume decreases.
Three methods of treating the milk were compared to determine if the protocol described in the Perkins-Elmer spectrophotometry manual and Milk Proteins (McKenzie) was the most efficient procedure available. The results of the milk treated with TCA only showed a significantly lower measured content of Ca2+ ions. This is attributed to interference caused by the formation of calcium compounds, such as calcium phosphate and sulfate, which are not easily dissociated in the flame. Without the addition of lanthanum to compete with calcium for these anions, these compounds form readily and result in approximately 45-50% reduction in detectable calcium content. The data clearly shows that lanthanum is necessary to prevent interference with calcium caused by sulfur and phosphorus. The addition method, the protocol of adding lanthanum or strontium to milk to prevent interference, is the accepted procedure when determining the content of calcium in milk (McKenzie, 174-175).
The results for the lanthanum only treatment and the TCA and lanthanum treatment (described by Perkins-Elmer) did not show significant differences in calcium content. TCA was selected as a reagent to precipitate the protein casein. These proteins bind with calcium and account for 75% of total calcium content of cow’s milk. It was necessary to liberate the calcium from the protein molecule. The data collected, however, does not show any significant variation between the two different treatment groups. The conclusion is that the flame was sufficiently hot to denature the protein and dissociate the calcium from the casein micelles. If this is the case, prior degradation of the protein molecules is not necessary. The conclusion from the results is that the addition of lanthanum, or any other element that exhibits similar favorable properties, is important in preventing interference with calcium due to the formation of calcium sulfate and calcium phosphate. However, acid precipitation of casein is not necessary. The most cost-effective and least labor-intensive method is the dilution of pure milk and addition of lanthanum only.
The conclusion regarding the most efficient treatment to determine the calcium concentration of milk may seem incongruous: sources cited in this paper recommend treating milk with TCA as well. The results of this report seem to suggest that not only is lanthanum treatment the most effective way to treat milk, but prevention of interference with lanthanum is the more important treatment step when testing milk. This is further evidenced by the observation that the TCA only treatment released just half of the total calcium in milk.
Precision & Error Analysis
Atomic absorption spectrophotometry is typically considered a very precise method for the determination of ion concentrations. The instrument itself provides excellent readings, and, when properly used, can yield excellent results. The primary sources of systematic error in this experiment, as determined by using the exact differential method, were the calibration curve and precision of instruments used in diluting the samples (see Appendix). The calibration curve regressions showed a good degree of fit (R2 > 0.995), but there are statistical uncertainties in the calculated slopes and intercepts of the calibration curves in the form of 95% confidence limits. The dilution factor is similarly a source of propagated uncertainty. Successive dilutions using the digital micropipetters can result in as much as a 2.70% variation in the dilution factor.
Further Considerations
One possible avenue of continued experimentation is determining the calcium content of milk from alternative sources. Currently, cow’s milk is by far the most prevalent dairy source. There does exist a small market for exotic dairy products derived from goat and yak milk, among others. There are also non-dairy alternatives like soymilk. One question that could be asked is whether cow’s milk is the ideal source for nutritional calcium. Clearly, other considerations besides the calcium content of determine milk’s nutritional value, including the presence of proteins, sugars, and other dissolved nutrients. For example, lactose intolerance prevents a significant portion of the population from consuming cow’s milk and derivative products. Dairy products, however, are nutritionally important primarily because they are the most enriched source of calcium found among the four food groups. Some studies have already been done on milk from different species of mammals, and these could serve as starting points (Hurley).
Another possible experiment would be to determine the amount of interference caused at different concentrations of calcium. This could be accomplished using recovery spiking. Furthermore, a relationship between the concentration of lanthanum and the amount of interference (if any) that occurs could also be quantified. Knowing the optimum amount of lanthanum to inhibit interference of a given concentration of calcium would allow researchers to limit the amount of lanthanum used.
References
1. Bioengineering Laboratory II Manual. Department of Bioengineering, Spring 1998.
2. “Dairy Nutrition”. Dairy Council of California. . © 1997
3. “Dairy Science and Technology”. University of Guelph. .
4. “Determination of Metals in Milk.” FP-11. Perkins-Elmer AAS Manual.
5. Devore, Jay L. Probability and Statistics for Engineering and the Sciences, 4th ed. Duxbury Press: New York, 1995.
6. Hurley, Walter L. “Lactation Biology”. Department of Animal Sciences, University of Illinois. . Jan. 26, 1997.
7. McKenzie, Hugh A., ed. Milk Proteins, Vol. 1. Academic Press: New York, 1970.
8. “Metals Analysis by Flame Atomic Absorption Spectrophotometry”. Stable Isotope Laboratory, Institute of Ecology, University of Georgia. . July 22, 1997.
9. “Preparation of Casein from Skim Milk.” Laboratorium voor kristallografie, Universiteit van Amsterdam. .
10. “USDA Nutrient Database for Standard Reference, Release 12”. Nutrient Data Laboratory, United States Department of Agriculture.
. March 30, 1998.
Appendix: Determination of Systematic Error
Systematic error was quantified using the exact differential method, summarized in the following equation:
(F(x,y,z) = ((F/(x((x + ((F/(y((y + ((F/(z((z, where (x, (y, and (z are the uncertainty values associated with their respective variables
The equation used to determine the concentration of milk is:
Cmilk = [D(A – b)]/m
D = dilution factor of sample; A = absorbance of sample; b = y-intercept of calibration curve; m = slope of calibration curve (in ppm-1)
The dilution factor was calculated using the equation:
D = (V1V2)/(VmilkVtreated)
V1 = final volume of initial dilution; V2 = final volume of final dilution; Vmilk = volume of milk used in initial dilution; Vtreated = volume of treated milk used in final dilution
Using these two formulas, the systematic error in the dilution factor and in the concentration of calcium can be determined:
(D = (V2/(VmilkVtreated) ((V1 + (V1/(VmilkVtreated) ((V2 + ((V1V2)/(VtreatedVmilk2) ((Vmilk + ((V1V2)/(VmilkVtreated2) ((Vtreated
(V1 = 0.1 mL; V1 = 10 mL
(V2 = 0.05 mL; V2 = 5 mL
(Vmilk = 5 mL; Vmilk = 0.001 mL
(Vtreated = 0.001 mL; Vtreated = 0.2-0.4 mL
(Cmilk = (D/m((A + (-D/m((b + (D(b-A)/m2((m + ((A - b)/m((D
Values inputted for this equation depend on the sample and test group to which it belonged.
These two formulas were used to calculate the propagated error values quoted in Results, Table 4.
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