G2 Gel and Ultra Report Mvh 90

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    Ultrafiltration and Gel Electrophoresis

    Alyssa Fiorenza, Kaitlin Spencer, Dilwinderpal Singh, Sam Forsythe

    Department of Chemical Engineering

    Penn State

    03/22/2012

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    Ultrafiltration and Gel Electrophoresis

    Alyssa Fiorenza, Kaitlin Spencer, Dilwinderpal Singh, Sam Forsythe

    Department of Chemical Engineering

    Penn State

    03/22/2012

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    Factor Comments PointsSummary (stands alone) (10) See comments

    A bit vague in spots

    9

    Introduction (must have industrial

    example of equip/process) (5)

    UF intro too short.

    Gel intro ok, but no objective.

    Typically put a strong objective statement atthe end of the introduction.

    2.5

    Theory (10) Not that much theory. Simply restating labmanual and explaining gel calc procedure.

    This is not what a theory section should be.

    7

    Experiment and methods (enough

    detail for experiment to be

    repeated, include diagram ofprocess/equipment) (5)

    UF: good

    Gel: good, but a bit wordy. See comments.

    A bit too much unnecessary detail in spots.

    5

    Results (15)

    Clearly presented

    Technically correctAppropriate level of detail andthoroughness of documentation

    (including appendix)

    good 15

    Discussion (20)

    Relate to theory

    Deviations explainedManual questions addressed

    Completeness of analysis and

    interpretation of data

    A few minor issues. See comments in

    report.

    18

    Conclusions (10)

    Most important pointssummarized (specific)

    Ramifications made clear

    ok 9

    Figures well labeled and easy to

    read (10)

    10

    Presentation (10)

    Grammar and spelling

    Uniform writing styleEasy to read

    9

    References (5)

    (several included and usedappropriately)

    5

    Total 90

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    Summary

    The purpose of this experiment is determine how flux (v), mass transfer coefficient (kc),

    and concentration of the solute at the membrane surface change at different applied pressures andsolute concentration values. The effects of pore clogging and osmotic pressure on the permeate

    flux were also evaluated. Through the experiment, it was determined that the flux, and

    concentration of membrane surface increased as the pressure increases. This deviates fromexpected behavior as the mass transfer coefficient should be increasing as the pressure increased.

    Did you find that mass transfer coefficient decreased with pressure? It was also concluded that

    the osmotic pressure becomes a factor only at higher concentrations. Is pore clogging a factor?The value of the mass transfer coefficient was found to be what? and varied from literaturevalues by approximately 98%.

    Gel electrophoresis is a technique which separates proteins and other macromolecules

    based on size. It may be used as a method protein characterization by identification of molecularweight. Samples of pure and crude pepsin, and mucor rennet were denatured and blanketed with

    a uniform charge; the samples were then run through a porous gel by an applied electric field insolution. By comparing the migration distances with known standards, the molecular weight of

    the individual protein samples were determined to be 34.61kDa for pepsin, and 41.24 kDa formucor rennet. These values deviated from the literature values for pepsin and mucor rennet by

    1.1% and 8.53%, respectively.

    Introduction

    The goal of the ultrafiltration study was to analyze the effects of osmotic pressure andmembrane clogging during an ultrafiltration process. Another objective of this experiment was

    to determine the mass transfer coefficient of the membrane used. Ultrafiltration is a process used

    to purify and concentrate solutions. A solution is run across a membrane that retains larger

    solutes while allowing for smaller solutes and the solution to pass through the pores of themembrane. The applications for ultrafiltration are widespread and diverse. For instance,

    ultrafiltration is employed in the purification of blood as well as the processing of wastewater.

    Reference?

    Gel electrophoresis involves quantifying migration distances of charged macromolecules

    through a porous gel as an electric field is applied. This technique can be adjusted so that theproteins are separated based on properties such as mass, charge density, or isoelectric points.

    Large particles such as proteins or DNA can be sorted and identified in the manner whencompared to known standards. The technique is also widely used in DNA sequencing. Several

    variations of gel electrophoresis can be adapted to separate proteins upon taking advantage of

    different protein properties. Proteins are amphoteric, meaning they can exist at different chargesdepending on the pH of the surrounding environment. Isoelectric focusing is a type of gel

    electrophoresis which relies on the difference in charge between proteins at a certain pH. If the

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    surrounding pH is below the isoelectric point of a certain protein, the protein will become

    positively charged and will migrate toward the negative end of the applied electric field. If thepH is above a proteins isoelectric point, it will become negative and migrate toward the positive

    end of the electric gradient. Proteins at the isoelectric point will have no charge and will be

    reluctant to migrate, forming a band in the middle. Another type of gel electrophoresis, known as

    native-PAGE, separates proteins by taking advantage of differences in charge to mass ratio, orcharge density, of their native structures. SDS-Page separates proteins based on size by

    eliminating all other differences in shape and charge via heat denaturation and charge coating.Focused a bit much on iso-electric focusing, which is not used at all here.

    Where is the gel objective?

    Theory

    Membranes used in the ultrafiltration process are designed with a molecular weight cut-

    off (MWCO). In theory, 90% of solute molecules at the MWCO will be retained by the

    membrane (1). The concentration of solute increases in the retentate while the fluid that flowsthrough the membrane is known as the permeate. Due to an osmotic pressure gradient across the

    membrane, the solvent in the permeate (low concentration) has the natural inclination to flowback through the membrane into the retentate (area of high concentration). In order to prevent

    this from occurring a pressure must be applied that is greater than the osmotic pressure that willforce the solution through the membrane.

    The permeate flux (v) can be related to the applied pressure (P) and osmotic pressuregradients () and the permeability coefficient (Qm) through Equation 1.

    v = Qm*(P-) (1)

    The permeability coefficient is a function of the membrane diameters parameter such asmembrane thickness, pore diameter and the number of pores in the membrane. When the pores

    in the membrane become clogged because of solute buildup the value of Qm will decrease. Thegreater the pore clogging the lower the permeability.

    When solutions flow through the system that contain no solutes at the MWCO, in thisstudy the buffer solution is an example of this, there is no concentration gradient and osmotic

    pressure is negligible. In this case, equation 1 may be simplified as seen in equation 2.

    v = Qm*P (2)

    This equation is used to determine whether pore clogging has affected the efficiency of a

    membrane by monitoring the flux of a buffer solution vs. the applied pressure before aconcentrated solution flows across the membrane and afterward. A decrease in the determined

    value of Qm is indicative of pore clogging.

    Furthermore, the flux of the permeate is related to the mass transfer coefficient of themembrane (kc) as well as to the bulk solute concentration (cB) and the concentration of solute thathas built up on the membrane surface (cs). This is described in Equation 3 below.

    v = kc*ln(cs/ cB) (3)

    The mass transfer coefficient is a function of the concentration polarization boundary layer

    thickness () and the diffusion of the solute through the boundary layer (Dv). This relationship

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    can be seen in Equation 4 below. Concentration polarization is the effect observed when solute

    builds up on the membrane surface (2).

    kc = Dv/ (4)

    good so far, but you can do a bit more than simply restating the manual.

    Sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) uses SDS andheat treatment to both denature proteins and coat them with a negative charge. Proteins have

    secondary and tertiary structures which can cause unwanted effects during the migration in thegel. Proteins also have varied charges, which will also affect its migration in an electric field.

    SDS denatures all complex structures so that the protein will migrate as a straight chain, and it

    also coats the proteins in a uniform negative charge. This ensures that the only variable that cancontrol the migration of the protein is mass, instead of shape or charge. After loading the proteins

    in appropriate lanes, an electric field is applied and the negatively charged proteins will migrate

    toward the positive end of the electric field. Proteins with high molecular weights will migrate

    slowest, and lightweight proteins will travel fastest, why?? creating a separation based solely onsize. Standards of known molecular size are run in lanes adjacent to the proteins so that a basis is

    created on which to quantitatively relate the migration distance and molecular weight. A graphcan be obtained of the normalized migration distance and the logarithm of the molecular weight,in order to obtain a relationship which can then be used to determine unknown weights from the

    normalized migration distance for specific proteins. Why is this linear?

    A 95% confidence interval will be determined for our results. This confidence interval

    can be derived from both the standard error (SE) and standard deviation (SD) of the data. Thestandard deviation quantifies how closely the data points group around the mean and can be

    determined by the following equation:

    SD = (XiM)21 (5)Where Xi is the data point in question, M is the mean of the data, and N is the number of datapoints.

    The standard deviation can then be used to find the standard error. The standard error

    corrects the standard deviation based upon the size of the sample surveyed. The larger the study,

    the less chance rogue points will distort the true value of the mean. The standard error is

    represented by the following equation:

    = (6)The confidence interval (CI) quantifies a range in the data in which confidence exists that

    the true mean actually describes the data in this range. The equation for a 95% confidence

    interval is as follows:

    95% = (1.96 ) (7)Gel portion reads more like a calculation method section than a theory section. Explain the

    theory behind gel electrophoresis. Why can you make the linear correlation? Why do smaller

    proteins travel further through the gel?

    Experimental Procedure

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    The ultrafiltration study used a membrane with a MWCO of 10kDa. The membrane was

    secured onto a membrane holder and placed at the base of a Millipore 8010 Stirred Ultrafiltration

    Cell. 50mL of deionized water was run through the membrane to prepare it for the experimental

    runs. In this study, 1mg/mL and 2mg/mL porcine pepsin solutions were run. These solutionswere prepared in a 20mM sodium acetate solution at pH 5.

    Ultrafiltration

    Figure 1 displays the experimental setup of this ultrafiltration study. As seen in this

    figure the source of the applied pressure was a nitrogen tank where the pressure would be

    controlled via a regulator valve. A feed tank is aligned between the nitrogen tank and the cell

    body to hold excess fluid as the cell can only hold 70mL. Permeate was collected from the feed

    tank into 10mL graduated cylinders. The rate at which the permeate collected was monitored by

    recording the time at which each milliliter accumulated.

    Figure 1: Experimental Setup of Ultrafiltration System

    Three different 200mL solutions were run through the membrane, a pure sodium acetate

    buffer solution as well as the two pepsin solutions. The experiment began by running a buffer

    solution followed by the 1mg/mL pepsin solution, the 2mg/mL pepsin solution and finally the

    buffer solution once more. The pressure was applied to the system in increments of 10psi

    ranging from 30 to 50psi. The permeate flux was monitored over 20mL of permeate collected

    for each solution at each pressure variation. The full experimental procedure can be found in the

    Ultrafiltration and Gel Electrophoresis Manual (1).

    Four individual protein solutions were made. These solutions include were made with 5

    mg protein per ml of deionized water, and included 5 mg/ml crude porcine pepsin, 5 mg/ml

    Gel Electrophoresis

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    mucor rennet, 5 mg/ml mix of crude pepsin and mucor rennet, and 5 mg/ml of pure pepsin. Each

    solution included 65 microliters of a specific protein solution, 25 microliters of 4X NuPAGE

    LDS Sample Buffer, and 10 microliters of NuPAGE 10X Reducing Reagent. All of these

    solutions were vortexed and placed in microfuge vials in the heating block at 70C for a total of

    10 minutes.

    As the protein solutions were heating, the SDS running buffer solution was prepared by

    combining 40ml of NuPAGE SDS Running Buffer (20X) with 760 ml of purified water. This

    overall solution was separated into a 600 ml portion and a 200 ml portion, and 500 microliters of

    NuPAGE Antioxidant was added to the 200 ml portion and mixed.

    The gel box was retrieved from the refrigerator and cut open with scissors. Not needed

    The cassette type of gel used is important was rinsed off with distilled water, and the locations of

    the wells on the front of the cassette were marked with a permanent marker. The comb was

    carefully removed from the top of the cassette, and the tape was removed from the bottom. The

    cassette was then properly placed into the front of the gel box, and the white electrode connectorwas slid into the gel box behind the gel. A dummy gel was inserted into the box behind this

    electrode connector, and the entire apparatus was secured by a clamp behind the dummy gel.

    The inner chamber was then filled with the remainder of the 200 mL running buffer. The

    experimental setup can be seen in Figure 2.

    Figure 2. Experimental Setup of Gel Electrophoresis

    The gel samples were removed from the heating block and vortexed. Using the

    micropipette, 10 microliters of each prepared gel sample and protein marker standard were

    loaded into the correct lanes of the gel. The protein standard marker was loaded into lanes 2, 3, 6,

    9. Pure pepsin solution was added to lane 4, the mixture of pepsin and mucor rennet was added

    to lane 5, crude pepsin solution was added to lane 7, and mucor rennet solution was added to lane

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    8. Sample location on gel is not really important. Just show the appropriate lanes on the gel

    figure in the results section. The outer chamber was then filled with the 600 mL buffer without

    antioxidant. The lid was placed on the box and aligned with the positive and negative poles.

    After this was accomplished, the power was turned on, the voltage was set for 200V, and the

    timer was set to run for 45 minutes. After setting these specifications, the on button was pressed

    and the gel was allowed to run. Not needed too much info

    After 45 minutes, the wires were unplugged from the power source; the lid of the gel box

    was removed, as well as the wedges holding the setup together. The gel cassette was removed

    and rinsed with distilled water. Approximately one inch of deionized water was added to the

    staining container. The gel cassette was then carefully cracked open, one side of the gel was

    discarded, and the gel was placed into the water immediately. Too much detail. Simply state gel

    removed from cassette and rinsed The other side of the cassette was slowly and carefully

    removed, allowing the gel to fall directly into the distilled water. The gel was washed for 5

    minutes with 100 mL of DI water with gentle agitation. This process was repeated two more

    times.

    After dispensing the DI water, the gel was covered entirely with stain and allowed to sit

    with gentle agitation for 45 minutes. After this, the stain was discarded and the gel was de-

    stained with distilled water several times for 45 minutes, and until the bands were clearly visible

    on the gel. The gel was placed within a piece of clear plastic wrap, and a picture of the gel was

    taken with a digital camera before marking with a permanent marker. After fully labeling the gel

    with lane numbers and traced bands, another picture was taken. The latter picture was used to

    determine the percent distance traveled of the protein solutions.

    Results and Discussion

    From Figure3, it can be seen that the permeate flux is directly proportional to the

    applied pressure. As the pressure increased, the flux increased. The relationship between

    filtration rate and pressure is the same because the filtration rate is calculated by multiplying

    membrane area by flux. Therefore, as the pressure increased, the filtration rate would also

    increase.

    Ultrafiltration

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    Figure 3: Graph of permeate flux versus applied pressure for four different runs

    In order to determine whether osmotic pressure was an issue during this experiment,

    Figure 3 was analyzed comparing buffer runs to protein solution runs. During the buffer runs

    there is no osmotic pressure because there is no solute to build up. The flux () for buffer runs

    can be simplified to Equation 2 where Qm is the permeability coefficient andPis the applied

    pressure (either 30, 40, or 50psi). this would be good place to state Qm for this experiment

    However, when the protein solutions are run across the membrane the accumulation of

    solute in the retentate causes the osmotic pressure to increase. The flux can be related to the

    applied pressure (P) through Equation 1 where is the osmotic pressure difference across the

    membrane.

    Figure 3 displays the values of flux versus applied pressure for each of the four solutions

    tested. The flux values obtained for the first protein solution (1mg/mL) at 40psi do not follow

    expected trends. There may have been error in the applied pressure of this run and thus these

    values will not be considered in the analyses performed in this study. The profile of Solution 2 is

    evidence of the effect of osmotic pressure on the permeate flux. The flux values are well below

    the flux values of the buffer solutions at the same applied pressure.

    Membrane clogging is an issue that is commonly present in ultrafiltration systems but didnot appear to be a problem in this study. From equation 2 it can be seen that the slope of the flux

    vs. pressure line for the buffer solutions is equal to the permeability coefficient (Qm). The slope

    of the lines for the buffer run at the beginning of the experiment and the buffer run at the end of

    the experiment were compared. The slopes were found to be about the same, 9E-5 untis? for the

    pre-buffer and 9.1E-5 for the post-buffer. This indicates that the permeability coefficient of the

    0.002

    0.0025

    0.003

    0.0035

    0.004

    0.0045

    0.005

    0.0055

    30 35 40 45 50 55

    permeateflux(mg/mlcm^2)

    Pressure (psi)

    Average permeate flux versus Pressure

    Pre Buffer

    Post Buffer

    Protein Solution 1mg/ml

    Protein solution 2 mg/ml

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    membrane remained constant and pore clogging was not an issue. The non-linearity of the

    2mg/mL protein solution is thus attributed to osmotic pressure effects.

    The osmotic pressures of each protein solution at different applied pressures were

    determined be using Equation 1. It was assumed that the permeability coefficient (Qm) remained

    constant. In our case, the value of flux is very small so the value of osmotic pressure isdependent on applied pressure. As the pressure increased, the osmotic pressure also increased.

    Show some of your results. This is long report. You have room.

    There was a change found in the values of the mass transfer coefficients between the

    calculated values and estimated value what do you mean by these terms? Jonnsons and dilute

    ideal solution? Both are estimates when the solution was assumed to be dilute and ideal. This is

    due to the fact that the surface concentration Cs is different in both cases. The percent errors you

    mean % difference between the calculated value and ideal solution values for 1 mg/ml

    concentration can be found in Table 1. The difference between the calculated values and ideal

    solution is greater at a higher concentration of 2mg/ml. In order to calculate the surfaceconcentration, Cs, two different methods were used. The first used the Jonsson equation (and

    solver) and then the surface concentration was determined assuming dilute and ideal conditions.

    Under these conditions, surface concentration Cs was calculated by multiplying molarity by

    molecular weight. In both cases flux and bulk concentration Cb remains constant and equation 3

    was used to calculate the mass transfer coefficient. The difference between the calculated values

    and estimated values are shown in Table 1.

    Table 1. Calculated mass transfer coefficient values compare to the estimated values.significant figures!!

    Calculated Dilute and Ideal % Error

    1 mg/ml Pressure ( psi) K c( cm/sec) What is this? Kc?

    Difference orerror? If error,

    from what?

    30 0.001073488 0.000481468 55.14%

    40 0.00068063 0.000478953 29.63%

    50 0.001187155 0.000732534 38.29%

    2 mg/ml Pressure ( psi) Kc ( cm/sec)

    30 0.001474224 0.000594276 59.68%

    40 0.001015118 0.00057982 42.88%

    50 0.000987457 0.000594671 39.77%

    The value of the mass transfer coefficient kc is different for both concentrations at differentpressures which is shown is Table 2. From the Table 2, it can be seen that the percent error is

    decreasing as the pressure increases. The mass transfer coefficient Kc was calculated using

    equation # ?? and it should increase as the pressure increased but in our case as the pressure

    increased the mass transfer coefficient decreased. It increased for 1 mg/ml but not for 2 mg/ml

    (nearly constant for dilute and ideal case) It could be because our data is not perfect. The

    surface concentration Cs should also increase as the pressure increased but in our case for 1

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    mg/ml at 50 psi, it is lower than the value of Cs at 40 psi. This is because our osmotic pressure at

    50 psi is lower than the 40 psi. this is not stated correctly. The osmotic pressure increased as the

    pressure increased but this is not happening in our case at 50 psi for 1mg/ml. The literature

    value of the mass transfer coefficient is 1.77E-5cm2/sec. what is this for? Pepsin? Or some other

    protein? This is very different from the calculated values. The difference between the calculated

    values and literature values of mass transfer is big and it is shown in the Table 3. More

    experiments should be done to confirm the results so the difference between the literature value

    and calculated value could be lower. Your % error is much greater than 100%. You are an order

    of magnitude off. Its more like 300%.

    Table 2. Compare Cs and Kc values calculated for the 1mg/ml and 2 mg/ml.

    1 mg/ml 2 mg/ml % Error

    Pressure ( psi) Kc( cm2/sec) Cs K c( cm

    2/sec) Cs Kc Cs

    30 0.000482403 45.68 0.00061148 20.82 26.75626 54.42207

    40 0.000534545 114.04 0.00065122 89.46 21.82623 21.55384

    50 0.000798779 84.95 0.0007006 150.82 12.29088 77.53973

    Table 3. Difference between calculated value and literature value.

    1 mg/ml

    Calculated Literature3

    Pressure Kc( cm2/sec) Kc( cm

    2/sec) % Error

    30 0.000734171 1.77E-05 97.58

    40 0.000708797 1.77E-05 97.50

    50 0.001115723 1.77E-05 98.41

    2 mg/ml

    Pressure Kc( cm2/sec) Kc( cm2/sec) % Error

    30 0.001254105 1.77E-05 98.58

    40 0.000945409 1.77E-05 98.12

    50 0.000954769 1.77E-05 98.14

    The gel electrophoresis technique gave very clear, sharp bands, as evident in Figure 4.

    Gel Electrophoresis

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    Figure 4: Gel electrophoresis results show very clean sharp bands after staining; the large band

    represents pure pepsin. The bands were marked with a black marker.

    After measuring the migration distance of bands of interest, a plot was created of the

    percent migration distance and the log of the molecular weights of the marker and superimposed

    with a linear trendline (Figure 5).

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    Figure 5: A graph of thepercent migration of the marker versus the logarithm of the molecular

    weight. The percent migrations were calculated using a trendline equation with a 95%

    confidence interval.

    Using the trendline equation and the percent migration values for the protein samples, the

    molecular weights for each protein was calculated and presented in Table 4.f you show 2 bands

    for mucor rennet and 3 for the mix. You should id all the bands in the table.

    Table 4: Pertinent information for each of the proteins of interest, including normalized

    migration distances and molecular weight. Significant figures!

    The error ranges were calculated for both mucor rennet and pepsin using a 95%

    confidence interval. After determining the values for the standard deviation and standard error ofthe data, which were 0.368 and 0.122 respectively, equation 7 was used to find a 95% confidence

    interval for the logarithm of the molecular weights of pepsin and mucor rennet. These upper and

    lower ranges for pepsin and mucor rennet were 1.809, 1.268, 1.866 and 1.364 respectively and

    are graphed in Figure 5. More useful if max and min are given in kDa.

    The calculated values of mucor rennet and porcine pepsin were determined to be

    41.24kDa and 34.62kDa, respectively. The literature values of these proteins are 38kDa and

    Sample Name Sample Lane Number Migration Distance % Migration Distance Log(MW) MW of Samples (kDa)

    Pure Pepsin 4 13.5 73.7704918 1.539262 34.61483734

    Mucor Rennet (in mixture) 5a 12.3 67.21311475 1.615328 41.24087479

    Crude Pepsin (in mixture) 5b 13.5 73.7704918 1.539262 34.61483734

    Crude Pepsin 7 13.5 73.7704918 1.539262 34.61483734

    Mucor Rennet 8 12.3 67.21311475 1.615328 41.24087479

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    35kDa, respectively. The calculated molecular weight of pepsin carried with it a percent error of

    1.1%, and the calculated molecular weight of Mucor Rennet has a percent error of 8.53%. The

    calculated values are within the error range of the method.

    There were some differences between the crude and pure pepsin in terms of how they

    migrated through the gel. Both bands created by pure pepsin and crude pepsin can be identifiedbecause the band for crude pepsin aligns with the center of the band for pure pepsin. The pure

    pepsin band was much wider compared to that for crude pepsin, which looked narrow and sharp

    like the other bands. This smearing may have been caused by the high concentration of pure

    pepsin present in the injected sample. good

    There were a few extraneous bands in the lanes which contained mucor rennet. Lane 8,

    which contained only mucor rennet, showed two bands, one for the mucor rennet protein and

    another for a component with less mass. This component may be another protein variation of

    mucor rennet or more likely a contaminant in the mucor rennet solution. This same solution was

    used to make the pepsin and mucor rennet mixture; the unknown band is also present in lane 5.

    Conclusion

    In the ultrafiltration experiment, it was concluded that an increasing pressure resulted in

    increasing flux. The Jonssons equation was used to calculate the surface concentration Cs and

    it was determined that the surface concentration increases as the pressure increased. During the

    buffer runs there is no osmotic pressure because there is no solute to build up so the osmotic

    pressure was calculated only for protein concentrations and not for pre and post buffer solution.

    It was concluded that the osmotic pressure has a linear relationship with pressure and it increased

    as the pressure increased. The values of calculated mass transfer coefficient were different than

    the estimated mass transfer coefficient. be a bit more specific by giving actual values.

    Using SDS-PAGE gel electrophoresis, the molecular weights of pepsin and mucor rennet

    were experimentally determined to be 34.61kDa for pepsin, and 41.24 kDa sign figs too high for

    mucor rennet. This was accomplished by denaturing the proteins and coating them with a

    uniform negative charge so that molecular weight would become the only factor in migration

    distance. These distances were then compared with known standards in order to calculate each of

    the proteins molecular weight and their respective standard error. The 95% confidence intervalof pepsin ranged from 18.6 kDa to 64.5 kDa, and 23.2 kDa to 73.5 kDa for mucor rennet. The

    calculated values were well within these ranges.

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    References

    (1) "Ultrafiltration and Gel Electrophoresis Manual, Chemical Engineering 480Undergraduate Chemical Engineering Laboratory. The Pennsylvania State UniversityDepartment of Chemical Engineering, 2011.

    (2) Sechurl, Kim. Concentration Polarization in Pressure-Driven Crossflow Membrane

    Filtration. http://www.yale.edu/env/elimelech/Conc-Polarization/sld001.htm

    (3) Brandani, Stefano, Loredana Spera, Vicenazo Brandani, and Gabrieledi Giacomo.

    "Enzyme and Microbial Technology." (1996). Web. 21 Mar. 2012.

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    APPENDIX- Scanned Prelab Pages

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