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Media Formulation, Media Optimisation,

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Media Formulation, Media Optimisation, Criteria for good media, Placket Burman Design, PB Design, Response Surface Methodology, RSM

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Media Formulation, Media Optimisation,

  1. 1. Criteria for good medium • It will produce the maximum yield of product or biomass per gram of substrate used • It will produce the maximum concentration of biomass or product • It will permit the maximum rate of product formation • There will be minimum yield of undesired products • It will be of consistent quality and available throughout the year • It will cause minimal problems during medium sterilization • Other aspects of production process such as aeration, agitation, downstream processing, waste treatment
  2. 2.  Medium designed will affect the design of fermenter ex oxidation of hydrocarbons highly aerobic process –air lift reactor  Problems will be encountered in scaling up. Since large reactors will have low mass transfer rate  High viscous medium will consume more power.  Besides growth and product formation medium will influence the pH variation, foam formation, morphological form of organism etc.,
  3. 3. Use of complex nutrients will influence downstream processing Variation in complex nutrients will result in batch to batch variations. Medium cost has to be considered depending on the product type. Eg. For single cell protein production medium cost is more than 50 % of production cost. In the case of pencillin it is 30% and in recombinant products it is less than 10 %.
  4. 4. Medium formulation Medium formulation is essential stage in manufacturing process Carbon & Nitrogen other Energy + sources + O2 + nutrients Sources Biomass + products + CO2 +H2O +heat  Elemental composition of microorganisms may be taken as guide  Design of medium will influence the oxygen requirements
  5. 5. Elemental composition Element Bacteria Yeast Fungi Carbon 50-53 45-50 40-63 Hydrogen 7 7 7 Nitrogen 12-15 7.5-11 7-10 Phosphorus 2-3 0.8-2.6 0.4-4.5 Sulphur 0.2-1.0 0.01-0.24 0.1-0.5 Potassium 1.0-4.5 1-4 0.2-2.5 Sodium 0.5-1.0 0.01-0.1 0.02-0.5 Calcium 0.01-1.1 0.1-0.3 0.1-1.4 Magnesium 0.1-0.5 0.1-0.5 0.1-0.5 Chloride 0.5 -- -- Iron 0.02-0.2 0.01-0.5 0.1-0.2
  6. 6. WATER Assessing suitability of water - pH - dissolved salts - effluent contamination In olden days mineral content is important - High Ca for dark beers - High carbonate for stouts Nowadays - Deionisation of water Reuse of water is important - It reduces water cost by 50% - Effluent treatment cost by 10 fold
  7. 7. Carbon sources Factors influencing the carbon source - Cost of the product - rate at which it is metabolized - geographical locations - government regulations - cellular yield coefficient Methane - 0.62 Alkanes - 1.03 Glucose - 0.51 Acetate - 0.34
  8. 8. Examples of carbon sourcesExamples of carbon sources Carbohydrates Starch – max 2% Molasses (Beet – sucrose 48.5% Raffinose 1.0% Invert sugar 1.0% same in cane molasses 33.4%, 0%, 21.2%) Sucrose Glucose Malt (Barley grains germinated and heat treated) Other materials of plant origin like soy bean meal, pharmedia
  9. 9. Oils and fats Oils are first used as antifoams and later used as carbon sources (soya oil, olive oil, maize oil, linseed oil etc.,) Factors favouring oil 2.4 times energy than glucose Hence volume advantage of 4 times. some organisms can use only oils for efficient production Eg. antibiotics (Methyl oleate is used in cephalosporin)
  10. 10. Hydrocarbons and their derivatives Now it is expensive two times carbon and three times energy than that of carbohydrates
  11. 11. Nitrogen sourcesNitrogen sources Inorganic Ammonia gas, ammonium chloride, ammonium sulphate, ammonium nitrates, sodium nitrates Ammonia gas used for pH control Ammonium salts produces acid conditions when ammonia is utilised. pH drift Sodium nitrate produces alkaline drift
  12. 12. Organic Organic nitrogen may be supplied by amino acids, protein, urea Growth will be faster. These are commonly added as complex nitrogen sources such as soy bean meal, corn steep liquor etc., (During storage these sources are affected by moisture, temperature and ageing)
  13. 13. Factors influencing choice of nitrogenFactors influencing choice of nitrogen sourcesource - Nitrate reductase enzyme is repressed by ammonium ion. Hence ammonia or ammonium salts are preferred - Ammonium ions represses amino acid uptake in fungal cultivations - also ammonia regulates acid and alkaline protease production - antibiotic production by many fungi is influenced by the nitrogen source.
  14. 14. - soy bean meal is preferred in polyene antibiotics production due to slow hydrolysis which prevents ammonia accumulation and in turn aminoacid repression by it - in gibberellin production, nitrogen source influence production of gibberellins - some complex nitrogen sources may not be utilised by some microorganisms which may cause problem in downstream processing
  15. 15. MineralsMinerals All microorganisms require minerals for growth and product formation Magnesium, phosphorus, potassium, sulphur, calcium, chlorine are essential components Cobalt, copper, manganese, iron, molybdenum, zinc are also essential but in traces. Also depending on product analysis apart from biomass minerals will be decided. E.g sulphur in pencillins, cephalosporins, chlorine in chlortetracyclin etc.,
  16. 16. Concentration of phosphate in medium is normally required in excess for buffering the medium. Phosphate concentration in the medium are critical in antibiotic production since some enzymes of biosynthesis are influenced by phosphate Other metal ions influence the production of secondary metabolites The functions of each vary from serving in coenzyme functions to catalyze many reactions, vitamin synthesis, and cell wall transport. Citric acid & Penicillin production – Fe, Zn, Cu Protease production – Mn
  17. 17. ChelatorsChelators Many media cannot be prepared without precipitation during autoclaving. Hence some chelating agents are added to form complexes with metal ions which are gradually utilised by microorganism Examples of chelators: EDTA, citric acid, polyphosphates etc., It is important to check the concentration of chelators otherwise it may inhibit the growth. In many media these are added separately after autoclaving Or yeast extract, peptone complex with these metal ions
  18. 18. Mandel and Weber, 1969 (g l-1 ) Urea = 0.3 g (NH4)2 SO4 = 1.4 g K2HPO4 = 2 g MnSO4. 7H2O = 1.6 mg CoCl2.6H2O = 2 mg CaCl2. 2H2O = 0.4 g Mg SO4.7H2O = 0.3 g FeSO4. 7H2O = 5 mg ZnSO4. 7H2O = 1.4 mg Peptone = 1 g Yeast extract = 0.25 g Maize / steep liquor= 10 g
  19. 19. Growth FactorsGrowth Factors • Some microorganisms cannot synthesize a full complement of cell components and therefore require preformed compounds called growth factors • Eg.: vitamins, aminoacids, fatty acids or sterols • Complex media sources contain most of these compounds. Careful blending of these will give the required growth factors. • For vinegar production – Calcium Pantothenate • For Glutamic acid – Biotin
  20. 20. PrecursorsPrecursors • Some chemicals when added to certain fermentations are directly incorporated into the desired product. • Eg: Improving the yields of Pencillin production
  21. 21. InhibitorsInhibitors • When certain inhibitors are added to fermentation more of a specific product may be produced • Eg : Glycerol fermentation • Glycerol production depends on modifying ethanol fermentation by removing acetaldehyde • Addition of sodium bisulphite forms acetaldehyde bi sulphite. Acetaldehyde is no longer available and dihydroxy acetone is formed.
  22. 22. InducersInducers • Majority of the enzymes are inducible • Substrates or substrates analogues are used as inducers. • Enzymes are produced in response to the presence of these compounds in the environment. • Heterologous protein production in E.coli, yeast etc.,
  23. 23. AntifoamsAntifoams • Most fermentations foaming is major problem. • It may be due to component in the medium or some factor produced by the microorganism. • Foaming can be controlled by • Modification of medium • Mechanical foam breakers • Chemical agents antifoams are added Eg: Fatty acids, silicones, PPG 2000
  24. 24. • Antifoams are surface active agents reducing the surface tension in the foam and destabilising the protein films • An ideal antifoam should have the following properties • Disperse readily and have fast action • Active at low concentrations • Long acting in preventing new foam • Should not be metabolized • Should not be toxic to m.o, humans etc • Cheap, should not cause problem in fermentation
  25. 25. Medium OptimizationMedium Optimization
  26. 26. When considering the biomass growth phase in isolation, it must be recognized that efficiently grown biomass produced by an ‘optimized’ high productivity growth phase is not necessarily best suited for its ultimate purpose, such as synthesizing the desired product.
  27. 27.  Classical designClassical design Changing one variable at timeChanging one variable at time Total no of experiments will be xTotal no of experiments will be xnn x – no of levelx – no of level n - no of variables or factorsn - no of variables or factors For ex 3 levels and 6 variables have toFor ex 3 levels and 6 variables have to be tested then the number ofbe tested then the number of experiments will be 3experiments will be 366 =729=729  Statistical optimization techniqueStatistical optimization technique Plackett Burman designPlackett Burman design Response surface methodologyResponse surface methodology  Optimization through modellingOptimization through modelling
  28. 28. Design of Experiments (DOE) oHelp you improve your processes. You can screen the factors to determine which are important for explaining process variation. oAfter you screen the factors, Minitab / Design expert software helps you understand how those factors interact and drive your process.
  29. 29. Plackett Burman designPlackett Burman design  More than five variables it is usefulMore than five variables it is useful  It will be useful in screening theIt will be useful in screening the most important variablemost important variable  Here n no of experiments will beHere n no of experiments will be conducted for n-1 variablesconducted for n-1 variables  Where n is the multiples of 4 likeWhere n is the multiples of 4 like 8,12,16,20…1008,12,16,20…100  Authors give a series ofAuthors give a series of experimental design known asexperimental design known as balanced incomplete blocksbalanced incomplete blocks
  30. 30.  Variables which is not having influenceVariables which is not having influence in the process is designated as dummyin the process is designated as dummy variablesvariables  Dummy variables are required toDummy variables are required to estimate the error in theestimate the error in the experimentationexperimentation  Minimum one or two dummy variablesMinimum one or two dummy variables should be included in the experimentalshould be included in the experimental setset  More can be included if the realMore can be included if the real variables are lessvariables are less
  31. 31. RowRow f1f1 f2f2 f3f3 f4f4 f5f5 f6f6 f7f7 r1r1 ++ ++ ++ -- ++ -- -- r2r2 -- ++ ++ ++ -- ++ -- r3r3 -- -- ++ ++ ++ -- ++ r4r4 ++ -- -- ++ ++ ++ -- r5r5 -- ++ -- -- ++ ++ ++ r6r6 ++ -- ++ -- -- ++ ++ r7r7 ++ ++ -- ++ -- -- ++ r8r8 -- -- -- -- -- -- --
  32. 32. RowRow f1f1 f2f2 f3f3 f4f4 f5f5 f6f6 f7f7 r1r1 ++ ++ ++ -- ++ -- -- r2r2 -- ++ ++ ++ -- ++ -- r3r3 -- -- ++ ++ ++ -- ++ r4r4 ++ -- -- ++ ++ ++ -- r5r5 -- ++ -- -- ++ ++ ++ r6r6 ++ -- ++ -- -- ++ ++ r7r7 ++ ++ -- ++ -- -- ++ r8r8 -- -- -- -- -- -- --
  33. 33. RowRow f1f1 f2f2 f3f3 f4f4 f5f5 f6f6 f7f7 r1r1 ++ ++ ++ -- ++ -- -- r2r2 -- ++ ++ ++ -- ++ -- r3r3 -- -- ++ ++ ++ -- ++ r4r4 ++ -- -- ++ ++ ++ -- r5r5 -- ++ -- -- ++ ++ ++ r6r6 ++ -- ++ -- -- ++ ++ r7r7 ++ ++ -- ++ -- -- ++ r8r8 -- -- -- -- -- -- --
  34. 34. Row f1 f2 f3 f4 f5 f6 f7 Y r1 + + + - + - - 1.1 r2 - + + + - + - 6.3 r3 - - + + + - + 1.2 r4 + - - + + + - 0.8 r5 - + - - + + + 6.0 r6 + - + - - + + 0.9 r7 + + - + - - + 1.1 r8 - - - - - - - 1.4 Σ H 3.9 14.5 9.5 9.4 9.1 14.0 9.2 Σ L 14.9 4.3 9.3 9.4 9.7 4.8 9.6 Σ H - Σ L -11.0 10.2 0.2 0.0 -0.6 9.2 -0.4 Effect -2.75 2.55 0.05 0.00 -0.15 2.30 -0.10 Mean sq 15.12 13.01 0.005 0.000 0.045 10.58 0.020 Error mean sq 0.033 0.033 0.033 0.033 0.033 0.033 0.033 F test 465.4 400.2 3.255 0.000 - 325.6 -
  35. 35. Fungal system experimented for exopolysaccharideFungal system experimented for exopolysaccharide productionproduction Variable High Low f1:Corn steep liquor 1% 0.5% f2:Sucrose 3% 1.5% f3:K2HPO4 0.2% 0.1% f4:MgSO4.5H20 1.0% 0.5% f5:FeSO4.7H20 0.01% 0% f6:KNO3 0.2% 0.1% f7:Dummy Variable NaCl 0.2% 0.1%
  36. 36.    f1f1 f2f2 f3f3 f4f4 f5f5 f6f6 f7f7 BiomassBiomass PolysacPolysac 11 ++ ++ ++ -- ++ -- -- 17.1517.15 2.2902.290 22 -- ++ ++ ++ -- ++ -- 15.3415.34 1.9681.968 33 -- -- ++ ++ ++ -- ++ 14.8914.89 1.0041.004 44 ++ -- -- ++ ++ ++ -- 15.0215.02 1.5571.557 55 -- ++ -- -- ++ ++ ++ 15.3215.32 1.7651.765 66 ++ -- ++ -- -- ++ ++ 14.3514.35 1.8721.872 77 ++ ++ -- ++ -- -- ++ 17.7017.70 2.5632.563 88 -- -- -- -- -- -- -- 12.8212.82 0.5560.556
  37. 37.    f1f1 f2f2 f3f3 f4f4 f5f5 f6f6 f7f7 BiomassBiomass 11 ++ ++ ++ -- ++ -- -- 17.1517.15 22 -- ++ ++ ++ -- ++ -- 15.3415.34 33 -- -- ++ ++ ++ -- ++ 14.8914.89 44 ++ -- -- ++ ++ ++ -- 15.0215.02 55 -- ++ -- -- ++ ++ ++ 15.3215.32 66 ++ -- ++ -- -- ++ ++ 14.3514.35 77 ++ ++ -- ++ -- -- ++ 17.717.7 88 -- -- -- -- -- -- -- 12.8212.82 EHEH 64.2264.22 65.5165.51 61.7361.73 62.9562.95 62.3862.38 60.0360.03 62.2662.26    ELEL 58.3758.37 57.0857.08 60.8660.86 59.6459.64 60.2160.21 62.5662.56 60.3360.33    EH-ELEH-EL 5.855.85 8.438.43 0.870.87 3.313.31 2.172.17 -2.53-2.53 1.931.93    EffectEffect 1.461.46 2.112.11 0.220.22 0.830.83 0.540.54 -0.63-0.63 0.480.48    Mean squareMean square 4.284.28 8.888.88 0.090.09 1.371.37 0.590.59 0.800.80 0.470.47    FtestFtest 9.189.18 19.0619.06 0.200.20 2.942.94 1.261.26 1.721.72 --   
  38. 38.    f1f1 f2f2 f3f3 f4f4 f5f5 f6f6 f7f7 PolysacPolysac 11 ++ ++ ++ -- ++ -- -- 2.2902.290 22 -- ++ ++ ++ -- ++ -- 1.9481.948 33 -- -- ++ ++ ++ -- ++ 1.0041.004 44 ++ -- -- ++ ++ ++ -- 1.5571.557 55 -- ++ -- -- ++ ++ ++ 1.7651.765 66 ++ -- ++ -- -- ++ ++ 1.8721.872 77 ++ ++ -- ++ -- -- ++ 2.5632.563 88 -- -- -- -- -- -- -- 0.5560.556 EHEH 8.288.28 8.578.57 7.117.11 7.077.07 6.626.62 7.147.14 7.207.20    ELEL 5.275.27 4.994.99 6.446.44 6.486.48 6.946.94 6.416.41 6.356.35    EH-ELEH-EL 3.013.01 3.583.58 0.670.67 0.590.59 -0.32-0.32 0.730.73 0.850.85    EffectEffect 0.750.75 0.890.89 0.170.17 0.150.15 -0.08-0.08 0.180.18 0.210.21    Mean squareMean square 1.131.13 1.601.60 0.060.06 0.040.04 0.010.01 0.070.07 0.090.09    FtestFtest 2.432.43 3.433.43 0.120.12 0.090.09 0.030.03 0.140.14 --   
  39. 39. The first row forThe first row for Plackett-BurmanPlackett-Burman designs.designs. nn kk StringString 1111 1212 + + - + + + - - - + -+ + - + + + - - - + - 1515 1616 + + + + - + - + + - - + - - -+ + + + - + - + + - - + - - - 1919 2020 + + - - + + + + - + - + - - - - + + -+ + - - + + + + - + - + - - - - + + - 2323 2424 + + + + + - + - + + - - + + - - + - + - - - -+ + + + + - + - + + - - + + - - + - + - - - -
  40. 40. Plackett-Burman Design in 12 Runs for up to 11 FactorsPlackett-Burman Design in 12 Runs for up to 11 Factors Pattern X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 1 +++++++++++ +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 2 -+-+++---+- -1 +1 -1 +1 +1 +1 -1 -1 -1 +1 -1 3 --+-+++---+ -1 -1 +1 -1 +1 +1 +1 -1 -1 -1 +1 4 +--+-+++--- +1 -1 -1 +1 -1 +1 +1 +1 -1 -1 -1 5 -+--+-+++-- -1 +1 -1 -1 +1 -1 +1 +1 +1 -1 -1 6 --+--+-+++- -1 -1 +1 -1 -1 +1 -1 +1 +1 +1 -1 7 ---+--+-+++ -1 -1 -1 +1 -1 -1 +1 -1 +1 +1 +1 8 +---+--+-++ +1 -1 -1 -1 +1 -1 -1 +1 -1 +1 +1 9 ++---+--+-+ +1 +1 -1 -1 -1 +1 -1 -1 +1 -1 +1 10 +++---+--+- +1 +1 +1 -1 -1 -1 +1 -1 -1 +1 -1 11 -+++---+--+ -1 +1 +1 +1 -1 -1 -1 +1 -1 -1 +1 12 +-+++---+-- +1 -1 +1 +1 +1 -1 -1 -1 +1 -1 -1
  41. 41. When to use PBWhen to use PB  Screening multi components at 2 levelsScreening multi components at 2 levels  It will give the range at which you haveIt will give the range at which you have to optimize the experiments furtherto optimize the experiments further Limitations:Limitations:  It will not give optimum concentration ofIt will not give optimum concentration of the variablethe variable
  42. 42. Response SurfaceResponse Surface MethodologyMethodology  Response surface methodology is aResponse surface methodology is a method of optimization using statisticalmethod of optimization using statistical techniques based upon the specialtechniques based upon the special factorial design of Box and Behnken etc.,factorial design of Box and Behnken etc.,  It is a scientific approach to determine theIt is a scientific approach to determine the optimum conditions which combines theoptimum conditions which combines the special experimental designs and Taylorspecial experimental designs and Taylor first order and second order equationfirst order and second order equation
  43. 43. Sequential nature of RSMSequential nature of RSM
  44. 44. How to ProceedHow to Proceed  Select critical factors and regions to be testedSelect critical factors and regions to be tested  Design the experiment based on box behnkenDesign the experiment based on box behnken or central composite designor central composite design  Do the experimentDo the experiment  Fit the data to Taylor series, determineFit the data to Taylor series, determine coefficients to build modelcoefficients to build model  Validate model by selecting values in theValidate model by selecting values in the region testedregion tested  Draw the contour plot and find optimumDraw the contour plot and find optimum concentrationconcentration
  45. 45. Design of experimentsDesign of experiments Variable 1 Variable2 Low High High Low
  46. 46. Coding the variablesCoding the variables Value of the variable - Middle pointValue of the variable - Middle point Coding =Coding = Difference/2Difference/2 Glucose = 10 – 30 g/lGlucose = 10 – 30 g/l Coding 10 g/l glucose = [10-20]/(20/2) = -1Coding 10 g/l glucose = [10-20]/(20/2) = -1 Coding 30 g/l = ?Coding 30 g/l = ? Coding 20 g/l ??Coding 20 g/l ??
  47. 47. Taylor seriesTaylor series Yield Y =Yield Y = ββ00 ++ ββ11 XX11 ++ ββ1111 XX11 22 Constant term + Linear term + Quadratic termConstant term + Linear term + Quadratic term Y=Y= ββ00 ++ ββ11 XX11 ++ ββ22 XX22 ++ ββ1111 XX11 22 ++ ββ2222 XX22 22 ++ ββ1212 XX11 XX22 αα = [2= [2nn ]]1/41/4
  48. 48. Design of experimentsDesign of experiments [0,0] [-1,-1] [+1,+1] [+1,_1] [-1,+1] [-1.414,0] [+1.414,0] [0,+1.414] [0,-1.414,0] Variable 1 Variable2
  49. 49. Design the experiments for theDesign the experiments for the following variable concentrationsfollowing variable concentrations Corn steep Liquor = 0.5% to 1.5 % Sucrose = 1.5% to 4.5 % Write the coding equation for both Corn Steep Liquor and Sucrose For CSL = (Value-10)/5 For Sucrose = (Value -30)/15
  50. 50. Run No CSL Sucrose Coded Uncoded Coded Uncoded 1 -1 5 -1 15 2 -1 5 +1 45 3 +1 15 -1 15 4 +1 15 +1 45 5 -1.414 2.93 0 30 6 +1.414 17.07 0 30 7 0 10 -1.414 8.79 8 0 10 +1.414 51.21 9 0 10 0 30 10 0 10 0 30 11 0 10 0 30
  51. 51. run order Csl (g/l) Sucrose (g/l) response 1 15 15 1.748 2 10 30 2.572 3 15 45 1.464 4 17.07 30 1.678 5 10 51.21 1.326 6 10 8.79 1.604 7 5 45 1.533 8 10 30 2.584 9 10 30 2.543 10 10 30 2.564 11 2.93 30 1.846 12 5 15 1.089 13 10 30 2.558
  52. 52. • 13 equations will be obtained from 13 experiments. • Resulting equations will be solved by least square method of matrix solving • All the equations will be represented in the form of Y = βX β = (X’X)-1 (X’Y)
  53. 53.   VARIABLE ESTIMATE ERROR         β0 Intercept 2.564219 0.070235 β1 X1 0.044063 0.05553 β2 X2 -0.029141 0.05553 β11 X1*X1 -0.43992 0.059558 β22 X2*X2 -0.588465 0.059558 β12 X1*X2 -0.182 0.078526 Standard Error of Mean = 0.043558 R-SQUARED 0.9529 ADJ R-SQUARED 0.9193 C.V. 8.13% Y = β0 +β1 * X1 +β2 * X2 +β11 * X1 2 +β22 * X2 2 +β12 * X1 *X2 Y = 2.564 + 0.044 X1 - 0.029 X2 - 0.44 X1 2 - 0.589 X2 2 - 0.182 X1 X2
  54. 54. http://www.itl.nist.gov/ div898/handbook/index.htm
  55. 55. • Using the actual values makes it easy to calculate the response from the coefficients since it is not necessary to go through coding process • The reason for coding the variables is to eliminate the effect that the magnitude of the variable has on the regression coefficient
  56. 56. • Prob>F is less than 0.05 indicated significant model terms • The standard error of estimate yields information concerning the reliability of the values predicted by the regression equation. The greater the standard error of estimate, the less reliable the predicted value. • Coefficient of variation less than 10 % indicate high degree of precision and reliability of experimental values
  57. 57. • The mathematical model is reliable with R2 value. Closer the value to 1 is the more reliable the model. • R2 value 0.9529 suggests that the model was unable to explain 4.71% variations occurred • R2 Value can be increased by including model terms. Sometimes even higher value may result in poor predictions. • Adj R2 value will be verified. If this value differs dramatically then insignificant model terms have been included in the model
  58. 58. Ord VALUE VALUE RESIDUAL Run ACTUAL PREDICTED   1 1.748 1.791037 -0.043037 2 2.572 2.564219 0.007781 3 1.464 1.368755 0.095245 4 1.678 1.746948 -0.068948 5 1.326 1.346438 -0.020438 6 1.604 1.428849 0.175151 7 1.533 1.644629 -0.111629 8 2.584 2.564219 0.019781 9 2.543 2.564219 -0.021219 10 2.564 2.564219 -0.000219 11 1.846 1.622339 0.223661 12 1.089 1.338911 -0.249911 13 2.558 2.564219 -0.006219
  59. 59. Residuals Vs Run order -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0 2 4 6 8 10 12 14 run order residuals
  60. 60. CSL Vs Residual -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0 5 10 15 20 CSL Residual
  61. 61. Sucrose Vs residuals -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0 10 20 30 40 50 60 Sucrose Residuals
  62. 62. Contour plotContour plot • A contour plot is a graphical technique for representing a 3- dimensional surface by plotting constant z slices, called contours, on a 2-dimensional format. • That is, given a value for z, lines are drawn for connecting the (x,y) coordinates where that z value occurs.
  63. 63. Stationary ridge
  64. 64. RISING RIDGERISING RIDGE
  65. 65. Y = β0+β1* X1+β2* X2+β11* X12+β22* X22+β12* X1*X2 Y = β0 + X’ b + X’ B X X= X1 b = β1 B = β11 β12/2 X2 β2 β12/2 β22 ∂y/∂x =0 Xs = -1/2 B-1 b
  66. 66. Application of response surfaceApplication of response surface methodology to cell immobilizationmethodology to cell immobilization for the production of palatinosefor the production of palatinose
  67. 67. Design based on Alpha factor = 1
  68. 68. • Optimum alginate concentration, cell loading and bead diameter were 5%, 15 g /l and 2.25 mm, respectively. • R2 value of 0.9259 • A very low value of coefficient of the variation (C.V.) (4.46%)
  69. 69. Residuals Vs run order -6 -4 -2 0 2 4 6 0 5 10 15 20 Run order Residuals

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