Abstract:
A novel polyamine oxidase, polyamine oxidase PC-3, takes an important role participating in decomposition and metabolism and polyamines such as spermidine and spermine.

Description:
FIELD OF THE INVENTION 
     The present invention relates to novel polyamine oxidase PC-3 derived from a microorganism. Polyamine oxidases are ordinarily enzymes having a catalytic activity for oxidative deamination of polyamines, and in the living body they take an important role participating in decomposition and metabolism of polyamines such as spermidine and spermine. 
     BACKGROUND OF THE INVENTION 
     Recently, the interrelation between cancer and an increase of amounts of polyamines in body fluids such as blood, urine and lymph has attracted attention, and the use of a polyamine oxidase as an enzyme for diagnosis of cancers has been developed (see Japanese Patent Application Laid-Open Specification No. 9492/75). 
     Polyamine oxidases derived from animal and plant tissues as supply sources have heretofore been used. However, each of the polyamine oxidases derived from animal and plant tissues is poor in activity, and it is difficult to obtain them in large quantities. Furthermore, it is very difficult to produce these polyamine oxidases at low costs on an industrial scale. 
     SUMMARY OF THE INVENTION 
     As a result of research made with a view of developing a process capable of producing a polyamine oxidase at a low cost on an industrial scale, we found that when Penicillium chrysogenum IFO 4626, which is capable of growing with spermidine or spermine as a single carbon-nitrogen source or a single carbon or single nitrogen source, is cultured in a culture medium containing spermidine or spermine, a novel polyamine oxidase PC-3 is produced and accumulated in a large quantity in the culture product. We have now completed the present invention based on this finding. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a pH activity curve of polyamine oxidase PC-3 of the present invention, and 
     FIGS. 2, 3 and 4 show the pH stability, optimum temperature and temperature stability, respectively. 
     FIG. 5 shows the absorption spectrum. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Microbial polyamine oxidase PC-3 according to the present invention has the following physicochemical properties. 
     (1) Reactivity: 
     As shown by the following reaction formula, the oxidase effects reaction of H 2  O and O 2  with spermidine to form 1 mol of putrescine, 1 mol of 3-aminopropionaldehyde and 1 mol of hydrogen peroxide from 1 mol of spermidine, and the oxidase effects reaction of H 2  O and O 2  with spermine to form 1 mol of putrescine, 2 mols of 3-aminopropionaldehyde and 2 mols of hydrogen peroxide. ##STR1## (2) Substrate Specificity: 
     As shown in Table 1, the oxidase effects reaction of O 2  and H 2  O with spermidine and spermine. 
     
                       TABLE 1______________________________________          Relative ActivitySubstrate (2 mM) pH = 6.5 pH = 7.5______________________________________Methylamine      0.0      0.0Ethylamine       0.0      0.0Propylamine      0.0      0.0Butylamine       0.0      0.0Phenethylamine   0.0      0.0Tyramine         0.0      0.0Dopamine         0.0      0.0Tryptamine       0.0      0.0Serotonin        0.0      0.0Benzylamine      0.0      0.0Histamine        0.0      0.0Agmatine         0.0      0.0Cadaverine       0.0      0.0Putrescine       0.0      0.0Spermidine       10.9     0.0Spermine         100      100______________________________________ 
    
     (3) Optimum pH: 
     The optimum pH for reaction with spermidine is about 5.0 and the optimum pH for reaction with spermine is about 9.5 (see FIG. 1). 
     (4) pH Stability: 
     In the case where the substrate is either spermidine or spermine, when the oxidase is treated at 30° C. for 10 minutes at pH 3.0 to 5.0, the residual ratio of the activity is higher than 85% (see FIG. 2). 
     (5) Optimum Temperature: 
     When spermidine is a substrate, the optimum temperature is about 25° C. at pH 6.5, and when spermine is a substrate, the optimum temperature is about 35° C. at pH 6.5 and is about 40° C. at pH 7.0 (see FIG. 3). 
     (6) Temperature Stability: 
     In the case where spermine is a substrate, when the oxidase is treated at 35° C. for 10 minutes at pH 4.0 the residual ratio of the activity is higher than 95%, and when the oxidase is treated at 20° C. for 10 minutes at pH 7.0, the residual ratio of the activity is higher than 85% (see FIG. 4). 
     (7) Absorption Spectrum and Coenzyme: 
     From the fact that maximum absorptions are observed at 280, 375 and 450 nm in the absorption spectrum, it is confirmed that the oxidase is a flavin protein (see FIG. 5), and FAD is present as a coenzyme in an amount of 2 molecules per molecule of the enzyme. 
     (8) Influences of Inhibitors and Metal Ions: 
     (a) Influences of various inhibitors are shown in Table 2 (the concentration of PCMB is 140 μM). 
     
                       TABLE 2______________________________________           Relative Activity (%)Inhibitor (1.4 mM)             SPM     SPD______________________________________Hydroxylamine     100     91.9Hydrazine         100     100Phenylhydrazine   100     94.6Semicarbazide     100     91.9Isoniazid         98.6    70.3Iproniazid        98.6    83.4α,α&#39;-Dipyridyl             77.7    1008-Hydroxyquinoline             91.5    100o-Phenanthroline  86.2    94.6Sodium azide      88.3    100EDTA              95.7    95.7PCMB              1.1     68.4Monoiodoacetic acid             9.6     65.4Not added         100     100______________________________________ Note EDTA: ethylenediamine tetraacetate PCMB: pchloromercurybenzoate 
    
     (b) Influences of metal ions (1.4 mA) are shown in Table 3. 
     
                       TABLE 3______________________________________          Relative Activity (%)Metal Ion        SPM    SPD______________________________________NH.sub.4.sup.+   95.1   100Ag.sup.+         2.4    0.0Li.sup.+         94.1   97.2Ni.sup.2+        45.9   85.7Cu.sup.2+        36.4   108.6Zn.sup.2+        24.4   97.1Mg.sup.2+        80.0   65.7Hg.sup.2+        0.0    40.0Pb.sup.2+        47.6   62.9Fe.sup.3+        --     42.9Al.sup.3+        91.5   0.0______________________________________ 
    
     In Tables 2 and 3, SPM stands for spermine and SPD stands for spermidine, and the activity is one as measured at pH 9.5 in case of SPM or at pH 5.0 in case of SPD. 
     (9) Isoelectric Point: 
     The isoelectric point is 5.4 to 5.6 as measured according to the ampholyte isoelectric point electrophoresis method. 
     (10) Molecular Weight: 
     The molecular weight is 160,000 as determined according to the gel filtration method using Sephadex G-200. 
     (11) Molecular Weight of Subunit: 
     The molecular weight of the subunit is 80,000. 
     (12) Crystal Form: 
     The oxidase takes the form of a needle crystal. 
     Microbial polyamine oxidase PC-3 having the abovementioned physicochemical properties is a novel polyamine oxidase which is obviously different from polyamine oxidases derived from animals and plants and other polyamine oxidases derived from microorganisms. 
     In Table 4, properties of this novel polyamine oxidase is compared with those of polyamine oxidases derived from various origins. 
     Beef plasma amine oxidase is one disclosed by H. Yamada et al. in The Journal of Biological Chemistry, 237, pages 1511 to 1516 (1962), and rat liver polyamine oxidase is one disclosed by E. Hollta in Biochemistry, 16, pages 91 to 100 (1977). Pea polyamine oxidase is one disclosed by P. J. G. Mann in Biochemical Journal, 79, pages 623 to 631 (1961) and Method in Enzymology, 17B, pages 730 to 735, and barley polyamine oxidase is one disclosed by P. A. Smith in Phytochemistry, 13, pages 2437 to 2443 (1974) and ibid, 11, pages 899 to 910 (1972). Serratia marcescens spermidine dehydrogenase is one disclosed by C. W. Tabor et al. in The Journal of Biological Chemistry, 245, pages 5424 to 5433 (1970) and Pseudomonas aeruginosa polyamine oxidase is one disclosed by S. Razin et al. in Biochemical Journal, 71, pages 551 to 558 (1959). 
     
                                           TABLE 4__________________________________________________________________________         Polyamine oxidase         PC-3 of Present                     Beef plasma                               Rat Liver Poly-                                         Pea Polyamine         Invention   amine Oxidase                               amine Oxidase                                         Oxidase__________________________________________________________________________Substrate     reacting only                     reacting with                               reacting with                                         strongly react-Specificity   with spermidine                     spermidine,                               spermidine                                         ing with cada-         and spermine                     spermine and                               and spermine                                         verine and                     other monamine      putrescine and                                         reacting with                                         spermidineDecomposition Pro-         NH.sub.2 (CH.sub.2).sub.2 CHO,                     OHC(CH.sub.2).sub.2 NH--                               NH.sub.2 (CH.sub.2).sub.2 CHO,                                         NH.sub.2 (CH.sub.2).sub.3                                         NH--duct of NH.sub.2 (CH.sub.2).sub.3 --         NH.sub.2 (CH.sub.2).sub.4 NH.sub.2,H.sub.2 O.sub.2                     (CH.sub.2).sub.4 NH.sub.2,                               NH.sub.2 (CH.sub.2).sub.4 NH.sub.2,                                         (CH.sub.2).sub.3 CHO,NH(CH.sub.2).sub.4 NH.sub.2 (spermidine)                     NH.sub.3, H.sub.2 O.sub.2                               H.sub.2 O.sub.2                                         H.sub.2 O.sub.2, NH.sub.3Decomposition Pro-         NH.sub.2 (CH.sub.2).sub.2 CHO,                     OHC(CH.sub.2).sub.2 NH--                               NH.sub.2 (CH.sub.2).sub.2 CHO,duct of NH.sub.2 (CH.sub.2).sub.3 --         NH.sub.2 (CH.sub.2).sub.4 NH.sub.2,H.sub.2 O.sub.2                     (CH.sub.2).sub.4 NH(CH.sub.2).sub.2 --                               NH.sub.2 (CH.sub.2).sub.4 NH.sub.2,NH(CH.sub.2).sub.4 NH(CH.sub.2).sub.3 NH.sub.2                     CHO, NH.sub.3, H.sub.2 O.sub.2                               H.sub.2 O.sub.2(spermine)Inhibitor     not inhibited by      inhibited by                                         inhibited by         carbonyl reagent      carbonyl  carbonyl                               reagent   reagent,                                         chelate com-                                         pound and Cu.sup.2+Optimum pH    5.0 (to spermidine),                     7.2       about 10  7.0 (to putre-         9.5 (to spermine)               scine)Molecular Weight         160,000     240,000   55,000-61,000                                         96,000Isoelectric Point         5.4-5.6               4.9Coenzyme, etc.         2 molecules of                     Cu.sup.2+ less than 1                                         Cu.sup.2+         FAD in one molecule                     contained molecule of FAD                               in one molecule__________________________________________________________________________               Barley       Serratia               Polyamine    Spermidine                                     Pseudomonas Poly-               Oxidase      dehydrogenase                                     amine Oxidase__________________________________________________________________________Substrate           strongly react-                            strongly reacting with spermidine,Specificity         ing with     reacting with                                     spermine, cadaverine,               spermine and putrescine and                                     putrescine and agmatine               reacting with                            spermidine and               spermidine   reacting with                            spermineDecomposition Pro-  NH.sub.2 (CH.sub.2).sub.3 CHO,                            NH.sub.2 (CH.sub.2).sub.3 CHO,                                     NH.sub.2 (CH.sub.2).sub.3                                     NH.sub.2,duct of NH.sub.2 (CH.sub.2).sub.3 --               NH.sub.2 (CH.sub.2).sub.3 NH.sub.2,                            NH.sub.2 (CH.sub.2).sub.3 NH.sub.2                                     NH.sub.2 (CH.sub.2).sub.3 CHONH(CH.sub.2).sub.4 NH.sub.2 (spermidine)               H.sub.2 O.sub.2Decomposition Pro-  NH.sub.2 (CH.sub.2).sub.3 NH(CH.sub.2).sub.3 --                            NH.sub.2 (CH.sub.2).sub.3 NH--                                     NH.sub.2 (CH.sub.2).sub.3                                     NH(CH.sub.2).sub.4 NH.sub.2,duct of NH.sub.2 (CH.sub.2).sub.3 --               CHO, NH.sub.2 (CH.sub.2).sub.3 NH.sub.2,                            (CH.sub.2).sub.3 CHO,                                     NH.sub.2 (CH.sub.2).sub.2 CHONH(CH.sub.2).sub.4 NH(CH.sub.2).sub.3 NH.sub.2               H.sub.2 O.sub.2                            NH.sub.2 (CH.sub.2).sub.3 NH.sub.2(spermine)InhibitorOptimum pH          6.5 (spermidine),                            6.5      7.0-7.2               4.5 (spermine)Molecular Weight                 76,000Isoelectric PointCoenzyme, etc.      FAD          FAD__________________________________________________________________________ 
    
     As will be apparent from Table 4, none of polyamine oxidases derived from animals, plants and microorganisms are in agreement with polyamine oxidase PC-3 of the present invention in all of the substrate specificity, the mode of decomposition of spermidine and spermine, the behaviors to inhibitors, the optimum pH, the molecular weight and the isoelectric point. 
     Novel polyamine oxidase PC-3 is obtained by culturing Penicillium chrysogenum IFO 4626. Any of synthetic and natural culture media containing appropriate amounts of carbon sources, nitrogen sources, inorganic substances and other nutrients may be used. Either liquid media or solid media may be used, but a liquid medium is oridinarily used. At least one polyamine oxidase PC-3 inducer such as spermidine or spermine is appropriately incorporated in such culture medium. 
     The cultivation conditions will now be described. The pH at the start of culturing is ordinarily 4.0 to 7.0 and preferably about 5.0 to about 6.0. The culturing temperature is ordinarily 20° to 40° C. and preferably 25° to 35° C. If cultivation is conducted under these conditions for 12 to 120 hours, polyamine oxidase PC-3 is formed and accumulated in a large amount in the culture product. 
     Polyamine oxidase PC-3 thus formed and accumulated in the culture product is collected according to the following procedures. Since polyamine oxidase PC-3 present mainly in cells, after completion of cultivation the cells are collected by filtration or the like, washed with water or a buffer solution and suspended in an appropriate buffer solution having a pH value of 5.0 to 8.0 to extract polyamine oxidase PC-3 contained in the cells. 
     In order to further purify crude polyamine oxidase PC-3 obtained from the cell extract, the pH value of the extract is adjusted to 2.5 to 4.5 by addition of an acid or dialysis to precipitate polyamine oxidase PC-3. The operation of solubilizing the precipitate at a salt concentration corresponding to a level of 1 to 40% of the saturation concentration of ammonium sulfate and the operation of dialyzing the solubilized precipitate solution by an acidic buffer solution having a pH of 2.5 to 4.5 to form a precipitate of polyamine oxidase PC-3 are repeated. By this treatment, the specific activity is increased to a level about 100 times the original activity. The enzyme solution formed by solubilizing the precipitate is then passed through a Sephadex G-200 column, and the recovered active fraction is passed through DEAE-cellulose equilibrated with a buffer solution having a pH of 3.0 to 4.0 and then passed through DEAE-cellulose equilibrated with a buffer solution having a pH of 4.0 to 6.0. The recovered active fraction is passed through a Sephadex G-200 column again. Polyamine oxidase PC-3 which has been purified to show a single spot at the disc electrophoresis is crystallized by ammonium sulfate. The specific activities and recovery ratios at the steps in the purifing procedure from the cell extract to the passage through the Sephadex G-200 column are shown in Table 5. 
     
                                           TABLE 5__________________________________________________________________________                        Specific     Capacity          SPM-act*                 Protein**                        Activity                             Recovery     (ml) (pH = 6.5)                 (280 nm)                        (U/mg)                             Ratio (%)__________________________________________________________________________Cell extract     8200 33.8   34.4   1.0  100          277160 282080Ammonium sulfate     1540 170    9.66   17.6 94.5solubilization-1          261800 14877Ammonium sulfate     106  1931   20.65  93.5 78.2solubilization-2          204730 2189First Sephadex     160  932    1.45   642  53.8G-200          149120 232First DEAE-     200  743    0.597  1245 53.6cellulose      148600 119.4Second DEAE-     65   1502   0.610  2460 35.7cellulose      97650  39.7Second Sephadex     71   1366   0.555  2460 35.0G-200          97000  39.4__________________________________________________________________________ Note *the upper value shows the unit activity (U/ml) and the lower value shows the total activity in case of spermine as the substrate. **the upper value shows the unit amount mg/ml and the lower value shows the total amount (mg). 
    
     The method used in the present invention for determining the activity of polyamine oxidase PC-3 will now be described. 
     In 100 ml of a 0.1 M potassium phosphate buffer solution (pH 6.5) are dissolved 10 mg of 4-aminoantipyrine, 0.2 ml of phenol and 10 mg of peroxidase, and 0.5 ml of spermine (10 mM) or spermidine (10 mM) and 0.5 ml of the enzyme solution are added to 1.5 ml of the so formed coloring reagent and reaction is carried out at 35° C. The quantity of the change of the absorbance at 505 nm per minute is measured. The polyamine oxidase activity units of the enzyme solution are calculated in the following manner. The amount of the polyamine oxidase forming 1.0 μM of hydrogen peroxide per minute is defined as 1 unit. This one unit of the polyamine oxidase corresponds to increase of 0.008 of the absorbance at 505 nm per minute. 
     The new procedures to determine putrescine, spermidine and spermine were firstly established by the end point assay method using polyamine oxidase PC-3 and putrescine oxidase. 
     Method 1: Spermidine and spermine were first oxidized with polyamine oxidase (step A). To the reaction mixture, putrescine oxidase was added to oxidize putrescine (step B). Putrescine and spermidine in another reaction mixture were oxidized with putrescine oxidase (step C). 
     Method 2: Putrescine and spermidine were first oxidized with putrescine oxidase (step A). To the reaction mixture, polyamine oxidase was added to oxidize spermine (step B). Spermidine and spermine in another reaction mixture were oxidized with polyamine oxidase (step C). The amounts of putrescine, spermidine and spermine were determined from the absorbance values at each step A, B and C. 
     The present invention will now be described with reference to the following example. 
     EXAMPLE 1 
     Penicillium chrysogenum IFO 4626 was inoculated on 30 l of a culture medium comprising 0.1% of NaNO 3 , 0.1% of KH 2  PO 4 , 0.05% of MgSO 4 .7H 2  O, 0.05% of KCl and 3.0% of glucose (the pH value before sterilization was 5.5) and cultivation was conducted at 28° C. for 48 hours. The so obtained seed culture liquid was added to 220 l of a culture medium comprising 0.1% of glucose, 0.02% of MgSO 4 .7H 2  O, 0.15% of K 2  HPO 4 , 0.1% of KH 2  PO 4  and 0.025% of spermidine (the pH before sterilization was 5.5), and culturing was conducted at 28° C. for 48 hours. The culture medium was filtered to obtain about 1.7 Kg of cells. The cells were washed several times with a 0.01 M potassium phosphate buffer solution (pH 6.0), suspended in about 6 l of the same buffer solution and disrupted by a Dyno mill. The obtained extract was subjected to centrifugal separation at 7000 rpm for 20 minutes to separate the cell residue and obtain 8200 ml of the supernatant. The enzymatic activity of the supernatant was 33.8 U/ml. The pH value of the supernatant was adjusted to 3.8 by acetic acid and the formed precipitate was separated from the supernatant by centrifugal separation at 7000 rpm for 20 minutes. Polyamine oxidase PC-3 contained in the precipitate was solubilized by suspending the precipitate in a 0.01 M acetate buffer solution and adding ammonium sulfate so that the concentration corresponded to 10% of the saturation concentration. The isoluble fraction was removed by centrifugal separation at 7000 rpm for 20 minutes to obtain 1540 ml of the supernatant. The enzyme in the supernatant was transferred to the precipitate fraction by dialysis with a 0.01 M acetate buffer solution (pH 3.8). The enzyme in the precipitate fraction was collected by the same centrifugal separation as described above and dissolved in 106 ml of a 0.01 M acetate buffer solution containing ammonium sulfate at a concentration corresponding to 10% of the saturation concentration. The solubilized polyamine oxidase was precipitated by increasing the ammonium sulfate concentration to 90% of the saturation concentration and was then condensed (10 ml) was passed through a Sephadex G-200 column equilibrated with a 0.01 M acetate buffer solution containing ammonium sulfate at a concentration corresponding to 10% of the saturation concentration. The obtained active fraction (160 ml) was passed through a column of DEAE-cellulose (100 ml) equilibrated with a 0.01 M acetate buffer solution (pH 3.8) and dialyzed by a 0.01 M acetate buffer solution (pH 3.8). The dialyzed enzyme solution was passed again through a DEAE-cellulose column (the volume was 20 ml) equilibrated with a 0.01 M acetate buffer solution, and the enzyme solution was concentrated and passed through a Sephadex G-200 column (the volume was 300 ml) equilibrated with a 0.01 M acetate buffer solution. The obtained active fraction was concentrated and ammonium sulfate was added to effect crystallization. Polyamine oxidase PC-3 was obtained in the form of a needle crystal in a yield of 35%. 
     Differential determination of putrescine, spermidine and spermine by using polyamine oxidase PC-3 will be shown. 
     Method 1: In the presence of putrescine, spermidine and spermine, spermidine and spermine are first oxidized with polyamine oxidase PC-3 at pH 5.0. After completion of the reaction, its pH was adjusted to around 8.5 and the absorbance value (by 505 nm) is measured (step A). At step A, putrescine is not oxidized. Spermidine and spermine are completely oxidized to putrescine according to Scheme. 
     The absorbance change at step A shows the molar concentrations of spermidine plus twice of spermine. Putrescine oxidase is then added to the reaction mixture at step A, and the reaction is continued until putrescine is completely oxidized (step B). At step B, total putrescine, which consists of firstly presented one and that produced by polyamine oxidations at step A, are oxidized. Therefore, the absorbance change at step B shows the total concentrations of putrescine plus spermidine plus spermine. Where as the absorbance value, which is measured at the end of step B, shows the absorbance change at step A plus that at step B, the absorbance change at step B is obtained by subtracting the absorbance value at step A from that at step B. When another reaction mixture containing putrescine, spermidine and spermine is also oxidized with putrescine oxidase at pH 8.5, putrescine and spermidine are completely oxidized (step C). The absorbance change at step C shows the concentrations of putrescine plus spermidine. From these results, the absorbance changes at steps A, B and C (Y a , Y b , Y c ) were defined by eqs. 1, 2 and  3, respectively. 
     
         Y.sub.a =[SPD]+2[SPM]                                      (1) 
    
     
         Y.sub.b =[PUT]+[SPD]+[SPM]                                 (2) 
    
     
         Y.sub.c =[PUT]+[SPD]                                       (3) 
    
     Where, [PUT], [SPD] and [SPM] represent the concentrations of putrescine, spermidine and spermine, respectively. Therefore, the concentrations or the amounts of putrescine, spermidine and spermine could be calculated as follows. 
     
         [PUT]=2Y.sub.b -Y.sub.a -Y.sub.c                           (4) 
    
     
         [SPD]=Y.sub.a +2Y.sub.c -2Y.sub.b                          (5) 
    
     
         [SPM]=Y.sub.b -Y.sub.c                                     (6) 
    
     Method 2: In the presence of putrescine, spermidine and spermine, putrescine and spermidine are first oxidized with putrescine oxidase at pH 8.5. After completion of the reaction, its pH was adjusted to around 5.0 and the absorbance value (by 505 nm) is measured (step A). Step A is identical to step C of Method 1, in which the absorbance change shows the concentrations of putrescine plus spermidine. Polyamine oxidase PC-3 is then added to the reaction mixture at step A, and the reaction is continued until spermine is completely oxidized (step B). The absorbance change at step B shows twice of molar concentration of spermine. Where as the absorbance value, which was measured at the end of step B, shows the adsorbance change at step A plus that at step B, the absorbance change at step B was obtained by subtracting the absorbance value at step A from that at step B. When another reaction mixture containing putrescine, spermidine and spermine is oxidized with polyamine oxidase PC-3 at pH 5.0, spermidine and spermine are completely oxidized without oxidation of putrescine just as step A of Method 1. The absorbance change at step C shows the molar concentrations of spermidine plus twice of spermine. From these results, the absorbance changes at steps A, B and C (Y a , Y b , Y c ) are defined by eqs. 7, 8 and 9, respectively. 
     
         Y.sub.a =[PUT]+[SPD]                                       (7) 
    
     
         Y.sub.b =2 [SPM]                                           (8) 
    
     
         Y.sub.c =[SPD]+2[SPM]                                      (9) 
    
     Therefore, the concentrations or the amounts of putrescine, spermidine and spermine could be calculated by eqs. 10, 11 and 12. 
     
         [PUT]=Y.sub.a +Y.sub.b -Y.sub.c                            (10) 
    
     
         [SPD]=Y.sub.c -Y.sub.b                                     (11) 
    
     
         [SPM]=1/2Y.sub.b                                           (12)