Abstract:
A kit for the determination of L-carnitine or short-chain acyl L-carnitines consisting of only two vials complete with all the necessary reactants, with the exception of standards, preferably the kit contains the reactants in lyophilized form.

Description:
This application is the US national phase of international application PCT/IT01/00166 filed 30 Mar. 2001 which designated the U.S. 
    
    
     The invention described herein relates to a kit for the determination of L-carnitine in biological fluids. 
     BACKGROUND TO THE INVENTION 
     L-carnitine plays a fundamental role in metabolism, being a key element in the oxidation of long-chain fatty acids and thus in the production of energy. 
     There are many pathological states the underlying cause of which is a deficiency of L-carnitine, and L-carnitine determination is necessary in order to establish the precise a etiology of the related disease processes. 
     There has been a growing awareness among clinicians over recent years of the importance of L-carnitine deficiencies (Bieber et is al. Fed. Proc. 41, 2858 (1982); Stanley, Adv. Pediatr. 34, 59 (1987). 
     One of the first methods used for determining L-carnitine (hereinafter called carnitine for short) was described by Marquis and Fritz in 1964 (Journal of Lipid Research 5, 184-187). Various other methods have been described, such as, for example, those by Marzo et al., J. Chromatogr. 527, 247 (1990); and Hoppel, in: Hommes (ed.), Techniques in Diagnostic Human Biochemical Genetics, New York, Wiley-Liss, 309-326 (1991). 
     The most widespread methods are based on the reaction of the enzyme carnitine acetyl transferase (CAT; EC 2.3.1.7): 
                        
 
     One very widespread method for the indirect determination of carnitine is based on the reaction of acetyl-Coenzyme A, released by the preceding reaction with 5,5′-dithiobis-2-nitrobenzoate (DTNB), which in turn releases the thiophenylate ion, which is determined spectrophotometrically at 412 nm (see, in addition to the above-mentioned Marquis, Seccombe D. W., Clinical Chemistry, 22, No. 10, 1589-1592, 1976; Pearson, Methods of Enzymatic Analysis, 4, 1758-1771, 2nd edition—Bergmeyer; Casillas E. R. Biochimica et Biophysica Acta, 184, 566-577, 1969; Cederblad G. Clinica Chimica Acta, 33, 117.123, 1971; Carrier H. N., Muscle &amp; Nerve July/August 326-328, 1980). This method determines free carnitine. For the determination of the short-chain acyl carnitines, and thus of total carnitines, the sample is subjected to alkaline hydrolysis, converting the acyl carnitines to free carnitine. 
     The known methods entail elaborate preparation phases, or use techniques which are only poorly conducive to automation of the analyses. For a discussion of the subject, see U.S. Pat. No. 5,316,917, filed in the name of Duke University, and incorporated herein for reference purposes. This patent aims to solve the problem of the automation of the analyses. This need is strongly felt in clinical laboratories that have to carry out large numbers of determinations. The Duke University patent offers the solution of an automated spectrophotometric method, consisting in the following steps:
     1) addition of a plurality of samples of deproteinized biological fluids to a set of wells of a centrifugal spectrophotometric analyzer;   2) addition to each sample of:
       a) acetyl-Coenzyme A in an amount sufficient to react essentially with all the free carnitine in the sample to produce acetyl-carnitine and free Coenzyme A;   b) DTNB in an amount sufficient to convert essentially all the Coenzyme A produced in the previous reaction to thiophenylate, and then   c) simultaneously combine CAT, in each sample, in an amount sufficient to set off the reaction between acetyl-Coenzyme A and free carnitine and bring it to completion, and then   d) determine the amount of thiophenylate present in the sample simultaneously by spectrophotometry.   The kit used to implement the method described in the patent cited includes:
           a) a first container containing a solution of DTNB at a concentration ranging from 0.27 to 27 mmol/L, at a pH ranging from 6.5 to 8.5, and   b) a second container containing a solution consisting of acetyl-Coenzyme A at a concentration ranging from 1.2 to 120 mmol/L, where the two solutions can be mixed together prior to use to form a solution containing DTNB at a concentration ranging from 0.23 to 23 mmol/L and acetyl-Coenzyme A at a concentration ranging from 0.17 to 17 mmol/l.   
           
       

     In actual fact, the kit must also include a third container containing from 4 to 40 kU/L of CAT, for example in the form of a solution at a concentration ranging from 1.72 to 172 kU/L. It is envisaged that the third container should contain CAT in lyophilized form. Also envisaged in the kit are containers with carnitine standards in aqueous solution from 0.1 to 10 mmol/L and of octanoyl L-carnitine from 0.1 to 10 mmol/L. Also provided in the kit is a fourth container containing a 3-[N-morpholine]propanesulphonic acid hydrochloric solution, from 0.1 to 10 mmol/L. 
     The execution of the procedure entails the preparation of 4 solutions:
         1. DTNB; HEPES; EDTA at pH 7.5   2. MOPS-HCl   3. KOH       

     In fact, the procedure described in the patent is called “three reagent chemistry”. 
     It is known that the solutions envisaged in the kit described above must be stored at low temperature, from 0 to 4° C., as prescribed in the patent cited. 
     U.S. Pat. No. 6,027,690, a divisional patent of U.S. Pat. No. 5,872,008, filed in the name of Bair and Shug, provides a kit for the diagnosis of premenstrual syndrome, based on the determination of free and total carnitine in the blood. Apart from the specific indication of the method, to implement the method the kit consists of:
         a) a first container containing a solution of acetyl-Coenzyme A at a concentration ranging from 1.2 to 120 mmol/L, and   b) a second container containing a solution consisting of DTNB or N-(p-2(benzimidazolyl)phenyl)maleimide at a concentration ranging from 0.27 to 27 mmol/L at a pH ranging from 6.5 to 8.5, where the two solutions can be mixed together prior to use to form a solution consisting of DTNB or N-(p-2(benzimidazolyl)phenyl)maleimide at a concentration ranging from 0.23 to 23 mmol/L and acetyl-Coenzyme A at a concentration ranging from 0.17 to 17 mmol/l.       

     In the execution of the procedure according to U.S. Pat. No. 6,072,690, the method described in U.S. Pat. No. 5,316,917 can be adopted amongst others. 
     A Boehringer Mannheim kit is commercially available for the determination of L-carnitine in plasma, seminal fluid, and urine. The determination is based on the following reactions: 
                        
 
The amount of NADH consumed during the reaction is equivalent to half the amount of L-carnitine. NADH is determined by absorbance at 334 (Hg), 340 or 365 (Hg) nm.
 
     The kit comprises:
         1) 3 vials (1) each containing 0.7 g of a Coenzyme/buffer mixture consisting of Tris buffer pH 7.0, NADH 5 mg, ATP 6 mg, acetyl-Coenzyme A 4 mg, PEP 3 mg, magnesium acetate, and stabilizing agents.   2) Vial (2) containing approximately 3 ml of enzyme suspension consisting of acetyl-CoA synthetase (ACS), 2U approx., myokinase (MK), 160 U approx., lactate dehydrogenase (LDH), 240 U approx., and pyruvate kinase (PK), 240 U approx.   3) Vial (3) containing 0.2 ml of carnitine acetyl transferase (CAT) enzyme suspension, 60 U approx.   4) Vial (4) containing L-carnitine standard.   5) Vial (5) containing detergent solution.       

     Prior to use, the contents of one vial (1) are diluted with 10 ml of distilled water and 1 ml is added from vial (5). The other vials are used as such. The procedure consists in the addition of the sample (or standard) to solution (1), then addition of suspension (2), measurement of absorbance, then addition of suspension (3) and subsequent measurement of absorbance. 
     BRIEF SUMMARY OF THE INVENTION 
     It has now been found that it is possible to provide a kit for the determination of L-carnitine or short-chain acyl L-carnitines consisting of only two vials complete with all the necessary reactants, with the exception of the standards. Conveniently, the kits contain the reactants in lyophilized form. 
     One of the advantages afforded by the realization of the invention described herein consists in the possibility of determining carnitine over a broad range of concentrations. 
     The kit according to the invention comprises:
         a) a first container containing Reagent 1, said Reagent 1 consisting of HEPES, EDTA, acetyl-Coenzyme A and DTNB;   b) a second container containing Reagent 2, said Reagent 2 consisting of carnitine acetyl transferase.       

     Therefore, one subject of the invention described herein is a kit for the determination of L-carnitine in biological tissues and fluids, its use for the determination of L-carnitine in biological tissues and fluids and methods for the determination of L-carnitine in biological tissues and fluids using the kit. 
     According to the invention described herein, the kit permits the determination of L-carnitine in biological fluids and tissues. Examples of biological fluids and tissues are blood, plasma and seminal fluid. When suitably treated according to conventional techniques, other tissues can be analyzed with the kit according to the invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In a first preferred form, Reagent 1 consists of: 
     
       
         
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 HEPES 
                 0.1 M, pH 7.5 
               
               
                   
                 EDTA 
                 50 mM, pH 7 
               
               
                   
                 acetyl-Coenzyme A 
               
               
                   
                 DTNB 
                 10, 1 mM 
               
               
                   
                   
               
             
          
         
       
     
     Preferably, Reagent 1 has the following composition per ml: 
     
       
         
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 HEPES 
                 0.1 M, pH 75 
                 0.652 mL 
               
               
                   
                 EDTA 
                 50 mM, pH 7 
                 0.174 mL 
               
               
                   
                 acetyl-Coenzyme A 
                   
                 0.087 mL 
               
               
                   
                 DTNB 
                 10.1 mM 
                 0.087 mL 
               
               
                   
                   
               
             
          
         
       
     
     The Reagent 1 container preferably contains 3 mL of Reagent 1. 
     In a first preferred form, Reagent 2 consists of:
         carnitine acetyl transferase 0.500 mL       

     If deemed appropriate, the kit may also contain other elements such as L-carnitine standards, other reactants for the preparation of samples, e.g. plasma or seminal fluid. Reagents 1 and 2 may also essentially contain, in addition to the basic reactants necessary for the reactions, i.e. acetyl-Coenzyme A, DTNB and carnitine acetyl transferase, additional substances useful for the analysis, or alternative substances to those contained in the kit capable of producing the same effect, e.g. buffers, chelating agents, complexing agents, pH correctors, preservatives, and stabilizing agents. Any changes or improvements to the kit supplied on the basis of the invention described herein, which substantially lead to the same result and afford the same advantages fall within the compass of the invention described herein. 
     The preferred form of the kit is that in which the reagents are in lyophilized form. This form permits prolonged storage of the reagents in normal ambient conditions, without particular precautions, with obvious advantages from the point of view of the marketing of the kit. The lyophilization is done according to the conventional techniques used in the field and requires no further description. 
     The kit according to a first embodiment of the invention described herein (3 mL of Reagent 1 and 0.500 mL of Reagent 2) is sufficient for approximately 13 determinations, if the manual method is used, or for approximately 60 determinations, if the automatic method is used. Both methods are described in detail here below. 
     A first preferred embodiment of the invention described herein relates to the determination of carnitine in plasma. 
     The invention described herein is based on the reaction that takes place between L-carnitine and acetyl-CoA in the presence of the enzyme carnitine acetyl transferase (CAT). The Coenzyme A (CoA) produced by this reaction reacts in turn with 5.5°-dithiobis-2-nitrobenzoate (DTNB), releasing thiophenylate ions (TNB−) which absorb at a wavelength of 412 nm, in the case of the use of a manual spectrophotometer, or at a wavelength of 405 nm, in the case of the use of an automatic-type spectrophotometer. The reactions involved are all quantitative, and therefore the TNB− absorbance value can be used to determine the carnitine concentration in the sample. 
     The invention is illustrated with reference to a preferred form of its embodiment, namely for the determination of carnitine in plasma. It is understood that the principles involved in the invention described herein are equally applicable to other tissues, which are treated according to their nature, using conventional procedures which are a matter of general knowledge to people with average experience in the field. The determination method comprises the following steps: 
     a) deproteinizing of the plasma sample in an acid milieu; 
     b) neutralization of the sample; 
     c) incubation. 
     It is in step c) that the enzymatic reactions occur using the kit according to the invention described herein: 
                        
 
     The amount of TNB− ions forming in the latter reaction is equivalent to that of the L-carnitine initially present in the sample. 
     Ambient pH weakly influences the reactions and therefore the result of the analysis; in fact, at pH above 8.5 CAT is inactivated, whereas at pH values below 7 the dissociation of DTNB is incomplete, and therefore the L-carnitine values will be underestimated. 
     As an alternative to steps a) and b) described above, the sample can be deproteinized by simple filtration. 
     EXAMPLE 1 
     Preparation of Solutions 
     Acetyl-CoA 12.35 mM: solubilize 86 mg of acetyl-CoA in 8.6 mL of bidistilled water. This solution will be used to prepare Reagent 1. 
     Carnitine acetyl-transferase (CAT): dilute the CAT with bidistilled water (1 volume of CAT+11 volumes of bidistilled water). This solution will be used to prepare Reagent 2. If not used immediately, the reagent can be stored at −20° C. and defrosted at the time of use. 
     EDTA 50 mM pH 7.0: solubilize 2.2 g of EDTA in 50 mL of bidistilled water in a 100 mL calibrated flask. Bring the pH to 7.0 with glacial acetic acid and top up to volume with bidistilled water. The solution is stable for 6 months at 4° C. 
     DTNB 10 mM: solubilize 34.4 mg of DTNB with 8.6 ml of Hepes 0.1 M at pH 7.5. 
     Hepes 0.1 M at pH 7.5: solubilize 2.38 g of Hepes in 50 mL of bidistilled water in a 100 mL calibrated flask. Bring the pH to 7.5 with potash 1.25 M, and top up to volume with bidistilled water. The solution is stable for 6 months at 4° C. 
     Perchloric acid 2.75 M: dilute 23.2 mL of 70% perchloric acid in bidistilled water in a 100 mL calibrated flask. The solution is stable for 6 months at ambient temperature. 
     Potassium carbonate 1.2 M: solubilize 16.6 g of potassium carbonate with 80 mL of bidistilled water. Mix and top up to volume with bidistilled water. The solution is stable for 6 months at ambient temperature. 
     Potassium hydroxide 1.25 M: solubilize 8.25 g of potassium hydroxide with 80 mL of bidistilled water a 100 mL calibrated flask. Mix and top up to volume with bidistilled water. The solution is stable for 6 months at ambient temperature. 
     Reagent 1: prepare 100 mL of reagent: to 65.5 mL of Hepes 0.1 M at pH 7.5 add 17.3 mL of EDTA 50 mM, pH 7.0, 8.6 mL of DTNB 10 mM and 8.6 mL of acetyl-CoA 12.35 mM. The solution is stable for 6 months at −20° C. 
     Deproteinizing of Plasma/Serum and Neutralization of Sample 
     Transfer 300 μL of plasma/serum and 40 μL of perchloric acid 2.75 M into a 1.5 ml Eppendorf tube. Mix well and then centrifuge at 10,000×g for 5 min at 4° C. Transfer 250 μL of the supernatant and add 40 μL of potassium carbonate 1.2 M in a 1.5 ml Eppendorf tube. Mix and then leave the samples to digest in ice for 10 min. Centrifuge again at 10,000×g for 5 min at 4° C. Remove the supernatant for analysis. 
     Deproteinizing of Plasma/Serum by Filtration 
     Load the sample of plasma/serum on AMICON type filters with cut-off ranging from 5000 to 20000 NMW. Load the sample (400 μL approx.) in an Eppendorf tube containing the filter, to be centrifuged at 15000×g for 30-40 minutes at 4° C. Remove the filtrate for analysis. 
     Enzymatic Analysis 
     A) Manual type spectrophotometry. 
     Varian DMS-80 UV/VIS spectrophotometer 
     Wavelength: 412 nm 
     Cuvette: single-use, disposable, 1 cm optical path 
     Temperature: 20-25° C. 
     Measurement: against air. 
     Incubation: 
     transfer to cuvette 
     
       
         
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Blank (μL) 
                 Sample (μL) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Bidistilled water 
                 1000 
                 750 
               
               
                   
                 Sample 
                 — 
                 250 
               
               
                   
                 Reagent 1 
                  230 
                 230 
               
               
                   
                   
               
             
          
         
       
     
     Stir. After 5 minutes measure the absorbance of the blank and the sample (A 1 ). On completion of reading, add 20 μL of CAT (Reagent 2) to each test tube and mix. After another 10 minutes repeat the measurement of the blank and the sample (A 2 ). 
     The concentration is calculated as follows: 
       C   =         Δ   ⁢           ⁢   A       ɛ   ×   d       ×   F   ×   1000         
         where:   C=concentration of sample (nmol/mL)   ΔA=(A 2 −A 1 ) sample −(A 2 −A 1 ) blank      ε=coefficient of molar extinction of TNB−
 
(412 nm=13.6 L×μmol −1 ×cm)
   d=optical path length (cm)   F=dilution factor (6.55)   1000=conversion factor to obtain the result in nmol/mL.       

     Example of calculation: 
     
       
         
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 A 1   
                 A 2   
                 A 2 -A 1   
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Blank 
                 0.169 
                 0.172 
                 0.003 
               
               
                   
                 Sample 
                 0.170 
                 0.242 
                 0.072 
               
               
                   
                   
               
             
          
         
       
     
     Applying the formula indicated above: C=33.2 nmol/mL. 
     B) Automatic Type Spectrophotometer 
     Before starting the analysis, dilute Reagent 1 and Reagent 2 5 times with bidistilled water (e.g., to 1 mL of Reagent 1 add 4 mL of bidistilled water; to 1 mL of Reagent 2 add 4 mL of bidistilled water). 
     Experimental Conditions 
     Procedure for programming the Roche mod. Cobas-Mira S automatic analyzer (software used N* 8347) 
     
       
         
               
             
               
               
               
             
               
               
               
               
               
             
               
               
               
             
               
               
               
               
             
           
               
                   
               
               
                 FREE CARNITINE 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 SW 884*7 
                 COBAS MIRA S 
               
               
                   
                 GENERAL 
               
               
                   
                 MEASUREMENT MODE 
                 ABSORB 
               
               
                   
                 REACTION MODE 
                 D-R-S-SRI 
               
               
                   
                 CALIBRATION MODE 
                 LIN REGR 
               
               
                   
                 REAGENT BLANK 
                 REAG/SOL 
               
               
                   
                 CLEANER 
                 NO 
               
               
                   
                 WAVELENGTH 
                 405 nm 
               
               
                   
                 DECIMAL POSITION 
                  2 
               
               
                   
                 UNIT 
                 μmol/L 
               
               
                   
                 ANALYSIS 
               
               
                   
                 DILUTION NAME 
                 H 2 O 
               
               
                   
                 FACTOR 
                 NO 
               
               
                   
                 TIME 
                 NO 
               
               
                   
                 STD: 
                 MAIN DIRECT 
               
               
                   
                 MAIN STD 
                 200 μmol/L 
               
               
                   
                 POST DIL FACTOR 
                  3 
               
               
                   
                 CONC. FACTOR 
                 NO 
               
               
                   
                 SAMPLE CYCLE 
                  1 
               
               
                   
                 VOLUME 
                  50 μL 
               
               
                   
                 DILUTION NAME 
                 H 2 O 
               
               
                   
                 VOLUME 
                  10 μL 
               
               
                   
                 REAGENT CYCLE 
                  1 
               
               
                   
                 VOLUME 
                 250 μL 
               
               
                   
                 START R1 CYCLE 
                  7 
               
               
                   
                 VOLUME 
                  40 μL 
               
               
                   
                 DILUTION NAME 
                 H 2 O 
               
               
                   
                 VOLUME 
                  10 μL 
               
               
                   
                 CALCULATION 
               
               
                   
                 SAMPLE LIMIT 
                  0.1 
               
               
                   
                 POINT 
                 T1 
               
               
                   
                 REAC. DIRECTION 
                 INCREASE 
               
               
                   
                 CHECK 
                 ON 
               
               
                   
                 CONVERS. FACTOR 
                  1 
               
               
                   
                 OFFSET 
                  0 
               
               
                   
                 TEST RANGE LOW 
                 ON 
               
               
                   
                 HIGH 
                 ON 
               
               
                   
                 NORMAL RANGE LOW 
                 YES 
               
               
                   
                 HIGH 
                 NO 
               
               
                   
                 NUMBERS OF STEPS 
                  1 
               
               
                   
                 CALC. STEP A 
                 ENDPOINT 
               
               
                   
                 FIRST READING 
                  6 
               
               
                   
                 LAST READING 
                 30 
               
               
                   
                 CALIBRATION 
               
               
                   
                 CALIB. INTERVAL 
                 ON REQUEST 
               
               
                   
                 BLANK 
               
               
                   
                 REAGENT RANGE LOW 
                 −0.0001 
               
               
                   
                 HIGH 
                  0.1000 
               
               
                   
                 BLANK RANGE LOW 
                 −0.0050 
               
               
                   
                 HIGH 
                  0.0050 
               
               
                   
                 STANDARD POS: 
                  1 
               
             
          
           
               
                   
                 1: 
                 200 μmol/L 
                 2: 
                 100      μmol/L 
               
               
                   
                 3: 
                  75 μmol/L 
                 4: 
                  50 μmol/L 
               
               
                   
                 5: 
                  30 μmol/L 
                 6: 
                  20 μmol/L 
               
               
                   
                 7: 
                  10 μmol/L 
                 8: 
                  0 μmol/L 
               
             
          
           
               
                   
                 REPLICATE 
                 DUPLICATE 
               
               
                   
                 DEVIATION 
                 10% 
               
               
                   
                 CORRECTION STD 
                 NO 
               
               
                   
                 CONTROL 
               
             
          
           
               
                   
                 CS1* POS: 11 LOW 
                 90 
                 mol/L 
               
               
                   
                 ASSIGN 
                 100 
                 μmol/L 
               
               
                   
                 HIGH 
                 110 
                 μmol/L 
               
               
                   
                 CS2* POS: 12 LOW 
                 40 
                 μmol/L 
               
               
                   
                 ASSIGN 
                 50 
                 μmol/L 
               
               
                   
                 HIGH 
                 60 
                 μmol/L 
               
               
                   
                 CS3* POS: 13 LOW 
                 12 
                 μmol/L 
               
               
                   
                 ASSIGN 
                 20 
                 μmol/L 
               
               
                   
                 HIGH 
                 28 
                 μmol/L 
               
               
                   
                   
               
             
          
         
       
     
     Note: the samples called CS1, CS2 e CS3 refer to the reference standards and are prepared by scalar dilution of the mother solution of L-carnitine inner salt at a concentration of 200 μmol/L. 
     The calculation of the concentrations of the blanks is done automatically by the analyzer which extrapolates them from a straight calibration line to be prepared fresh for each analysis session (possibly in duplicate). 
     The above-described sample preparation and analysis conditions being equal, it is possible to calculate the carnitine concentration for an unknown sample immediately by multiplying its absorbance value by the factor 1028.382. In this case neither the calibration line nor the control samples will be used. 
     Whenever the unknown samples have been deproteinized by acidification and subsequent neutralization with the procedure described above, the value of the concentration obtained must be multiplied by the factor 1.3146. 
     Given here below, by way of an example, is a table directly correlating the L-carnitine concentrations with the absorbance readings. 
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 CALCULATION OF L-CARNITINE CONCENTRATIONS USING THE FACTOR 481.62 
               
             
          
           
               
                 Abs 
                 μmoli/L 
                 Abs 
                 μmoli/L 
                 Abs 
                 μmoli/L 
                 Abs 
                 μmoli/L 
                 Abs 
                 μmoli/L 
                 Abs 
                 μmoli/L 
               
               
                   
               
             
          
           
               
                 0.001 
                 0.482 
                 0.051 
                 24.563 
                 0.101 
                 48.644 
                 0.151 
                 72.725 
                 0.201 
                 96.806 
                 0.251 
                 120.89 
               
               
                 0.002 
                 0.963 
                 0.052 
                 25.044 
                 0.102 
                 49.125 
                 0.152 
                 73.206 
                 0.202 
                 97.287 
                 0.252 
                 121.37 
               
               
                 0.003 
                 1.445 
                 0.053 
                 25.526 
                 0.103 
                 49.607 
                 0.153 
                 73.688 
                 0.203 
                 97.769 
                 0.253 
                 121.85 
               
               
                 0.004 
                 1.926 
                 0.054 
                 26.007 
                 0.104 
                 50.088 
                 0.154 
                 74.169 
                 0.204 
                 98.250 
                 0.254 
                 122.33 
               
               
                 0.005 
                 2.408 
                 0.055 
                 26.489 
                 0.105 
                 50.570 
                 0.155 
                 74.651 
                 0.205 
                 98.732 
                 0.255 
                 122.81 
               
               
                 0.006 
                 2.890 
                 0.056 
                 26.971 
                 0.106 
                 51.052 
                 0.156 
                 75.133 
                 0.206 
                 99.214 
                 0.256 
                 123.29 
               
               
                 0.007 
                 3.371 
                 0.057 
                 27.452 
                 0.107 
                 51.533 
                 0.157 
                 75.614 
                 0.207 
                 99.695 
                 0.257 
                 123.78 
               
               
                 0.008 
                 3.853 
                 0.058 
                 27.934 
                 0.108 
                 52.015 
                 0.158 
                 76.096 
                 0.208 
                 100.18 
                 0.258 
                 124.26 
               
               
                 0.009 
                 4.335 
                 0.059 
                 28.416 
                 0.109 
                 52.497 
                 0.159 
                 76.578 
                 0.209 
                 100.66 
                 0.259 
                 124.74 
               
               
                 0.010 
                 4.816 
                 0.060 
                 28.897 
                 0.110 
                 52.978 
                 0.160 
                 77.059 
                 0.210 
                 101.14 
                 0.260 
                 125.22 
               
               
                 0.011 
                 5.298 
                 0.061 
                 29.379 
                 0.111 
                 53.460 
                 0.161 
                 77.541 
                 0.211 
                 101.62 
                 0.261 
                 125.70 
               
               
                 0.012 
                 5.779 
                 0.062 
                 29.860 
                 0.112 
                 53.941 
                 0.162 
                 78.022 
                 0.212 
                 102.10 
                 0.262 
                 126.18 
               
               
                 0.013 
                 6.261 
                 0.063 
                 30.342 
                 0.113 
                 54.423 
                 0.163 
                 78.504 
                 0.213 
                 102.59 
                 0.263 
                 126.67 
               
               
                 0.014 
                 6.743 
                 0.064 
                 30.824 
                 0.114 
                 54.905 
                 0.164 
                 78.986 
                 0.214 
                 103.07 
                 0.264 
                 127.15 
               
               
                 0.015 
                 7.224 
                 0.065 
                 31.305 
                 0.115 
                 55.386 
                 0.165 
                 79.467 
                 0.215 
                 103.55 
                 0.265 
                 127.63 
               
               
                 0.016 
                 7.706 
                 0.066 
                 31.787 
                 0.116 
                 55.868 
                 0.166 
                 79.949 
                 0.216 
                 104.03 
                 0.266 
                 128.11 
               
               
                 0.017 
                 8.188 
                 0.067 
                 32.269 
                 0.117 
                 56.350 
                 0.167 
                 80.431 
                 0.217 
                 104.51 
                 0.267 
                 128.59 
               
               
                 0.018 
                 8.669 
                 0.068 
                 32.750 
                 0.118 
                 56.831 
                 0.168 
                 80.912 
                 0.218 
                 104.99 
                 0.268 
                 129.07 
               
               
                 0.019 
                 9.151 
                 0.069 
                 33.232 
                 0.119 
                 57.313 
                 0.169 
                 81.394 
                 0.219 
                 105.47 
                 0.269 
                 129.56 
               
               
                 0.020 
                 9.632 
                 0.070 
                 33.713 
                 0.120 
                 57.794 
                 0.170 
                 81.875 
                 0.220 
                 105.96 
                 0.270 
                 130.04 
               
               
                 0.021 
                 10.114 
                 0.071 
                 34.195 
                 0.121 
                 58.276 
                 0.171 
                 82.357 
                 0.221 
                 106.44 
                 0.271 
                 130.52 
               
               
                 0.022 
                 10.596 
                 0.072 
                 34.677 
                 0.122 
                 58.758 
                 0.172 
                 82.839 
                 0.222 
                 106.92 
                 0.272 
                 131.00 
               
               
                 0.023 
                 11.077 
                 0.073 
                 35.158 
                 0.123 
                 59.239 
                 0.173 
                 83.320 
                 0.223 
                 107.40 
                 0.273 
                 131.48 
               
               
                 0.024 
                 11.559 
                 0.074 
                 35.640 
                 0.124 
                 59.721 
                 0.174 
                 83.802 
                 0.224 
                 107.88 
                 0.274 
                 131.96 
               
               
                 0.025 
                 12.041 
                 0.075 
                 36.122 
                 0.125 
                 60.203 
                 0.175 
                 84.254 
                 0.225 
                 108.36 
                 0.275 
                 132.45 
               
               
                 0.026 
                 12.522 
                 0.076 
                 36.603 
                 0.126 
                 60.684 
                 0.176 
                 84.765 
                 0.226 
                 108.85 
                 0.276 
                 132.93 
               
               
                 0.027 
                 13.004 
                 0.077 
                 37.085 
                 0.127 
                 61.166 
                 0.177 
                 85.247 
                 0.227 
                 109.33 
                 0.277 
                 133.41 
               
               
                 0.028 
                 13.485 
                 0.078 
                 37.566 
                 0.128 
                 61.647 
                 0.178 
                 85.728 
                 0.228 
                 109.81 
                 0.278 
                 133.89 
               
               
                 0.029 
                 13.967 
                 0.079 
                 38.048 
                 0.129 
                 62.129 
                 0.179 
                 86.210 
                 0.229 
                 110.29 
                 0.279 
                 134.37 
               
               
                 0.030 
                 14.449 
                 0.080 
                 38.530 
                 0.130 
                 62.611 
                 0.180 
                 86.692 
                 0.230 
                 110.77 
                 0.280 
                 134.85 
               
               
                 0.031 
                 14.930 
                 0.081 
                 39.011 
                 0.131 
                 63.092 
                 0.181 
                 87.173 
                 0.231 
                 111.25 
                 0.281 
                 135.34 
               
               
                 0.032 
                 15.412 
                 0.082 
                 39.493 
                 0.132 
                 63.574 
                 0.182 
                 87.655 
                 0.232 
                 111.74 
                 0.282 
                 135.82 
               
               
                 0.033 
                 15.893 
                 0.083 
                 39.974 
                 0.133 
                 64.055 
                 0.183 
                 88.136 
                 0.233 
                 112.22 
                 0.283 
                 136.30 
               
               
                 0.034 
                 16.375 
                 0.084 
                 40.456 
                 0.134 
                 64.537 
                 0.184 
                 88.618 
                 0.234 
                 112.70 
                 0.284 
                 136.78 
               
               
                 0.035 
                 16.857 
                 0.085 
                 40.938 
                 0.135 
                 65.019 
                 0.185 
                 89.100 
                 0.235 
                 113.18 
                 0.285 
                 137.26 
               
               
                 0.036 
                 17.338 
                 0.086 
                 41.419 
                 0.136 
                 65.500 
                 0.186 
                 89.581 
                 0.236 
                 113.66 
                 0.286 
                 137.74 
               
               
                 0.037 
                 17.820 
                 0.087 
                 41.901 
                 0.137 
                 65.982 
                 0.187 
                 90.063 
                 0.237 
                 114.14 
                 0.287 
                 138.22 
               
               
                 0.038 
                 18.302 
                 0.088 
                 42.383 
                 0.138 
                 66.464 
                 0.188 
                 90.545 
                 0.238 
                 114.63 
                 0.288 
                 138.71 
               
               
                 0.039 
                 18.783 
                 0.089 
                 42.864 
                 0.139 
                 66.945 
                 0.189 
                 91.026 
                 0.239 
                 115.11 
                 0.289 
                 139.19 
               
               
                 0.040 
                 19.265 
                 0.090 
                 43.346 
                 0.140 
                 67.427 
                 0.190 
                 91.508 
                 0.240 
                 115.59 
                 0.290 
                 139.67 
               
               
                 0.041 
                 19.746 
                 0.091 
                 43.827 
                 0.141 
                 67.908 
                 0.191 
                 91.989 
                 0.241 
                 116.07 
                 0.291 
                 140.15 
               
               
                 0.042 
                 20.228 
                 0.092 
                 44.309 
                 0.142 
                 68.390 
                 0.192 
                 92.471 
                 0.242 
                 116.55 
                 0.292 
                 140.63 
               
               
                 0.043 
                 20.710 
                 0.093 
                 44.791 
                 0.143 
                 68.872 
                 0.193 
                 92.953 
                 0.243 
                 117.03 
                 0.293 
                 141.11 
               
               
                 0.044 
                 21.191 
                 0.094 
                 45.272 
                 0.144 
                 69.353 
                 0.194 
                 93.434 
                 0.244 
                 117.52 
                 0.294 
                 141.60 
               
               
                 0.045 
                 21.673 
                 0.095 
                 45.754 
                 0.145 
                 69.835 
                 0.195 
                 93.916 
                 0.245 
                 118.00 
                 0.295 
                 142.08 
               
               
                 0.046 
                 22.155 
                 0.096 
                 46.236 
                 0.146 
                 70.317 
                 0.196 
                 94.398 
                 0.246 
                 118.48 
                 0.296 
                 142.56 
               
               
                 0.047 
                 22.636 
                 0.097 
                 46.717 
                 0.147 
                 70.798 
                 0.197 
                 94.879 
                 0.247 
                 118.96 
                 13.297 
                 143.04 
               
               
                 0.048 
                 23.118 
                 0.098 
                 47.199 
                 0.148 
                 71.280 
                 0.198 
                 95.361 
                 0.248 
                 119.44 
                 0.298 
                 143.52 
               
               
                 0.049 
                 23.599 
                 0.099 
                 47.680 
                 0.149 
                 71.761 
                 0.199 
                 95.842 
                 0.249 
                 119.92 
                 0.299 
                 144.00 
               
               
                 0.050 
                 24.081 
                 0.100 
                 48.162 
                 0.150 
                 72.243 
                 0.200 
                 96.324 
                 0.250 
                 120.41 
                 0.300 
                 144.49