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A preliminary approach to the study of thiamine phosphorylation and dephosphorylation in some rat nervous regions and the liver
482
Brain Research, 199 (1980) 482 487 (~i', Elsevier/North-Holland Biomedical Pres~
A preliminary approach to the study of thiamine phosphorylation and dephosphorylation in some rat nervous regions and the liver
VALERIANO COMINCIOLI, CARLO REGGIAN1, CESARE PATRINI and GIANGU1DO RINDI* Inst#utes of Mathematics (V.C.) and Human Physiology at the University of Pavia, Pavia (Italy) Key words: thiamine - - phosphorylation - - dephosphorylation - - turnover - - mathematical model -
rat Free and phosphorylated thiamine were determined in the liver and 9 regions of rat nervous system, after i.p. injection of labeled thiamine. A compartmental model was used to evaluate the rates of the phosphorylation of thiamine and the complete dephosphorylation of its phosphates. Remarkable differences between the liver and the nervous tissue as well as among different nervous regions were shown : high rates were found in hypothalamus, midbrain and cerebellum, low rates in cerebral cortex. Recently, we studied the total thiamine uptake and turnover in the liver and different nervous regions of the rat, using labeled thiamine as a tracer 11. Here we report an extension of that study, where we have investigated, under the same conditions within the same structures, the course of the phosphorylation o f thiamine and the complete dephosphorylation of thiamine phosphates into thiamine, utilizing a c o m p a r t m e n t a l model. In all m a m m a l i a n tissues thiamine is present both in free and phosphorylated f o r m ; the latter represents 95-98 ~/o of the total thiamine and includes mono-, pyroand triphosphothiamine 7,s, 10. Clearly, the consideration of only two forms o f thiamine in the tissues, free and phosphorylated, is too simplistic. However, such a simplification has been made to permit a preliminary test for the general trend o f thiamine phosphorylation and dephosphorylation in the liver and different nervous regions. A more detailed study of the single forms of thiamine is now in progress. As in our previous study 11, 30 #g o f [2-14C]thiazole thiamine (Radiochemical Center, Amersham, England; spec. act. 14 m C i / m m o l ) were i.p. injected into female Wistar rats. Since this thiamine a m o u n t corresponds to the rat's daily requirement 1, a thiamine-deficient diet was given to the rats during the following 24 h, after which a complete diet was again administered (steady-state condition). A t time intervals from 5 min to 96 h after injection, the rats were sacrified by decapitation and the different nervous structures dissected in the cold. Thiamine was extracted from the tissues with cold 0.5 N HC1, and 40 ~ trichloroacetic acid was used for deproteinization. After drying suitable samples on planchets, thiamine radioactivity was determined by a * To whom reprint requests should be sent.
483
ialp alo~l Eo
I'
I a21= E2
Fig. 1 The compartmental model used for the liver and for each nervous region. Eo, exchange compartment (total of free thiamine in the plasma and the rest of the body); El, free thiamine in the structures studied; E2, phosphorylated thiamine in the structures studied. The connection air, indicated with a dashed line, is present only in the liver compartment.
Geiger-Mtiller low background flow-counter (Nuclear Chicago, mod. 512). The experimental curves, obtained from measurements of radioactivity, were interpreted by means of a compartmental model developed from that used for the study of the kinetics of labeled total thiamine n. In each region the kinetics of the tracer were evaluated in two compartments, related respectively to the labeled free and phosphorylated thiamine. These compartments were bidirectionally connected to each other. Moreover, the free thiamine compartment (Fig. 1: El) was bidirectionally connected to an exchange compartment (Fig. 1 : E0), which was assumed to represent the total of free thiamine in the plasma and in the rest of the body. The phosphorylated thiamine compartment (Fig. 1: E2) was connected with E0 only in one direction (efltux). The model was based on the following assumptions: (a) all thiamine phosphates are treated as a single compartment, since the chemical method for their determinations did not discriminate among the different compounds; (b) free thiamine is the only form entering the tissues from the plasma; (c) thiamine catabolism and efllux toward the plasma are processes that cannot be differentiated, though both of which involve free and phosphorylated thiamine. For the liver, since the tracer was i.p. administered, the probability of a distinct route of influx to E1 must be considered, corresponding to the peritoneum and portal vena (Fig. 1 : alP). Thiamine uptake and transformations (enzymatic phosphorylation and dephosphorylation) are non-linear saturable processesS,6,13,14. However, they can be described by linear differential equations, owing to the quite small amount of labeled thiamine which was used. According to the above assumptions, the following system of differential equations can be written for the liver and each nervous structure considered: ~1 = a]oyo + alp yp + a12 y 2 - - (aol + a~l) yl y2 = a21 yt - - (a12 q- a02) y2
yl(O) ---- 0 y2 (0) = 0
(1) (2)
where yl(t), y2(t) are the radioactivities (nCi/g) respectively of the El, E2 compartments; yo(t) is the radioactivity in plasma and in the rest of the body obtained from the general model of thiamine kinetics11, and yv(t) is the radioactivity of free thiamine in the peritoneum compartment. For all nervous regions the parameter aao is zero. While the parameters axo, alv, a01, a02 (where aol=ao2) have been previously 11
484 estimated, a12 and a21 have been newly evaluated in this investigation. The minimization procedure was carried out separately for each region, using the yo (t) obtained from the general model of thiamine kinetics and minimizing the following cost function : F(a) =
2 E J;== 1
Nj (yti(a) - - Yo*)2 E i--1 trtj
of each curve, where Nj is the number of experimental points, Yu*, Yo (a) are the solutions of the equations 1 and 2 for a set of parameters, a, tr0 are the standard deviations related to the experimental data. The minimization was performed by a combination of the Levenberg-Marquardt method with the steepest descent method 4. For a given set of a parameters the equation system 1 was numerically solved by a variable order-variable step formulation of the Adams predictor-corrector method xz. The accuracy of the parameter values was determined, calculating an approximation of the variance-covariance matrix, and from this the standard deviations were identified for each parameter. The a parameters have the dimensions of h -1 and can be considered as the relative rate at which the tracer leaves or enters a compartment: so they can be defined as fractional turnover rates (FRC)L Since at steady-state both labeled and unlabeled thiamine enter (or leave) a compartment at exactly the same rate, the FRC multiplied by the size of the compartment (#g/g, i.e. the traced compound concentration) gives the values of the flux of the material into or out of the compartment. These fluxes have the dimensions #g/g.h and can be indicated as mass turnover rates or simply turnover rates (TR)L Tables I and II report the concentrations of free and phosphorylated thiamine (i.e. the sizes of the El and E2 compartments), as previously determined tl, together with the results of the identification procedure outlined above. The values of the parameters permit the description of the metabolism of thiamine in the different regions studied. However, our experimental work and mathematical analysis suffer of the following limitations: (a) the marked simplicity of the mathematical model used; (b) the indirect knowledge of the E0 compartment, this being deduced from the more general model describing total thiamine distribution 11. These limitations could produce some errors in the evaluation of the thiamine kinetics, as can be seen from the values on Tables I and lI, and thereby possibly affect the reliability of the final conclusions. A clear-cut difference between the liver and the nervous tissue was evidenced. In the liver the thiamine phosphorylation TR was at least 20 times greater than that of the mean nervous structure. A greater ratio was also found for the dephosphorylation process. From the TR values of both thiamine phosphorylation and dephosphorylation (Table II) it can be calculated that 96 ~o of the thiamine phosphorylated in the liver was then dephosphorylated to free thiamine. In all the nervous areas there was a constant ratio between thiamine phosphorylation and influx rates (Table I: TR values). This should indicate that almost all the thiamine entering a nervous region was immediately phosphorylated. However, in the cerebellum the ratio was lower (i.e. only a portion of the thiamine that entered was phosphorylated) and in the
485
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487 midbrain it was higher. Moreover, some areas (Table I: TR values) appeared to have a rather high phosphorylating rate (hypothalamus> cerebellum > midbrain > medulla > pons), while others had a less effective phosphorylative process (sciatic nerve > corpus striatum > spinal cord > cerebral cortex). Unlike the liver, in all the nervous regions studied only a fraction (ranging from 6 ~ to 40 %) of phosphorylated thiamine was completely dephosphorylated into thiamine (Table I1). However, the TR values of dephosphorylation, as well as phosphorylation, were different in each region: higher in the cerebellum, hypothalamus and midbrain, as compared to the sciatic nerve, pons, corpus striatum, medulla and spinal cord. The lowest turnover rate value of dephosphorylation as well as for phosphorylation was that of the cerebral cortex (Table II). Excluding the cerebral cortex and corpus striatum, where free thiamine efflux TR is extremely low, all nervous area released thiamine both in free and in phosphorylated form (Tables I and II). At this time, the differences observed between nervous regions cannot easily be explained : different rates of metabolic activity, different ratios of neuronal to glial cells as well as different functions of thiamine could be tentatively considered. The mathematical section, developed by V.C. and C.R., was supported by C.N.R., Rome through the "Laboratorio di Analisi Numerica", Pavia, Italy. 1 Brown, R. A. and Sturtevant, M., The vitamin requirements of the growing rat, Vitam. Horm., 7 (1949) 171-199. 2 Butch, H. B. Bessey, O. A., Love, R. H. and Lowry, O. H., The determination of thiamine and thiamine phosphates in small quantities of blood and blood cells, J. biol. Chem., 198 (1952) 477-490. 3 Glowinski, J. and Iversen, L. L., Regional studies of catecholamines in the rat brain. I. The disposition of [aH]norepinephrine, [~H] dopamine and [ZH] DOPA in various regions of the brain, J. Neurochem., 13 (1966) 655-669. 4 Hillstrom, K. E., Minpaek L ,4 Study in the Modularization of a Package of Computer Algorithms for the Unconstrained Non-Linear Optimization Problem, Tech. Memo. TM-22, Argonne Nat. Lab., 1974. 5 Iwata, H., Baba, A., Matsuda, T. and Terashita, Z., Some properties of the enzyme system degrading phosphorylated thiamines in the brain and the effect of chloropromazine. In C. J. Gubler, M. Fujiwara and P. M. Dreyfus (Eds.), Thiamine, Wiley, New York, 1976, pp. 213-221 6 Nose, Y., Iwashima, A. and Nishino, H., Thiamine uptake by rat brain slices. In C. J. Gubler, M. Fujiwara and P. M. Dreyfus (Eds.), Thiamine, Wiley, New York, 1976, pp. 157-168. 7 Penttinen, H. K., Determination of thiamine and its phosphate esters by electrophoresis and fluorometry, ,4cta chem. scand. B, 32 (1978) 609-612. 8 Pincus, J. H. and Grove, J., Distribution of thiamine phosphate esters in normal and thiaminedeficient brain, Exp. NeuroL, 28 (1970) 477483. 9 Rescigno, A. and Beck, J. S., Compartments. In R. Rosen (Ed.), Foundations of Mathematical Biology, Vol. 2, Academic Press, New York, 1972, pp. 255-322. 10 Rindi, G. and de Giuseppe, L., A new chromatographic method for the determination of thiamine and its mono-, di- and tri-phosphates in animal tissues, Biochem. J., 78 (1961) 602-606. 11 Rindi, G., Patrini, C., Comincioli, V. and Reggiani, C., Thiamine content and turnover rates of some rat nervous regions, using labeled thiamine as a tracer, Brain Research, 181 (1980) 369-380. 12 Shampine, L. F. and Gordon, M. K., Computer Solution of Ordinary Differential Equations. The Initial Value Problem, W. H. Freeman, San Francisco, Calif., 1975. 13 Sharma, S. K. and Quastel, J. H., Transport and metabolism of thiamine in rat brain cortex in vitro, Biochem. J., 94 (1965) 790--800. 14 Spector, R., Thiamine transport in the central nervous system, ,4met. J. Physiol., 230 (1976) 1101-1107.
Brain Research, 199 (1980) 482 487 (~i', Elsevier/North-Holland Biomedical Pres~
A preliminary approach to the study of thiamine phosphorylation and dephosphorylation in some rat nervous regions and the liver
VALERIANO COMINCIOLI, CARLO REGGIAN1, CESARE PATRINI and GIANGU1DO RINDI* Inst#utes of Mathematics (V.C.) and Human Physiology at the University of Pavia, Pavia (Italy) Key words: thiamine - - phosphorylation - - dephosphorylation - - turnover - - mathematical model -
rat Free and phosphorylated thiamine were determined in the liver and 9 regions of rat nervous system, after i.p. injection of labeled thiamine. A compartmental model was used to evaluate the rates of the phosphorylation of thiamine and the complete dephosphorylation of its phosphates. Remarkable differences between the liver and the nervous tissue as well as among different nervous regions were shown : high rates were found in hypothalamus, midbrain and cerebellum, low rates in cerebral cortex. Recently, we studied the total thiamine uptake and turnover in the liver and different nervous regions of the rat, using labeled thiamine as a tracer 11. Here we report an extension of that study, where we have investigated, under the same conditions within the same structures, the course of the phosphorylation o f thiamine and the complete dephosphorylation of thiamine phosphates into thiamine, utilizing a c o m p a r t m e n t a l model. In all m a m m a l i a n tissues thiamine is present both in free and phosphorylated f o r m ; the latter represents 95-98 ~/o of the total thiamine and includes mono-, pyroand triphosphothiamine 7,s, 10. Clearly, the consideration of only two forms o f thiamine in the tissues, free and phosphorylated, is too simplistic. However, such a simplification has been made to permit a preliminary test for the general trend o f thiamine phosphorylation and dephosphorylation in the liver and different nervous regions. A more detailed study of the single forms of thiamine is now in progress. As in our previous study 11, 30 #g o f [2-14C]thiazole thiamine (Radiochemical Center, Amersham, England; spec. act. 14 m C i / m m o l ) were i.p. injected into female Wistar rats. Since this thiamine a m o u n t corresponds to the rat's daily requirement 1, a thiamine-deficient diet was given to the rats during the following 24 h, after which a complete diet was again administered (steady-state condition). A t time intervals from 5 min to 96 h after injection, the rats were sacrified by decapitation and the different nervous structures dissected in the cold. Thiamine was extracted from the tissues with cold 0.5 N HC1, and 40 ~ trichloroacetic acid was used for deproteinization. After drying suitable samples on planchets, thiamine radioactivity was determined by a * To whom reprint requests should be sent.
483
ialp alo~l Eo
I'
I a21= E2
Fig. 1 The compartmental model used for the liver and for each nervous region. Eo, exchange compartment (total of free thiamine in the plasma and the rest of the body); El, free thiamine in the structures studied; E2, phosphorylated thiamine in the structures studied. The connection air, indicated with a dashed line, is present only in the liver compartment.
Geiger-Mtiller low background flow-counter (Nuclear Chicago, mod. 512). The experimental curves, obtained from measurements of radioactivity, were interpreted by means of a compartmental model developed from that used for the study of the kinetics of labeled total thiamine n. In each region the kinetics of the tracer were evaluated in two compartments, related respectively to the labeled free and phosphorylated thiamine. These compartments were bidirectionally connected to each other. Moreover, the free thiamine compartment (Fig. 1: El) was bidirectionally connected to an exchange compartment (Fig. 1 : E0), which was assumed to represent the total of free thiamine in the plasma and in the rest of the body. The phosphorylated thiamine compartment (Fig. 1: E2) was connected with E0 only in one direction (efltux). The model was based on the following assumptions: (a) all thiamine phosphates are treated as a single compartment, since the chemical method for their determinations did not discriminate among the different compounds; (b) free thiamine is the only form entering the tissues from the plasma; (c) thiamine catabolism and efllux toward the plasma are processes that cannot be differentiated, though both of which involve free and phosphorylated thiamine. For the liver, since the tracer was i.p. administered, the probability of a distinct route of influx to E1 must be considered, corresponding to the peritoneum and portal vena (Fig. 1 : alP). Thiamine uptake and transformations (enzymatic phosphorylation and dephosphorylation) are non-linear saturable processesS,6,13,14. However, they can be described by linear differential equations, owing to the quite small amount of labeled thiamine which was used. According to the above assumptions, the following system of differential equations can be written for the liver and each nervous structure considered: ~1 = a]oyo + alp yp + a12 y 2 - - (aol + a~l) yl y2 = a21 yt - - (a12 q- a02) y2
yl(O) ---- 0 y2 (0) = 0
(1) (2)
where yl(t), y2(t) are the radioactivities (nCi/g) respectively of the El, E2 compartments; yo(t) is the radioactivity in plasma and in the rest of the body obtained from the general model of thiamine kinetics11, and yv(t) is the radioactivity of free thiamine in the peritoneum compartment. For all nervous regions the parameter aao is zero. While the parameters axo, alv, a01, a02 (where aol=ao2) have been previously 11
484 estimated, a12 and a21 have been newly evaluated in this investigation. The minimization procedure was carried out separately for each region, using the yo (t) obtained from the general model of thiamine kinetics and minimizing the following cost function : F(a) =
2 E J;== 1
Nj (yti(a) - - Yo*)2 E i--1 trtj
of each curve, where Nj is the number of experimental points, Yu*, Yo (a) are the solutions of the equations 1 and 2 for a set of parameters, a, tr0 are the standard deviations related to the experimental data. The minimization was performed by a combination of the Levenberg-Marquardt method with the steepest descent method 4. For a given set of a parameters the equation system 1 was numerically solved by a variable order-variable step formulation of the Adams predictor-corrector method xz. The accuracy of the parameter values was determined, calculating an approximation of the variance-covariance matrix, and from this the standard deviations were identified for each parameter. The a parameters have the dimensions of h -1 and can be considered as the relative rate at which the tracer leaves or enters a compartment: so they can be defined as fractional turnover rates (FRC)L Since at steady-state both labeled and unlabeled thiamine enter (or leave) a compartment at exactly the same rate, the FRC multiplied by the size of the compartment (#g/g, i.e. the traced compound concentration) gives the values of the flux of the material into or out of the compartment. These fluxes have the dimensions #g/g.h and can be indicated as mass turnover rates or simply turnover rates (TR)L Tables I and II report the concentrations of free and phosphorylated thiamine (i.e. the sizes of the El and E2 compartments), as previously determined tl, together with the results of the identification procedure outlined above. The values of the parameters permit the description of the metabolism of thiamine in the different regions studied. However, our experimental work and mathematical analysis suffer of the following limitations: (a) the marked simplicity of the mathematical model used; (b) the indirect knowledge of the E0 compartment, this being deduced from the more general model describing total thiamine distribution 11. These limitations could produce some errors in the evaluation of the thiamine kinetics, as can be seen from the values on Tables I and lI, and thereby possibly affect the reliability of the final conclusions. A clear-cut difference between the liver and the nervous tissue was evidenced. In the liver the thiamine phosphorylation TR was at least 20 times greater than that of the mean nervous structure. A greater ratio was also found for the dephosphorylation process. From the TR values of both thiamine phosphorylation and dephosphorylation (Table II) it can be calculated that 96 ~o of the thiamine phosphorylated in the liver was then dephosphorylated to free thiamine. In all the nervous areas there was a constant ratio between thiamine phosphorylation and influx rates (Table I: TR values). This should indicate that almost all the thiamine entering a nervous region was immediately phosphorylated. However, in the cerebellum the ratio was lower (i.e. only a portion of the thiamine that entered was phosphorylated) and in the
485
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487 midbrain it was higher. Moreover, some areas (Table I: TR values) appeared to have a rather high phosphorylating rate (hypothalamus> cerebellum > midbrain > medulla > pons), while others had a less effective phosphorylative process (sciatic nerve > corpus striatum > spinal cord > cerebral cortex). Unlike the liver, in all the nervous regions studied only a fraction (ranging from 6 ~ to 40 %) of phosphorylated thiamine was completely dephosphorylated into thiamine (Table I1). However, the TR values of dephosphorylation, as well as phosphorylation, were different in each region: higher in the cerebellum, hypothalamus and midbrain, as compared to the sciatic nerve, pons, corpus striatum, medulla and spinal cord. The lowest turnover rate value of dephosphorylation as well as for phosphorylation was that of the cerebral cortex (Table II). Excluding the cerebral cortex and corpus striatum, where free thiamine efflux TR is extremely low, all nervous area released thiamine both in free and in phosphorylated form (Tables I and II). At this time, the differences observed between nervous regions cannot easily be explained : different rates of metabolic activity, different ratios of neuronal to glial cells as well as different functions of thiamine could be tentatively considered. The mathematical section, developed by V.C. and C.R., was supported by C.N.R., Rome through the "Laboratorio di Analisi Numerica", Pavia, Italy. 1 Brown, R. A. and Sturtevant, M., The vitamin requirements of the growing rat, Vitam. Horm., 7 (1949) 171-199. 2 Butch, H. B. Bessey, O. A., Love, R. H. and Lowry, O. H., The determination of thiamine and thiamine phosphates in small quantities of blood and blood cells, J. biol. Chem., 198 (1952) 477-490. 3 Glowinski, J. and Iversen, L. L., Regional studies of catecholamines in the rat brain. I. The disposition of [aH]norepinephrine, [~H] dopamine and [ZH] DOPA in various regions of the brain, J. Neurochem., 13 (1966) 655-669. 4 Hillstrom, K. E., Minpaek L ,4 Study in the Modularization of a Package of Computer Algorithms for the Unconstrained Non-Linear Optimization Problem, Tech. Memo. TM-22, Argonne Nat. Lab., 1974. 5 Iwata, H., Baba, A., Matsuda, T. and Terashita, Z., Some properties of the enzyme system degrading phosphorylated thiamines in the brain and the effect of chloropromazine. In C. J. Gubler, M. Fujiwara and P. M. Dreyfus (Eds.), Thiamine, Wiley, New York, 1976, pp. 213-221 6 Nose, Y., Iwashima, A. and Nishino, H., Thiamine uptake by rat brain slices. In C. J. Gubler, M. Fujiwara and P. M. Dreyfus (Eds.), Thiamine, Wiley, New York, 1976, pp. 157-168. 7 Penttinen, H. K., Determination of thiamine and its phosphate esters by electrophoresis and fluorometry, ,4cta chem. scand. B, 32 (1978) 609-612. 8 Pincus, J. H. and Grove, J., Distribution of thiamine phosphate esters in normal and thiaminedeficient brain, Exp. NeuroL, 28 (1970) 477483. 9 Rescigno, A. and Beck, J. S., Compartments. In R. Rosen (Ed.), Foundations of Mathematical Biology, Vol. 2, Academic Press, New York, 1972, pp. 255-322. 10 Rindi, G. and de Giuseppe, L., A new chromatographic method for the determination of thiamine and its mono-, di- and tri-phosphates in animal tissues, Biochem. J., 78 (1961) 602-606. 11 Rindi, G., Patrini, C., Comincioli, V. and Reggiani, C., Thiamine content and turnover rates of some rat nervous regions, using labeled thiamine as a tracer, Brain Research, 181 (1980) 369-380. 12 Shampine, L. F. and Gordon, M. K., Computer Solution of Ordinary Differential Equations. The Initial Value Problem, W. H. Freeman, San Francisco, Calif., 1975. 13 Sharma, S. K. and Quastel, J. H., Transport and metabolism of thiamine in rat brain cortex in vitro, Biochem. J., 94 (1965) 790--800. 14 Spector, R., Thiamine transport in the central nervous system, ,4met. J. Physiol., 230 (1976) 1101-1107.