- Email: [email protected]
Digital simulation of the glucose metabolism of Avena coleoptiles
Laboratorium voor Plantenbiochemie, Carnoy-instituut, Leuven, Belgium
Digital Simulation of the Glucose Metabolism of Avena Coleoptiles A.
J. VAN LAERE
With 2 figures Received July 16, 19'73
Summary With the results of a previous paper on the glucose metabolism of Avena coleoptiles a model was worked out with which quantitative aspects of the glucose metabolism have been simulated. The agreement and discrepancies of simulated and experimental incubation in glucose14C, followed by a chase period, are discussed.
Introduction
The behaviour of a system, representing a complicated network, is impossible to predict without time consuming calculation. So the use of a computer and simulation techniques are needed to verify whether the parameters calculated from an experiment yield the original results in a model system. Simulation indeed allows the comparison of different quantitative data in a complex system. The balancing of data can be done in a dynamic system and be compared with kinetic data; this, imposes harder criteria to different parameters than the fit with single values. The results of simulation never yield unique results but sometin1es allow to reject some possibilities. The formulation of a model on itself pinpoints much better the missing information and can be very suggestive for furter experiments while the results of simulations show much better the interrelationship between different components of the system and allow a better planning of experiments. We present here some preliminary results concerning the simulation of the glucose metabolism of Avena coleoptiles. Up to now we only attempted to simulate the flux of glucose carbon without including any control points. The model presented includes many simplifications of which some at least might be the object of further research. Materials and Methods The experimental data of the glucose metabolism in Avena coleoptiles have been presented in a previous paper (VAN LAERE and CARLIER, 1974). The program was written in CSMP
z.
Pjlanzenphysiol. Bd. 71. S. 175-180. 1974.
176
A. ].
VAN LAERE
(Continuous System Modeling Program)1). The convenient input and output of CSMP allows a combination of the handling facilities of an analog computer with the larger possibilities of a digital computer. The program was run on a IBM 370/155 computer. The integration procedure was trapezoidal with time steps of 0.0025 hour. The program needed 142 K.
Formulation of the model The drawing of the model includes many simplifications and/or assumptions e.g. related metabolites, present in very small amounts, are lumped. - oxidation of fats, amino acids, organic acids and the synthesis of nucleic acids and proteins is neglected. - the organic acids and amino acids found are all supposed to be derived from the Krebs cycle and none from the PP pathway. - cell wall synthesis is considered to be irreversible. - the turnover rate (mass. time-1) is assumed to be constant during the periods concerned. - the exchange of radioactivity within the glucose molecule is accounted for by a parameter and the mechanism is not included in the model. Applying those simplifications to the known metabolic network results in the left part of fig. 1. The values of the turnover rates in glycolysis and PP Pathway are from the last three hours (nearly the mean of the three) of table 9 in our previous paper (VAN LAERE and CARLIER, 1974) or could be computed from them taking into account the metabolic pathways and the percentage incorporation of radioactivity in fats, CO 2 , amino acids and organic acids. Knowing the relative amount of phosphate esters (TREwAvAs et aI., 1967) and the amount of G-6-P and UDPG to be about 25 nanomoles per 20 segments the amount of intermediates was set to integer values. The organic acids were split in two compartments; since the radioactivity in these fractions does not decrease much during a chase experiment the amount of mitochondrialacids was kept rather small (20 nanomoles). For the same reason the amount of cytoplasmic glucose must be small. A simulation of 50 nanomoles in this compartment results in a small decrease of radioactivity in the glucose fraction at the beginning of a chase experiment. This was never found experimentally so that value (50/ 12000 = 0.4 %) would be a maximal one. The metabolism of sucrose, glucose and fructose has been discussed in our previous paper. We simulated synthesis of sucrose by sucrosephosphate synthetase, followed by transport to the vacuole. Most authors (vid. HASSID, 1967) indeed claim that sucrose synthesis proceeds by sucrose phosphate synthetase and the symmetrical labelling of sucrose upon incubation in glucose-HC (vid. our previous paper) indeed pleads for this pathway. Whether sucrose phosphate is hydrolysed to sucrose before, during 1) IBM application program: System/360 Continuous System Modeling Program (360ACX-16X) Users Manual.
z.
Pjlanzenphysiol. Bd. 71. S. 175-180. 1974.
Digital Simulation of the Glucose Metabolism of Avena Coleoptiles or after transport to the vacuole as sucrose is only hydrolysed in ably the case since the increase is about half of the disappeared
177
has no bearing on the results by this model as long the vacuole to glucose and fructose. This is probof radioactivity in glucose during a chase period radioactivity in sucrose. The other half of the dis-
Fig. 1: Model of the glucose metabolism of Avena coleoptile segments. The squares stand for metabolites or groups of related metabolites. The figures within the squares are quantities of intermediates in nanomoles glucose equivalents per 20 segments. Figures between the squares are turnover rates in nanomoles glucose equivalents per hour and per 20 segments. Abbreviations are: (GE) external glucose; (GC) cytoplasmic glucose; (HP) hexose phosphates; (UDH) nucleoside diphosphate hexoses; (CWH) cell wall hexoses; (UDU) nucleoside diphosphate uronic acids; (CWU) cell wall uronic acids; (UDP) nucleoside diphosphate pentoses; (CWP) cell wall pentoses; (GP) gluconic acid phosphate; (PP) heptose, pentose and tetrose phosphates from the PP pathway; (TP) three carbon intermediates of glycolysis and PP pathway; (AC) acetate; (OAM) mitochondrial organic acids; (OAC) extramitochondrial organic acids; (AA) amino acids; (SPG) glucose part of sucrose phosphate; (SPF) fructose part of sucrose phosphate; (SVG) glucose moiety of vacuolar sucrose; (SVF) fructose moiety of vacuolar sucrose; (GV) vacuolar glucose; (FV) vacuolar fructose; (FC) cytoplasmic fructose.
z.
Pflanzenphysiol. Bd. 71. S. 175-180. 1974.
178
A.
J.
VAN LAERE
appeared radioactivity in sucrose would go to fructose, that however would be reutilised in metabolism. The amounts of glucose, fructose and sucrose were set to 12000, 6000 and 1600 nanomoles/20 segments, as this is the mean of several experiments. For reasons discussed above glucose must be nearly entirely vacuolar and we accepted a similar situation for sucrose and fructose in our model. The greater radioactivity in glucose compared to fructose, both originating from symmetrically labelled sucrose, could not be accounted for by reutilisation of fructose alone. Therefore we accepted an extra exchange-diffusion mechanism between vacuolar and cytoplasmic glucose. Since there is no measurable increase in glucose quantity we simulated a further leaching of vacuolar glucose, equal to the amount formed by sucrose hydrolysis. The turnover rate of sugars could roughly be estimated from their increases in radioactivity. The final choice of parameters was a result of several simulation runs with different constants. The finally accepted model is given in fig. 1. This model can be formulated to simulate incubation in differently labelled glucose by use of three constants. In those constants we included a label exchange within the glucose molecule of 20 >0/ 0 as this is about the mean of previously described values (CARLIER and VAN ASSCHE, 1968; VAN LAERE and CARLIER, 1974). The values of the factors A (gluconate decarboxylation), B (glucuronate decarboxylation) and C (pyruvate decarboxylation) are given in table 1. Table 1: Values of the factors for decarboxylation of gluconate (A), glucuronate (B) and pyruvate (C) when simulating incubation in differently labelled glucose.
glucose-l-14 C glucose-2 _14C glucose-6- 14 C glucose-U _14 C
A
B
C
0.8 O. 0.2 1/6
0.2 O. 0.8 1/6
O. O. 1/3
o.
Results The comparison of an experimental and simulated incubation in glucose-1- 14 C, -2-14 C and -6- 14 C is given in table 2. The results of simulation and experiment are indeed very similar. The most obvious differences are: a 5-10 % higher cell wall radioactivity in the simulated incubation probably due to a somewhat faster saturation; a slightly lower radioactivity in triose phosphate derivatives (fats, amino acids, organic acids) from glucose-1- 14 C compared to glucose-6- 14 C than experimentally found. Some possible reasons are a small underestimation of the PP pathway, a nonequilibrium between triose phosphates, or the absence of recycling of PP pathway fructose-6- P.
Z. Pflanzenphysiol. Bd. 71. S. 175-180. 1974.
Digital Simulation of the Glucose Metabolism of Avena Coleoptiles
179
Table 2: Radioactivity in different fractions as found after 4 hours simulated (S) and experimental (E) incubation. glucose-l- 14 C
Cell wall hexoses - pentoses - uronic acids CO 2 Fats Amino acids Acids -0
glucose-2- 14 C
glucose-6-14 C
S
E
S
E
S
36,595 21,956 10,419 4,221 16,492 5,414 5,925 3,311
34,421
40,396 22,626 13,421 4,349
37,246
29,435 22,454 2,664 4,316 21,269 5,965 6,527 3,649
20,223:~)
10,224 3,974~:-)
20,223~~)
13,049 3,974::-)
16,545 5,264 5,770 2,735
E 26,676 20,223::") 2,479 3,974 21,770 6,032 6,856 3,404
::-) These values are the mean of glucose-l- 14 C, -2- 14 C and -6-14 C.
As can be seen from the radioactivity in cell wall hexoses the simulated recycling has only a very minor influence on the SA. of glucose-6-P as the % PP pathway is very small.
E C' CI>
en
incubation -
0 N
"
«
......!.~- chase ~ I
40
0
E
a. u c
~ >
~
20
IU 0
"C IU
ex:
Time in hours
Fig. 2: Radioactivity of different fractions in function of time as result of a simulation run with glucose-U- 14 C in the model of fig. 1. glucose ( ) cell wall (_._._) CO 2 ( - - - ) fructose (- - - - - -)
sucrose (_ .. _ .. _) amino acids (X-X-X) fats (_._._) organic acids (- - -)
z.
Pflanzenphysiol. Bd. 71. S. 175-180. 1974.
180
A. ]. VAN LAERE
Although most constants were derived from experiments with glucose-1-, -2- and -6- 14 C we find a good agreement between experimental and simulated incubation and chase experiments with glucose-V- 14 C. (Compare fig. 2 with fig. 2 and fig. 3 from VAN LAERE and CARLIER, 1974.) The most obvious differences are a lower radioactivity in sucrose in the experimental situation, due to a smaller quantity of sucrose in that experiment. The amount of sugars indeed shows rather great variations between different experiments. Simulation gives a faster saturation, especially of 14C02 _ Some possible explanations are slow-down of saturation by diffusion during experiments. - diminishing glucose utilisation (cfr. table 9 in our previous paper) causing a lasting increase when uptake stays constant; simulation on the contrary was done with constant turnover rates. the experimental 14C02 -production could be somewhat retarded by CO 2 pools in the tissue. Concerning the chase period some discrepancies are: - radioactivity in cell wall material increases during simulated chase. This is probably due to the constant turnover rates simulated while we found experimentally a decrease in cell wall synthesis. - 14C02-release is decreasing faster than experimentally, possibly due to CO 2 pools. - the radioactivity in amino acids increases further during simulated chase as no oxidation or any utilisation of amino acids was simulated. - the course of radioactivity in fructose is not wholy comparable. Conclusion
Even with the mentioned simplifications in the model, and although there are some discrepancies between the results of simulation and those of the experiments, both agree fairly well. Although it cannot be claimed that this model is unique it gives a good summary of our present knowledge about the quantitative aspects of glucose metabolism. By including some minor modifications it offers the possibility to test alternative mechanisms or hypotheses. Although up to now no control points have been included the model can further be improved to test the importance of possible regulatory points in metabolism. References CARLIER, A., and J. VAN ASSCHE: Z. Pflanzenphysiol. 59, 353 (1968). HASSID, W. Z.: Ann. Rev. Plant Physiol. 18, 253 (1967). TREWAVAS, A. J., I. R. JOHNSTON and E. M. CROOK: Biochim. Biophys. Acta 136, 301 (1967). VAN LAERE, A. J., and A. R. CARLIER: Z. pflanzenphysiol. 71, 163 (1974). Dr. A. VAN LAERE, Laboratorium voor Plantenbiochemie, Carnoy instituut, Vaartstraat, 24, B-3000 Leuven, Belgium.
z.
Pjlanzenphysiol. Ed. 71. S. 175-180. 1974.
Digital Simulation of the Glucose Metabolism of Avena Coleoptiles A.
J. VAN LAERE
With 2 figures Received July 16, 19'73
Summary With the results of a previous paper on the glucose metabolism of Avena coleoptiles a model was worked out with which quantitative aspects of the glucose metabolism have been simulated. The agreement and discrepancies of simulated and experimental incubation in glucose14C, followed by a chase period, are discussed.
Introduction
The behaviour of a system, representing a complicated network, is impossible to predict without time consuming calculation. So the use of a computer and simulation techniques are needed to verify whether the parameters calculated from an experiment yield the original results in a model system. Simulation indeed allows the comparison of different quantitative data in a complex system. The balancing of data can be done in a dynamic system and be compared with kinetic data; this, imposes harder criteria to different parameters than the fit with single values. The results of simulation never yield unique results but sometin1es allow to reject some possibilities. The formulation of a model on itself pinpoints much better the missing information and can be very suggestive for furter experiments while the results of simulations show much better the interrelationship between different components of the system and allow a better planning of experiments. We present here some preliminary results concerning the simulation of the glucose metabolism of Avena coleoptiles. Up to now we only attempted to simulate the flux of glucose carbon without including any control points. The model presented includes many simplifications of which some at least might be the object of further research. Materials and Methods The experimental data of the glucose metabolism in Avena coleoptiles have been presented in a previous paper (VAN LAERE and CARLIER, 1974). The program was written in CSMP
z.
Pjlanzenphysiol. Bd. 71. S. 175-180. 1974.
176
A. ].
VAN LAERE
(Continuous System Modeling Program)1). The convenient input and output of CSMP allows a combination of the handling facilities of an analog computer with the larger possibilities of a digital computer. The program was run on a IBM 370/155 computer. The integration procedure was trapezoidal with time steps of 0.0025 hour. The program needed 142 K.
Formulation of the model The drawing of the model includes many simplifications and/or assumptions e.g. related metabolites, present in very small amounts, are lumped. - oxidation of fats, amino acids, organic acids and the synthesis of nucleic acids and proteins is neglected. - the organic acids and amino acids found are all supposed to be derived from the Krebs cycle and none from the PP pathway. - cell wall synthesis is considered to be irreversible. - the turnover rate (mass. time-1) is assumed to be constant during the periods concerned. - the exchange of radioactivity within the glucose molecule is accounted for by a parameter and the mechanism is not included in the model. Applying those simplifications to the known metabolic network results in the left part of fig. 1. The values of the turnover rates in glycolysis and PP Pathway are from the last three hours (nearly the mean of the three) of table 9 in our previous paper (VAN LAERE and CARLIER, 1974) or could be computed from them taking into account the metabolic pathways and the percentage incorporation of radioactivity in fats, CO 2 , amino acids and organic acids. Knowing the relative amount of phosphate esters (TREwAvAs et aI., 1967) and the amount of G-6-P and UDPG to be about 25 nanomoles per 20 segments the amount of intermediates was set to integer values. The organic acids were split in two compartments; since the radioactivity in these fractions does not decrease much during a chase experiment the amount of mitochondrialacids was kept rather small (20 nanomoles). For the same reason the amount of cytoplasmic glucose must be small. A simulation of 50 nanomoles in this compartment results in a small decrease of radioactivity in the glucose fraction at the beginning of a chase experiment. This was never found experimentally so that value (50/ 12000 = 0.4 %) would be a maximal one. The metabolism of sucrose, glucose and fructose has been discussed in our previous paper. We simulated synthesis of sucrose by sucrosephosphate synthetase, followed by transport to the vacuole. Most authors (vid. HASSID, 1967) indeed claim that sucrose synthesis proceeds by sucrose phosphate synthetase and the symmetrical labelling of sucrose upon incubation in glucose-HC (vid. our previous paper) indeed pleads for this pathway. Whether sucrose phosphate is hydrolysed to sucrose before, during 1) IBM application program: System/360 Continuous System Modeling Program (360ACX-16X) Users Manual.
z.
Pjlanzenphysiol. Bd. 71. S. 175-180. 1974.
Digital Simulation of the Glucose Metabolism of Avena Coleoptiles or after transport to the vacuole as sucrose is only hydrolysed in ably the case since the increase is about half of the disappeared
177
has no bearing on the results by this model as long the vacuole to glucose and fructose. This is probof radioactivity in glucose during a chase period radioactivity in sucrose. The other half of the dis-
Fig. 1: Model of the glucose metabolism of Avena coleoptile segments. The squares stand for metabolites or groups of related metabolites. The figures within the squares are quantities of intermediates in nanomoles glucose equivalents per 20 segments. Figures between the squares are turnover rates in nanomoles glucose equivalents per hour and per 20 segments. Abbreviations are: (GE) external glucose; (GC) cytoplasmic glucose; (HP) hexose phosphates; (UDH) nucleoside diphosphate hexoses; (CWH) cell wall hexoses; (UDU) nucleoside diphosphate uronic acids; (CWU) cell wall uronic acids; (UDP) nucleoside diphosphate pentoses; (CWP) cell wall pentoses; (GP) gluconic acid phosphate; (PP) heptose, pentose and tetrose phosphates from the PP pathway; (TP) three carbon intermediates of glycolysis and PP pathway; (AC) acetate; (OAM) mitochondrial organic acids; (OAC) extramitochondrial organic acids; (AA) amino acids; (SPG) glucose part of sucrose phosphate; (SPF) fructose part of sucrose phosphate; (SVG) glucose moiety of vacuolar sucrose; (SVF) fructose moiety of vacuolar sucrose; (GV) vacuolar glucose; (FV) vacuolar fructose; (FC) cytoplasmic fructose.
z.
Pflanzenphysiol. Bd. 71. S. 175-180. 1974.
178
A.
J.
VAN LAERE
appeared radioactivity in sucrose would go to fructose, that however would be reutilised in metabolism. The amounts of glucose, fructose and sucrose were set to 12000, 6000 and 1600 nanomoles/20 segments, as this is the mean of several experiments. For reasons discussed above glucose must be nearly entirely vacuolar and we accepted a similar situation for sucrose and fructose in our model. The greater radioactivity in glucose compared to fructose, both originating from symmetrically labelled sucrose, could not be accounted for by reutilisation of fructose alone. Therefore we accepted an extra exchange-diffusion mechanism between vacuolar and cytoplasmic glucose. Since there is no measurable increase in glucose quantity we simulated a further leaching of vacuolar glucose, equal to the amount formed by sucrose hydrolysis. The turnover rate of sugars could roughly be estimated from their increases in radioactivity. The final choice of parameters was a result of several simulation runs with different constants. The finally accepted model is given in fig. 1. This model can be formulated to simulate incubation in differently labelled glucose by use of three constants. In those constants we included a label exchange within the glucose molecule of 20 >0/ 0 as this is about the mean of previously described values (CARLIER and VAN ASSCHE, 1968; VAN LAERE and CARLIER, 1974). The values of the factors A (gluconate decarboxylation), B (glucuronate decarboxylation) and C (pyruvate decarboxylation) are given in table 1. Table 1: Values of the factors for decarboxylation of gluconate (A), glucuronate (B) and pyruvate (C) when simulating incubation in differently labelled glucose.
glucose-l-14 C glucose-2 _14C glucose-6- 14 C glucose-U _14 C
A
B
C
0.8 O. 0.2 1/6
0.2 O. 0.8 1/6
O. O. 1/3
o.
Results The comparison of an experimental and simulated incubation in glucose-1- 14 C, -2-14 C and -6- 14 C is given in table 2. The results of simulation and experiment are indeed very similar. The most obvious differences are: a 5-10 % higher cell wall radioactivity in the simulated incubation probably due to a somewhat faster saturation; a slightly lower radioactivity in triose phosphate derivatives (fats, amino acids, organic acids) from glucose-1- 14 C compared to glucose-6- 14 C than experimentally found. Some possible reasons are a small underestimation of the PP pathway, a nonequilibrium between triose phosphates, or the absence of recycling of PP pathway fructose-6- P.
Z. Pflanzenphysiol. Bd. 71. S. 175-180. 1974.
Digital Simulation of the Glucose Metabolism of Avena Coleoptiles
179
Table 2: Radioactivity in different fractions as found after 4 hours simulated (S) and experimental (E) incubation. glucose-l- 14 C
Cell wall hexoses - pentoses - uronic acids CO 2 Fats Amino acids Acids -0
glucose-2- 14 C
glucose-6-14 C
S
E
S
E
S
36,595 21,956 10,419 4,221 16,492 5,414 5,925 3,311
34,421
40,396 22,626 13,421 4,349
37,246
29,435 22,454 2,664 4,316 21,269 5,965 6,527 3,649
20,223:~)
10,224 3,974~:-)
20,223~~)
13,049 3,974::-)
16,545 5,264 5,770 2,735
E 26,676 20,223::") 2,479 3,974 21,770 6,032 6,856 3,404
::-) These values are the mean of glucose-l- 14 C, -2- 14 C and -6-14 C.
As can be seen from the radioactivity in cell wall hexoses the simulated recycling has only a very minor influence on the SA. of glucose-6-P as the % PP pathway is very small.
E C' CI>
en
incubation -
0 N
"
«
......!.~- chase ~ I
40
0
E
a. u c
~ >
~
20
IU 0
"C IU
ex:
Time in hours
Fig. 2: Radioactivity of different fractions in function of time as result of a simulation run with glucose-U- 14 C in the model of fig. 1. glucose ( ) cell wall (_._._) CO 2 ( - - - ) fructose (- - - - - -)
sucrose (_ .. _ .. _) amino acids (X-X-X) fats (_._._) organic acids (- - -)
z.
Pflanzenphysiol. Bd. 71. S. 175-180. 1974.
180
A. ]. VAN LAERE
Although most constants were derived from experiments with glucose-1-, -2- and -6- 14 C we find a good agreement between experimental and simulated incubation and chase experiments with glucose-V- 14 C. (Compare fig. 2 with fig. 2 and fig. 3 from VAN LAERE and CARLIER, 1974.) The most obvious differences are a lower radioactivity in sucrose in the experimental situation, due to a smaller quantity of sucrose in that experiment. The amount of sugars indeed shows rather great variations between different experiments. Simulation gives a faster saturation, especially of 14C02 _ Some possible explanations are slow-down of saturation by diffusion during experiments. - diminishing glucose utilisation (cfr. table 9 in our previous paper) causing a lasting increase when uptake stays constant; simulation on the contrary was done with constant turnover rates. the experimental 14C02 -production could be somewhat retarded by CO 2 pools in the tissue. Concerning the chase period some discrepancies are: - radioactivity in cell wall material increases during simulated chase. This is probably due to the constant turnover rates simulated while we found experimentally a decrease in cell wall synthesis. - 14C02-release is decreasing faster than experimentally, possibly due to CO 2 pools. - the radioactivity in amino acids increases further during simulated chase as no oxidation or any utilisation of amino acids was simulated. - the course of radioactivity in fructose is not wholy comparable. Conclusion
Even with the mentioned simplifications in the model, and although there are some discrepancies between the results of simulation and those of the experiments, both agree fairly well. Although it cannot be claimed that this model is unique it gives a good summary of our present knowledge about the quantitative aspects of glucose metabolism. By including some minor modifications it offers the possibility to test alternative mechanisms or hypotheses. Although up to now no control points have been included the model can further be improved to test the importance of possible regulatory points in metabolism. References CARLIER, A., and J. VAN ASSCHE: Z. Pflanzenphysiol. 59, 353 (1968). HASSID, W. Z.: Ann. Rev. Plant Physiol. 18, 253 (1967). TREWAVAS, A. J., I. R. JOHNSTON and E. M. CROOK: Biochim. Biophys. Acta 136, 301 (1967). VAN LAERE, A. J., and A. R. CARLIER: Z. pflanzenphysiol. 71, 163 (1974). Dr. A. VAN LAERE, Laboratorium voor Plantenbiochemie, Carnoy instituut, Vaartstraat, 24, B-3000 Leuven, Belgium.
z.
Pjlanzenphysiol. Ed. 71. S. 175-180. 1974.