Molecular and Cellular Biochemistry 98: 149-159, 1990. © 1990 Kluwer Academic Publishers. Printed in the Netherlands.
Role of fatty acid-binding protein in cardiac fatty acid oxidation N.C. Fournier and M.A. Richard Nestld Research Centre, Nestec Ltd, B.P. 353, CH-1800 Vevey, Switzerland
Key words: FABP, fatty acid, cardiac energy Summary Although abundant in most biological tissues and chemically well characterized, the fatty acid-binding protein (FABP) was until recently in search of a function. Because of its strong affinity for long chain fatty acids and its cytoplasmic origin, this protein was repeatedly claimed in the literature to be the transcytoplasmic fatty acid carrier. However, techniques to visualize and quantify the movements of molecules in the cytoplasm are still in their infancy. Consequently the carrier function of FABP remains somewhat speculative. However, FABP binds not only fatty acids but also their CoA and carnitine derivatives, two typical molecules of mitochondrial origin. Moreover, it has been demonstrated and confirmed that FABP is not exclusively cytoplasmic, but also mitochondrial. A function for FABP in the mitochondrial metabolism of fatty acids plus CoA and carnitine derivatives would therefore be anticpated. Using spin-labelling techniques, we present here evidence that FABP is a powerful regulator of acylcarnitine flux entering the mitochondrial [3-oxidative system. In this perspective FABP appears to be an active link between the cytoplasm and the mitochondria, regulating the energy made available to the cell. This active participation of FABP is shown to be the consequence of its gradient-like distribution in the cardiac cell, and also of the coexistence of multispecies of this protein produced by self-aggregation.
Introduction Long-chain fatty acids, which are catabolized by the mitochondrial [3-oxidative system, are considered as the major fuel of energy production in the heart [1-4]. The accepted general consensus states that acylchains are translocated from the cytoplasm into the mitochondria, then B-oxidized in the mitochondrial matrix, yielding acetyl-CoA to the Krebs cycle and NADHz plus FADH2 to the respiratory chain and finally ATP by oxidative phosphorylation. A few years ago, a major point was brought up [5-7]: what mechanisms regulate the energy output of this fatty acid-dependent system, so as to match the frequent boosts of energy required by the heart? Studies with the isolated perfused rat heart, sup-
plemented with palmitate, have shown [5] that, when the energy requirement was low (low ventricular pressure, 60 mmHg, and thus low rate of oxidative phosphorylation) palmitate-derived acetyl CoA accumulated, as if its entrance into the Krebs cycle was the limiting step of energy production. However, when the cardiac energy requirement was high (high ventricular pressure, 120mmHg, and thus high rate of oxidative phosphorylation) the accumulating species was acylcarnitine, suggesting that the translocation of acylcarnitine through the mitochondrial membranes is the limiting step of cardiac energy production [5]. The mechanisms behind this acylcarnitine-dependent energy regulation have not yet been investigated. Any explicative model should take into account the possible participation of the following four elements which are linked to the acylcarnitine
150 and the resulting control exerted by FABP on the acylcarnitine translocation into the mitochondria, might be the central element behind this acylcarnitine-dependent energy production in the cardiac muscle.
Experimentalprocedures FABP purification, measurement and localization; mitochondria isolation; [3-oxidation rate measurements; fatty acid, CoA and carnitine derivative quantitation; electron spin resonance (ESR) and computer procedures; 16-doxylstearoyl carnitine synthesis, as described in references [8-9]. Mathematical background and determination of parameters required for the modelling are described in reference [10].
Synthesis of l6-doxyl Stearoyl CoA
Fig. 1. Subcellular detection of FABP in rat heart by the immunogold method. The procedure is detailed in ref. 9. MYO, myofibrils; MITOC, mitochondria.
metabolism in the mitochondria: 1. The acylcarnitine transferase I, bound to the outher surface of the inner mitochondrial membrane, and controlling the transformation of acylCoA into acylcarnitine. 2. The acylcarnitine translocase, bound to the inner mitochondrial membrane, and controlling the shuttling of acylcarnitine through the inner mitochondrial membrane. 3. The acylcarnitine transferase II, bound to the inner surface of the inner mitochondrial membrane, and controlling the transformation of acylcarnitine into acylCoA, as a preliminary step before acylCoA [5-oxidation in the mitochondrial matrix. 4. The fatty acid-binding protein (FABP), localized in all cell compartments, including mitochondria [9], and able to bind not only fatty acids and acylCoA but also acylcarnitine [8]. Evidence will be presented here, showing that FABP binding and interactions with acylcarnitine,
As a first step, coenzyme A (Boehringer) was purified by chromatography on Kieselgel60 - F254 0,25 ram-plates (Merck). The solvent was Chloroform - methanol - water (45 : 45 : 10, by vol). The major band detected under UV (254nm) was scratched, extracted with water, and finally lyophilized. Fifty/~moles 16-doxylstearic acid (Aldrich) were mixed for 60 min with 60 ~moles 1,1'-carbonydiimidazol in 2 ml tetrahydrofuran. After evaporation under N2, the sample was solubilized in 1 ml tetrahydrofuran-water (2: 1, v/v), then mixed with 55/zmoles of the purified CoA solubilized in 5 ml tetrahydrofuran-water (2 : 1, v/v). After setting the pH between 7 and 7,5 with 0,5 N NaOH, the solution was stirred overnight at room temperature, under N2, and then lyophilized. The yield was about 60 mg and was divided in two portions of 30 mg. The next step was the purification on Sep-Pack C18 Cartridge (Waters). The micro-column was washed with 2 ml methanol, then 5 ml water. The above 30 mg were solubilized in 4 ml (methanolwater, 5: 5), then applied on the column. The filtrate was recycled 10 times through the column.
151
14.72%
O0 ill
6177 % .iI
© > L.LJ >
73.91 °/o
I-,< ._J UJ rr-
2.14 2.44
% %
% of TOTAL I IIll IiI I
FATTY ACID-BINDING PROTEIN
CONC.
Fig. 2. Subcellular distribution of FABP in rat heart. The techniqaue is described in ref. 9
Finally the adsorbed compounds were eluted with 30 ml volume of the following successive solvents: (A) water; (B) methanol: water v/v, 1 : 9; (C) 2 : 8; (D) 3 : 7; (E) 4 ;6; (F) 5 : 5; (G) 6 : 4; (H) 7 : 3; (I) 8 : 2; (J) 9 : 1; (K) methanol. The B, C, D, E fractions containing partially purified acylCoA, plus residual fatty acid, were pooled and lyophilized. After solubilization in 2 ml methanol, a biphasic system was obtained by adding 5 ml hexane and shaking. This washing procedure was repeated 6 times. The final methanolic phase was evaporated and the residue solubilized in 3 ml n-butanol. Four ml water saturated with n-butanol were added. The solution was shaken and left overnight at 4° C. The butanolic upper phase was collected and mixed with 4 ml water saturated with n-butanol. After 1 h at 4° C, the sample was centrifuged 5 min at 350 g. The water containing phase was collected and contained pure 16-doxylstearoyl CoA, as confirmed by TLC (single spot), ESR (typical nitroxide radical triplet) and spectrophotometry (characteristic CoA peak between 230--300 nm.
Results
The subcellular localization of FABP was determined by using specific FABP polyclonal antibodies conjugated to small (19 mm) gold particles (Fig. 1). Most of FABP (73,9% was found on the myofibrils (Fig. 2). However, remarkably 14,7% was detected in the mitochondria (Figs 1-2). A strong FABP concentration gradient delineates the myofibrils (6.9mg. m1-1) from the mitochondria (2.2 mg. ml-1). Although named fatty acid-binding protein, FABP also binds acylCoA and acylcarnitine, two typical derivatives synthetized by the mitochondria in the cardiac muscle. This is readily shown by the electron spin resonance technique (ESR) applied to 16-doxylstearic acid, stearoyl CoA and stearoylcarnitine, interacting with FABP (Fig. 3). In the presence of FABP the ESR signal of these three compounds (Fig. 3) is enlarged and the amplitudes of the peaks decrease. This is the typical behaviour of a nitroxide-labelled molecule when its motion is restricted by binding to a macromolecule. Because of its mitochondrial localization and the capacity to bind typical acylchains normally pro-
152
40uM 16-DOXYL, 'STEA.._.RI!C.. ACIOJ
FAB_P g.I-1
J
o
f-11.4
11.4
C A R N I ~
17,1
Fig. 3. Binding of fatty acid, acylCoA and acylcarnitine to FABP. Purified FABP from rat heart, as described in ref. 9, was mixed in 50 ~1 glass capillaries with 16-doxylstearate (K salt), 16-doxylstearoylCoA or 16-doxylstearoylcarnitine, in a buffer containing 7.9x 10-3M sodium phosphate (pH7.4), 3.97 x 10-4M EDTA, 6.7 x 10-2M KC1 and 0.1M sucrose. The electron spin resonance signals were recorded at 37° C on a Varian E line spectrometer (X band) using 100-kHz field modulation.
cessed by the mitochondria, such as fatty acids, acylCoA and acylcarnitine, an important function for the mitochondrial FABP can be anticipated. To investigate this hypothesis, we isolated intact (Fig. 4) and biochemically coupled mitochondria [8] from rat heart. Using [I-14C] stearate as a precursor and F A B P as a carrier, the mitochondrial [3-oxidative output was analyzed, as a function of variable FABP concentrations (Fig. 5). The [3-oxidation profile is quite dependent upon the FABP concentration. When FABP increases, the [3-oxidation output is exponentially decreasing. How-
ever, very remarkably, a strong boost of activity is observed around 2g- 1-a (Fig. 5). We speculated [9] that such a profile could be the consequence of the self-aggregated nature of FABP. One of the FABP isoforms might be more competent than the others in controlling the [3oxidative system. In fact, the theoretical model which was partially developed elsewhere [10] and detailed later herein, predicts such a boost of activity when considering an enzymatic system where a self-aggregated protein is the carrier providing the substrate. In this model (Fig. 6), we studied the activity(R) of an enzyme bound to a membrane (M), when the substrate (S) could be supplied to the enzyme by a self-aggregated protein (P). What is the influence of the self-aggregation capacity of the protein on the final activity of the enzyme? This model was applied here to the mitochondrial ~-oxidative system when the substrate supplier was considered to be FABP, a self-aggregated protein. In an equilibrium system containing isolated mitochondria, FABP and fatty acid, the latter is expected to partition between the aqueous medium (As), the mitochondrial membranes (A~,) and bound (Ab) to FABP (Fig. 6). To find the dependence of the ~-oxidative activity R upon the self-aggregated FABP, the following set of equations is required: R-
Rmax[S]
(1)
K m + [S]
This equation assumes that the dependence of the enzyme activity R on the fatty acid substrate concentration [S] is of the Michaelis-Menten type. The following arbitrarily chosen values have been assigned: Rmax= 5.08 × 10-4M • min -1 (g of protein) -1, Km = 2.5X 10-4M. Hence: 5.08 X 10 -4 IS l
(2)
R = 2.5 x 10-4+ [S] The three following sources of [S] were considered:
153
Fig. 4. Electron microscopyof isolated mitochondriafrom rat heart. Isolationprocedure as describedin ref. 9. After fixationin 2%
glutaraldehydeand post-fixationin 1% OSO4,the pellets were embeddedin EPON. The sectionswere contrastedfor i min. with lead citrate accordingto Reynolds [11]. Enlargement 10400x. a) A s is the source o f substrate
This means that the substrate for the B-oxidative enzymes is assumed to be the fatty acid which is free in the aqueous medium, and reaches the enzymes by simple diffussion. Before substituting (S) by (As) in eq, 2, an explicit value of (As) as a function of the carrier (P) is required. The following set of equations delineate the final expression required: [As] = f[P]. [At] = [Ai.] + [Asl + [Ab]
(3)
[As] = [ A t ] - [ A ~ ] - [Ab]
(4)
Equations 3 and 4 state that the total fatty acid [At] considered, is distributed between the mitochon-
drial membrane [Ai~], free in the medium [As], and bound [Ab] to the carrier [P]. [At] was arbitrarily set equal to 1 × 10 -4 M. [As] = 10-4- lAin] - [Ab]
(5)
To define [As], explicit values of [Ain] and [Ab], as a function of [P] remain to be determined. [Ab]/[P] = v
(6)
[Ab] = v [P]
(7)
Equations 6 and 7 describe the binding isotherm v, of fatty acid to the carrier (P). v is defined by the following phenomenological equation, explicited in ref (10):
154 ~'.r -
R
5
E
¢N
o
E
4
LtJ
uJ~
I.< rr
Z
t-> I-0 60
.N 40 Z bJ
[Abs3] = v [$31
I
I
I
I
I
I
O.S
1.2
1,6
2.0
2.4
2.8
I
PROTEIN (g. Iq) Fig. 7. Computer simulationof the enzyme activity(R) in the model of Fig. 6. The substrate for the enzyme is the freely diffusing fatty acids (As), or the fatty acid (Ab) specifically bound to $3, one of the different self-aggregatedspecies of the protein.
(16)
Equation 15 characterizes the binding isotherm of fatty acid to FABP, and equation 16 the binding isotherm of fatty acid Abs3 to 53, one of the selfaggregated FABP species. To define [Abs3] as a function of [P], explicit values of v and [$3] must be found as'a function of [P] in equation 16.
1) Explicitation of v (17)
[At] = [A~n]+ [As] + [Ab] and giving the arbitrary value 1 (g- prot) -1 to [M], the activity R of the enzyme can be computer calculated as a function of F A B P concentrations, [P], when the fatty acid supplied to the [3-oxidative enzymes is diffusing from the aqueous medium. Increasing the concentration of FABP, from 0.8 to 2.8 g. 1-1, induces and exponential decrease of the enzyme activity (Fig. 7a).
From equations 7 and 10, we can write: [At] = p" [As] [M] + [As] + VmaxI
VmaxlI
]_
[P] ( 1 + KI/[As] + 1 + (KII/[As]) nlI VmaxlII
"~
1 + (KIII/[As]nlllj
(18)
As stated previously we arbitrarily attributed the following values: [At] = 1 x 10-4M; [M] = l ( g . prot) -1, and p was calculated to be equal to 3.55 l(g. prot) -1. The numerical values of parameters Vma~,Ki and ni, can be found in reference [10].
156 Finally, the explicit values of v as a function of [P], are obtained by extracting [As] from eq. 18 and then subtituting it in eq. 8.
2) Explicitation of [$3] According to our previous studies [10], explicit values of [$3] as a function of [P] are defined by:
[p] [p1.3+.2 [pp3 F = 1 + ~3-.3 + a3
. >-
80_
,7
-
-
Role of fatty acid-binding protein in cardiac fatty acid oxidation N.C. Fournier and M.A. Richard Nestld Research Centre, Nestec Ltd, B.P. 353, CH-1800 Vevey, Switzerland
Key words: FABP, fatty acid, cardiac energy Summary Although abundant in most biological tissues and chemically well characterized, the fatty acid-binding protein (FABP) was until recently in search of a function. Because of its strong affinity for long chain fatty acids and its cytoplasmic origin, this protein was repeatedly claimed in the literature to be the transcytoplasmic fatty acid carrier. However, techniques to visualize and quantify the movements of molecules in the cytoplasm are still in their infancy. Consequently the carrier function of FABP remains somewhat speculative. However, FABP binds not only fatty acids but also their CoA and carnitine derivatives, two typical molecules of mitochondrial origin. Moreover, it has been demonstrated and confirmed that FABP is not exclusively cytoplasmic, but also mitochondrial. A function for FABP in the mitochondrial metabolism of fatty acids plus CoA and carnitine derivatives would therefore be anticpated. Using spin-labelling techniques, we present here evidence that FABP is a powerful regulator of acylcarnitine flux entering the mitochondrial [3-oxidative system. In this perspective FABP appears to be an active link between the cytoplasm and the mitochondria, regulating the energy made available to the cell. This active participation of FABP is shown to be the consequence of its gradient-like distribution in the cardiac cell, and also of the coexistence of multispecies of this protein produced by self-aggregation.
Introduction Long-chain fatty acids, which are catabolized by the mitochondrial [3-oxidative system, are considered as the major fuel of energy production in the heart [1-4]. The accepted general consensus states that acylchains are translocated from the cytoplasm into the mitochondria, then B-oxidized in the mitochondrial matrix, yielding acetyl-CoA to the Krebs cycle and NADHz plus FADH2 to the respiratory chain and finally ATP by oxidative phosphorylation. A few years ago, a major point was brought up [5-7]: what mechanisms regulate the energy output of this fatty acid-dependent system, so as to match the frequent boosts of energy required by the heart? Studies with the isolated perfused rat heart, sup-
plemented with palmitate, have shown [5] that, when the energy requirement was low (low ventricular pressure, 60 mmHg, and thus low rate of oxidative phosphorylation) palmitate-derived acetyl CoA accumulated, as if its entrance into the Krebs cycle was the limiting step of energy production. However, when the cardiac energy requirement was high (high ventricular pressure, 120mmHg, and thus high rate of oxidative phosphorylation) the accumulating species was acylcarnitine, suggesting that the translocation of acylcarnitine through the mitochondrial membranes is the limiting step of cardiac energy production [5]. The mechanisms behind this acylcarnitine-dependent energy regulation have not yet been investigated. Any explicative model should take into account the possible participation of the following four elements which are linked to the acylcarnitine
150 and the resulting control exerted by FABP on the acylcarnitine translocation into the mitochondria, might be the central element behind this acylcarnitine-dependent energy production in the cardiac muscle.
Experimentalprocedures FABP purification, measurement and localization; mitochondria isolation; [3-oxidation rate measurements; fatty acid, CoA and carnitine derivative quantitation; electron spin resonance (ESR) and computer procedures; 16-doxylstearoyl carnitine synthesis, as described in references [8-9]. Mathematical background and determination of parameters required for the modelling are described in reference [10].
Synthesis of l6-doxyl Stearoyl CoA
Fig. 1. Subcellular detection of FABP in rat heart by the immunogold method. The procedure is detailed in ref. 9. MYO, myofibrils; MITOC, mitochondria.
metabolism in the mitochondria: 1. The acylcarnitine transferase I, bound to the outher surface of the inner mitochondrial membrane, and controlling the transformation of acylCoA into acylcarnitine. 2. The acylcarnitine translocase, bound to the inner mitochondrial membrane, and controlling the shuttling of acylcarnitine through the inner mitochondrial membrane. 3. The acylcarnitine transferase II, bound to the inner surface of the inner mitochondrial membrane, and controlling the transformation of acylcarnitine into acylCoA, as a preliminary step before acylCoA [5-oxidation in the mitochondrial matrix. 4. The fatty acid-binding protein (FABP), localized in all cell compartments, including mitochondria [9], and able to bind not only fatty acids and acylCoA but also acylcarnitine [8]. Evidence will be presented here, showing that FABP binding and interactions with acylcarnitine,
As a first step, coenzyme A (Boehringer) was purified by chromatography on Kieselgel60 - F254 0,25 ram-plates (Merck). The solvent was Chloroform - methanol - water (45 : 45 : 10, by vol). The major band detected under UV (254nm) was scratched, extracted with water, and finally lyophilized. Fifty/~moles 16-doxylstearic acid (Aldrich) were mixed for 60 min with 60 ~moles 1,1'-carbonydiimidazol in 2 ml tetrahydrofuran. After evaporation under N2, the sample was solubilized in 1 ml tetrahydrofuran-water (2: 1, v/v), then mixed with 55/zmoles of the purified CoA solubilized in 5 ml tetrahydrofuran-water (2 : 1, v/v). After setting the pH between 7 and 7,5 with 0,5 N NaOH, the solution was stirred overnight at room temperature, under N2, and then lyophilized. The yield was about 60 mg and was divided in two portions of 30 mg. The next step was the purification on Sep-Pack C18 Cartridge (Waters). The micro-column was washed with 2 ml methanol, then 5 ml water. The above 30 mg were solubilized in 4 ml (methanolwater, 5: 5), then applied on the column. The filtrate was recycled 10 times through the column.
151
14.72%
O0 ill
6177 % .iI
© > L.LJ >
73.91 °/o
I-,< ._J UJ rr-
2.14 2.44
% %
% of TOTAL I IIll IiI I
FATTY ACID-BINDING PROTEIN
CONC.
Fig. 2. Subcellular distribution of FABP in rat heart. The techniqaue is described in ref. 9
Finally the adsorbed compounds were eluted with 30 ml volume of the following successive solvents: (A) water; (B) methanol: water v/v, 1 : 9; (C) 2 : 8; (D) 3 : 7; (E) 4 ;6; (F) 5 : 5; (G) 6 : 4; (H) 7 : 3; (I) 8 : 2; (J) 9 : 1; (K) methanol. The B, C, D, E fractions containing partially purified acylCoA, plus residual fatty acid, were pooled and lyophilized. After solubilization in 2 ml methanol, a biphasic system was obtained by adding 5 ml hexane and shaking. This washing procedure was repeated 6 times. The final methanolic phase was evaporated and the residue solubilized in 3 ml n-butanol. Four ml water saturated with n-butanol were added. The solution was shaken and left overnight at 4° C. The butanolic upper phase was collected and mixed with 4 ml water saturated with n-butanol. After 1 h at 4° C, the sample was centrifuged 5 min at 350 g. The water containing phase was collected and contained pure 16-doxylstearoyl CoA, as confirmed by TLC (single spot), ESR (typical nitroxide radical triplet) and spectrophotometry (characteristic CoA peak between 230--300 nm.
Results
The subcellular localization of FABP was determined by using specific FABP polyclonal antibodies conjugated to small (19 mm) gold particles (Fig. 1). Most of FABP (73,9% was found on the myofibrils (Fig. 2). However, remarkably 14,7% was detected in the mitochondria (Figs 1-2). A strong FABP concentration gradient delineates the myofibrils (6.9mg. m1-1) from the mitochondria (2.2 mg. ml-1). Although named fatty acid-binding protein, FABP also binds acylCoA and acylcarnitine, two typical derivatives synthetized by the mitochondria in the cardiac muscle. This is readily shown by the electron spin resonance technique (ESR) applied to 16-doxylstearic acid, stearoyl CoA and stearoylcarnitine, interacting with FABP (Fig. 3). In the presence of FABP the ESR signal of these three compounds (Fig. 3) is enlarged and the amplitudes of the peaks decrease. This is the typical behaviour of a nitroxide-labelled molecule when its motion is restricted by binding to a macromolecule. Because of its mitochondrial localization and the capacity to bind typical acylchains normally pro-
152
40uM 16-DOXYL, 'STEA.._.RI!C.. ACIOJ
FAB_P g.I-1
J
o
f-11.4
11.4
C A R N I ~
17,1
Fig. 3. Binding of fatty acid, acylCoA and acylcarnitine to FABP. Purified FABP from rat heart, as described in ref. 9, was mixed in 50 ~1 glass capillaries with 16-doxylstearate (K salt), 16-doxylstearoylCoA or 16-doxylstearoylcarnitine, in a buffer containing 7.9x 10-3M sodium phosphate (pH7.4), 3.97 x 10-4M EDTA, 6.7 x 10-2M KC1 and 0.1M sucrose. The electron spin resonance signals were recorded at 37° C on a Varian E line spectrometer (X band) using 100-kHz field modulation.
cessed by the mitochondria, such as fatty acids, acylCoA and acylcarnitine, an important function for the mitochondrial FABP can be anticipated. To investigate this hypothesis, we isolated intact (Fig. 4) and biochemically coupled mitochondria [8] from rat heart. Using [I-14C] stearate as a precursor and F A B P as a carrier, the mitochondrial [3-oxidative output was analyzed, as a function of variable FABP concentrations (Fig. 5). The [3-oxidation profile is quite dependent upon the FABP concentration. When FABP increases, the [3-oxidation output is exponentially decreasing. How-
ever, very remarkably, a strong boost of activity is observed around 2g- 1-a (Fig. 5). We speculated [9] that such a profile could be the consequence of the self-aggregated nature of FABP. One of the FABP isoforms might be more competent than the others in controlling the [3oxidative system. In fact, the theoretical model which was partially developed elsewhere [10] and detailed later herein, predicts such a boost of activity when considering an enzymatic system where a self-aggregated protein is the carrier providing the substrate. In this model (Fig. 6), we studied the activity(R) of an enzyme bound to a membrane (M), when the substrate (S) could be supplied to the enzyme by a self-aggregated protein (P). What is the influence of the self-aggregation capacity of the protein on the final activity of the enzyme? This model was applied here to the mitochondrial ~-oxidative system when the substrate supplier was considered to be FABP, a self-aggregated protein. In an equilibrium system containing isolated mitochondria, FABP and fatty acid, the latter is expected to partition between the aqueous medium (As), the mitochondrial membranes (A~,) and bound (Ab) to FABP (Fig. 6). To find the dependence of the ~-oxidative activity R upon the self-aggregated FABP, the following set of equations is required: R-
Rmax[S]
(1)
K m + [S]
This equation assumes that the dependence of the enzyme activity R on the fatty acid substrate concentration [S] is of the Michaelis-Menten type. The following arbitrarily chosen values have been assigned: Rmax= 5.08 × 10-4M • min -1 (g of protein) -1, Km = 2.5X 10-4M. Hence: 5.08 X 10 -4 IS l
(2)
R = 2.5 x 10-4+ [S] The three following sources of [S] were considered:
153
Fig. 4. Electron microscopyof isolated mitochondriafrom rat heart. Isolationprocedure as describedin ref. 9. After fixationin 2%
glutaraldehydeand post-fixationin 1% OSO4,the pellets were embeddedin EPON. The sectionswere contrastedfor i min. with lead citrate accordingto Reynolds [11]. Enlargement 10400x. a) A s is the source o f substrate
This means that the substrate for the B-oxidative enzymes is assumed to be the fatty acid which is free in the aqueous medium, and reaches the enzymes by simple diffussion. Before substituting (S) by (As) in eq, 2, an explicit value of (As) as a function of the carrier (P) is required. The following set of equations delineate the final expression required: [As] = f[P]. [At] = [Ai.] + [Asl + [Ab]
(3)
[As] = [ A t ] - [ A ~ ] - [Ab]
(4)
Equations 3 and 4 state that the total fatty acid [At] considered, is distributed between the mitochon-
drial membrane [Ai~], free in the medium [As], and bound [Ab] to the carrier [P]. [At] was arbitrarily set equal to 1 × 10 -4 M. [As] = 10-4- lAin] - [Ab]
(5)
To define [As], explicit values of [Ain] and [Ab], as a function of [P] remain to be determined. [Ab]/[P] = v
(6)
[Ab] = v [P]
(7)
Equations 6 and 7 describe the binding isotherm v, of fatty acid to the carrier (P). v is defined by the following phenomenological equation, explicited in ref (10):
154 ~'.r -
R
5
E
¢N
o
E
4
LtJ
uJ~
I.< rr
Z
t-> I-0 60
.N 40 Z bJ
[Abs3] = v [$31
I
I
I
I
I
I
O.S
1.2
1,6
2.0
2.4
2.8
I
PROTEIN (g. Iq) Fig. 7. Computer simulationof the enzyme activity(R) in the model of Fig. 6. The substrate for the enzyme is the freely diffusing fatty acids (As), or the fatty acid (Ab) specifically bound to $3, one of the different self-aggregatedspecies of the protein.
(16)
Equation 15 characterizes the binding isotherm of fatty acid to FABP, and equation 16 the binding isotherm of fatty acid Abs3 to 53, one of the selfaggregated FABP species. To define [Abs3] as a function of [P], explicit values of v and [$3] must be found as'a function of [P] in equation 16.
1) Explicitation of v (17)
[At] = [A~n]+ [As] + [Ab] and giving the arbitrary value 1 (g- prot) -1 to [M], the activity R of the enzyme can be computer calculated as a function of F A B P concentrations, [P], when the fatty acid supplied to the [3-oxidative enzymes is diffusing from the aqueous medium. Increasing the concentration of FABP, from 0.8 to 2.8 g. 1-1, induces and exponential decrease of the enzyme activity (Fig. 7a).
From equations 7 and 10, we can write: [At] = p" [As] [M] + [As] + VmaxI
VmaxlI
]_
[P] ( 1 + KI/[As] + 1 + (KII/[As]) nlI VmaxlII
"~
1 + (KIII/[As]nlllj
(18)
As stated previously we arbitrarily attributed the following values: [At] = 1 x 10-4M; [M] = l ( g . prot) -1, and p was calculated to be equal to 3.55 l(g. prot) -1. The numerical values of parameters Vma~,Ki and ni, can be found in reference [10].
156 Finally, the explicit values of v as a function of [P], are obtained by extracting [As] from eq. 18 and then subtituting it in eq. 8.
2) Explicitation of [$3] According to our previous studies [10], explicit values of [$3] as a function of [P] are defined by:
[p] [p1.3+.2 [pp3 F = 1 + ~3-.3 + a3
. >-
80_
,7
-
-
