(Received for publication, January 31, 1996)
From the
Rate constants for the interaction of fatty acids (FA) with
fatty acid binding proteins (FABP) from adipocyte (A-FABP), heart
(H-FABP), and intestine (I-FABP) were determined by using stopped-flow
fluorometry and ADIFAB, the fluorescent probe of free fatty acids
(FFA), or a new FFA probe, ADIFAB2, constructed by derivatizing with
acrylodan the Leu
Ala mutant of I-FABP. ADIFAB2,
because its binding affinities are about 10-fold greater than ADIFAB,
was found to be more accurate for monitoring the kinetics of the higher
affinity reactions. On- (k
) and off- (k
) rate constants were determined as a function
of temperature. Our results reveal that in all cases the FA-FABP
equilibrium is achieved within 2 s at 37 °C and within 20 s at 10
°C. Off-rate constants varied by about 10-fold among the different
underivatized FABPs; k
values were smallest for
H-FABP and largest for A-FABP, while k
values for
these proteins generally varied by less than 2-fold. The results show
that the previously reported larger affinities of I- and H-FABPs as
compared to A-FABP are primarily a reflection of larger k
values for I-FABP and smaller k
values for H-FABP. Eyring transition state
theory was used to evaluate the activation thermodynamic parameters for
both on- and off-reactions and the results show that in virtually all
cases the rate-limiting steps are predominately enthalpic. Activation
free energies for binding to ADIFAB are generally composed of about 8
kcal/mol unfavorable enthalpy and about a 1 kcal/mol favorable entropic
contribution. For the underivatized FABPs the activation free energies
are all about 7 ± 0.3 kcal/mol, suggesting that the transition
state for entering or leaving the binding site involves a common
protein structural change. We suggest that entering or leaving the FABP
binding cavity involves similar mechanisms for all 3 FABPs and may
involve amino acid residues located within the portal regions of these
proteins.
Fatty acid binding proteins (FABP) ()are a family of
14-15-kDa proteins found in the cytosols of various
cells(1, 2, 3, 4, 5, 6, 7, 8) .
Although the three-dimensional structures of these proteins are
similar, individual members of this family exhibit considerable
variation in their amino acid
sequences(9, 10, 11, 12) . In
addition, the conformation of the fatty acid (FA) within the binding
site differs for different FABPs and, to varying degrees, for different
FA within the same
protein(9, 10, 11, 12) . Consistent
with these amino acid sequence and FA conformational differences, we
have recently found considerable differences in the binding affinities
of FA to FABPs from adipocyte, heart, and
intestine(12, 13, 14) . Using the fluorescent
probe ADIFAB, we found that equilibrium binding constants differ by
about 3 orders of magnitude, depending upon FA and FABP type. This
heterogeneity was also reflected in the equilibrium thermodynamic
parameters for binding; for adipocyte and heart FABP, the enthalpy of
binding becomes more favorable with increasing FA unsaturation and,
correspondingly, the entropy becomes less favorable, while for
intestinal FABP the enthalpy is roughly constant for all FA, but the
entropy term becomes less favorable with increasing unsaturation (14) .
Although structural and binding studies provide insight into the interactions of FA and FABP at equilibrium, they leave unanswered questions concerning the kinetic features of these reactions, which are key to understanding a number of functional and structural properties of the FABPs. Determination of the rates of binding and dissociation of FA from FABPs is essential for understanding the kinetic constraints that govern intracellular FA trafficking and metabolism and the mechanism by which FA enter and leave the FABP binding cavity. Measurements of the rate constants and their temperature dependence should provide information about the thermodynamic parameters of the activation barrier for entering and leaving the binding site and the comparison of rate constants for site-specific mutants will provide information about how FA gain access to the binding cavity.
With the exception of our initial results discussed in (12) and (14) , no measurement of the kinetics of FA-FABP binding and dissociation have been reported. However, Storch and colleagues (15, 16, 17) have carried out extensive measurements of the transfer of the chemically modified anthroyloxy-FA from FABPs to membranes. These measurements revealed considerable heterogeneity among the FABPs both in the rates and in the transfer mechanism itself. These AOFA results together with our results for unmodified FA and FABPs(12, 14) , suggest that rate constants for binding and dissociation of unmodified FA are also sensitive functions of FA and FABP type.
In the present study we
have determined the rate constants for the binding of a set of
unmodified FA to the fluorescently labeled I-FABP, ADIFAB. ADIFAB,
which exhibits distinct fluorescence spectra in the FA-bound and
FA-unbound states, was then used to monitor the rate of dissociation of
FA from adipocyte, heart, and intestinal FABPs. We also report the
development of a new higher affinity FFA probe, ADIFAB2, and describe
its use in determining rate constants for higher affinity FA-FABP
interactions. The measured dissociation rate constants (k) were used to calculate k
values from k
= k
/K
, where the
equilibrium dissociation constants K
,
were determined previously(12, 13, 14) .
Thermodynamic characteristics of the energy barriers corresponding to
binding and dissociation were determined from the temperature
dependence of the measured rate constants using Eyring transition-state
theory.
The fluorescence properties of
the acrylodan-derivatized Leu
Ala I-FABP (ADIFAB2)
are significantly different than ADIFAB's (data not shown). The
positions of the emission maxima occur at longer wavelengths, 440 nm
for apo-ADIFAB2 and 550 nm for holo-ADIFAB2, compared to 432 and 505 nm
for ADIFAB, and the optimal excitation wavelength is at 375 nm for
ADIFAB2 as compared to 386 nm for ADIFAB. These two different sets of
excitation and emission wavelengths were used in the present study for
measurements using ADIFAB2 and ADIFAB, respectively. Furthermore, the
parameters that define the equilibrium binding properties, R
, R
, and Q of of (13) , are also significantly different for
ADIFAB2 and, in contrast to ADIFAB, the values of these parameters are
FA and temperature dependent. Thus for oleate, R
and Q range between 1.6 and 2.5, and between 7.5 and 12,
respectively, for temperatures between 10 and 37 °C, and these
values are all approximately 10% higher for palmitate.
Three separate types of kinetic measurements were done: 1) dissociation of FA from ADIFAB, 2) binding of FA to ADIFAB, and 3) dissociation of FA from FABP. Dissociation of FA from ADIFAB was measured by mixing a solution of FA and ADIFAB in one syringe of the stopped-flow device with excess fatty acid-free BSA in the second syringe. The binding of FA to ADIFAB was measured by mixing solutions of FA in one syringe with ADIFAB in the second syringe. The dissociation of FA from FABP was measured by mixing a solution of FA and FABP in one syringe with ADIFAB in the second syringe.
where FA binding and dissociation are k and k
, respectively. The off- and on-rate
constants for ADIFAB and the FABP or BSA proteins are designated with
superscript AF and Prot, respectively. The subscripts b and f designate the FA bound and free concentrations,
respectively.
With appropriate boundary conditions, describe models used to analyze all
three types of kinetic measurements. The initial conditions (t = 0) that apply to each of these types of measurements are:
1) for measurements of the off-rate from ADIFAB, [Protein(0)]
= 0, and [ADIFAB(0)] and
[FFA(0)] are both determined from the equilibrium condition
that exists before mixing, using the previously measured equilibrium
constants(14) ; 2) for ADIFAB on-rate measurements,
[ADIFAB(0)]
= 0 and [FFA(0)]
= [FFA
]; and 3) for the FABP off-rate
measurements, [ADIFAB(0)]
= 0, and
[FABP(0)]
and [FFA(0)] were determined
from equilibrium conditions. The solutions to yield the concentrations of FA
bound ADIFAB, FA bound Protein, and FFA as a function of time.
The
quantity that is actually measured in these studies is the time
dependent change in the ratio of the fluorescence intensity of ADIFAB
at 505 and 432 nm (R(t)). To obtain rate constants
from these measurements, R(t) must be expressed in
terms of the solutions to ,
[ADIFAB(t)] and
[FFA(t)]. This can be done by expressing the
intensities at each wavelength in terms of the contributions of the
bound and free forms of ADIFAB as described
previously(13, 21, 22) . Thus the
fluorescence intensity at the emission wavelength
is given by,
in which [ADIFAB] and
[ADIFAB]
are the bound and free concentrations of
ADIFAB and I
(
) and I
(
) are the
specific fluorescence intensities of these components. The ratio of
intensities at 505 and 432 nm is therefore the following,
Dividing the numerator and denominator of the right-hand side of by [ADIFAB]I
(432)
we obtain,
where R is the value of R in the
absence of FA and the numerical constants were obtained from the
spectral properties of ADIFAB as described previously(13) , and
where [ADIFAB] is a solution of .
To obtain the rate constants
it is necessary to fit the measured R(t) values with
the values predicted by . The measurements to determine k from ADIFAB were done in the presence of
excess BSA, effectively eliminating the reverse reaction, and therefore
for this type of measurement [ADIFAB(t)]
is simply,
Upon substitution of into an
expression for R(t) is obtained that readily can be
fitted to measured R(t) values to obtain k. For measurements of type 2 and
type 3, were solved numerically.
Thus for type 2 and 3 measurements, values of the rate constants,
initial values, and any other boundary conditions are selected, are solved for these values, R(t) is obtained using the numerical values of
[ADIFAB(t)]
, and these calculated R(t) values are then compared with the measured ones.
This process was facilitated with the program MLAB (Civilized Software,
Bethesda, MD) which determines the model parameters by using a
Marquardt-Levenberg minimization to fit numerical solutions of and measured R(t)
values. Values obtained by this procedure were verified in selected
cases by solving using the
Runge-Kutta facility of the program Macsyma (Macsyma, Cambridge, MA).
Reliable fitting of the measured scans requires constraints in
addition to the initial conditions. Measurements of types 2 and 3
involve bimolecular interactions and therefore the reaction kinetics
depend upon the concentration of the reactants. Although the nominal
concentrations of FA in the reservoir syringes is known, the actual
concentration reaching the mixing chamber exhibits variations from scan
to scan because of surface absorption of the FA. To help reduce the
uncertainties in the rate constants resulting from these variations,
the observed values of the initial and equilibrium values of R(t), R, and R(
), in each scan were used to define the actual total
FA in the mixing chamber using,
All three terms on the right-hand side are evaluated using the
values of R and R(
) obtained from
the fit, together with the previously measured binding
constants(12) . Thus from Refs. 12, 13, and 23,
With these constraints, fitting of data for the type 2
measurements was done by allowing k, R
, and R(
) to vary. For the type 3
measurements the variable parameters were, k
and k
, with the constraint k
/k
= K
, R
, and R(
). These procedures resulted in well behaved fitting
characteristics in which the fit values of R
and R(
) returned values in agreement with the measured
values. The quality of fit was assessed by the sum of squares of the
theory experiment differences (SOSQ), fit residuals, and direct
observation, and generally gave excellent agreement between theory and
experiment, with typical SOSQ values <1
10
.
Figure 1:
Simulations of
the dissociation of oleate from I-FABP monitored by ADIFAB
fluorescence. Time courses of oleate dissociation from I-FABP at 37
°C were calculated using the kinetic model described by . For these simulations the total
concentrations of ADIFAB, FABP, and oleate were, respectively, 2, 1,
and 1 µM. Rate constants used for ADIFAB (Fig. 3)
were k = 10.7 s
, k
= 3.8
10
M
s
and for I-FABP k
was set equal to k
/K
, where K
= 30 nM(12) and k
values were varied
between 5 and 30 s
as indicated in the figure. A, concentrations of each the reactants
([ADIFAB
(t)],
[FFA(t)],
[FABP
(t)]) were obtained by
solving using the Runge Kutta
method. B, values of the ADIFAB fluorescence intensity ratio
were calculated using .
Figure 3:
Arrhenius plots of ADIFAB off- and on-rate
constants. Measured values are shown as symbols and the
results of linear regressions are shown as solid lines through
the data. A, log of k
. B, log
of k
. Abbreviations
are as listed in Table 1.
These limits on resolution of FABP off-rates are
also apparent in the time course of R(t), the
quantity actually measured. As Fig. 1B indicates, the
time course approaches a limiting function as k increases. The ability of ADIFAB to resolve dissociation rate
constants depends upon the experimental uncertainty in R(t) and is a function of both the off-rate from FABP
and the FABP's equilibrium constant. In the example of Fig. 1, ADIFAB would resolve k
values
<30 s
for I-FABP (K
=
36 nM). Resolution of off-rate constants from the less tightly
binding A-FABP (K
= 60 nM),
however, would be <50 s
(data not shown). This
resolving power of ADIFAB is a direct reflection of the rate of
response of ADIFAB to FA binding and therefore is proportional to the
on-rate constant as well as ADIFAB's binding affinity relative to
the donor FABP. Thus ADIFAB2, for which values and binding affinities
are larger than for ADIFAB (see below), has been used in the present
study to help resolve dissociation in those cases where large k
values and/or small K
values limit the response rate of ADIFAB.
where T is temperature in degrees of Kelvin, is
the transmission coefficient and is set to unity in these calculations, k
is Boltzman's, and h is
Planck's constant, and
G
and is the free
energy of activation. The activation enthalpy was determined from the
slope of Arrhenius plots of the rate constants as the following,
and the activation entropy was determined as,
In using this analysis it is assumed that the thermodynamic
model provides a reliable representation of the formation of the
transition state and that the activation enthalpies and entropies are
temperature independent. Recently, studies of equilibrium reactions
have called into question the use of the van't Hoff analysis, and
therefore the temperature independence of equilibrium enthalpies and
entropies, to determine thermodynamic parameters from binding
measurements(25, 26) . Whether such reservations apply
to the activation parameters is unclear. However, two observations
suggest that at least for FA-FABP interactions thermodynamic parameters
calculated assuming temperature independence may be accurate. First, as
discussed by Weber(25) , the errors made in assuming
temperature independence may be small when, as is the case in the
present study (Table 4), the activation free energies are
predominantly enthalpic. Second, the predominance of enthalpy also
applies to the equilibrium thermodynamic parameters for FA binding to
FABP as determined by both van't Hoff (14) and
calorimetry measurements(27, 28) , although the
van't Hoff determined H are larger (more favorable)
by about 3 kcal/mol.
Figure 2:
Measured time courses for dissociation of
linoleate from ADIFAB. These measurements were done by monitoring the
ADIFAB R(t) value after stopped-flow mixing
ADIFAB-linoleate complexes with fatty acid-free BSA at temperatures
between 5 and 37 °C. Each time course is an average of at least
three separate measurements and initial reactant concentrations were:
ADIFAB, 1 µM; linoleate, 1 µM; and BSA, 5
µM. Solid lines are least squares fits to the
data using from which were obtained the k values plotted in Fig. 3.
Time courses
for binding of FA to ADIFAB were measured by mixing FA and ADIFAB; our
results for oleate binding at temperatures between 15 and 37 °C are
shown in Fig. 4. Also shown in this figure are the fits to these
measured time courses obtained with the kinetic model represented by . These fits were obtained by
allowing both k and k
to
vary with the constraint that k
/k
= K
, where K
values were those
measured previously(12) . The results of this analysis as seen
in Fig. 3and Table 1, yields k
values that range between 1
10
and 5
10
M
s
and k
values that are virtually identical with those
obtained directly from measurements of FA transfer from ADIFAB to BSA
described above. As was seen for the time course of dissociation, the
rate of binding increases with increasing temperature. However, in
contrast to the significant variation of k
with
FA type, virtually identical k
values were
obtained for all FA (Table 1).
Figure 4:
Measured time courses for oleate binding
to ADIFAB. The ADIFAB fluorescence ratio (R(t)) was
monitored following stopped-flow mixing of ADIFAB (1 µM)
and oleate (nominal concentration 1 µM) at temperatures
between 15 and 37 °C. Solid lines are least squares fit to
the data using the solutions of to
obtain the k values plotted in Fig. 3.
Arrhenius plots of the on- and
off-rate constants (Fig. 3) were analyzed in terms of Eyring
transition state theory which yielded the thermodynamic parameters of
activation shown in Table 2. As these results indicate, the free
energies of activation for dissociation range between about 16 and 17
kcal/mol and show a decrease with increasing double bond number for the
18 carbon length FA. Table 2also shows that for all FA the
enthalpic portion of the activation energy is significantly larger,
between about 12 and 13 kcal/mol, than the entropic component
(3-4 kcal/mol). For the binding step the thermodynamic parameters
are quite similar for all FA and in particular indicate that the
activation barrier is predominantly enthalpic with average H
values of about 9.5 kcal/mol (Table 2).
Figure 5: van't Hoff plots of the equilibrium and Arrhenius plots of the rate constants for ADIFAB2. Equilibrium measurements were done as described previously for ADIFAB (13) and rate constants were determined by the same methods as for ADIFAB. A, equilibrium dissociation constants for palmitate and oleate. B and C, off- and on-rate constants for palmitate and oleate. Measured values are shown as symbols and the results of linear regressions are shown as solid lines through the data.
The equilibrium thermodynamic parameters
are qualitatively similar to those obtained previously for ADIFAB,
showing substantial enthalpic and entropic components; in contrast, for
the native I-FABP, enthalpies are about 12 kcal/mol and the entropic
components are approximately zero (12) . Just as for ADIFAB and
the underivatized proteins, the activation free energies for binding to
ADIFAB2 (7 kcal/mol) are dominated by enthalpies which are 8.6 and
10.6 kcal/mol for oleate and palmitate, respectively (Table 3).
Enthalpies also dominate the dissociation of FA from ADIFAB2, with
values that are between ADIFAB (Table 2) and I-FABP (Table 4).
Figure 6:
Measured time courses for FA dissociation
from underivatized FABPs monitored by ADIFAB fluorescence. Total
reactant concentrations in all measurements were: ADIFAB, 2
µM; FABP, 1 µM; and FA, 1 µM. A, dissociation of palmitate from human A-FABP monitored with
ADIFAB at 5 °C intervals for temperatures between 10 and 30 °C
and at 37 °C. Solid lines are least squares fits to the
data using and k values determined from this analysis are plotted in Fig. 7. B, dissociation of arachidonate from A-FABP,
H-FABP, and I-FABP at 25 °C. Fits to these data using the kinetic
model were used to obtain the k
values shown in Table 1.
Figure 7:
Arrhenius plots of A-FABP off- and on-rate
constants. Measured values are shown as symbols and the
results of linear regressions are shown as solid lines through
the data. Values for k were calculated using the
measured k
values and K
values from (14) . A, log
of k
. B, log
of k
. Abbreviations are as listed in Table 1.
The Arrhenius plots for the A-FABP rate constants were analyzed using the Eyring transition state model (Table 4). The results show that the free energy needed to form the transition state for dissociation (about 17 kcal/mol) is composed of a large enthalpic (13-16 kcal/mol) and a smaller entropic (0-4 kcal/mol) component. Within the uncertainties of these results (1-3 kcal/mol), the thermodynamic parameters are similar for all of the FA. Thermodynamic parameters for the binding step are also similar for all FA and reveal that, with the exception of arachidonate, the activation free energies which are about 8 kcal/mol, are predominantly enthalpic (Table 4).
Figure 8:
Arrhenius plots of H-FABP off- and on-rate
constants. Measured values are shown as symbols and the
results of linear regressions are shown as solid lines through
the data. Values for k were calculated using the
measured k
values and K
values from (14) . A, log
of k
. B, log
of k
. AD2 indicates that these measurements
were done using ADIFAB2 and other abbreviations as in Table 1.
Figure 9:
Arrhenius plots of I-FABP off- and on-rate
constants. Measured values are shown as symbols and the
results of linear regressions are shown as solid lines through
the data. Values for k were calculated using the
measured k
values and K
values from (14) . A, log
of k
. B, log
of k
. AD1 and AD2 indicates that
these measurements were done using ADIFAB and ADIFAB2, respectively,
and other abbreviations as in Table 1.
In the present study we have determined on- and off-rate
constants as a function of temperature for binding of five of the
physiologically most important FA to ADIFAB, ADIFAB2, adipocyte, heart,
and intestinal FABPs. In all cases the FA-FABP equilibrium is rapid,
occurring within about 2 s and 20 s at 37 and 10 °C, respectively.
Off-rate constants varied by about 10-fold among the different FABPs,
where k values were smallest for H-FABP and
largest for A-FABP. On-rate constants are 10-100-fold smaller
than the values predicted for diffusion limited rates, indicating a
significant activation barrier for binding and these values also varied
by about 10-fold among the different FABPs. The results demonstrate
that the kinetic basis for achieving equilibrium is different in
different FABPs; the larger affinity of I- and H-FABPs as compared to
A-FABP are primarily a reflection of larger k
values for I-FABP and smaller k
values for
H-FABP. For the native FABPs the activation free energies corresponding
to these kinetic processes are primarily enthalpic and are of similar
magnitude, suggesting that the activation state for entering or leaving
the binding site may involve a common protein structural change. In the
following we discuss how the results of the present study can be used
to provide insight about the nature of the transition state.
Once in the transition state,
the FAADIFAB complex can convert to the holo state where FA is
bound within the internal cavity of the FABP and the acrylodan moiety
is highly mobile and in a polar environment. As Table 2indicates, the activation enthalpy for the formation of
the transition state from the holo state is constant with FA type and
unfavorable by about 12.6 kcal/mol. Because the equilibrium enthalpy is
about 3-4 kcal/mol (12) the remaining 9 kcal/mol is used
to reform the transition state, consistent with the binding activation
parameters. The entropic contribution to activate the transition state
upon dissociation is also unfavorable and varies from about 4 for the
saturated and mono-unsaturated FA to 3 kcal/mol for the unsaturated FA.
At least part of this entropic cost may be due to the reduction in
rotational mobility of the acrylodan as it reorients from the highly
mobile holo state to the transition state. For example, if the
transition were from a rotationally isotropic to immobile state, the
entropic loss would be about 2 kcal/mol(36) .
The characteristics of ADIFAB2 are consistent with a qualitatively similar transition state as for ADIFAB. ADIFAB2 does, however, exhibit an approximately 0.5 kcal/mol smaller activation free energy for binding as compared to ADIFAB. This smaller energy of activation is consistent with the observed longer emission wavelength maximum in the apo state; 440 nm for ADIFAB2 as compared to 432 nm for ADIFAB (data not shown), assuming that the acrylodan moiety binds less tightly to regions of higher polarity. The substantially larger activation free energy for dissociation from ADIFAB2 (1 kcal/mol greater than for ADIFAB) is consistent with the greater FA affinities for the underivatized L72A-I-FABP as compared to the wild type protein. The smaller entropies for dissociation may also be a reflection of the weaker binding of acrylodan in ADIFAB2, the holo to transition state decrease in entropy being smaller than in the case of the more tighter binding and therefore more constrained ADIFAB.
These results for ADIFAB and
ADIFAB2 are consistent with the suggestion that the acrylodan moiety
must be displaced in order for FA to gain entry to the ADIFAB binding
cavity(13) . Based upon an examination of the x-ray
crystallographic structure of I-FABP, Sacchettini et al.(29) have suggested that a specific region
(``portal'') at the surface of the protein serves as the
entry port for FA access to the binding cavity. The current study
provides support for this suggestion because the acrylodan moiety is
attached to I-FABP at position 27, which is one of the residues that
forms the orifice defining the portal region, and this attachment
reduces the k values by approximately
5-10-fold relative to the underivatized I-FABP (Table 1).
Although the native FABPs
may share a common type of transition state, several aspects of the
kinetic and equilibrium results suggest that this state is distinctly
different for the acrylodan derivatives of I-FABP and, additionally
that acrylodan derivatization perturbs the FA-FABP interactions within
the binding cavity. Obviously if acrylodan is involved in the
transition state of the derivatized proteins then this state is per
se different than for the native proteins. Further evidence that
these states are different are: 1) the average activation free energy
for FA binding to ADIFAB is 1.1 kcal/mol greater than for the native
protein, and 2) the binding activation enthalpy (9.5 kcal/mol) for
ADIFAB is, with the exception of arachidonate, independent of FA type
while H
for I-FABP reveals a monotonic
decrease from 10 to 4 kcal/mol from palmitate to arachidonate. These
results suggest that if the orifice presents a barrier for access to
the cavity in the native protein, that derivatization of
Lys
, one of the key residues within the portal structure
alters the structure of this region so that the orifice does not
present a rate-limiting barrier in the derivatized protein. Differences
between ADIFAB and I-FABP are particularly evident in the activation
enthalpies for dissociation for which ADIFAB reveals a virtually
constant value of 12.7 kcal/mol for each of the FA while for I-FABP
H
decreases monotonically from 24 to 15
kcal/mol from palmitate to arachidonate. These results suggest that
derivatization affects interactions within the binding cavity,
consistent with the equilibrium results which indicate that the free
energy of binding to I-FABP is almost entirely enthalpic while for
ADIFAB the equilibrium free energy is composed of appreciable
admixtures of entropic and enthalpic components.