From the
In recent years, considerable effort has been devoted to defining lipid signaling pathways, purification of the involved enzymes, and cloning of the genes encoding for these enzymes. However, much less is known about the mechanism, specificity of reaction, and the regulation of the catalytic activity of lipid-dependent enzymes and enzymes involved in generating lipid second messengers. The enzymes in lipid signaling pathways include lipid biosynthetic enzymes, lipid degrading enzymes, and enzymes that utilize lipid activators (cofactors). These enzymes have hydrophobic or amphipathic lipid substrates, activators, inhibitors, and products that exist as large aggregated structures in water. Many of these enzymes are themselves water-insoluble integral membrane proteins. Thus, lipid-dependent enzymes act in an environment in which both three-dimensional bulk interactions occur in solution and two-dimensional surface interactions occur, both of which must be taken into account by any kinetic model that describes the action of these enzymes. A kinetic model, termed ``surface dilution kinetics,'' that takes into account both types of interaction has been developed(1, 2) . This work introduced the important concept that both the surface concentration of lipid and the bulk concentration play critical roles in defining the kinetic parameters of lipid-dependent enzymes.
This review focuses on both theoretical and experimental considerations of surface dilution kinetics and its application to defining the kinetic parameters of a large variety of lipid-dependent enzymes. While surface dilution kinetics applies to all lipid interfaces, be they micelles, vesicles, liposomes, or membranes, the detergent mixed micelle system offers several advantages for carrying out in vitro surface dilution studies. Since the Triton X-100 mixed micelle system has been successfully employed with numerous lipid-dependent enzymes, we have focused our discussion on examples that employ this detergent.
Dennis and co-workers (1, 2, 3, 4) developed surface
dilution kinetics to explain the action of cobra venom phospholipase
A on Triton X-100/phosphatidylcholine mixed micelles. This
system will be used to describe the principles of surface dilution
kinetics that are presented in .
In this scheme, a soluble enzyme (E) first associates with the Triton X-100/lipid mixed micelle (A) to form an enzyme-mixed micelle complex (EA). This association is a function of the bulk concentrations of both E and A. If the enzyme nonspecifically binds to the micelle surface, the term A is defined as the sum of the molar concentrations of Triton X-100 and lipid substrate. This model is illustrated in Fig.1as the ``surface binding model.'' If, on the other hand, the enzyme specifically binds to a substrate molecule in the micelle surface during this first binding step, the term A is defined as the molar concentration of lipid substrate. This model is illustrated in Fig.1as the ``phospholipid binding model.''
Figure 1:
Illustration of the application of
``surface dilution kinetics'' to the phospholipase
A-catalyzed hydrolysis of phospholipids contained in mixed
micelles with nonionic surfactants such as Triton X-100. Two
possibilities are shown: top, the ``surface binding
model'' whereby the enzyme first associates nonspecifically with
the micelle surface; and bottom, the ``phospholipid
binding model'' whereby the enzyme first associates specifically
with phospholipid in the micelle surface. In both cases, in a
subsequent step, the enzyme associated with the micelle binds a
phospholipid substrate molecule in the micelle in its catalytic site
and carries out hydrolysis producing as products a lysophospholipid and
a fatty acid, which may be released to solution or be retained in the
micelle surface. Phospholipid molecules are depicted in red,
detergent molecules in gold, and the enzyme in blue.
Adapted with permission from (2) and (3) .
Once
the enzyme has associated with the Triton X-100/lipid mixed micelle, it
then binds an individual lipid molecule (B) in the catalytic site
forming the EAB complex. Since both components of this
association are sequestered at the surface, the association is a
function of the surface concentrations of both EA and B. Thus,
the concentration of lipids in the mixed micelle, term B, is expressed
in surface concentration terms such as mole fraction,
[lipid]/([lipid] + [detergent]) or
mol % (mole fraction 100). As catalysis occurs, the products
(Q) are formed and EA is regenerated.
The illustrations
shown in Fig.1are representative of water-soluble enzymes (e.g. cobra venom phospholipase A(1, 2, 3, 4) ). For a
water-insoluble integral membrane enzyme (e.g. phosphatidylserine decarboxylase (5) or
phosphatidylinositol 4-kinase(6, 7) ), the protein is
delivered to the assay as a detergent/protein mixed micelle. In this
case, the enzyme concentration, E, actually represents the
concentration of the enzyme-detergent complex. This differs from the
phospholipase A
model where a soluble enzyme interacts with
a surface. With integral membrane enzymes, two surfaces are
interacting, one containing enzyme and the other containing lipid. The
enzyme/micelle can maintain its integrity and bounce from micelle to
micelle or it can fuse with lipid/micelles. In either case, this
confers the bulk concentration dependence to the
kinetics(5, 6, 8, 9) .
The kinetic equation for the surface dilution scheme has been derived (2, 4) and is given in ,
where K = k
/k
and K
= (k
+ k
)/k
. The V
is the true V
at an infinite mole fraction
and an infinite bulk concentration of phospholipid substrate, K
is the interfacial
Michaelis constant (expressed in surface concentration units), and K
is the dissociation
constant (expressed in bulk concentration terms) for the mixed micelle
binding site. The following assumptions are made with this
scheme(2) . The size and aggregation number of mixed micelles
remain constant over the concentration range employed as the bulk
concentration or surface concentration of substrate is varied; the
average surface area per molecule of Triton X-100 is the same as the
lipid substrate; both remain constant as the bulk concentration or the
surface concentration of substrate is varied; the micellar surface area
per enzyme binding site remains constant; and the enzyme has access to
the entire lipid pool.
To carry out a surface dilution kinetic analysis of a lipid-dependent enzyme, both the substrate's bulk concentration, expressed in terms of molarity, and its surface concentration, expressed in terms of mole fraction, must be varied. This produces a matrix of kinetic data points that is then analyzed to determine the various kinetic parameters. While varying the bulk substrate concentration is trivial, varying its surface concentration is not. To accomplish the latter, the mole fraction of substrate in the surface is varied by adding or removing other components of the surface. Ideally, these other surface components should be neutral dilutors, that is they should not interact directly with the catalytic or modulator sites of the enzyme. They can, however, interact in nonspecific ways with the enzyme as Triton X-100 does when it is used to solubilize integral membrane proteins. In addition, changing the surface concentration of the substrate with a neutral dilutor should not dramatically change the physical characteristics of the surface, e.g. size, area per molecule, or surface charge. Such changes can dramatically affect the activities of some enzymes and would complicate any kinetic analysis.
We have found that nonionic detergents come close to meeting these requirements. Nonionic detergents form micelles of relatively uniform size at concentrations above their critical micelle concentration (reviewed in (10, 11, 12, 13) ). The addition of low concentrations of lipids into these detergent micelles appears to have little effect on micelle structure and results in the solubilization of these molecules into a homogeneous micelle phase. One of the most frequently employed detergents is Triton X-100. Triton X-100 mixed micelles, illustrated in Fig.2, containing up to 15 mol % lipids, are similar to the structure of pure Triton X-100 micelles (14) but are slightly larger in size(13, 15, 16) . Triton X-100 has been shown to form uniform mixed micelles with a variety of lipid molecules including phosphatidylcholine(13, 15, 17) , phosphatidylethanolamine(16) , phosphatidylinositol(6) , phosphatidate(9) , phosphatidylserine(5) , CDP-diacylglycerol(8) , diacylglycerol(18) , palmitic acid(16) , and sphingoid bases(16, 19, 20) .
Figure 2: Schematic view of the ``classical'' oblate ellipsoid model and the ``non-classical'' spherical model for a mixed micelle containing the nonionic surfactant Triton X-100 and a low molecular fraction of phospholipid (<0.1). The micelle model shapes were calculated (14) based on a Stokes radius of 44 Å at 40 °C and a hydration (taken from the value for the Triton X-100 micelle at 25 °C) of 1.3 g of water/g of Triton X-100. Using volume/density calculations for the hydrophobic core, A is a classical micelle with the shape of an oblate ellipsoid with an approximately 2:1 axial ratio. For the spherical micelle model B, the octylphenyl groups cannot pack in a spherical core to form a classical micelle. Therefore, in this model some oxyethylene units must be included in the hydrophobic core. It is not possible to precisely calculate the arrangement of groups in this non-classical model because one does not have the limits imposed by a distinct hydrophobic/hydrophilic boundary, but all of the octylphenyl groups are shown in the core plus the relevant portion of the oxyethylene chains that are attached to the octylphenyl groups. It is assumed that the hydrophilic region extends one oxyethylene chain length (16 Å) beyond the hydrophobic core making the radius of the whole micelle about 44 Å. Reproduced with permission from (16) .
These nonionic detergents are also often required to solubilize integral membrane proteins(11, 12, 13) . In such cases, their inclusion into assays is often unavoidable. If the assay system is using vesicles, liposomes, or membranes, the introduction of these detergents can alter the physical state of the substrate and in turn enzymatic activity. Using a detergent mixed micelle assay system, containing the same detergent used in the solubilization and purification of the enzyme, can greatly simplify the kinetic analysis and helps to ensure that the substrate will be maintained in the same physical state.
Experimental Considerations, Phosphatidylinositol
4-Kinase as an Example
To examine an enzyme according to surface dilution kinetics, activity is measured as a function of the bulk concentration of lipid substrate (A of ) at a series of set surface concentrations of lipid substrate (B of ). An example of a surface dilution kinetic analysis is shown in Fig.3and 4. In this example, yeast phosphatidylinositol 4-kinase activity is plotted as a function of the substrate's bulk concentration at set surface concentrations of phosphatidylinositol. These data are plotted in two ways. In Fig.3A the surface binding model is employed, and the enzyme activity is plotted versus the sum of the molar concentrations of detergent and substrate, i.e. the enzyme binds nonspecifically to the entire surface. In Fig.4A the phospholipid binding model is employed, and the same data used in Fig.3are now plotted as activity versus the concentration of substrate alone, i.e. the enzyme binds specific phospholipids in the surface and does not bind to the other components that make up the surface.
Figure 3:
Activity of phosphatidylinositol 4-kinase
toward phosphatidylinositol in mixed micelles with Triton X-100
according to the ``surface binding model.'' PanelA, phosphatidylinositol 4-kinase activity
(µmol/min/mg) was measured as a function of the sum of the molar
concentrations of Triton X-100 (TX) plus phosphatidylinositol (PI) at set mole fractions of phosphatidylinositol: ,
0.0157;
, 0.0079;
, 0.0039; ▾, 0.0026. PanelB, reciprocal plot of the data in panelA. PanelC, replot of 1/V intercepts obtained in panelBversus the reciprocal of the mole fraction of phosphatidylinositol. PanelD, replot of slopes obtained in Bversus the reciprocal of the mole fraction of
phosphatidylinositol. The lines drawn are a result of a
least-squares analysis of the data. Reproduced with permission from (6) .
Figure 4:
Activity of phosphatidylinositol 4-kinase
toward phosphatidylinositol in mixed micelles with Triton X-100
according to the ``phospholipid binding model.'' The same
data as plotted in Fig.3are replotted as follows. PanelA, phosphatidylinositol 4-kinase activity
(µmol/min/mg) was measured as a function of the molar concentration
of phosphatidylinositol (PI) at set mole fractions of
phosphatidylinositol: , 0.0157;
, 0.0079;
, 0.0039;
▾, 0.0026. PanelB, reciprocal plot of the data
in panelA. PanelC, replot of
1/V intercepts obtained in panelBversus the reciprocal of the mole fraction of
phosphatidylinositol. PanelD, replot of slopes
obtained in Bversus the reciprocal of the mole
fraction of phosphatidylinositol. The lines drawn are a result
of a least-squares analysis of the data. TX, Triton X-100.
Reproduced with permission from (6) .
As predicted by the models,
phosphatidylinositol 4-kinase activity exhibits typical saturation
kinetics with respect to the bulk concentration of substrate, whether
the latter is represented as Triton plus phospholipid or as
phospholipid alone. Also, as the surface concentration of
phosphatidylinositol in the mixed micelle is diluted, there is a
decrease in the apparent V (Figs. 3A and 4A). Hence, the reason for describing this phenomenon
as ``surface dilution kinetics.''
Double-reciprocal plots
confirm that the kinetic data exhibit saturation kinetics when the bulk
concentration of phosphatidylinositol is varied at each fixed surface
concentration of phosphatidylinositol (Fig.3B and
4B). The pattern of lines shown in Fig.3B and
4B is consistent with an equilibrium-ordered reaction as
predicted by . predicts that a replot of the
1/V intercepts from Fig.3B and 4Bversus 1/B should be linear, that the intercept
of the 1/V intercept axis of the replot is
1/V, and that the intercept of the 1/B axis is -1/K
.
Replots of the data are linear (Fig.3C and
4C) and yield the same values for V
and K
(6.1 µmol/min/mg and
0.0036 mole fraction, respectively).
also predicts that
a replot of the slopes from Figs. 3B and 4Bversus 1/B should be linear and pass through the
origin. The slope of the replot is equal to KK
/V
.
From this, K
can be
calculated since K
and V
are determined above. The replot of slopes versus 1/mole fraction of phosphatidylinositol from Fig.4Bversus 1/B, shown in Fig. 4D, is linear and passes through the origin as
predicted by the phospholipid binding model. Although the analogous
plot in Fig.3D is also linear, the line does not pass
through the origin as predicted by the surface binding model. The
dissociation constants (K
)
calculated for the mixed micelle binding site from the data in Fig.3D and 4D are 118 and 0.26 mM,
respectively. While this analysis indicates that the phospholipid
binding model fits better, one should not conclude that the enzyme
follows this model unless supported by other independent data. The
slope replot is two replots away from the primary data and thus is
subject to a fair amount of error and should not be used as a rigorous
proof of which model applies.
The example of phosphatidylinositol 4-kinase demonstrates the utility of surface dilution kinetics. It should be noted that this linearized, graphical method is a traditional tool used by biochemists to analyze kinetic data. This method is helpful in visualizing the data and how well the data fit the models. Modern non-linear regression computer algorithms are also important tools to be used in analyzing surface dilution kinetics.
It should also be noted that a common practice is to hold one of the terms, either A or B, constant, often at saturating levels, while varying the other, thus creating a single kinetic line. The kinetic constants obtained from this single line are only apparent kinetic constants. These constants contain both the true kinetic constant and terms due to the variable that was held constant. In order to separate these terms and obtain the true constants both variables must be varied. In addition, to get good kinetic data, all terms must be varied over a concentration range that extends well above and below the various binding constants. This can often be a problem with lipid-dependent enzymes because many substrates are soluble over narrow ranges or can be solubilized in micelles only over a small surface concentration range.
Examples of Enzymes That Follow the Surface Dilution
Kinetic Model
Surface dilution kinetics has been useful for the kinetic
analysis of several lipid-dependent enzymes. These enzymes include
phospholipid biosynthetic enzymes (phosphatidylinositol
4-kinase(6, 7) , phosphatidylserine
synthase(8) , phosphatidylserine decarboxylase (5) ,
phosphatidate phosphatase(9) , and phosphatidate
kinase(21) ) as well as phospholipid degrading enzymes
(phospholipase A(22) , phospholipase
A
(1, 2, 23) ,
phosphatidylcholine-phospholipase C(24) , and
phosphatidylinositol-phospholipase C(25) ). Whereas some
enzymes are most consistent with the surface binding model (e.g. phosphatidylserine synthase(8) , phosphatidylserine
decarboxylase(5) , phosphatidate phosphatase(9) , and
phosphatidate kinase(21) ), other enzymes are most consistent
with the phospholipid binding model (e.g. phosphatidylinositol
4-kinase(6, 7) , phospholipase
A
(22) ).
Substrate specificity with respect to acyl chain length and degree of fatty acyl unsaturation is of great interest in lipid enzymology. The study of lipid substrate specificities of phospholipid biosynthetic enzymes is required to explain the mechanism by which these enzymes contribute to the molecular species distribution of the membrane phospholipid bilayer(26) . Phospholipid acyl group composition governs membrane structure and function and regulates lipid signaling pathways. Studies that attempt to determine the specificity of lipid-dependent enzymes for different phospholipids are plagued by changes in the phospholipid physical state. Changing the head group or fatty acid chain composition of a phospholipid can produce significant changes in the characteristics of the interfaces they form. These changes have been shown to dramatically affect the activity of these enzymes. Therefore, an observed difference in activity of an enzyme hydrolyzing two different phospholipids could be due to either a true specificity difference or to changes in the physical characteristics of the surface. The nonionic detergent mixed micelle systems offer a distinct advantage in regard to this problem. These mixed micelles present the phospholipid in a uniform matrix of detergent. Incorporation of different phospholipids into these structures cause much less distortion.
The utilization of surface dilution kinetics
has resulted in useful information on acyl group specificity for
substrates of several lipid-dependent enzymes including phosphatidate
phosphatase (9) , phosphatidylserine synthase(8) ,
phosphatidylethanolamine N-methyltransferase(27) ,
diacylglycerol kinase(28, 29) , phospholipase
A(22, 30) , and
phosphatidylinositol-phospholipase C(31) .
Expanding the Surface Dilution Model
The surface dilution kinetic scheme was developed for
nonspecific (surface binding model) and specific (phospholipid binding
model) binding of cobra venom phospholipase A to Triton
X-100/phospholipid mixed
micelles(1, 2, 3, 4) . This enzyme
catalyzes the hydrolysis of a single substrate molecule. However, many
phospholipid biosynthetic enzymes carry out more complicated reactions.
For example, yeast phosphatidylinositol 4-kinase catalyzes a BiBi
reaction involving phosphatidylinositol and ATP. The surface dilution
model can be expanded to include these more complex enzymatic
reactions. In the case of phosphatidylinositol 4-kinase, is modified to include the reaction of ATP. A rate equation
can then be derived that is comparable with by using
either the rapid equilibrium or the steady state assumptions and
standard kinetic derivations(32) . Care must be taken to
distinguish between bulk events and surface events and to ensure that
the appropriate concentration terms are used. For phosphatidylinositol
4-kinase, the binding of the enzyme to the surface is in bulk terms,
the binding of the substrate to the catalytic site of the enzyme is in
surface terms, and the binding of ATP to the enzyme is in bulk terms
because ATP does not intercalate into the surface. A detailed kinetic
analysis, similar to that described above, can then be carried out and
analyzed either graphically or via non-linear regression to determine
if the model fits the data and if it does to determine the kinetic
parameters. Carman and co-workers(6, 7) have used
surface dilution kinetics to determine kinetic constants for
phosphatidylinositol and ATP.
Activation, Inhibition, and Surface Dilution Kinetics
One of the current challenges of lipid enzymology is
developing pharmacologically active modulators of enzymes involved in
signal transduction pathways. In addition, the activity of many
membrane-associated enzymes is dependent on or regulated by membrane
lipids(33) . Most of the activators and inhibitors found to
date are themselves surface-active compounds that readily incorporate
into lipid surfaces. This fact makes the use of surface dilution
kinetics imperative in analyzing inhibition and activation data. For
example, numerous phospholipid analogs have been found that will
inhibit the various intracellular and extracellular phospholipase
As. As one increases the concentration of such an inhibitor
in the assay, two things occur. The inhibitor interacts with the enzyme
directly to produce inhibition, e.g. competitive inhibition.
At the same time, the inhibitor increases the surface area of the
interface because it is a surface-active compound and incorporates into
the surface. This effectively decreases the surface concentration of
the substrate, even though its bulk concentration remains constant,
which can then decrease the enzymatic rate. This would in itself appear
as competitive inhibition even if the compound did not interact with
the enzyme directly. These two effects must be separated to accurately
determine the nature and extent of the true inhibition. Yu and Dennis (34) have derived the surface dilution kinetic equations for
competitive inhibition and applied them to the evaluation of thioether
amide analogs of phospholipids with phospholipase
A
(35) . Similar treatments are also possible for
other forms of inhibition.
The use of surface dilution kinetics has
facilitated well defined kinetic analyses of lipid activator
requirements and lipid inhibitors of several lipid-dependent enzymes
(for review, see (26) ). These include phospholipid
biosynthetic enzymes (e.g. phosphatidate
phosphatase(36) , phosphatidylserine synthase(37) ,
phosphatidylinositol synthase(37) , diacylglycerol
cholinephosphotransferase(38) , diacylglycerol
ethanolaminephosphotransferase(38) , phosphocholine
cytidylyltransferase(39) , phosphatidylinositol
4-kinase(40) , and phosphatidylinositol 4-phosphate
kinase(41) ), enzymes of neutral lipid metabolism (e.g. monoacylglycerol acyltransferase (42) and diacylglycerol
kinase(28, 43, 44, 45) ), lipid
degrading enzymes (phospholipase A(23) and
phosphatidylinositol-phospholipase C(46) ), and lipid signal
transduction enzymes (e.g. protein kinase
C(18, 20, 47, 48, 49, 50, 51) ;
for review, see (52) ). The analyses of these enzymes using
surface dilution kinetics have resulted in: (a) the
identification of lipid activators and inhibitors; (b)
information on the structural requirements for activation and
inhibition; (c) determination of the mechanism of activation
and inhibition; (d) information on lipid-protein interactions;
and (e) information on the regulatory roles of lipid
activators and inhibitors of enzymes in vivo.
In this review, we have discussed the theory, experimental considerations, and applications of surface dilution kinetics. This approach provides a useful framework for the kinetic analysis of lipid-dependent enzymes involved in biosynthesis, degradation, and lipid signaling pathways. With this basis, we should be able to advance our fundamental understanding of the mechanism of action, activation, and inhibition of enzymes that act in or on membranes and other lipid-water interfaces. This approach should allow investigators to better study and characterize important biological processes and phenomena that reside in membranes.