Low-density lipoproteins (LDL) play a key role in the
delivery of photosensitizers to tumor cells in photodynamic therapy. The interaction of deuteroporphyrin, an amphiphilic porphyrin, with LDL
is examined at equilibrium and the kinetics of association/dissociation are determined by stopped-flow. Changes in apoprotein and porphyrin fluorescence suggest two classes of bound porphyrins. The first class,
characterized by tryptophan fluorescence quenching, involves four
well-defined sites. The affinity constant per site is 8.75 × 107 M
1 (cumulative affinity 3.5 × 108 M1). The second class corresponds to the
incorporation of up to 50 molecules into the outer lipidic layer of LDL
with an affinity constant of 2 × 108
M1. Stopped-flow experiments involving direct LDL
porphyrin mixing or porphyrin transfer from preloaded LDL to albumin
provide kinetic characterization of the two classes. The rate constants
for dissociation of the first and second classes are 5.8 and 15 s1; the association rate constants are 5 × 108 M1 s1 per site and 3 × 109 M1 s1, respectively.
Both fluorescence and kinetic analysis indicate that the first class
involves regions at the boundary between lipids and the apoprotein. The
kinetics of porphyrin-LDL interactions indicates that changes in the
distribution of photosensitizers among various carriers could be very
sensitive to the specific tumor microenvironment.
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INTRODUCTION |
The retention of certain porphyrins by solid
tumors, as compared to normal surrounding tissues, has been recognized
for many years. This retention and the ability of these molecules to
generate short-lived toxic species upon light irradiation are at the
basis of a selective therapeutic approach, photodynamic therapy (PDT). In recent years, this therapy has benefited from the development of
lasers and optical fibers and is now an established procedure for the
treatment of certain cancers (Pass, 1993
; Dougherty et al., 1998).
Regulatory approval for PDT with a porphyrin-based preparation,
Photofrin, has been given. Second-generation photosensitizers are now
being developed with improved light absorption in the red region (Boyle
and Dolphin, 1996). Although various factors come into play in the
overall efficiency of PDT, correlation has been established
between the lipophilic character of photosensitizers and their
accumulation in tumors (Henderson et al., 1997) and, consequently,
their photosensitizing efficiency (Lavi et al., 2002).
It has been well established that the affinity of lipophilic
photosensitizers for serum lipoproteins, in particular low-density lipoproteins (LDL), plays an important role in the delivery of these
drugs to tumor cells (Jori et al., 1984; Reyftmann et al., 1984;
Candide et al., 1986; Kessel, 1986). The physiological role of LDL is
providing cells with cholesterol via cellular uptake. This is achieved
by receptor-mediated endocytosis resulting in the delivery of
components of LDL to the lysosomal compartment (Brown and Goldstein,
1976). The distribution pattern of some porphyrins has been found to be
correlated with the relative numbers of LDL receptors in different
tissues (Kessel, 1986). Several authors have pointed out an increased
cholesterol catabolism and over-expression of LDL receptors in tumor
cells (Gal et al., 1981; Vitols et al., 1992). The cellular uptake and
photoactivity of porphyrins have been increased through
potentialization of LDL catabolism by lovastatin (Biade et al., 1993).
By contrast, PDT-resistant tumor cells exhibit low activity of
LDL-related receptors (Luna et al., 1995). These data taken together
suggest that the selectivity of lipophilic photosensitizing antitumoral
agents arises from a favored low-density lipoprotein receptor pathway
(Maziere et al., 1991). This specific pathway also plays a key role in
the mechanism of other PDT modalities used to treat atherosclerotic lesions (de Vries et al., 1999) or to treat choroidal
neovascularization associated with age-related macular degeneration
(Miller et al., 1995).
Low-density lipoproteins are constituted of phospholipids, cholesterol
(esterified or not), triglycerides, and the B100 apoprotein which
contains, among other residues, 37 tryptophans and 151 tyrosines (Yang
et al., 1986). A consensus model has been proposed (Segrest et al.,
2001) consisting of a monolayer of phospholipids and cholesterol surrounding a lipid core made of triglycerides and cholesterol esters.
Although the exact shape of LDL particles is still debated, they can be
viewed as spherical with a diameter of 22 nm (Schumaker et al., 1994;
Segrest et al., 2001). A tentative representation is shown in Fig.
1.
Drugs bound to LDL could be distributed among the three major
components of these particles, i.e., the apolipoprotein, the phospholipid envelope, and the lipid core. The efficiency of LDL particles as carriers depends on the overall number of exogenous molecules they can bind. However, the integrity of the particle and,
more particularly, that of the receptor-binding site on apoB100 must be
preserved. It is of particular importance to consider the interactions
from a dynamic point of view. The rates of exchange of the
photosensitizer between LDL and the other serum proteins in blood must
be considered. Indeed, the photosensitizer distribution may be modified
by the particular environment provided by the interstitial compartment
of neoplastic tissues (Jain, 1987), or even be modified in the course
of the LDL endocytosis process.
The capacity of LDL to bind some photosensitizers and their
functionality have been examined in a few studies (Reyftmann et al.,
1984; Candide et al., 1986; Beltramini et al., 1987; de Smidt et al.,
1993). Except for results on isolated rabbit lipoprotein fractions
(Beltramini et al., 1987), no data are available concerning the
distribution of porphyrins in the various LDL compartments. To our
knowledge, no information about the dynamics of porphyrin interactions
with LDL has been published so far.
In the present paper, we investigate the interaction of an amphiphilic
porphyrin, deuteroporphyrin (DP), with LDL. This dicarboxylic porphyrin
was chosen because its structure corresponds to the framework of the
components of Photofrin, and approaches that of protoporphyrin, another
photosensitizer of therapeutic interest. Moreover, it can be purified
to a high degree and is less sensitive to photodegradation than
protoporphyrin. The different classes of binding sites are identified
and characterized by monitoring the intrinsic fluorescence of LDL or
that of the porphyrin. The dynamics of the interactions of LDL and
porphyrin and transfer to albumin are investigated using a stopped-flow
apparatus. All these processes are shown to be fast. This approach has
implications beyond the immediate problem of photosensitizer transport
by endogenous lipoproteins, but also relates to the behavior of other
drugs (Rudling et al., 1983; Shaw et al., 1987) as well as the design of artificial lipid particles for drug targeting (Rensen et al., 2001).
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MATERIALS AND METHODS |
Chemicals
All the experiments were carried out at pH 7.4 in saline
phosphate buffer (PBS) prepared from
Na2HPO4/KH2PO4 (total
phosphate, 9.57 × 103 M), NaCl, 0.15 M and KCl,
2.68 × 103 M. Deuteroporphyrin (DP), the structure
of which is shown in Fig. 2, was prepared
as described previously (Brault et al., 1986). Its purity was
determined to be better than 99% by HPLC. A stock solution
(103 M) was prepared in distilled tetrahydrofuran (THF)
and kept at 
18°C. Experimental solutions were obtained by
evaporating an aliquot of the stock solution to make a film that was
dissolved in PBS. These were used without delay and renewed frequently. This procedure was found to minimize aggregation and adsorption of DP
on glass. The porphyrin solutions were handled in the dark to avoid any
photobleaching.
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FIGURE 2
Structure of deuteroporphyrin (inset).
Fluorescence emission (top) and excitation spectra
(bottom) of 5 × 108 M deuteroporphyrin
in phosphate buffer (dashed line), bound to
107 M LDL (solid line), and to excess (5 × 106 M) HSA (dotted line). Excitation and
emission wavelengths were set at 396 and 625 nm for emission and
excitation spectra, respectively.
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Human low-density lipoproteins (LDL) were purchased from Calbiochem
(San Diego, CA), or were prepared by sequential ultracentrifugation (Havel et al., 1955). The commercial material was conditioned in 0.15 M
NaCl aqueous solution at pH 7.4 with 0.01% EDTA. The protein content
of LDL solutions that we isolated was determined as described elsewhere
(Peterson, 1977). The integrity of the LDL after storage and after
mixing in the stopped-flow apparatus was assessed by acrylamide (7.5%)
SDS-PAGE electrophoresis and Tris-glycine native agarose gel
electrophoresis (1% agarose, 25 mM Tris base, 192 mM glycine, pH 8.4)
according to protocols described elsewhere (Carr et al., 2000). When
stored at 4°C, the stock solutions were found to be stable for about
one month. Human serum albumin (HSA) essentially fatty acid-free was
purchased from Sigma (St. Louis, MO), and stored at 4°C.
Measurements
Steady-state fluorescence measurements
Emission and excitation fluorescence spectra were recorded at
20°C using a SPEX spectrofluorimeter (Edison, NJ). Recording generally commenced 2 min after the preparation of the solutions under
study. Data were fitted by using the Kaleidagraph software (Synergy
Software, Reading, PA). The Levenberg-Marquard algorithm was used for
nonlinear curve fitting. The Mathcad software (Mathsoft, Inc.,
Cambridge, MA) was used for numerical simulations of porphyrins binding
to LDL.
Kinetic measurements
Measurements were performed at 20°C with the aid of an Applied
Photophysics (Leatherhead, UK) stopped-flow apparatus with mixing time
of 1.2 ms. The mixing ratio was 1:1. The excitation light provided by a
150 W xenon arc lamp was passed through a monochromator with slits
generally set to give a bandwidth of 4.65 nm. Fluorescence emission was
collected above 610 nm using a low-cut filter (Oriel, Palaiseau,
France). The fluorescence signal was fed on a RISC workstation
(Acorn Computers, Cambridge, UK) and analyzed using the software
provided by the manufacturer.
Kinetic models
Interaction of porphyrin with LDL
Experimental results led us to consider two classes of
porphyrins bound to LDL (defined as class P and class L). In a first approximation, we assume that binding of any molecule does not depend
on the state of LDL occupancy. In other words, pseudo-first-order conditions are assumed. Also, the two binding classes are considered to
be independent. Then,
where kaP and kdP
are the association and dissociation rate constants for the class P
sites, kaL and kdL are
those for DP binding to the lipid phase (class L).
PF stands for the free porphyrin in aqueous solution.
The set of differential equations describing the system is:
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(1a)
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(1b)
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(1c)
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where k'aP and
k'aL are apparent association rate
constants as functions of the LDL concentration according to:
The solution can be easily found by using Laplace transforms
(Connors, 1990). With the initial conditions
PF(t=0) = P0 and PL(t=0) = PP(t=0) = 0, the system is transformed into:
where s stands for the Laplace transform of the
derivative function, and PP,
PL, and PF for the
Laplace transforms of PP,
PL, and PF.
It follows:
where
The inverse Laplace transforms yield the time dependence of
PF, PL, or
PP concentrations. Biexponential functions with
the same rate constants, k1 and
k2, are obtained for the three species. These
rate constants are the two roots (with sign inversion) of the
polynomial D. The rate constants k1
and k2 (abbreviated k1,2) are:
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(2)
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where
For PF, the Laplace transform method
yields:
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(3)
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where
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(4)
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The amplitudes of these two exponential terms are:
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(5)
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(6)
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A biexponential signal would be expected. However, it reduces to
a monoexponential when kdP 
kdL, an approximation that appears to be valid for the
present system (see Results). Indeed, substituting
k'aP and
k'aL by kaP × [LDL] and kaL × [LDL], and kdP kdL by
kd, we obtain:
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(7)
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![k<SUB>2</SUB>≅(k<SUB><UP>aP</UP></SUB>+k<SUB><UP>aL</UP></SUB>)×[<UP>LDL</UP>]+k<SUB><UP>d</UP></SUB>](/content/vol83/issue6/fulltext/3470/img025.gif)
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(8)
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![A<SUB>1</SUB>≅P<SUB><UP>F</UP>(<UP>t=0</UP>)</SUB>×<FR><NU>(k<SUP><UP>2</UP></SUP><SUB><UP>d</UP></SUB>−2k<SUP><UP>2</UP></SUP><SUB><UP>d</UP></SUB>+k<SUP><UP>2</UP></SUP><SUB><UP>d</UP></SUB>)</NU><DE>k<SUB><UP>d</UP></SUB>×(k<SUB><UP>aP</UP></SUB>+k<SUB><UP>aL</UP></SUB>)×[<UP>LDL</UP>]</DE></FR>](/content/vol83/issue6/fulltext/3470/img026.gif)
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(9)
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![A<SUB>2</SUB>≅<UP>−</UP>P<SUB><UP>F</UP>(<UP>t=0</UP>)</SUB>×<FR><NU>(k<SUB><UP>aP</UP></SUB>+k<SUB><UP>aL</UP></SUB>)×[<UP>LDL</UP>]</NU><DE>k<SUB><UP>d</UP></SUB>+(k<SUB><UP>aP</UP></SUB>+k<SUB><UP>aL</UP></SUB>)×[<UP>LDL</UP>]</DE></FR>](/content/vol83/issue6/fulltext/3470/img027.gif)
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(10)
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However, the numerator of Eq. 9, giving the amplitude
A1, tends to zero. In addition, the presence of
the LDL term only in the denominator further reduces the contribution
of the first exponential at high lipoprotein concentration. The
expressions describing the evolution of PL and
PP have been calculated in the same way. They
also involve the rate constants k1 and
k2, and the amplitude of the first exponential
terms tends to zero under the same conditions. As a consequence, when
kdL and kdP approach one
another, only the second exponential characterized by the rate constant
k2 is observed.
Numerical simulations using the Matcad software were carried out to
estimate the range of validity for this approximation. Biexponential
signals were generated with various
kdL/kdP ratios and LDL
concentrations according to Eqs. 2-6. They were then fitted by a
single exponential, and residuals (signal minus curve fit) normalized
to the total signal amplitude were calculated. When kdL and kdP differ by a
factor of 2.6 (the value obtained from data analysis reported below),
deviation cannot be distinguished from noise for LDL concentrations
equal to or higher than 1 × 108 M (see Results).
When the ratio is 5, deviation starts to be visible for a LDL
concentration equal to 2 × 108 M. A ratio of 10 leads to deviation in the all range of LDL concentrations investigated.
Transfer of porphyrin from LDL to HSA
The transfer of porphyrin from preloaded LDL to HSA was assumed
to occur via the aqueous phase according to the following equilibria:
where k'aH is the
pseudo-first-order association rate constant and
kdH the dissociation rate constant relative to
porphyrin-HSA binding. It was further assumed that under our
experimental conditions, the interactions of the free porphyrin with
LDL and albumin are pseudo-first-order processes. Then, the kinetics of
the transfer process is described by the system of equations:
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(11a)
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(11b)
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(11c)
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(11d)
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The solution of this system involves exponential terms with
complex analytical expressions. However, owing to the large LDL and HSA
concentrations used experimentally, a considerable simplification can
be obtained. Indeed, the rate constants of the association of DP to
albumin or LDL are much larger than the dissociation constants.
Consequently, the steady-state approximation of Bodenstein holds, i.e.,
dPF/dt = 0 (except during a
short initial period). Thus, we can express PF
as a function of PP, PL,
and PH. Moreover, considering that in our
experiments [HSA] 
[LDL], the rate constant of the association
of DP to albumin (k'aH = kaH × [HSA]) is much larger than constants of
the association with LDL. Then,
By using Laplace transforms with the initial conditions
PF(t=0) = PH(t=0) = 0 and PL(t=0) = PL0, PP(t=0) = PP0 and neglecting terms that become small when
[HSA] [LDL], we obtain:
with
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(12)
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The inverse Laplace transforms give the expressions describing
the evolution of PH, PL,
and PP as a function of time. Each expression
consists of the sum of one constant and two exponential terms. The rate
constants k1 and k2 are
the roots (with sign inversion) of Eq. 12 for D = 0.
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(13)
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(14)
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For each of the exponentials noted 1 and 2, the contributions of
the various forms of the porphyrin (noted H, P, L) to the amplitudes
(A) are:
It can be easily shown that the contributions of each form to
the two exponential terms are similar, even when the values of
kdP and kdL are close.
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RESULTS |
Steady-state measurements
Fluorescence spectra
The fluorescence emission spectra of DP in buffer, bound to LDL or
HSA, are shown in Fig. 2. The concentrations of LDL (107
M) or HSA (5 × 106 M) were sufficient to ensure
total porphyrin binding (see equilibrium constants below). The
excitation wavelength was set at 396 nm, the maximum of the excitation
spectrum of DP bound to LDL. The main emission band is shifted from 609 nm in PBS to 621 nm and 623 nm when the porphyrin is bound to LDL and
HSA, respectively. Albumin and LDL do not fluoresce in this spectral
range. As shown in Fig. 2, the emission and excitation spectra appear
to be different enough to easily monitor changes in the porphyrin
environment. A specific peak around 280 nm can be noted in the
excitation spectrum of DP bound to LDL. No fluorescence excitation band
below 300 nm is observed for free deuteroporphyrin.
Upon excitation at 280 nm, LDL displays an intrinsic fluorescence
emission band around 330 nm due to tryptophan residues. As shown in
Fig. 3, there is a significant overlap
between the emission spectrum of LDL and the absorption spectrum of DP.
Then, fluorescence resonance energy transfer (FRET) from tryptophan residues of apoB100 to DP is thus possible. According to
Förster's equation, the efficiency of the transfer varies as the
inverse sixth power of the distance between the two partners and is
therefore strongly distance-dependent. The Förster's distance
that corresponds to half of the energy transferred has been estimated
to be ~1.7 nm for a related porphyrin-tryptophan couple (Moan et al.,
1985). Hence, porphyrin molecules close to tryptophan residues, i.e., bound to apoprotein B100 or at the frontier between the protein and
lipids can be characterized by FRET.
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FIGURE 3
Fluorescence emission spectrum of LDL in the absence of
deuteroporphyrin (excitation 280 nm, left scale) and
absorption spectrum of LDL-bound deuteroporphyrin corrected for LDL
absorption (right scale). The overlap of spectra
demonstrates the feasibility of fluorescence resonance energy transfer
(FRET).
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Quantification of porphyrin binding to LDL by tryptophan
fluorescence quenching
The peak around 280 nm in the excitation spectrum of DP bound to
LDL corresponds to the excitation maximum of tyrosine/tryptophan fluorescence indicating FRET. This gives a clear indication of the
existence of porphyrin sites close to the protein. Concomitantly, as
shown in Fig. 4 A, the
intrinsic fluorescence of apoprotein B100 is quenched upon binding of
porphyrin in a concentration-dependent way. This first class of sites
will be denoted as class P, hereafter. A linear relation between FRET
efficiency and the number of porphyrins bound to LDL is not expected,
however. Indeed, for each binding site, the efficiency will depend on
the distance and relative orientation of the porphyrin and the nearest
tryptophan residues. Hence, we used the method developed by Nishida
(Halfman and Nishida, 1972) as follows. By definition, for any LDL
concentration,
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(15)
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where 
is the number of porphyrin molecules bound per LDL
molecule and PT the total porphyrin
concentration. The Nishida method is based on the existence of pairs of
PT and LDL concentrations yielding the same
value of . Then, for two pairs noted a and b
it follows from the direct relation between PF
and and from Eq. 15:
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(16)
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![P<SUB><UP>F</UP></SUB>=<FR><NU><UP>LDL<SUB>a</SUB></UP>×<UP>LDL<SUB>b</SUB></UP></NU><DE><UP>LDL<SUB>a</SUB></UP>−<UP>LDL<SUB>b</SUB></UP></DE></FR> [(P<SUB><UP>Tb</UP></SUB>/<UP>LDL<SUB>b</SUB></UP>)−(P<SUB><UP>Ta</UP></SUB>/<UP>LDL<SUB>a</SUB></UP>)]](/content/vol83/issue6/fulltext/3470/img056.gif)
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(17)
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It is further assumed that a value of corresponds to a unique
value of the relative change of a protein property. Here, this property
is the tryptophan fluorescence expressed as the ratio
F/F0, where F and
F0 are the fluorescence intensities in the
presence and absence of DP, respectively. The quenching efficiency was
measured, for two close concentrations of LDL, as a function of the
total DP concentration (Fig. 4 B). The decrease of
F/F0 upon addition of relatively low amounts of
DP indicates the presence of high-affinity sites. Pairs of
PT and LDL concentrations yielding the same
value of F/F0 were selected, and the values of
and PF were derived according to Eqs. 16 and
17. Then, results were plotted according to the Scatchard method:
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(18)
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As shown in Fig. 5, the Scatchard
plot led to the identification of about four sites. The mean intrinsic
affinity per site, Kpi, was found to be 9 × 107 M1. It can be noted that similar
results were obtained with commercial and laboratory-made LDL.
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FIGURE 4
Quenching of LDL intrinsic fluorescence (excitation
wavelength: 280 nm) upon deuteroporphyrin binding. (A)
Fluorescence spectra of LDL (4 × 108 M) as a
function of DP concentration; PT/LDL: 0, 5, 7, 11, 15, 19 in the arrow direction; (B) relative fluorescence
intensity (F/F0, %) at 330 nm vs.
PT/LDL. ( ) [LDL] = 6 × 108 M;
( ) [LDL] = 4 × 108 M. Fluorescence intensities
for PT = 0 (F0) are
normalized to 100%.
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FIGURE 5
Quantification of binding of deuteroporphyrin to LDL
followed by changes of LDL intrinsic fluorescence at 330 nm (excitation
wavelength 280 nm). The Scatchard plot is obtained from data computed
according to the Halfman and Nishida method. The three symbols
correspond to LDL from various origins; (,  ) home-made LDL; ( )
commercial LDL.
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Porphyrin fluorescence changes upon binding to LDL
As shown in Fig. 2, binding of porphyrin to LDL leads to important
fluorescence modifications. The emission spectrum is characteristic of
that for porphyrin in a lipidic environment (Brault et al., 1986;
Kuzelova and Brault, 1994). Preliminary fluorescence studies with
increasing lipoprotein concentrations showed that the binding capacity
of LDL greatly exceeds that of the four sites identified above.
Nevertheless, when the LDL concentration was large enough to bind all
the porphyrin molecules, emission and excitation spectra of DP did not
depend on the ratio DP/LDL. Thus, the fluorescence characteristics of
DP bound to different locations are similar. Overall binding can be
monitored by changes in the porphyrin fluorescence without
distinguishing sites.
In the range of concentrations used, the fluorescence of any solution
is a linear combination of the fluorescence of the individual porphyrin
components at a given wavelength. We considered the porphyrin free in
solution (PF) and the porphyrin bound to LDL (PB) with main peaks at 609 nm and 621 nm,
respectively. We can write for these two wavelengths:
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(19)
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(20)
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The proportionality factors fF,609,
fF,621, fB,609, and
fB,621 were derived from calibration experiments
on free DP and LDL-bound DP (LDL in excess) at the two wavelengths,
respectively. Then, the concentrations PF and
PB were calculated from the above set of linear
equations for any solution of intermediate composition. The number of
porphyrin molecules bound per LDL molecule, , was calculated
accordingly. As shown in Fig. 6, the
Scatchard plot, /PF vs. , thus obtained
shows a marked curvature indicating that more than one class of sites
is involved.
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FIGURE 6
Quantification of binding of deuteroporphyrin to LDL
followed by changes of DP fluorescence at 621 nm (excitation wavelength
396 nm). The curve is computed according to Eq. 22.
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The overall binding capacity of LDL has been estimated by recording the
fluorescence emission spectra of solutions containing a fixed
lipoprotein amount and increasing porphyrin concentrations. Bound and
free DP concentrations were calculated according to Eqs. 19 and 20. The
bound DP concentration increased, reaching a plateau at ~55 porphyrin
molecules per LDL, which corresponds to lipoprotein saturation (data
not shown).
Overall binding scheme
The number of class P sites being limited to about four, other LDL
compartments including the outer phospholipid layer and the inner core
should be involved (class L binding sites). The overall binding would
then be described by:
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(21)
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where KPi,
KLi, nP, and
nL are the intrinsic microscopic affinity
constants and the corresponding number of sites for the P and L
classes, respectively.
In keeping with earlier studies (Beltramini et al., 1987), the second
interaction type would be better viewed as a partition of DP between
the bulk aqueous phase and the lipidic phase of LDL (see Fig. 1). The
above equation can be rewritten using the same formalism but with the
following assumption: the porphyrin can reach a large number of lipidic
"sites" possessing a low intrinsic affinity
(PF × KLi 
1). It
follows that:
We can define a macroscopic affinity constant,
KL = nL × KLi. Then,
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(22)
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Experimental data have been fitted according to Eq. 22 by
nonlinear regression analysis, the overall affinity constant being fixed at 5.8 × 108 M1, in agreement
with results presented below. The values of
KPi, np, and
KL thus derived are given in Table
1. The theoretical fit is shown in Fig. 6
as a Scatchard plot.
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TABLE 1
Values of equilibrium and rate constants of association of
deuteroporphyrin with the low-density lipoproteins
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The association of DP with LDL was also studied by varying the LDL
concentration for a constant porphyrin concentration. Analysis of
fluorescence data according to the method previously used for liposomes
(Brault et al., 1986; Kuzelova and Brault, 1994) led to an overall
association constant of (5.8 ± 1.2) × 108
M1.
Kinetic measurements
Association of deuteroporphyrin and LDL
To follow the association of DP with LDL, different porphyrin
solutions were mixed with a series of LDL solutions in the stopped-flow apparatus and fluorescence changes were recorded versus time. The
porphyrin concentrations were 1 × 108, 5 × 108, and 1 × 107 M, and those of LDL
5 × 109, 1 × 108, 1.5 × 108, 2 × 108, and 3 × 108 M after mixing. The number of porphyrin molecules
bound per LDL at sites of class P and in the lipid moiety after
completion of equilibria have been calculated by using the equilibrium
constants determined above. The values are given in Fig. 7,
A-C.
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FIGURE 7
Stacked column representation of the number of
porphyrins per LDL at equilibrium under various experimental
conditions. The numbers of porphyrins bound to class P sites and
incorporated into the LDL lipid phase are shown in black and grid
areas, respectively. The number of accessible class P sites is
indicated by a dashed line. The overall binding capacity of LDL is
~55 porphyrin molecules. The values have been computed using the
equilibrium constants reported in Table 1.
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A typical fluorescence signal is shown in Fig. 8
A for the more diluted
porphyrin solution. The changes were found to be fairly fast and the
signal nicely fitted by a monoexponential (see Fig. 8 B). No
other change was recorded over seconds in stopped-flow experiments or
over at least 2 h when solutions were mixed manually and
fluorescence recorded by using a conventional spectrofluorimeter. The
signals for the other sets of concentrations were very similar, except
the quality of the monoexponential fit was less for the highest
porphyrin/LDL ratios. At the lower porphyrin concentration, the sites
of class P are far from being saturated. On average, less than one site
among four is occupied. In the same way, the binding capacity of the
lipid phase greatly exceeds the number of bound porphyrins. In these
conditions, the interactions of DP with LDL are considered as
pseudo-first-order processes.
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FIGURE 8
Kinetics of binding of deuteroporphyrin to LDL.
(A) Fluorescence intensity changes recorded upon mixing LDL
(final concentration: 2 × 108 M) with
deuteroporphyrin (1 × 108 M); excitation
wavelength, 405 nm. Signals recorded by using two time scales are
shown. The best monoexponential fit leading to the observed
pseudo-first-order rate constant kobs is
superimposed on the signals. (B) Normalized residuals of the
monoexponential fit of experimental data. (C) Normalized
residuals of the monoexponential fit of a biexponential signal
simulated using the rate constant values given in Table 1.
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According to the theoretical model presented in the previous section,
in the most general case, the evolution of the concentration of
PF, PP, and
PL, should be described by a biexponential under pseudo-first-order conditions. However, when the dissociation rate
constants for the two classes of sites are close
(kdP kdL kd), the amplitude of the slower component vanishes.
Even if these rate constants are not equal, it would be very difficult to distinguish a small slow component from the large fast signal. Numerical simulations (see above section) show that the dissociation rate constants must differ by a factor of at least five to yield significant deviation from monoexponential fit. An example of simulation is given in Fig. 8 C. The rate constants
(kdP = 5.8, kdL = 15) determined by the method of transfer to albumin described below
were used. The relative amplitude of the slow exponential was found to
be only 2.3% of the total. The comparison of the residuals obtained
from the fit of data (Fig. 8 B) and from simulation (Fig. 8
C) clearly shows that the deviation introduced by the monoexponential approximation cannot be distinguished from the experimental noise. Only one exponential is observed experimentally. Thus, results were analyzed to a first approximation as a
pseudo-first-order single process leading to an observed rate constant
kobs that corresponds to
k2 in our theoretical model.
Data shown in Fig. 9 are well-fitted by
straight lines according to,
![k<SUP><UP>obs</UP></SUP>=k<SUP><UP>obs</UP></SUP><SUB><UP>a</UP></SUB>×[<UP>LDL</UP>]+k<SUP><UP>obs</UP></SUP><SUB><UP>d</UP></SUB>](/content/vol83/issue6/fulltext/3470/img063.gif)
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(23)
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Although all the values of kobs are
depicted on the plot, only those corresponding to <10% of overall
site occupancy were retained for the linear fit to obey
pseudo-first-order approximation. The apparent association rate
constant k
was found to be fairly
independent on experimental conditions, with a value of
k = (4.65 ± 0.10) × 109 M1 s1. The intercept of the
linear fit, k
, ranges between 9 and 21 s1. The highest value was found for the highest porphyrin
concentration, i.e., when the number of molecules incorporated into the
lipid phase greatly exceeds that of porphyrins bound to class P sites (see Fig. 7, A-C). This suggests that
kdL might be somewhat larger than
kdP.
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FIGURE 9
Plot of the observed pseudo-first-order rate constant
(kobs) versus LDL concentration. The porphyrin
concentrations are () 1 × 108 M, () 5 × 108 M, and ( ) 1 × 107 M.
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Transfer of deuteroporphyrin from LDL to albumin
To better approximate the values of kdP and
kdL, the transfer of the porphyrin from
preloaded LDL to albumin in excess was investigated. In previous
studies, this approach was found to be quite efficient to determine
exit rate constants of porphyrins from liposomes (Kuzelova and Brault,
1994; Maman and Brault, 1998).
According to our theoretical model, the transfer from LDL would be
described by two exponentials under two limiting conditions. First, the
concentration of LDL must be sufficient to bind most of the porphyrin
molecules. Second, a complete porphyrin transfer must be ensured by
using albumin in large excess (k'aH = kaH × [HSA]
k'aP,
k'aL). Then, the exponential factors give
kdL and kdP directly.
Remarkably, the amplitudes of the two exponentials are of the same
order of magnitude, contrary to observations for the direct interaction
of the porphyrin with LDL. Thus, fitting is greatly facilitated.
Experimentally, solutions of porphyrin were first incubated with LDL
for 2 h at room temperature. The repartition of porphyrins molecules between the two binding classes is indicated in Fig. 7
D. They were then mixed in the stopped-flow apparatus with
solutions of albumin in large excess (104 M after
mixing). The transfer was followed by fluorescence (see Fig. 2 for
spectra) with the excitation wavelength set at 396 nm, to yield the
largest signal. A typical trace is shown in Fig. 10
A. Clearly, the signal is
better fitted by two exponentials with almost equal amplitudes, as
predicted by our model (see Fig. 10, B and C). As
expected from the spectra shown in Fig. 2, when excitation was set at
410 nm the fluorescence increased, but the rate constants and the
relative amplitudes of the two phases remained unchanged. Rate
constants of ~5 s1 and ~15 s1 were
obtained from the fits. On the basis of the results for the interaction
of DP with LDL described above, the lower value was assigned to
kdP.
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FIGURE 10
Kinetics of the transfer of deuteroporphyrin from LDL
to HSA. (A) Fluorescence intensity changes recorded upon
mixing LDL preloaded with porphyrin and HSA. Final concentrations:
DP = 1.5 × 107 M; LDL = 2 × 108 M; HSA = 1 × 104 M. Excitation wavelength 396 nm. (B) Residuals from the best
monoexponential fit. The sum of the squared differences between
experimental data and the curve fit ( 2) is 0.093339. (C) Residual from the best biexponential fit.
2 is reduced to 0.078282. (D) Fluorescence
intensity changes recorded over longer time.
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The dissociation rate constants being known, it is possible to
calculate the association rate constants from the equilibrium constants
derived independently from the Scatchard plots, assuming that
K = ka/kd. Values of
the rate constants are summarized in Table 1.
As shown in Fig. 10 D, a slower phase with a rate constant
around 0.1 s1 was also detected. Its direction was always
opposite to that of the main signal, whatever the excitation
wavelength. The inversion of the signal was observed at the same
excitation wavelength (around 406 nm) for the fast and the slow phases.
However, the amplitude of the slow phase never exceeded ~10% of the
total signal.
To further sustain the above models and the approximations made to
analyze data, the kinetics of the interactions of the porphyrin with
LDL and the kinetics of the transfer of the porphyrin from LDL to
albumin were simulated by using the Mathcad mathematical software. The
program involves the original sets of differential equations 1a-c and
11a-d without any assumptions and does not presuppose
pseudo-first-order conditions. The rate constants for albumin were
taken as kaH = 6.75 × 107
M1 s1 and kdH = 3.5 s1 (Kuzelova and Brault, 1994). The known initial
concentrations and estimates for the rate constants
kaP, kaL,
kdP, and kdL were entered into
the program. The simulated curves were fitted by exponentials in the
same way as experimental data. The values of the rate constants
kaP, kaL,
kdP, and kdL were adjusted so that the exponential factors obtained from the fit of experimental traces and simulated curves were the same. The values of
kaP, kaL,
kdP, and kdL that were retained
allowed adequate simulations of all the kinetics, including the
transfer to albumin. These values were found to be similar to those
given in Table 1. The validity of the approximations made and the fact
that kdL is higher than
kdP were confirmed. However, simulations did not
predict a third slow phase. Thus, the aqueous phase transfer model
accounts for the fast steps but does not explain the slower step. That will be discussed below.
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DISCUSSION |
TOP
ABSTRACT
INTRODUCTION
![±<RAD><RCD>(&Sgr;k)<SUP>2</SUP>−4×(k<SUB><UP>dP</UP></SUB>×k<SUB><UP>dL</UP></SUB>+k<UP>′<SUB>aL</SUB></UP>×k<SUB><UP>dP</UP></SUB>+k<UP>′<SUB>aP</SUB></UP>×k<SUB><UP>dL</UP></SUB>)</RCD></RAD>]](/content/vol83/issue6/fulltext/3470/img018.gif)
