Phosphorescence Kinetics of Singlet Oxygen Produced byPhotosensitization in Spherical Nanoparticles. Part II. The Case ofHypericin-Loaded Low-Density Lipoprotein ParticlesShubhashis Datta,† Andrej Hovan,‡ Annamaria Jutkova,‡ Sergei G. Kruglik,§ Daniel Jancura,†,‡

Pavol Miskovsky,†,‡ and Gregor Bano*,†,‡

†Center for Interdisciplinary Biosciences, Technology and Innovation Park, and ‡Department of Biophysics, Faculty of Science, P. J.Safarik University, Jesenna 5, 041 54 Kosice, Slovak Republic§Laboratoire Jean Perrin, Sorbonne Universites, UPMC Univ. Paris 6, CNRS UMR 8237, 4 place Jussieu, 75005 Paris, France

*S Supporting Information

ABSTRACT: The phosphorescence kinetics of singlet oxygenproduced by photosensitized hypericin (Hyp) molecules insidelow-density lipoprotein (LDL) particles was studied exper-imentally and by means of numerical and analytical modeling.The phosphorescence signal was measured after short laserpulse irradiation of aqueous Hyp/LDL solutions. The Hyptriplet state lifetime determined by a laser flash-photolysismeasurement was 5.3 × 10−6 s. The numerical and theanalytical model described in part I of the present work (DOI:10.1021/acs.jpcb.8b00658) were used to analyze the observedphosphorescence kinetics of singlet oxygen. It was shown thatsinglet oxygen diffuses out of LDL particles on a time scaleshorter than 0.1 μs. The total (integrated) concentration ofsinglet oxygen inside LDL is more than an order of magnitude smaller than the total singlet oxygen concentration in the solvent.The time course of singlet oxygen concentrations inside and outside the particles was calculated using simplified representationsof the LDL internal structure. The experimental phosphorescence data were fitted by a linear combination of theseconcentrations using the emission factor E (the ratio of the radiative singlet oxygen depopulation rate constants inside andoutside LDL) as a fitting parameter. The emission factor was determined to be E = 6.7 ± 2.5. Control measurements were carriedout by adding sodium azide, a strong singlet oxygen quencher, to the solution.

■ INTRODUCTION

Photodynamic therapy (PDT) utilizes highly reactive oxygenspecies (mostly singlet oxygen) to induce cell death incancerous tissues.1−4 During the (type-II) photodynamicaction, singlet oxygen is produced by energy transfer fromphotoexcited photosensitizer molecules to molecular oxygen.The presence of singlet oxygen either in solutions or inside cellscan be detected through its phosphorescence emission at1270 nm.5−8

Various nanocarrier systems are investigated extensively tofacilitate targeted transport of photosensitizer molecules in thehost body.9 Production of singlet oxygen inside nanoparticles isusually studied through time-resolved phosphorescence meas-urements. The phosphorescence kinetics of singlet oxygenproduced in nanoparticle solutions following short (nano orsub-nanosecond range) laser pulses is affected by the diffusionof singlet oxygen in the heterogeneous environment. Because ofthis fact, as it was shown by several authors,10−12 special caremust be taken when interpreting the experimental phosphor-escence kinetics data. The lifetime of singlet oxygen inside theparticles may differ from that in the particle exterior, that is, in

the surrounding solvent. Moreover, the rate of singlet oxygenradiative deactivation depends on the local environment. Tocalculate the time course of the overall phosphorescenceintensity detected in a time-resolved experiment, the amount ofsinglet oxygen both inside and outside the particles needs to beknown. Two theoretical models (a numerical and an analyticalone) describing the phosphorescence kinetics of singlet oxygenproduced in nanoparticles were presented in part I of this work(DOI: 10.1021/acs.jpcb.8b00658). The second part is focusedon a particular application of the presented models. Namely,the numerical simulation procedure is used to explain theexperimentally observed time course of singlet oxygenphosphorescence measured after irradiation of hypericin-loadedlow-density lipoprotein (LDL) particles. Besides that, a set ofLDL-related parametersto be used in the analytical modelis derived, too.

Received: January 19, 2018Revised: April 30, 2018Published: April 30, 2018

Article

pubs.acs.org/JPCBCite This: J. Phys. Chem. B 2018, 122, 5154−5160

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Hypericin (Hyp) is a natural photosensitizer extracted fromthe plants of the genus Hypericum. The possibilities of Hyp-based PDT have been summarized in several reviewarticles.13−17 Hyp forms biologically inactive nonfluorescentaggregates in water.18,19 By contrast, Hyp has a high affinity tolipid membrane structures, where it is primarily dissolved in themonomer (fluorescent), biologically active form.20−24 Only themonomer form of Hyp can produce singlet oxygen.25

LDL particles were used previously as a carrier of severalanticancer drugs.26−28 The interaction of Hyp with LDL wasinvestigated in our previous studies.25,29−33 It was shown thatHyp is dissolved as a monomer in LDL particles up to a Hyp/LDL concentration ratio of 30:1.31 Higher concentrations ofHyp inside the LDL particles lead to Hyp aggregation anddynamic self-quenching of Hyp fluorescence. Phosphorescencestudies of singlet oxygen produced by photosensitized Hypinside LDL particles were published.25 These earlier resultsobtained with Hyp/LDL complexes are updated and completedin this work by laser flash-photolysis measurements of tripletstate Hyp lifetimes. To get a better insight into thephosphorescence kinetics of singlet oxygen present in theparticle interior and exterior, the measurements were carriedout also in the presence of sodium azide, a strong singletoxygen quencher that is preferentially localized in the aqueousphase. The numerical model helped us to shed light on thedetails of the observed singlet oxygen phosphorescencekinetics. The analytical description, when combined with theLDL-related modeling parameters presented in this work, canbe used for fast analysis of other LDL-based systems in aqueoussolutions.

■ EXPERIMENTAL METHODSDimethyl sulfoxide (DMSO) [high-performance liquid chro-matography (HPLC), ≥99%] and hypericin (HPLC, ≥95%)were purchased from Sigma-Aldrich, Germany. LDL (SDS-PAGE, ≥95%) was purchased from Calbiochem, USA. A stocksolution of 2.0 × 10−3 M Hyp in DMSO was prepared. Hyp-loaded LDL particles were prepared in PBS buffer (pH = 7.4),setting the Hyp/LDL ratio to 30:1. The concentration of Hypin the sample was 4.0 × 10−6 M. The percentage of DMSO inthe solution did not exceed 1%. The samples prepared withsodium azide contained 10 mM of the quencher.The laser excitation system consisted of a pulsed OPO

(GWU basiScan-M) pumped with the third harmonic of aNd:YAG laser (Spectra-Physics, Quanta-Ray, INDI-HG-10S).The repetition rate of the 5−7 ns long laser pulses was set to10 Hz. The OPO wavelength was tuned to 598 nm, matchingthe absorption maximum of Hyp. The sample (2.5 mL) wasplaced in a 10 × 10 × 40 mm quartz cuvette equipped with anoverhead-type glass stirrer and was kept at room temperature(ca. 298 K). To minimize sample bleaching, the average laserpower was set to approximately 0.15 mW. The singlet oxygenphosphorescence signal passed through a 1250−1300 nm band-pass filter and was detected with a photomultiplier tube(Hamamatsu H10330A-75) operated in a photon countingmode. The time course of the phosphorescence was acquiredwith a multichannel scaler PCI card (Becker&Hickl, MSA-300).Typically, the signal of 30 000 laser pulses was integrated ateach experimental condition. To suppress the backgroundsignal originating from the optical components and the possiblephosphorescence of Hyp, the emission signal was measuredwith two additional band-pass filters in the 1200−1250 nm andthe 1300−1350 nm spectral range. It was assumed that the

background signal (as detected by the present setup) hadslowly varying wavelength dependence in the covered spectralrange. The time course of singlet oxygen phosphorescence wascalculated by subtracting the average of the two auxiliarymeasurements (acquired in the adjacent spectral regions) fromthe signal measured in the 1250−1300 nm range. This way thebackground phosphorescence was efficiently suppressed.The optical setup was equipped with an additional 532 nm

CW laser (Cobolt, Samba) used to monitor the Hyp tripletstate lifetime in a flash-photolysis experiment.34,35 The laserbeam was passing through the sample area excited with thepulsed laser. The polarization of the cw laser was oriented atthe magic angle with respect to the excitation beampolarization. Time-resolved absorption (at 532 nm) wasmeasured with an avalanche photodiode (Thorlabs,APD110A2) connected to a digitizing oscilloscope (Tektronix,DPO 7254).

■ THEORETICAL METHODSNumerical Model. The numerical model employed to

simulate the concentration [Δ] of singlet oxygen produced byphotosensitized Hyp-loaded LDL particles was described inpart I of this work (DOI: 10.1021/acs.jpcb.8b00658). Shortly,the spatio-temporal distribution of singlet oxygen wascalculated by solving the diffusion equation complementedwith the source and depletion terms for singlet oxygen

τ∂ Δ

∂= ∇ Δ + − Δ − Δ

ΔtD S k

[ ]([ ])

[ ][azide][ ]2

q(1)

D and τΔ are the singlet oxygen diffusion coefficient andlifetime, respectively, and S is the production rate of singletoxygen. The last term in eq 1 stands for singlet oxygenquenching by sodium azide, where kq is the quenching rateconstant. The abovementioned equation was solved numeri-cally on a radial grid of equal spacing. The details of thenumerical scheme are given in part I of the present paper(DOI: 10.1021/acs.jpcb.8b00658).The internal structure of LDL particles is depicted in Figure

1. LDL consists of a hydrophobic core predominantly formed

of cholesteryl esters and triglycerides and an outer layer ofphospholipids, cholesterol, and the ApoB-100 protein.36 Theapplied numerical model was derived for spherically symmetricparticles because of which a simplified LDL representation wasintroduced in the simulations. The particles were divided intotwo concentric regions, the core and the ApoB-100 protein-containing (3 nm thick) outer shell,37 assuming a homogeneouslocal environment in both of them (see Figure 1). The outerdiameter of LDL was set to 21 nm. The radial distribution ofsinglet oxygen concentration inside and outside the particle wascalculated as a function of time and was used to predict the

Figure 1. Schematic view of LDL particles and the approximationsused in the numerical and the analytical models.

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time course of the experimental phosphorescence signal. Thetime step used in the simulations was 0.25 × 10−12 s.The lifetime of singlet oxygen is influenced by the

environment through the local unimolecular (pseudo-first-order) rate constants of singlet oxygen radiative and non-radiative deactivation: 1/τΔ = kr + knr. The phosphorescenceemitted by singlet oxygen molecules at a certain position isproportional to the product of the radiative deactivation rateconstant kr and the local concentration of singlet oxygen. Therate constant of the radiative deactivation may be different inthe particle core, the shell, and the surrounding solvent.38,39

The physicochemical mechanisms of singlet oxygen interactionwith the environment and the effect of the environment on thesinglet oxygen radiative (and nonradiative) deactivation rateconstants have been published.40,41 For the sake of simplicity, asingle emission factor E = kr

IN/krsolv was assigned to the entire

LDL particle in the present work, including both the core andshell regions. With this simplification, the phosphorescencesignal P(t) is proportional to the linear combination of the totalamount of singlet oxygen inside and outside the particle (Δtot

IN

and ΔtotOUT) and can be expressed as follows [see eqs 7 and 8 in

part I (DOI: 10.1021/acs.jpcb.8b00658)]:

= Δ + ΔP t A E( ) ( )totIN

totOUT

(2)

A is a proportionality factor, which is specific for the givenexperimental arrangement.There is an indication that Hyp dissolved in LDL particles is

preferentially located close to the particle surface.29,30 Toaccount for this fact, the nonzero source of singlet oxygen wasonly used in the outer shell of the particle. The time course ofthe source term was approximated by an exponential decay asmeasured for the Hyp triplet state concentration in the laserflash-photolysis experiment. As the absolute value of the singletoxygen source term S (see eq 1) is not known, only the relativeconcentration of singlet oxygen is calculated by the model.The three compartments (the core, the shell, and the

solvent) of the simulated system were characterized by theirown set of physical parameters (diffusion coefficients andsinglet oxygen lifetime values). Besides that, partitioning ofsinglet oxygen between the LDL particle and the aqueoussurroundings was taken into account. Only a single effectivepartition coefficient K was assigned to the whole particleinterior. In principle, all the mentioned parameters can bedetermined by fitting the computational results to theexperimental data. However, one needs to be aware of thelimitations of this approach, mostly originating from the quality(signal to noise ratio and time resolution) of the availableexperimental data. The philosophy of the present work was topresent a description of the studied Hyp/LDL system in twosteps. First, the diffusion coefficient, lifetime, and partitioncoefficient values were estimated based on the data available inthe literature, and only the emission factor E was varied to fitthe computational results to the experimental phosphorescencecurve. In the next step, the effect of the assumed modelingparameters on the obtained emission factor was investigated byrunning the simulations with modified parameter sets (see theResults and Discussion section).The chosen primary set of input parameters is shown in

Table 1. Detailed justification of the used diffusion coefficient,singlet oxygen lifetime, and partition coefficient values is givenin the Supporting Information.Analytical Model. The analytical model introduced in

part I of the present work (DOI: 10.1021/acs.jpcb.8b00658)

approximates the nanoparticles by homogeneous spheres.Singlet oxygen is created uniformly in the entire volume ofthe particle. The diffusion of singlet oxygen out of the particle ischaracterized by a single effective diffusion time, τD

eff, which canbe calculated by the semi-empirical formula [see part I (DOI:10.1021/acs.jpcb.8b00658)] when the singlet oxygen diffusioncoefficients DIN and DOUT, the lifetime of singlet oxygen in thesolvent τΔ

IN, the particle radius R, and the partition coefficientbetween the particle interior and exterior K are known. Themodel describes the time course of the singlet oxygenconcentration inside and outside the particle in a formof analytical formulas. The capability of the simplifiedanalytical description to reproduce the numerical results wastested in this work for LDL particles. The followingLDL‑related input parameters were used in the analyticalmodel: DIN = 0.6 × 10−9 m2 s−1, τΔ

IN = 20 × 10−6 s. Theremaining parameters were identical to the ones presented inTable 1. The calculated effective diffusion time τD

eff was 0.066 ×10−6 and 0.053 × 10−6 s for the solvent without and withsodium azide, respectively.

■ RESULTS AND DISCUSSIONThe results of Hyp triplet state transient absorption measure-ments are shown in Figure 2. The intensity of the 532 nm laserbeam detected by the avalanche photodiode (following shortpulse excitation) is shown as a function of time for the Hyp/LDL solutions without sodium azide (Figure 2a) and in thepresence sodium azide (Figure 2b). The signals were fitted withsingle exponential curves. The obtained lifetimes of the Hyp

Table 1. Primary Set of LDL-Related Parameters

D [×10−9 m2 s−1] τΔ [×10−6 s ] τT [×10−6 s ] K

LDL core 0.7 20 3LDL shell 0.49 10 5.3 ± 0.1, 3

5.1 ± 0.1 (withazide)

solvent 2.0 3.5,0.23 (withazide)

Figure 2. Kinetics of hypericin triplet state decay measured by flashphotolysis on Hyp-loaded LDL particles in PBS buffer without (a) andwith (b) sodium azide. The acquired raw data are indicated by theopen symbols. The solid circles represent the smoothed signal. Thesolid lines are single exponential fits to the original data points.

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triplet state were (5.3 ± 0.1) × 10−6 s and (5.1 ± 0.1) × 10−6 sfor the samples without and in the presence of sodium azide,respectively. The shorter Hyp triplet state lifetime measured inthe presence of azide indicates a minor effect of azide on Hypmolecules embedded in LDL particles. This observation can berationalized by the fact that Hyp molecules dissolved in LDLparticles are preferentially located close to the particlesurface.29,30

The numerical simulations were run for the parameter set ofTable 1. The source term S (see eq 1) was set to beproportional to the exponentially decaying Hyp triplet stateconcentration detected in the laser flash-photolysis experiment(Figure 2). The obtained kinetics of singlet oxygen totalconcentration inside and outside the LDL particles, ascalculated by the numerical and the analytical model, areshown in Figure 3. In the case of pure Hyp/LDL solution

without azide (Figure 3a), the calculated total concentration inthe particle exterior is significantly larger than the concentrationinside LDL, except for the very first 100 ns, when singletoxygen is predominantly located in the particle interior (see theinset in Figure 3a). This clearly shows that singlet oxygendiffuses out of LDL very fast. Indeed, the duration of the fastconcentration increase inside the particle (during the first400 ns) is limited by singlet oxygen diffusion out of LDL. Thedifference between the numerical and analytical results is mostpronounced in this initial time period. In the numerical model,the source of singlet oxygen is located close to the particlesurface, which may be the reason for the faster concentrationincrease outside the particle, as compared to the analytical data.The exponential late-time decay of the singlet oxygen

concentration inside the particle is determined by the Hyptriplet state lifetime. The concentration of singlet oxygenoutside the particle reaches its maximum at about 4 μs. Ingeneral, there is a good match between the analytical and

numerical results in the late-time period. It is interesting to notethat because of the short diffusion time, the concentrationkinetics of singlet oxygen in the solvent can be well-fitted by theconventional two-exponential time dependence of singletoxygen kinetics in homogeneous media (not shown), usingthe Hyp triplet state lifetime and the lifetime of singlet oxygenin the solvent. The experimental phosphorescence kinetics,however, contains the contribution from singlet oxygen bothinside and outside the particles.When sodium azide is added to the solution, the kinetics of

the singlet oxygen concentration changes dramatically. As aresult of strong quenching by azide, the calculated maximalconcentration of singlet oxygen in the solvent drops by anorder of magnitude. At the same time, the concentration ofsinglet oxygen inside LDL is not affected considerably (seeFigure 3b, note the different scales in panels a and b). At theseconditions, the late-time decay of singlet oxygen is set, bothoutside and inside the particle, by the Hyp triplet state lifetime.The experimental time course of singlet oxygen phosphor-

escence is shown in Figure 4 for Hyp/LDL solutions in the

absence and presence of sodium azide. The measured data werefitted by eq 2 (starting at 0.5 μs after the laser pulse) using thesinglet oxygen concentrations calculated by the numericalmodel (see Figure 3). The emission factor E was set to differentvalues between 2 and 12, and the sum of squared differences(SSDs) of the measured and calculated data sets was minimizedby tuning the A parameter of eq 2. It is important to note thatthe two curves (with and without azide) were treated in a singlefitting procedure, using the same A parameter for both. TheSSD values obtained by this way are shown in the inset ofFigure 4 as a function of the emission factor E. It can be seenthat E = 6.7 gives the best match of the calculated andmeasured curves. The corresponding theoretical phosphor-escence time courses of singlet oxygen are plotted by blacksolid lines in Figure 4. In general, the kinetics of thephosphorescence signal and the intensity ratio of the twoexperimental curves are well-reproduced by the numericalmodel. It is noted, however, that the reliability of the emissionfactor determined by this way is limited by the quality of the

Figure 3. Kinetics of the singlet oxygen concentration calculated bythe numerical and analytical models for Hyp/LDL solutions withoutsodium azide (a) and in the presence of sodium azide (b). The opensymbols represent the total (integrated) singlet oxygen concentrationin the solvent and inside LDL, as calculated by the numerical model.The parameters of Table 1 were used for the calculations. The resultsof the analytical model are plotted by solid lines. The first 500 nsperiod is zoomed-in in the inset of panel (a).

Figure 4. Experimental phosphorescence kinetics of singlet oxygenproduced by photosensitized Hyp/LDL complexes. The experimentalcurves were fitted by eq 2 using singlet oxygen concentrationscalculated by the numerical model (see Figure 3). Only the amplitudeparameter A was varied during the fitting procedure. The black linesrepresent the theoretical phosphorescence kinetics obtained foremission factor of E = 6.7 that describe the experimental data thebest. Inset: the SSDs between the experimental and theoretical curvesobtained for different emission factors.

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experimental data and the validity of the modeling assumptions.The obtained value of the emission factor E = 6.7 falls betweenthe one reported by the Roder group for phospholipidmembranes11 E = 3.25 ± 0.5 and the value derived for theprotein environment inside myoglobin10 E = 8.1 ± 1.3. This isin agreement with the expectations for the LDL interiorcomposed of lipid and protein components.The effect of the experimental and modeling uncertainties is

analyzed as follows. The time course of the singlet oxygenconcentration (inside and outside LDL, see Figure 3) can bedivided into two parts. First, there is a fast increase of theconcentration inside the particle during the first 400 ns periodafter the laser pulse. This fast increase is set by the diffusiontime of singlet oxygen out of the particle, which in the case ofthe numerical model mostly depends on the diffusioncoefficient values estimated for the LDL core and the LDLshell (Table 1). As already mentioned, the effective diffusiontime of singlet oxygen τD

eff is explicitly included in the analyticalmodel. In the presence of sodium azide, the concentration ofsinglet oxygen reaches its maximum within 1 μs after the laserpulse not only inside but also outside the particle (Figure 3b).This fast concentration increase is reflected in the fast onset ofthe phosphorescence signal which is observed experimentally inthe presence of azide (Figure 4). Detailed comparison betweencalculated and measured phosphorescence kinetics in this initialtime period is hindered by the limited time resolution and thenoise level of the experimental phosphorescence data.The calculated kinetics of singlet oxygen concentration after

the initial 0.5 μs period can be readily correlated with themeasured phosphorescence signal. The time dependence of thesinglet oxygen concentration in this later period is mainlydetermined by the two most reliable parameters included in themodel, the Hyp triplet state lifetime (measured experimentally)and the lifetime of singlet oxygen in the solvent τΔ

OUT = 3.5 ×10−6 s.42 The uncertainty of the LDL-related parameters (Dcore,Dshell, τΔ

core, τΔshell, and K) is higher. These parameters, however,

when changed in a reasonable range (keeping the relations τDeff

≪ τΔOUT < τt), only affect the relative ratio of singlet oxygen

concentrations inside and outside the particle and have littleeffect on the concentration kinetics. As a consequence, andbecause the phosphorescence signal is a linear combination ofsinglet oxygen concentrations inside and outside the particle(eq 2), minor variation of the mentioned modeling parameters(Dcore, Dshell, τΔ

core, τΔshell, and K) does not affect the accuracy by

which the experimental data are reproduced by the model. Onthe other hand, these parameters are important as they have animpact on the emission factor E determined by the fittingprocedure.To gain a better understanding of the modeling results and

to estimate the importance of the individual parameters, thenumerical simulations were run with modified values (one pertime) of the most uncertain input parameters. Namely, thepartition coefficient K was varied between 2 and 4; the lifetimeof singlet oxygen in the shell τΔ

shell was set to the two extremevalues derived for the protein environment, τΔ

shell = 0.24 × 10−6

s, and the lifetime estimated for the lipid regions, τΔshell = 20 ×

10−6 s (for details see the Supporting Information), and finally,the diffusion coefficient of singlet oxygen in the LDL shell Dshellwas arbitrarily reduced and increased by a factor of two. Allthese changes correspond to a reasonable estimate for the rangeof the input parameter uncertainties. The new simulationresults were used to fit the experimental phosphorescencekinetics of singlet oxygen. The obtained sums of squared

differences between the experimental and simulated data areplotted in Figure 5 as a function of the emission factor. It can

be seen that the modification of the selected input parametersresults in a change of the optimal emission factor E for whichthe smallest SSD is obtained. Changing the value of τΔ

shell has aminor effect on the emission factor. However, the decrease ofthe partition coefficient K (from 3 to 2) or the increase of thediffusion coefficient Dshell (from 0.49 × 10−9 to 0.98 × 10−9 m2

s−1) increases the emission factor from E = 6.7 approximatelyto E = 8.5. When these two parameters are changed in theopposite direction (K = 4 or Dshell = 0.24 × 10−9 m2 s−1), theemission factor decreases to about E = 5.0−5.5. At the sametime, the minimal SSD value is almost identical at allconditions. This proves that the experimental data can bereproduced with the same accuracy for different inputparameter sets when the emission factor is tuned properly. Itfollows that on the basis of the present data, it is not possible toreduce the uncertainty of the model inputs, unless the emissionfactor is determined in an independent way (or vice versa).Taking the uncertainty of the input parameters into account, weconclude that the effective emission factor of singlet oxygen inLDL particles falls into the range of E = 6.7 ± 2.5.

■ CONCLUSIONSThe phosphorescence of singlet oxygen produced by photo-sensitized Hyp loaded in LDL particles was measured in a time-resolved experiment using pulsed laser excitation. The acquiredphosphorescence signal of singlet oxygen was analyzed bymeans of the two models presented in part I of the presentwork (DOI: 10.1021/acs.jpcb.8b00658). The kinetics of thesinglet oxygen concentration inside and outside the LDLparticles were calculated numerically (solving the diffusionequation completed with source and depletion terms) andanalytically using the formulas presented in part I (DOI:10.1021/acs.jpcb.8b00658).It was shown by the theoretical analysis that singlet oxygen

diffuses out of LDL very fast (within 0.1 μs) and spends most

Figure 5. SSDs between the experimental and the numerical modelingresults, as calculated for the different parameter sets indicated in thelegend. The solid circles represent the conditions of Table 1 and areidentical to the ones shown in the inset of Figure 4.

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of the time in the surrounding solvent. The total (integrated)concentration of singlet oxygen inside LDL is more than anorder of magnitude smaller than the total (integrated) singletoxygen concentration in the solvent, except for the very first 0.1μs after the excitation pulse. In spite of this fact, the measuredphosphorescence kinetics of singlet oxygen is influenced by theemission originating from the particle interior. Our numericalmodel indicates that the rate constant of radiative singletoxygen depletion is 6.7 times larger in the LDL interior ascompared to the aqueous surroundings. The number ofparameters entering the numerical model is relatively large.Taking the uncertainty of these parameters into account, weconclude that the emission factor (the ratio of the radiativesinglet oxygen depopulation rate constants inside and outsideLDL) falls into the range of E = 6.7 ± 2.5.The singlet oxygen phosphorescence kinetics changes

considerably when sodium azide is added to the solvent. Inthis case, because of the strong quenching of singlet oxygen inthe particle exterior, the total amount of singlet oxygen in thesolvent exceeds that in the particle interior by only 3 times. Thephosphorescence kinetics of singlet oxygen in the presence ofazide is also well-reproduced by the present theoreticaldescription.The numerical and analytical models presented in part I of

this work (DOI: 10.1021/acs.jpcb.8b00658) in combinationwith the parameter set presented for LDL in this part can beused for analysis of singlet oxygen phosphorescence kinetics ofother pts-loaded LDL systems or other pts/nanoparticlecomplexes.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpcb.8b00659.

Justification of the modeling parameters included inTable 1 (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: gregor.bano@upjs.sk. Phone: +421 55 2342253.ORCIDSergei G. Kruglik: 0000-0002-2945-3092Daniel Jancura: 0000-0003-1968-8709Gregor Bano: 0000-0002-8807-2118NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was supported by the APVV-15-0485 grant of theSlovak Ministry of Education and the projects (ITMS codes:26220120040 and 26220120039) of the Operation ProgramResearch and Development funded by the European RegionalDevelopment Fund.

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