Sensing Temperature in Vitro and in Cells Using a BODIPY Molecular Probe

Article abstract of DOI:10.1021/acs.jpcb.9b04384

Boron dipyrromethene (BODIPY) molecular rotors have shown sensitivity toward viscosity, polarity, and temperature. Here, we report a 1,3,5,7-tetramethyl-8-phenyl-BODIPY modified with a polyethylene glycol (PEG) chain, for temperature sensing and live cell

Full text of DOI:10.1021/acs.jpcb.9b04384

Article
pubs.acs.org/JPCB
Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX
Sensing Temperature in Vitro and in Cells Using a BODIPY Molecular
Probe
Meredith M. Ogle,† Ashleigh D. Smith McWilliams,† Matthew J. Ware,⊥ Steven A. Curley,⊥,#
Stuart J. Corr,⊥,‡,∇,¶ and Angel A. Martí*,†,‡,§
‡
§
†Department of Chemistry, Department of Bioengineering, and Department of Materials Science and Nanoengineering, Rice
University, 6100 Main St MS60, Houston, Texas 77005, United States
⊥Department of Surgery, Baylor College of Medicine, Houston, Texas 77030, United States
#Department of Surgery, CHRISTUS Trinity Mother Frances, 800 E. Dawson, Tyler, Texas 75701, United States
∇Department of Biomedical Engineering, University of Houston, Houston, Texas 77204, United States
¶School of Medicine, Swansea University, Swansea, Wales SA2 8PP, U.K.
S
* Supporting Information
ABSTRACT: Boron dipyrromethene (BODIPY) molecular rotors have shown sensitivity
toward viscosity, polarity, and temperature. Here, we report a 1,3,5,7-tetramethyl-8-phenyl-
BODIPY modified with a polyethylene glycol (PEG) chain, for temperature sensing and live
cell imaging. This new PEG-BODIPY dye presents an increase in nonradiative decay as
temperature increases, which directly influences its lifetime. This change in lifetime is
dependent on changes in both temperature and viscosity at low viscosity values, but is only
dependent on temperature at high viscosity values. The dependence of fluorescence lifetime
with temperature allows for temperature monitoring in vitro and in cells, with sub degree
resolution. When in contact with cells, the PEG-BODIPY spontaneously penetrates and stains
the cell but not the nucleus. Furthermore, no significant cell toxicity was found even at 100
μM concentration. Using fluorescence lifetime imaging microscopy (FLIM), we were able to
observe the changes in the lifetime of PEG-BODIPY within the cell at different temperatures.
The use of FLIM and molecular probes such as PEG-BODIPY can provide important information about cellular temperature
and heat dissipation upon medically relevant stimuli, such as radiofrequency ablation and photodynamic therapy.
each cell.1,2,4,6 The ratiometric approach self-calibrates and also
INTRODUCTION
■
allows for quick measurement; however, these are often
Changes in temperature provide some of the most basic signs
of energy and work. Methodologies for measuring temperature
at the macroscopic scale are well developed and understood,
with probes including analog thermometers (based on liquid
polymers that are also affected by pH and ionic strength7 and
have large dimensions1,8,11,20 which could affect their internal-
ization, diffusion, and function in cells. The advantage of using
lifetime as the temperature indicator is that the values
expansion), thermocouples, strips, thermal imaging cameras,
calculated are independent of concentration and photo-
and infrared probes. Nonetheless, measuring the temperature
bleaching (because bleached molecules simply will not be
of microscopic objects such as cells, with dimensions of just a
measured). Current research leaves room for improvement
few micrometers, is a complicated challenge. In the past 10
with small dynamic ranges,1,11,16,17 pH sensitivity,1,7 or low
years, work toward fluorescent nanothermometers has
exploded as researchers find ways to measure the temperature
inside microscopic reactors, cells, and living organisms. The
thermal resolution.2,10,17,20 Furthermore, most cellular ther-
mometers are based on nanoparticles and polymers; with
limited research in molecular thermometers which to date have
ability to measure temperature with high spatial and temporal
shown low photostability,2,18,21 large uncertainties,21 and small
resolution would increase our understanding of microreactions,
pathologies, and advance effective therapies at the cellular level.
Three of the most studied approaches to designing a
range of temperature tested within cells2,18,21,22 and have not
taken full advantage of lifetime detection.
Boron-dipyrromethene (BODIPY)-based dyes have been
fluorescent nanothermometer are changes in emission
intensity,1−5 ratiometric fluorescence,6−15 and changes in
used profusely as biological dyes because of their modularity,
photostability, and biocompatibility.23−27 It is well known that
the placement of a phenyl ring on the BODIPY core (meso- or
lifetime.16,17 Each method has its advantages and disadvantages
including photobleaching,18 sensitivity to pH1,19 or ionic
strength, and concentration dependence. Using changes in
emission intensity allows for rapid measurements, but each
experiment must be calibrated with a baseline and is greatly
affected by photobleaching and the concentration of probe in
Received: May 8, 2019
Revised: July 24, 2019
© XXXX American Chemical Society
A
DOI: 10.1021/acs.jpcb.9b04384
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The Journal of Physical Chemistry B
Article
8 position) allows for rotation and quenching of fluores-
cence.28−30 When the phenyl group is free to rotate, these
molecular rotors have been shown to be sensitive to viscosity,
polarity, and temperature.31−37 In this paper, we discuss the
design and synthesis of a polyethylene glycol (PEG)-BODIPY
dye that bears methyl groups on the 1 and 7 positions
modulating the free rotation of the phenyl group. We found
that the fluorescence from these BODIPY sensors displays
negative correlation toward changes in temperature and that
this effect is independent of viscosity at moderately high
viscosity values. They are also permeable to cells, are
biocompatible, and can be used to measure the internal
temperature of cells using fluorescence lifetime imaging
microscopy (FLIM).
BODIPY and copper powder (100 mg, 1.57 mmol) were
dissolved in 80 mL of 3:1 THF/H2O and purged with N2 for
30 min. In a separate vial, CuSO4·H2O (70 mg, 0.28 mmol)
and sodium ascorbate (140 mg, 0.71 mmol) were dissolved in
20 mL of 3:1 THF/H2O. The cupric sulfate mixture was
purged with N2 and sonicated for 20 min. Azido-PEG5-alcohol
(150 mg, 0.57 mmol) was added to the acetylene−BODIPY
mixture via a syringe. Then, the cupric sulfate mixture was
transferred by cannula to the acetylene−BODIPY mixture and
heated to 70 °C for 6 h. After cooling to room temperature, the
solvent was extracted with ethyl acetate and washed with water.
The combined organic fractions were dried over Na2SO4, and
the solvent was removed under reduced pressure. The dark red
solid was purified on a silica column with 20−0% hexanes in
ethyl acetate (Rf: 0.12 in 20% hexanes/EtOAc) and a
subsequent alumina column with 0−3% methanol in ethyl
acetate (Rf: 0.61 in 2% MeOH/EtOAc). Yield 101.2 mg, 0.165
mmol, 29%. Spectra shown in Supplemental Information
Figures S1 and S2. 1H NMR (500 Hz, CDCl3): δ 8.13 (s, 2H)
8.00 (dd, 2H, J = 6.5, 2.0) 7.34 (dd, 2H, J = 6.3, 2.0) 5.98 (s,
2H) 4.63 (t, 2H, J = 5.0) 3.93 (t, 2H, J = 5.0) 3.64−3.70 (m,
14H) 3.57−3.63 (m, 2H) 2.55 (s, 6H) 1.44 (s, 6H). 13C NMR
(500 Hz, CDCl3): δ 155.8, 147.1, 143.3, 141.6, 134.8, 131.8,
131.6, 128.8, 126.5, 121.7, 121.5, 72.72, 70.78, 70.75, 70.71,
70.69, 70.43, 69.75, 61.07, 60.61, 50.62, 14.84, 14.81. ESI mass
spec. calcd for C31H41BF2N5O5 [M + H]+, 612.32; found,
612.3469.
EXPERIMENTAL SECTION
■
General. All reagents are commercially available. UV-Vis
spectra were taken on a Shimadzu UV-2450. Steady-state
fluorescence spectra were measured on a HORIBA Jobin Yvon
Fluorolog 3. Time-correlated single photon counting (TC-
SPC) bulk experiments were performed on an Edinburgh OB
920 with 444 nm pulsed laser diode. Samples were heated with
an Eppendorf water circulator. Flow cytometry measurements
were taken on a BD Canto II. Colocalization images were
taken on a Zeiss LSR780 confocal microscope and processed
using ImageJ.
Synthesis of PEG-BODIPY. p-Iodophenyl BODIPY. The
synthesis of 1,3,5,7-tetramethyl-4,4′-difluoro-4-bora-8-(p-iodo-
phenyl)-3a,4a-diaza-s-indacene was adapted from a previous
publication.38 p-Iodobenzoyl chloride (1.32 g, 4.95 mmol) was
dissolved in 50 mL of dry dichloroethane and purged with N2.
Freshly distilled 2,4-dimethylpyrrole (1 mL, 9.6 mmol) was
added via a syringe and refluxed for 13 h. The reaction was
cooled to room temperature, and 3.5 mL of triethylamine was
added via a syringe. The mixture was stirred for 10 min, then
boron trifluoride etherate (5.1 mL, 41 mmol) was added and
refluxed for 2 h. The reaction was then cooled, and the solvent
was removed under reduced pressure. An orange solid was
purified through a silica column (1−3% EtOAc/hexanes).
Quantum Yield. The quantum yield of PEG-BODIPY was
measured in water (φ = 0.28) at room temperature (23 °C)
using fluorescein (φ = 0.95)39 as a standard. The fluorescence
intensity was then measured at different temperatures, and
using the assumption that the absorbance did not change
significantly over the same temperature range, the quantum
yield at each temperature was calculated. The radiative decay
constant (kr) was calculated from the lifetimes measured across
the same temperature range using eq 1.
ϕ
τ
kr =
(1)
1
Yield 0.64 g, 1.4 mmol, 29%. H NMR (400 MHz, CDCl3): δ
The nonradiative decay constant (knr) was then calculated
for each temperature using eq 2 and the kr from eq 1.
7.88 (d, 2H, J = 8.0 Hz) 7.04 (d, 2H, J = 8.0 Hz) 6.05 (s, 2H)
2.57 (s, 6H) 1.44 (s, 6H).
kr
TMSacetylene-BODIPY. p-Iodophenyl BODIPY (640 mg,
1.4 mmol), Pd(PPh3)2Cl2 (49 mg, 0.07 mmol), and CuI (27
mg, 0.14 mmol) were dissolved in a mixture of 20 mL of
tetrahydrofuran (THF) and 10 mL of triethylamine under N2.
Trimethylsilylacetylene (0.3 mL, 2.1 mmol) was added via a
syringe, and the reaction was stirred at room temperature for
12 h. The solvent was removed under reduced pressure, and
the residue was purified through a silica column [20%
dichloromethane (DCM)/hexanes] to produce a red-orange
ϕ =
kr + knr
(2)
Resolution. The resolution of lifetime versus temperature
curves were calculated as previously reported16 using eq 3
where ∂T/∂τ represents the inverse of the tangential slope and
δτ represents the error of the lifetime determination given by
the reconvolution fit, unless stated otherwise.
i∂T y
j
j
j
z
z
z
1
δT =
δτ
solid. Yield 434 mg, 1.02 mmol, 73%. H NMR (400 MHz,
(3)
∂τ
k
{
CDCl3): δ 7.60 (d, 2H, J = 8.4 Hz) 7.24 (d, 2H, J = 8.4) 5.98
(s, 2H) 2.55 (s, 6H) 1.39 (s, 6H) 0.29 (s, 9H).
Cell Culture. Cells were maintained at 37 °C in 5% CO2
environment. Panc-1 cells were grown in Dulbecco’s modified
Eagle media (DMEM) supplemented with 10% fetal bovine
serum (FBS) and 1% penicillin and streptomycin. HPNE cells
were grown in 3:1 DMEM (low glucose)/M3Base, supple-
mented with 5% FBS, EGF, and puromycin.
PEG-BODIPY. TMSacetylene-BODIPY (434 mg, 1.02
mmol) was dissolved in 50 mL of 1:1 MeOH/THF under
N2. Potassium carbonate (280 mg, 2.03 mmol) was added, and
the mixture was stirred at room temperature for 1 h. The
reaction was quenched with 50 mL of 15% aqueous NH4Cl
and extracted with DCM. The organic fractions were
combined and dried over MgSO4, and the solvent was
removed under reduced pressure. The red solid was used
without further purification. The deprotected acetylene-
Biocompatibility. Cells were plated at 1.0 × 105 cells/mL
in a 12-well plate and allowed to adhere overnight. Cells were
stained with PEG-BODIPY in growth media (10, 50, 100, 200,
300, and 500 μM) for 2 h and rinsed with phosphate-buffered
B
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Article
Scheme 1. Synthesis of PEG-BODIPY
saline (PBS). Fresh growth media were replenished, and cells
were incubated for 24 or 48 h. Controls were killed with heat
shock by placing cells in an oven at 70 °C for 10 min and
allowed to recover for 1 h. All cells were then collected and
stained according to the Invitrogen Annexin V/PI staining kit.
Flow-assisted cell sorting measuring the PEG-BODIPY
(λex:488 nm, λem: 530/30 nm), annexin V AF647 (λex:633
nm, λem:660/20 nm), and propidium iodide (λex:561 nm,
λem:610/20 nm) was run until 10 000 events were recorded.
Gating was set to exclude debris and aggregates.
reported here, the alkyne group is directly attached to the
benzyl group in BODIPY, which is a straight forward way of
obtaining this functionalization.
PEG-BODIPY has an absorbance peak at 498 nm and a
fluorescence maximum at 511 nm in water, which is consistent
with other BODIPY derivatives (Figure 1a).29 We first probed
Dye Colocalization. Cells were plated on glass cover slips
at 1.0 × 105 cells/mL, stained with 200 μM PEG-BODIPY in
growth medium, and incubated for 2 h. Cells were stained with
either MitoTracker Orange, LysoTrack DR 99, ERTracker
BPY-TR, or Phalloidin Alexa Fluor 555, according to
Invitrogen protocols. Cells were then mounted using ProLong
Gold AntiFade with DAPI. Cells were imaged using a 63× oil
immersion objective.
FLIM Temperature Measurements. Cells were plated at
1.0 × 105 cells/mL on Bioptech Delta T plates and allowed to
adhere overnight. Cells were incubated with PEG-BODIPY in
growth media for 2 h (Panc-1 100 μM and HPNE 200 μM).
Then, cells were rinsed with PBS, and plates were replenished
with medium without phenol red. FLIM images were obtained
on a Nikon A1 confocal with PicoQuant TimeHarp 300
attachment, and microscope plates were heated using a
Bioptech Delta T system. FLIM images were processed using
SymPhoTime software. A background threshold of 1000
photons/pixel was fixed, and each decay was fit to a
biexponential decay.
Figure 1. (a) Normalized absorbance (black), excitation (blue
dashed), and fluorescence (red) spectra from PEG-BODIPY in
water. (b) Steady-state emission intensity of PEG-BODIPY as a
function of temperature in water (23−49 °C). (Inset) Plot of
integrated intensity vs temperature. (c) PEG-BODIPY temperature-
dependent lifetime in water (23−49 °C). λexc = 444 nm λem = 515 nm.
(d) PEG-BODIPY in water shows reproducible lifetime measure-
ments upon heating (red) and cooling (blue). The average resolution
is 0.4 °C, calculated from eq 3 using the standard deviation from three
different experiments. (Inset) Five cycles of heating and cooling, blue
line shows average lifetime at 25 °C (2.70 ns) and red line show
average lifetime at 50 °C (1.72 ns).
RESULTS
■
The 1,3,5,7-tetramethyl-4,4′-difluoro-4-bora-8-(4-triazol-1-
pentaethylene-glycol)-3a,4a-diaza-s-indacene (PEG-BODIPY)
was synthesized in a five step process, purified using silica and
alumina column chromatography, and confirmed with NMR
(Scheme 1, and Figures S1-S2).38 The last step of the synthesis
is a convenient copper click reaction, which could easily be
modified to add a specific functionality; in this case, a PEG
group was chosen for water solubility and cell permeability.
Other groups have previously reported PEG-BODIPY
conjugates, particularly through ether linkages40 or succini-
midyl esters.41,42 Uppal et al.43 attached a PEG group to a
BODIPY dye using click chemistry; however, this procedure
involved attaching the alkyne group through an ether
functionality to the benzyl rotor in BODIPY. In the approach
the dependence of the fluorescence intensity of PEG-BODIPY
on changes in temperature and observed that the fluorescence
intensity decreases with increasing temperature from 23 to 49
°C (Figure 1b). In addition, we examined the fluorescence
lifetime over the same range of temperatures. In aqueous
solution, the probe shows a monoexponential lifetime which is
negatively correlated with temperature. Over the 26 °C
temperature range, we see a decrease in the PEG-BODIPY
lifetime of ca. 40% (Figure 1c). In the biologically relevant
range, we observed that temperature could be obtained from
changes in PEG-BODIPY lifetime with a resolution of 0.4 °C
(Figure 1d). The temperature response is reproducible, giving
equal responses in heating and cooling cycles (Figure 1d
C
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inset). Control studies show that PEG-BODIPY lifetime is not
greatly affected by pH or ionic strength (Figure S3). These
results show that the PEG-BODIPY could be used as a
molecular thermometer, by correlating its fluorescence lifetime
with temperature. It is important to note that many 8-phenyl
substituted BODIPY molecular rotors are used as viscosity
probes, and thus, the effect of viscosity on the lifetime cannot
be ignored (see below).31,32,34−36,44
viscosity by studying PEG-BODIPY in water−glycerol
mixtures (Figure 3a). As expected, the PEG-BODIPY lifetime
The decrease of fluorescence intensity and lifetime has been
attributed to the rotation of the phenyl group at the 8 position
of BODIPY, and methyl groups were strategically placed at
positions 1 and 7 to hinder the free rotation of the phenyl ring.
Methyl groups in these positions are known to produce an
increase in fluorescence quantum yield.45,46 The increase in
temperature increases the probability for PEG-BODIPY to
explore the excited-state energy surface and find a channel for
nonradiative relaxation, increasing the rate of nonradiative
decay, therefore, decreasing the fluorescence intensity and
shortening the lifetime. To study this, we obtained the
quantum yield and lifetime of PEG-BODIPY at multiple
temperatures (Figure 2), between 23 and 49 °C, and used
Figure 3. (a) Isothermal plot of lifetime as a function viscosity in
water−glycerol mixtures at 22 °C. (b) Log−log plot of the region
from 0.96 to 14.6 cP in Figure 3a. The slope of the graph represents
the value of α in eq 4 and is 0.28.
increases with viscosity up to 14.6 cP, with saturation in
lifetime being reached at ca. 41.1 cP and further. The
dependence of lifetime on viscosity can be evaluated by
determining the parameter α in eq 4 from the slope of a log−
log plot of Figure 3b, which is 0.28 for the viscosity-dependent
region (from 0.94 to 14.6 cP) and virtually zero above 41.1 cP.
Interestingly, similar observations have been made for the
orientational correlation times of different dyes in water−
glycerol mixtures.49 This is explained as a change in the
boundary conditions from a stick to a slip boundary at high
viscosities, which leads to the formation of cavities.49,50 At high
viscosities, the cavity achieves a limiting rigidity that does not
change with further changes in viscosities, and thus, the
lifetime becomes independent of viscosity. Furthermore, it is
expected that the rotational friction coefficient (on a partial slip
boundary condition) also displays a saturation effect with
viscosity.47 Because we know α and the dependence of
viscosity of water with temperature by using Korson et al.
equation51
Figure 2. Quantum yield (black squares), kr (open blue circles), and
knr (blue circles) of PEG-BODIPY in water at different temperatures.
them to calculate the radiative and nonradiative decay rate
constants. Figure 2 shows the increase in the nonradiative
decay constant with temperature, while the radiative decay
constant remains unchanged. This is consistent with an
increase in the rotational freedom of the 8-phenyl and a
consequent increase in nonradiative deactivation pathways as
temperature increases.
As we mentioned before, changes in temperature are also
accompanied by changes in the viscosity of the solvent, which
is expected to influence the lifetime. While this would not
prevent using lifetime as a way to determine temperature, it is
important to analyze the interrelation between temperature,
viscosity, and lifetime. The shape of the curve of lifetime versus
temperature in Figure 1d can be understood in terms of knr by
eq 447,48
A(20 − T) − B(T − 20)2
T + C
η
η20
t
log
=
(6)
where T is the temperature in celsius, A = 1.1709, B =
0.001827, C = 89.20, and η20 = 1.0020, we fit the data in Figure
1d to an expression from the combination of eqs 4, 5 and 6
−1
i
j
y
z
v
j
j
z
z
z
a
j
τ = k +
e− E /R(T+273)
j
z
r
2
j
j
z
z
(η2010A(20−T)−B(T−20) /T+C α
)
k
{
(7)
resulting in a value of the internal barrier for rotation of 14 kJ/
mol (see curve in Figure 1d). The good fit of eq 7 to the data
in Figure 1d indicates that the shape of the lifetime versus
temperature curve in the low-viscosity regime is modulated by
both changes in temperature and viscosity as dictated by eq 4.
Given the dependence of the PEG-BODIPY lifetime with
viscosity, we decided to examine the dependence of lifetime
with temperature at different viscosity values (in water−
glycerol mixtures), and the results are shown in Figures 4 and
S4. Two things are evident from Figure 4: First, as previously
noted in Figure 3, the lifetime is essentially independent of
viscosity at values larger than 41.1 cP. Second, the graphs of
temperature versus viscosity are curved downward in contrast
with the behavior of the probe in pure water. While we do not
completely understand this discrepancy, it is likely that other
factors come into play at high viscosities that affect the excited
v
a
knr
=
e− E /RT
ηα
(4)
where Ea is the barrier for internal rotation, R is the gas
constant, T is the temperature, η is the viscosity of the
medium, v is the limiting pressure exerted on the rotor, and α
is associated with the frictional forces between the rotor and
solvent. The measured lifetime is related to knr by
1
τ =
kr + knr
(5)
Changes in temperature cause concurrent changes in
viscosity, and both parameters affect knr in eq 4. On the
other hand, we can study the isothermal behavior of τ with
D
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(Figure 5b), but at 48 h, that dropped considerably to 84%
viability (Figure 5d). Staining was kept to 100 μM for the rest
of the experiments because the Panc-1 cell line maintained a
92% viability after 48 h.
We also studied the localization of PEG-BODIPY within
cells. We stained cells with PEG-BODIPY, and either
MitoTracker Orange, LysoTracker DR 99, ERTracker
BODIPY-TR, or Phalloidin AF 555 and mounted slides with
ProLong Antifade Gold with DAPI. Colocalization measure-
ments were done using the Costes threshold; all values
reported were above the calculated threshold. In both cell lines,
there is punctation of the dye; however, the two cell lines show
opposite colocalization with PEG-BODIPY. Panc-1 cells show
high correlation with LysoTracker (Figure 6a) and moderate
Figure 4. Lifetime of PEG-BODIPY in water−glycerol mixtures at
different temperatures. The water−glycerol mixture viscosities at
different temperatures are plotted in one of the axes as obtained by
Cheng.53,54
state potential energy surface and then the dependence of the
excited state relaxation to the ground state with increasing
temperature. For example, it has been proposed that at high
viscosities internal conversion mechanisms play an important
role in the excited state deactivation.30,52 Thus, further
theoretical research on the behavior of molecular rotors at
high viscosity environments would be beneficial.
The reliable lifetime response of PEG-BODIPY to temper-
ature changes and its independence at high viscosities indicates
that it could be used as a molecular thermometer, particularly
for microscopic applications such as determination of cellular
temperature. To these means, we first studied the toxicity of
PEG-BODIPY in cancerous (Panc-1) and nonmalignant
(HPNE) cell lines. The dosing time was first determined for
each cell line based on fluorescence intensity per cell after
incubation with 200 μM PEG-BODIPY in growth media (2 h
optimum). Both cell lines can uptake the dye, and viability was
studied by an annexin V/propidium iodide apoptosis assay
(Figure 5) with raw data reported in the Supporting
Information (Tables S1 and S2 and Figures S5 and S6).
HPNE cells maintained a 95% viability after being exposed to
PEG-BODIPY for 24 h at a 500 μM (Figure 5a) concentration
with viability reducing to 90% after 48 h (not particularly
different from control cells: 93%) (Figure 5c). The Panc-1 cell
line had a 93% viability at 24 h with a concentration of 200 μM
Figure 6. Colocalization studies of Panc-1 (a) and HPNE (b,c) cell
lines. All scale bars at 50 μm.
correlation with MitoTracker and ERTracker but no
correlation with Phalloidin (actin filaments) (Figure S7). On
the other hand, HPNE cells show moderate correlation with
ERTracker (Figure 6c) and no correlation with LysoTracker
(Figure 6b), MitoTraker, or Phalloidin (Figure S8). We do
note that there are differences in PEG-BODIPY staining of
cells treated with Phalloidin than in the other tests. This is due
to the procedure required for Phalloidin staining, where cells
must be permeabilized, which likely leads to leaching of the
PEG-BODIPY from the cells. From these studies, we conclude
that the PEG-BODIPY dye is either encapsulated within
lysosomes or the membranes of mitochondria and the
endoplasmic reticulum depending on the kind of cell, but
there is still some nonspecific binding throughout the cells
(probably nonspecific binding to membranes). However, it is
never seen localizing in the nucleus of live cells. Nuclear
exclusion is common for BODIPY derivatives, even for those
modified with a nuclear targeting moiety.55
FLIM of cells stained with PEG-BODIPY was performed
using a Nikon A1 microscope with a PicoQuant TC-SPC
attachment. In contrast with experiments in aqueous solution
and cell extract, the decay curves did not fit a single
exponential decay law. The FLIM experiments showed
biexponential lifetimes, which is expected because PEG-
BODIPY can be found in different environments throughout
the cell. To measure lifetime at different temperatures, a heated
stage temperature controller was used. While both cell lines
show a decrease in lifetime with temperature the initial values
for different cell lines differ slightly. This is again expected
given that cell types have varied microenvironments, for
Figure 5. Viability data from FACS Annexin V/PI assay of HPNE
(a,c) and Panc-1 (b,d) at 24 (a,b) and 48 (c,d) h after incubation.
The blue lines show the percentage of cells that fully retained the
PEG-BODIPY dye at time of assay. Positive controls were killed by
heat shock and had 1.1−6.6% viability (Tables S1 and S2 and Figures
S5 and S6).
E
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example, different polarities (see Figure S9) and biomolecules
present. It was also noted that one of the deconvoluted
components was longer than what was reported for PEG-
BODIPY in water. We believe that the multiexponential
lifetime is due to the noncovalent binding of PEG-BODIPY to
proteins and different membranes. This will increase the
relative rigidity of the environment around PEG-BODIPY
displaying an increased lifetime. The short component lifetime
(which is also the component of lowest abundance) is
consistent with a low viscosity environment, although it is
also possible that it is due to PEG-BODIPY being quenched in
certain compartments of the cell or by certain amino acids in
proteins. While it would be reasonable to think that the decay
is a combination of multiple exponential decays, a
biexponential fit is enough to fit the data.
The exposure of the dye to different environments would
explain the different lifetimes (Figure S9). To assess the
interaction of PEG-BODIPY with proteins, it was dissolved in
growth media containing FBS, and the lifetime was measured
at various temperatures. The PEG-BODIPY interacts with
many proteins in the serum and gives a biexponential decay
and broadening of the emission spectra, which is consistent
with the FLIM data (Figure S10). Furthermore, BODIPY dyes
are known to aggregate; thus, we measured the lifetime of
PEG-BODIPY in water at different concentrations. Figure S11
shows monoexponential lifetimes of ca. 2.9 ns for all
concentrations from 1 to 500 μM. Figure 7a shows FLIM
shape and range of change in lifetime of the observations in
high viscosity water−glycerol mixtures (Figures 4 and S4).
This is of importance given that we have shown PEG-BODIPY
displays lifetime independence of viscosity at high viscosity
values, as should be expected when attached to a variety of
biomolecules, lipids, membranes, and proteins in cells. While
we expect the viscosity inside the cell changes with
temperature, we do not expect it to become lower than 41.1
cP, which is the limit at which the lifetime of the PEG-
BODIPY dye starts reacting to viscosity again. Therefore, it can
be concluded that the particular dependence of the PEG-
BODIPY lifetime in cells is due to temperature and
independent of changes in viscosity due to its interactions
with viscous cellular components as seen in Figures 4 and 7.
This observation also has implications in understanding the
fate of dyes that are internalized in cells and their potential
binding to proteins and membranes.
CONCLUSIONS
■
In conclusion, we have synthesized a modular BODIPY probe
that can sense temperature through changes in the non-
radiative decay rate constant. The steric hindrance of the 1,7-
methyl groups restrict the rotation of the 8-phenyl group,
which increases the lifetime and quantum yield of PEG-
BODIPY and prevents its sensitivity to viscosity at large
viscosity values. The temperature responses measured with
lifetime, steady state, and quantum yield are consistent with
accepted mechanisms for molecular rotors. We show
reproducible lifetime measurements upon heating and cooling
and only slight variations with pH or ionic strength. PEG-
BODIPY is readily water soluble, incorporated by cells, and
nontoxic at high concentrations (100 μM). Although there is
no nuclear uptake of PEG-BODIPY, there is diffuse staining in
the cytosol and the ER in multiple cells lines. FLIM images of
HPNE cells stained with PEG-BODIPY show biexponential
decays that decrease with temperature. We show live cell
imaging results that are consistent with the bulk solution
experiments, although the dependence of the fluorescence
lifetime with temperature is different from that in aqueous
solution. This is likely due to the interaction of PEG-BODIPY
with membranes and biomolecules as demonstrated by
experiments using growth medium with serum. PEG-BODIPY
is a fully functional live cell fluorescent nanothermometer that
can be used across multiple cell lines; however, it is
recommended that for every new cell line used, a calibration
curve be made. PEG-BODIPY could be used in studying heat
shock response, metabolism, and hyperthermia therapies.
While PEG-BODIPY has a PEG chain that makes it water
soluble, this could be modified to target a specific organelle or
cell line. The versatility of the copper click reaction would
allow the BODIPY compound to be tagged to a specific
protein and probe specific cells or areas within a cell. In
addition, we noticed that while PEG-BODIPY is not as
sensitive to viscosity (at high viscosity values) as other
BODIPY probes, it is still affected by its microenvironment.
Nanoencapsulation of PEG-BODIPY would allow it to sense
temperature without being affected by changes in the cellular
environment or from it binding to cellular components such as
proteins. Current work is focused on isolating BODIPY
derivatives from the cellular matrix to achieve a more uniform
thermal response in all cells.
Figure 7. (a) FLIM images of an HPNE cell stained with PEG-
BODIPY false colored with scale 4.6 ns (blue) to 5.2 ns (red). Scale
bar 40 μm. (b) Lifetime decays of the cell. (c) Plot of the long lifetime
component vs temperature showing a quadratic dependence with
temperature (red curve). Quadratic fit: τ = 5.23 − 0.009T −
0.00041T2. R2 = 0.999. Black curve represents the experimental
resolution in degrees (right axis).
images of the long lifetime component of an HPNE cell. The
lifetime dependence with temperature can be fit to a quadratic
function, which allows the determination of the temperature
resolution for each point. As can be seen in Figure 7c, the
resolution increases with temperature (down to 0.17 °C),
allowing appropriate temperature determination. Similar
results were obtained for Panc-1 cells (Figure S12). The
fitting data for HPNE and Panc-1 cells at different temper-
atures is presented in Tables S4 and S5.
It is important to note that the quadratic (downward)
dependence of lifetime with temperature in cells is in contrast
with the behavior observed in water and buffer solution.
Nonetheless, the dependence of the lifetime with temperature
of PEG-BODIPY in growth medium also displays a quadratic
downward behavior that is consistent with the FLIM images
(Figure S10b). More importantly, this behavior mimics in
F
DOI: 10.1021/acs.jpcb.9b04384
J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B
Article
Association between the Excited States of 4-(N,N-Dimethylamino)-
benzonitrile and β-Cyclodextrin. Anal. Chem. 1998, 70, 3974−3977.
(11) Pietsch, C.; Vollrath, A.; Hoogenboom, R.; Schubert, U. S. A
Fluorescent Thermometer Based on a Pyrene-Labeled Thermores-
ponsive Polymer. Sensors 2010, 10, 7979−7990.
ASSOCIATED CONTENT
* Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.jpcb.9b04384.
■
S
(12) Brandao-Silva, A. C.; Gomes, M. A.; Macedo, Z. S.; Avila, J. F.
̃
NMR spectra of PEG-BODIPY, temperature depend-
ence of PEG-BODIPY lifetime with temperature at
different pH and ionic strengths, variation of PEG-
BODIPY lifetime with viscosity, flow cytometry experi-
ments, colocalization images, lifetime dependence of
PEG-BODIPY in DMEM, and FLIM images of Panc-1
cells at different temperatures (PDF)
M.; Rodrigues, J. J., Jr.; Alencar, M. A. R. C. Multiwavelength
Fluorescence Intensity Ratio Nanothermometry: High Sensitivity over
a Broad Temperature Range. J. Phys. Chem. C 2018, 122, 20459−
20468.
(13) Xu, M.; Zou, X.; Su, Q.; Yuan, W.; Cao, C.; Wang, Q.; Zhu, X.;
Feng, W.; Li, F. Ratiometric Nanothermometer in Vivo Based on
Triplet Sensitized Upconversion. Nat. Commun. 2018, 9, 2698.
(14) Xu, F.; Ba, Z.; Zheng, Y.; Wang, Y.; Hu, M.; Xu, X.; Wang, J.;
Zhang, Z. Rare-Earth-Doped Optical Nanothermometer in Visible
and near-Infrared Regions. J. Mater. Sci. 2018, 53, 15107−15117.
AUTHOR INFORMATION
Corresponding Author
*E-mail: amarti@rice.edu.
ORCID
Angel A. Martí: 0000-0003-0837-9855
Notes
The authors declare no competing financial interest.
■
́
(15) Quintanilla, M.; Zhang, Y.; Liz-Marzan, L. M. Subtissue
Plasmonic Heating Monitared with CaF2:Nd3+,Y3+ Nanothermom-
eters in the Second Biological Window. Chem. Mater. 2018, 30,
2819−2828.
(16) Okabe, K.; Inada, N.; Gota, C.; Harada, Y.; Funatsu, T.;
Uchiyama, S. Intracellular Temperature Mapping with a Fluorescent
Polymeric Thermometer and Fluorescence Lifetime Imaging Micros-
copy. Nat. Commun. 2012, 3, 705.
ACKNOWLEDGMENTS
(17) Donner, J. S.; Thompson, S. A.; Kreuzer, M. P.; Baffou, G.;
Quidant, R. Mapping Intracellular Temperature Using Green
Fluorescent Protein. Nano Lett. 2012, 12, 2107−2111.
(18) Arai, S.; Lee, S.-C.; Zhai, D.; Suzuki, M.; Chang, Y. T. A
Molecular Fluorescent Probe for Targeted Visualization of Temper-
ature at the Endoplasmic Reticulum. Sci. Rep. 2015, 4, 6701.
(19) Khattab, T. A.; Tiu, B. D. B.; Adas, S.; Bunge, S. D.; Advincula,
R. C. Solvatochromic, Thermochromic and pH-Sensory DCDHF-
Hydrazone Molecular Switch: Response to Alkaline Analytes. RSC
Adv. 2016, 6, 102296−102305.
(20) Takei, Y.; Arai, S.; Murata, A.; Takabayashi, M.; Oyama, K.;
Ishiwata, S. i.; Takeoka, S.; Suzuki, M. A Nanoparticle-Based
Ratiometric and Self-Calibrated Fluorescent Thermometer for Single
Living Cells. ACS Nano 2014, 8, 198−206.
(21) Homma, M.; Takei, Y.; Murata, A.; Inoue, T.; Takeoka, S. A
Ratiometric Fluorescent Molecular Probe for Visualization of
Mitochondrial Temperature in Living Cells. Chem. Commun. 2015,
51, 6194−6197.
(22) Huang, Z.; Li, N.; Zhang, X.; Wang, C.; Xiao, Y. Fixable
Molecular Thermometer for Real-Time Visualization and Quantifica-
tion of Mitochondrial Temperature. Anal. Chem. 2018, 90, 13953−
13959.
(23) Loudet, A.; Burgess, K. BODIPY Dyes and Their Derivatives:
Syntheses and Spectroscopic Properties. Chem. Rev. 2007, 107, 4891−
4932.
(24) Benniston, A. C.; Copley, G. Lighting the Way Ahead with
Boron Dipyrromethene (Bodipy) Dyes. Phys. Chem. Chem. Phys.
2009, 11, 4124.
(25) Kowada, T.; Maeda, H.; Kikuchi, K. BODIPY-Based Probes for
the Fluorescence Imaging of Biomolecules in Living Cells. Chem. Soc.
Rev. 2015, 44, 4953.
(26) Kue, C. S.; Ng, S. Y.; Voon, S. H.; Kamkaew, A.; Chung, L. Y.;
Kiew, L. V.; Lee, H. B. Recent Strategies to Improve Boron
Dipyrromethene (BODIPY) for Photodynamic Cancer Therapy: An
Updated Review. Photochem. Photobiol. Sci. 2018, 17, 1691−1708.
(27) Sunahara, H.; Urano, Y.; Kojima, H.; Nagano, T. Design and
Synthesis of a Library of BODIPY-Based Environmental Polarity
Sensors Utilizing Photoinduced Electron-Transfer-Controlled Fluo-
rescence ON/OFF Switching. J. Am. Chem. Soc. 2007, 129, 5597−
5604.
(28) Li, F.; Yang, S. I.; Ciringh, Y.; Seth, J.; Martin, C. H.; Singh, D.
L.; Kim, D.; Birge, R. R.; Bocian, D. F.; Lindsey, D.; et al. Design,
Synthesis, and Photodynamics of Light-Harvesting Arrays Comprised
of a Porphyrin and One, Two, or Eight Boron-Dipyrrin Accessory
Pigments. J. Am. Chem. Soc. 1998, 120, 10001−10017.
■
This project was funded by the Dunn Collaborative Research
Grant Program. This project was supported by the Optical
Imaging and Vital Microscopy Core at the Baylor College of
Medicine with the assistance of Jason Kirk and the Cytometry
and Cell Sorting Core at Baylor College of Medicine with
funding from the NIH (CA125123 and RR024574) and the
expert assistance of Joel M. Sederstrom.
REFERENCES
■
(1) Su, S.; Wei, J.; Zhang, K.; Qiu, J.; Wang, S. Thermo- and pH-
Responsive Fluorescence Behaviors of Sulfur-Functionalized Deto-
nation Nanodiamond-Poly(N-Isopropylacrylamide). Colloid Polym.
Sci. 2015, 293, 1299−1305.
(2) Arai, S.; Suzuki, M.; Park, S.-J.; Yoo, J. S.; Wang, L.; Kang, N.-Y.;
Ha, H.-H.; Chang, Y.-T. Mitochondria-Targeted Fluorescent
Thermometer Monitors Intracellular Temperature Gradient. Chem.
Commun. 2015, 51, 8044−8047.
(3) Mirenda, M.; Levi, V.; Bossi, M. L.; Bruno, L.; Bordoni, A. V.;
Regazzoni, A. E.; Wolosiuk, A. Temperature Response of
Luminescent Tris(Bipyridine)Ruthenium(II)-Doped Silica Nano-
particles. J. Colloid Interface Sci. 2013, 392, 96−101.
(4) Ke, G.; Wang, C.; Ge, Y.; Zheng, N.; Zhu, Z.; Yang, C. J. l-DNA
Molecular Beacon: A Safe, Stable, and Accurate Intracellular Nano-
thermometer for Temperature Sensing in Living Cells. J. Am. Chem.
Soc. 2012, 134, 18908−18911.
(5) Sadhanala, H. K.; Senapati, S.; Nanda, K. K. Temperature
Sensing Using Sulfur-Doped Carbon Nanoparticles. Carbon 2018,
133, 200−208.
(6) Jonstrup, A. T.; Fredsøe, J.; Andersen, A. H. DNA Hairpins as
Temperature Switches, Thermometers and Ionic Detectors. Sensors
2013, 13, 5937−5944.
(7) Hu, J.; Zhang, X.; Wang, D.; Hu, X.; Liu, T.; Zhang, G.; Liu, S.
Ultrasensitive Ratiometric Fluorescent pH and Temperature Probes
Constructed from Dye-Labeled Thermoresponsive Double Hydro-
philic Block Copolymers. J. Mater. Chem. 2011, 21, 19030.
(8) Liu, J.; Guo, X.; Hu, R.; Xu, J.; Wang, S.; Li, S.; Li, Y.; Yang, G.
Intracellular Fluorescent Temperature Probe Based on Triarylboron
Substituted Poly N-Isopropylacrylamide and Energy Transfer. Anal.
Chem. 2015, 87, 3694−3698.
(9) Dong, J.; Zink, J. I. Taking the Temperature of the Interiors of
Magnetically Heated Nanoparticles. ACS Nano 2014, 8, 5199−5207.
(10) Figueroa, I. D.; el Baraka, M.; Quinones, E.; Rosario, O.;
̃
́
Deumie, M. A Fluorescent Temperature Probe Based on the
G
DOI: 10.1021/acs.jpcb.9b04384
J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B
Article
(29) Kee, H. L.; Kirmaier, C.; Yu, L.; Thamyongkit, P.; Youngblood,
W. J.; Calder, M. E.; Ramos, L.; Noll, B. C.; Bocian, D. F.; Scheidt, W.
R.; et al. Structural Control of the Photodynamics of Boron−Dipyrrin
Complexes. J. Phys. Chem. B 2005, 109, 20433−20443.
(30) Alamiry, M. A. H.; Benniston, A. C.; Copley, G.; Elliott, K. J.;
Harriman, A.; Stewart, B.; Zhi, Y.-G. A Molecular Rotor Based on an
Unhindered Boron Dipyrromethene (Bodipy) Dye. Chem. Mater.
2008, 20, 4024−4032.
(49) Megens, M.; Sprik, R.; Wegdam, G. H.; Lagendijk, A.
Orientational Relaxation Times of Rhodamine 700 in Glycerol-
Water Mixtures. J. Chem. Phys. 1997, 107, 493.
(50) Rice, S. A.; Kenney-Wallace, G. A. Time-Resolved Fluorescence
Depolarization Studies of Rotational Relaxation in Viscous Media.
Chem. Phys. 1980, 47, 161−170.
(51) Korson, L.; Drost-Hansen, W.; Millero, F. J. Viscosity of Water
at Various Temperatures. J. Phys. Chem. 1969, 73, 34−39.
(52) Velsko, S. P.; Fleming, G. R. Solvent Influence on Photo-
chemical Isomerizations: Photophysics of DODCI. Chem. Phys. 1982,
65, 59−70.
(53) Cheng, N.-S. Formula for the Viscosity of a Glycerol−Water
Mixture. Ind. Eng. Chem. Res. 2008, 47, 3285−3288.
(54) Westbrook, C. Calculate density and viscosity of glycerol/water
mixtures. http://www.met.reading.ac.uk/~sws04cdw/viscosity_calc.
html (accessed Apr 22, 2019).
(55) Edelson, B. S.; Best, T. P.; Olenyuk, B.; Nickols, N. G.; Doss, R.
M.; Foister, S.; Heckel, A.; Dervan, P. B. Influence of Structural
Variation on Nuclear Localization of DNA-Binding Polyamide-
Fluorophore Conjugates. Nucleic Acids Res. 2004, 32, 2802−2818.
(31) Kuimova, M. K.; Yahioglu, G.; Levitt, J. A.; Suhling, K.
Molecular Rotor Measures Viscosity of Live Cells via Fluorescence
Lifetime Imaging. J. Am. Chem. Soc. 2008, 130, 6672−6673.
(32) Kuimova, M. K. Mapping Viscosity in Cells Using Molecular
Rotors. Phys. Chem. Chem. Phys. 2012, 14, 12671−12686.
́
(33) Lopez-Duarte, I.; Vu, T. T.; Izquierdo, M. A.; Bull, J. A.;
Kuimova, M. K. A Molecular Rotor for Measuring Viscosity in Plasma
Membranes of Live Cells. Chem. Commun. 2014, 50, 5282−5284.
̌
(34) Vysniauskas, A.; Qurashi, M.; Gallop, N.; Balaz, M.; Anderson,
H. L.; Kuimova, M. K. Unravelling the Effect of Temperature on
Viscosity-Sensitive Fluorescent Molecular Rotors †. Chem. Sci. 2015,
6, 5773.
́
(35) Vu, T. T.; Meallet-Renault, R.; Clavier, G.; Trofimov, B. A.;
Kuimova, M. K. Tuning BODIPY Molecular Rotors into the Red:
Sensitivity to Viscosity vs. Temperature. J. Mater. Chem. C 2016, 4,
2828−2833.
̌
́
(36) Vysniauskas, A.; Lopez-Duarte, I.; Duchemin, N.; Vu, T.-T.;
̃
Wu, Y.; Budynina, E. M.; Volkova, Y. A.; Pena Cabrera, E.; Ramírez-
Ornelas, D. E.; Kuimova, M. K. Exploring Viscosity, Polarity and
Temperature Sensitivity of BODIPY-Based Molecular Rotors. Phys.
Chem. Chem. Phys. 2017, 19, 25252.
́
́
́
(37) Chambers, J. E.; Kubankova, M.; Huber, R. G.; Lopez-Duarte,
I.; Avezov, E.; Bond, P. J.; Marciniak, S. J.; Kuimova, M. K. An Optical
Technique for Mapping Microviscosity Dynamics in Cellular
Organelles. ACS Nano 2018, 12, 4398−4407.
́
(38) García-Lopez, V.; Chu, P.-L. E.; Chiang, P.-T.; Sun, J.; Martí, A.
A.; Tour, J. M. Synthesis of a Light-Driven Motorized Nanocar. Asian
J. Org. Chem. 2015, 4, 1308−1314.
(39) Lakowicz, J. R. Principles of Fluorescence Spectroscopy, 2nd ed.;
Kluwer Academic/Plenum Publishers: New York, 1999.
(40) Zhu, S.; Zhang, J.; Vegesna, G.; Luo, F.-T.; Green, S. A.; Liu, H.
Highly Water-Soluble Neutral BODIPY Dyes with Controllable
Fluorescence Quantum Yields. Org. Lett. 2011, 13, 438−441.
(41) Ruan, Z.; Zhao, Y.; Yuan, P.; Liu, L.; Wang, Y.; Yan, L. PEG
Conjugated BODIPY-Br
as Macro-Photosensitizer for Efficient
2
Imaging-Guided Photodynamic Therapy. J. Mater. Chem. B 2018, 6,
753−762.
(42) Nepomnyashchii, A. B.; Pistner, A. J.; Bard, A. J.; Rosenthal, J.
Synthesis, Photophysics, Electrochemistry and Electrogenerated
Chemiluminescence of PEG-Modified BODIPY Dyes in Organic
and Aqueous Solutions. J. Phys. Chem. C 2013, 117, 5599−5609.
(43) Uppal, T.; Bhupathiraju, N. V. S. D. K.; Vicente, M. G. H.
Synthesis and cellular properties of Near-IR BODIPY-PEG and
carbohydrate conjugates. Tetrahedron 2013, 69, 4687−4693.
(44) Suhina, T.; Amirjalayer, S.; Woutersen, S.; Bonn, D.; Brouwer,
A. M. Ultrafast Dynamics and Solvent-Dependent Deactivation
Kinetics of BODIPY Molecular Rotors. Phys. Chem. Chem. Phys.
2017, 19, 19998−20007.
(45) Baki, C. N.; Akkaya, E. U. Boradiazaindacene-Appended
Calix[4]Arene: Fluorescence Sensing of pH Near Neutrality. J. Org.
Chem. 2001, 66, 1512−1513.
(46) Yamada, K.; Toyota, T.; Takakura, K.; Ishimaru, M.; Sugawara,
T. Preparation of BODIPY Probes for Multicolor Fluorescence
Imaging Studies of Membrane Dynamics. New J. Chem. 2001, 25,
667−669.
(47) Velsko, S. P.; Waldeck, D. H.; Fleming, G. R. Breakdown of
Kramers Theory Description of Photochemical Isomerization and the
Possible Involvement of Frequency Dependent Friction. J. Chem.
Phys. 1983, 78, 249−258.
(48) Bagchi, B. Isomerization Dynamics in Solution. Int. Rev. Phys.
Chem. 1987, 6, 1−33.
H
DOI: 10.1021/acs.jpcb.9b04384
J. Phys. Chem. B XXXX, XXX, XXX−XXX