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Interfaces: Adsorption, Reactions, Films, Forces, Measurement Techniques, Charge Transfer, Electrochemistry, Electrocatalysis, Energy Production and Storage
Kinetics of Nanoparticle-Membrane Adhesion Mediated by Multivalent Interactions Roberta Lanfranco, Pritam Kumar Jana, Lucia Tunesi, Pietro Cicuta, Bortolo Matteo Mognetti, Lorenzo Di Michele, and Gilles Bruylants Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b02707 • Publication Date (Web): 14 Jan 2019 Downloaded from http://pubs.acs.org on January 14, 2019
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Langmuir
Kinetics of Nanoparticle-Membrane Adhesion Mediated by Multivalent Interactions Roberta Lanfranco,
∗,†,‡
¶
Pritam Kumar Jana,
¶
Bortolo Matteo Mognetti,
†Biological
Lucia Tunesi,
∗,†
Lorenzo Di Michele,
†
Pietro Cicuta,
and Gilles Bruylants
†
∗,‡
and Soft Systems, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
‡Université
libre de Bruxelles (ULB), Engineering of Molecular NanoSystems, 50 av. F.D. Roosevelt, 1050 Brussels, Belgium
¶Université
Libre de Bruxelles (ULB), Interdisciplinary Center for Nonlinear Phenomena
and Complex Systems, Campus Plaine, CP 231, Blvd. du Triomphe, B-1050 Brussels, Belgium E-mail:
[email protected];
[email protected];
[email protected] Abstract
anchored receptors and of the bulk concentration of nanoparticles, and is observed to de-
Multivalent adhesive interactions mediated by a
crease substantially in regimes where the num-
large number of ligands and receptors underpin
ber of available receptors is limited compared
many biological processes, including cell adhe-
to the overall number of ligands. We attribute
sion and the uptake of particles, viruses, para-
such peculiar behaviour to the rapid sequestra-
sites, and nanomedical vectors. In materials sci-
tion of available receptors after initial nanopar-
ence, multivalent interactions between colloidal
ticle adsorption. The experimental trends and
particles have enabled unprecedented control
the proposed interpretation are supported by
over the phase behavior of self-assembled ma-
numerical simulations.
terials.
Theoretical and experimental studies
have pinpointed the relationship between equi-
Introduction
librium states and microscopic system parameters such as ligand-receptor binding strength and their density. In regimes of strong interac-
Adhesive interactions between nanoscale ob-
tions, however, kinetic factors are expected to
jects and lipid membranes are central for a num-
slow down equilibration, and lead to the emer-
ber of biological processes, including cell-cell
gence
communication mediated by extracellular vesi-
of
long-lived
out-of-equilibrium
states
13
viral infection,
46
cles,
self-assembly experiments and the adhesion of
therapeutic and diagnostic nanomedicine, nd-
particles to biological membranes. Here we ex-
ing reliable strategies to control the interaction
perimentally investigate the kinetics of adhe-
between biological membranes and nanoscale
sion of nanoparticles to biomimetic lipid mem-
probes is a key issue.
branes.
Multivalent interactions are produced
diated by specic ligands on the surface of the
by strongly interacting DNA constructs, play-
nano-objects that target specialised receptors
ing the role of both ligands and receptors. The
expressed on the cell membranes. The resulting
rate of nanoparticle adhesion is investigated as
multivalent interactions, mediated by a large
a function of the surface density of membrane-
number of interacting molecular agents, give
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1012
and endocytosis.
79
that may signicantly inuence the outcome of
In
Adhesion is often me-
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Page 2 of 19
rise to complex phase behaviours, which emerge
adopted model system, Large Unilamellar lipid
from the interplay between enthalpic contribu-
Vesicles (LUVs) are targeted by gold nanopar-
tions to individual ligand/receptor interactions
ticles (NPs), and complementary DNA con-
and congurational/combinatorial entropic ef-
structs anchored on both substrates play the
fects.
The (bio)physics of multivalent inter-
role of ligands and receptors, where the latter
actions has been thoroughly characterised both
are able to freely diuse, as in many biologically
experimentally and theoretically, by means of
relevant situations.
analytical and numerical approaches.
1318
15,1822
15,4853
The programmabil-
In
ity and selectivity of Watson-Crick base pairing
the context of materials science, the acquired
ensures accurate control over the bond forma-
understanding enabled the design of colloidal or
tion, enabling a quantitative characterization of
nanoscale units, whose self-assembly behaviour
kinetic eects as a function of dierent param-
can be precisely prescribed.
eters characterizing the ligands, the receptors
2328
In targeted
drug delivery, multivalent interactions can be
and their complexes.
exploited to improve the binding selectivity of
Scattering (DLS), nanoparticle adsorption ki-
vectors, which can be designed to target cell
netics is characterized as a function of the sur-
membranes only if certain receptors are overex-
face density of membrane-anchored DNA recep-
pressed allowing one to discern between healthy
tors as well as the overall bulk concentration of
and diseased cells.
nanoparticles. We observe a substantial reduc-
Our
current
2932
understanding
of
the
Using Dynamic Light
equilib-
tion in adsorption rates in regimes where the
is not
number of available receptors is limited com-
matched by systematic studies of kinetic ef-
pared to the number of nanoparticles. The ob-
fects,
rium features of multivalent systems which
where
are
suciently
in
regimes
served trend is ascribed to the rapid and near-
interactions
become
irreversible sequestration of most of the initially
often
ligand-mediated
relevant
into
available receptors, following the adsorption of
long-lived metastable congurations that dif-
a relatively small number of nanoparticles. Re-
fer substantially from the equilibrium ground
ceptor depletion is a direct consequence of the
state.
Interactions of such strength can oc-
mobility of membrane-anchored DNA linkers,
cur in biological recognition schemes, where
and is expected to occur also in biological sys-
ligand-receptor binding free energies can ex-
tem, where adhesion is mediated by proteins
ceed
strong,
33
25 kB T .
tems,
34
kinetic
In
driving
the
multivalent has
been
colloidal
sys-
that can diuse in the membrane. Experimen-
characterised
tal evidence is backed up by state-of-the-art
and exploited to design self-protected inter-
simulations that accurately account for the
action schemes or sequential self-assembly pro-
eect of molecular reaction rates on the ad-
tocols.
sorption dynamics of the nanoparticles.
3539
arrest
system
Yet, with the exception of a lim-
ited number of studies
4045
including the recent
Our ndings demonstrate that, in the presence
investigation of the adhesion kinetics of DNA-
of strong ligand-receptor interactions, factors
functionalized
dendrimers
such as receptor mobility and concentration
systematic quantitative
should be taken into account when designing
poly(amidoamine)
to solid surfaces,
46,47
nanoscale probes for membrane targeting.
investigations have not been reported on the kinetics of multivalent nanoparticle-surface interactions.
Particularly signicant and unex-
plored is the role of kinetic eects in the pres-
Materials and Experimental
ence of mobile likers, in these directions will
Methods
be relevant to the understanding and design of the aforementioned biological and nanomedical processes.
DNA
In this paper, we present a quantitative inves-
ligands
and
receptors
tigation of the adsorption kinetics of nanopar-
Single stranded DNA was purchased from IDT
ticles to biomimetic lipid membranes.
(Integrated DNA Technologies, Leuven, Bel-
In the
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Langmuir Strands mimicking ligands (5' -TGC
extrusion, using an Avanti mini-extruder. First,
GTG TGT GCG TTT TTT TTTT-Thiol-3') 0 feature a thiol modication on their 3 end, en-
a dry lipid lm is obtained by evaporation of a
Receptor strands (5'
The lipid lm is then rehydrated with experi-
-56FAM-TCG CAC ACA CGC TTTT TTT
mental buer (10 mM phosphate buer pH 7.4
TTT-Chol-3') are modied with both a uores0 0 cein (5 ) and a cholesterol molecule (3 ) (Fig. 1).
+ 0.5M NaCl).
The latter is connected to the DNA via a Tri-
incubating for 1 hour.
Ethylene Glycol (TEG) spacer,
and enables
extruded 31 times through a poly-carbonate
Ligand and Re-
membrane featuring track-etched pores with a
ceptor strands feature mutually complementary
diameter of 200 nm (Whatman). A high num-
sticky ends of 11 nucleotides, driving their hy-
ber of extrusion steps is necessary to obtain a
bridization and NP-membrane adhesion. Poly-
homogeneous size distribution of the liposomes.
T domains are included between the sticky over-
As prescribed by the manufacturer of the extru-
hangs and the grafting moieties to improve con-
sion kit (Avanti Polar Lipids), an odd number
gurational freedom.
of steps is required so that any particulate con-
gium).
abling grafting to NPs.
grafting onto lipid bilayers.
chloroform solution under vacuum for 1 hour.
Rehydration is facilitated by
vortexing the sample for 1 min and further The solution is then
taminant larger than the pore size is blocked by the membrane and removed from the sample. The formed liposomes have a hydrodynamic diameter, measured with DLS (Malvern Zetasizer NanoZS, Malvern, UK), of either 160±31 nm or 189±37 nm (SI, section 1.1).
The overall
lipid concentration (2 mM) and the hydrodynamic diameter were used to estimate the bulk concentration of the liposomes.
Vesicles were
functionalized with dierent concentrations of Receptor strands, to obtain surface densities in a biologically relevant range
54,55
(SI, sec-
tion 1.2). Functionalization was performed by adding DNA Receptors to the LUV solution and agitating on an Eppendorf thermomixer for 16 hours at 750 rpm. The cholesterol moiety spontaneously inserts into the lipid bilayer, providing a mobile but stable anchoring.
5658
Figure 1: Hybridization between DNA ligands
To demonstrate the grafting of all DNA strands
and receptors drives the adhesion of a NP to a
to the LUVs, samples were analysed by Ultra
lipid membrane.
Centrifugation (Optima LE-80K from Beck-
The sequences of ligand and
receptor DNA strands are reported. They fea-
man) in a sucrose gradient (SI, section 1.3).
ture, respectively, a thiol and a TEG-cholesterol moiety to anchor them to NPs and LUVs.
NPs
synthesis,
functionalization,
and characterization The
Liposome preparation, functional-
materials
used
to
synthesize
NPs:
Potassium gold (III) tetrachloride (KAuCl4 ,
ization, and characterization
CAS
number
Large Unilamellar Vesicles (LUVs) were pre-
CAS
number
pared
1-palmitoyl-2-oleoyl-glycero-3-
(Na3 C6 H5 O7 , CAS number 51 804), and Tris-
phosphocholine (POPC) lipids (Avanti Polar
HCl buer (1 M, pH 7, CAS number T6455),
Lipids, CAS number 26853-31-6) by membrane
were
from
dithiothreitol
3483-12-3),
purchased
ACS Paragon Plus Environment 3
450235),
from
trisodium
Sigma-Aldrich,
(DTT, citrate
while
Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 19
phosphate buer and NaCl used for particle
NaCl + 10 mM phosphate buer at concentra-
functionalization were purchased from Merck.
tions reported in the paragraph List of Sam-
Gold nanoparticles (NPs) were produced via a
ples, tipically in the range of 0.1 - 0.2 nM,
modied Turkevich method
and immediately
was characterized via DLS. The scattering au-
dialyzed against a 0.1 mM citrate solution. The
tocorrelation function (ACF) was used to quan-
nanoparticles were characterized by TEM, UV-
tify the diusion parameters of free NPs, dis-
vis absorption, and DLS measurements, as re-
cussed in the Results and Discussion section.
ported in SI, section 2.
Then, LUVs were added to reach the sought
59
An average diameter
of 16.5±1.3 nm was determined by processing
NPs:LUVs bulk concentration ratio
TEM images with ImageJ. NPs were then func-
and
tionalized with DNA Ligands using thiol chem-
pipette.
istry.
cally 10 s after mixing, and 60 ACFs were ac-
60
The grafting density was estimated by
the
sample
was
rapidly
RNP:LUV ,
mixed
with
a
DLS data acquisition started typi-
measuring the DNA concentration of the su-
quired at 5 s intervals.
pernatant after a 20-minute centrifugation step
tween subsequent measurements was then in-
at 18,000 g. The concentration of DNA in the
creased to 30 seconds, 3 minutes, and 15 min-
supernatants after the rst washing step was
utes to monitor adhesion over the following
measured as 2.24
µM,
concentration was 3.23
while the initial DNA
µM,
14 h. All measurements were performed at 25°C
demonstrating the
occurrence of DNA grafting.
The time interval be-
and in 0.5 M NaCl ionic strength.
Higher-
Afterwards, the
than-physiological ionic strength of 0.5 M NaCl
same washing procedure was repeated 5 times
was used in this study to obtain suciently
to remove all the non-grafted DNA. We ob-
high ligand-receptor binding strength to allow
tained an average of 300 Ligand strands per
the emergence of signicant kinetic eects as-
NP. The presence of a DNA layer on NPs was
sociated to the near-irreversibility of the NP
conrmed by both DLS and UV-vis, as reported
adhesion to the target vesicles.
in SI, section 2.
of a higher-than-physiological ionic strength is
61
The eect
largely limited to the DNA-hybridization free energy, and therefore our results are readily ap-
Characterizing NP-LUV adhesion
plicable to any system with comparably strong
and dissociation temperature.
ligand-receptor interactions, regardless of the
The adhesion of NPs to LUVs was conrmed by
ionic strength. Similar ionic conditions are rou-
means of UV-vis absorption spectroscopy (Schi-
tinely used in DNA-nanosystems to make DNA
madzu UV-3600 equipped with a Peltier T con-
duplexes more stables.
6265
troller) monitoring the shift in the wavelength of the NP extinction peak induced by the re-
List of samples
ciprocal proximity between LUV-bound NPs. The dissociation temperature of the NP-LUV
A number of samples were tested with dier-
complexes was also determined and found to
ent surface concentration of receptors on the
increase with increasing surface density of the
LUVs,
receptors
ρR−LUV .
ρR−LUV ,
vant range,
Details are provided in SI,
54,55
concentration
section 3.
spanning a biologically releand dierent NP:LUV bulk
ratios,
RNP:LUV .
All
conditions are listed in Table 1. ples
Characterizing NP-LUV adhesion
with
a
nanoparticles
with Dynamic Light Scattering
-10
RNP:LUV =7
and
concentration
M, while RNP:LUV =290 ρN P =2.2×10-10 M. 10
Experiments to monitor the adhesion kinetics of NPs to LUVs were carried out using Dynamic Light Scattering (DLS). Initially, a sample of DNA-functionalized NPs in 0.5 M
ACS Paragon Plus Environment 4
70,
ρN P
tested
For samthe
bulk
is
1.1×
corresponds to
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Langmuir
Table 1:
List of tested samples:
RNP:LUV
Simulation Algorithm
in-
dicates the NP:LUV bulk concentration ratio,
ρR−LUV
We model NPs as hard spheres freely dius-
the average surface concentration
NR−LUV
the aver-
ing in a parallelepipedal simulation box (Fig. 2).
age total number of receptors on each LUV,
Nanoparticles interact with the basal surface
of receptors on the LUVs,
A,
equal to
number of Receptors available for each NP in
that of a LUV. The surface carries
NR−LUV
the system.
The number of ligands on each
receptors, a number compatible with the one
nanoparticle is xed and equal to 300, see SI,
used in experiments. As often done when mod-
section 1.2 for details on the estimation of these
elling DNA-functionalized surfaces ,
values.
glect receptorreceptor,
NR−NP = NR−LUV /RNP:LUV
and
(nm-2 )
of the simulation box having area
the average
16,18
we ne-
receptorligand,
ligandligand steric interactions.
and
We assume
Sample
RNP:LUV
1
7
3.9 10-3
370
53
2
7
8.2 10-3
770
110
-3
1190
170
pable of free diusion within a layer of thick-
-3
ness
3
ρR−LUV
7
12.7 10 17.5 10
NR−LUV
NR−NP
4
7
1640
234
5
70
3.9 10-3
370
5
6
70
8.2 10-3
770
11
7
70
12.7 10-3
1190
17
8
70
17.5 10-3
1640
23
370
1
that the sticky ends tethered to the surface of the LUV are uniformly distributed and ca-
` = 3 nm
surrounding the surface of the
LUV (see Fig. 2).
`
has been estimated using
typical endtoend distances of ssDNA.
66
Sim-
ilarly, nucleic acids on the NPs are simulated as
10
290
770
3
11
290
12.7 10-3
NL−NP sticky-ends uniformly distributed within a shell of thickness ` surrounding the parti-
1190
4
12
290
17.5 10-3
1640
6
cle (see Fig.
9
290
-3
3.9 10
-3
8.2 10
2).
Given that in our mod-
elling all ligands can bind,
NL−NP
has been es-
timated by calculating the maximum number of ligands that could bind the surface using a geometrical construction (see SI, section 4).
Nanoparticle
To improve computational eciency, also the ligands are regarded as freely diusive, rather than anchored to a point on the NP surface. This approximation has a negligible eect on the results of this work. We apply the simula-
LUV modeled as a flat surface
tion algorithm presented in reference
67
to study
DNA-directed self-assembly of LUVs, adapted to the present system.
Improving on conven-
tional algorithms, our method synchronizes the
0 Figure 2:
n
binding kinetics of DNA with the diusion ki-
25
netics of the nanoparticles,
enabling one to
study the eects of nite interaction rates on
Modelling ligand-receptor mediated
interactions between NPs and membranes. Lig-
the adsorption kinetics.
and and receptor stickyends are uniformly
does not account for the deformability of the
distributed, respectively, in the blue and red
LUVs.
stained regions surrounding the NP and the
tainly pivotal in processes such as endocyto-
membrane surface. Inset: simulation snapshot
sis
showing NPs anchored at the surface or freely
tween bound particles,
diusing in bulk. The colormap represents the
little role in the present study to the extent
number of formed NP-membrane bonds.
that reactions between dierent ligand-receptor
6873
Note that our model
While membrane deformability is ceror membranemediated interaction be-
74,75
it is expected to play
pairs can be considered as independent events. We have veried this hypothesis in a recent publication
19
using a more detailed model account-
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Page 6 of 19
of the paper. Indeed, here we describe how re-
λi ({r}) are geometric factors (see SI, section 4), ∆G0 is the hybridization free energy of 61 0 is free sticky ends in solution, β = 1/kB T , kon the on rate of the sticky ends, and ρ0 is the stan-
ceptors, once bound, no longer participate in
dard concentration equals to 1 mole per liter. In
the later stages of the adsorption.
the following we report on rates in simulation 0,∗ 0 2 −1 units: kon = kon ρ0 ` D . In physical units, −1 0 0,∗ = 3.1 × 106 ρ−1 = 1 corresponds to kon kon 0 s .
ing for membrane deformability. We also notice
where
that an eventual wrapping of the NPs by the lipid bilayer would not change the conclusions
This sce-
nario is not aected by the NPs being wrapped or not.
→
Nanoparticle positions (ri ) are updated (ri
ri + ∆ri )
Using the rates of Eq. 3 we calculate the probi i abilities pon / poff of forming / breaking a bond between nanoparticle i and the membrane, de-
using a Brownian dynamics scheme
∆ri = ri (t + ∆t) − ri (t) =
ned as (1)
√ D ∆t + D∆tN (0, 1) , fi kB T where
D
fi
aion
is the total force acting on NP
i,
Boltzmann constant and the index dividual NPs.
i
box.
is the
∼ exp[−¯ τ /atot ]). We increment a reaction clock (τreac ) by τ ¯ (τreac = τreac + τ¯) and, if τreac < ∆t, we update the vals s ues of {ni , ni , n }, the anities and probabili-
kB
for it to happen (Prob(¯ τ)
a short-range force fij due to entropic compres-
fi
Using Eq. 4, we sample one of all possi-
labels in-
Fig. 2), nanoparticles repel each other through
18
ties (Eqs. 5, 4), and re another reaction until
(Eq. 1) is then given
j fij , where fR,i is the force between the surface and NP i
τreac > ∆t.
fR,i = kB T [nsi Γ1 ({r}) − ns Γ2 ({r}) − ni Γ3 ({r})] .
at time
by
f = fR,i +
(5)
ble reactions, along with the average time (τ ¯)
In the (very diluted) bulk (see
sion of grafted DNA.
aioff
total number of nanoparticles in the simulation
is a vector of inde-
pendent normal-distributed numbers,
(4)
aion and aioff are the corresponding aniPNp i i ties and atot = i=1 (aon +aoff ) , where Np is the
in diluted conditions (estimated using Stokes7 2 −1 Einstein equation as 2.8 × 10 nm s ), ∆t is
N
aioff atot i = nsi koff ,
pioff =
where
is the nanopaticle bulk diusion coecient
the integration step,
aion , atot i = ni ns kon
pion =
Importantly, the last reaction is s s never used to update the values of {ni , ni , n }. Using the outcomes of the Gillespie algorithm
P
∆t,
we calculate forces using Eq. 2 and
(2) update nanoparticle positions using Eq.1. At which point, we reiterate the algorithm startIn Eq. 2,
nsi
ing from the calculation of the new on /o rates
is the number of ligandreceptor
bonds between nanoparticle i and the mems brane, n is the number of free receptors, and
(Eq. 3).
ni the number of free ligands on particle i. Γ1 , Γ2 and Γ3 are geometric factors and have been
To simulate the low dilution regimes used in experiments, we use grandcanonical moves in
derived in SI, section 4. s s We estimate ni , n , and ni using the Gille76 spie method. At a given conguration {r}, i i we calculate all the on /o rates (kon /koff ) of
which we insert/delete nanoparticles at the top
forming/breaking a bond between nanoparticle
more of them are adsorbed by the membrane us-
i and the membrane, with the assumption i i kon = koff = 0 if nanoparticle i is not in
con-
ing µ = µ0 + log (1 − nadh /RNP:LUV ), where µ0 , nadh , and RNP:LUV are, respectively, a reference
tact with the interface. In the SI, section 4, we
chemical potential, the number of adsorbed par-
prove that
ticles, and the stoichiometric ratio between NPs
layer of the simulation box. To simulate a xed NP:LUV concentration ratio, we gradually decrease the chemical potential
that
39
i 0 kon = kon λi ({r})
i 0 koff = kon ρ0 exp[β∆G0 ],
µ
of the NPs as
and LUVs. Grandcanonical moves are neces(3)
sary to design aordable simulations but intro-
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Langmuir
Figure 3:
Quantifying adhesion kinetics with DLS. A) Autocorrelation functions acquired with
DLS for a system with dierent times yellow
t=490 s,
t
RNP:LUV = 70
and
ρR−LUV =17.5 ×
at the mixing LUVs and NPs (dark blue
orange
t=2220 s,
red
t=7200 s,
pink
10
-3
-2
nm . The ACF was collected after
t=0 s,
t=18000 s
light blue
t=120 s,
green
t=57600 s.)
and purple
t=290 s,
B) Fraction
fadh , is obtained by tting the data from panel A with Eq. 6, extracting the two Afree (t) and Aadh (t), and using Eq. 7. The color code is as in panel A. The fraction adhering nanoparticles, fadh , for all the perfomed experiments are reported in SI, section 9, Fig
of bound NPs, amplitudes of
S9.1. Notice that only a subset of the collected ACFs are reported in panel A.
duce a bias in the diusion time required by
to longer decay times of the scattering auto-
nanoparticles to reach the membrane, making
correlation function (ACF), as demonstrated in
it signicantly faster than in reality.
Fig. 3A, which can thus be monitored to gain information on nanoparticle adhesion. For any measurement, we can identify two distinct NP
Results and Discussion
populations: free nanoparticles and nanoparticles bound to the LUVs. Over time, the popula-
We use DLS to investigate kinetic aspects of
tion of free NPs progressively shrinks, while the
the interaction between NPs and LUVs deco-
bound population grows.
rated by DNA ligands and receptors (Fig. 1)
sured ACF can be decomposed into the sum
as a function of receptor surface density on the LUVs, ratio,
of two exponentials, one describing the free
ρR−LUV , and NP:LUV stoichiometric
RNP:LUV ,
in Table 1.
Therefore the mea-
NPs population and the second associated to
spanning the ranges described
membrane-bound NPs
In DLS experiments, the signal
α 2τ/τ free )
is dominated by the strongly scattering NPs,
ACF(t, τ ) = Afree (t)e−(
−2τ/τcomp
+Aadh (t)e
while owing to the similarity between the re-
(6)
fractive index of the vesicles and that of the
where
surrounding medium, the scattering contribu-
of the experiment, and
tion of the LUVs is comparatively negligible.
time over which each scattering-intensity cor-
(see SI, section 5).
relation is calculated. The timescales
When an individual NP
adheres to a liposome, whose size is approxi-
τ comp
t
is the time elapsed from the beginning
τ
indicates the delay
τ free
and
are related to the diusion coecient of
mately one order of magnitude larger, the dy-
the free nanoparticles and the NP-LUV com-
namic diusion coecient of the nanoparticle is
plexes, respectively, while
drastically reduced. After NPs are exposed to
the polydispersity of the NP population.
LUVs, this eect produces a progressive shift
that using a stretched exponential to model the
ACS Paragon Plus Environment 7
α < 1
follows from
77
Note
,
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Page 8 of 19
Figure 4: Adhesion kinetics depends on receptor density and nanoparticle concentration. A) Adhe-
τadh for three dierent NP:LUV concentration ratios RNP:LUV as a function of the receptor surface density ρR−LUV . B) The same data as in panel A, shown as a function of the average number of receptors per NP in the system NR−NP . The vertical dashed line marks the maximum number max of bonds a nanoparticle can form due to geometrical limitations Nbonds = 25 (see SI, section 7.1). sim sim C) Simulated adhesion times τadh , using τadh = −∆t/log(1 − f (∆t)), where f (∆t) is the fraction of nanoparticles adsorbed at time ∆t, with ∆t small enough to allow tting data with an exponential sion times
function.
The predictions of panel A are bigger than the values of panel B because the average
time between consecutive NP-LUV encounter is smaller in simulations. Nevertheless, the similarity between the two gures conrms that the reaction kinetics is limiting adsorption.
contribution of the complexes did not improve
7, 70,
the ts, and the stretching factor was always
exponential trend hints at a hindered adsorp-
found to be comparable to 1. In Eq. 6, the am-
tion dynamics in which the rate of NP ad-
plitudes
Afree (t)
and
Aadh (t)
are directly pro-
and 290, respectively.
The stretched-
hesion decreases over time.
Similar trends
portional to the number of free and adhering
have been ascribed to a number of processes
nanoparticles, which allows us to extract the
including depletion of adsorbing agents,
fraction of bound nanoparticles as
steric hindrance and irreversible adsorption.
Aadh (t) . fadh (t) = [Aadh (t) + Afree (t)]
The progressive decrease of
RNP:LUV
(7)
parameters
and kept constant.
describe intrinsic char-
The decay time
τ comp
de-
the
evolution over the course of an experiment is (8)
analysed in a dedicated section below.
adhesion ss timescales, and the plateau value fadh represents the steady state fraction of adsorbed nanoparticles.
α
scribes the diusion of NP-LUV complexes and
γ t ss fadh (t) = fadh 1 − exp − , τadh quanties
and
and can therefore be independently determined
increases with time as a
stretched exponential
τadh
τ free
acteristics of NPs that do not change over time,
vated and discussed in SI, section 6. Figure 3B
where
we observed indicates that the specic
nanoparticles increases. Note that in Eq. 6 the
This assumption is moti-
fadh
with increasing
comes more severe as the number of available
and membrane-bound NPs have the same scat-
demonstrates how
80
factor limiting adsorption in our system be-
Eq. 7 is valid under the assumption that free tering eciency.
γ
78,79
typical
Reaction-limited
γ
in the range
of 0.9-1, 0.6-0.7 and 0.4-0.5 for
RNP:LUV =
ad-
hesion and receptor depletion
Optimal tting is obtained by
restricting the stretching factor
nanoparticle
Figure
4A
demonstrates
the adhesion time
ACS Paragon Plus Environment 8
τadh
the
dependence
of
on the NP:LUV rela-
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Langmuir
Figure 5:
Simulations highlight the eect of kinetic rates on particle adhesion.
A) Number of 0,∗ adhering nanoparticles nadh as a function of time for dierent reaction rates parametrized by kon 0,∗ (see sections on Simulation Algorithm). When kon < ∞ the system fails to reach the equilibrium 0,∗ state corresponding to the steady value of the kon = ∞ trajectory. Receptors surface density was −3 −2 set to ρR−LUV =4.2×10 nm and the NP:LUV concentration ratio to RNP:LUV = 70. B) Average number of bonds
nbonds
formed by each adhering nanoparticle for the simulated trajectories of panel
A.
RNP:LUV
and the sur-
netic trends can be proposed by comparing the
face density of DNA receptors on the LUVs
timescales of the individual processes leading to
ρR−LUV .
observed to
NP adhesion. Adsorption is initiated by a colli-
If the lat-
sion between a NP and a LUV, and the average
tive concentration ratio For xed
ρR−LUV , τadh is RNP:LUV .
increase with increasing
τadh decreases monotonically with increasing ρR−LUV . The samples with the lowest RNP:LUV , where τadh remains con-
time
stant, constitute an exception.
These trends
ing each collision, the NP-LUV spend a much
can
studying
of
shorter time within their interaction range, τcoll ≈ `2 /D = 0.3 µs. While a NP is in contact
receptors per NP, obtained by dividing the av-
with a LUV, the time required for the forma-
ter is kept xed,
be
better
dependence of erage number on each LUV
rationalized
τadh
by
NR−LUV of receptors by RNP:LUV (Table 1).
and 450 ms (see SI, section 8.1). However, dur-
τbond . 200 ms
anchored
tion of a ligand-receptor bond is
The data
(see Eq.3 and SI, section 8.2), indicating that
in Fig. 4B show indeed a smooth trend, and clearly highlight two distinct regimes:
τadh
several thousands of unsuccessful collisions (natt
is
NR−NP , while increasNR−NP decreases below a
low and constant for high ing monotonically as
between two of these events, at the
beginning of the experiment, ranges between 80
the
NR−NP
on the number
τdiff
≈ τbond /τcoll )
natt
are on average required for
a NP to dock on a LUV. Assuming a collision −1 rate of the order of ∼ τdiff , τdiff < 0.5 s, the typical timescale at which particles start adsorbing 3 can then be estimated using natt · τdiff ≈ 10 4 10 s which is compatible with Fig. 4A. After
threshold. The switching point coincides with
NR−NP ∼ 20 − 50, which matches well the maximum number of ligand-receptor bonds that a single NP can form due to geometrical limitamax tions, estimated as Nbonds ∼ 25 (see SI, section 7.1).
the rst bond is established, preventing the LUV and NP from diusing apart, more connections are quickly formed as mobile receptors are converging towards the adhesion zone. Re-
A qualitative explanation of the observed ki-
ceptor accumulation occurs on the timescale
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Page 10 of 19
Figure 6: Receptor availability inuences steady state conguration. A) Steady state fraction of ss adhering NPs fadh as estimated from experiments (full symbols) and simulations (empty symbols) as a function of RNP:LUV and ρR−LUV . B) Experimental estimate of the steady-state average number ss of bonds per adhering NP nbonds .
τbond natt · τdiff ,
so that before another NP
trends in Fig. 4A supporting the interpretation
has a chance to bind with the LUV, the rst
that the reaction kinetics is the factor limit-
has already maximised the number of bonds, max capturing Nbonds receptors. If NR−NP exceeds max , the process continues until all nanoparNbonds max ticles have formed Nbonds connections, leaving
ing NP adsorption in experiments.
free receptors on the LUVs. In turn, for lower
that, as compared to experiments, drastically
NR−NP ,
reduces the time between successive NP-LUV
in simulations the typical adhesion timescales are much faster than the experimental ones. This is due to the simulation scheme employed
the system enters a regime where the
τdiff , while properly reproducing reτbond , and the time taken by NPs
initially binding NPs quickly deplete receptors,
encounters,
drastically reducing their availability.
action times,
tor scarcity causes
τbond
Note that
Recep-
to increase, reducing
to diuse away from the interacting region,
the chances of a successful docking and sub-
τcoll .
stantially slowing down adhesion.
In our ex-
used above to justify the timescale of Fig. 4A,
periments, receptor depletion is expected to be
explains the similarity between simulation and
eectively irreversible due to the strong anity
experimental proles that only dier by a time
between DNA ligands and receptors resulting i 6 in a bond breakup rate koff ∼ 10 exp (β∆G0 ) s−1 (see Eq. 3). The initial transient, therefore,
given by the ratio between the experimental
drives the system out of equilibrium. At high
tion rates on adsorption kinetics, in Fig. 5A we
RNP:LUV = 290
visualize the time evolution of the number of
steric hindrance can further limit nanoparti-
adsorbed nanoparticles, calculated using dier-
cle adsorption at later stages given that at full NP (SI, section 7.2).
ent reaction rates. The latter are controlled by 0,∗ changing kon while keeping the ligand-receptor binding free energy, and therefore the ther-
These qualitative arguments can be veried by
modynamics of the system, constant.
comparing experimental data with simulated
sequently, the ligand-receptor o rate is also i 0,∗ rescaled as koff ∝ kon (Eq. 3). 0,∗ i For kon , koff = ∞, the system experiences no
NP:LUV concentration ratio
packing a LUV can host a maximum of
and simulated
τdiff .
To better clarify the role played by the reac-
∼ 150
trends. Figure 4C reports adhesion timescales sim τadh , estimated by tting the early stages of adsorption as detailed in the caption of Fig. 4.
This argument, along with the reasoning
Con-
kinetic hindrance from ligand-receptor reac-
Simulation results reproduce experimental
tions, and can therefore reach thermodynamic
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Langmuir
equilibrium.
In these conditions, mobile re-
tions, but the latter appear to underestimate ss in regimes of low NR−NP . We ascribe fadh this deviation to the fact that, in simulations, ss the average number of bonds Nbonds formed by each adhering NP at steady state is always max maximised, and equal to Nbonds = 25 (Fig. 5).
ceptors are observed to redistribute instantaneously among available NPs, progressively decreasing the average number of bonds per NP to stabilize a greater number of adsorbed nanoparticles, as displayed in Fig. 5B. In turn, Fig.
5A shows that for nite reaction rates
This is not always the case in experiments, ss as shown in Fig. 6B. Nbonds is estimated experimentally by assuming that i) all receptors
the asymptotic number of adsorbed nanoparticles is much smaller than the one observed 0,∗ 0,∗ with kon = ∞, implying that for kon < ∞ the system fails to reach equilibrium. Indeed, 0,∗ even for the largest (nite) kon value we could i −9 test, koff becomes negligibly small (≈ 10 −1 s ) owing to the strong ligand-receptor an-
are bound, and
ii)
receptors are evenly parti-
depletion eect hypothesized above, where all
tioned among adsorbed NPs. We observe that ss the experimental Nbonds is aways smaller than, max or comparable to Nbonds . More specically ss Nbonds increases as a function of ρR−LUV for max for the highRNP:LUV = 70, approaching Nbonds est tested receptor density, while remaining rel-
adhering NPs quickly and irreversibly max-
atively small and constant for
imise the number of formed bonds, which in max simulations is set to Nbonds = 25 (Fig. 5B). To enter a regime where adsorption is not lim-
Note that condition
ited by DNA denaturation, one would need 0,∗ kon & exp [−β∆G0 ]. Unfortunately, such val0,∗ ues of kon are not computationally aordable. 0,∗ For kon = ∞ bond formation occurs instantly
Fig. 6. There are a number of eects that can max ss result in Nbonds < Nbonds , not accounted for in simulations. First, in Fig. 6B we assume that
upon NP-LUV collision, implying that initial
adsorbed NPs, while it should not be excluded
aggregation is diusion limited and occurs over
that those adhering at later stages may form
ity. Bond irreversibility results in the receptor-
typical timescales
RNP:LUV = 7,
receptors are evenly distributed among all the
Figure 5 shows that, at 5 0,∗ early times, the curve calculated for kon = 10 follows the same trend, indicating that in this
τbonds
i) cannot be veried for max NR−NP > Nbonds , thus the
estimates for these samples are not included in
τdiff .
regime the bond formation time
where
RNP:LUV = 290.
less bonds than earlier nanoparticles. This nonideal behavior could emerge, for instance, as a consequence of nonselective (e.g.
steric) in-
is still
teractions between ligands and receptors, that
signicantly smaller than the collision time 0,∗ τcoll . The same is no longer true if kon ≤ 10−1 , for which the onset of NP adhesion is signif-
could signicantly slow down bond formation and receptor sequestration by increasing
τbond ,
permanent NP-LUV bond upon collision is pro-
allowing more nanoparticles to bind the LUV. ss max Additionally, Nbonds < Nbonds may imply a degree of bond reversibility enabling recep-
gressively reduced.
tor redistribution.
icantly delayed as the likelihood of forming a
This could be explained
by an underestimation of the o rates, which in crowded environments may deviate sensibly from the theoretical predictions obtained
Steady state
in diluted conditions (Eq.
From the time evolution of the fraction of
fadh (t)
once again that for
LUV-adhering
3).
81
We point out
RNP:LUV = 290
there is
NPs we can extract the ss asymptotic value fadh , corresponding to fraction of adhering nanoparticles at steady state ss (Eq. 8). In Fig. 6A, the experimental fadh is show as a function of RNP:LUV and ρR−LUV
not enough room on the LUVs to accomodate
(full symbols), and compared to simulations re-
asymptotic fractions experimentally observed
sults (empty symbols). We observe qualitative
for
all available nanoparticles, regardless on receptor availability.
The geometrical limit to NP
adsorption per LUV is to
fadh ∼ 0.5.
ACS Paragon Plus Environment 11
corresponding
This value is similar to the
RNP:LUV = 290
agreement between experiments and simula-
∼ 150,
in Fig. 6A.
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Page 12 of 19
Figure 7: Diusion time of NP-LUV complexes suggest LUV clustering. Decay time
τcomp , describ-
ing the diusivity of NP-LUV complexes shown as a function of the receptor surface density on LUVs
ρR−LUV
for dierent NP:LUV concentration ratios
RNP:LUV = 7,
70 and 290.
The dashed
lines represent the characteristic diusion time of a 180 nm diameter liposome. The grey areas mark the range of adhesion times
LUVs
aggregation
τadh
measured for the dierent
driven
by
NP
ρR−LUV
(Fig. 4).
eectively passivate the LUV surface against NP bridging.
bridging
Note that LUV aggregation is
not expected to aect our ability to quantify Further information on the evolution of the sys-
the fraction of bound NPs, used to monitor ad-
tem can be gathered by monitoring the time
sorption kinetics: all NPs, whether adhering to
dependence of the diusion timescale
τcomp
of
an individual LUV or bridging two of them,
the NP-LUV complexes (equation 7). As shown
would still be considered as bound.
τcomp exhibits dierent trends deon ρR−LUV (shown in dierent colors)
in Fig. 7, pending
RNP:LUV (shown in dierent panels). cases τcomp remains roughly constant for and
In turn,
NP-mediated LUV bridging may have an eect on aggregation kinetics, as NPs can no longer
In all
be considered as "inactivated" after adhering
times
to a LUV, and would still be able to seques-
shorter than the typical adhesion timescale τadh ,
trate more receptors by forming LUV-NP-LUV
marked as a grey-shaded band spanning the ad-
bridges. However, in view of the faster diusion
ρR−LUV .
kinetics of individual NPs compared to that of
hesion timescales observed for dierent For
RNP:LUV = 7,
an increase of
τadh
above
NP-LUV complexes, the adhesion of free NPs to
the value expected for an individual LUV is
LUVs is expected to dominate over the forma-
observed at later times, suggesting the possi-
tion of aggregates, as long as free NPs remain
bility of NPs mediated LUV-LUV aggregation.
available.
The latter can occur because, after all NP are adsorbed, for
RNP:LUV = 7
the system still
Conclusions
features free receptors that can bind NPs on other LUVs, causing aggregation. Consistently, the same phenomenon is observed for samples
In summary, through a combination of dedi-
RNP:LUV = 70 and large receptor densities,
cated experiments and coarse-grained simula-
which as demonstrated in Fig. 6A also reach
tions, we investigated the kinetics of adhesion
a regime where NPs are depleted but recep-
of gold nanoparticles to articial lipid vesicles
tors are still available. As expected, in samples
mediated by near-irreversible ligand-receptor
with
with
RNP:LUV = 290,
bonds.
LUVs remain monodis-
DNA strands grafted onto the surface
perse at all times, as the large excess of NPs
of the nanoparticles and the liposomes play
is always sucient to deplete all receptors and
the role of both ligands and receptors.
This
model system is chosen to mimic interactions
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Langmuir
between nanoscale vectors and the surface of
modeling community. In particular, they high-
biological cells, a key process in several biolog-
light the importance of explicitly considering
ical and medical scenarios, including cell inva-
reaction rates when designing numerical simu-
sion by viruses and parasites and cell targeting
lations.
by means of synthetic nanomedical vectors. The rate of nanoparticle-vesicle adhesion is
Acknowledgement
studied over a broad range of biologically and technologically relevant conditions,
and GB acknowledge support from the Wiener-
by vary-
Anspach foundation. LDM acknowledges sup-
ing the surface density of available membrane-
port from the Leverhulme Trust and the Isaac
anchored receptors and the bulk concentration
Newton Trust through an Early Career Fel-
of nanoparticles. In both experiments and sim-
lowship (ECF-2015-494),
ulations, we nd that adhesion rates are heavily
ship (UF160152).
in excess compared to available receptors. Ob-
CAPITALS (EP/J017566/1). PKJ and BMM
the timescales of individual kinetic processes
are supported by the Fonds de la Recherche
at play, including the frequency and duration
Scientique de Belgique - FNRS under grant ◦ n MIS F.4534.17. Computational resources
of nanoparticle-vesicle collisions and the typical time required to form a ligand-receptor
have been provided by the Consortium des
We determine that the observed slow
Équipements de Calcul Intensif (CECI), funded
kinetics arises from receptor depletion, as difmembrane-anchored
receptors
by the Fonds de la Recherche Scientique de ◦ Belgique - FNRS under grant n 2.5020.11. RL
quickly
segregate within the nanoparticle-vesicle adhe-
acknowledge Simon Croegaert for the produc-
sion region upon initial docking of individual
tion of AuNPs and TEM images, Jonathan
nanoparticles. Nanoparticles adhering at early
Goole from Pharmaceutics and Biopharmaceu-
aggregation stages therefore sequestrate a sig-
tics group (Université libre de Bruxelles) to give
nicant proportion of the available receptors,
her access to Malvern Zetasizer NanoZS and
reducing the rate of bond formation for late-
Guy Vandenbussche from Structure and Func-
coming nanoparticles and slowing down their adhesion.
tion of Biological Membranes group (Université
The near-irreversibility of ligand-
libre de Bruxelles) for letting her use Ultra Cen-
receptor connections hinder bond redistribution,
PC and LDM acknowledge
support from the EPSRC Programme Grant
served trends are rationalized by comparing
fusive
and the Royal So-
ciety through a University Research Fellow-
suppressed in regimes where nanoparticles are
bond.
RL, BMM, PC, LDM
trifuge.
leading to kinetically trapped congu-
rations in which the number of membrane-
Supporting Information Avail-
adsorbed nanoparticles is not maximised. Our observations have direct application in the
able
design of medical nanovectors targeting cell membrane receptors: for a xed receptor sur-
The Supporting Information is available free of
face density, the adsorption rate of nanoscale
charge.
probes can be maximised by improving bond reversibility or by reducing the number of con-
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