outsidein: (towards) mapping nanoparticle dosage across a
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www.systemscytometry.org
OutsideIn: (Towards) Mapping Nanoparticle Dosage Across a Biological Interface
Rowan Brown College of Engineering
Swansea University UK
General theme – Measurement and comprehension of cellular populations
via probability mass distributions to infer biological function, evolution and
application
• Today’s Focus – Application of Nanoparticles to elucidate
biological function
• Flow Cytometry
• Understanding nanoparticle uptake and redistribution across a large
cellular populations
• AMNIS ImageStream
• High-throughput microscopy
• Understanding nanoparticle dose and heterogeneity at the cell level
• In Cell 2000/6000
• Transmission electron microscope
• Understanding nanoparticle dose, heterogeneity and redistribution
at the endosome/lysosome level
• CryoTEM
G1
S M(A)
M(M) G2
G0 Cancer biology: study cell cycle and its perturbation via drug interactions Need to consider the effects of heterogeneity single cell resolution across a whole population flow cytometry with nanoparticle markers
control
drug treated 0
2
4
6
8
10
12
14
16
18
20
0 40 80 120
time (hours)
Facto
r ch
an
ge in
cell n
um
ber
Control
0.1 TPT
1.0 TPT
10 TPT
Cell cycle, lineage and inheritance
Population tracking with Nanoparticles - quantum dots
• Nanoparticles – Invitrogen q-tracker 705nm quantum dot system
• 4.5nM dose – non-toxic
• QD Nanoparticles: photo and bio-stable with high quantum yield, h > 50%
• Taken-up by cell through endocytosis
• Nanoparticle signal provides identification of generation by optical intensity
1
1/2
1/4
15 nm
Statistics of inheritance – Flow Cytometry
0
20
40
60
1 10 100 1000 10000
fluorescence intensity
cell
nu
mb
er
24 hr
48 hr
If 𝑥 halves upon cell division then:
𝜇 → 𝜇
2
𝜎 → 𝜎
2
Equates to a rigid shift of distribution in 𝑥
• Actually measure red curve at 48 hours
• Peak reduction and increasing 𝜎: signal dispersion
• Unequal partitioning of nanoparticle intensity across cellular population
𝜇 = 𝑥𝑖
𝑛
𝑖=1
𝜎 = (𝑥𝑖 − 𝜇)
2
𝑛
𝑛
𝑖=1
Fluorescence Intensity
Num
ber
of
Cells
Computational statistics : in-silico populations
Lect. Notes Comput. Sci. 2007;4695:96–105.
a, Da t, Dt
Stochastic Cell-Cycle Model • Initial experimental distribution initialises
using in-silico agent population, 𝑃 𝑡 = 𝑡1 • Maximisation correlation to that of a
second measured distribution some time later 𝑃 𝑡 = 𝑡2 , 𝑡2 > 𝑡1
Variables:
• Mean and standard deviation of inter-mitotic time
• 𝜏 and Δ𝜏
• Partition fraction, how intensity is redistributed to daughter cells
• 𝛼 and Δ𝛼
𝜏 – controls translation of fluorescence
𝛼 – controls the dispersion of the intensity
Application: Modelling pharmacodynamics
Pulse-chase assay – block for 18 hours, release and measure 6 hours later QD tracking used to quantify blocking and release efficiency
24 48 36
measurement pts.
drug block
time (hrs)
100
101
102
103
104
0
10
20
30
40
50
60
70
drug blocked 24 hrs
drug wash-out 48 hrs
QD control 48 hrs
Fluorescence Intensity N
um
ber
of C
ells
‘Flow-Based Cytometric Analysis of Cell Cycle via Simulated Cell Populations', PLoS
Computational Biology, 2010 April; 6(4)
control division blocked
block and release
IMT (hrs) 22 ± 4 21 ± 4 21.5 ± 4
Partitioning %
72 ± 2 68 ± 5 76 ± 4
Proliferative fraction (%)
98 ± 2 8 ± 2 61 ± 5
Cell division parameters
Model fits at 48 hours
0
25
50
75
10 100 1000 10000
fluorescence intensity
cell
nu
mb
er
0
25
50
75
cell
nu
mb
er
0
25
50
75
cell
nu
mb
er
drug present
drug wash out
control
Cell cycle, Vol 9. P121-130(2010)
Application: Modelling pharmacodynamics
Application: Signal recovery
• How long is it possible to quantify NP fluorescence signal
against intrinsic noise?
• Challenge: Account for intrinsic background auto-
fluorescence
• As the quantum dot fluorescence signal is
genealogically redistributed we approach
background autofluorescence
• After 8 days 80% of measured total intensity across
the cellular population overlaps with intrinsic
autofluorescence
• Solution: include an autofluorescence component in the
in-silico model
• Autofluorescence signal – static/machine/setting
dependent
• randomly sampled from measured distribution
(Black curve)
Application: Signal recovery
Long term tracking of cells using nanoparticles as markers Cytometry A, 77A: 933-940, (2010).
• Robustness (1000 runs of in-silico population)
• IMT, 𝜏(Δ𝜏) – 23(7) hours
• Splitting %, 𝛼 Δ𝛼 − 83(6)
• This systems biology approach provides insight
into both cell heterogeneity and division
dynamics within the population and furthermore
informs on the lineage history of its members
Total measured signal
(grey curve)
Total in-silico signal
(red circles)
Decoupled signals
Measured autofluorescence (grey curve)
In-silico autofluorescence
(black curve)
Quantum dot fluorescence
(blue curve)
However, from a statistical view-point (free-energy), It is not obvious why asymmetric
splitting of intensity signal occurs
We need to quantify exactly what is inherited.
The statistics of inheritance - ImageStream
0 5 10 15 20 25 300
100
200
300
400
500
600
700
800
900
1000
1100
QD cluster number
cell
num
ber
48 hr to 72 hr dispersion
Particle dose
knk ppknk
npnkB
1
!!
!,,
Amnis – ImageStream
Binomial hypothesis:
Independent and random inheritance of
each vesicle by a given daughter
n is measured (bins on histogram) only
variable is p, probability of inheritance
Indicates non-linear fluorescent
re-distribution through mitosis
i.e. p = 0.59
Nature Nanotechnology, 6, 170-174, (2011)
0 2 4 6 8 10 12 14 16 18 200
100
200
300
400
500
600
700
800
900
1000
1100
QD cluster number
cell n
um
ber
Particle dose
p=0.59
Single solution dose 705nm
Random delivered particle dose?
In Cell Analyser 2000 – cell imaging in flow direct analysis of nanoparticle cluster uptake and dispersion of 100,000 cells (> 100Gb of image data)
The statistics of dose variability – In Cell
Phase Contrast image of NP loaded cells
The statistics of dose variability – In Cell
• Thresholding and peak detect algorithms used to mask and
count NP clusters per cell
• Uptake histogram well described by a the discrete Polya
distribution or negative binomial distribution
• NB - is a discrete probability distribution of the number of
successes, p, in a sequence of Bernoulli trials before a
specified (non-random) number of failures occur, r
o Random Poisson distribution does not fit o Cannot describe uptake by random chance alone
o Why over-dispersed?
o Super-linear relationships?
o Need to consider dose presented to cell and the
possibility of biological processing
Number of loaded NP vesicles
rk ppkrk
rkprkNB
1
! !
)!1(,,
Random sampling to predict NP cellular dose
nnbeaenP 21
nanoparticles per vesicle vesicle per cell
0 0.5 10
0.05
0.1
0.15
0.2
vesicle partition fraction
pro
ba
bili
ty
knk pp
knk
npnkB
1
!!
!,,
vesicle per daughter
rk ppkrk
rkprkNB
1
! !
)!1(,,
Number of NP clusters per vesicle Number of vesicles per cell
frequ
ency
frequ
ency
Modelling of nanoparticle uptake and inheritance at the single particle level:
104
105
106
107
0
10
20
30
40
50
60
70
80
90
nanoparticles per cell
frequency
Quantification of Nanoparticle Dose and Vesicular Inheritance in Proliferating Cells, ACS Nano, 2013, 7, 7.
n = 4
S = 3
n = 2
S = 2
n = 2
S = 1
S = 1
S = 0.5
24 hr
48 hr
The statistics of inheritance – In Cell
Result – intensity inheritance 75:25
vesicle inheritance 55:45
Tracking individual cells in the population
Why try to image the whole cell?
Cell labelling with nanoparticles - moving light displays
Use quantum dots to create point light sources from which cells can be identified and tracked – clustering algorithms
Bright Field Fluorescence Binary Element
Tracking proliferation and motility
PLoS ONE 7(7): 2012. doi:10.1371/journal.pone.0040835
Quantifying cell mitosis from cluster analysis
• Cluster number iterates to find optimal cluster number
using k-means and silhouette algorithms
• Estimation of mitotic phase
Cell barcoding – RGB Space
• Uptake of 3 NP types - 705nm, 585nm, 525nm
• Sequential loading - 1 hour uptake – 1 hour rest – per NP type
Information on biology – 40,000 cells
Correlation matrix Green Red Blue
Green 1 0.35 0.40
Red 0.35 1 0.47
Blue 0.40 0.47 1
Number of loaded vesicles
Number of loaded vesicles
Results - Histogram of the number of cells which share the same code with other cells in the population
• Among labeled cells, 43% have unique codes (red bar ~17,000)
• The remainder share a code with a small number of cells in the experiment.
• 8,842 cells which have one other cell within the population with the same code
• 5,601 cells which have two other cell within the population and so on.
Stochastic Model • To better understand the observed 3-colour
distributions we developed a stochastic model
• Generation of correlated random variables – non-trivial
• Use of Coplua’s only return correlation not correlated distributions
• Combination of stochastically applied noise, a donor distribution and the application of a evolutionary algorithm
Frequency of repeated codes
• Blue, green, red and cyan curves represent the calculated number of codes available as a function of distribution correlation
• Black datum – is the measured number of codes for 3 colours with the parameters discussed previously
• All curves were generated from a donor distribution where both 𝜇 and 𝑏 are the averages of that measured experimentally
• Implies use of 4 colours could achieve individual labelling for 40,000 cells for correlations between distribution < 0.6
• Simulation suggests that you could increase number of codes by simply reducing correlation between loads
• Change uptake duration • Dose
Application – 3-colour Cell tracking
Application – 3-colour Cell tracking
• Challenge: Quantify robustness of cell identification by RGB map alone
• How does this compare to alternative methods that require some form of spatial cross-correlation of objects across time points • E.g. cytoplasm overlap within a given radius
• Cells were imaged and their associated bar codes
quantified at 0.5 hours post nanoparticle washout (frame 1)
• At 15 minute time intervals, cells were imaged and we attempted to match every cell to a cell labeled in frame 1 based purely on its bar code
• The accuracy of this assignment (blue) is ~70% after 4.5 hours
• Cell overlap-based tracking fails completely after 2 hours (red) i.e. no overlap with initial position
Application - Phenotype identification
a. Stitched 16X20 fields of view each point represents one cell and the colour the RGB representation of the three colour code b. Dot plot of the total number of NLVs per cell versus the nuclear area again the colour of each point is the RGB representation of the cell c. One field of view highlighting a polyploidy cell which is easily recognisable from the dot plot or the wide field representation of the cell population due to its light blue colouration
Nature Methods 11(11) 2014 pp. 1177
OutsideIn: Quantifying Actual Nanoparticle Dose
Electron Microscopy: measurement of nanoparticle position
Nicole Hondow, Andy Brown and Rik Brydson
• 3D reconstruction of cell
• Image analysis of TEM images
• Number of NPs per vesicle
Journal of Nanoparticle Research 14:977 (2012)
• What is in each endosome?
• Gatan 3-View system
• Serial sectioning and imaging of a resin-embedded sample in an SEM
Application: Quantification of Actual Nanoparticle Dose
• Measured number of nanoparticles as a function of time via TEM
• Analysed 25 randomly chosen cells from large population
• 500 different endosome compartments from with in these cells
• 𝑃𝑀(𝑥) and 𝑃𝐸(𝑥) are the experimentally determined PMFs of the number of NPs per agglomerate, 𝑥, in Media and Endosomes
• How are the individual states translated from
the 𝑃𝑀(𝑥) measured one hour later 𝑃𝐸 𝑥 ?
• Shift suggests aggregation events • Actually whole host of endosome dynamics
going-on
Data-driven modelling of nanoparticle sedimentation and cellular uptake over a 1 hour period
NP transport to cell surface • NP agglomerate are introduced to the cell
media • NP agglomerate variability is represented by
black disks of varying diameter
• Transport properties calculated via the in-vitro sedimentation, diffusion and dosimetry (ISDD) model [Hinderliter et al., Part. Fibre Toxicol, 7 (2010) 36]
• Black line is the mean transport rate of agglomerate to the cell surface, 𝛾(𝑥)
• The minimum of 𝛾(𝑥)at 𝑥~100 NPs suggests agglomerates around this size are transported least rapidly to the cell surface
Diffusion
dominated
Sedimentation
dominated
Data-driven modelling of nanoparticle sedimentation and cellular uptake over a 1 hour period
Observe - random endosomal uptake of NPs [NNano 6, 170-174, (2011) ]
• Dashed red circles illustrate endoctyic active domains (EADs) on the surface of the cell that are undergoing internalisation event
• Assumptions o NP agglomerate attachment to surface receptors are irreversible – all attached agglomerates are
aggregated and internalised by the cell (red disks) o EADs appear randomly on the cell surface and persist for a mean lifetime, 𝜏 , where 𝜏 ≪ 1 hour
• Need to estimate the number, 𝑵(𝒙), of distinct NP agglomerates of size 𝒙 that land on each EAD
during its lifetime
• Can then deduce number of NPs per endosome:
𝑁𝐸 = 𝑁 𝑥 .
𝑥
𝑥
Data-driven modelling of nanoparticle sedimentation and cellular uptake over a 1 hour period
Non-Homogeneous Poisson Distribution Rate parameter, 𝜆(𝑥), is a function of NP agglomerate size, 𝑥
𝑁 𝑥 =𝜆 𝑥 𝑒𝜆 𝑥
𝑥!
Where
𝜆 𝑥 = 𝐸 𝑥 . 𝛼 𝑥 𝐸 𝑥 is a weighting factor whose magnitude is dependent on what has been experimentally measured
𝐸 𝑥 = 𝑃𝑀 𝑥 . 𝑥 𝑃𝑀 𝑥 is the PMF of the number of NPs per agglomerate measured in media – Data driven
𝑁(𝑥) may be described as an arrival event within a Non-Homogeneous Poisson Process
𝛼(𝑥) driven by the biophysics of the experimental system under investigation:
𝛼 𝑥 = 𝑁𝐸𝐴𝐷. 𝛾 𝑥 . 𝜏 Where 𝑁𝐸𝐴𝐷 is the number NP agglomerates that may land per EAD per unit time – dependent upon NP concentration (perceived dose) and mean capture area 𝛾 𝑥 is the transport rate 𝜏 is the mean lifetime of a EAD
Data-driven modelling of nanoparticle sedimentation and cellular uptake over a 1 hour period
• We can deduce calculate the number of NPs per endosome 1 hour after NP dosage
𝑁𝐸 = 𝑁 𝑥 .
𝑥
𝑥
• Illustrated by solid Red disks in schematic figure (c)
Comparison of the CDFs measured and that predicted
(a) The blue curve with ‘x’ markers is the optimised CDF predicted by the NHPP methodology, 𝐹𝑁𝐻𝑃𝑃𝐸 𝑥
• Mean lifetime of the EAD , 𝜏 = 63 s when mean capture radii = 213 nm • Both magnitudes are close to that previously reported (see):
B. Huang et al., Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy, Science, 319 (2008) 810-813 M. Ehrlich et al., Endocytosis by random initiation and stabilization of clathrin-coated pits, Cell, 118 (2004) S.H. Hansen et al., Internalization efficiency of the transferrin receptor, Exp. Cell Res., 199(1992) 28.
(b) The predicted number NP agglomerates per EAD - Poisson distribution (black dashed line) ~3 NP agglomerates in media combine to form larger aggregates within the endosome (c) Data points (circle markers) indicate the PMF associated with number of NPs per agglomerate that will merge across the endosome population.
Sensitivity analysis of model
(a) Optimised ‘best-fit’
(b) Mean radii of a EAD range over the experimentally determined interval [62 497] nm holding τ fixed at optimum value (63 s)
(c) Mean radii of a EAD is fixed at the sample average (213 nm) and τ varied over [30 240] seconds
Grey shaded areas are ± one standard deviation of the mean value of 𝐹𝑁𝐻𝑃𝑃𝐸 𝑥
• General probabilistic framework driven by measured data Limitations – population sampling: 25 cells – 500 agglomerates (media) 500 endosomes We are slowly working towards 100 cells – quantify actual population NP dose
Rachel Errington, Paul Smith, Sally Chappell, Marie Wiltshire
Nicole Hondow, Andy Brown, Rik Brydson
Huw Summers, Paul Rees, James Tonkin, Mark Holton
Thank you to………
EP/M000621/1