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Supporting InformationCockburn et al. 10.1073/pnas.1303858110SI Experimental ProceduresMathematical Modeling of T-Cell Cluster Formation. To describe thekinetics of formation of clusters around a Plasmodium yoelii-infected hepatocyte we used a simple “birth–death” model. In thismodel we defined a probability to observe k cells in a cluster at timet as Pk(t). Cells are recruited into the cluster at a rate λk and exitfrom the cluster at a rate μk. In general, both rates may depend onthe number of cells in the cluster. The dynamics of the probabilityto observe k cells in a cluster of lymphocytes around an infected cellis given by the following system of differential equations:
dP0
dt= − λ0P0 + μ1P1;
dP1
dt= − ðλ1 + μ1ÞP1 + μ2P2 + λ0P0;
dPk
dt= − ðλk + μkÞPk + μk+1Pk+1 + λk−1Pk−1; k> 1: [S1]
Because in our experimental data most clusters are largely formedbefore the time of imaging and few cells exit or enter the clustersin the observed time period, we focus on the analysis of the steady-state distribution of cluster sizes. Kinetics of the formation of clus-ters will be analyzed elsewhere. The steady-state distribution ofcluster sizes can be found by letting each of the above equationsequal 0. After some algebra we find
Pk =P0∏k−1
i= 0λi
∏ki= 1μi
; k> 0: [S2]
and Pk=0 = P0, where P0 is found by normalizing Eq. S2 so thesum is equal to 1. The following models describe specific sol-utions depending on how the entrance rate into a cluster of sizek, λk, and exit rate from a cluster of size k, μk, depend on thecluster size, k.Density-independent recruitment, density-dependent exit model (randomentry and exit). Our first model assumes a constant, cluster size-independent entrance rate of cells into a cluster and constant percapita exit rate, λk = λ and μk = kμ. In this scenario we assume thatthere is a constant influx of cells into cluster and the total rate ofexit of any cell from a cluster is proportional to the cluster size.Then the probability of forming a cluster of size k is
Pk =P0∏k−1
i= 0λi
∏ki= 1μi
=P0λk
μkk!=
θk
k!e−θ; [S3]
where θ = λ/μ.Density-dependent recruitment model (cells are attracted to a cluster).The density-dependent entry model modifies the entrance rateto be a combination of constant flux and density-dependent rate,λk = λ + kλ1. The assumption is that cells in a larger size clusterwill attract more cells than cells in a smaller size cluster. The percapita exit rate is constant, and thus the exit rate is μk = kμ.Cluster of size k has the following probability of forming:
Pk =P0∏k−1
i= 0λi
∏ki= 1μi
=P0∏k−1
i= 0ðλ+ iλ1Þμkk!
=P0∏k−1
i= 0ðθ+ iθ1Þk!
; [S4]
where θ = λ/μ and θ1 = λ1/μ, and P0 is found by numericallynormalizing Eq. S4 by letting the maximal cluster size to be kmax,
so P0 = 1.Pkmax
k=1∏k−1
i=0 ðθ+ iθ1Þk! :
Density-independent exit model (cells keep each other from leaving cluster).Our third model leaves the entrance rate of cells into a clusterconstant but considers the per capita exit rate to be density-dependent, so that the overall exit rate from the cluster is in-dependent of the cluster size [i.e., λk = λ and μk = k × (μ/k) = μ]. Inthis model there is a constant exit of lymphocytes from the cluster,and the number of cells exiting per unit of time is independent ofthe cluster size. This model allows for bigger clusters to increase insize more rapidly because they will lose fewer cells per capita. Inthis case the formation of a cluster of size k has the probability
Pk =P0∏k−1
i= 0λi
∏ki= 1μi
=P0λk
μk= ð1−θÞθk; [S5]
where θ = λ/μ.Maximum likelihood estimation of the model parameters.The likelihoodof the experimental data given the model parameters is defined as
Lðdatajθ; θ1Þ=∏kmaxk= 0P
xðkÞk ;
where Pk is the probability of seeing a cluster of size k, given theparameters θ and θ1 (Eqs. S3–S5), x(k) is the number of clustersof size k, and kmax is the maximal cluster size set to be 30 in fits.By maximizing the likelihood with respect to the parameters,best-fit parameters can be found. It should be noted, however,that because we are assuming a steady-state distribution of clus-ter sizes we are unable to estimate individual rate parameterssuch as λ and μ but only their ratio.The model fitting, parameter estimation, and the statistical
comparison of the models were done using R software (version2.15.1). Confidence intervals for the parameters of the modelswere computed using the confint tool in R, which uses thelikelihood profile method (1). The relative goodness-of-fit ofthe three models were calculated using the Akaike informationcriterion (AIC), which evaluates each model by its level of vari-ance from the data and the number of its parameters (2, 3). Morespecifically, we calculate Akaike weights for every model usingstandard techniques (3), which are interpreted as the relativeweight of a given model among all tested models. A low weightvalue for a particular model (e.g., <0.01) indicates that this modelis inferior at describing experimental data compared with othertested models.
Imaging Analysis. T-cell analysis was performed using Imaris.T-cell movement was manually tracked and the distance of theT cell from the nearest parasite determined at each time point.T cells were defined as clustering if they were within 40 μm ofa parasite. The cluster score for each parasite was the number ofclustering T cells at each time point measured/time. By mappingthe migration of T cells we were able to determine the speed(track length/time), displacement rate, and meandering index(total displacement/track length) for T cells inside and outsideclusters. If a T cell entered or exited the clustering area theT-cell track was split into sections accordingly. Tracks were onlyincluded if they lasted >5 min. We also calculated the entry rateof T cell in clusters—T cells were defined as entering clusters ifthey came within 40 um of parasites and remained there for >5
Cockburn et al. www.pnas.org/cgi/content/short/1303858110 1 of 8
min. Parasite vitality indices (VI) were determined in ImageJ bytaking the log10 ratio of the brightness of the parasite/brightnessof the background based on maximal Z projections.
Immunofluorescence Staining. Immunofluorescence staining of liversections was performed essentially as described previously (4).Briefly livers were perfused with HBSS followed by PLP buffer[0.05 M phosphate buffer containing 0.1 M L-lysine (pH 7.4),2 mg/mL NaIO4, and 10 mg/mL paraformaldehyde], fixed for anadditional 12 h, and dehydrated in 30% (wt/vol) sucrose beforeembedding in OCT freezing media (Tissue-Tek). Sections of 20μm were cut on a CM3050S cryostat (Leica) and adhered toSuperfrost Plus slides (Electron Microscopy Services). Sectionswere permeabilized and blocked in PBS containing 0.1% TritonX-100 (Sigma) and 10% (vol/vol) goat serum followed by stainingin PBS containing 0.01% Triton X-100 and 5% (vol/vol) goatserum. The following antibodies were used: α-CD146 (cloneEPR3208; Merck Milipore), followed by goat α-rabbit Ig Alexa488 (Invitrogen) and α-CD8 eFluor615 (clone 53-6.7; eBio-science). Stained slides were mounted with Prolong Gold (In-vitrogen), and images were acquired on an LSM 710 confocalmicroscope (Carl Zeiss).
In Vitro Cytoxicity Assay.Cytoxicity of T cells was measured in vitroas previously described (5). Briefly A20 target cells either pulsedwith peptide, or control cells that were left unpulsed, were la-beled with carboxyfluorescein succinimidyl ester (CFSE) andincubated with effector PyTCR CD8+ T cells at a range of ef-
fector to target ratios. After 6 h the number of remaining targetcells was counted by flow cytometry. Acquisition was normalizedbetween samples by the addition of 50 μL of counting beads(Invitrogen). Specific lysis was determined by measuring thenumber of remaining peptide pulsed target cells as a percentageof the number of remaining unpulsed cells.
Intracellular Cytokine Staining. For analysis of T-cell functionalitybased on cytokine production, spleen cells were incubated withpeptide-coated target cells in the presence of protein transportinhibitors and then stained for intracellular cytokines. Briefly,A20 target cells were pulsedwith SYVPSAEQI peptide (2 μg/mL),and control A20 cells were incubated without peptide. Peptide-coated or control target cells (6 × 105 per well) were added toa 96-well V-bottom plate with 2 × 106 effector PyTCR CD8+
T cells. To measure cytokine production, cells were incubatedwith brefeldin A (GolgiPlug; BD Biosciences) to block proteintransport. Cells were stimulated for 5 h at 37 °C and thenwashed twice in cold media and then surface stained with α-CD8(clone 53-6.7) and α-Thy-1.1. Cells were then permeabilized andfixed using a Cytofix/Cytoperm kit (BD Biosciences) according tothe manufacturer’s instructions and stained for intracellular cy-tokines using α-IFN-γ (clone XMG1.2), α-TNF-α (clone MP6-XT22; both from eBioscience) at predetermined concentrations.Cells were then washed and analyzed on a FACSCalibur flowcytometer (BD Bioscience).
1. Johnson JB, Omland KS (2004) Model selection in ecology and evolution. Trends EcolEvol 19(2):101–108.
2. Akaike H, Tanabe K, Parzen E, Kitagawa G (1998) Selected Papers of Hirotugu Akaike(Springer, New York) p VIII.
3. Burnham KP, Anderson DR (2002) Model Selection and Multimodel Inference: APractical Information-Theoretic Approach (Springer, New York), 2nd Ed, p xxvi.
4. Egen JG, et al. (2011) Intravital imaging reveals limited antigen presentation and T celleffector function in mycobacterial granulomas. Immunity 34(5):807–819.
5. Jedema I, van der Werff NM, Barge RM, Willemze R, Falkenburg JH (2004) New CFSE-based assay to determine susceptibility to lysis by cytotoxic T cells of leukemic precursorcells within a heterogeneous target cell population. Blood 103(7):2677–2682.
Cells transferred separatelyA
Cells transferred togetherB
0 5 10 15 20 250
25
50
75
100 OT-I CD8+ T cells
Num
ber o
f inf
ecte
d h
epat
ocyt
es
Density-dependent recruitmentw = 0.224Density-independent exit w = 0.555
Poisson w = 0.221
Observed
OT-I cells in 40μm radius / infected hepatocyte
i
i
ii
ii
0 5 10 15 20 250
25
50
75
100 PyTCR CD8+ T cells
Density-dependent recruitmentw = 1Density-independent exit w = 0
Poisson w = 0
Observed
PyTCR cells in 40μm radius / infected hepatocyte
Num
ber o
f inf
ecte
d h
epat
ocyt
es
0 6 120
10
20
30
40
Density-dependent recruitmentw = 0.998Density-independent exit w = 0.002
Poisson w = 0
Observed
PyTCR CD8+ T cells
PyTCR cells in 40μm radius/ infected hepatocyte
Num
ber o
f inf
ecte
d h
epat
ocyt
es
0 6 120
10
20
30
40 OT-I CD8+ T cells
Density-dependent recruitmentw = 0.993Density-independent exit w = 0.007
Poisson w = 0
Observed
OT-I cells in 40μm radius/ infected hepatocyte
Num
ber o
f inf
ecte
d h
epat
ocyt
es
Fig. S1. Modeling of clustering formation by specific and nonspecific T cells. (A) Frequency distribution of (i) OT-1 CD8+ T cells and (ii) PyTCR CD8+ T cellsaround infected hepatocytes when transferred to different animals compared with the distribution that would be expected for three different models forT-cell clustering: random entry and exit (red line), density-independent exit (gray line), and density-dependent recruitment (green line; data from Fig. 2A). (B)Frequency distribution of (i) OT-1 CD8+ T cells and (ii) PyTCR CD8+ T cells around infected hepatocytes when transferred to the same animal compared with thedistribution that would be expected for three different models for T-cell clustering: random entry and exit (red line), density-independent exit (gray line), anddensity-dependent recruitment (green line; data from Fig. 2B). Akaike weights (w) for every model fitted to the experimental data are shown on individualpanels. Estimated parameters for these models and their 95% confidence intervals (CIs) are given in Table S1.
Cockburn et al. www.pnas.org/cgi/content/short/1303858110 2 of 8
40µm
iii
P. yoelii-GFP Py-TCR track OT-I track
Speed (μm
/min)
Dis
tanc
e fro
m in
fect
ed h
epat
ocyt
e (μ
m)
cell entering cluster
cell leaving cluster
0 10 20 30 400
25
50
75
100
0
5
10
15
20
0 10 20 30 400
25
50
75
100
0
5
10
15
20ii
i
Time (mins)
A B
Fig. S2. Real time analysis of T-cell behavior. (A) PyTCR CD8+ T-cell (red) and OT-I CD8+ T-cell trails (gray) relative to a PyGFP-infected hepatocyte in a rep-resentative movie. The dashed white line indicates a circle of 40-μm radius drawn around the parasite-infected cell, marking the clustering region. (B) Graphs ofthe velocity and distance from parasite of (i) a PyTCR CD8+ T cell entering the clustering area, and (ii) an OT-I CD8+ T cell exiting the clustering region. Grayregions represent the time the cell is inside the clustering area.
naïve -3 18 24 1.0x104
1.0x105
1.0x106
1.0x107
1.0x108
time of PyTCR transfer(hrs p.i.)
******
***
Par
asite
18S
rRN
A (A
U)
Fig. S3. Effector PyTCR CD8+ T cells eliminate parasites when transferred 20 h after infection. RT-PCR of P. yoelii 18S RNA was used to determine the parasiteload in the livers of naïve mice (black bars) and mice that had received PyTCR CD8+ T cells at the designated times (white bars). Data are mean ± SE of four miceper group from one of two independent experiments. *** indicates a P value of < 0.0001 by Student’s t test.
Cockburn et al. www.pnas.org/cgi/content/short/1303858110 3 of 8
spee
d (μ
m/m
in)
0.0
2.5
5.0
7.5
10.0
12.5p < 0.0001
outsidecluster
insidecluster
B
mea
nder
ing
inde
x
0.00
0.25
0.50
0.75
1.00p < 0.0001A
outsidecluster
insidecluster
Fig. S4. Motility of PyTCR CD8+ T cells in BALB/c mice. (A) Speed and (B) meandering indices of PyTCR CD8+ T-cell motility in P. yoelii-infected mice for cellsinside and outside of the clustering region around infected hepatocytes (based on the experiment as described in Fig. 3).
30 min
0.0
0.5
1.0V
I
30 min
0.0
0.5
1.0
VI36/39
3/39
15μm
15μm
P. yoelii - GFP
P. yoelii - GFP
A
B
Fig. S5. Fate of parasites in naïve mice with no PyTCR CD8+ T cells transferred. Naïve BALB/c mice were inoculated with 3 × 105 PyGFP parasites and imaged for2 h starting 24–29 h after parasite inoculation. Figure shows montages of representative parasites illustrating (A) parasites that survive the imaging period and(B) parasites that show significant GFP loss during the experiment. Images are maximal projections of 9–15 Z sections, each 5 μm apart; graphs show the changein VI over time, with symbols showing when the montage images were taken.
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20 22 24 26 28 30 32 34
refs
narT
oN
Pyre
fsna
rTR
CT
CellTransfer
Hours post-infection
~1/ 50 h(Death events/recording time)
~1/ 8 h(Death events/recording time)
~1/4 h(Death events/interaction time)
Infected hepatocyte (interacting with PyTCR CD8+ T cell)Infected hepatocyte (no interaction)Death event
Fig. S6. Outline of the timing and duration of imaging for all P. yoelii parasites imaged in Fig. 3 and Fig. S5. Time (in hours after infection) is indicated on they axis. Each parasite is represented by a colored bar corresponding to the time of imaging. Green indicates that the parasite was not associated with a PyTCRCD8+ T cell, whereas red indicates the time that parasites were associated with at that time. Arrowheads to mark death events are placed the point where theparasite VI became ≤0.21 [the lower 95% CI for live control parasites (Fig. 3C)].
C
Cel
l lys
is (%
of c
ontro
l)
0.25 1 40
10
20
30
40
50
60
70Vehicle+PTx
Effector:Target
D
0
25
50
75
100
% o
f PyT
CR
++
-+
+-
--
Vehicle+PTx
ns
ns ns
ns
Par
ench
ymal
A
Sin
usoi
dal
PyTCR CD8+ T cell Mergeanti-CD8 anti-CD146
B
Vehicle +PTx0
25
50
75
100
% o
f cel
ls in
par
ench
yma ns
Fig. S7. PTx-treated PyTCR CD8+ T cells have intact cytotoxic activity and cytokine secretion. PyTCR transgenic cells were purified, treated with PTx or PBS(vehicle), labeled with Cell Tracker Blue CMAC (Invitrogen), and transferred to BALB/c mice. Four hours later the livers were taken, fixed, sectioned, and stained.(A) Representative images of PyTCR transgenic cells (i) within the parenchyma and (ii) in the sinusoids. Liver sinusoidal endothelial cells were identified withanti-CD146, whereas anti-CD8 was used to costain the transferred T cells. (A) Representative confocal images of PyTCR CD8+ T cells in the parenchyma and thesinusoid. (B) Proportion of PyTCR CD8+ T cells in the parenchyma in mice that received vehicle treated cells (white bar) or PTx-treated cells (black bar) based onthree mice per group; data analyzed by unpaired Student’s t test. (C) Day-9 effector PyTCR CD8+ T cells were incubated with PTx or vehicle and their ability tospecifically lyse peptide pulsed A20 cells measured at different effector to target cell ratios. (D) Secretion of IFN-γ and TNF-α by effector PyTCR CD8+ T cells thathad been treated with PTx (black bars) or vehicle alone (white bars). Graphs indicate the proportion of PyTCR CD8+ T cells producing different combinations ofcytokines upon stimulation with peptide pulsed A20 cells. Data were analyzed by paired Student’s t tests.
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Table S1. Estimates of the parameters of the three basic models fitted to experimental data oncluster formation
Condition Model θ θ1 AIC
Endogenous Random entry/exit 4.2 (3.75–4.74) — 461DD recruitment 0.7 (0.47–1.1) 0.8 (0.74–0.94) 337DI exit 0.8 (0.77–0.87) — 338
OT1 cells alone Random entry/exit 0.16 (0.10–0.26) — 91DD recruitment 0.12 (0.06–0.22) 0.24 (0.01–0.77) 90DI exit 0.14 (0.083–0.21) — 89
PyTCR cells alone Random entry/exit 1.6 (1.4–1.8) — 772DD recruitment 0.20 (0.14–0.28) 0.88 (0.81–0.94) 391DI exit 0.61 (0.56–0.66) — 448
OT1 cells mixed Random entry/exit 1.1 (0.80–1.36) — 208DD recruitment 0.22 (0.12–0.38) 0.79 (0.62–0.92) 140DI exit 0.51 (0.42–0.61) — 150
PyTCR cells mixed Random entry/exit 1.2 (0.95–1.6) — 231DD recruitment 0.21 (0.12–0.37) 0.83 (0.68–0.94) 149DI exit 0.55 (0.46–0.64) — 162
Fits of the data by the models are shown in Fig. 1C and Fig. S1. Parameter estimates (and their 95% CIs) forthe three models [random entry/exit, density-dependent (DD) recruitment, density-independent (DI) exit] fittedto each dataset. Here θ is the ratio of the entrance to exit rate, and θ1 denotes the density-dependent additionalentrance rate, λ1, divided by the exit rate, μ. The prediction of the model with DD recruitment was normalizedassuming that kmax = 30.The lowest AIC score indicates the best fitting model for each dataset. AIC values wereused to calculate Akaike weights shown in Fig. 1C and Fig. S1. Dash (–), not applicable.
Movie S1. Clustering of specific and nonspecific CD8+ T cells around an infected hepatocyte. Time-lapse movie of PyTCR CD8+ T cells (red) and OT-I CD8+
T cells (cyan) clustering around a P. yoelii GFP-infected hepatocyte. Note the blebbing of the GFP body and the loss of the GFP signal over time. Time stampindicates hours after infection.
Movie S1
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Movie S2. Parasite destruction by PyTCR CD8+ T cells (DP1). Time-lapse movie of a Py-GFP parasite (green) undergoing rapid loss of GFP while in associationwith effector PyTCR CD8+ T cells (red). Note the residual halo of GFP after 25 h. Time stamp indicates number of hours after infection.
Movie S2
Movie S3. Parasite destruction by PyTCR CD8+ T cells (DP2). Time-lapse movie of a Py-GFP parasite (green) undergoing progressive loss of GFP while in as-sociation with effector PyTCR CD8+ T cells (red). Time stamp indicates number of hours after infection.
Movie S3
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Movie S4. Parasite destruction by PyTCR CD8+ T cells (DP3). Time-lapse movie of a single parasite (green) dying while in association with effector PyTCR CD8+
T cells (red). Note blebbing of parasite material out of the infected cell. Time stamp indicates number of hours after infection.
Movie S4
Movie S5. Parasite destruction by PyTCR CD8+ T cells (DP4). Time-lapse movie of a Py-GFP parasite (green) undergoing rapid loss of GFP while in associationwith a PyTCR CD8+ T-cell (red). Note that the loss of GFP signal in this case seems to be absolute. Time stamp indicates number of hours after infection.
Movie S5
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