aggregation kinetics of well- and poorly differentiated prostate cancer cells r. enmon, k....
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Aggregation Kinetics of Well-Aggregation Kinetics of Well-and Poorly Differentiated Prostate and Poorly Differentiated Prostate
Cancer CellsCancer Cells
R. Enmon, K. O’Connor, H. Song, D. LacksR. Enmon, K. O’Connor, H. Song, D. Lacksand D. Schwartzand D. Schwartz
Tulane University and Medical SchoolTulane University and Medical SchoolUniversity of Colorado, BoulderUniversity of Colorado, Boulder
ObjectivesObjectives
• Evaluate responsiveness of kinetic model to: – Phenotype – Aggregate size – Cell Concentration
• Gain insight into aggregation mechanisms
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Previous ResearchPrevious Research
Attachment IndependentAttachment Independent Attachment DependentAttachment Dependent
Bovine Corneal Endothelial Bovine Corneal Endothelial CellsCells
(Muhitch et al., 2000.(Muhitch et al., 2000.CytotechnolCytotechnol. . 3232: : 253-263)253-263)
ChondrocytesChondrocytes
(Vunjak-Novakovic et al., 1998. (Vunjak-Novakovic et al., 1998. Biotechnol. ProgBiotechnol. Prog. . 1414: 193-202): 193-202)
DU 145 Human Prostate CellsDU 145 Human Prostate Cells
((Enmon et al., 2001. Enmon et al., 2001. Biotechnol. Bioeng.Biotechnol. Bioeng.
7272: 579-91: 579-91))
Jurkat Human T-CellsJurkat Human T-Cells
((Neelamegham and Zygourakis, 1997. Neelamegham and Zygourakis, 1997. Ann. Biomed. Eng.Ann. Biomed. Eng. 2525: 180-9): 180-9)
Blood PlateletsBlood Platelets
(Huang and Hellums, 1993. (Huang and Hellums, 1993. Biophys. J.Biophys. J. 6565: : 344-355)344-355)
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Phases of Spheroid AssemblyPhases of Spheroid Assembly
1 hr1 hr0 hr0 hr 24 hr24 hrend of end of cultureculture
Inoculation: random cell distribution
Redistribution: loss of cell-cell interaction, random cell movement
Aggregation: no dissociation, no growth, inter-spheroid interactions, constant rate parameter
Ripening: cell growth, differentiation, intra-spheroid interactions
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Human Prostate Cancer Human Prostate Cancer Cell LinesCell Lines
• LNCaP: retains an epithelial phenotype and is weakly invasive
• DU 145: poorly differentiated and moderately invasive
• PC 3: poorly differentiated and highly invasive
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Transition in Spheroid AssemblyTransition in Spheroid Assembly
Legend:
Aggregation
Ripening
DU 145
LNCaP
PC 3
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0.0E+00
1.0E+03
2.0E+03
3.0E+03
4.0E+03
5.0E+03
6.0E+03
1 10 100
Time (hours)
Average Spheroid Projected Area
(μm
2 )
Aggregation of DU 145 CellsAggregation of DU 145 Cells1 hr1 hr 1 hr 40 min1 hr 40 min
5 hr5 hr 16 hr16 hr
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Area/Cell Number CorrelationsArea/Cell Number CorrelationsDU 145DU 145
LNCaPLNCaP
PC 3PC 3
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0.0E+00
3.0E+03
6.0E+03
9.0E+03
1.2E+04
0 10 20 30 40
Cells/Spheroid
Spheroid Projected Area
(μm2)
LNCaP 3PC 145DU
A
proj
=
202 . 1 ⋅ i
1 . 1
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ i ≤ 8
477 . 2 ⋅ i
0 . 67
⋅ ⋅ ⋅ ⋅ i ≥ 9
⎫
⎬
⎪
⎭
⎪
⎧
⎨
⎪
⎩
⎪
Aproj =290.6⋅i1.0
Aproj =
258.1⋅i1.0 ⋅ ⋅⋅⋅⋅⋅ ⋅⋅⋅⋅⋅ ⋅i<6
(258.1⋅i1.0)(15−i
9)+
(989.1⋅i0.62)(i−6
9)⋅⋅⋅6≤i≤15
989.1⋅i0.62⋅⋅⋅⋅⋅ ⋅⋅⋅⋅⋅⋅ ⋅⋅i >15
⎫
⎬
⎪ ⎪ ⎪ ⎪
⎭
⎪ ⎪ ⎪ ⎪
⎧
⎨
⎪ ⎪ ⎪ ⎪
⎩
⎪ ⎪ ⎪ ⎪
Kinetic ModelKinetic Model
Accumulation = Input - OutputAccumulation = Input - Output
dCdC11/dt = - C/dt = - C11 CCjj k kijij(1+(1+1j1j) single cells) single cells
dCdCii/dt = 0.5/dt = 0.5CCjjCCi-ji-jkkj,i-jj,i-j(1+(1+j,i-jj,i-j) ) - C- Cii CCjjkkijij(1+(1+ijij) spheroids) spheroids
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Kinetic Rate ConstantsKinetic Rate Constants
• kii = a + bi+ ci2 + di3
• symmetric across diagonal: ki,j = kj,i
• ki,j = (ki,i + kj,j )/2 ki,j = (ki,ikj,j)1/2
Rate Constant Matrix
kk1,11,1 k k10,110,1 k k20,120,1
kk1,101,10 k k10,1010,10 k k20,1020,10
kk1,201,20 k k10,2010,20 k k20,2020,20
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Model PredictionsModel Predictions[S
ph
eroi
ds]
X 1
0[S
ph
eroi
ds]
X 1
055
Time (hours)Time (hours)
DU 145DU 145 LNCaPLNCaP PC 3PC 3
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1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
0 5 10 15 20 25
single dimeri=4 i=6i=8 i=10
A
1.0E-01
1.0E+00
1.0E+01
1.0E+02
0 5 10 15 20 25
i=12 i=14i=16 i=18i=20 i=22i=24 B
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
0 5 10 15 20 25
single dimeri=4 i=6i=8 i=10
C
1.0E-01
1.0E+00
1.0E+01
1.0E+02
0 5 10 15 20 25
i=12 i=14i=16 i=18i=20 i=22i=24
D
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
0 5 10 15 20 25
single dimeri=4 i=6i=8 i=10
E
1.0E-01
1.0E+00
1.0E+01
1.0E+02
0 5 10 15 20 25
i=12 i=14i=16 i=18i=20
F
Cell Concentration EffectsCell Concentration Effects
Rate Constants for 2 x 104 cells/cm2:
kii (h-1) = -0.4 + 1.1i - 0.11i2 + 0.01i3
kij = (kiikjj)1/2
Cell Concentration: 1 x 104 cells/cm2
Cell/Volume Ratio: 1.6 x 105 cells/ml
DU 145DU 145
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1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
0 5 10 15 20 25
Time (hours)
[Spheroid] X 10
5
single dimer n=4
n=6 n=8 n=10
n=12
Self-Aggregation RatesSelf-Aggregation Rates
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1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
0 5 10 15 20 25
Cells/Spheroid
kii (h
-1)
DU 145LNCaPPC 3
0.0E+00
3.0E+03
6.0E+03
9.0E+03
1.2E+04
0 10 20 30 40
Cells/Spheroid
Spheroid Projected Area
(μm2)
LNCaP 3PC 145DU
Physical Interpretation of Rate Physical Interpretation of Rate ParameterParameter
Smoluchowski Expression:Smoluchowski Expression:
kkIJIJ = = (R (RII + R + RJJ) (D) (DII +D +DJJ))
Ideal CaseIdeal Case
spheroid is perfect spherespheroid is perfect sphere
max. radius = rmax. radius = rII
= 1= 1
RRII = r = rII
DDII 1/r1/rII
Spheroid Self-AssemblySpheroid Self-Assembly
spheroid is not perfect spherespheroid is not perfect sphere
max. radius > rmax. radius > rII
< 1< 1
RRII f(cell number) f(cell number)
DDII f(cell number) f(cell number)
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Cell MotilityCell Motility
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1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
0 5 10 15 20 25
Cells/Spheroid
kii (h
-1)
DU 145LNCaPPC 3
1.0E+00
1.0E+01
1.0E+02
0 5 10 15 20 25
Cells/Spheroid
Diffusion Coefficient
(μm
2 / )min
DU 145LNCaP
PC 3 Einstein
PC 3 PRW
Adhesion ProbabilityAdhesion Probabilityclass of % of successful
interaction collisions
DU 145 PC 3 LNCaP
cell-cell 16.6 ± 4.1a 11 ± 3.1a 100
cell-spheroid 83.1 ± 9.1a 63 ± 7.3b 100
dimer-spheroid 52.4 ± 6.7a 63 ± 8.2b 100
trimer-spheroid 33.3 ± 6.7a 69 ± 8.3b 100
spheroid-spheorid 55.6 ± 6.7a 71 ± 8.4b 100ab indicates statistically significantgroups
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1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
0 5 10 15 20 25
Cells/Spheroid
kii (h-1)
DU 145LNCaPPC 3
Intra-Spheroidal AdhesionIntra-Spheroidal Adhesion
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1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
0 5 10 15 20 25
Cells/Spheroid
kii (h
-1)
DU 145LNCaPPC 3
E-Cadherin ExpressionE-Cadherin Expression
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T-FlaskT-Flask Liquid-Overlay CultureLiquid-Overlay Culture
DU 145DU 145 DU 145DU 145 LNCaPLNCaP PC 3PC 3
FluorescenceFluorescenceMicroscopyMicroscopy
Phase-ContrastPhase-ContrastMicroscopyMicroscopy
E-Cadherin ExpressionE-Cadherin Expression
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Liquid-Overlay Cultures Single Cell Spheroid
Cell Line % Positive Intensity a% Positive Intensity a
DU145 18 ± 4 25.8 ± 10.8 100 27.3 ± 7.1
LNCaP 100 94.2 ± 9.1 100 88.7 ± 8.2
PC 3 11 ± 3 19.6 ± 4.3 28 ± 6 22.1 ± 4.0aintensity reported as % above background per ( μm
2)
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
0 5 10 15 20 25
Cells/Spheroid
kii (h-1)
DU 145LNCaPPC 3
Collagen IV ExpressionCollagen IV Expression
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Liquid-Overlay CultureLiquid-Overlay Culture
DU 145DU 145 LNCaPLNCaP PC 3PC 3
Phase-ContrastPhase-ContrastMicroscopyMicroscopy
FluorescenceFluorescenceMicroscopyMicroscopy
Collagen IV ExpressionCollagen IV Expression
Liquid-Overlay Culture Single Cell Spheroid
Cell Line % Positive Intensity a% Positive Intensity a
DU 145 35 ± 6 27.3 ± 11.5 91 ± 7 17.81 ± 12.3
LNCaP 100 42.0 ± 11.7 100 40.0 ± 11.5
PC 3 33 ± 4 20.5 ± 10.7 46 ± 8 29.9 ± 13.78aintensity reported as % above background per ( μm
2)
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1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
0 5 10 15 20 25
Cells/Spheroid
kii (h-1)
DU 145LNCaPPC 3
ConclusionsConclusions
Aggregation rates– Responsive to cell concentration
– Consistent with adhesive properties than with motilities
– Sensitive to phenotypic differences in cell lines
– Described size-dependent changes in aggregation at a fine resolution
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ApplicationsApplications
• Spheroid production for tissue engineering and in vitro drug testing
• Assay to evaluate adhesive capacity
• Cell flocculation in suspension cultures and for bioseparation
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AcknowledgementsAcknowledgements
This research was funded with grants from
NASA and the Tulane Cancer Center.
Time lapse images and additional information is
available at our web site:
http://www.tulane.edu/~kim/oconnor.html
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