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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