Experimental setup
1
Experimental setup Human articul ar cartila ge biopsy three donors (A, B and C) Introduction EXPERIMENTAL AND MATHEMATICAL STUDY OF THE INFLUENCE OF GROWTH FACTORS ON THE GROWTH KINETICS OF ADULT HUMAN ARTICULAR CHONDROCYTES ¹A. Barbero, ²V. Palumberi, 3 B. Wagner, ¹R. Sader, ²M.J. Grote and ¹I. Martin ¹Department of Surgery and of Research, University Hospital Basel, Switzerland; [email protected] ²Department of Mathematics, University of Basel, Switzerland 3 Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany Growth curves AHAC Prolonged expansion Conclusion 0h, 8h, 16h, 24h, ..... Microcolony test Generation time (G T ): Kinetic parameters Growth curves 1000 cells/cm 2 2.5 cells/cm 2 A B C D E F G I L M H N days Ncells 0 80000 160000 240000 320000 400000 0 2 4 6 8 10 12 tim e in culture (day) N um ber cells/cm q * * * * * * * * 0 20 40 60 80 100 0 16 32 48 64 80 96 112 128 144 tim e in culture (hours) % ofm icrocolonies 0 20 40 60 80 100 0 16 32 48 64 80 96 112 128 144 tim e in culture (hours) % ofm icrocolonies 1 cell 2 cells 4 cells P1 AHAC P2 AHAC CTR TFP CTR TFP CTR TFP Mathematical Model Time of first cell division (Tcd): Percentage of quiescent cells (Qc): Fraction of cells dividing per G T (Fc(T)): Time required by each seeded cell to reach the stage of a 2-cell microcolony Time required by each 2-cell microcolony to reach the stage of a 4-cell microcolony Percentage of cells that did not reach the stage of 2-cell microcolonies DFi: ratio between the new cells that appear in the i-th interval and the cells at the previous interval; N: number of time intervals; T : total observation time T 1 N 1 i T/G DFi Fc(T) Microcolony test CTR TFP 0 20 40 60 80 100 <16 17-32 >33 Percentage ofcells group I Tcd16h group II Tc 17-32h group III Tcd33h * 0 20 40 60 80 100 fast middle slow Percentage ofcells * * group I G T 16h group II G T 17-32h group III G T 33h CTR TFP CTR TFP 0 20 40 60 80 100 8--16 17-32 >33 group I G T 16h group II G T 17-32h group III G T 33h Percentage of cells CTR TFP Tim e offirstcelldivision (Tcd,hours) 55.5 ± 8.0 40.7 ± 11.0* Percentage ofquiescentcells (Q c) 23.5 ± 6.0 13.5 ± 6.9* G eneration tim e (G T ,hours) 28.6 ± 2.9 23.8 ± 2.7* Fraction ofcelldividing perG T (Fc(T)) 0.86 ± 0.01 0.87 ± 0.02 Time of first cell division (Tcd) Generation time (G T ) Time of first cell division (Tcd) 0 20 40 60 80 100 8--16 17-32 >33 16h 17-32h 33h group I Tcd16h group II Tcd 17-32h group III Tcd33h Percentage of cells 0 20 40 60 80 100 8--16 17-32 >33 group I Tcd16h group II Tcd 17-32h group III Tcd33h Percentage of cells CTR 0 20 40 60 80 100 8--16 17-32 >33 group I G T 16h group II G T 17-32h group III G T 33h Percentage of cells Generation time (G T ) CTR TFP TFP p1 p2 p1 p2 Kinetic parameters Microcolony progression analysis Data Fitting Carrying capacity (K): CTR TFP P1 P2 P1 P2 Tim e offirstcelldivision (hours) 53.6 ± 21.9 41.9 ± 18.3* 53.3 ± 16.9 25.5 ± 14.7* Percentage ofquiescentcells 30.3 4.4 21.2 2.6 G eneration tim e (g T ,hours) 31.1 ± 13.0 27.5 ± 9.7 25.6 ± 12.2 26.1 ± 7.9 Fraction ofcells dividing pergT 0.85 ± 0.14 0.88 ± 0.13 0.87 ± 0.1 0.85 ± 0.12 expansion References Growth curves of AHAC expanded in CTR and TFP medium; cell number was measured every 12 hours and normalized to the dish surface area; values are the mean ± SD of cells from 3 donors. * = P< 0.05 from AHAC expanded in CTR. Parameters are reported as mean ± SD of values calculated for three donors .* = P < 0.05 from CTR medium. Microcolony progression analysis of AHAC from one characteristic donor expanded in CTR or TFP medium. The number of a given microcolony type observed is expressed as a percent of the total observed. Time of first cell division and generation time of cells expanded in CTR or TFP medium, following subdivision in arbitrary groups. * = P< 0.05 from AHAC expanded in CTR Values of G T , or K are fitted by (I) or (III) to the experimental data. Parameters are reported as mean ± SD of values calculated for three donors = N(t - G T ); t 0 dN dt N(t) = Ψ(t), - G T t < 0 = N(t - G T ) 1 - ; t>0, N(0) = N 0 dN dt N(t) K Delay model ( d, e ) Logistic delay model (I) (III) N(t) = Ψ(t), - G T t < 0 Kinetic parameters Experimental ( for CTR and TF for TFP medium) and predicted (- - - for CTR, — for TFP medium) growth curves of cells from donors A, B or C Time of first cell division (T cd ) and generation time (G T ) in cells from patient C cultured for one passage (P1) or two passages (P2) in CTR and TFP medium, following subdivision in arbitrary groups. Growth curves of P2 cells from donor C obtained applying G T of 16 (‑‑‑) or 26 (—) hours in the logistic model. Describe that the mathematical model was able to predict the effective temporal growth in cell number only if the measured G T , but not a shorter G T , was given as input. The circles ( F ) indicate the experimentally determined number of cells. Summary of growth kinetic parameters derived for cells from patient C cultured for one passage (P1) or two passages (P2) in CTR or TFP medium. * = P < 0.05 from P1 cells. Human adult articular chondrocytes (AHAC) were culture for one (P1) or two (P2) passages without (CTR) or with TGF-, FGF-2 and PDGF-BB (TFP) and used for the kinetic studies. Growth curves AHAC were seeded in CTR or TFP medium at a density of 1000 cells/cm 2 . Cell proliferation was assessed fluorimetrically during 12 days' culture. Microcolony tests AHAC were seeded in CTR or TFP medium at a density of 2.5 cells/cm 2 . The number of cells in each microcolony was counted each 8 hours using phase contrast microscopy CTR TFP 1 day 4 days 8 days 12 days Representative pictures of adult human articular chondrocytes (AHAC) expanded up to 12 days in CTR andr TFP medium. Bar = 100m. Cell morphology To investigate how growth factors (GF) during cell expansion increase cell number, the monitoring of several growth kinetic parameters is essential. Recently we reported that the number of adult human articular chondrocytes (AHAC) obtained following monolayer culture is markedly increased by the use of TGF1, FGF-2, or PDGF- BB ( a ), especially when used in combination (TFP) ( b ). The goals of this study are: (1) to determine how specific growth kinetic parameters of AHAC growth are modulated by TFP using the microcolony test ( c ); (2) to develop a delay model with a logistic term to capture the kinetic parameters and to enable the description of the complete growth process of the cell culture; (3) to investigate using the experimental and mathematical methods, whether prolonged expansion induces an enrichment in the fraction of the fastest proliferating cells. The mathematical model fits well the experimental data of the growth kinetic, confirms the value of G T and provides estimates for the carrying capacity of the system (K) and the proliferation rate () Prolonged expansion does not increase the fraction of the fastest proliferating AHAC, but rather the fraction of AHAC with a higher propensity to initiate duplication, particularly in the presence of TFP CTR TFP G eneration tim e (G T,hours) 25.4 ± 5.3 23.0 ± 5.6 Proliferation rate ( ) 0.90 ± 0.18 1.37 ± 0.25 D oubling tim e (D T ,hours) 32.4 ± 2.0 24.0 ± 1.7 C arring capacity (K ) 10.5 ± 2.0 38.5 ± 1.8 Donor A Donor B Donor C TFP medium increases the number of AHAC in monolayer culture by reducing Qc, Tcd, and G T . AHAC expanded in TFP contain a higher fraction of cells with short Tcd and G T TFP medium permits to obtain larger number of AHAC with small and elongated shape (1) TFP medium increases the number of chondrocytes in monolayer culture by reducing (i) the percentage of Q c , (ii) the mean time required for single cells to enter the first division (T cd ), and (iii) the mean cell division time of cells (generation time, G T ) (2) Our mathematical model confirmed the value of G T and provided estimates for the carrying capacity of the system (K) and the proliferation rate (), which were higher in chondrocytes cultured in TFP (3) Our results for chondrocytes from the same donor at different passages in culture indicate that prolonged expansion does not increase the fraction of the fastest proliferating AHAC, but rather the fraction of AHAC with a higher propensity to initiate duplication, particularly in the presence of TFP. Further studies are in progress to extend the mathematical model to predict cell growth in relation to spatial cell distribution and migration. Fc(T) is an index of the ''exponentiality'’: it is equals 1 for an ideal exponential growth number of cells in the monolayer which can be reached at confluence (a) Jakob et al. 2001. J Cell Biochem 81:368-377 (b) Barbero et al. 2004. Osteoarthritis Cartilage 12:476-484 (c) Sherley et al. 1995. Proc Natl Acad Sci USA 92:136-140 (d) Baker et al. 1998. J Math Biol 37:341-371 (e) Sherley et al. 1995. Cell Prolif 28:137-144. = Proliferation rate G T = Generation time Ψ(t) defines the rate at which new cells appear over [0, G T ]. For an asynchronous growth, Ψ(t) is a constant equals to N 0 /(G T ). Considering that the behaviour of (I) tends to that of an exponential model at long times, we can calculate the Doubling time (D T ): D T = ln(2)/ where is a solution of the transcendental equation = exp(-G T ) Here the growth rate is no longer the single parameter but is given by (1 - N(t)/K), which decreases to zero as the number of cells N(t) tends to the constant K. This study is published as: Barbero A., Palumberi V., Wagner B., Sader R., Grote MJ & Martin I. J Cell Physiol. 2005 Sep;204(3):830-8
description
group II G T 17-32h. group II Tcd 17-32h. group II Tcd 17-32h. group II G T 17-32h. group II Tc 17-32h. group II G T 17-32h. group III G T 33h. group III Tcd 33h. group III Tcd 33h. group III G T 33h. group III Tcd 33h. group III G T 33h. group I G T 16h. - PowerPoint PPT Presentation
Transcript of Experimental setup
Experimental setupHuman articularcartilage biopsy
three donors(A, B and C)
Introduction
EXPERIMENTAL AND MATHEMATICAL STUDY OF THE INFLUENCE OF GROWTH FACTORS ON THE GROWTH KINETICS OF ADULT HUMAN ARTICULAR CHONDROCYTES
¹A. Barbero, ²V. Palumberi, 3B. Wagner, ¹R. Sader, ²M.J. Grote and ¹I. Martin¹Department of Surgery and of Research, University Hospital Basel, Switzerland; [email protected]
²Department of Mathematics, University of Basel, Switzerland 3Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany
Growth curves
AHAC Prolonged expansion Conclusion
0h, 8h, 16h, 24h, .....
Microcolony test
Generation time (GT):
Kinetic parameters
Growth curves
1000 cells/cm2
2.5 cells/cm2
A B C
D
EF
G
I
L
M
H N
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0 2 4 6 8 10 12time in culture (day)
Nu
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er
cells/c
mq
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**
** * *
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0 16 32 48 64 80 96 112 128 144
time in culture (hours)
% o
f m
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0 16 32 48 64 80 96 112 128 144
time in culture (hours)
% o
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1 cell2 cells4 cells
P1 AHAC
P2 AHAC
CTR
TFP
CTR
TFP
CTR
TFP
Mathematical Model
Time of first cell division (Tcd):
Percentage of quiescent cells (Qc):
Fraction of cells dividing per GT (Fc(T)):
Time required by each seeded cell to reach the stage of a 2-cell microcolony
Time required by each 2-cell microcolony to reach the stage of a 4-cell microcolony
Percentage of cells that did not reach the stage of 2-cell microcolonies
DFi: ratio between the new cells that appear in the i-th interval and the cells at the previous interval; N: number of time intervals; T : total observation time
T
1N
1i
T/G
DFiFc(T)
Microcolony test
CTR
TFP
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20
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<16 17-32 >33
Per
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e o
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lls
group ITcd16h
group IITc 17-32h
group IIITcd33h
*
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fast middle slow
Per
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group IGT 16h
group IIGT 17-32h
group IIIGT 33h
CTRTFP
CTRTFP
16h 17-32h 33h
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8--16 17-32 >33group IGT 16h
group IIGT 17-32h
group IIIGT 33h
Per
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CTR TFP
Time of first celldivision (Tcd, hours) 55.5 ± 8.0 40.7 ± 11.0*
Percentage of quiescent cells (Qc) 23.5 ± 6.0 13.5 ± 6.9*
Generation time (GT, hours) 28.6 ± 2.9 23.8 ± 2.7*
Fraction of cell dividing per GT (Fc(T)) 0.86 ± 0.01 0.87 ± 0.02
Time of first cell division (Tcd)
Generation time (GT)
Time of first cell division (Tcd)
0
20
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8--16 17-32 >3316h 17-32h 33hgroup ITcd16h
group IITcd 17-32h
group IIITcd33h
Per
cen
tag
e o
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lls
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20
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8--16 17-32 >33group ITcd16h
group IITcd 17-32h
group IIITcd33h
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e o
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lls CTR
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8--16 17-32 >33group IGT 16h
group IIGT 17-32h
group IIIGT 33h
Per
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Generation time (GT)
CTR
TFP
TFP
p1p2
p1p2
Kinetic parametersMicrocolony progression analysis
Data Fitting
Carrying capacity (K):
CTR TFPP1 P2 P1 P2
Time of first cell division (hours) 53.6 ± 21.9 41.9 ± 18.3* 53.3 ± 16.9 25.5 ± 14.7*
Percentage of quiescent cells 30.3 4.4 21.2 2.6
Generation time (gT, hours) 31.1 ± 13.0 27.5 ± 9.7 25.6 ± 12.2 26.1 ± 7.9
Fraction of cells dividing per gT 0.85 ± 0.14 0.88 ± 0.13 0.87 ± 0.1 0.85 ± 0.12
expansion
References
Growth curves of AHAC expanded in CTR and TFP medium; cell number was measured every 12 hours and normalized to the dish surface area; values are the mean ± SD of cells from 3 donors. * = P< 0.05 from AHAC expanded in CTR.
Parameters are reported as mean ± SD of values calculated for three donors .* = P < 0.05 from CTR medium.
Microcolony progression analysis of AHAC from one characteristic donor expanded in CTR or TFP medium. The number of a given microcolony type observed is expressed as a percent of the total observed.
Time of first cell division and generation time of cells expanded in CTR or TFP medium, following subdivision in arbitrary groups. * = P< 0.05 from AHAC expanded in CTR
Values of GT, or K are fitted by (I) or (III) to the experimental data. Parameters are reported as mean ± SD of values calculated for three donors
= N(t - GT); t 0dNdt
N(t) = Ψ(t), - GT t < 0
= N(t - GT) 1 - ; t>0, N(0) = N0
dNdt
N(t)K
Delay model (d, e)
Logistic delay model
(I)
(III)
N(t) = Ψ(t), - GT t < 0
Kinetic parameters
Experimental ( for CTR and TF for TFP medium) and predicted (- - - for CTR, — for TFP medium) growth curves of
cells from donors A, B or C
Time of first cell division (Tcd) and generation time (GT) in cells from patient C cultured for one passage (P1) or two passages (P2) in CTR and TFP medium,
following subdivision in arbitrary groups.
Growth curves of P2 cells from donor C obtained applying GT of 16 (‑‑‑) or 26 (—) hours in the logistic model. Describe that the mathematical model was able to predict the effective temporal growth in cell number only if the measured GT, but not a shorter GT, was given as input. The circles ( F )
indicate the experimentally determined number of cells.
Summary of growth kinetic parameters derived for cells from patient C cultured for one passage (P1) or two passages (P2) in CTR or TFP medium. * = P < 0.05 from P1 cells.
Human adult articular chondrocytes (AHAC) were culture for one (P1) or two (P2) passages without (CTR) or with TGF-, FGF-2 and PDGF-BB (TFP) and used for the kinetic studies. Growth curves AHAC were seeded in CTR or TFP medium at a density of 1000 cells/cm2. Cell proliferation was assessed fluorimetrically during 12 days' culture. Microcolony tests AHAC were seeded in CTR or TFP medium at a density of 2.5 cells/cm2. The number of cells in each microcolony was counted each 8 hours using phase contrast microscopy
CT
RT
FP
1 day 4 days 8 days 12 days
Representative pictures of adult human articular chondrocytes (AHAC) expanded up to 12 days in CTR andr TFP medium. Bar = 100m.
Cell morphology
To investigate how growth factors (GF) during cell expansion increase cell number, the monitoring of several growth kinetic parameters is essential. Recently we reported that the number of adult human articular chondrocytes (AHAC) obtained following monolayer culture is markedly increased by the use of TGF1, FGF-2, or PDGF-BB (a), especially when used in combination (TFP) (b).
The goals of this study are:
(1) to determine how specific growth kinetic parameters of AHAC growth are modulated by TFP using the microcolony test (c);
(2) to develop a delay model with a logistic term to capture the kinetic parameters and to enable the description of the complete growth process of the cell culture;
(3) to investigate using the experimental and mathematical methods, whether prolonged expansion induces an enrichment in the fraction of the fastest proliferating cells.
The mathematical model fits well the experimental data of the growth kinetic, confirms the value of GT and provides estimates for the carrying capacity of the system (K) and the proliferation rate ()
Prolonged expansion does not increase the fraction of the fastest proliferating AHAC, but rather the fraction of AHAC with a higher propensity to initiate duplication, particularly in the presence of TFP
CTR TFP
Generation time (GT, hours) 25.4 ± 5.3 23.0 ± 5.6
Proliferation rate () 0.90 ± 0.18 1.37 ± 0.25
Doubling time (DT, hours) 32.4 ± 2.0 24.0 ± 1.7
Carring capacity (K) 10.5 ± 2.0 38.5 ± 1.8
Donor A Donor B
Donor C
TFP medium increases the number of AHAC in monolayer culture by reducing Qc, Tcd, and GT. AHAC expanded in TFP contain a higher fraction of cells with short Tcd and GT
TFP medium permits to obtain larger number of AHAC with small and elongated shape
(1) TFP medium increases the number of chondrocytes in monolayer culture by reducing (i) the percentage of Qc, (ii) the mean time required for single cells to enter the first division (Tcd), and (iii) the mean cell division time of cells (generation time, GT)
(2) Our mathematical model confirmed the value of GT and provided estimates for the carrying capacity of the system (K) and the proliferation rate (), which were higher in chondrocytes cultured in TFP
(3) Our results for chondrocytes from the same donor at different passages in culture indicate that prolonged expansion does not increase the fraction of the fastest proliferating AHAC, but rather the fraction of AHAC with a higher propensity to initiate duplication, particularly in the presence of TFP.
Further studies are in progress to extend the mathematical model to predict cell growth in relation to spatial cell distribution and migration.
Fc(T) is an index of the ''exponentiality'’: it is equals 1 for an ideal exponential growth
number of cells in the monolayer which can be reached at confluence
(a) Jakob et al. 2001. J Cell Biochem 81:368-377
(b) Barbero et al. 2004. Osteoarthritis Cartilage 12:476-484
(c) Sherley et al. 1995. Proc Natl Acad Sci USA 92:136-140
(d) Baker et al. 1998. J Math Biol 37:341-371
(e) Sherley et al. 1995. Cell Prolif 28:137-144.
= Proliferation rate GT = Generation time
Ψ(t) defines the rate at which new cells appear over [0, GT]. For an asynchronous growth, Ψ(t) is a constant equals to N0 /(GT ).
Considering that the behaviour of (I) tends to that of an exponential model at long times, we can calculate the Doubling time (DT): DT = ln(2)/where is a solution of the transcendental equation = exp(-GT)
Here the growth rate is no longer the single parameter but is given by (1 - N(t)/K), which decreases to zero as the number of cells N(t) tends to the constant K.
This study is published as:
Barbero A., Palumberi V., Wagner B., Sader R., Grote MJ & Martin I. J Cell Physiol. 2005 Sep;204(3):830-8
