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Blood, Vol. 112, Issue 13, 4874-4883, December 15, 2008
Characterization and quantification of clonal heterogeneity among hematopoietic stem cells: a model-based approach
Blood Roeder et al.
112: 4874
Supplemental materials for: Roeder et al
Files in this Data Supplement:
- Table S1. Model parameters (PDF, 261 KB) -
Given are the numerical values of the model parameters that have been applied in all the simulations described in this work. They are based on estimates obtained in a previous model application described in 22 with a quantitative adjustment of the transition functions fα and fω, because we consider HSC pools of a different size.
- Figure S1. Model outline (JPG, 70.2 KB)
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(A) HSC are assumed to reside in two signalling contexts (A – dark gray, Ω − light gray). Whereas cells in Ω proliferate (cell cycle duration τC), cells in A are quiescent (G0). The propensity of cells to reside in A is given by a cell-intrinsic affinity a. Whereas a is gradually lost in Ω, it is regained in A. If a becomes smaller than amin, the cell loses its potential to change into context A. Such cells (denoted as differentiated cells) initiate the formation of clones, which transiently expand (proliferating precursors) for a fixed time λp. Thereafter, these clones exist for a fixed lifetime λn without further expansion (comprising non-proliferating precursors and terminally differentiated cells). To account for clonal heterogeneity of the stem cell population, the model parameters d (differentiation coefficient), r (regeneration coefficient), τC (cell cycle duration), as well as the transition characteristics fα and fω are specified for each clone i=1,2,… separately. Once an individual cell has been assigned a particular set of model parameters (at initiation/“birth” of the system), these are inherited without any change to the daughter cells, generating a HSC clone with fixed parameters. (B,C) Shown are the transition characteristics fα and fω together with their four characterizing parameters fα(0), fα(Ñ/2), fα(Ñ), Ñ, and fω(0), fω (Ñ′/2), fω(Ñ′), Ñ′, respectively. These values (see Table S1) represent the function values at cell numbers 0, Ñ/2 (Ñ′/2), Ñ (Ñ′), and the scaling cell number Ñ (Ñ′). The fifth parameter fα/ω(∞) that characterizes the asymptotic behavior of the characteristics is assumed to be fixed at the value 0 and is not shown. For technical details of the model implementation, the reader is referred to 23 and 27.
- Figure S2. Goodness-of-fit illustration (JPG, 180 KB)
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Shown are different parameter region and corresponding goodness-of-fit values as calculated by simulating 87 primary host engraftment kinetics with clonal parameters randomly chosen from the depicted regions and comparing them to the 87 experimentally observed engraftment kinetics.
- Figure S3. Simulated engraftment kinetics in primary and secondary recipients using the estimated parameter heterogeneity with respect to d and fα(Ñ) (JPG, 96.5 KB)
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(A–B) Shown are representative examples of simulated engraftment kinetics in primary (A) and secondary (B) hosts, obtained by applying the parameter configuration that yields an optimal concordance of experimentally observed and simulated primary host engraftment kinetics (cf. Fig. 4B in the main text). As in Fig. 1 of the main text, identical color codes indicate identical clonal origin in primary and secondary recipients. (C) Distributions of engraftment levels at 7 months post transplantation in primary hosts. (D–E) Distributions of engraftment trends (i.e. differences in engraftment levels between month 3 and month 7 post transplantation) in primary (B) and secondary (C) hosts. According to the number of experimentally determined engraftment kinetics, we simulated the repopulation of n=87 primary hosts and 8 pairs (n=16) of secondary hosts. Boxplots show the median (black line), the inter-quartile range (box), and the total range (whiskers, or circles in case of “outliers,” i.e. data point that deviate from the median more than 1.5 times the box range). P-values are given for the Bartlett-test of equality of variances.
- Figure S4. Additional simulation results on individual clone competition (JPG, 90.2 KB)
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(See Fig. 5 in the main text.) (A–B) Simulated primary host engraftments of clones with slightly differing parameters: (A) d = 1.0655, fα(Ñ) = 0.0075; (B) d = 1.0665, fα(Ñ) = 0.008. (C–D) Examples of secondary engraftment kinetics induced by in silico transplantation of HSCs from clonally repopulated primary hosts shown in panel (A) and (B), respectively. (E–Q) Examples of secondary engraftment kinetics induced by in silico co-transplantation of equal numbers of HSCs from clonally repopulated primary hosts shown in panel (A) and (B).
- Figure S5. Clonal heterogeneity for transition characteristic fα (JPG, 22.9 KB)
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The hatched regions illustrate the considered range of variation (clonal heterogeneity) of transition characteristic fα for different HSC clones within one mouse strain considered in the model. Between-strain variation of transition characteristics is illustrated for B6 mice (black) and for D2 mice (gray).
- Figure S6. Model-predicted engraftment kinetics depending on different strain backgrounds of host and/or donor cells (JPG, 244 KB)
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Simulated engraftment kinetics and corresponding numerical description of the engraftment distributions depending on the choice of model parameters d and fα(Ñ). The size of the used parameter regions is chosen according to the best-fit estimate for the clonal heterogeneity in B6 mice (panel C, cf. Fig. 4 in original publication). Each individual color dot represents the qualitative engraftment kinetics for one particular parameter combination according to the qualitative engraftment behavior (+, −, π) in the intervals 1–3 months and 3–7 months post-transplantation. Totally, 55074 different parameter combinations are shown in each panel. (A) DBA/2 (D2) donor cells transplanted into D2 hosts: Simulations were initiated with one donor cell with the particular d and fα(Ñ) values (according to the position in the diagram) and four competing host cells with reference D2 parameters d=1.07 and fα(Ñ)=0.015. All other parameter had been fixed to D2 reference values, identically for donor and host cells. (B) D2 donor cells transplanted into B6 hosts: see panel (A), but using donor cells with B6 reference values. (C) Scenario of B6 donor cells transplanted into B6 hosts (reproduction of Fig. 4B in the main text).
- Figure S7. Non-competitive repopulation of different individual clones (JPG, 59.6 KB)
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Given are simulated repopulation kinetics (total stem cell numbers) for the seven parameter configurations depicted in (A). Whereas five clones (2 × green, 2 × red, black) are chosen from within the parameter region estimated to account for the experimentally observed clonal heterogeneity (cf. Fig. 4 in original publication), two clones (light and dark blue) are chosen from different regions of the parameters space. Despite d and fα(Ñ) all other parameters are fixed at their reference values. (B) Repopulation of empty model systems (i.e. true non-competitive setting); each system is initiated by a single stem cell with different (clonal) properties regarding parameters d and fα(Ñ). The color codes refer to the particular parameter choice shown in (A). (C) See (B), but this time a non-clonal competitive situtation, i.e. competitive repopulation with 100 identical donor and four residual host cells.
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