Feedback Signals in Myelodysplastic Syndromes: Increased Self-Renewal of the Malignant Clone Suppresses Normal Hematopoiesis

Myelodysplastic syndromes (MDS) are triggered by an aberrant hematopoietic stem cell (HSC). It is, however, unclear how this clone interferes with physiologic blood formation. In this study, we followed the hypothesis that the MDS clone impinges on feedback signals for self-renewal and differentiation and thereby suppresses normal hematopoiesis. Based on the theory that the MDS clone affects feedback signals for self-renewal and differentiation and hence suppresses normal hematopoiesis, we have developed a mathematical model to simulate different modifications in MDS-initiating cells and systemic feedback signals during disease development. These simulations revealed that the disease initiating cells must have higher self-renewal rates than normal HSCs to outcompete normal hematopoiesis. We assumed that self-renewal is the default pathway of stem and progenitor cells which is down-regulated by an increasing number of primitive cells in the bone marrow niche – including the premature MDS cells. Furthermore, the proliferative signal is up-regulated by cytopenia. Overall, our model is compatible with clinically observed MDS development, even though a single mutation scenario is unlikely for real disease progression which is usually associated with complex clonal hierarchy. For experimental validation of systemic feedback signals, we analyzed the impact of MDS patient derived serum on hematopoietic progenitor cells in vitro: in fact, MDS serum slightly increased proliferation, whereas maintenance of primitive phenotype was reduced. However, MDS serum did not significantly affect colony forming unit (CFU) frequencies indicating that regulation of self-renewal may involve local signals from the niche. Taken together, we suggest that initial mutations in MDS particularly favor aberrant high self-renewal rates. Accumulation of primitive MDS cells in the bone marrow then interferes with feedback signals for normal hematopoiesis – which then results in cytopenia.


Mathematical modeling of normal hematopoiesis and MDS
The mathematical model developed in this study describes the interaction of physiological hematopoiesis and MDS cells. It is based on a previously proposed model of the hematopoietic system [1] that was extended to describe leukemia dynamics [2]. According to the classical understanding, hematopoiesis is assumed to be a multi-step process [3,4] in which cells move through an ordered sequence of different maturation stages (compartments). The following maturation stages are considered: (1) long-term repopulating stem cells (LT-HSCs), (2) short-term repopulating stem cells (ST-HSCs), (3) multi-potent progenitor cells (MPPs), (4) committed progenitor cells (CPCs), (5) precursors and (6) mature cells. For simplicity, we take only one hematopoietic lineage into account.
We assume that daughter cells arising from division can either belong to the same type as the mother cell (self-renewal) or to a more mature cell type (differentiation). Time dynamics of each compartment are governed by cell gain due to self-renewal and by cell loss due to differentiation or apoptosis. The following cell properties are considered [1]: (1) proliferation rate, describing how many cell divisions take place per unit of time. We assume that mature blood cells and the most differentiated dysplastic cells are post-mitotic. (2) Fraction of self-renewal, describing which fraction of daughter cells belongs to the same maturation stage as their mother cell. (3) Apoptosis rate, describing which fraction of a cell population dies per unit of time.
It is further assumed that physiological hematopoiesis is regulated by feedback signals. In contrast to previous models, we consider two different feedback signals: (1) The signal for proliferation is inversely correlated with the number of mature cells -resulting in higher proliferation upon cytopenia. This signal is motivated by the regulation of hematopoiesis by cytokines such as G-CSF or EPO, which increase if there is a shortage of mature cells [5,6]. For simplicity, we assume that this signal acts on all mitotic cells although some cell lineages and maturation stages are probably more sensitive than others. It is well known that many cytokines act on more than one cell type, e.g. G-CSF acts on the myeloid lineage and on HSC at the same time [6].
(2) The signal regulating self-renewal is dependent on the number of stem and progenitor cells in the marrow niche and acts on the cells residing in the niche. This signal is motivated by the fact that primitive cells require an appropriate microenvironment to maintain stemness [4,7]. We assume that if cells are outcompeted from this microenvironment, they can no longer perform self-renewal. For this reason, self-renewal rates decrease if the number of cells in the niche increases. For simplicity, we assume that the three most primitive cell types of each lineage are located in the bone marrow niche.
It is assumed that the MDS clone is maintained by cells with stem cell-like properties. It is known that MDS cells possess variable potential to differentiate into mature cells [8,9]. For simplicity, we assume in this model that no mature cells are produced by MDS cells (this does not account for the alternative model presented in Figure S1). Therefore, we consider five compartments of aberrant cells (MDS-LT-HSCs, MDS-ST-HSCs, MDS-MPPs, MDS-CPCs, and dysplastic progenitors). This maturation process is also regulated by the feedback signals mentioned above. We have tested various parameters for the MDS clone. The results -and mathematical analysis [2] -demonstrate that the MDS-LT-HSC must reveal higher self-renewal potential than LT-HSCs for sustained disease progression. For different parameter values, qualitative behavior is very similar. Cell numbers and self-renewal rates for each compartment are chosen such that they adopt the same steady state behavior as described in our previous work [1]. For numerical simulations, we have used the ODE solver ode23t from Matlab (MathWorks, Natick, MA).

Derivation of the mathematical model
We use ordinary differential equations (ODEs) to describe interaction of hematopoietic and dysplastic cells. Time evolution of each maturation stage (compartment) is described by one ODE. We denote the concentration of healthy cells in maturation stage i at time t as for all t and 0 ) ( (this does not account for the alternative model in Figure 1 in Text S1).
At time t , the flux to mitosis in hematopoietic compartment i ( This amount of cells disappears from compartment i and gives rise to We assume that proliferation and self-renewal change over time due to the feedback signals ( 1 s and 2 s ). As derived from a quasi-steady-state approximation in our previous work [1], 1 s has the form The positive constant k depends on the rates of cytokine production and elimination. In analogy to our previous study [1], we assume that ( ) were chosen such that the physiological equilibrium of mature cells is of the order of 10 9 cells / L of blood and such that proliferation rates could increase about 3 to 4 fold under regenerative pressure [10]. Parameters for the hematopoietic system were chosen as previously described [1,11].

Model of hematopoiesis in presence of dysplastic cells
We assume that, similar to the hematopoietic system, all dysplastic cells depended on the signal 1 s and that the three most primitive dysplastic cell types depend on the signal for self-renewal 2 s .
Including modulation of 2 s by primitive MDS-cells leads to the following expression for 2 s : The positive constant l depends on production or elimination of signal molecules. This expression is motivated below.
For the interaction of healthy and dysplastic cells, the following ODE system is obtained: , for 3 ,..., 1 = j , the system describing healthy hematopoiesis is obtained.

Derivation of the feedback signal in presence of dysplastic cells
The concentration of the signal regulating self-renewal at time is denoted by ) (t S . We assume that self-renewal is the default pathway with signal production at constant rate S α . Degradation of this signal is assumed to be proportional to the cells in the bone marrow niche at a rate S β . We further assume a cell independent degradation at rate S γ . In analogy, we assume that dysplastic cells secrete an inhibitor I proportional to their concentrations at a rate I α and that this inhibitor is degraded at a constant rate I γ . The complex of inhibitor and signal molecules, denoted by IS , is supposed to be formed at a rate 1 k . After formation of the complex, the signal molecule is degraded at a rate 2 k . For simplicity, backward reactions are neglected. Dynamics of signal and inhibitor are described by the following ODE system: We assume that molecular dynamics are fast in comparison to cell proliferation and differentiation, i.e. they are in a quasi-steady-state. We denote steady state concentrations of I , S and IS in the above system as I , S and S I . We express them as a function of the level of hematopoietic and dysplastic cells. It holds:  Table 2 in Text S1.

Supplemental Figures
Legend on next page (A) In comparison to parameters of Figure 1, we used slightly different parameters for this alternative simulation: 1) MDS cells can progress to a dysplastic mature stage in peripheral blood which then also feeds back on proliferation, i.e. ̂ ; 2) proliferation rate of MDS cells of all differentiation stages is much higher than in normal hematopoiesis; and 3) dysplastic progenitors and dysplastic mature cells both undergo apoptosis at a much shorter half-life as compared to normal mature cells.
This is in accordance with higher apoptosis rates observed in MDS patient bone marrow and peripheral blood [12,13,14]. The corresponding parameters are indicated for each cell type.   Table 2 in Text S1. Error bars represent SEM (*p < 0.05, **p < 0.01).    Concentrations of SCF, bFGF and TPO in MDS-serum and healthy control serum samples were detected using RayBio Human ELISA Kits. Although there are tendencies to a higher amount of bFGF and TPO in MDS-serum samples, these differences were not statistically significant. Error bars represent SD.