An Integrative multi-lineage model of variation in leukopoiesis and acute myelogenous leukemia
- Joyatee M. Sarker^{1},
- Serena M. Pearce^{1},
- Robert P. NelsonJr.^{2},
- Tamara L. Kinzer-Ursem^{1},
- David M. Umulis^{1, 3}Email authorView ORCID ID profile and
- Ann E. Rundell^{1}
https://doi.org/10.1186/s12918-017-0469-2
© The Author(s) 2017
Received: 8 February 2017
Accepted: 11 August 2017
Published: 25 August 2017
Abstract
Background
Acute myelogenous leukemia (AML) progresses uniquely in each patient. However, patients are typically treated with the same types of chemotherapy, despite biological differences that lead to differential responses to treatment.
Results
Here we present a multi-lineage multi-compartment model of the hematopoietic system that captures patient-to-patient variation in both the concentration and rates of change of hematopoietic cell populations. By constraining the model against clinical hematopoietic cell recovery data derived from patients who have received induction chemotherapy, we identified trends for parameters that must be met by the model; for example, the mitosis rates and the probability of self-renewal of progenitor cells are inversely related. Within the data-consistent models, we found 22,796 parameter sets that meet chemotherapy response criteria. Simulations of these parameter sets display diverse dynamics in the cell populations. To identify large trends in these model outputs, we clustered the simulated cell population dynamics using k-means clustering and identified thirteen ‘representative patient’ dynamics. In each of these patient clusters, we simulated AML and found that clusters with the greatest mitotic capacity experience clinical cancer outcomes more likely to lead to shorter survival times. Conversely, other parameters, including lower death rates or mobilization rates, did not correlate with survival times.
Conclusions
Using the multi-lineage model of hematopoiesis, we have identified several key features that determine leukocyte homeostasis, including self-renewal probabilities and mitosis rates, but not mobilization rates. Other influential parameters that regulate AML model behavior are responses to cytokines/growth factors produced in peripheral blood that target the probability of self-renewal of neutrophil progenitors. Finally, our model predicts that the mitosis rate of cancer is the most predictive parameter for survival time, followed closely by parameters that affect the self-renewal of cancer stem cells; most current therapies target mitosis rate, but based on our results, we propose that additional therapeutic targeting of self-renewal of cancer stem cells will lead to even higher survival rates.
Keywords
Acute myelogenous leukemia Mathematical model Personalized medicine Hematopoiesis LeukopoiesisBackground
Acute myelogenous leukemia (AML) is a cancer of the white blood cells stemming from the myeloid lineage that produces cells including neutrophils and monocytes [1]. On average, four in 100,000 individuals will develop AML, with a median age of 67 years at diagnosis. AML has the highest mortality rate of all of the different types of leukemia [2]. The French-American-British (FAB) co-operative group identified eight different subcategories of AML, M0-M7, based on the specific cell population from which AML arises [3]. More recent classification systems now exist that include other criteria besides white cell morphology [4, 5]. Regardless, the majority of patients with AML receive essentially identical induction chemotherapy with drugs that target DNA replication [6]. Unfortunately, for the patients over 55 years of age diagnosed with AML, the 5-year survival rate is 10% and the relapse rate is 80% [7]. Given the variability of AML progression among patients, understanding determinants of disease progression will lead to therapeutic advances that result in lower rates of relapse and higher rates of survival.
Computational modeling is an effective tool to personalize therapies for improved patient outcomes. Model-based personalized therapy has improved several medical interventions including: glucose control in type I diabetes [8, 9]; automatic control of anesthesia dosage [10–12]; and pacemaker control of heart rate variability [13]. Presently, AML treatment is not benefiting from model-based personalized approaches, in part due to a lack of multi-lineage AML computational models [14, 15]. Key features of a computational model of hematopoiesis includes: normal formation of mature cells from hematopoietic stem cells (HSCs) [16–24]; abnormal development leading to leukemia [18, 25–27]; treatment using chemotherapy or transplantation [17, 25, 26]; movement of cells between the bone marrow/tissue and the peripheral blood where AML is frequently measured [20, 28–35]; and the feedback signals from cytokines that participate in the regulation of hematopoiesis [20, 25, 26, 28]. Previous models that contain various elements of these key features exist (summarized in Additional file 1: Table S1 in Supplement 1). Here, we focus on the development of a multi-lineage AML model that captures patient variability and use the model to identify patient sub-types and identify potential novel therapeutic targets.
In this work, we develop a semi-mechanistic multi-lineage multi-compartment computational model of hematopoiesis and AML. The model describes the interactions of various lineages of hematopoietic stem cells, including neutrophils, lymphocytes, and monocytes. Patient data is used to constrain the model, creating a large number of data-consistent solutions that differ in their responses to chemotherapy. We apply the constraints from patient data to characterize normal hematopoiesis versus leukemic differentiation and growth in unique parameter sets representing 22,796 simulated patient dynamics. To identify trends in dynamical variability, we clustered the simulated dynamics into thirteen ‘representative patient’ groups. We find that our mathematical model can be used to demonstrate the typical variation in the dynamics of AML progression and patient clinical outcomes. Using sensitivity analysis and correlation analysis, we identified important parameters whose variation most affects the development of leukemia.
Methods
Model Configuration
The leukopoiesis process consists of a set of discrete stages of cellular differentiation. There are three different stages of cell development representing the maturation of the stem cells into mature leukocytes (Fig. 1, solid black circles). The first stage contains the hematopoietic stem cells (HSCs) that either asymmetrically self-renew or differentiate. We assume this HSC compartment consists of many stages of cells that have the capability to differentiate into various lineages, as previous work has shown that the dynamics of mature cells are appropriately represented in a two-compartment system [36–38]. The stem cells proportionally differentiate into distinct progenitors, including common lymphoid progenitors and granulocyte/myeloid progenitors that then clonally amplify their branching lineages [39]. All three lineages are necessary to demonstrate lineage dominance and cell-cell interactions amongst the three most-commonly measured white blood cell types (see Additional file 1: Supplement 3, Table S5 for further justification of these three lineages). Other multi-lineage models do not consider these three lineages [21–24]. Granulocyte/myeloid progenitors produce mature neutrophils and monocytes, which have relatively short life-spans and are replaced daily. Lymphoid progenitors branch into immature B-lymphocytes and T-lymphocytes, yielding more complex and less predictable dynamics than those of myeloid cells. Thus, we focused on studying myeloid cell production, destruction, and deviations associated with myeloid leukemias instead of the less predictable lymphoid leukemias. The process of proliferation and differentiation in our model ensures a physiological mechanism that repopulates the bone marrow after chemotherapy and ensures that the formation of a single mutated cell in the HSC compartment can result in AML.
Mature cells are maintained in three different compartments: the bone marrow or tissue (yellow compartment in Fig. 1), the circulating peripheral blood (red compartment in Fig. 1), and the non-circulating peripheral blood, or marginal pool (blue compartment in Fig. 1). Cells migrate from both the bone marrow and marginal pool to the peripheral blood and are recruited to the bone marrow or marginal pools from the peripheral blood [40–42]. Since the concentration of normal white blood cells in the bone marrow and peripheral blood may vary over several orders of magnitude [40], it is essential to compute the dynamics of the proliferation of cells within the bone marrow and the mobilization of cells. Other multi-lineage models do not demonstrate movement of cells amongst compartments [21–24], and mobilization is typically limited to neutrophils or monocytes [20, 27–31, 33–35]. Additionally, neutrophils and monocytes also remain in non-circulating peripheral blood pools, or marginal pools, to allow for massive demargination upon a trigger event, such as chemotherapy [40, 43].
Here, X _{0} is the state of interest; p _{0} is the proliferation term, typically described as asymmetric self-renewal (circular arrows in Fig. 1; based on [19]; described further in Additional file 1: Supplement 3); s _{−1} is the differentiation (specialization) term from a stem cell or progenitor state, X _{−1}, to the state of interest, X _{0}; s _{0} is the differentiation term from the state of interest, X _{0}, to a more mature state (straight solid arrows in Fig. 1); m _{−1} is the mobilization or margination term from the corresponding bone marrow or peripheral blood state, X _{ b m/p b }, to the state of interest, X _{0} (forward dashed arrows in Fig. 1); r _{0} is the recruitment term of X _{0} to another compartment (backward dashed arrows in Fig. 1); and d _{0} is the loss, or death rate (x’s in Fig. 1). Further details of this model are described in Additional file 1: Supplement 3. A few key physiological details, including feedback and cell-cell interactions in the multi-lineage model, are described below.
Feedback
Here, k is the Michaelis-Menten constant; C is the concentration of the cell state that produces cytokines for feedback; r is the rate the feedback modifies; and X is the cell state targeted by cytokines. To model the formation of AML from monocytes, we simulated the multiple-hit hypothesis and assumed all feedback signals did not effect a single normal monocyte progenitor, as expected from literature [49].
Inhibitory feedback prevents cells from growing uncontrollably in any state. Thus, our model has several inhibition mechanisms to regulate the concentration of cells. In particular, inhibition feedback modifies every rate except cell death in our model. All movement is inhibited by the concentration of cells in the compartment to which cells are moving to prevent overcrowding using Michaelis-Menten type kinetics (Eq. 2). Proliferation and differentiation are hindered by inhibiting the associated self-renewal probability of stem cells [19]. For progenitor cells, this inhibition occurs from cytokines produced by mature cells of the same lineage in the peripheral blood [50]. However, for stem cell proliferation and differentiation, this inhibition occurs from a scaled combination of the concentration of stem cells to ensure that sufficient stem cells are in the hematopoietic system and the concentration of cells in the bone marrow (yellow compartment in Fig. 1) do not exceed the capacity of the marrow. All negative feedback signals are pictorially described in Additional file 1: Figure S1. The derivation of both the form for asymmetric self-renewal and the capacity of the bone marrow are in Additional file 1: Supplement 3.
In contrast, several physiological processes in hematopoiesis are triggered by positive feedback. In response to an inflammatory event, mature white blood cells proliferate to accommodate this response. We include two states in our model that demonstrate the effect of debris clearance due to chemotherapy. Monocytes are recruited into the bone marrow to become activated macrophages to help clear excessive cellular debris [41], which we have modeled as the ‘Apoptosis’ state. Macrophages assist in recruiting other white blood cells, such as lymphocytes, neutrophils, and monocytes, during inflammation or other diseases [41], which we have also incorporated into the model. Positive feedback is used in our model to demonstrate several processes, including inducing proliferation of macrophages by apoptotic debris; promoting the recruitment of neutrophils, lymphocytes, and other monocytes into the tissue in response to high levels of macrophages; and increasing the clearing rate of apoptosis due to a high level of macrophages. All positive feedback signals are pictorially described in Additional file 1: Figure S2. Additional file 1: Table S4 in Supplement 2 describes each of the feedback processes in detail.
Results
Parameter selection
Capabilities of multi-lineage hematopoiesis model
Healthy dynamical acceptability criteria |
---|
1. Peripheral blood recovers > 80 cells/ μL [58] |
2. Stem cells recover > 1 cell/ μL [58] |
3. Final dynamic values are within acceptable ranges (Additional file 1: Supplement 4) [40, 59] |
4. Marginal pool is within one order of magnitude of peripheral blood [43] |
5. Cell counts reduce with chemotherapy to < 20% of original value [63] |
6. Recovery overshoot < 12 times value five days after overshoot [hematopoietic stem cell transplant patient data from Dr. Robert Nelson, shown in Additional file 1: Supplement 5]. |
7. Amplitude of the second peak of oscillations deviates < 18% from the amplitude of the first peak [cutoff calculated, explained in Additional file 5: Supplement 5]. |
Physiological capabilities of model
- 1.
Peripheral blood recovers > 80 cells/ μ L: This ensures that the peripheral blood sufficiently recovers after chemotherapy treatment, and the final peripheral blood cell count must be > 80 cells/ μL [58].
- 2.
Stem cells recovery > 1 cell/ μ L: The final stem cell concentration must be between 1 and 100 cells/ μL. If the stem cell concentration is within the acceptable bounds, the stem cells should also show recovery after chemotherapy occurring [58].
- 3.
Final dynamic values are within acceptable ranges: The final uni-lineage peripheral blood cell counts after chemotherapy must be within the upper limits of expected normal peripheral blood cell counts [40, 59]. Neutropenia (low number of neutrophils in the peripheral blood) is very common after undergoing chemotherapy [60], but neutrophilia mostly occurs if another underlying disease exists to cause the high number of neutrophils. We do not want to model neutrophilia during recovery from chemotherapy because that is not a typical response in patients with AML. The values each cell state must be within are depicted in Additional file 1: Supplement 4, Table S6.
- 4.
Marginal pool is within one order of magnitude of peripheral blood: The final concentration of the cells in the marginal pool must be within one order of magnitude of the final concentration of the peripheral blood because the size of the marginal pool and peripheral blood compartments are approximately the same [43, 61, 62]. Though a marginal pool can exist for lymphocytes, it is much smaller than that of neutrophils and monocytes [43]. Thus, we do not incorporate a lymphocyte marginal pool in our model.
- 5.
Cell counts reduce with chemotherapy to <20 % of original value: The concentration of cells remaining at the end of chemotherapy should be less than 20% of the concentration of cells before chemotherapy begins [63].
- 6.
Recovery overshoot < 12 times value five days after overshoot: Patients experience lymphopenia, or low white blood cell concentrations, during chemotherapy. After the chemotherapy regimen is completed, patients’ cell counts almost always increase. In some instances, patient cell counts increase and peak above their final homeostatic cell concentration. Here, we define this overshoot level as the maximum concentration of cells after chemotherapy administration is completed. If the overshoot level is more than twelve times the concentration of cells five days after the overshoot (or the concentration of cells at the end of the simulation, whichever comes first), the solution is rejected. This overshoot was the maximum observed in the HSCT patient data from the Simon Cancer Center (Additional file 1: Figure S6 in Supplement 5).
- 7.
Amplitude of the second peak of oscillations deviates < 18% from the amplitude of the first peak: Several simulations produced oscillations. Though some small oscillations are reasonable and can occur physiologically, large oscillations are unlikely because they will not maintain normal homeostasis in the body and most patients who are treated for AML do not report large oscillations in cell counts. We manually classified 100 simulations for sufficiently dampened oscillations. We calculated that a simulation was sufficiently dampened if the cell concentration of the second peak value post-chemotherapy was less than an 18% decrease from the first peak post-chemotherapy. Thus, we implemented this cutoff for all of our simulations. An example of a simulation that does not meet this criteria and a simulation that does meet this criteria are shown in Additional file 1: Figure S7 in Supplement 5.
For each uni-lineage parameter search, two criteria were salient in determining which models met the physiological features required based on responses to chemotherapy. The remainder of the criteria are mostly robust in constraining the parameter space. One of the salient criteria was the lack of oscillations for each uni-lineage model. This implies that the need to maintain a steady-state concentration of cells for each of the lineages independently is one of the key constraints in normal hematopoiesis and is consistent with parameters that lead to balanced feedback. The second criteria that largely determined the acceptable uni-lineage models were the final peripheral blood acceptable dynamics of the neutrophil uni-lineage model, stem cell recovery for the lymphocyte uni-lineage model, and sufficient response to chemotherapy for the monocyte uni-lineage model (indicated with asterisks in Fig. 3). This reflects the necessity of maintaining high concentrations of neutrophils in homeostasis and the ability of cells to repopulate cell populations for appropriate recovery. If we relaxed the constraints imposed on the model set by the features of normal physiological dynamics, the acceptable parameter sets would be larger as well.
Parameter constraints with separatrix method
The separatrix method distinguishes between parameter regions of acceptable solutions and regions of unacceptable solutions, and in log-space, this manifests as a clear separatrix. We first constrain to the acceptable range of each parameter (dashed black box in Fig. 4). For each unique pair of uni-lineage parameters, we then divide the parameter range rectangle into 10×10 equally sized bins. If the acceptable parameter set is uniformly distributed in parameter space, every bin has a cutoff of (number of acceptable simulations)/100 acceptable parameter sets. Thus, each of the 100 bins is either acceptable or unacceptable depending on whether more acceptable parameter sets existed in the bin than the cutoff value. We then further constrain this acceptable parameter density by removing corners of the range rectangle that did not maintain a cutoff density of acceptable parameter sets (dashed green lines in Fig. 4). Thus, we found a set of inequalities for each unique pair of parameter sets in the uni-lineage parameterization in log space. We used this separatrix constraint on the parameter search space for multi-lineage parameterization.
The separatrices of each pair-wise parameter relationship confirm parameter relationships from previous works, and we identified additional required relationships in the acceptable solutions. As Getto et al. [38] and Stiehl et al. [52] show, the mitosis rate of stem cells and the probability of self-renewal are inversely related. However, we found that this also extends to all progenitor cells (Fig. 4 a-c). Specifically, a linear relationship emerges between the log of the self-renewal probability and the log of the mitosis rate. Solutions that have larger mitosis rate or self-renewal probabilities produce oscillations (red x’s in Fig. 4), which we constrained against in our dynamical acceptability criteria (Criteria 7 in Table 1). We also found a similar inverse linear relationship between the log of the self-renewal probability of neutrophil progenitors and the log of the homeostatic constant of neutrophils in the peripheral blood; solutions that have lower values of either of these two parameters becomes unacceptable (Fig. 4 d). Overall, this finding means that a specific relationship is maintained between the probability of self-renewal and the mitosis rate for all cells that are capable of self-renewing to ensure that the cell population remains steady. Additionally, due to the high concentration of neutrophils, a constrained feedback mechanism exists between the self-renewal probability of neutrophil progenitors and the cytokines produced by neutrophils in the peripheral blood to maintain appropriate homeostatic concentrations of those cells. Overall, we confirmed the dependence on the mitosis rate and self-renewal probability of stem cells found by other groups (Fig. 4 e), but we also found additional dependencies on these same parameters of progenitor cells, as well as a specific dependence of the cytokines produced by neutrophils in the peripheral blood and the self-renewal probability of neutrophil progenitor cells.
Multi-lineage acceptable solutions
Sensitivity analysis reveals importance of self-renewal probability and cytokines
We carried out a sensitivity analysis on the multi-lineage solutions to determine the most important parameters whose variation most greatly affected output. Using a partial rank correlation coefficient (PRCC) method [66–68], we determined the parameters that were most impactful in determining concentrations of stem cells, neutrophils in the peripheral blood, lymphocytes in the peripheral blood, and monocytes in the peripheral blood. We found that, in general, the probability of self-renewal and the Michaelis-Menten constant that modifies both the rate of self-renewal probability and the movement of mature cells into the peripheral blood were the most important parameters for their respective cell states. This indicates that the probability of a cell to self-renew is very sensitive to changes in the system and can cause very drastic outcomes in the final cell concentration if this rate is affected, which corroborates with findings in Marciniak-Czochra et al. [19]. Additionally, for stem cells, the feedback cytokines from the concentration of cells in the bone marrow and the concentration of stem cells were very important parameters. These constants also modify the probability of self-renewal in the stem cells. Finally, many parameters that are associated with neutrophil homeostasis (self-renewal probability of neutrophil progenitors, mitosis rate, Michaelis-Menten constant, and mobilization rate) all were very important in the stem cell concentration. This is probably due to the large concentration of neutrophils affecting the homeostasis values of stem cells. The PRCC results are in Additional file 1: Supplement 6.
Representative patient clusters
Modeling leukemia
AML is a derivative of common granulocyte macrophage progenitor cells [3, 69]. Thus, leukemia is modeled parallel to the manner in which monocytes are modeled. We assume that the cancer stem cells self-renew and proliferate at the same rate as monocytic progenitor cells. These then differentiate into mature cancer within the bone marrow, which can mobilize into the peripheral blood. The only difference in the model between leukemic stem cells and monocytes is that the leukemic cells do not maintain homeostasis, so all feedback that regulates self-renewal [18, 70], differentiation, and movement were removed and the cancer cells cannot be recruited back to the tissue. Since we have modeled feedback from various signals, the mutated cancer cell that grows indefinitely is the product of several mutations that cause all feedback to be inhibited, as currently hypothesized in literature [49].
For a simple validation to ensure that cancer is not growing too slowly in our model, we can compare overall survival times of the simulations without treatments to trials in which patients received low-dose treatments. The majority of clinical patients who are unable to receive traditional chemotherapy and received hydroxyurea as a treatment post-diagnosis with AML died within one year of diagnosis even with favorable stratification [74]. We find the survival time in all of our simulations to be less than four months in after diagnosis of AML >20% blasts (Fig. 8 b). Thus, cancer growth fits within an expected bound of patient survival.
Cancer parameter bounds
Parameter | Lower bound | Upper bound |
---|---|---|
d _{ Mc } | 0.0001d _{ M } | d _{ M } |
a _{ M c2} | 0.01a _{ M2} | 1 |
m r _{ M c2} | 0.5m r _{ M2} | 30 |
m b _{ Mc } | 0.0001m b _{ M } | m b _{ M } |
Discussion
When a patient is diagnosed with AML, physicians assess the white blood cell counts of the patient to guide the course of action for treating the leukemia. Many patients are successfully treated with a stem cell or bone marrow transplant from a matched donor. However, for those patients who are unable to receive a transplant, chemotherapy is administered periodically to lower the cancer load on the patient. Generally, a high white blood cell count makes the patient a candidate for chemotherapy. However, it is likely that factors other than the absolute cell count are important for determining a patient’s prognosis. Using a multi-lineage model of the formation of white blood cells, we find that (1) certain physiological rate relationships are necessary to prevent unstable cell population growth and (2) the rate of growth of the cancer is an important prognostic factor in determining the survival time of patients.
We determined that there are specific physiological rates and cell concentrations that are crucial in maintaining homeostasis. As expected, progenitor cells are very important in homeostatic mechanisms. A sensitivity analysis demonstrated that the probability of self-renewal of all progenitor cells and parameters that modify this probability are the most important parameters in hematopoietic dynamics. Other groups have found similar results [19] in the context cancer [75, 76] and specifically AML [77]. Additionally, we found an inverse relationship between the self-renewal probability of stem cells and the mitosis rate of stem cells (Fig. 4 e), corroborating findings of other groups [38, 52]. This relationship between mitosis rate and self-renewal probability also exists for progenitor cells (Fig. 4 a-c), which was not found previously. In general, solutions that have high mitosis rates or self-renewal probabilities lead to oscillations in the cell concentrations. This oscillation is highly undesirable and can occur in diseases such as cyclic neutropenia. Previous work has shown that “re-entry" into the stem cell compartment was found to be one of the factors that control oscillation in cyclic neutropenia [22]. Our work suggests that the analogous self-renewal probability and mitosis rate of the same cell, whether it is the stem cell or another progenitor cell, are both crucial to control to prevent diseases such as cyclic neutropenia. Chemotherapy that targets only one of these rates may not be sufficient in controlling physiological oscillations. Thus, we recommend that the feedback mechanisms that govern the self-renewal probabilities are explored as potential pharmaceutical targets in AML treatment.
We found that peripheral blood concentration levels of neutrophils and lymphocytes are important factors in maintaining homeostasis in our model (Fig. 6), specifically in the multi-lineage context. This was evidenced in three ways. First, when we identified the capabilities of our multi-lineage model, we found that lymphocyte dynamics constrained the range of acceptable solutions for all three lineages (Fig. 5). This is likely due to the high selection rate of lymphocytes in the thymus (dL3, which is modeled as the tissue/bone marrow compartment) [54] and low death rate of lymphocytes in the peripheral blood (dL3pb) [25]; this can lead to fast dynamic changes if not constrained appropriately. Second, the inverse relationship between the self-renewal probability of neutrophil progenitors and the homeostatic term for neutrophil progenitors is a novel relationship in hematopoietic modeling that tightly regulates healthy neutrophil behavior (Fig. 4 d). This means that in order to maintain healthy levels of neutrophils at homeostasis, either the fraction of neutrophil progenitor cells that self-renew has to be low or the feedback mechanism that maintains neutrophil homeostasis has to have a low threshold for turning self-renewal off. Thus, self-renewal is very tightly regulated to ensure that cells do not grow indefinitely. To reduce the cancer load for potential treatment, physicians could target the feedback mechanisms associated with self renewal probability, in particular focusing on cytokine signaling. Third, the large concentration of neutrophils cause the parameters associated with neutrophils to be important parameters in determining the concentration of stem cells, as determined by global sensitivity analysis. We confirmed the importance of neutrophils in relation to lymphocytes in the multi-lineage model by testing the robustness of the multi-lineage model in Additional file 1: Supplement 6. We also found that the neutrophils in our multi-lineage model might be over-constrained by comparing to clinical overshoot data in comparison to the uni-lineage models. Specifically, the neutrophil overshoot of the multi-lineage model only reflected the neutrophil overshoot in 85% of clinical data (Additional file 1: Figure S6 in Supplement 5). Thus, our model encompasses most of the dynamics of the patient population. Furthermore, this reflects the importance of the sensing mechanism of each of these cells to maintain appropriate homeostatic levels. When we modeled cancer, removing these homeostatic terms from our model allowed the cancer to grow indefinitely, as expected. Thus, treatment that targets the feedback receptors on cancer cells can drastically help reduce the cancer load.
Individual patients are likely to develop unique phenotypes of AML. The dynamics and relative ratios of the absolute concentrations of neutrophils, lymphocytes, and monocytes vary widely across the patient population. Furthermore, phenotypic variability of leukemia may depend on the specific source cell within the population of common granulocyte progenitors that first becomes cancerous. Here, we develop a mathematical model that is able to describe patient variability in AML. We find that though cancer will form when homeostatic mechanisms are altered, additional mutations that increase the mitosis rate of cancer will reduce the survival of the patient without intervention (Fig. 8 e). Current chemotherapy regimens inhibit DNA replication, which corresponds to inhibiting the mitosis rate of the cancer [78]. However, we also find that if the mechanism that determines the probability of self-renewal of cancer cells is mutated, then this can be an additional target for pharmaceutical treatments (Fig. 8 f), similar to what has been found in other work [75, 77].
The multi-lineage model developed in this work can be modified to explore mechanisms governing hematopoiesis and leukopoiesis. For example, the model could be adapted to discriminate amongst chemotherapy regimens on simulated patients to identify characteristics of patients that would benefit from certain regimens. Then, this could lead to identification of treatment schedules optimized for individual patients. The patient clusters could be used to stratify real patients by using the dynamics of patients’ responses to chemotherapy to match to a specific simulation and its outcome. Additionally, since we found that the probability of self-renewal is a potential secondary target for chemotherapy, various specific feedback mechanisms could be incorporated to identify the exact cytokine signal that would be the best target for therapy. This could be further used to identify the feedback signals that are most sensitive to cause AML growth. Furthermore, the linear relationship in log-log space between mitosis rates and self-renewal probabilities that was found in our model could be tested experimentally to ensure these relationships exist, though mediating cytokines properly is very difficult. Though we did not find specific relationships amongst the different lineages, the signaling mechanisms that control bone marrow size could also be explored experimentally and compared with the model to regulate overproduction of a particular cell lineage with respect to other lineages. Specifically, GM-CSF is often used to regulate the stem cell production of neutrophils and macrophages [79]. This could be manipulated to identify effects in lymphocyte counts and the production of AML. Overall, the multi-lineage model we present here can be extended to characterize many aspects of hematopoiesis.
The multi-lineage model of hematopoiesis and leukopoiesis developed in this work can be readily adapted and expanded to incorporate many other immunological effects. Various groups have already modeled bone marrow transplantation and its potential complications [31, 33, 34]. Using our model, bone marrow or stem cell transplantation and transplant rejection can be integrated to predict graft rejection, and different lymphocyte sub-types can be added to the model, such as natural killer cells, to model an alternative outcome of transplantation: graft versus host disease. Lymphocytic leukemias can be explored by altering the homeostatic mechanisms of lymphocytes; analogously, myelodysplastic syndromes and minimal residual disease could be further characterized by determining parameter changes that lead to appropriate model behavior. Additionally, a wide array of other immunological diseases or the wide array of patient responses (including a large T-cell repertoire) can be adapted into this multi-lineage model to characterize the complexity of normal function and other immunological diseases. More specifically, future work could characterize the mechanisms that cause spontaneous remission of AML in the presence of bacterial infection [80].
Conclusions
The multi-lineage mathematical model we have created of hematopoiesis and leukopoiesis can help identify how individuals differ in their white blood cell and leukemia production. This model is useful for several reasons. We have determined crucial parameters and parameter relationships that can be used as potential drug targets for both AML and other potential immunological disorders. For many chemotherapeutic drugs, DNA replication is targeted [78], which aligns with targeting the mitosis rate. However, a combination therapy that also addresses the probability of a cancer cell to self-renew could be potentially helpful for patients whose cancer becomes resistant to the initial therapy. There is no current way to experimentally determine how these different lineages interact and limit each other. Thus, this multi-lineage model is a very powerful tool that can aid in understanding how blood forms normally and misforms into AML in individual patients. In addition, the model captures multiple dynamics that represent specific patient subgroups. By clustering the wide population of individual differences, we find that one advantage of this multi-lineage model is that it can be readily extended to investigate personalization of treatment schedules of individual patients to prolong overall survival.
Declarations
Acknowledgements
Not applicable.
Funding
Support for this research comes from the National Institutes of Health under Grant R01HD073156 and the Indiana CTSI TL1 Award, funded in part by Grant UL1TR001108.
Availability of data and materials
The clinical data that support the findings of this study are available from Dr. Robert P. Nelson, Jr., but restrictions apply to the availability of these data, which were used under IRB approval for the current study, and so are not publicly available. The remaining data are however available from the authors upon reasonable request.
Authors’ contributions
JMS and SR created the multi-lineage model. JMS completed the model analysis and drafted the written work. RPN contributed to the conception, interpretation, and revision of the work. AER, DMU, and TKU contributed to the study design, interpretation, and revision of the written work. All authors read and approved the final manuscript.
Ethics approval and consent to participate
De-identified clinical data was used under Purdue University’s IRB Protocol# 1011009928 from the Indiana University Simon Cancer Center from patients who received hematopoietic stem cell transplants during a study approved by the IRB of Indiana University-Purdue University Indianapolis.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
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Authors’ Affiliations
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