Model Based Analysis of Clonal Developments Allows for Early Detection of Monoclonal Conversion and Leukemia

<div><p>The availability of several methods to unambiguously mark individual cells has strongly fostered the understanding of clonal developments in hematopoiesis and other stem cell driven regenerative tissues. While cellular barcoding is the method of choice for experimental studies, patients that underwent gene therapy carry a unique insertional mark within the transplanted cells originating from the integration of the retroviral vector. Close monitoring of such patients allows accessing their clonal dynamics, however, the early detection of events that predict monoclonal conversion and potentially the onset of leukemia are beneficial for treatment. We developed a simple mathematical model of a self-stabilizing hematopoietic stem cell population to generate a wide range of possible clonal developments, reproducing typical, experimentally and clinically observed scenarios. We use the resulting model scenarios to suggest and test a set of statistical measures that should allow for an interpretation and classification of relevant clonal dynamics. Apart from the assessment of several established diversity indices we suggest a measure that quantifies the extension to which the increase in the size of one clone is attributed to the total loss in the size of all other clones. By evaluating the change in relative clone sizes between consecutive measurements, the suggested measure, referred to as <i>maximum relative clonal expansion</i> (<i>mRCE</i>), proves to be highly sensitive in the detection of rapidly expanding cell clones prior to their dominant manifestation. This predictive potential places the <i>mRCE</i> as a suitable means for the early recognition of leukemogenesis especially in gene therapy patients that are closely monitored. Our model based approach illustrates how simulation studies can actively support the design and evaluation of preclinical strategies for the analysis and risk evaluation of clonal developments.</p></div

Clonal developments described by <i>mRCE</i>.

<p>Subfigures show time courses of the <i>mRCE</i> (solid line) and the largest clones size (dotted line) for a scenario without (A) and with a mutated clone (B). Both scenarios are initialized with identical initial conditions. In subfigure (B) the mutation is initialized at month 3 after simulation start.</p

Performance comparison of <i>mRCE</i> vs. classical indices.

<p>(A) Time courses of <i>mRCE</i> values of 10 individual runs of pathological and healthy simulations. (B) The plot shows the distribution of the <i>mRCE</i> values for healthy (blue) and pathological (black) contributions (circles). These distributions are used to fit a binomial glm (lines indicate the probability for the occurrence of pathological (black) and physiological (blue) scenarios). (C) AUC comparison of different measures. (D) Positive likelihood ratio comparison over time of different.</p

Scale representation of <i>mRCE</i> measurement.

<p><i>ΣΔ</i>⁻ denotes the sum of all shrinking clones and <i>maxΔ</i>⁺ the clone with the highest expansion between two consecutive points in time. Only the case of one dominantly expanding clone balances the scale and indicates a high risk for rapid monoclonal conversion (<i>mRCE</i> = 1).</p

Clonal developments within cancer scenarios.

<p>(A) Simulation with one malignant cell (increased proliferation rate <i>p</i>) initiated in the third month. The clone in which the mutation occurs is depicted in grey. (B) The average time until clonal dominance beginning at the time point of cancer initiation.</p

Clonal developments described by classical indices.

<p>(A) Time courses of the Simpson and Shannon index as well as species Richness for a non-mutated scenario (clonal pattern in inset). For reference, the size of the largest clone is given by the dotted line. (B) Similar time courses based on a mutation scenario (as provided in the inset). The mutation event occurs after ~3 months.</p

Temporal clonal developments.

<p>(A) & (B) Simulation without heterogeneity between the clones (<i>σ</i> = 0) for 2 years and till monoclonality is reached (~8 years), respectively. (C) Simulation with no aging effect (<i>α</i> = 0) and a simulated heterogeneity of the differentiation rate <i>d</i>_<i>i</i> (<i>σ</i> > 0). (D) Average time to reach monoclonality on a logarithmic scale in years vs. the clonal heterogeneity defined by <i>σ</i>. (E) Simulation of an aging effect (<i>α</i> > 0) and no difference in the differentiation rates <i>d</i>_<i>i</i> between the clones (<i>σ</i> = 0). (F) Shows the change in the average time to reach monoclonality depending on the aging effect <i>α</i>.</p

Stem cell proliferation and quiescence--two sides of the same coin.

The kinetics of label uptake and dilution in dividing stem cells, e.g., using Bromodeoxyuridine (BrdU) as a labeling substance, are a common way to assess the cellular turnover of all hematopoietic stem cells (HSCs) in vivo. The assumption that HSCs form a homogeneous population of cells which regularly undergo cell division has recently been challenged by new experimental results. For a consistent functional explanation of heterogeneity among HSCs, we propose a concept in which stem cells flexibly and reversibly adapt their cycling state according to systemic needs. Applying a mathematical model analysis, we demonstrate that different experimentally observed label dilution kinetics are consistently explained by the proposed model. The dynamically stabilized equilibrium between quiescent and activated cells leads to a biphasic label dilution kinetic in which an initial and pronounced decline of label retaining cells is attributed to faster turnover of activated cells, whereas a secondary, decelerated decline results from the slow turnover of quiescent cells. These results, which support our previous model prediction of a reversible activation/deactivation of HSCs, are also consistent with recent findings that use GFP-conjugated histones as a label instead of BrdU. Based on our findings we interpret HSC organization as an adaptive and regulated process in which the slow activation of quiescent cells and their possible return into quiescence after division are sufficient to explain the simultaneous occurrence of self-renewal and differentiation. Furthermore, we suggest an experimental strategy which is suited to demonstrate that the repopulation ability among the population of label retaining cells changes during the course of dilution