Dynamical models of mutated chronic myelogenous leukemia cells for a post-imatinib treatment scenario: Response to dasatinib or nilotinib therapy.

Clemens Woywod,Franz X. Gruber,Richard A. Engh,Tor Flå,Natalia L. Komarova

doi:10.1371/journal.pone.0179700

Clemens Woywod, Franz X. Gruber + Show 3 more

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https://doi.org/10.1371/journal.pone.0179700

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Journal: PloS one	Publication Date: Jul 5, 2017
Citations: 8	License type: CC BY 4.0

Affiliation: UiT The Arctic University of Norway

Abstract

Targeted inhibition of the oncogenic BCR-ABL1 fusion protein using the ABL1 tyrosine kinase inhibitor imatinib has become standard therapy for chronic myelogenous leukemia (CML), with most patients reaching total and durable remission. However, a significant fraction of patients develop resistance, commonly due to mutated ABL1 kinase domains. This motivated development of second-generation drugs with broadened or altered protein kinase selectivity profiles, including dasatinib and nilotinib. Imatinib-resistant patients undergoing treatment with second-line drugs typically develop resistance to them, but dynamic and clonal properties of this response differ. Shared, however, is the observation of clonal competition, reflected in patterns of successive dominance of individual clones. We present three deterministic mathematical models to study the origins of clinically observed dynamics. Each model is a system of coupled first-order differential equations, considering populations of three mutated active stem cell strains and three associated pools of differentiated cells; two models allow for activation of quiescent stem cells. Each approach is distinguished by the way proliferation rates of the primary stem cell reservoir are modulated. Previous studies have concentrated on simulating the response of wild-type leukemic cells to imatinib administration; our focus is on modelling the time dependence of imatinib-resistant clones upon subsequent exposure to dasatinib or nilotinib. Performance of the three computational schemes to reproduce selected CML patient profiles is assessed. While some simple cases can be approximated by a basic design that does not invoke quiescence, others are more complex and require involvement of non-cycling stem cells for reproduction. We implement a new feedback mechanism for regulation of coupling between cycling and non-cycling stem cell reservoirs that depends on total cell populations. A bifurcation landscape analysis is also performed for solutions to the basic ansatz. Computational models reproducing patient data illustrate potential dynamic mechanisms that may guide optimization of therapy of drug resistant CML.

Highlights

With the discovery of tyrosine kinase inhibitor (TKI) drugs, a diagnosis of early stage chronic myelogenous leukemia (CML) became associated with a prognosis of normal life expectancy [1]
We have analysed the behavior of three models of CML dynamics in patients who have been placed under new treatment after diagnosis of resistance to imatinib
This study represents the first theoretical investigation of competition dynamics of imatinibresistant CML strains exposed to second-line medication as observed in recent clinical trials [40, 41]

Summary

Introduction

With the discovery of tyrosine kinase inhibitor (TKI) drugs, a diagnosis of early stage chronic myelogenous leukemia (CML) became associated with a prognosis of normal life expectancy [1]. The following coupled system of six first order nonlinear differential equations represents the dynamics of the six cell populations and defines model A: dxs1ðtÞ dt ð1 À n2 À n3Þz1ðxsðtÞÞa1xs1ðtÞ À d1xs1ðtÞ ; ð4aÞ dxd1ðtÞ dt pðxdðtÞÞa1xs1ðtÞ À d1xd1ðtÞ ; ð4bÞ dxs2ðtÞ dt n2a1z1ðxsðtÞÞxs1ðtÞ þ z2ðxsðtÞÞa2xs2ðtÞ À d2xs2ðtÞ ; ð4cÞ dxd2ðtÞ dt pðxdðtÞÞa2xs2ðtÞ À d2xd2ðtÞ ; ð4dÞ dxs3ðtÞ dt n3a1z1ðxsðtÞÞxs1ðtÞ þ z3ðxsðtÞÞa3xs3ðtÞ À d3xs3ðtÞ ; ð4eÞ dxd3ðtÞ dt pðxdðtÞÞa3xs3ðtÞ À d3xd3ðtÞ ; ð4f Þ where the parameters δi and di are the net decay rate constants of stem and differentiated cells, respectively; αi and ai are the symmetric and asymmetric division rate constants, modulated by the population dependent growth or negative feedback switch functions zi(xs(t)) and p (xd(t)), respectively; and the rate constants for mutation of clone 1 to clones 2 and 3 during “quasi-symmetric” division are ν2 and ν3, respectively. With the definitions c1 ≔ 100 and c2 ≔ 0, the function σ(x) represents a close approximation to H(x)

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