Eradication of chronic myeloid leukemia stem cells: a novel mathematical model predicts no therapeutic benefit of adding G-CSF to imatinib

Imatinib mesylate induces complete cytogenetic responses in patients with chronic myeloid leukemia (CML), yet many patients have detectable BCR-ABL transcripts in peripheral blood even after prolonged therapy. Bone marrow studies have shown that this residual disease resides within the stem cell compartment. Quiescence of leukemic stem cells has been suggested as a mechanism conferring insensitivity to imatinib, and exposure to the Granulocyte-Colony Stimulating Factor (G-CSF), together with imatinib, has led to a significant reduction in leukemic stem cells in vitro. In this paper, we design a novel mathematical model of stem cell quiescence to investigate the treatment response to imatinib and G-CSF. We find that the addition of G-CSF to an imatinib treatment protocol leads to observable effects only if the majority of leukemic stem cells are quiescent; otherwise it does not modulate the leukemic cell burden. The latter scenario is in agreement with clinical findings in a pilot study administering imatinib continuously or intermittently, with or without G-CSF (GIMI trial). Furthermore, our model predicts that the addition of G-CSF leads to a higher risk of resistance since it increases the production of cycling leukemic stem cells. Although the pilot study did not include enough patients to draw any conclusion with statistical significance, there were more cases of progression in the experimental arms as compared to continuous imatinib. Our results suggest that the additional use of G-CSF may be detrimental to patients in the clinic

Optimizing Combination Therapies with Existing and Future CML Drugs

Small-molecule inhibitors imatinib, dasatinib and nilotinib have been developed to treat Chromic Myeloid Leukemia (CML). The existence of a triple-cross-resistant mutation, T315I, has been a challenging problem, which can be overcome by finding new inhibitors. Many new compounds active against T315I mutants are now at different stages of development. In this paper we develop an algorithm which can weigh different combination treatment protocols according to their cross-resistance properties, and find the protocols with the highest probability of treatment success. This algorithm also takes into account drug toxicity by minimizing the number of drugs used, and their concentration. Although our methodology is based on a stochastic model of CML microevolution, the algorithm itself does not require measurements of any parameters (such as mutation rates, or division/death rates of cells), and can be used by medical professionals without a mathematical background. For illustration, we apply this algorithm to the mutation data obtained in [1], [2]

Cell killing and resistance in pre-operative breast cancer chemotherapy

<p>Abstract</p> <p>Background</p> <p>Despite the recent development of technologies giving detailed images of tumours <it>in vivo</it>, direct or indirect ways to measure how many cells are actually killed by a treatment or are resistant to it are still beyond our reach.</p> <p>Methods</p> <p>We designed a simple model of tumour progression during treatment, based on descriptions of the key phenomena of proliferation, quiescence, cell killing and resistance, and giving as output the macroscopically measurable tumour volume and growth fraction. The model was applied to a database of the time course of volumes of breast cancer in patients undergoing pre-operative chemotherapy, for which the initial estimate of proliferating cells by the measure of the percentage of Ki67-positive cells was available.</p> <p>Results</p> <p>The analysis recognises different patterns of response to treatment. In one subgroup of patients the fitting implied drug resistance. In another subgroup there was a shift to higher sensitivity during the therapy. In the subgroup of patients where killing of cycling cells had the highest score, the drugs showed variable efficacy against quiescent cells.</p> <p>Conclusion</p> <p>The approach was feasible, providing items of information not otherwise available. Additional data, particularly sequential Ki67 measures, could be added to the system, potentially reducing uncertainty in estimates of parameter values.</p

Nonlinear deterministic equations in biological evolution

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in the simplest setting, the equations are necessarily nonlinear due to the mixing of the parental genetic material. The solutions of such nonlinear equations display interesting features such as multiple equilibria and phase transitions. We mainly discuss those models for which an analytical understanding of such nonlinear equations is available.Comment: Invited review for J. Nonlin. Math. Phy

New Studies of the Pulsar Wind Nebula in the Supernova Remnant CTB 80

We investigated the kinematics of the pulsar wind nebula (PWN) associated with PSR B1951+32 in the old supernova remnant CTB 80 using the Fabry-Perot interferometer of the 6m Special Astrophysical Observatory telescope. In addition to the previously known expansion of the system of bright filaments with a velocity of 100-200km/s, we detected weak high-velocity features in the H-alpha line at least up to velocities of 400-450km/s. We analyzed the morphology of the PWN in the H-alpha, [SII], and [OIII] lines using HST data and discuss its nature. The shape of the central filamentary shell, which is determined by the emission in the [OIII] line and in the radio continuum, is shown to be consistent with the bow-shock model for a significant (about 60 degrees) inclination of the pulsar's velocity vector to the plane of the sky. In this case, the space velocity of the pulsar is twice higher than its tangential velocity, i.e., it reaches ~500 km/s, and PSR B1951+32 is the first pulsar whose line-of-sight velocity (of about 400 km/s) has been estimated from the PWN observations. The shell-like H-alpha-structures outside the bow shock front in the east and the west may be associated with both the pulsar's jets and the pulsar-wind breakthrough due to the layered structure of the extended CTB 80 shell.Comment: to appear in Astronomy Letters, 12 pages, 6 postscript figures, two in colour; for a version with high resolution figures see http://www.sao.ru/hq/grb/team/vkom/CTB80_fine.pd

Термодинамико-топологический анализ бутанольно-толуольной смеси

The object of the research is a butanol-toluene mixture (BLS), which is a waste product of organosilicon enamels and consists of organic substances. In order to create a basic technological scheme of separation, thermodynamic-topological analysis was applied that takes into account the peculiarities of the rectification process in the poly-azeotrope mixture. The presence of 7 binary and 5 ternary azeotropes in the system was found. Singular points of the pentatope are considered. The distillation and rectification zones are determined. Flow graphs options separation were drawn, which can be the basis for the development of a technological scheme for the separation of the studied mixtures.В работе проведен термодинамико-топологический анализ бутанольно-толуольной смеси, образующейся в качестве отхода в лакокрасочной промышленности. Представлен анализ концентрационного образа изучаемой смеси - пентатопа, рассмотрены составляющие его симплексы меньшей размерности - тетраэдры. Синтезированы основные пути разделения бутанольно-толуольной смеси в виде потоковых графов

Analysis of a microscopic stochastic model of microtubule dynamic instability

A novel theoretical model of dynamic instability of a system of linear (1D) microtubules (MTs) in a bounded domain is introduced for studying the role of a cell edge in vivo and analyzing the effect of competition for a limited amount of tubulin. The model differs from earlier models in that the evolution of MTs is based on the rates of single unit (e.g., a heterodimer per protofilament) transformations, in contrast to postulating effective rates/frequencies of larger-scale changes, extracted, e.g., from the length history plots of MTs. Spontaneous GTP hydrolysis with finite rate after polymerization is assumed, and theoretical estimates of an effective catastrophe frequency as well as other parameters characterizing MT length distributions and cap size are derived. We implement a simple cap model which does not include vectorial hydrolysis. We demonstrate that our theoretical predictions, such as steady state concentration of free tubulin, and parameters of MT length distributions, are in agreement with the numerical simulations. The present model establishes a quantitative link between microscopic parameters governing the dynamics of MTs and macroscopic characteristics of MTs in a closed system. Lastly, we use a computational Monte Carlo model to provide an explanation for non-exponential MT length distributions observed in experiments. In particular, we show that appearance of such non-exponential distributions in the experiments can occur because the true steady state has not been reached, and/or due to the presence of a cell edge.Comment: 14 pages, 7 figure

The optical identifcation of events with poorly defined locations: The case of the Fermi GBM GRB140801A

We report the early discovery of the optical afterglow of gamma-ray burst (GRB) 140801A in the 137 deg$^2$ 3-$\sigma$ error-box of the Fermi Gamma-ray Burst Monitor (GBM). MASTER is the only observatory that automatically react to all Fermi alerts. GRB 140801A is one of the few GRBs whose optical counterpart was discovered solely from its GBM localization. The optical afterglow of GRB 140801A was found by MASTER Global Robotic Net 53 sec after receiving the alert, making it the fastest optical detection of a GRB from a GBM error-box. Spectroscopy obtained with the 10.4-m Gran Telescopio Canarias and the 6-m BTA of SAO RAS reveals a redshift of $z=1.32$. We performed optical and near-infrared photometry of GRB 140801A using different telescopes with apertures ranging from 0.4-m to 10.4-m. GRB 140801A is a typical burst in many ways. The rest-frame bolometric isotropic energy release and peak energy of the burst is $E_\mathrm{iso} = 5.54_{-0.24}^{+0.26} \times 10^{52}$ erg and $E_\mathrm{p, rest}\simeq280$ keV, respectively, which is consistent with the Amati relation. The absence of a jet break in the optical light curve provides a lower limit on the half-opening angle of the jet $\theta=6.1$ deg. The observed $E_\mathrm{peak}$ is consistent with the limit derived from the Ghirlanda relation. The joint Fermi GBM and Konus-Wind analysis shows that GRB 140801A could belong to the class of intermediate duration. The rapid detection of the optical counterpart of GRB 140801A is especially important regarding the upcoming experiments with large coordinate error-box areas.Comment: in press MNRAS, 201

Evolutionary dynamics of imatinib-treated leukemic cells by stochastic approach

The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a statistical approach. Cancer progression is explored by applying a Monte Carlo method to simulate the stochastic behavior of cell reproduction and death in a population of blood cells which can experience genetic mutations. In CML front line therapy is represented by the tyrosine kinase inhibitor imatinib which strongly affects the reproduction of leukemic cells only. In this work, we analyze the effects of a targeted therapy on the evolutionary dynamics of normal, first-mutant and cancerous cell populations. Several scenarios of the evolutionary dynamics of imatinib-treated leukemic cells are described as a consequence of the efficacy of the different modeled therapies. We show how the patient response to the therapy changes when an high value of the mutation rate from healthy to cancerous cells is present. Our results are in agreement with clinical observations. Unfortunately, development of resistance to imatinib is observed in a proportion of patients, whose blood cells are characterized by an increasing number of genetic alterations. We find that the occurrence of resistance to the therapy can be related to a progressive increase of deleterious mutations.Comment: Submitted to Central European Journal of Physic

Effect of Cellular Quiescence on the Success of Targeted CML Therapy

Similar to tissue stem cells, primitive tumor cells in chronic myelogenous leukemia have been observed to undergo quiescence; that is, the cells can temporarily stop dividing. Using mathematical models, we investigate the effect of cellular quiescence on the outcome of therapy with targeted small molecule inhibitors.According to the models, the initiation of treatment can result in different patterns of tumor cell decline: a biphasic decline, a one-phase decline, and a reverse biphasic decline. A biphasic decline involves a fast initial phase (which roughly corresponds to the eradication of cycling cells by the drug), followed by a second and slower phase of exponential decline (corresponding to awakening and death of quiescent cells), which helps explain clinical data. We define the time when the switch to the second phase occurs, and identify parameters that determine whether therapy can drive the tumor extinct in a reasonable period of time or not. We further ask how cellular quiescence affects the evolution of drug resistance. We find that it has no effect on the probability that resistant mutants exist before therapy if treatment occurs with a single drug, but that quiescence increases the probability of having resistant mutants if patients are treated with a combination of two or more drugs with different targets. Interestingly, while quiescence prolongs the time until therapy reduces the number of cells to low levels or extinction, the therapy phase is irrelevant for the evolution of drug resistant mutants. If treatment fails as a result of resistance, the mutants will have evolved during the tumor growth phase, before the start of therapy. Thus, prevention of resistance is not promoted by reducing the quiescent cell population during therapy (e.g., by a combination of cell activation and drug-mediated killing).The mathematical models provide insights into the effect of quiescence on the basic kinetics of the response to targeted treatment of CML. They identify determinants of success in the absence of drug resistant mutants, and elucidate how quiescence influences the emergence of drug resistant mutants