Modeling Imatinib-Treated Chronic Myelogenous Leukemia: Reducing the Complexity of Agent-Based Models

We develop a model for describing the dynamics of imatinib-treated chronic myelogenous leukemia. Our model is based on replacing the recent agent-based model of Roeder et al. (Nat. Med. 12(10):1181–1184, 2006) by a system of deterministic difference equations. These difference equations describe the time-evolution of clusters of individual agents that are grouped by discretizing the state space. Hence, unlike standard agent-base models, the complexity of our model is independent of the number of agents, which allows to conduct simulation studies with a realistic number of cells. This approach also allows to directly evaluate the expected steady states of the system. The results of our numerical simulations show that our model replicates the averaged behavior of the original Roeder model with a significantly reduced computational cost. Our general approach can be used to simplify other similar agent-based models. In particular, due to the reduced computational complexity of our technique, one can use it to conduct sensitivity studies of the parameters in large agent-based systems.     

伊马替尼血药浓度监测指导慢性粒细胞白血病患者的研究

目的 观察是否可以通过对伊马替尼(Imatinib,IM)进行血药浓度监测提高疗效,减少药物不良反应。方法 选取2013~2018年就诊于我院的慢性粒细胞白血病(chronic myelogenous leukemia, CML)患者,分为试验组(药物监测组),对照组(常规经验治疗组)。对服药3个月、6个月、12个月、18个月,进行疗效及不良反应评估及比较。结果 共有51人入选此次临床试验。其中试验组35人,对照组16人。结果 服用伊马替尼400mg/d时,血药浓度568.00~3 989.66ng/ml,均数(标准差):1 716.46ng/ml(788.96);服用伊马替尼300mg/d时,血药浓度720.89~1 497.11ng/ml,均数(标准差):971.67ng/ml(204.02)。达到主要分子学反应(major molecular response, MMR)的伊马替尼血药浓度高于未达到稳态时的伊马替尼血药浓度。两组不良反应评级有统计学差异。试验组III级及以上不良反应发生率明显小于对照组。结论 伊马替尼的稳态血浆药物谷浓度存在较大个体差异,这种个体差异与疗效和不良反应存在相关性。通过治疗药物监测(therapeutic drug monitoring, TDM)可以在确保疗效的同时,减少伊马替尼在治疗慢性粒细胞白血病中的不良反应。结果尚需大样本临床试验进一步验证。伊马替尼药物代谢个体差异的原因需要大样本遗传药理学研究进一步探讨。     

慢性髓细胞性白血病病人骨髓单个核细胞中差异表达基因的筛选

目的:筛选慢性髓细胞性白血病(CML)病人骨髓单个核细胞与正常人的差异表达基因,探讨CML的发病机制.方法:提取正常人和CML病人单个核细胞的RNA,逆转录成cDNA并用地高辛标记,应用全基因组表达谱基因芯片对差异表达基因进行研究,采用Jubilant病理/疾病分类法对CML相关差异表达基因进行分析.结果:共筛选出CM...     

An “Age” Structured Model of Hematopoietic Stem Cell Organization with Application to Chronic Myeloid Leukemia

Previously, we have modeled hematopoietic stem cell organization by a stochastic, single cell-based approach. Applications to different experimental systems demonstrated that this model consistently explains a broad variety of in vivo and in vitro data. A major advantage of the agent-based model (ABM) is the representation of heterogeneity within the hematopoietic stem cell population. However, this advantage comes at the price of time-consuming simulations if the systems become large. One example in this respect is the modeling of disease and treatment dynamics in patients with chronic myeloid leukemia (CML), where the realistic number of individual cells to be considered exceeds 10⁶. To overcome this deficiency, without losing the representation of the inherent heterogeneity of the stem cell population, we here propose to approximate the ABM by a system of partial differential equations (PDEs). The major benefit of such an approach is its independence from the size of the system. Although this mean field approach includes a number of simplifying assumptions compared to the ABM, it retains the key structure of the model including the “age”-structure of stem cells. We show that the PDE model qualitatively and quantitatively reproduces the results of the agent-based approach.     

A peptide biosensor for detecting intracellular Abl kinase activity using matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Many cancers are characterized by changes in protein phosphorylation as a result of kinase dysregulation. Disruption of Abl kinase signaling through the Philadelphia chromosome (causing the Bcr-Abl mutation) in chronic myeloid leukemia (CML) has provided a paradigm for development of kinase inhibitor drugs such as the specific inhibitor imatinib (also known as STI571 or Gleevec). However, because patients are treated indefinitely with this drug to maintain remission, resistance is increasingly becoming an issue. Although there are many ways to detect kinase activity, most lack the ability to “multiplex” the analysis (i.e., to detect more than one substrate simultaneously). Here we report a novel biosensor for detecting Abl kinase activity and sensitivity to inhibitor in live intact cells overexpressing a CML model Abl kinase construct. This straightforward methodology could eventually provide a new tool for detecting kinase activity and inhibitor drug response in cancer cells that overexpress oncogenic kinases.     

BCR-ABL Gene Expression Is Required for Its Mutations in a Novel KCL-22 Cell Culture Model for Acquired Resistance of Chronic Myelogenous Leukemia

Acquired resistance through genetic mutations is a common phenomenon in several cancer therapies using molecularly targeted drugs, best exemplified by the BCR-ABL inhibitor imatinib in treating chronic myelogenous leukemia (CML). Overcoming acquired resistance is a daunting therapeutic challenge, and little is known about how these mutations evolve. To facilitate understanding the resistance mechanisms, we developed a novel culture model for CML acquired resistance in which the CML cell line KCL-22, following initial response to imatinib, develops resistant T315I BCR-ABL mutation. We demonstrate that the emergence of BCR-ABL mutations do not require pre-existing BCR-ABL mutations derived from the original patient as the subclones of KCL-22 cells can form various BCR-ABL mutations upon imatinib treatment. BCR-ABL mutation rates vary from cell clone to clone and passages, in contrast to the relatively stable mutation rate of the hypoxanthine-guanine phosphoribosyltransferase gene. Strikingly, development of BCR-ABL mutations depends on its gene expression because BCR-ABL knockdown completely blocks KCL-22 cell relapse on imatinib and acquisition of mutations. We further show that the endogenous BCR-ABL locus has significantly higher mutagenesis potential than the transduced randomly integrated BCR-ABL cDNA. Our study suggests important roles of BCR-ABL gene expression and its native chromosomal locus for acquisition of BCR-ABL mutations and provides a new tool for further studying resistance mechanisms.     

Post-transplantation dynamics of the immune response to chronic myelogenous leukemia

We model the immune dynamics between T cells and cancer cells in leukemia patients after bone marrow transplants, using a system of six delay differential equations to track the various cell-populations. Our approach incorporates time delays and accounts for the progression of cells through different modes of behavior. We explore possible mechanisms behind a successful cure, whether mediated by a blood-restricted immune response or a cancer-specific graft-versus-leukemia (GVL) effect. Characteristic features of this model include sustained proliferation of T cells after initial stimulation, saturated T cell proliferation rate, and the possible elimination of cancer cells, independent of fixed-point stability. In addition, we use numerical simulations to examine the effects of varying initial cell concentrations on the likelihood of a successful transplant. Among the observed trends, we note that higher initial concentrations of donor-derived, anti-host T cells slightly favor the chance of success, while higher initial concentrations of general host blood cells more significantly favor the chance of success. These observations lead to the hypothesis that anti-host T cells benefit from stimulation by general host blood cells, which induce them to proliferate to sufficient levels to eliminate cancer.     

Stochastic modeling of drug resistance in cancer

One of the main causes of failure in the treatment of cancer is the development of drug resistance by the cancer cells. Employing multi-drug therapeutic strategies is a promising way to prevent resistance and improve the chances of treatment success. We formulate and analyse a stochastic model for multi-drug resistance and investigate the dependence of treatment outcomes on the initial tumor load, mutation rates and the turnover rate of cancerous cells. We elucidate the general principles of the emergence and evolution of resistant cells inside the tumor, before and after the start of treatment. We discover that for non-mutagenic drugs, pre-existence contributes more to resistance generation than the treatment phase; this result holds for the case where all drugs are applied simultaneously, and is not applicable for sequential therapy models. The application of mathematical modelling to aspects of adjuvant chemotherapy scheduling. J. Math. Biol. 48(4), 375-422]. Also, we find that treatment success is independent on the turnover rate for one drug, and it depends strongly on it for multi-drug therapies. For low-turnover rates, increasing the number of drugs will increase the probability of successful therapy. For very high-turnover rates, increasing the number of drugs used does not significantly increase the chances of treatment success.     

Use of moving optical gradient fields for analysis of apoptotic cellular responses in a chronic myeloid leukemia cell model

To facilitate quantitation of cellular apoptotic responses to various antineoplastic agents, a laser-based technology, Optophoresis, has been developed to provide analysis of cells without any need for labeling or cell processing. Optophoresis is defined as the analysis of the motion of cells, where the motion is either induced or modified by a moving optical gradient field, which produces radiation pressure forces on the cells in an aqueous suspension. Quantitation of the induced motion provides a basis for distinguishing one population of cells from another. One Optophoretic technique, Fast Scan, measures the distribution of distances traversed by a population of cells when exposed to a fast-moving optical gradient. Fast Scan was validated using a cell-based model of chronic myeloid leukemia treated with Gleevec, a specific inhibitor of aberrant Bcr-Abl protein kinase. The Optophoretic measurements were quantitatively comparable to reference assays with regard to drug selectivity and potency and to target specificity, demonstrating the suitability of this technology for pharmaceutical and clinical applications.     

胆固醇对K562及耐药株K562G细胞增殖及伊马替尼敏感性的影响

目的:探讨胆固醇对K562及耐药株K562G细胞增殖及伊马替尼(Imatinib,IM)敏感性的影响。方法:通过qRT-PCR方法检测K562和K562G细胞的胆固醇代谢途径相关蛋白的表达;以不同药物组合处理K562细胞、K562G细胞,采用CCK-8方法检测细胞增殖情况。结果:耐药K562G细胞胆固醇合成酶(人角鲨烯单加氧酶SQLE,细胞色素P450酶家族51亚家族A1 CYP51A1,固醇C5去饱和酶SC5D)表达下降、而低密度脂蛋白受体LDLR、固醇酰基转移酶SOAT1、ATP结合盒转运体A1 ABCA1表达量增加;0.5μg/m L、0.75μg/m L胆固醇处理K562细胞,其增殖率比对照组K562细胞分别增加(9.51±2.84)%和(19.88±3.00)%;使用阿托伐他汀(20μM)、GW3965 (20μM)、MβCD (10 m M)降低K562G细胞胆固醇使其增殖抑制率分别为(50.73±2.34)%,(49.42±1.13)%,(76.54±1.48)%;两种浓度胆固醇使IM处理的K562细胞增殖抑制率分别减少51.59%及53.80%;MβCD联合IM使K562及K562G细胞存活率分别降低至6.89%及23.34%。结论:IM抵抗的K562G细胞与IM敏感的K562细胞相比胆固醇代谢增强;增加胆固醇能够促进K562细胞增殖,降低细胞对IM的敏感性;MβCD可能通过降低胆固醇增强K562、K562G细胞对IM敏感性。     

A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction

In this paper, we propose and analyse a mathematical model for chronic myelogenous leukemia (CML), a cancer of the blood. We model the interaction between naive T cells, effector T cells, and CML cancer cells in the body, using a system of ordinary differential equations which gives rates of change of the three cell populations. One of the difficulties in modeling CML is the scarcity of experimental data which can be used to estimate parameters values. To compensate for the resulting uncertainties, we use Latin hypercube sampling (LHS) on large ranges of possible parameter values in our analysis. A major goal of this work is the determination of parameters which play a critical role in remission or clearance of the cancer in the model. Our analysis examines 12 parameters, and identifies two of these, the growth and death rates of CML, as critical to the outcome of the system. Our results indicate that the most promising research avenues for treatments of CML should be those that affect these two significant parameters (CML growth and death rates), while altering the other parameters should have little effect on the outcome.     

Hybridization biosensor using 2-nitroacridone as electrochemical indicator for detection of short DNA species of Chronic Myelogenous Leukemia

A new acridone derivative 2-nitroacridone (NAD) was synthesized in this paper, and it was found that NAD had excellent electrochemical activity on the glassy carbon electrode (GCE) with a couple reversible redox peaks at 0.051 V and 0.103 V, respectively. Voltammetry was used to investigate the electrochemical behavior of NAD and the interaction between NAD and salmon sperm DNA. In pH 4.0 phosphate buffer solution, the binding ratio between NAD and salmon sperm DNA was calculated to be 2:1 and the binding constant was 3.19 × 10⁵ L/mol. A Chronic Myelogenous Leukemia (CML, Type b₃a₂) DNA biosensor was developed by immobilizing covalently single-stranded CML DNA fragments to a modified GCE. The surface hybridization of the immobilized single-stranded CML DNA fragment with its complementary DNA fragment was evidenced by electrochemical methods using NAD as a novel electrochemical indicator, with a detection limit of 6.7 × 10⁻⁹ M and a linear response range of 1.8 × 10⁻⁸ M to 9.1 × 10⁻⁸ M for CML DNA. Selective determination of complementary ssDNA was achieved using differential pulse voltammetry (DPV).     

Model and analysis of chemotactic bacterial patterns in a liquid medium

 A variety of spatial patterns are formed chemotactically by the bacteria Escherichia coli and Salmonella typhimurium. We focus in this paper on patterns formed by E. coli and S. typhimurium in liquid medium experiments. The dynamics of the bacteria, nutrient and chemoattractant are modeled mathematically and give rise to a nonlinear partial differential equation system. We present a simple and intuitively revealing analysis of the patterns generated by our model. Patterns arise from disturbances to a spatially uniform solution state. A linear analysis gives rise to a second order ordinary differential equation for the amplitude of each mode present in the initial disturbance. An exact solution to this equation can be obtained, but a more intuitive understanding of the solutions can be obtained by considering the rate of growth of individual modes over small time intervals. Received: 10 March 1998 / Revised version: 7 June 1998     

A General Model for the Dynamics of the Cell Volume

The conservation of the cell volume within values compatible with the overall cell functions represents an ubiquitous property, shared by cells comprising the whole biological world. Water transport across membranes constitutes the main process associated to the dynamics of the cell volume, its chronic and acute regulations therefore represent crucial aspects of cell homeostasis. In spite of the biological diversity, the dynamics of the cell volume exhibits common basic features in the diverse types of cells. The purpose of this study is to show that there is a general model capable to describe the basic aspects of the dynamics of the cell volume. It is demonstrated here that the steady states of this model represent asymptotically stable configurations. As illustrations, several cases of non-polarized (i.e., symmetrical) and polarized (e.g., epithelial) cells performing water transport are shown here to represent particular cases of the general model. From a biological perspective, the existence of a general model for the dynamics of the cell volume reveals that, in spite of physiological and morphological peculiarities, there is a basic common design of the membrane transport processes. In view of its stability properties, this basic design may represent an ancestral property that has proven to be successful regarding the overall homeostatic properties of cells.     

A numerical study of the nonsteady transport of gases in the pulmonary capillaries

A mathematical model is formulated for simulating the unsteady transport of gases in the blood flowing through the pulmonary capillaries. The formulation takes into account the transport mechanisms of molecular diffusion, convection and facilitated diffusion of the species due to haemoglobin. A time dependent situation is created by allowing to vary suddenly the partial pressures of the gases either in the venous blood or in the alveolar air. A numerical technique is described to solve the resulting time-dependent system of nonlinear coupled partial differential equations with the physiologically relevant boundary, entrance and initial conditions. The time required by the gases to achieve equilibrium is computed. It is shown that the dissolved oxygen takes longest in reaching equilibration whereas the carbon dioxide is the fastest. The various physiologically relevant unsteady situations have been examined.     

A condition for setting off ectopic waves in computational models of excitable cells

The purpose of this paper is to study the stability of steady state solutions of the Monodomain model equipped with Luo-Rudy I kinetics. It is well established that re-entrant arrhythmias can be created in computational models of excitable cells. Such arrhythmias can be initiated by applying an external stimulus that interacts with a partially refractory region, and spawn breaking waves that can eventually generate extremely complex wave patterns commonly referred to as fibrillation. An ectopic wave is one possible stimulus that may initiate fibrillation. Physiologically, it is well known that ectopic waves exist, but the mechanism for initiating ectopic waves in a large collection of cells is poorly understood. In the present paper we consider computational models of collections of excitable cells in one and two spatial dimensions. The cells are modeled by Luo-Rudy I kinetics, and we assume that the spatial dynamics is governed by the Monodomain model. The mathematical analysis is carried out for a reduced model that is known to provide good approximations of the initial phase of solutions of the Luo-Rudy I model. A further simplification is also introduced to motivate and explain the results for the more complicated models. In the analysis the cells are divided into two regions; one region (N) consists of normal cells as model by the standard Luo-Rudy I model, and another region (A) where the cells are automatic in the sense that they would act as pacemaker cells if they where isolated from their surroundings. We let delta denote the spatial diffusion and a denote a characteristic length of the automatic region. It has previously been shown that reducing diffusion or increasing the automatic region enhances ectopic activity. Here we derive a condition for the transition from stable resting state to ectopic wave spread. Under suitable assumptions on the model we provide mathematical and computational arguments indicating that there is a constant eta such that a steady state solution of this system is stable whenever delta approximately > etaa(2), and unstable whenever delta approximately < etaa(2).     

A Bifurcation Analysis of a Differential Equations Model for Mutualism

We develop from basic principles a two-species differential equations model which exhibits mutualistic population interactions. The model is similar in spirit to a commonly cited model [Dean, A.M., Am. Nat. 121(3), 409–417 (1983)], but corrects problems due to singularities in that model. In addition, we investigate our model in more depth by varying the intrinsic growth rate for each of the species and analyzing the resulting bifurcations in system behavior. We are especially interested in transitions between facultative and obligate mutualism. The model reduces to the familiar Lotka–Volterra model locally, but is more realistic for large populations in the case where mutualist interaction is strong. In particular, our model supports population thresholds necessary for survival in certain cases, but does this without allowing unbounded population growth. Experimental implications are discussed for a lichen population.     

松嫩平原碱化草地植物-环境系统的仿真模拟

 本研究以系统仿真的方法对松嫩平原碱化草地植物—环境系统进行模拟。模型的系统变量包括植物种的地上、地下生物量,土壤水分、有机质。可溶性和交换性Na+和Ca++浓度和植物的凋落物生物量。模型所考虑的过程有：不同土壤碱化条件下的植物生长季节动态;土壤水、盐运动;植物的蒸腾作用;土壤表面的蒸发;凋落物的积累和分解;土壤有机质的积累和矿化;地下生物量对土壤持水和导水特性的控制作用,以及收获强度对系统平衡的影响等。模型成功地解释了植物生物量形成过程与环境之间的动态耦合、相关作用。模拟结果说明：与地下生物量密切相关的土壤非毛管孔隙度与土壤的碱化和脱碱过程有极强的相关作用,这种作用是通过改变土壤的饱和持水量来实现的。非毛管孔隙度随地下生物量增加,导致饱和含水量增加和脱碱作用加强。收获强度过大导致地下生物量的减少、非毛管孔隙度的减少和碱化作用的加强。     

A Model for a Proportional Treatment Effect on Disease Progression

Treatments intended to slow the progression of chronic diseases are often hypothesized to reduce the rate of further injury to a biological system without improving the current level of functioning. In this situation, the treatment effect may be negligible for patients whose disease would have been stable without the treatment but would be expected to be an increasing function of the progression rate in patients with worsening disease. This article considers a variation of the Laird Ware mixed effects model in which the effect of the treatment on the slope of a longitudinal outcome is assumed to be proportional to the progression rate for patients with progressive disease. Inference based on maximum likelihood and a generalized estimating equations procedure is considered. Under the proportional effect assumption, the precision of the estimated treatment effect can be increased by incorporating the functional relationship between the model parameters and the variance of the outcome variable, particularly when the magnitude of the mean slope of the outcome is small compared with the standard deviation of the slopes. An example from a study of chronic renal disease is used to illustrate insights provided by the proportional effect model that may be overlooked with models assuming additive treatment effects.     

A Mouse Model for Pathogen-induced Chronic Inflammation at Local and Systemic Sites

Chronic inflammation is a major driver of pathological tissue damage and a unifying characteristic of many chronic diseases in humans including neoplastic, autoimmune, and chronic inflammatory diseases. Emerging evidence implicates pathogen-induced chronic inflammation in the development and progression of chronic diseases with a wide variety of clinical manifestations. Due to the complex and multifactorial etiology of chronic disease, designing experiments for proof of causality and the establishment of mechanistic links is nearly impossible in humans. An advantage of using animal models is that both genetic and environmental factors that may influence the course of a particular disease can be controlled. Thus, designing relevant animal models of infection represents a key step in identifying host and pathogen specific mechanisms that contribute to chronic inflammation.Here we describe a mouse model of pathogen-induced chronic inflammation at local and systemic sites following infection with the oral pathogen Porphyromonas gingivalis, a bacterium closely associated with human periodontal disease. Oral infection of specific-pathogen free mice induces a local inflammatory response resulting in destruction of tooth supporting alveolar bone, a hallmark of periodontal disease. In an established mouse model of atherosclerosis, infection with P. gingivalis accelerates inflammatory plaque deposition within the aortic sinus and innominate artery, accompanied by activation of the vascular endothelium, an increased immune cell infiltrate, and elevated expression of inflammatory mediators within lesions. We detail methodologies for the assessment of inflammation at local and systemic sites. The use of transgenic mice and defined bacterial mutants makes this model particularly suitable for identifying both host and microbial factors involved in the initiation, progression, and outcome of disease. Additionally, the model can be used to screen for novel therapeutic strategies, including vaccination and pharmacological intervention.