Publications by authors named "Dominik Wodarz"

120 Publications

Quantifying the dynamics of viral recombination during free virus and cell-to-cell transmission in HIV-1 infection.

Virus Evol 2021 Jan 22;7(1):veab026. Epub 2021 Mar 22.

Department of Basic Science, New York University College of Dentistry, 921 Schwartz Building, 345 East 24th Street, New York, NY 10010-9403, USA.

Recombination has been shown to contribute to human immunodeficiency virus-1 (HIV-1) evolution , but the underlying dynamics are extremely complex, depending on the nature of the fitness landscapes and of epistatic interactions. A less well-studied determinant of recombinant evolution is the mode of virus transmission in the cell population. HIV-1 can spread by free virus transmission, resulting largely in singly infected cells, and also by direct cell-to-cell transmission, resulting in the simultaneous infection of cells with multiple viruses. We investigate the contribution of these two transmission pathways to recombinant evolution, by applying mathematical models to experimental data on the growth of fluorescent reporter viruses under static conditions (where both transmission pathways operate), and under gentle shaking conditions, where cell-to-cell transmission is largely inhibited. The parameterized mathematical models are then used to extrapolate the viral evolutionary dynamics beyond the experimental settings. Assuming a fixed basic reproductive ratio of the virus (independent of transmission pathway), we find that recombinant evolution is fastest if virus spread is driven only by cell-to-cell transmission and slows down if both transmission pathways operate. Recombinant evolution is slowest if all virus spread occurs through free virus transmission. This is due to cell-to-cell transmission 1, increasing infection multiplicity; 2, promoting the co-transmission of different virus strains from cell to cell; and 3, increasing the rate at which point mutations are generated as a result of more reverse transcription events. This study further resulted in the estimation of various parameters that characterize these evolutionary processes. For example, we estimate that during cell-to-cell transmission, an average of three viruses successfully integrated into the target cell, which can significantly raise the infection multiplicity compared to free virus transmission. In general, our study points towards the importance of infection multiplicity and cell-to-cell transmission for HIV evolution.
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http://dx.doi.org/10.1093/ve/veab026DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8117450PMC
January 2021

Network models and the interpretation of prolonged infection plateaus in the COVID19 pandemic.

Epidemics 2021 06 8;35:100463. Epub 2021 May 8.

Department of Population Health and Disease Prevention, Program in Public Health, Susan and Henry Samueli College of Health Science, University of California Irvine, Irvine, CA, 92697, United States. Electronic address:

Non-pharmaceutical intervention measures, such as social distancing, have so far been the only means to slow the spread of SARS-CoV-2. In the United States, strict social distancing during the first wave of virus spread has resulted in different types of infection dynamics. In some states, such as New York, extensive infection spread was followed by a pronounced decline of infection levels. In other states, such as California, less infection spread occurred before strict social distancing, and a different pattern was observed. Instead of a pronounced infection decline, a long-lasting plateau is evident, characterized by similar daily new infection levels. Here we show that network models, in which individuals and their social contacts are explicitly tracked, can reproduce the plateau if network connections are cut due to social distancing measures. The reason is that in networks characterized by a 2D spatial structure, infection tends to spread quadratically with time, but as edges are randomly removed, the infection spreads along nearly one-dimensional infection "corridors", resulting in plateau dynamics. Further, we show that plateau dynamics are observed only if interventions start sufficiently early; late intervention leads to a "peak and decay" pattern. Interestingly, the plateau dynamics are predicted to eventually transition into an infection decline phase without any further increase in social distancing measures. Additionally, the models suggest that a second wave becomes significantly less pronounced if social distancing is only relaxed once the dynamics have transitioned to the decline phase. The network models analyzed here allow us to interpret and reconcile different infection dynamics during social distancing observed in various US states.
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http://dx.doi.org/10.1016/j.epidem.2021.100463DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8105306PMC
June 2021

Adaptive Therapy and the Cost of Drug-Resistant Mutants.

Authors:
Dominik Wodarz

Cancer Res 2021 02;81(4):811-812

Department of Population Health and Disease Prevention, Program in Public Health, Susan and Henry Samueli College of Health Sciences, University of California Irvine, Irvine, California.

The concept of adaptive cancer therapy proposes that the use of drugs at less than maximum tolerated dose can provide clinical benefits by allowing persisting drug-sensitive cells to competitively suppress drug-resistant cells; this can delay the outgrowth of these cell clones. The adaptive therapy concept has been developed with mathematical models and has subsequently been explored in clinical trials with promising results. In studies performed so far, a fitness cost of drug-resistant cells has been invoked for this treatment approach to be beneficial. In new work, it is shown that a clinical benefit can be achieved even in the absence of a fitness cost for resistant cells, which broadens the applicability of adaptive therapy..
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http://dx.doi.org/10.1158/0008-5472.CAN-20-4079DOI Listing
February 2021

Role of high-dose exposure in transmission hot zones as a driver of SARS-CoV-2 dynamics.

J R Soc Interface 2021 03 31;18(176):20200916. Epub 2021 Mar 31.

Department of Microbiology and Immunology and Baker Institute, Cornell University College of Veterinary Medicine, Cornell University, Ithaca, NY 14853, USA.

Epidemiological data about SARS-CoV-2 spread indicate that the virus is not transmitted uniformly in the population. The transmission tends to be more effective in select settings that involve exposure to relatively high viral dose, such as in crowded indoor settings, assisted living facilities, prisons or food processing plants. To explore the effect on infection dynamics, we describe a new mathematical model where transmission can occur (i) in the community at large, characterized by low-dose exposure and mostly mild disease, and (ii) in so-called transmission hot zones, characterized by high-dose exposure that can be associated with more severe disease. The model yields different types of epidemiological dynamics, depending on the relative importance of hot zone and community transmission. Interesting dynamics occur if the rate of virus release/deposition from severely infected people is larger than that of mildly infected individuals. Under this assumption, we find that successful infection spread can hinge upon high-dose hot zone transmission, yet the majority of infections are predicted to occur in the community at large with mild disease. In this regime, residual hot zone transmission can account for continued virus spread during community lockdowns, and the suppression of hot zones after community interventions are relaxed can cause a prolonged lack of infection resurgence following the reopening of society. This gives rise to the notion that targeted interventions specifically reducing virus transmission in the hot zones have the potential to suppress overall infection spread, including in the community at large. Epidemiological trends in the USA and Europe are interpreted in light of this model.
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http://dx.doi.org/10.1098/rsif.2020.0916DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8098709PMC
March 2021

Effect of feedback regulation on stem cell fractions in tissues and tumors: Understanding chemoresistance in cancer.

J Theor Biol 2021 01 29;509:110499. Epub 2020 Oct 29.

Department of Mathematics, University of California Irvine, Irvine, CA 92697, United States. Electronic address:

While resistance mutations are often implicated in the failure of cancer therapy, lack of response also occurs without such mutants. In bladder cancer mouse xenografts, repeated chemotherapy cycles have resulted in cancer stem cell (CSC) enrichment, and consequent loss of therapy response due to the reduced susceptibility of CSCs to drugs. A particular feedback loop present in the xenografts has been shown to promote CSC enrichment in this system. Yet, many other regulatory loops might also be operational and might promote CSC enrichment. Their identification is central to improving therapy response. Here, we perform a comprehensive mathematical analysis to define what types of regulatory feedback loops can and cannot contribute to CSC enrichment, providing guidance to the experimental identification of feedback molecules. We derive a formula that reveals whether or not the cell population experiences CSC enrichment over time, based on the properties of the feedback. We find that negative feedback on the CSC division rate or positive feedback on differentiated cell death rate can lead to CSC enrichment. Further, the feedback mediators that achieve CSC enrichment can be secreted by either CSCs or by more differentiated cells. The extent of enrichment is determined by the CSC death rate, the CSC self-renewal probability, and by feedback strength. Defining these general characteristics of feedback loops can guide the experimental screening for and identification of feedback mediators that can promote CSC enrichment in bladder cancer and potentially other tumors. This can help understand and overcome the phenomenon of CSC-based therapy resistance.
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http://dx.doi.org/10.1016/j.jtbi.2020.110499DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8445233PMC
January 2021

Role of high-dose exposure in transmission hot zones as a driver of SARS-CoV2 dynamics.

medRxiv 2020 Oct 9. Epub 2020 Oct 9.

Department of Microbiology and Immunology and Baker Institute, Cornell University College of Veterinary Medicine, Cornell University, Ithaca, NY 14853.

Epidemiological data on the spread of SARS-CoV-2 in the absence and presence of various non-pharmaceutical interventions indicate that the virus is not transmitted uniformly in the population. Transmission tends to be more effective in select settings that involve exposure to relatively high viral dose, such as in crowded indoor settings, assisted living facilities, prisons, or food processing plants. To explore the effect on infection dynamics, we describe a new mathematical model where transmission can occur (i) in the community at large, characterized by low dose exposure and mostly mild disease, and (ii) in so called transmission hot zones, characterized by high dose exposure that can be associated with more severe disease. Interestingly, we find that successful infection spread can hinge upon high-dose hot zone transmission, yet the majority of infections are predicted to occur in the community at large with mild disease. This gives rise to the prediction that targeted interventions that specifically reduce virus transmission in the hot zones (but not in the community at large) have the potential to suppress overall infection spread, including in the community at large. The model can further reconcile seemingly contradicting epidemiological observations. While in some locations like California, strict stay-home orders failed to significantly reduce infection prevalence, in other locations, such as New York and several European countries, stay-home orders lead to a pronounced fall in infection levels, which remained suppressed for some months after re-opening of society. Differences in hot zone transmission levels during and after social distancing interventions can account for these diverging infection patterns. These modeling results warrant further epidemiological investigations into the role of high dose hot zone transmission for the maintenance of SARS-CoV-2 spread.
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http://dx.doi.org/10.1101/2020.10.07.20208231DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7553173PMC
October 2020

Patterns of the COVID-19 pandemic spread around the world: exponential versus power laws.

J R Soc Interface 2020 09 30;17(170):20200518. Epub 2020 Sep 30.

Department of Population Health and Disease Prevention, Program in Public Health, Susan and Henry Samueli College of Health Science, University of California Irvine, Irvine, CA 92697, USA.

We have analysed the COVID-19 epidemic data of more than 174 countries (excluding China) in the period between 22 January and 28 March 2020. We found that some countries (such as the USA, the UK and Canada) follow an exponential epidemic growth, while others (like Italy and several other European countries) show a power law like growth. Regardless of the best fitting law, many countries can be shown to follow a common trajectory that is similar to Italy (the epicentre at the time of analysis), but with varying degrees of delay. We found that countries with 'younger' epidemics, i.e. countries where the epidemic started more recently, tend to exhibit more exponential like behaviour, while countries that were closer behind Italy tend to follow a power law growth. We hypothesize that there is a universal growth pattern of this infection that starts off as exponential and subsequently becomes more power law like. Although it cannot be excluded that this growth pattern is a consequence of social distancing measures, an alternative explanation is that it is an intrinsic epidemic growth law, dictated by a spatially distributed community structure, where the growth in individual highly mixed communities is exponential but the longer term, local geographical spread (in the absence of global mixing) results in a power law. This is supported by computer simulations of a metapopulation model that gives rise to predictions about the growth dynamics that are consistent with correlations found in the epidemiological data. Therefore, seeing a deviation from straight exponential growth may be a natural progression of the epidemic in each country. On the practical side, this indicates that (i) even in the absence of strict social distancing interventions, exponential growth is not an accurate predictor of longer term infection spread, and (ii) a deviation from exponential spread and a reduction of estimated doubling times do not necessarily indicate successful interventions, which are instead indicated by a transition to a reduced power or by a deviation from power law behaviour.
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http://dx.doi.org/10.1098/rsif.2020.0518DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7536045PMC
September 2020

Mutant Evolution in Spatially Structured and Fragmented Expanding Populations.

Genetics 2020 09 13;216(1):191-203. Epub 2020 Jul 13.

Department of Mathematics, University of California Irvine, California 92697

Mutant evolution in spatially structured systems is important for a range of biological systems, but aspects of it still require further elucidation. Adding to previous work, we provide a simple derivation of growth laws that characterize the number of mutants of different relative fitness in expanding populations in spatial models of different dimensionalities. These laws are universal and independent of "microscopic" modeling details. We further study the accumulation of mutants and find that, with advantageous and neutral mutants, more of them are present in spatially structured, compared to well-mixed colonies of the same size. The behavior of disadvantageous mutants is subtle: if they are disadvantageous through a reduction in division rates, the result is the same, and it is the opposite if the disadvantage is due to a death rate increase. Finally, we show that in all cases, the same results are observed in fragmented, nonspatial patch models. This suggests that the patterns observed are the consequence of population fragmentation, and not spatial restrictions We provide an intuitive explanation for the complex dependence of disadvantageous mutant evolution on spatial restriction, which relies on desynchronized dynamics in different locations/patches, and plays out differently depending on whether the disadvantage is due to a lower division rate or a higher death rate. Implications for specific biological systems, such as the evolution of drug-resistant cell mutants in cancer or bacterial biofilms, are discussed.
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http://dx.doi.org/10.1534/genetics.120.303422DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7463292PMC
September 2020

The effects of phenotypic plasticity on the fixation probability of mutant cancer stem cells.

J Theor Biol 2020 10 27;503:110384. Epub 2020 Jun 27.

Department of Applied Mathematics, University of Waterloo, Waterloo N2L 3G1, Canada.

The cancer stem cell hypothesis claims that tumor growth and progression are driven by a (typically) small niche of the total cancer cell population called cancer stem cells (CSCs). These CSCs can go through symmetric or asymmetric divisions to differentiate into specialised, progenitor cells or reproduce new CSCs. While it was once held that this differentiation pathway was unidirectional, recent research has demonstrated that differentiated cells are more plastic than initially considered. In particular, differentiated cells can de-differentiate and recover their stem-like capacity. Two recent papers have considered how this rate of plasticity affects the evolutionary dynamic of an invasive, malignant population of stem cells and differentiated cells into existing tissue (Mahdipour-Shirayeh et al., 2017; Wodarz, 2018). These papers arrive at seemingly opposing conclusions, one claiming that increased plasticity results in increased invasive potential, and the other that increased plasticity decreases invasive potential. Here, we show that what is most important, when determining the effect on invasive potential, is how one distributes this increased plasticity between the compartments of resident and mutant-type cells. We also demonstrate how these results vary, producing non-monotone fixation probability curves, as inter-compartmental plasticity changes when differentiated cell compartments are allowed to continue proliferating, highlighting a fundamental difference between the two models. We conclude by demonstrating the stability of these qualitative results over various parameter ranges. Keywords: cancer stem cells, plasticity, de-differentiation, fixation probability.
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http://dx.doi.org/10.1016/j.jtbi.2020.110384DOI Listing
October 2020

Evolutionary dynamics of culturally transmitted, fertility-reducing traits.

Proc Biol Sci 2020 04 15;287(1925):20192468. Epub 2020 Apr 15.

Department of Mathematics, University of California, Irvine, CA 92697, USA.

Human populations in many countries have undergone a phase of demographic transition, characterized by a major reduction in fertility at a time of increased resource availability. A key stylized fact is that the reduction in fertility is preceded by a reduction in mortality and a consequent increase in population density. Various theories have been proposed to account for the demographic transition process, including maladaptation, increased parental investment in fewer offspring, and cultural evolution. None of these approaches, including formal cultural evolutionary models of the demographic transitions, have addressed a possible direct causal relationship between a reduction in mortality and the subsequent decline in fertility. We provide mathematical models in which favours the cultural selection of low-fertility traits. This occurs because reduced mortality slows turnover in the model, which allows the cultural transmission advantage of low-fertility traits to outrace their reproductive disadvantage. For mortality to be a crucial determinant of outcome, a cultural transmission bias is required where slow reproducers exert higher social influence. Computer simulations of our models that allow for exogenous variation in the death rate can reproduce the central features of the demographic transition process, including substantial reductions in fertility within only one to three generations. A model assuming continuous evolution of reproduction rates through imitation errors predicts fertility to fall below replacement levels if death rates are sufficiently low. This can potentially explain the very low preferred family sizes in Western Europe.
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http://dx.doi.org/10.1098/rspb.2019.2468DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7211447PMC
April 2020

Beyond the pair approximation: Modeling colonization population dynamics.

Phys Rev E 2020 Mar;101(3-1):032404

Department of Mathematics, University of California Irvine, Irvine, California 92697, USA.

The process of range expansion (colonization) is one of the basic types of biological dynamics, whereby a species grows and spreads outwards, occupying new territories. Spatial modeling of this process is naturally implemented as a stochastic cellular automaton, with individuals occupying nodes on a rectangular grid, births and deaths occurring probabilistically, and individuals only reproducing onto unoccupied neighboring spots. In this paper we derive several approximations that allow prediction of the expected range expansion dynamics, based on the reproduction and death rates. We derive several approximations, where the cellular automaton is described by a system of ordinary differential equations that preserves correlations among neighboring spots (up to a distance). This methodology allows us to develop accurate approximations of the population size and the expected spatial shape, at a fraction of the computational time required to simulate the original stochastic system. In addition, we provide simple formulas for the steady-state population densities for von Neumann and Moore neighborhoods. Finally, we derive concise approximations for the speed of range expansion in terms of the reproduction and death rates, for both types of neighborhoods. The methodology is generalizable to more complex scenarios, such as different interaction ranges and multiple-species systems.
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http://dx.doi.org/10.1103/PhysRevE.101.032404DOI Listing
March 2020

Effect of synaptic cell-to-cell transmission and recombination on the evolution of double mutants in HIV.

J R Soc Interface 2020 03 25;17(164):20190832. Epub 2020 Mar 25.

Department of Mathematics, Susan and Henry Samueli College of Health Sciences, University of California, Irvine, CA 92697, USA.

Recombination in HIV infection can impact virus evolution in complex ways, as has been shown both experimentally and mathematically. The effect of free virus versus synaptic, cell-to-cell transmission on the evolution of double mutants, however, has not been investigated. Here, we do so by using a stochastic agent-based model. Consistent with data, we assume spatial constraints for synaptic but not for free-virus transmission. Two important effects of the viral spread mode are observed: (i) for disadvantageous mutants, synaptic transmission protects against detrimental effects of recombination on double mutant persistence. Under free virus transmission, recombination increases double mutant levels for negative epistasis, but reduces them for positive epistasis. This reduction for positive epistasis is much diminished under predominantly synaptic transmission, and recombination can, in fact, lead to increased mutant levels. (ii) The mode of virus spread also directly influences the evolutionary fate of double mutants. For disadvantageous mutants, double mutant production is the predominant driving force, and hence synaptic transmission leads to highest double mutant levels due to increased transmission efficiency. For advantageous mutants, double mutant spread is the most important force, and hence free virus transmission leads to fastest invasion due to better mixing. For neutral mutants, both production and spread of double mutants are important, and hence an optimal mixture of free virus and synaptic transmission maximizes double mutant fractions. Therefore, both free virus and synaptic transmission can enhance or delay double mutant evolution. Implications for drug resistance in HIV are discussed.
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http://dx.doi.org/10.1098/rsif.2019.0832DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7115232PMC
March 2020

Aspirin and the chemoprevention of cancers: A mathematical and evolutionary dynamics perspective.

Wiley Interdiscip Rev Syst Biol Med 2020 09 12;12(5):e1487. Epub 2020 Mar 12.

Department of Population Health and Disease Prevention, Program in Public Health, Susan and Henry Samueli College of Health Sciences, University of California Irvine, Irvine, California, USA.

Epidemiological data indicate that long-term low dose aspirin administration has a protective effect against the occurrence of colorectal cancer, both in sporadic and in hereditary forms of the disease. The mechanisms underlying this protective effect, however, are incompletely understood. The molecular events that lead to protection have been partly defined, but remain to be fully characterized. So far, however, approaches based on evolutionary dynamics have not been discussed much, but can potentially offer important insights. The aim of this review is to highlight this line of investigation and the results that have been obtained. A core observation in this respect is that aspirin has a direct negative impact on the growth dynamics of the cells, by influencing the kinetics of tumor cell division and death. We discuss the application of mathematical models to experimental data to quantify these parameter changes. We then describe further mathematical models that have been used to explore how these aspirin-mediated changes in kinetic parameters influence the probability of successful colony growth versus extinction, and how they affect the evolution of the tumor during aspirin administration. Finally, we discuss mathematical models that have been used to investigate the selective forces that can lead to the rise of mismatch-repair deficient cells in an inflammatory environment, and how this selection can be potentially altered through aspirin-mediated interventions. This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Analytical and Computational Methods > Analytical Methods Analytical and Computational Methods > Computational Methods.
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http://dx.doi.org/10.1002/wsbm.1487DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7486281PMC
September 2020

A comprehensive in vivo and mathematic modeling-based kinetic characterization for aspirin-induced chemoprevention in colorectal cancer.

Carcinogenesis 2020 07;41(6):751-760

Center for Gastrointestinal Research, Center from Translational Genomics and Oncology, Baylor Scott and White Research Institute and Charles A. Sammons Cancer Center, Baylor University Medical Center, Dallas, TX, USA.

Accumulating evidence suggests that aspirin has anti-tumorigenic properties in colorectal cancer (CRC). Herein, we undertook a comprehensive and systematic series of in vivo animal experiments followed by 3D-mathematical modeling to determine the kinetics of aspirin's anti-cancer effects on CRC growth. In this study, CRC xenografts were generated using four CRC cell lines with and without PIK3CA mutations and microsatellite instability, and the animals were administered with various aspirin doses (0, 15, 50, and 100 mg/kg) for 2 weeks. Cell proliferation, apoptosis and protein expression were evaluated, followed by 3D-mathematical modeling analysis to estimate cellular division and death rates and their impact on aspirin-mediated changes on tumor growth. We observed that aspirin resulted in a dose-dependent decrease in the cell division rate, and a concomitant increase in the cell death rates in xenografts from all cell lines. Aspirin significantly inhibited cell proliferation as measured by Ki67 staining (P < 0.05-0.01). The negative effect of aspirin on the rate of tumor cell proliferation was more significant in xenograft tumors derived from PIK3CA mutant versus wild-type cells. A computational model of 3D-tumor growth suggests that the growth inhibitory effect of aspirin on the tumor growth kinetics is due to a reduction of tumor colony formation, and that this effect is sufficiently strong to be an important contributor to the reduction of CRC incidence in aspirin-treated patients. In conclusion, we provide a detailed kinetics of aspirin-mediated inhibition of tumor cell proliferation, which support the epidemiological data for the observed protective effect of aspirin in CRC patients.
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http://dx.doi.org/10.1093/carcin/bgz195DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7351132PMC
July 2020

The 2019 mathematical oncology roadmap.

Phys Biol 2019 06 19;16(4):041005. Epub 2019 Jun 19.

Department of Computational and Quantitative Medicine, Division of Mathematical Oncology, City of Hope National Medical Center, Duarte, CA 91010, United States of America. Author to whom any correspondence should be addressed.

Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.
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http://dx.doi.org/10.1088/1478-3975/ab1a09DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6655440PMC
June 2019

Multiple infection of cells changes the dynamics of basic viral evolutionary processes.

Evol Lett 2019 Feb 31;3(1):104-115. Epub 2018 Dec 31.

Department of Ecology and Evolutionary Biology, 321 Steinhaus Hall University of California Irvine CA 92697.

The infection of cells by multiple copies of a given virus can impact viral evolution in a variety of ways, yet some of the most basic evolutionary dynamics remain underexplored. Using computational models, we investigate how infection multiplicity affects the fixation probability of mutants, the rate of mutant generation, and the timing of mutant invasion. An important insight from these models is that for neutral and disadvantageous phenotypes, rare mutants initially enjoy a fitness advantage in the presence of multiple infection of cells. This arises because multiple infection allows the rare mutant to enter more target cells and to spread faster, while it does not accelerate the spread of the resident wild-type virus. The rare mutant population can increase by entry into both uninfected and wild-type-infected cells, while the established wild-type population can initially only grow through entry into uninfected cells. Following this initial advantageous phase, the dynamics are governed by drift or negative selection, respectively, and a higher multiplicity reduces the chances that mutants fix in the population. Hence, while increased infection multiplicity promotes the presence of neutral and disadvantageous mutants in the short-term, it makes it less likely in the longer term. We show how these theoretical insights can be useful for the interpretation of experimental data on virus evolution at low and high multiplicities. The dynamics explored here provide a basis for the investigation of more complex viral evolutionary processes, including recombination, reassortment, as well as complementary/inhibitory interactions.
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http://dx.doi.org/10.1002/evl3.95DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6369963PMC
February 2019

A call to arms: Unifying the fight against resistance.

Sci Signal 2018 10 23;11(553). Epub 2018 Oct 23.

Institute of Drug Resistance, Worcester, MA 01605, USA.

This Editorial discusses the state of research on drug resistance in the fields of cancer, infectious disease, and agriculture. Reaching across the aisle for a more cross-collaborative approach may lead to exciting breakthroughs toward tackling the challenges of drug resistance in each field.
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http://dx.doi.org/10.1126/scisignal.aav0442DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6464114PMC
October 2018

Virus and CTL dynamics in the extrafollicular and follicular tissue compartments in SIV-infected macaques.

PLoS Comput Biol 2018 10 18;14(10):e1006461. Epub 2018 Oct 18.

Division of Infectious Diseases, University of Arizona, Tucson, Arizona, United States of America.

Data from SIV-infected macaques indicate that virus-specific cytotoxic T lymphocytes (CTL) are mostly present in the extrafollicular (EF) compartment of the lymphoid tissue, with reduced homing to the follicular (F) site. This contributes to the majority of the virus being present in the follicle and represents a barrier to virus control. Using mathematical models, we investigate these dynamics. Two models are analyzed. The first assumes that CTL can only become stimulated and expand in the extrafollicular compartment, with migration accounting for the presence of CTL in the follicle. In the second model, follicular CTL can also undergo antigen-induced expansion. Consistent with experimental data, both models predict increased virus compartmentalization in the presence of stronger CTL responses and lower virus loads, and a more pronounced rise of extrafollicular compared to follicular virus during CD8 cell depletion experiments. The models, however, differ in other aspects. The follicular expansion model results in dynamics that promote the clearance of productive infection in the extrafollicular site, with any productively infected cells found being the result of immigration from the follicle. This is not observed in the model without follicular CTL expansion. The models further predict different consequences of introducing engineered, follicular-homing CTL, which has been proposed as a therapeutic means to improve virus control. Without follicular CTL expansion, this is predicted to result in a reduction of virus load in both compartments. The follicular CTL expansion model, however, makes the counter-intuitive prediction that addition of F-homing CTL not only results in a reduction of follicular virus load, but also in an increase in extrafollicular virus replication. These predictions remain to be experimentally tested, which will be relevant for distinguishing between models and for understanding how therapeutic introduction of F-homing CTL might impact the overall dynamics of the infection.
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http://dx.doi.org/10.1371/journal.pcbi.1006461DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6207320PMC
October 2018

The role of telomere shortening in carcinogenesis: A hybrid stochastic-deterministic approach.

J Theor Biol 2019 01 10;460:144-152. Epub 2018 Oct 10.

Department of Mathematics, University of California, Irvine, California, United States; Department of Ecology and Evolutionary Biology, University of California, Irvine, California, United States.

Genome instability is a characteristic of most cancers, contributing to the acquisition of genetic alterations that drive tumor progression. One important source of genome instability is linked to telomere dysfunction in cells with critically short telomeres that lack p53-mediated surveillance of genomic integrity. Here we research the probability that cancer emerges through an evolutionary pathway that includes a telomere-induced phase of genome instability. To implement our models we use a hybrid stochastic-deterministic approach, which allows us to perform large numbers of simulations using biologically realistic population sizes and mutation rates, circumventing the traditional limitations of fully stochastic algorithms. The hybrid methodology should be easily adaptable to a wide range of evolutionary problems. In particular, we model telomere shortening and the acquisition of two mutations: Telomerase activation and p53 inactivation. We find that the death rate of unstable cells, and the number of cell divisions that p53 mutants can sustain beyond the normal senescence setpoint determine the likelihood that the first double mutant originates in a cell with telomere-induced instability. The model has applications to an influential telomerase-null mouse model and p16 silenced human cells. We end by discussing algorithmic performance and a measure for the accuracy of the hybrid approximation.
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http://dx.doi.org/10.1016/j.jtbi.2018.09.003DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6234035PMC
January 2019

Passenger mutations can accelerate tumour suppressor gene inactivation in cancer evolution.

J R Soc Interface 2018 06;15(143)

Department of Mathematics, Rowland Hall, University of California, Irvine, CA 92697, USA.

Carcinogenesis is an evolutionary process whereby cells accumulate multiple mutations. Besides the 'driver mutations' that cause the disease, cells also accumulate a number of other mutations with seemingly no direct role in this evolutionary process. They are called passenger mutations. While it has been argued that passenger mutations render tumours more fragile due to reduced fitness, the role of passenger mutations remains understudied. Using evolutionary computational models, we demonstrate that in the context of tumour suppressor gene inactivation (and hence fitness valley crossing), the presence of passenger mutations can accelerate the rate of evolution by reducing overall population fitness and increasing the relative fitness of intermediate mutants in the fitness valley crossing pathway. Hence, the baseline rate of tumour suppressor gene inactivation might be faster than previously thought. Conceptually, parallels are found in the field of turbulence and pattern formation, where instabilities can be driven by perturbations that are damped (disadvantageous), but provide a richer set of pathways such that a system can achieve some desired goal more readily. This highlights, through a number of novel parallels, the relevance of physical sciences in oncology.
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http://dx.doi.org/10.1098/rsif.2017.0967DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6030626PMC
June 2018

Effect of cellular de-differentiation on the dynamics and evolution of tissue and tumor cells in mathematical models with feedback regulation.

Authors:
Dominik Wodarz

J Theor Biol 2018 07 30;448:86-93. Epub 2018 Mar 30.

Department of Ecology and Evolutionary Biology & Department of Mathematics, 321 Steinhaus Hall, University of California, Irvine, CA 92617, USA. Electronic address:

Tissues are maintained by adult stem cells that self-renew and also differentiate into functioning tissue cells. Homeostasis is achieved by a set of complex mechanisms that involve regulatory feedback loops. Similarly, tumors are believed to be maintained by a minority population of cancer stem cells, while the bulk of the tumor is made up of more differentiated cells, and there is indication that some of the feedback loops that operate in tissues continue to be functional in tumors. Mathematical models of such tissue hierarchies, including feedback loops, have been analyzed in a variety of different contexts. Apart from stem cells giving rise to differentiated cells, it has also been observed that more differentiated cells can de-differentiate into stem cells, both in healthy tissue and tumors, aspects of which have also been investigated mathematically. This paper analyses the effect of de-differentiation on the basic and evolutionary dynamics of cells in the context of tissue hierarchy models that include negative feedback regulation of the cell populations. The models predict that in the presence of de-differentiation, the fixation probability of a neutral mutant is lower than in its absence. Therefore, if de-differentiation occurs, a mutant with identical parameters compared to the wild-type cell population behaves like a disadvantageous mutant. Similarly, the process of de-differentiation is found to lower the fixation probability of an advantageous mutant. These results indicate that the presence of de-differentiation can lower the rates of tumor initiation and progression in the context of the models considered here.
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http://dx.doi.org/10.1016/j.jtbi.2018.03.036DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6173950PMC
July 2018

Spatial evolution of regularization in learned behavior of animals.

Math Biosci 2018 05 14;299:103-116. Epub 2018 Mar 14.

Department of Mathematics, University of California Irvine, Irvine, CA 92697, USA; Department of Ecology and Evolutionary Biology, University of California Irvine, Irvine, CA 92697, USA. Electronic address:

Stochastic population dynamics of learned traits are studied, where individual learners behave according to a reinforcement learner model, which is a nonlinear version of the Bush-Mosteller model. Depending on a regularization parameter (parameter a), the learners may possess different degrees of overmatching (regularization behavior, 0 ≤ a < 1), frequency matching (corresponding to a=1), or undermatching behavior (a > 1). Both non-spatial and spatial models are considered, to study the interplay of individual heterogeneity of behavior, spatial and temporal effects of learning, and the possibility of emergence of regional culture. In non-spatial models, we observe that populations of individuals learning from each other converge to a universally shared, deterministic rule (either rule "1" or rule "0"), only if they to some extent possess the ability to generalize (a < 1). Otherwise, a low-coherence solution where both rules are used intermittently by everyone, is achieved. If the evolution of the regularization ability is included, then we find that a initially evolves toward lower values, and a shared solution is established when everyone reliably uses the same rule. The spatial (2D) model has two well known limiting cases: if a=0 (the strongest degree of regularization), the model converges to a threshold voter model, and if a=1 (frequency matching), it is equivalent to the discrete diffusion equation. If 0 < a < 1 (the case where individuals regularize), spatial patterns emerge, where patches of different usage of the rule are formed. Smaller values of a lead to sharper and longer lived patches. Values of a < 1 close to unity result in probabilistic outcomes where patches only survive if they are attached to the boundary. Analytical treatment of the 1D case reveals the existence of approximate equilibria that have front structure, where spatially intermittent deterministic usage of one and the other rule are separated by interfaces whose analytical form is derived.
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http://dx.doi.org/10.1016/j.mbs.2018.03.005DOI Listing
May 2018

Effect of cell cycle duration on somatic evolutionary dynamics.

Evol Appl 2017 12 12;10(10):1121-1129. Epub 2017 Oct 12.

Department of Ecology and Evolutionary Biology University of California Irvine CA USA.

Cellular checkpoints prevent damage and mutation accumulation in tissue cells. DNA repair is one mechanism that can be triggered by checkpoints and involves temporary cell cycle arrest and thus delayed reproduction. Repair-deficient cells avoid this delay, which has been argued to lead to a selective advantage in the presence of frequent damage. We investigate this hypothesis with stochastic modeling, using mathematical analysis and agent-based computations. We first model competition between two cell types: a cell population that enters temporary cell cycle arrest, corresponding to repair (referred to as arresting cells), and one that does not enter arrest (referred to as nonarresting cells). Although nonarresting cells are predicted to grow with a faster rate than arresting cells in isolation, this does not translate into a selective advantage in the model. Interestingly, the evolutionary properties of the nonarresting cells depend on the measure (or observable) of interest. When examining the average populations sizes in competition simulations, nonarresting and arresting cells display neutral dynamics. The fixation probability of nonarresting mutants, however, is lower than predicted for a neutral scenario, suggesting a selective disadvantage in this setting. For nonarresting cells to gain a selective advantage, additional mechanisms must be invoked in the model, such as small, repeated phases of tissue damage, each resulting in a brief period of regenerative growth. The same properties are observed in a more complex model where it is explicitly assumed that repair and temporary cell cycle arrest are dependent on the cell having sustained DNA damage, the rate of which can be varied. We conclude that repair-deficient cells are not automatically advantageous in the presence of frequent DNA damage and that mechanisms beyond avoidance of cell cycle delay must be invoked to explain their emergence.
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http://dx.doi.org/10.1111/eva.12518DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5680637PMC
December 2017

Effect of aspirin on tumour cell colony formation and evolution.

J R Soc Interface 2017 09;14(134)

Department of Ecology and Evolutionary Biology, University of California, Irvine, CA 92617, USA.

Aspirin is known to reduce the risk of colorectal cancer (CRC) incidence, but the underlying mechanisms are not fully understood. In a previous study, we quantified the growth kinetics of different CRC tumour cell lines treated with varying doses of aspirin, measuring the rate of cell division and cell death. Here, we use these measured parameters to calculate the chances of successful clonal expansion and to determine the evolutionary potential of the tumour cell lines in the presence and absence of aspirin. The calculations indicate that aspirin increases the probability that a single tumour cell fails to clonally expand. Further, calculations suggest that aspirin increases the evolutionary potential of an expanding tumour cell colony. An aspirin-treated tumour cell population is predicted to result in the accumulation of more mutations (and is thus more virulent and more difficult to treat) than a cell population of the same size that grew without aspirin. This indicates a potential trade-off between delaying the onset of cancer and increasing its evolutionary potential through chemoprevention. Further work needs to investigate to what extent these findings apply to settings, and to what degree they contribute to the epidemiologically documented aspirin-mediated protection.
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http://dx.doi.org/10.1098/rsif.2017.0374DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5636273PMC
September 2017

Early Stochastic Dynamics in Human Cytomegalovirus Infection.

J Virol 2017 09 24;91(18). Epub 2017 Aug 24.

Department of Ecology and Evolutionary Biology, University of California, Irvine, California, USA, and Department of Mathematics, University of California, Irvine, California, USA.

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http://dx.doi.org/10.1128/JVI.00949-17DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5571241PMC
September 2017

Pyroptosis, superinfection, and the maintenance of the latent reservoir in HIV-1 infection.

Sci Rep 2017 06 19;7(1):3834. Epub 2017 Jun 19.

Department of Basic Science, 921 Schwartz Building, New York University College of Dentistry, New York, NY, 10010, USA.

A long-lived reservoir of latently infected T cells prevents antiretroviral therapy from eliminating HIV-1 infection. Furthering our understanding of the dynamics of latency generation and maintenance is therefore vital to improve treatment outcome. Using mathematical models and experiments, we suggest that the death of latently infected cells brought about by pyroptosis, or to a lesser extent by superinfection, might be key mechanisms to account for the size and composition of the latent reservoir. Pyroptosis is a form of cell death that occurs in a resting (and thus latently infected) T cell when a productively infected cell attempts cell-to-cell transmission of virus. Superinfection of latently infected cells by productive virus could similarly remove those cells through active virus replication and resulting cytopathicity. The mathematical models presented can explain a number of previously published clinical observations including latent reservoir size and the relationships to viral load in acute HIV infection, measurements of the latent reservoir in chronic infection, and the replacement of wild-type virus by CTL escape mutants within the latent reservoir. Basic virus dynamics models of latency that do not take into account pyroptosis, superinfection, or other potential complexities cannot account for the data.
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http://dx.doi.org/10.1038/s41598-017-04130-9DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5476677PMC
June 2017

Determining the role of inflammation in the selection of JAK2 mutant cells in myeloproliferative neoplasms.

J Theor Biol 2017 07 10;425:43-52. Epub 2017 May 10.

Department of Mathematics, USA; Department of Ecology and Evolutionary Biology, University of California Irvine, Irvine, CA 92697, USA. Electronic address:

Myeloproliferative neoplasm (MPN) is a hematologic malignancy characterized by the clonal outgrowth of hematopoietic cells with a somatically acquired mutation most commonly in JAK2 (JAK2). This mutation endows upon myeloid progenitors cytokine independent growth and consequently leads to excessive production of myeloid lineage cells. It has been previously suggested that inflammation may play a role in the clonal evolution of JAK2 mutants. In particular, it is possible that one or more cellular kinetic parameters of hematopoietic stem cells (HSCs) are affected by inflammation, such as division or death rates of cells, and the probability of HSC differentiation. This suggests a mechanism that can steer the outcome of the cellular competition in favor of the mutants, initiating the disease. In this paper we create a number of mathematical evolutionary models, from very abstract to more concrete, that describe cellular competition in the context of inflammation. It is possible to build a model axiomatically, where only very general assumptions are imposed on the modeling components and no arbitrary (and generally unknown) functional forms are used, and still generate a set of testable predictions. In particular, we show that, if HSC death is negligible, the evolutionary advantage of mutant cells can only be conferred by an increase in differentiation probability of HSCs in the presence of inflammation, and if death plays a significant role in the dynamics, an additional mechanism may be an increase of HSC's division-to-death ratio in the presence of inflammation. Further, we show that in the presence of inflammation, the wild type cell population is predicted to shrink under inflammation (even in the absence of mutants). Finally, it turns out that if only the differentiation probability is affected by the inflammation, then the resulting steady state population of wild type cells will contain a relatively smaller percentage of HSCs under inflammation. If the division-to-death rate is also affected, then the percentage of HSCs under inflammation can either decrease or increase, depending on other parameters.
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http://dx.doi.org/10.1016/j.jtbi.2017.05.012DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5689470PMC
July 2017

Cellular Hierarchy as a Determinant of Tumor Sensitivity to Chemotherapy.

Cancer Res 2017 05 24;77(9):2231-2241. Epub 2017 Feb 24.

Department of Ecology and Evolutionary Biology, University of California, Irvine, California.

Chemotherapy has been shown to enrich cancer stem cells in tumors. Recently, we demonstrated that administration of chemotherapy to human bladder cancer xenografts could trigger a wound-healing response that mobilizes quiescent tumor stem cells into active proliferation. This phenomenon leads to a loss of sensitivity to chemotherapy partly due to an increase in the number of tumor stem cells, which typically respond to chemotherapy-induced cell death less than more differentiated cells. Different bladder cancer xenografts, however, demonstrate differential sensitivities to chemotherapy, the basis of which is not understood. Using mathematical models, we show that characteristics of the tumor cell hierarchy can be crucial for determining the sensitivity of tumors to drug therapy, under the assumption that stem cell enrichment is the primary basis for drug resistance. Intriguingly, our model predicts a weaker response to therapy if there is negative feedback from differentiated tumor cells that inhibits the rate of tumor stem cell division. If this negative feedback is less pronounced, the treatment response is predicted to be enhanced. The reason is that negative feedback on the rate of tumor cell division promotes a permanent rise of the tumor stem cell population over time, both in the absence of treatment and even more so during drug therapy. Model application to data from chemotherapy-treated patient-derived xenografts indicates support for model predictions. These findings call for further research into feedback mechanisms that might remain active in cancers and potentially highlight the presence of feedback as an indication to combine chemotherapy with approaches that limit the process of tumor stem cell enrichment. .
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http://dx.doi.org/10.1158/0008-5472.CAN-16-2434DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5487257PMC
May 2017

Aspirin-Induced Chemoprevention and Response Kinetics Are Enhanced by PIK3CA Mutations in Colorectal Cancer Cells.

Cancer Prev Res (Phila) 2017 Mar 2;10(3):208-218. Epub 2017 Feb 2.

Center for Gastrointestinal Research; Center for Translational Genomics and Oncology, Baylor Scott and White Research Institute and Sammons Cancer Center, Baylor University Medical Center, Dallas, Texas.

This study was designed to determine how aspirin influences the growth kinetics and characteristics of cultured colorectal cancer cells that harbor a variety of different mutational backgrounds, including - and -activating mutations, and the presence or absence of microsatellite instability. Colorectal cancer cell lines (HCT116, HCT116 + Chr3/5, RKO, SW480, HCT15, CACO2, HT29, and SW48) were treated with pharmacologically relevant doses of aspirin (0.5-10 mmol/L) and evaluated for proliferation and cell-cycle distribution. These parameters were fitted to a mathematical model to quantify the effects and understand the mechanism(s) by which aspirin modifies growth in colorectal cancer cells. We also evaluated the effects of aspirin on key G-G cell-cycle genes that are regulated by the PI3K-Akt pathway. Aspirin decelerated growth rates and disrupted cell-cycle dynamics more profoundly in faster growing colorectal cancer cell lines, which tended to be mutants. Additionally, microarray analysis of 151 colorectal cancer cell lines identified important cell-cycle regulatory genes that are downstream targets of PIK3 and were also dysregulated by aspirin treatment ( and ). Our study demonstrated what clinical trials have only speculated, that -mutant colorectal cancers are more sensitive to aspirin. Aspirin inhibited cell growth in all colorectal cancer cell lines regardless of mutational background, but the effects were exacerbated in cells with mutations. Mathematical modeling combined with bench science revealed that cells with -mutations experience significant G-G arrest and explains why patients with mutant colorectal cancers may benefit from aspirin use after diagnosis. .
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http://dx.doi.org/10.1158/1940-6207.CAPR-16-0175DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5337164PMC
March 2017

Leukemia cell proliferation and death in chronic lymphocytic leukemia patients on therapy with the BTK inhibitor ibrutinib.

JCI Insight 2017 01 26;2(2):e89904. Epub 2017 Jan 26.

Karches Center for Chronic Lymphocytic Leukemia Research, The Feinstein Institute for Medical Research, Northwell Health, Manhasset, New York, USA.

Ibrutinib is an effective targeted therapy for patients with chronic lymphocytic leukemia (CLL) that inhibits Bruton's tyrosine kinase (BTK), a kinase involved in B cell receptor signaling. We used stable isotopic labeling with deuterated water (HO) to measure directly the effects of ibrutinib on leukemia cell proliferation and death in 30 patients with CLL. The measured average CLL cell proliferation ("birth") rate before ibrutinib therapy was 0.39% of the clone per day (range 0.17%-1.04%); this decreased to 0.05% per day (range 0%-0.36%) with treatment. Death rates of blood CLL cells increased from 0.18% per day (average, range 0%-0.7%) prior to treatment to 1.5% per day (range 0%-3.0%) during ibrutinib therapy, and they were even higher in tissue compartments. This study provides the first direct in vivo measurements to our knowledge of ibrutinib's antileukemia actions, demonstrating profound and immediate inhibition of CLL cell proliferation and promotion of high rates of CLL cell death. This trial was registered at clinicaltrials.gov (NCT01752426). This study was supported by a Cancer Center Support Grant (National Cancer Institute grant P30 CA016672), an NIH grant (CA081554) from the National Cancer Institute, MD Anderson's Moon Shots Program in CLL, and Pharmacyclics, an AbbVie company.
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http://dx.doi.org/10.1172/jci.insight.89904DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5256142PMC
January 2017
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