Publications by authors named "Alexander R A Anderson"

111 Publications

In Silico Investigations of Multi-Drug Adaptive Therapy Protocols.

Cancers (Basel) 2022 May 30;14(11). Epub 2022 May 30.

Arizona Cancer Evolution Center, Arizona State University, Tempe, AZ 85287, USA.

The standard of care for cancer patients aims to eradicate the tumor by killing the maximum number of cancer cells using the maximum tolerated dose (MTD) of a drug. MTD causes significant toxicity and selects for resistant cells, eventually making the tumor refractory to treatment. Adaptive therapy aims to maximize time to progression (TTP), by maintaining sensitive cells to compete with resistant cells. We explored both dose modulation (DM) protocols and fixed dose (FD) interspersed with drug holiday protocols. In contrast to previous single drug protocols, we explored the determinants of success of two-drug adaptive therapy protocols, using an agent-based model. In almost all cases, DM protocols (but not FD protocols) increased TTP relative to MTD. DM protocols worked well when there was more competition, with a higher cost of resistance, greater cell turnover, and when crowded proliferating cells could replace their neighbors. The amount that the drug dose was changed, mattered less. The more sensitive the protocol was to tumor burden changes, the better. In general, protocols that used as little drug as possible, worked best. Preclinical experiments should test these predictions, especially dose modulation protocols, with the goal of generating successful clinical trials for greater cancer control.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.3390/cancers14112699DOI Listing
May 2022

Spatial structure impacts adaptive therapy by shaping intra-tumoral competition.

Commun Med (Lond) 2022 25;2:46. Epub 2022 Apr 25.

Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL USA.

Background: Adaptive therapy aims to tackle cancer drug resistance by leveraging resource competition between drug-sensitive and resistant cells. Here, we present a theoretical study of intra-tumoral competition during adaptive therapy, to investigate under which circumstances it will be superior to aggressive treatment.

Methods: We develop and analyse a simple, 2-D, on-lattice, agent-based tumour model in which cells are classified as fully drug-sensitive or resistant. Subsequently, we compare this model to its corresponding non-spatial ordinary differential equation model, and fit it to longitudinal prostate-specific antigen data from 65 prostate cancer patients undergoing intermittent androgen deprivation therapy following biochemical recurrence.

Results: Leveraging the individual-based nature of our model, we explicitly demonstrate competitive suppression of resistance during adaptive therapy, and examine how different factors, such as the initial resistance fraction or resistance costs, alter competition. This not only corroborates our theoretical understanding of adaptive therapy, but also reveals that competition of resistant cells with each other may play a more important role in adaptive therapy in solid tumours than was previously thought. To conclude, we present two case studies, which demonstrate the implications of our work for: (i) mathematical modelling of adaptive therapy, and (ii) the intra-tumoral dynamics in prostate cancer patients during intermittent androgen deprivation treatment, a precursor of adaptive therapy.

Conclusion: Our work shows that the tumour's spatial architecture is an important factor in adaptive therapy and provides insights into how adaptive therapy leverages both inter- and intra-specific competition to control resistance.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1038/s43856-022-00110-xDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC9053239PMC
April 2022

Immunosuppressive niche engineering at the onset of human colorectal cancer.

Nat Commun 2022 04 4;13(1):1798. Epub 2022 Apr 4.

Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, 12902 Magnolia Drive, SRB 4, Tampa, FL, 336122, USA.

The evolutionary dynamics of tumor initiation remain undetermined, and the interplay between neoplastic cells and the immune system is hypothesized to be critical in transformation. Colorectal cancer (CRC) presents a unique opportunity to study the transition to malignancy as pre-cancers (adenomas) and early-stage cancers are frequently resected. Here, we examine tumor-immune eco-evolutionary dynamics from pre-cancer to carcinoma using a computational model, ecological analysis of digital pathology data, and neoantigen prediction in 62 patient samples. Modeling predicted recruitment of immunosuppressive cells would be the most common driver of transformation. As predicted, ecological analysis reveals that progressed adenomas co-localized with immunosuppressive cells and cytokines, while benign adenomas co-localized with a mixed immune response. Carcinomas converge to a common immune "cold" ecology, relaxing selection against immunogenicity and high neoantigen burdens, with little evidence for PD-L1 overexpression driving tumor initiation. These findings suggest re-engineering the immunosuppressive niche may prove an effective immunotherapy in CRC.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1038/s41467-022-29027-8DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8979971PMC
April 2022

Gattaca: Base-Pair Resolution Mutation Tracking for Somatic Evolution Studies using Agent-based Models.

Mol Biol Evol 2022 04;39(4)

Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL 33612, USA.

Research over the past two decades has made substantial inroads into our understanding of somatic mutations. Recently, these studies have focused on understanding their presence in homeostatic tissue. In parallel, agent-based mechanistic models have emerged as an important tool for understanding somatic mutation in tissue; yet no common methodology currently exists to provide base-pair resolution data for these models. Here, we present Gattaca as the first method for introducing and tracking somatic mutations at the base-pair resolution within agent-based models that typically lack nuclei. With nuclei that incorporate human reference genomes, mutational context, and sequence coverage/error information, Gattaca is able to realistically evolve sequence data, facilitating comparisons between in silico cell tissue modeling with experimental human somatic mutation data. This user-friendly method, incorporated into each in silico cell, allows us to fully capture somatic mutation spectra and evolution.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1093/molbev/msac058DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC9034688PMC
April 2022

Roadmap on plasticity and epigenetics in cancer.

Phys Biol 2022 04 18;19(3). Epub 2022 Apr 18.

Integrated Mathematical Oncology Department, Moffitt Cancer Center and Research Institute, Tampa, FL 33612, United States of America.

The role of plasticity and epigenetics in shaping cancer evolution and response to therapy has taken center stage with recent technological advances including single cell sequencing. This roadmap article is focused on state-of-the-art mathematical and experimental approaches to interrogate plasticity in cancer, and addresses the following themes and questions: is there a formal overarching framework that encompasses both non-genetic plasticity and mutation-driven somatic evolution? How do we measure and model the role of the microenvironment in influencing/controlling non-genetic plasticity? How can we experimentally study non-genetic plasticity? Which mathematical techniques are required or best suited? What are the clinical and practical applications and implications of these concepts?
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1088/1478-3975/ac4ee2DOI Listing
April 2022

Fluctuating methylation clocks for cell lineage tracing at high temporal resolution in human tissues.

Nat Biotechnol 2022 May 3;40(5):720-730. Epub 2022 Jan 3.

Department of Pathology, Keck School of Medicine, University of Southern California, Los Angeles, CA, USA.

Molecular clocks that record cell ancestry mutate too slowly to measure the short-timescale dynamics of cell renewal in adult tissues. Here, we show that fluctuating DNA methylation marks can be used as clocks in cells where ongoing methylation and demethylation cause repeated 'flip-flops' between methylated and unmethylated states. We identify endogenous fluctuating CpG (fCpG) sites using standard methylation arrays and develop a mathematical model to quantitatively measure human adult stem cell dynamics from these data. Small intestinal crypts were inferred to contain slightly more stem cells than the colon, with slower stem cell replacement in the small intestine. Germline APC mutation increased the number of replacements per crypt. In blood, we measured rapid expansion of acute leukemia and slower growth of chronic disease. Thus, the patterns of human somatic cell birth and death are measurable with fluctuating methylation clocks (FMCs).
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1038/s41587-021-01109-wDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC9110299PMC
May 2022

The role of memory in non-genetic inheritance and its impact on cancer treatment resistance.

PLoS Comput Biol 2021 08 30;17(8):e1009348. Epub 2021 Aug 30.

Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, Florida, United States of America.

Intra-tumour heterogeneity is a leading cause of treatment failure and disease progression in cancer. While genetic mutations have long been accepted as a primary mechanism of generating this heterogeneity, the role of phenotypic plasticity is becoming increasingly apparent as a driver of intra-tumour heterogeneity. Consequently, understanding the role of this plasticity in treatment resistance and failure is a key component of improving cancer therapy. We develop a mathematical model of stochastic phenotype switching that tracks the evolution of drug-sensitive and drug-tolerant subpopulations to clarify the role of phenotype switching on population growth rates and tumour persistence. By including cytotoxic therapy in the model, we show that, depending on the strategy of the drug-tolerant subpopulation, stochastic phenotype switching can lead to either transient or permanent drug resistance. We study the role of phenotypic heterogeneity in a drug-resistant, genetically homogeneous population of non-small cell lung cancer cells to derive a rational treatment schedule that drives population extinction and avoids competitive release of the drug-tolerant sub-population. This model-informed therapeutic schedule results in increased treatment efficacy when compared against periodic therapy, and, most importantly, sustained tumour decay without the development of resistance.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1371/journal.pcbi.1009348DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8432806PMC
August 2021

Normal tissue architecture determines the evolutionary course of cancer.

Nat Commun 2021 04 6;12(1):2060. Epub 2021 Apr 6.

Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA.

Cancer growth can be described as a caricature of the renewal process of the tissue of origin, where the tissue architecture has a strong influence on the evolutionary dynamics within the tumor. Using a classic, well-studied model of tumor evolution (a passenger-driver mutation model) we systematically alter spatial constraints and cell mixing rates to show how tissue structure influences functional (driver) mutations and genetic heterogeneity over time. This approach explores a key mechanism behind both inter-patient and intratumoral tumor heterogeneity: competition for space. Time-varying competition leads to an emergent transition from Darwinian premalignant growth to subsequent invasive neutral tumor growth. Initial spatial constraints determine the emergent mode of evolution (Darwinian to neutral) without a change in cell-specific mutation rate or fitness effects. Driver acquisition during the Darwinian precancerous stage may be modulated en route to neutral evolution by the combination of two factors: spatial constraints and limited cellular mixing. These two factors occur naturally in ductal carcinomas, where the branching topology of the ductal network dictates spatial constraints and mixing rates.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1038/s41467-021-22123-1DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8024392PMC
April 2021

Adaptive Therapy for Metastatic Melanoma: Predictions from Patient Calibrated Mathematical Models.

Cancers (Basel) 2021 Feb 16;13(4). Epub 2021 Feb 16.

Integrated Mathematical Oncology, H. Lee Moffitt Cancer and Research Institute, Tampa, FL 33612, USA.

Adaptive therapy is an evolution-based treatment approach that aims to maintain tumor volume by employing minimum effective drug doses or timed drug holidays. For successful adaptive therapy outcomes, it is critical to find the optimal timing of treatment switch points in a patient-specific manner. Here we develop a combination of mathematical models that examine interactions between drug-sensitive and resistant cells to facilitate melanoma adaptive therapy dosing and switch time points. The first model assumes genetically fixed drug-sensitive and -resistant popul tions that compete for limited resources. The second model considers phenotypic switching between drug-sensitive and -resistant cells. We calibrated each model to fit melanoma patient biomarker changes over time and predicted patient-specific adaptive therapy schedules. Overall, the models predict that adaptive therapy would have delayed time to progression by 6-25 months compared to continuous therapy with dose rates of 6-74% relative to continuous therapy. We identified predictive factors driving the clinical time gained by adaptive therapy, such as the number of initial sensitive cells, competitive effect, switching rate from resistant to sensitive cells, and sensitive cell growth rate. This study highlights that there is a range of potential patient-specific benefits of adaptive therapy and identifies parameters that modulate this benefit.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.3390/cancers13040823DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7920057PMC
February 2021

The harsh microenvironment in early breast cancer selects for a Warburg phenotype.

Proc Natl Acad Sci U S A 2021 01;118(3)

Department of Cancer Physiology, Moffitt Cancer Center and Research Institute, Tampa, FL 33612;

The harsh microenvironment of ductal carcinoma in situ (DCIS) exerts strong evolutionary selection pressures on cancer cells. We hypothesize that the poor metabolic conditions near the ductal center foment the emergence of a Warburg Effect (WE) phenotype, wherein cells rapidly ferment glucose to lactic acid, even in normoxia. To test this hypothesis, we subjected low-glycolytic breast cancer cells to different microenvironmental selection pressures using combinations of hypoxia, acidosis, low glucose, and starvation for many months and isolated single clones for metabolic and transcriptomic profiling. The two harshest conditions selected for constitutively expressed WE phenotypes. RNA sequencing analysis of WE clones identified the transcription factor KLF4 as potential inducer of the WE phenotype. In stained DCIS samples, KLF4 expression was enriched in the area with the harshest microenvironmental conditions. We simulated in vivo DCIS phenotypic evolution using a mathematical model calibrated from the in vitro results. The WE phenotype emerged in the poor metabolic conditions near the necrotic core. We propose that harsh microenvironments within DCIS select for a WE phenotype through constitutive transcriptional reprogramming, thus conferring a survival advantage and facilitating further growth and invasion.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1073/pnas.2011342118DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7826394PMC
January 2021

IsoMaTrix: a framework to visualize the isoclines of matrix games and quantify uncertainty in structured populations.

Bioinformatics 2020 Dec 16. Epub 2020 Dec 16.

Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, Tampa, 33612, Florida.

Evolutionary game theory describes frequency-dependent selection for fixed, heritable strategies in a population of competing individuals using a payoff matrix. We present a software package to aid in the construction, analysis, and visualization of three-strategy matrix games. The IsoMaTrix package computes the isoclines (lines of zero growth) of matrix games, and facilitates direct comparison of well-mixed dynamics to structured populations on a lattice grid. IsoMaTrix computes fixed points, phase flow, trajectories, (sub)velocities, and uncertainty quantification for stochastic effects in spatial matrix games. We describe a result obtained via IsoMaTrix's spatial games functionality, which shows that the timing of competitive release in a cancer model (under continuous treatment) critically depends on the initial spatial configuration of the tumor.

Availability: The code is available at: https://github.com/mathonco/isomatrix.

Supplementary Information: Supplementary data are available at Bioinformatics online.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1093/bioinformatics/btaa1025DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8016459PMC
December 2020

Comparative study between discrete and continuum models for the evolution of competing phenotype-structured cell populations in dynamical environments.

Phys Rev E 2020 Oct;102(4-1):042404

Department of Mathematical Sciences "G. L. Lagrange", Dipartimento di Eccellenza 2018-2022, Politecnico di Torino, Italy.

Deterministic continuum models formulated as nonlocal partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the adaptation of asexual species to periodically fluctuating environmental conditions. These models are usually defined on the basis of population-scale phenomenological assumptions and cannot capture adaptive phenomena that are driven by stochastic variability in the evolutionary paths of single individuals. In light of these considerations, in this paper we develop a stochastic individual-based model for the coevolution of two competing phenotype-structured cell populations that are exposed to time-varying nutrient levels and undergo spontaneous, heritable phenotypic changes with different probabilities. Here, the evolution of every cell is described by a set of rules that result in a discrete-time branching random walk on the space of phenotypic states, and nutrient levels are governed by a difference equation in which a sink term models nutrient consumption by the cells. We formally show that the deterministic continuum counterpart of this model comprises a system of nonlocal partial differential equations for the cell population density functions coupled with an ordinary differential equation for the nutrient concentration. We compare the individual-based model and its continuum analog, focusing on scenarios whereby the predictions of the two models differ. The results obtained clarify the conditions under which significant differences between the two models can emerge due to bottleneck effects that bring about both lower regularity of the density functions of the two populations and more pronounced demographic stochasticity. In particular, bottleneck effects emerge in the presence of lower probabilities of phenotypic variation and are more apparent when the two populations are characterized by lower fitness initial mean phenotypes and smaller initial levels of phenotypic heterogeneity. The emergence of these effects, and thus the agreement between the two modeling approaches, is also dependent on the initial proportions of the two populations. As an illustrative example, we demonstrate the implications of these results in the context of the mathematical modeling of the early stage of metastatic colonization of distant organs.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevE.102.042404DOI Listing
October 2020

Turnover Modulates the Need for a Cost of Resistance in Adaptive Therapy.

Cancer Res 2021 02 10;81(4):1135-1147. Epub 2020 Nov 10.

Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, Florida.

Adaptive therapy seeks to exploit intratumoral competition to avoid, or at least delay, the emergence of therapy resistance in cancer. Motivated by promising results in prostate cancer, there is growing interest in extending this approach to other neoplasms. As such, it is urgent to understand the characteristics of a cancer that determine whether or not it will respond well to adaptive therapy. A plausible candidate for such a selection criterion is the fitness cost of resistance. In this article, we study a general, but simple, mathematical model to investigate whether the presence of a cost is necessary for adaptive therapy to extend the time to progression beyond that of a standard-of-care continuous therapy. Tumor cells were divided into sensitive and resistant populations and we model their competition using a system of two ordinary differential equations based on the Lotka-Volterra model. For tumors close to their environmental carrying capacity, a cost was not required. However, for tumors growing far from carrying capacity, a cost may be required to see meaningful gains. Notably, it is important to consider cell turnover in the tumor, and we discuss its role in modulating the impact of a resistance cost. To conclude, we present evidence for the predicted cost-turnover interplay in data from 67 patients with prostate cancer undergoing intermittent androgen deprivation therapy. Our work helps to clarify under which circumstances adaptive therapy may be beneficial and suggests that turnover may play an unexpectedly important role in the decision-making process. SIGNIFICANCE: Tumor cell turnover modulates the speed of selection against drug resistance by amplifying the effects of competition and resistance costs; as such, turnover is an important factor in resistance management via adaptive therapy..
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1158/0008-5472.CAN-20-0806DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8455086PMC
February 2021

Education and Outreach in Physical Sciences in Oncology.

Trends Cancer 2021 01 7;7(1):3-9. Epub 2020 Nov 7.

Department of Biochemistry and Molecular Biology, Mayo Clinic, Jacksonville, FL, USA; Department of Physiology and Biomedical Engineering, Mayo Clinic, Jacksonville, FL, USA; Department of Transplantation, Mayo Clinic, Jacksonville, FL, USA; Center for Immunotherapeutic Transport Oncophysics, Houston Methodist Research Institute, Houston, TX, USA. Electronic address:

Physical sciences are often overlooked in the field of cancer research. The Physical Sciences in Oncology Initiative was launched to integrate physics, mathematics, chemistry, and engineering with cancer research and clinical oncology through education, outreach, and collaboration. Here, we provide a framework for education and outreach in emerging transdisciplinary fields.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1016/j.trecan.2020.10.007DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7895467PMC
January 2021

Sex differences in health and disease: A review of biological sex differences relevant to cancer with a spotlight on glioma.

Cancer Lett 2021 02 29;498:178-187. Epub 2020 Oct 29.

Mathematical NeuroOncology Laboratory, Precision Neurotherapeutics Innovation Program, Mayo Clinic, Phoenix, AZ, USA; Department of Neurological Surgery, Mayo Clinic, Phoenix, AZ, USA; School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA. Electronic address:

The influence of biological sex differences on human health and disease, while being increasingly recognized, has long been underappreciated and underexplored. While humans of all sexes are more alike than different, there is evidence for sex differences in the most basic aspects of human biology and these differences have consequences for the etiology and pathophysiology of many diseases. In a disease like cancer, these consequences manifest in the sex biases in incidence and outcome of many cancer types. The ability to deliver precise, targeted therapies to complex cancer cases is limited by our current understanding of the underlying sex differences. Gaining a better understanding of the implications and interplay of sex differences in diseases like cancer will thus be informative for clinical practice and biological research. Here we review the evidence for a broad array of biological sex differences in humans and discuss how these differences may relate to observed sex differences in various diseases, including many cancers and specifically glioblastoma. We focus on areas of human biology that play vital roles in healthy and disease states, including metabolism, development, hormones, and the immune system, and emphasize that the intersection of sex differences in these areas should not go overlooked. We further propose that mathematical approaches can be useful for exploring the extent to which sex differences affect disease outcomes and accounting for those in the development of therapeutic strategies.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1016/j.canlet.2020.07.030DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8409250PMC
February 2021

Searching for Goldilocks: How Evolution and Ecology Can Help Uncover More Effective Patient-Specific Chemotherapies.

Cancer Res 2020 12 15;80(23):5147-5154. Epub 2020 Sep 15.

Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, Florida.

Deaths from cancer are mostly due to metastatic disease that becomes resistant to therapy. A mainstay treatment for many cancers is chemotherapy, for which the dosing strategy is primarily limited by patient toxicity. While this MTD approach builds upon the intuitively appealing principle that maximum therapeutic benefit is achieved by killing the largest possible number of cancer cells, there is increasing evidence that moderation might allow host-specific features to contribute to success. We believe that a "Goldilocks Window" of submaximal chemotherapy will yield improved overall outcomes. This window combines the complex interplay of cancer cell death, immune activity, emergence of chemoresistance, and metastatic dissemination. These multiple activities driven by chemotherapy have tradeoffs that depend on the specific agents used as well as their dosing levels and schedule. Here we present evidence supporting the idea that MTD may not always be the best approach and offer suggestions toward a more personalized treatment regime that integrates insights into patient-specific eco-evolutionary dynamics.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1158/0008-5472.CAN-19-3981DOI Listing
December 2020

Evolutionary dynamics of neoantigens in growing tumors.

Nat Genet 2020 10 14;52(10):1057-1066. Epub 2020 Sep 14.

Evolution and Cancer Laboratory, Centre for Genomics and Computational Biology, Barts Cancer Institute, School of Medicine and Dentistry, Queen Mary University of London, London, UK.

Cancers accumulate mutations that lead to neoantigens, novel peptides that elicit an immune response, and consequently undergo evolutionary selection. Here we establish how negative selection shapes the clonality of neoantigens in a growing cancer by constructing a mathematical model of neoantigen evolution. The model predicts that, without immune escape, tumor neoantigens are either clonal or at low frequency; hypermutated tumors can only establish after the evolution of immune escape. Moreover, the site frequency spectrum of somatic variants under negative selection appears more neutral as the strength of negative selection increases, which is consistent with classical neutral theory. These predictions are corroborated by the analysis of neoantigen frequencies and immune escape in exome and RNA sequencing data from 879 colon, stomach and endometrial cancers.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1038/s41588-020-0687-1DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7610467PMC
October 2020

Histoecology: Applying Ecological Principles and Approaches to Describe and Predict Tumor Ecosystem Dynamics Across Space and Time.

Cancer Control 2020 Jul-Aug;27(3):1073274820946804

Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA.

Cancer cells exist within a complex spatially structured ecosystem composed of resources and different cell types. As the selective pressures imposed by this environment determine the fate of cancer cells, an improved understanding of how this ecosystem evolves will better elucidate how tumors grow and respond to therapy. State of the art imaging methods can now provide highly resolved descriptions of the microenvironment, yielding the data required for a thorough study of its role in tumor growth and treatment resistance. The field of landscape ecology has been studying such species-environment relationship for decades, and offers many tools and perspectives that cancer researchers could greatly benefit from. Here, we discuss one such tool, species distribution modeling (SDM), that has the potential to, among other things, identify critical environmental factors that drive tumor evolution and predict response to therapy. SDMs only scratch the surface of how ecological theory and methods can be applied to cancer, and we believe further integration will take cancer research in exciting new and productive directions. Here we describe how species distribution modeling can be used to quantitatively describe the complex relationship between tumor cells and their microenvironment. Such a description facilitates a deeper understanding of cancers eco-evolutionary dynamics, which in turn sheds light on the factors that drive tumor growth and response to treatment.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1177/1073274820946804DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7710396PMC
April 2021

High School Internship Program in Integrated Mathematical Oncology (HIP IMO): Five-Year Experience at Moffitt Cancer Center.

Bull Math Biol 2020 07 9;82(7):91. Epub 2020 Jul 9.

Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA.

Modern cancer research, and the wealth of data across multiple spatial and temporal scales, has created the need for researchers that are well versed in the life sciences (cancer biology, developmental biology, immunology), medical sciences (oncology) and natural sciences (mathematics, physics, engineering, computer sciences). College undergraduate education traditionally occurs in disciplinary silos, which creates a steep learning curve at the graduate and postdoctoral levels that increasingly bridge multiple disciplines. Numerous colleges have begun to embrace interdisciplinary curricula, but students who double major in mathematics (or other quantitative sciences) and biology (or medicine) remain scarce. We identified the need to educate junior and senior high school students about integrating mathematical and biological skills, through the lens of mathematical oncology, to better prepare students for future careers at the interdisciplinary interface. The High school Internship Program in Integrated Mathematical Oncology (HIP IMO) at Moffitt Cancer Center has so far trained 59 students between 2015 and 2019. We report here on the program structure, training deliverables, curriculum and outcomes. We hope to promote interdisciplinary educational activities early in a student's career.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1007/s11538-020-00768-1DOI Listing
July 2020

A Mathematical Dissection of the Adaptation of Cell Populations to Fluctuating Oxygen Levels.

Bull Math Biol 2020 06 16;82(6):81. Epub 2020 Jun 16.

School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, UK.

The disordered network of blood vessels that arises from tumour angiogenesis results in variations in the delivery of oxygen into the tumour tissue. This brings about regions of chronic hypoxia (i.e. sustained low oxygen levels) and regions with alternating periods of low and relatively higher oxygen levels, and makes it necessary for cancer cells to adapt to fluctuating environmental conditions. We use a phenotype-structured model to dissect the evolutionary dynamics of cell populations exposed to fluctuating oxygen levels. In this model, the phenotypic state of every cell is described by a continuous variable that provides a simple representation of its metabolic phenotype, ranging from fully oxidative to fully glycolytic, and cells are grouped into two competing populations that undergo heritable, spontaneous phenotypic variations at different rates. Model simulations indicate that, depending on the rate at which oxygen is consumed by the cells, dynamic nonlinear interactions between cells and oxygen can stimulate chronic hypoxia and cycling hypoxia. Moreover, the model supports the idea that under chronic-hypoxic conditions lower rates of phenotypic variation lead to a competitive advantage, whereas higher rates of phenotypic variation can confer a competitive advantage under cycling-hypoxic conditions. In the latter case, the numerical results obtained show that bet-hedging evolutionary strategies, whereby cells switch between oxidative and glycolytic phenotypes, can spontaneously emerge. We explain how these results can shed light on the evolutionary process that may underpin the emergence of phenotypic heterogeneity in vascularised tumours.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1007/s11538-020-00754-7DOI Listing
June 2020

Stromal reactivity differentially drives tumour cell evolution and prostate cancer progression.

Nat Ecol Evol 2020 06 11;4(6):870-884. Epub 2020 May 11.

Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA.

Prostate cancer (PCa) progression is a complex eco-evolutionary process driven by the feedback between evolving tumour cell phenotypes and microenvironmentally driven selection. To better understand this relationship, we used a multiscale mathematical model that integrates data from biology and pathology on the microenvironmental regulation of PCa cell behaviour. Our data indicate that the interactions between tumour cells and their environment shape the evolutionary dynamics of PCa cells and explain overall tumour aggressiveness. A key environmental determinant of this aggressiveness is the stromal ecology, which can be either inhibitory, highly reactive (supportive) or non-reactive (neutral). Our results show that stromal ecology correlates directly with tumour growth but inversely modulates tumour evolution. This suggests that aggressive, environmentally independent PCa may be a result of poor stromal ecology, supporting the concept that purely tumour epithelium-centric metrics of aggressiveness may be incomplete and that incorporating markers of stromal ecology would improve prognosis.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1038/s41559-020-1157-yDOI Listing
June 2020

Hybrid Automata Library: A flexible platform for hybrid modeling with real-time visualization.

PLoS Comput Biol 2020 03 10;16(3):e1007635. Epub 2020 Mar 10.

Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida, United States of America.

The Hybrid Automata Library (HAL) is a Java Library developed for use in mathematical oncology modeling. It is made of simple, efficient, generic components that can be used to model complex spatial systems. HAL's components can broadly be classified into: on- and off-lattice agent containers, finite difference diffusion fields, a GUI building system, and additional tools and utilities for computation and data collection. These components are designed to operate independently and are standardized to make them easy to interface with one another. As a demonstration of how modeling can be simplified using our approach, we have included a complete example of a hybrid model (a spatial model with interacting agent-based and PDE components). HAL is a useful asset for researchers who wish to build performant 1D, 2D and 3D hybrid models in Java, while not starting entirely from scratch. It is available on GitHub at https://github.com/MathOnco/HAL under the MIT License. HAL requires the Java JDK version 1.8 or later to compile and run the source code.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1371/journal.pcbi.1007635DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7105119PMC
March 2020

From cells to tissue: How cell scale heterogeneity impacts glioblastoma growth and treatment response.

PLoS Comput Biol 2020 02 26;16(2):e1007672. Epub 2020 Feb 26.

Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida, United States of America.

Glioblastomas are aggressive primary brain tumors known for their inter- and intratumor heterogeneity. This disease is uniformly fatal, with intratumor heterogeneity the major reason for treatment failure and recurrence. Just like the nature vs nurture debate, heterogeneity can arise from intrinsic or environmental influences. Whilst it is impossible to clinically separate observed behavior of cells from their environmental context, using a mathematical framework combined with multiscale data gives us insight into the relative roles of variation from different sources. To better understand the implications of intratumor heterogeneity on therapeutic outcomes, we created a hybrid agent-based mathematical model that captures both the overall tumor kinetics and the individual cellular behavior. We track single cells as agents, cell density on a coarser scale, and growth factor diffusion and dynamics on a finer scale over time and space. Our model parameters were fit utilizing serial MRI imaging and cell tracking data from ex vivo tissue slices acquired from a growth-factor driven glioblastoma murine model. When fitting our model to serial imaging only, there was a spectrum of equally-good parameter fits corresponding to a wide range of phenotypic behaviors. When fitting our model using imaging and cell scale data, we determined that environmental heterogeneity alone is insufficient to match the single cell data, and intrinsic heterogeneity is required to fully capture the migration behavior. The wide spectrum of in silico tumors also had a wide variety of responses to an application of an anti-proliferative treatment. Recurrent tumors were generally less proliferative than pre-treatment tumors as measured via the model simulations and validated from human GBM patient histology. Further, we found that all tumors continued to grow with an anti-migratory treatment alone, but the anti-proliferative/anti-migratory combination generally showed improvement over an anti-proliferative treatment alone. Together our results emphasize the need to better understand the underlying phenotypes and tumor heterogeneity present in a tumor when designing therapeutic regimens.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1371/journal.pcbi.1007672DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7062288PMC
February 2020

Mix and Match: Phenotypic Coexistence as a Key Facilitator of Cancer Invasion.

Bull Math Biol 2020 01 17;82(1):15. Epub 2020 Jan 17.

Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, OX2 6GG, Oxford, UK.

Invasion of healthy tissue is a defining feature of malignant tumours. Traditionally, invasion is thought to be driven by cells that have acquired all the necessary traits to overcome the range of biological and physical defences employed by the body. However, in light of the ever-increasing evidence for geno- and phenotypic intra-tumour heterogeneity, an alternative hypothesis presents itself: could invasion be driven by a collection of cells with distinct traits that together facilitate the invasion process? In this paper, we use a mathematical model to assess the feasibility of this hypothesis in the context of acid-mediated invasion. We assume tumour expansion is obstructed by stroma which inhibits growth and extra-cellular matrix (ECM) which blocks cancer cell movement. Further, we assume that there are two types of cancer cells: (i) a glycolytic phenotype which produces acid that kills stromal cells and (ii) a matrix-degrading phenotype that locally remodels the ECM. We extend the Gatenby-Gawlinski reaction-diffusion model to derive a system of five coupled reaction-diffusion equations to describe the resulting invasion process. We characterise the spatially homogeneous steady states and carry out a simulation study in one spatial dimension to determine how the tumour develops as we vary the strength of competition between the two phenotypes. We find that overall tumour growth is most extensive when both cell types can stably coexist, since this allows the cells to locally mix and benefit most from the combination of traits. In contrast, when inter-species competition exceeds intra-species competition the populations spatially separate and invasion arrests either: (i) rapidly (matrix-degraders dominate) or (ii) slowly (acid-producers dominate). Overall, our work demonstrates that the spatial and ecological relationship between a heterogeneous population of tumour cells is a key factor in determining their ability to cooperate. Specifically, we predict that tumours in which different phenotypes coexist stably are more invasive than tumours in which phenotypes are spatially separated.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1007/s11538-019-00675-0DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6968991PMC
January 2020

Towards Multidrug Adaptive Therapy.

Cancer Res 2020 04 16;80(7):1578-1589. Epub 2020 Jan 16.

Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, Florida.

A new ecologically inspired paradigm in cancer treatment known as "adaptive therapy" capitalizes on competitive interactions between drug-sensitive and drug-resistant subclones. The goal of adaptive therapy is to maintain a controllable stable tumor burden by allowing a significant population of treatment-sensitive cells to survive. These, in turn, suppress proliferation of the less-fit resistant populations. However, there remain several open challenges in designing adaptive therapies, particularly in extending these therapeutic concepts to multiple treatments. We present a cancer treatment case study (metastatic castrate-resistant prostate cancer) as a point of departure to illustrate three novel concepts to aid the design of multidrug adaptive therapies. First, frequency-dependent "cycles" of tumor evolution can trap tumor evolution in a periodic, controllable loop. Second, the availability and selection of treatments may limit the evolutionary "absorbing region" reachable by the tumor. Third, the velocity of evolution significantly influences the optimal timing of drug sequences. These three conceptual advances provide a path forward for multidrug adaptive therapy. SIGNIFICANCE: Driving tumor evolution into periodic, repeatable treatment cycles provides a path forward for multidrug adaptive therapy.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1158/0008-5472.CAN-19-2669DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7307613PMC
April 2020

EvoFreq: visualization of the Evolutionary Frequencies of sequence and model data.

BMC Bioinformatics 2019 Dec 16;20(1):710. Epub 2019 Dec 16.

Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, 33612, FL, USA.

Background: High throughput sequence data has provided in depth means of molecular characterization of populations. When recorded at numerous time steps, such data can reveal the evolutionary dynamics of the population under study by tracking the changes in genotype frequencies over time. This necessitates a simple and flexible means of visualizing an increasingly complex set of data.

Results: Here we offer EvoFreq as a comprehensive tool set to visualize the evolutionary and population frequency dynamics of clones at a single point in time or as population frequencies over time using a variety of informative methods. EvoFreq expands substantially on previous means of visualizing the clonal, temporal dynamics and offers users a range of options for displaying their sequence or model data.

Conclusions: EvoFreq, implemented in R with robust user options and few dependencies, offers a high-throughput means of quickly building, and interrogating the temporal dynamics of hereditary information across many systems. EvoFreq is freely available via https://github.com/MathOnco/EvoFreq.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1186/s12859-019-3173-yDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6916070PMC
December 2019

Model genotype-phenotype mappings and the algorithmic structure of evolution.

J R Soc Interface 2019 11 6;16(160):20190332. Epub 2019 Nov 6.

Department of Computer Science, University of Oxford, Oxford, UK.

Cancers are complex dynamic systems that undergo evolution and selection. Personalized medicine approaches in the clinic increasingly rely on predictions of tumour response to one or more therapies; these predictions are complicated by the inevitable evolution of the tumour. Despite enormous amounts of data on the mutational status of cancers and numerous therapies developed in recent decades to target these mutations, many of these treatments fail after a time due to the development of resistance in the tumour. The emergence of these resistant phenotypes is not easily predicted from genomic data, since the relationship between genotypes and phenotypes, termed the genotype-phenotype (GP) mapping, is neither injective nor functional. We present a review of models of this mapping within a generalized evolutionary framework that takes into account the relation between genotype, phenotype, environment and fitness. Different modelling approaches are described and compared, and many evolutionary results are shown to be conserved across studies despite using different underlying model systems. In addition, several areas for future work that remain understudied are identified, including plasticity and bet-hedging. The GP-mapping provides a pathway for understanding the potential routes of evolution taken by cancers, which will be necessary knowledge for improving personalized therapies.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1098/rsif.2019.0332DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6893500PMC
November 2019

Inferring Tumor Proliferative Organization from Phylogenetic Tree Measures in a Computational Model.

Syst Biol 2020 07;69(4):623-637

School of Mathematics and Statistics, University of Sheffield, Sheffield, UK.

We use a computational modeling approach to explore whether it is possible to infer a solid tumor's cellular proliferative hierarchy under the assumptions of the cancer stem cell hypothesis and neutral evolution. We work towards inferring the symmetric division probability for cancer stem cells, since this is believed to be a key driver of progression and therapeutic response. Motivated by the advent of multiregion sampling and resulting opportunities to infer tumor evolutionary history, we focus on a suite of statistical measures of the phylogenetic trees resulting from the tumor's evolution in different regions of parameter space and through time. We find strikingly different patterns in these measures for changing symmetric division probability which hinge on the inclusion of spatial constraints. These results give us a starting point to begin stratifying tumors by this biological parameter and also generate a number of actionable clinical and biological hypotheses regarding changes during therapy, and through tumor evolutionary time. [Cancer; evolution; phylogenetics.].
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1093/sysbio/syz070DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7302056PMC
July 2020

Evolutionary dynamics of competing phenotype-structured populations in periodically fluctuating environments.

J Math Biol 2020 02 22;80(3):775-807. Epub 2019 Oct 22.

School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, UK.

Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in ecology, which is used to explain how species may survive when faced with the evolutionary risks associated with temporally varying environments. In order to support a deeper understanding of the adaptive role of spontaneous phenotypic variations in fluctuating environments, we consider a system of non-local partial differential equations modelling the evolutionary dynamics of two competing phenotype-structured populations in the presence of periodically oscillating nutrient levels. The two populations undergo heritable, spontaneous phenotypic variations at different rates. The phenotypic state of each individual is represented by a continuous variable, and the phenotypic landscape of the populations evolves in time due to variations in the nutrient level. Exploiting the analytical tractability of our model, we study the long-time behaviour of the solutions to obtain a detailed mathematical depiction of the evolutionary dynamics. The results suggest that when nutrient levels undergo small and slow oscillations, it is evolutionarily more convenient to rarely undergo spontaneous phenotypic variations. Conversely, under relatively large and fast periodic oscillations in the nutrient levels, which bring about alternating cycles of starvation and nutrient abundance, higher rates of spontaneous phenotypic variations confer a competitive advantage. We discuss the implications of our results in the context of cancer metabolism.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1007/s00285-019-01441-5DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7028828PMC
February 2020

Leveraging transcriptional dynamics to improve BRAF inhibitor responses in melanoma.

EBioMedicine 2019 Oct 5;48:178-190. Epub 2019 Oct 5.

The Department of Tumor Biology, The Moffitt Cancer Center & Research Institute, 12902 Magnolia Drive, Tampa, FL, USA; Department of Cutaneous Oncology, The Moffitt Cancer Center & Research Institute, 12902 Magnolia Drive, Tampa, FL, USA. Electronic address:

Background: Melanoma is a heterogeneous tumour, but the impact of this heterogeneity upon therapeutic response is not well understood.

Methods: Single cell mRNA analysis was used to define the transcriptional heterogeneity of melanoma and its dynamic response to BRAF inhibitor therapy and treatment holidays. Discrete transcriptional states were defined in cell lines and melanoma patient specimens that predicted initial sensitivity to BRAF inhibition and the potential for effective re-challenge following resistance. A mathematical model was developed to maintain competition between the drug-sensitive and resistant states, which was validated in vivo.

Findings: Our analyses showed melanoma cell lines and patient specimens to be composed of >3 transcriptionally distinct states. The cell state composition was dynamically regulated in response to BRAF inhibitor therapy and drug holidays. Transcriptional state composition predicted for therapy response. The differences in fitness between the different transcriptional states were leveraged to develop a mathematical model that optimized therapy schedules to retain the drug sensitive population. In vivo validation demonstrated that the personalized adaptive dosing schedules outperformed continuous or fixed intermittent BRAF inhibitor schedules.

Interpretation: Our study provides the first evidence that transcriptional heterogeneity at the single cell level predicts for initial BRAF inhibitor sensitivity. We further demonstrate that manipulating transcriptional heterogeneity through personalized adaptive therapy schedules can delay the time to resistance.

Funding: This work was funded by the National Institutes of Health. The funder played no role in assembly of the manuscript.
View Article and Find Full Text PDF

Download full-text PDF

Source
http://dx.doi.org/10.1016/j.ebiom.2019.09.023DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6838387PMC
October 2019
-->