1
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Glass DS, Bren A, Vaisbourd E, Mayo A, Alon U. A synthetic differentiation circuit in Escherichia coli for suppressing mutant takeover. Cell 2024; 187:931-944.e12. [PMID: 38320549 PMCID: PMC10882425 DOI: 10.1016/j.cell.2024.01.024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Revised: 11/27/2023] [Accepted: 01/16/2024] [Indexed: 02/08/2024]
Abstract
Differentiation is crucial for multicellularity. However, it is inherently susceptible to mutant cells that fail to differentiate. These mutants outcompete normal cells by excessive self-renewal. It remains unclear what mechanisms can resist such mutant expansion. Here, we demonstrate a solution by engineering a synthetic differentiation circuit in Escherichia coli that selects against these mutants via a biphasic fitness strategy. The circuit provides tunable production of synthetic analogs of stem, progenitor, and differentiated cells. It resists mutations by coupling differentiation to the production of an essential enzyme, thereby disadvantaging non-differentiating mutants. The circuit selected for and maintained a positive differentiation rate in long-term evolution. Surprisingly, this rate remained constant across vast changes in growth conditions. We found that transit-amplifying cells (fast-growing progenitors) underlie this environmental robustness. Our results provide insight into the stability of differentiation and demonstrate a powerful method for engineering evolutionarily stable multicellular consortia.
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Affiliation(s)
- David S Glass
- Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot 76100, Israel.
| | - Anat Bren
- Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Elizabeth Vaisbourd
- Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Avi Mayo
- Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Uri Alon
- Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot 76100, Israel.
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2
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Mamis K, Zhang R, Bozic I. Stochastic model for cell population dynamics quantifies homeostasis in colonic crypts and its disruption in early tumorigenesis. Proc Biol Sci 2023; 290:20231020. [PMID: 37848058 PMCID: PMC10581771 DOI: 10.1098/rspb.2023.1020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Accepted: 09/22/2023] [Indexed: 10/19/2023] Open
Abstract
The questions of how healthy colonic crypts maintain their size, and how homeostasis is disrupted by driver mutations, are central to understanding colorectal tumorigenesis. We propose a three-type stochastic branching process, which accounts for stem, transit-amplifying (TA) and fully differentiated (FD) cells, to model the dynamics of cell populations residing in colonic crypts. Our model is simple in its formulation, allowing us to estimate all but one of the model parameters from the literature. Fitting the single remaining parameter, we find that model results agree well with data from healthy human colonic crypts, capturing the considerable variance in population sizes observed experimentally. Importantly, our model predicts a steady-state population in healthy colonic crypts for relevant parameter values. We show that APC and KRAS mutations, the most significant early alterations leading to colorectal cancer, result in increased steady-state populations in mutated crypts, in agreement with experimental results. Finally, our model predicts a simple condition for unbounded growth of cells in a crypt, corresponding to colorectal malignancy. This is predicted to occur when the division rate of TA cells exceeds their differentiation rate, with implications for therapeutic cancer prevention strategies.
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Affiliation(s)
- Konstantinos Mamis
- Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
| | - Ruibo Zhang
- Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
| | - Ivana Bozic
- Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
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3
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Uhl P, Lowengrub J, Komarova N, Wodarz D. Spatial dynamics of feedback and feedforward regulation in cell lineages. PLoS Comput Biol 2022; 18:e1010039. [PMID: 35522694 PMCID: PMC9116666 DOI: 10.1371/journal.pcbi.1010039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Revised: 05/18/2022] [Accepted: 03/18/2022] [Indexed: 11/19/2022] Open
Abstract
Feedback mechanisms within cell lineages are thought to be important for maintaining tissue homeostasis. Mathematical models that assume well-mixed cell populations, together with experimental data, have suggested that negative feedback from differentiated cells on the stem cell self-renewal probability can maintain a stable equilibrium and hence homeostasis. Cell lineage dynamics, however, are characterized by spatial structure, which can lead to different properties. Here, we investigate these dynamics using spatially explicit computational models, including cell division, differentiation, death, and migration / diffusion processes. According to these models, the negative feedback loop on stem cell self-renewal fails to maintain homeostasis, both under the assumption of strong spatial restrictions and fast migration / diffusion. Although homeostasis cannot be maintained, this feedback can regulate cell density and promote the formation of spatial structures in the model. Tissue homeostasis, however, can be achieved if spatially restricted negative feedback on self-renewal is combined with an experimentally documented spatial feedforward loop, in which stem cells regulate the fate of transit amplifying cells. This indicates that the dynamics of feedback regulation in tissue cell lineages are more complex than previously thought, and that combinations of spatially explicit control mechanisms are likely instrumental.
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Affiliation(s)
- Peter Uhl
- Department of Mathematics and Statistics, San Diego State University, San Diego, California, United States of America
- Department of Population Health and Disease Prevention, Program in Public Health, University of California, Irvine, California, United States of America
| | - John Lowengrub
- Department of Mathematics, University of California, Irvine, California, United States of America
| | - Natalia Komarova
- Department of Mathematics, University of California, Irvine, California, United States of America
| | - Dominik Wodarz
- Department of Population Health and Disease Prevention, Program in Public Health, University of California, Irvine, California, United States of America
- Department of Mathematics, University of California, Irvine, California, United States of America
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4
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Paul D, Komarova NL. Multi-scale network targeting: A holistic systems-biology approach to cancer treatment. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2021; 165:72-79. [PMID: 34428429 DOI: 10.1016/j.pbiomolbio.2021.08.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Revised: 08/05/2021] [Accepted: 08/10/2021] [Indexed: 11/15/2022]
Abstract
The vulnerabilities of cancer at the cellular and, recently, with the introduction of immunotherapy, at the tissue level, have been exploited with variable success. Evaluating the cancer system vulnerabilities at the organismic level through analysis of network topology and network dynamics can potentially predict novel anti-cancer drug targets directed at the macroscopic cancer networks. Theoretical work analyzing the properties and the vulnerabilities of the multi-scale network of cancer needs to go hand-in-hand with experimental research that uncovers the biological nature of the relevant networks and reveals new targetable vulnerabilities. It is our hope that attacking cancer on different spatial scales, in a concerted integrated approach, may present opportunities for novel ways to prevent treatment resistance.
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Affiliation(s)
- Doru Paul
- Medical Oncology, Weill Cornell Medicine, 1305 York Avenue 12th Floor, New York, NY, 10021, USA.
| | - Natalia L Komarova
- Department of Mathematics, University of California Irvine, Irvine, CA, 92697, USA.
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5
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Katzir I, Adler M, Karin O, Mendelsohn‐Cohen N, Mayo A, Alon U. Senescent cells and the incidence of age-related diseases. Aging Cell 2021; 20:e13314. [PMID: 33559235 PMCID: PMC7963340 DOI: 10.1111/acel.13314] [Citation(s) in RCA: 35] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Revised: 01/02/2021] [Accepted: 01/09/2021] [Indexed: 12/23/2022] Open
Abstract
Age-related diseases such as cancer, cardiovascular disease, kidney failure, and osteoarthritis have universal features: Their incidence rises exponentially with age with a slope of 6-8% per year and decreases at very old ages. There is no conceptual model which explains these features in so many diverse diseases in terms of a single shared biological factor. Here, we develop such a model, and test it using a nationwide medical record dataset on the incidence of nearly 1000 diseases over 50 million life-years, which we provide as a resource. The model explains incidence using the accumulation of senescent cells, damaged cells that cause inflammation and reduce regeneration, whose level rise stochastically with age. The exponential rise and late drop in incidence are captured by two parameters for each disease: the susceptible fraction of the population and the threshold concentration of senescent cells that causes disease onset. We propose a physiological mechanism for the threshold concentration for several disease classes, including an etiology for diseases of unknown origin such as idiopathic pulmonary fibrosis and osteoarthritis. The model can be used to design optimal treatments that remove senescent cells, suggeting that treatment starting at old age can sharply reduce the incidence of all age-related diseases, and thus increase the healthspan.
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Affiliation(s)
- Itay Katzir
- Department of Molecular Cell Biology Weizmann Institute of Science Rehovot Israel
| | - Miri Adler
- Department of Molecular Cell Biology Weizmann Institute of Science Rehovot Israel
- Broad Institute of Massachusetts Institute of Technology and Harvard Cambridge MA USA
| | - Omer Karin
- Department of Molecular Cell Biology Weizmann Institute of Science Rehovot Israel
| | | | - Avi Mayo
- Department of Molecular Cell Biology Weizmann Institute of Science Rehovot Israel
| | - Uri Alon
- Department of Molecular Cell Biology Weizmann Institute of Science Rehovot Israel
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6
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BAILEY LORAD, KOMAROVA NATALIAL. CELLULAR FEEDBACK NETWORKS AND THEIR RESILIENCE AGAINST MUTATIONS. J BIOL SYST 2021. [DOI: 10.1142/s0218339021400039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Many tissues undergo a steady turnover, where cell divisions are on average balanced with cell deaths. Cell fate decisions such as stem cell (SC) differentiations, proliferations, or differentiated cell (DC) deaths, may be controlled by cell populations through cell-to-cell signaling. Here, we examine a class of mathematical models of turnover in SC lineages to understand engineering design principles of control (feedback) loops, that may operate in such systems. By using ordinary differential equations that describe the co-dynamics of SCs and DCs, we study the effect of different types of mutations that interfere with feedback present within cellular networks. For instance, we find that mutants that do not participate in feedback are less dangerous in the sense that they will not rise from low numbers, whereas mutants that do not respond to feedback signals could rise and replace the wild-type population. Additionally, we asked if different feedback networks can have different degrees of resilience against such mutations. We found that all minimal networks, that is networks consisting of exactly one feedback loop that is sufficient for homeostatic stability of the wild-type population, are equally vulnerable. Mutants with a weakened/eliminated feedback parameter might expand from lower numbers and either enter unlimited growth or reach an equilibrium with an increased number of SCs and DCs. Therefore, from an evolutionary viewpoint, it appears advantageous to combine feedback loops, creating redundant feedback networks. Interestingly, from an engineering prospective, not all such redundant systems are equally resilient. For some of them, any mutation that weakens/eliminates one of the loops will lead to a population growth of SCs. For others, the population of SCs can actually shrink as a result of “cutting” one of the loops, thus slowing down further unwanted transformations.
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7
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Solé R, Aguadé-Gorgorió G. The ecology of cancer differentiation therapy. J Theor Biol 2020; 511:110552. [PMID: 33309530 DOI: 10.1016/j.jtbi.2020.110552] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Revised: 10/21/2020] [Accepted: 11/17/2020] [Indexed: 11/29/2022]
Abstract
A promising, yet still under development approach to cancer treatment is based on the idea of differentiation therapy (DTH). Most tumours are characterized by poorly differentiated cell populations exhibiting a marked loss of traits associated to communication and tissue homeostasis. DTH has been suggested as an alternative (or complement) to cytotoxic-based approaches, and has proven successful in some specific types of cancer such as acute promyelocytic leukemia (APL). While novel drugs favouring the activation of differentiation therapies are being tested, several open problems emerge in relation to its effectiveness on solid tumors. Here we present a mathematical framework to DTH based on a well-known ecological model used to describe habitat loss. The models presented here account for some of the observed clinical and in vitro outcomes of DTH, providing relevant insight into potential therapy design. Furthermore, the same ecological approach is tested in a hierarchical model that accounts for cancer stem cells, highlighting the role of niche specificity in CSC therapy resistance. We show that the lessons learnt from metapopulation ecology can help guide future developments and potential difficulties of DTH.
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Affiliation(s)
- Ricard Solé
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, 08003 Barcelona, Catalonia, Spain; Institut de Biologia Evolutiva (CSIC-UPF), Psg Maritim Barceloneta, 37, 08003 Barcelona, Catalonia, Spain; Santa Fe Institute, 1399 Hyde Park Road, Santa Fe NM 87501, USA
| | - Guim Aguadé-Gorgorió
- ICREA-Complex Systems Lab, Universitat Pompeu Fabra, 08003 Barcelona, Catalonia, Spain; Institut de Biologia Evolutiva (CSIC-UPF), Psg Maritim Barceloneta, 37, 08003 Barcelona, Catalonia, Spain
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8
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Weiss LD, van den Driessche P, Lowengrub JS, Wodarz D, Komarova NL. Effect of feedback regulation on stem cell fractions in tissues and tumors: Understanding chemoresistance in cancer. J Theor Biol 2020; 509:110499. [PMID: 33130064 DOI: 10.1016/j.jtbi.2020.110499] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2020] [Revised: 07/16/2020] [Accepted: 09/15/2020] [Indexed: 11/18/2022]
Abstract
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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Affiliation(s)
- Lora D Weiss
- Department of Mathematics, University of California Irvine, Irvine, CA 92697, United States
| | - P van den Driessche
- Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 2Y2, Canada
| | - John S Lowengrub
- Department of Mathematics, University of California Irvine, Irvine, CA 92697, United States
| | - Dominik Wodarz
- Department of Mathematics, University of California Irvine, Irvine, CA 92697, United States; Department of Population Health and Disease Prevention, Program in Public Health, Susan and Henry Samueli College of Health Sciences, University of California, Irvine, CA 92697, United States
| | - Natalia L Komarova
- Department of Mathematics, University of California Irvine, Irvine, CA 92697, United States.
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9
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Wang Y, Lo WC, Chou CS. Modelling stem cell ageing: a multi-compartment continuum approach. ROYAL SOCIETY OPEN SCIENCE 2020; 7:191848. [PMID: 32269805 PMCID: PMC7137970 DOI: 10.1098/rsos.191848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/23/2019] [Accepted: 02/10/2020] [Indexed: 06/11/2023]
Abstract
Stem cells are important to generate all specialized tissues at an early life stage, and in some systems, they also have repair functions to replenish the adult tissues. Repeated cell divisions lead to the accumulation of molecular damage in stem cells, which are commonly recognized as drivers of ageing. In this paper, a novel model is proposed to integrate stem cell proliferation and differentiation with damage accumulation in the stem cell ageing process. A system of two structured PDEs is used to model the population densities of stem cells (including all multiple progenitors) and terminally differentiated (TD) cells. In this system, cell cycle progression and damage accumulation are modelled by continuous dynamics, and damage segregation between daughter cells is considered at each division. Analysis and numerical simulations are conducted to study the steady-state populations and stem cell damage distributions under different damage segregation strategies. Our simulations suggest that equal distribution of the damaging substance between stem cells in a symmetric renewal and less damage retention in stem cells in the asymmetric division are favourable strategies, which reduce the death rate of the stem cells and increase the TD cell populations. Moreover, asymmetric damage segregation in stem cells leads to less concentrated damage distribution in the stem cell population, which may be more robust to the stochastic changes in the damage. The feedback regulation from stem cells can reduce oscillations and population overshoot in the process, and improve the fitness of stem cells by increasing the percentage of cells with less damage in the stem cell population.
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Affiliation(s)
- Yanli Wang
- Department of Mathematics, The Ohio State University, Columbus, OH, USA
| | - Wing-Cheong Lo
- Department of Mathematics, City University of Hong Kong, Hong Kong, People’s Republic of China
| | - Ching-Shin Chou
- Department of Mathematics, The Ohio State University, Columbus, OH, USA
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10
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A compartment size-dependent selective threshold limits mutation accumulation in hierarchical tissues. Proc Natl Acad Sci U S A 2020; 117:1606-1611. [PMID: 31907322 PMCID: PMC6983402 DOI: 10.1073/pnas.1913104117] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Renewed tissues of multicellular organism accumulate mutations that lead to aging and cancer. To mitigate these effects, self-renewing tissues produce cells along differentiation hierarchies, which have been shown to suppress somatic evolution both by limiting the number of cell divisions, and thus reducing mutational load, and by differentiation “washing out” mutations. Our analytical results reveal the existence of a third mechanism: a compartment size-dependent threshold in proliferative advantage, below which mutations cannot persist, but are rapidly expelled from the tissue by differentiation. In sufficiently small compartments, the resulting selective barrier can greatly slow down somatic evolution and reduce the risk of cancer by preventing the accumulation of mutations even if even they confer substantial proliferative advantage. Cancer is a genetic disease fueled by somatic evolution. Hierarchical tissue organization can slow somatic evolution by two qualitatively different mechanisms: by cell differentiation along the hierarchy “washing out” harmful mutations and by limiting the number of cell divisions required to maintain a tissue. Here we explore the effects of compartment size on somatic evolution in hierarchical tissues by considering cell number regulation that acts on cell division rates such that the number of cells in the tissue has the tendency to return to its desired homeostatic value. Introducing mutants with a proliferative advantage, we demonstrate the existence of a third fundamental mechanism by which hierarchically organized tissues are able to slow down somatic evolution. We show that tissue size regulation leads to the emergence of a threshold proliferative advantage, below which mutants cannot persist. We find that the most significant determinant of the threshold selective advantage is compartment size, with the threshold being higher the smaller the compartment. Our results demonstrate that, in sufficiently small compartments, even mutations that confer substantial proliferative advantage cannot persist, but are expelled from the tissue by differentiation along the hierarchy. The resulting selective barrier can significantly slow down somatic evolution and reduce the risk of cancer by limiting the accumulation of mutations that increase the proliferation of cells.
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11
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Bessonov N, Pinna G, Minarsky A, Harel-Bellan A, Morozova N. Mathematical modeling reveals the factors involved in the phenomena of cancer stem cells stabilization. PLoS One 2019; 14:e0224787. [PMID: 31710617 PMCID: PMC6844488 DOI: 10.1371/journal.pone.0224787] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Accepted: 10/22/2019] [Indexed: 12/15/2022] Open
Abstract
Cancer Stem Cells (CSC), a subset of cancer cells resembling normal stem cells with self-renewal and asymmetric division capabilities, are present at various but low proportions in many tumors and are thought to be responsible for tumor relapses following conventional cancer therapies. In vitro, most intriguingly, isolated CSCs rapidly regenerate the original population of stem and non-stem cells (non-CSCs) as shown by various investigators. This phenomenon still remains to be explained. We propose a mathematical model of cancer cell population dynamics, based on the main parameters of cell population growth, including the proliferation rates, the rates of cell death and the frequency of symmetric and asymmetric cell divisions both in CSCs and non-CSCs sub-populations, and taking into account the stabilization phenomenon. The analysis of the model allows determination of time-varying corridors of probabilities for different cell fates, given the particular dynamics of cancer cells populations; and determination of a cell-cell communication factors influencing these time-varying probabilities of cell behavior (division, transition) scenarios. Though the results of the model have to be experimentally confirmed, we can anticipate the development of several fundamental and practical applications based on the theoretical results of the model.
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Affiliation(s)
- Nikolay Bessonov
- Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint-Petersburg, Russia
| | - Guillaume Pinna
- Institute for Integrative Biology of the Cell (I2BC), CEA, CNRS, University Paris‐Sud, University Paris‐Saclay, Gif‐sur‐Yvette, France
| | - Andrey Minarsky
- Saint-Petersburg Academic University, Russian Academy of Sciences, Saint-Petersburg, Russia
| | - Annick Harel-Bellan
- Institute for Integrative Biology of the Cell (I2BC), CEA, CNRS, University Paris‐Sud, University Paris‐Saclay, Gif‐sur‐Yvette, France
- Institut des Hautes Etudes Scientiques (IHES), Bures-sur-Yvette, France
| | - Nadya Morozova
- Institute for Integrative Biology of the Cell (I2BC), CEA, CNRS, University Paris‐Sud, University Paris‐Saclay, Gif‐sur‐Yvette, France
- Institut des Hautes Etudes Scientiques (IHES), Bures-sur-Yvette, France
- * E-mail:
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12
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Buder T, Deutsch A, Klink B, Voss-Böhme A. Patterns of Tumor Progression Predict Small and Tissue-Specific Tumor-Originating Niches. Front Oncol 2019; 8:668. [PMID: 30687642 PMCID: PMC6335293 DOI: 10.3389/fonc.2018.00668] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2018] [Accepted: 12/18/2018] [Indexed: 01/06/2023] Open
Abstract
The development of cancer is a multistep process in which cells increase in malignancy through progressive alterations. Such altered cells compete with wild-type cells and have to establish within a tissue in order to induce tumor formation. The range of this competition and the tumor-originating cell type which acquires the first alteration is unknown for most human tissues, mainly because the involved processes are hardly observable, aggravating an understanding of early tumor development. On the tissue scale, one observes different progression types, namely with and without detectable benign precursor stages. Human epidemiological data on the ratios of the two progression types exhibit large differences between cancers. The idea of this study is to utilize data of the ratios of progression types in human cancers to estimate the homeostatic range of competition in human tissues. This homeostatic competition range can be interpreted as necessary numbers of altered cells to induce tumor formation on the tissue scale. For this purpose, we develop a cell-based stochastic model which is calibrated with newly-interpreted human epidemiological data. We find that the number of tumor cells which inevitably leads to later tumor formation is surprisingly small compared to the overall tumor and largely depends on the human tissue type. This result points toward the existence of a tissue-specific tumor-originating niche in which the fate of tumor development is decided early and long before a tumor becomes detectable. Moreover, our results suggest that the fixation of tumor cells in the tumor-originating niche triggers new processes which accelerate tumor growth after normal tissue homeostasis is voided. Our estimate for the human colon agrees well with the size of the stem cell niche in colonic crypts. For other tissues, our results might aid to identify the tumor-originating cell type. For instance, data on primary and secondary glioblastoma suggest that the tumors originate from a cell type competing in a range of 300 – 1,900 cells.
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Affiliation(s)
- Thomas Buder
- Center for Information Services and High Performance Computing, Technische Universität Dresden, Dresden, Germany.,Faculty of Informatics/Mathematics, HTW Dresden-University of Applied Sciences, Dresden, Germany
| | - Andreas Deutsch
- Center for Information Services and High Performance Computing, Technische Universität Dresden, Dresden, Germany
| | - Barbara Klink
- Institute for Clinical Genetics, Faculty of Medicine Carl Gustav Carus, Technische Universität Dresden, Dresden, Germany.,German Cancer Consortium (DKTK), Dresden, Germany.,German Cancer Research Center (DKFZ), Heidelberg, Germany.,Center for Molecular Tumor Diagnostics (CMTD), National Center for Tumor Diseases (NCT), Dresden, Germany
| | - Anja Voss-Böhme
- Center for Information Services and High Performance Computing, Technische Universität Dresden, Dresden, Germany.,Faculty of Informatics/Mathematics, HTW Dresden-University of Applied Sciences, Dresden, Germany
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13
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Cockrell C, Axelrod DE. Optimization of Dose Schedules for Chemotherapy of Early Colon Cancer Determined by High-Performance Computer Simulations. Cancer Inform 2019; 18:1176935118822804. [PMID: 30675100 PMCID: PMC6330731 DOI: 10.1177/1176935118822804] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2018] [Accepted: 11/29/2018] [Indexed: 01/08/2023] Open
Abstract
Cancer chemotherapy dose schedules are conventionally applied intermittently, with dose duration of the order of hours, intervals between doses of days or weeks, and cycles repeated for weeks. The large number of possible combinations of values of duration, interval, and lethality has been an impediment to empirically determine the optimal set of treatment conditions. The purpose of this project was to determine the set of parameters for duration, interval, and lethality that would be most effective for treating early colon cancer. An agent-based computer model that simulated cell proliferation kinetics in normal human colon crypts was calibrated with measurements of human biopsy specimens. Mutant cells were simulated as proliferating and forming an adenoma, or dying if treated with cytotoxic chemotherapy. Using a high-performance computer, a total of 28 800 different parameter sets of duration, interval, and lethality were simulated. The effect of each parameter set on the stability of colon crypts, the time to cure a crypt of mutant cells, and the accumulated dose was determined. Of the 28 800 parameter sets, 434 parameter sets were effective in curing the crypts of mutant cells before they could form an adenoma and allowed the crypt normal cell dynamics to recover to pretreatment levels. A group of 14 similar parameter sets produced a minimal time to cure mutant cells. A different group of nine similar parameter sets produced the least accumulated dose. These parameter sets may be considered as candidate dose schedules to guide clinical trials for early colon cancer.
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Affiliation(s)
- Chase Cockrell
- Department of Surgery and Pritzker School of Medicine, The University of Chicago, Chicago, IL, USA
- Department of Surgery, University of Vermont College of Medicine, Burlington, VT, USA
| | - David E Axelrod
- Department of Genetics and Cancer of New Jersey, Rutgers University, Piscataway, NJ, USA
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14
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Renardy M, Jilkine A, Shahriyari L, Chou CS. Control of cell fraction and population recovery during tissue regeneration in stem cell lineages. J Theor Biol 2018; 445:33-50. [PMID: 29470992 DOI: 10.1016/j.jtbi.2018.02.017] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2017] [Revised: 01/24/2018] [Accepted: 02/19/2018] [Indexed: 12/20/2022]
Abstract
Multicellular tissues are continually turning over, and homeostasis is maintained through regulated proliferation and differentiation of stem cells and progenitors. Following tissue injury, a dramatic increase in cell proliferation is commonly observed, resulting in rapid restoration of tissue size. This regulation is thought to occur via multiple feedback loops acting on cell self-renewal or differentiation. Models of ordinary differential equations have been widely used to study the cell lineage system. Prior modeling studies have suggested that loss of homeostasis and initiation of tumorigenesis can be contributed to the loss of control of these processes, and the rate of symmetric versus asymmetric division of the stem cells may also be altered. While most of the previous works focused on analysis of stability, existence and uniqueness of steady states of multistage cell lineage models, in this work we attempt to understand the cell lineage model from a different perspective. We compare three variants of hierarchical stem cell lineage tissue models with different combinations of negative feedbacks and use sensitivity analysis to examine the possible strategies for the cells to achieve certain performance objectives. Our results suggest that multiple negative feedback loops must be present in the stem cell lineage to keep the fractions of stem cells to differentiated cells in the total population as robust as possible to variations in cell division parameters, and to minimize the time for tissue recovery in a non-oscillatory manner.
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Affiliation(s)
- Marissa Renardy
- Department of Mathematics, Ohio State University, Columbus, OH, USA
| | - Alexandra Jilkine
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA
| | - Leili Shahriyari
- Mathematical Biosciences Institute, Ohio State University, Columbus, OH, USA
| | - Ching-Shan Chou
- Department of Mathematics, Ohio State University, Columbus, OH, USA; Mathematical Biosciences Institute, Ohio State University, Columbus, OH, USA.
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15
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Stiehl T, Ho AD, Marciniak-Czochra A. Mathematical modeling of the impact of cytokine response of acute myeloid leukemia cells on patient prognosis. Sci Rep 2018; 8:2809. [PMID: 29434256 PMCID: PMC5809606 DOI: 10.1038/s41598-018-21115-4] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2017] [Accepted: 01/30/2018] [Indexed: 12/14/2022] Open
Abstract
Acute myeloid leukemia (AML) is a heterogeneous disease. One reason for the heterogeneity may originate from inter-individual differences in the responses of leukemic cells to endogenous cytokines. On the basis of mathematical modeling, computer simulations and patient data, we have provided evidence that cytokine-independent leukemic cell proliferation may be linked to early relapses and poor overall survival. Depending whether the model of cytokine-dependent or cytokine-independent leukemic cell proliferation fits to the clinical data, patients can be assigned to two groups that differ significantly with respect to overall survival. The modeling approach further enables us to identify parameter constellations that can explain unexpected responses of some patients to external cytokines such as blast crisis or remission without chemotherapy.
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Affiliation(s)
- Thomas Stiehl
- Institute of Applied Mathematics, Interdisciplinary Center of Scientific Computing and BIOQUANT Center, Heidelberg University, Im Neuenheimer Feld 205, 69120, Heidelberg, Germany.
| | - Anthony D Ho
- Department of Medicine V, Heidelberg University Hospital, Im Neuenheimer Feld 410, 69120, Heidelberg, Germany
| | - Anna Marciniak-Czochra
- Institute of Applied Mathematics, Interdisciplinary Center of Scientific Computing and BIOQUANT Center, Heidelberg University, Im Neuenheimer Feld 205, 69120, Heidelberg, Germany
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16
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Ashcroft P, Manz MG, Bonhoeffer S. Clonal dominance and transplantation dynamics in hematopoietic stem cell compartments. PLoS Comput Biol 2017; 13:e1005803. [PMID: 28991922 PMCID: PMC5654265 DOI: 10.1371/journal.pcbi.1005803] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2017] [Revised: 10/19/2017] [Accepted: 09/29/2017] [Indexed: 01/16/2023] Open
Abstract
Hematopoietic stem cells in mammals are known to reside mostly in the bone marrow, but also transitively passage in small numbers in the blood. Experimental findings have suggested that they exist in a dynamic equilibrium, continuously migrating between these two compartments. Here we construct an individual-based mathematical model of this process, which is parametrised using existing empirical findings from mice. This approach allows us to quantify the amount of migration between the bone marrow niches and the peripheral blood. We use this model to investigate clonal hematopoiesis, which is a significant risk factor for hematologic cancers. We also analyse the engraftment of donor stem cells into non-conditioned and conditioned hosts, quantifying the impact of different treatment scenarios. The simplicity of the model permits a thorough mathematical analysis, providing deeper insights into the dynamics of both the model and of the real-world system. We predict the time taken for mutant clones to expand within a host, as well as chimerism levels that can be expected following transplantation therapy, and the probability that a preconditioned host is reconstituted by donor cells. Clonal hematopoiesis—where mature myeloid cells in the blood deriving from a single stem cell are over-represented—is a major risk factor for overt hematologic malignancies. To quantify how likely this phenomena is, we combine existing observations with a novel stochastic model and extensive mathematical analysis. This approach allows us to observe the hidden dynamics of the hematopoietic system. We conclude that for a clone to be detectable within the lifetime of a mouse, it requires a selective advantage. I.e. the clonal expansion cannot be explained by neutral drift alone. Furthermore, we use our model to describe the dynamics of hematopoiesis after stem cell transplantation. In agreement with earlier findings, we observe that niche-space saturation decreases engraftment efficiency. We further discuss the implications of our findings for human hematopoiesis where the quantity and role of stem cells is frequently debated.
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Affiliation(s)
- Peter Ashcroft
- Institut für Integrative Biologie, ETH Zürich, Zürich, Switzerland
- * E-mail:
| | - Markus G. Manz
- Division of Hematology, University Hospital Zürich and University of Zürich, Zürich, Switzerland
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