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Article ; Online: Beyond the pair approximation: Modeling colonization population dynamics.

Rodriguez-Brenes, Ignacio A / Wodarz, Dominik / Komarova, Natalia L

2020 Volume 101, Issue 3-1, Page(s) 32404

Abstract: The process of range expansion (colonization) is one of the basic types of biological dynamics, whereby a species grows and spreads outwards, occupying new territories. Spatial modeling of this process is naturally implemented as a stochastic cellular ... ...

Abstract	The process of range expansion (colonization) is one of the basic types of biological dynamics, whereby a species grows and spreads outwards, occupying new territories. Spatial modeling of this process is naturally implemented as a stochastic cellular automaton, with individuals occupying nodes on a rectangular grid, births and deaths occurring probabilistically, and individuals only reproducing onto unoccupied neighboring spots. In this paper we derive several approximations that allow prediction of the expected range expansion dynamics, based on the reproduction and death rates. We derive several approximations, where the cellular automaton is described by a system of ordinary differential equations that preserves correlations among neighboring spots (up to a distance). This methodology allows us to develop accurate approximations of the population size and the expected spatial shape, at a fraction of the computational time required to simulate the original stochastic system. In addition, we provide simple formulas for the steady-state population densities for von Neumann and Moore neighborhoods. Finally, we derive concise approximations for the speed of range expansion in terms of the reproduction and death rates, for both types of neighborhoods. The methodology is generalizable to more complex scenarios, such as different interaction ranges and multiple-species systems.
MeSH term(s)	Models, Statistical ; Population Dynamics ; Time Factors
Language	English
Publishing date	2020-04-11
Publishing country	United States
Document type	Journal Article
ZDB-ID	2844562-4
ISSN	2470-0053 ; 2470-0045
ISSN (online)	2470-0053
ISSN	2470-0045
DOI	10.1103/PhysRevE.101.032404
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Article ; Online: The role of telomere shortening in carcinogenesis: A hybrid stochastic-deterministic approach.

Rodriguez-Brenes, Ignacio A / Komarova, Natalia L / Wodarz, Dominik

Journal of theoretical biology

2018 Volume 460, Page(s) 144–152

Abstract: Genome instability is a characteristic of most cancers, contributing to the acquisition of genetic alterations that drive tumor progression. One important source of genome instability is linked to telomere dysfunction in cells with critically short ... ...

Abstract	Genome instability is a characteristic of most cancers, contributing to the acquisition of genetic alterations that drive tumor progression. One important source of genome instability is linked to telomere dysfunction in cells with critically short telomeres that lack p53-mediated surveillance of genomic integrity. Here we research the probability that cancer emerges through an evolutionary pathway that includes a telomere-induced phase of genome instability. To implement our models we use a hybrid stochastic-deterministic approach, which allows us to perform large numbers of simulations using biologically realistic population sizes and mutation rates, circumventing the traditional limitations of fully stochastic algorithms. The hybrid methodology should be easily adaptable to a wide range of evolutionary problems. In particular, we model telomere shortening and the acquisition of two mutations: Telomerase activation and p53 inactivation. We find that the death rate of unstable cells, and the number of cell divisions that p53 mutants can sustain beyond the normal senescence setpoint determine the likelihood that the first double mutant originates in a cell with telomere-induced instability. The model has applications to an influential telomerase-null mouse model and p16 silenced human cells. We end by discussing algorithmic performance and a measure for the accuracy of the hybrid approximation.
MeSH term(s)	Algorithms ; Animals ; Carcinogenesis/genetics ; Cyclin-Dependent Kinase Inhibitor p16/genetics ; Genomic Instability ; Humans ; Mice ; Telomerase/genetics ; Telomere Shortening/physiology
Chemical Substances	CDKN2A protein, human ; Cyclin-Dependent Kinase Inhibitor p16 ; Telomerase (EC 2.7.7.49)
Language	English
Publishing date	2018-10-10
Publishing country	England
Document type	Journal Article ; Research Support, N.I.H., Extramural
ZDB-ID	2972-5
ISSN	1095-8541 ; 0022-5193
ISSN (online)	1095-8541
ISSN	0022-5193
DOI	10.1016/j.jtbi.2018.09.003
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Article ; Online: Telomeres open a window on stem cell division.

Rodriguez-Brenes, Ignacio A / Wodarz, Dominik

eLife

2016 Volume 5, Page(s) e12481

Abstract: Measuring the length distribution of telomeres can reveal information about biological processes that are otherwise difficult to analyze experimentally. ...

Abstract	Measuring the length distribution of telomeres can reveal information about biological processes that are otherwise difficult to analyze experimentally.
MeSH term(s)	Cell Division ; Models, Biological ; Stem Cells/physiology ; Telomere/metabolism ; Telomere/ultrastructure
Language	English
Publishing date	2016-01-25
Publishing country	England
Document type	Journal Article
ZDB-ID	2687154-3
ISSN	2050-084X ; 2050-084X
ISSN (online)	2050-084X
ISSN	2050-084X
DOI	10.7554/eLife.12481
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Article ; Online: Complex Dynamics of Virus Spread from Low Infection Multiplicities: Implications for the Spread of Oncolytic Viruses.

Rodriguez-Brenes, Ignacio A / Hofacre, Andrew / Fan, Hung / Wodarz, Dominik

PLoS computational biology

2017 Volume 13, Issue 1, Page(s) e1005241

Abstract: While virus growth dynamics have been well-characterized in several infections, data are typically collected once the virus population becomes easily detectable. Earlier dynamics, however, remain less understood. We recently reported unusual early ... ...

Abstract	While virus growth dynamics have been well-characterized in several infections, data are typically collected once the virus population becomes easily detectable. Earlier dynamics, however, remain less understood. We recently reported unusual early dynamics in an experimental system using adenovirus infection of human embryonic kidney (293) cells. Under identical experimental conditions, inoculation at low infection multiplicities resulted in either robust spread, or in limited spread that eventually stalled, with both outcomes occurring with approximately equal frequencies. The reasons underlying these observations have not been understood. Here, we present further experimental data showing that inhibition of interferon-induced antiviral states in cells results in a significant increase in the percentage of robust infections that are observed, implicating a race between virus replication and the spread of the anti-viral state as a central mechanism. Analysis of a variety of computational models, however, reveals that this alone cannot explain the simultaneous occurrence of both viral growth outcomes under identical conditions, and that additional biological mechanisms have to be invoked to explain the data. One such mechanism is the ability of the virus to overcome the antiviral state through multiple infection of cells. If this is included in the model, two outcomes of viral spread are found to be simultaneously stable, depending on initial conditions. In stochastic versions of such models, the system can go by chance to either state from identical initial conditions, with the relative frequency of the outcomes depending on the strength of the interferon-based anti-viral response, consistent with the experiments. This demonstrates considerable complexity during the early phase of the infection that can influence the ability of a virus to become successfully established. Implications for the initial dynamics of oncolytic virus spread through tumors are discussed.
MeSH term(s)	Computational Biology ; HEK293 Cells ; Host-Pathogen Interactions/physiology ; Humans ; Models, Biological ; Oncolytic Viruses/chemistry ; Oncolytic Viruses/metabolism ; Oncolytic Viruses/pathogenicity ; Virus Replication/physiology
Language	English
Publishing date	2017-01-20
Publishing country	United States
Document type	Journal Article ; Research Support, N.I.H., Extramural ; Research Support, Non-U.S. Gov't
ZDB-ID	2193340-6
ISSN	1553-7358 ; 1553-734X
ISSN (online)	1553-7358
ISSN	1553-734X
DOI	10.1371/journal.pcbi.1005241
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Article ; Online: Quantifying replicative senescence as a tumor suppressor pathway and a target for cancer therapy.

Rodriguez-Brenes, Ignacio A / Wodarz, Dominik / Komarova, Natalia L

Scientific reports

2015 Volume 5, Page(s) 17660

Abstract: To study quantitatively replicative senescence as a tumor suppressor mechanism, we investigate the distribution of a growing clonal cell population restricted by Hayflick's limit. We find that in the biologically relevant range of parameters, if the ... ...

Abstract	To study quantitatively replicative senescence as a tumor suppressor mechanism, we investigate the distribution of a growing clonal cell population restricted by Hayflick's limit. We find that in the biologically relevant range of parameters, if the imbalance between cell division and death is moderate or low (high death-to-birth ratio), senescence offers significant protection against cancer by halting abnormal cell proliferation at early pre-diagnostic stages of tumor development. We also find that by the time tumors are typically detected, there is a high probability that telomerase is activated, even if the cell of origin was telomerase negative. Hence, the fact that most cancers are positive for telomerase is not necessarily an indication that cancer originated in a telomerase positive cell. Finally, we discuss how the population dynamics of cells can determine the outcomes of anti-telomerase cancer therapies, and provide guidelines on how the model could potentially be applied to develop clinically useful tools to predict the response to treatment by telomerase inhibitors in individual patients.
MeSH term(s)	Algorithms ; Cellular Senescence/genetics ; Humans ; Models, Biological ; Molecular Targeted Therapy ; Neoplasms/drug therapy ; Neoplasms/genetics ; Neoplasms/metabolism ; Signal Transduction ; Telomerase/antagonists & inhibitors ; Telomerase/genetics ; Telomerase/metabolism ; Tumor Suppressor Proteins/antagonists & inhibitors ; Tumor Suppressor Proteins/genetics ; Tumor Suppressor Proteins/metabolism
Chemical Substances	Tumor Suppressor Proteins ; Telomerase (EC 2.7.7.49)
Language	English
Publishing date	2015-12-09
Publishing country	England
Document type	Journal Article
ZDB-ID	2615211-3
ISSN	2045-2322 ; 2045-2322
ISSN (online)	2045-2322
ISSN	2045-2322
DOI	10.1038/srep17660
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Article ; Online: Characterizing inhibited tumor growth in stem-cell-driven non-spatial cancers.

Rodriguez-Brenes, Ignacio A / Wodarz, Dominik / Komarova, Natalia L

Mathematical biosciences

2015 Volume 270, Issue Pt A, Page(s) 135–141

Abstract: Healthy human tissue is highly regulated to maintain homeostasis. Secreted negative feedback factors that inhibit stem cell division and stem cell self-renewal play a fundamental role in establishing this control. The appearance of abnormal cancerous ... ...

Abstract	Healthy human tissue is highly regulated to maintain homeostasis. Secreted negative feedback factors that inhibit stem cell division and stem cell self-renewal play a fundamental role in establishing this control. The appearance of abnormal cancerous growth requires an escape from these regulatory mechanisms. In a previous study we found that for non-solid tumors if feedback inhibition on stem cell self-renewal is lost, but the feedback on the division rate is still intact, then the tumor dynamics are characterized by a relatively slow sub-exponential growth that we called inhibited growth. Here we characterize the cell dynamics of inhibited cancer growth by modeling feedback inhibition using Hill equations. We find asymptotic approximations for the growth rates of the stem cell and differentiated cell populations in terms of the strength of the inhibitory signal: stem cells grow as a power law t(1/k+1),and the differentiated cells grow as t(1/k), where k is the Hill coefficient in the feedback law regulating cell divisions. It follows that as the tumor grows, undifferentiated cells take up an increasingly large fraction of the population. Implications of these results for specific cancers including CML are discussed. Understanding how the regulatory mechanisms that continue to operate in cancer affect the rate of disease progression can provide important insights relevant to chronic or other slow progressing types of cancer.
MeSH term(s)	Cell Differentiation ; Cell Proliferation ; Disease Progression ; Feedback, Physiological ; Humans ; Mathematical Concepts ; Models, Biological ; Neoplasms/pathology ; Neoplastic Stem Cells/pathology
Language	English
Publishing date	2015-12
Publishing country	United States
Document type	Journal Article
ZDB-ID	1126-5
ISSN	1879-3134 ; 0025-5564
ISSN (online)	1879-3134
ISSN	0025-5564
DOI	10.1016/j.mbs.2015.08.009
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Article ; Online: Preventing clonal evolutionary processes in cancer: Insights from mathematical models.

Rodriguez-Brenes, Ignacio A / Wodarz, Dominik

Proceedings of the National Academy of Sciences of the United States of America

2015 Volume 112, Issue 29, Page(s) 8843–8850

Abstract: Clonal evolutionary processes can drive pathogenesis in human diseases, with cancer being a prominent example. To prevent or treat cancer, mechanisms that can potentially interfere with clonal evolutionary processes need to be understood better. ... ...

Abstract	Clonal evolutionary processes can drive pathogenesis in human diseases, with cancer being a prominent example. To prevent or treat cancer, mechanisms that can potentially interfere with clonal evolutionary processes need to be understood better. Mathematical modeling is an important research tool that plays an ever-increasing role in cancer research. This paper discusses how mathematical models can be useful to gain insights into mechanisms that can prevent disease initiation, help analyze treatment responses, and aid in the design of treatment strategies to combat the emergence of drug-resistant cells. The discussion will be done in the context of specific examples. Among defense mechanisms, we explore how replicative limits and cellular senescence induced by telomere shortening can influence the emergence and evolution of tumors. Among treatment approaches, we consider the targeted treatment of chronic lymphocytic leukemia (CLL) with tyrosine kinase inhibitors. We illustrate how basic evolutionary mathematical models have the potential to make patient-specific predictions about disease and treatment outcome, and argue that evolutionary models could become important clinical tools in the field of personalized medicine.
MeSH term(s)	Cell Lineage ; Cellular Senescence ; Clonal Evolution ; Humans ; Models, Biological ; Mutation/genetics ; Neoplasms/drug therapy ; Neoplasms/pathology ; Precancerous Conditions/genetics ; Precancerous Conditions/pathology ; Stem Cells/cytology ; Stochastic Processes
Language	English
Publishing date	2015-07-20
Publishing country	United States
Document type	Journal Article
ZDB-ID	209104-5
ISSN	1091-6490 ; 0027-8424
ISSN (online)	1091-6490
ISSN	0027-8424
DOI	10.1073/pnas.1501730112
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Article: Preventing clonal evolutionary processes in cancer: Insights from mathematical models

Rodriguez-Brenes, Ignacio A / Dominik Wodarz

Proceedings of the National Academy of Sciences of the United States of America. 2015 July 21, v. 112, no. 29

2015

Abstract	Clonal evolutionary processes can drive pathogenesis in human diseases, with cancer being a prominent example. To prevent or treat cancer, mechanisms that can potentially interfere with clonal evolutionary processes need to be understood better. Mathematical modeling is an important research tool that plays an ever-increasing role in cancer research. This paper discusses how mathematical models can be useful to gain insights into mechanisms that can prevent disease initiation, help analyze treatment responses, and aid in the design of treatment strategies to combat the emergence of drug-resistant cells. The discussion will be done in the context of specific examples. Among defense mechanisms, we explore how replicative limits and cellular senescence induced by telomere shortening can influence the emergence and evolution of tumors. Among treatment approaches, we consider the targeted treatment of chronic lymphocytic leukemia (CLL) with tyrosine kinase inhibitors. We illustrate how basic evolutionary mathematical models have the potential to make patient-specific predictions about disease and treatment outcome, and argue that evolutionary models could become important clinical tools in the field of personalized medicine.
Keywords	cell senescence ; defense mechanisms ; drug resistance ; evolution ; human diseases ; lymphocytic leukemia ; mathematical models ; medicine ; pathogenesis ; prediction ; telomeres ; therapeutics ; tyrosine ; clonal evolution ; cancer ; targeted therapy
Language	English
Dates of publication	2015-0721
Size	p. 8843-8850.
Publishing place	National Academy of Sciences
Document type	Article
ZDB-ID	209104-5
ISSN	1091-6490 ; 0027-8424
ISSN (online)	1091-6490
ISSN	0027-8424
DOI	10.1073/pnas.1501730112
Database	NAL-Catalogue (AGRICOLA)

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Article ; Online: Cancer-associated mutations in healthy individuals: assessing the risk of carcinogenesis.

Rodriguez-Brenes, Ignacio A / Komarova, Natalia L / Wodarz, Dominik

Cancer research

2014 Volume 74, Issue 6, Page(s) 1661–1669

Abstract: Mutations associated with hematopoietic malignancies have been repeatedly identified in healthy individuals. For certain cases, such as the t(14;18) translocation and monoclonal B-cell lymphocytosis, no clear link between the presence of aberrant cells ... ...

Abstract	Mutations associated with hematopoietic malignancies have been repeatedly identified in healthy individuals. For certain cases, such as the t(14;18) translocation and monoclonal B-cell lymphocytosis, no clear link between the presence of aberrant cells and the later development of cancer has been established. Intriguingly, longitudinal studies suggest that these abnormalities persist for long periods of time in some individuals, but in others are transient in which they disappear completely. Here, we present a mathematical model, based on cellular replication limits, that provides a possible explanation for these seemingly contradictory findings. It proposes that the transient and persistent nature of the phenotypes depends on the stage in the differentiation pathway of a given lineage in which the mutation originates. Our work suggests that cellular replication limits may not only prevent cancer by aborting clonal expansion of cells, but also by influencing the fate of altered but nonneoplastic cells in healthy tissue.
MeSH term(s)	Algorithms ; Carcinogenesis/genetics ; Carcinogenesis/pathology ; Cell Proliferation ; Genes, Neoplasm ; Humans ; Models, Genetic ; Mutation ; Neoplasms/genetics ; Neoplasms/pathology ; Risk Factors ; Stem Cells/physiology
Language	English
Publishing date	2014-01-22
Publishing country	United States
Document type	Journal Article
ZDB-ID	1432-1
ISSN	1538-7445 ; 0008-5472
ISSN (online)	1538-7445
ISSN	0008-5472
DOI	10.1158/0008-5472.CAN-13-1452
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Article ; Online: Telomeres open a window on stem cell division

Ignacio A Rodriguez-Brenes / Dominik Wodarz

eLife, Vol

2016 Volume 5

Abstract: Measuring the length distribution of telomeres can reveal information about biological processes that are otherwise difficult to analyze experimentally. ...

Abstract	Measuring the length distribution of telomeres can reveal information about biological processes that are otherwise difficult to analyze experimentally.
Keywords	telomere length distribution ; stem cell ; mathematical modelling ; hematopoiesis ; self renewal ; personalised medicine ; Medicine ; R ; Science ; Q ; Biology (General) ; QH301-705.5
Language	English
Publishing date	2016-01-01T00:00:00Z
Publisher	eLife Sciences Publications Ltd
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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