scholarly journals The Poisson process is the universal law of cancer development: driver mutations accumulate randomly, silently, at constant average rate and for many decades, likely in stem cells

2017 ◽  
Author(s):  
Aleksey V. Belikov ◽  
Alexey D. Vyatkin ◽  
Sergey V. Leonov
Keyword(s):  
Stem Cells ◽  
Probability Distribution ◽  
Poisson Process ◽  
Old Age ◽  
Average Rate ◽  
Age Distribution ◽  
Cancer Development ◽  
Driver Mutations ◽  
Erlang Distribution ◽  
Universal Law

AbstractBackgroundIt is assumed that cancers develop upon acquiring a particular number of (epi)mutations in driver genes, but the law governing the kinetics of this process is not known. We have recently shown that the age distribution of incidence for 20 most prevalent cancers of old age is best approximated by the Erlang probability distribution. The Erlang distribution describes the probability of several successive random events occurring by the given time according to the Poisson process, which allows to predict the number of critical driver events.ResultsHere we show that the Erlang distribution is the only classical probability distribution that can adequately model the age distribution of incidence for all studied childhood and young adulthood cancers, in addition to cancers of old age.ConclusionsThis validates the Poisson process as the universal law describing cancer development at any age and the Erlang distribution as a useful tool to predict the number of driver events for any cancer type. The Poisson process signifies the fundamentally random timing of driver events and their constant average rate. As waiting times for the occurrence of the required number of driver events are counted in decades, it suggests that driver mutations accumulate silently in the longest-living dividing cells in the body - the stem cells.

scholarly journals The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e11976
Author(s):  
Aleksey V. Belikov ◽  
Alexey Vyatkin ◽  
Sergey V. Leonov
Keyword(s):  
Probability Distribution ◽  
Poisson Process ◽  
Old Age ◽  
Young Adulthood ◽  
Age Distribution ◽  
The Body ◽  
Driver Mutations ◽  
Erlang Distribution ◽  
Cancer Type ◽  
Global Parameter

Background It is widely believed that cancers develop upon acquiring a particular number of (epi) mutations in driver genes, but the law governing the kinetics of this process is not known. We have previously shown that the age distribution of incidence for the 20 most prevalent cancers of old age is best approximated by the Erlang probability distribution. The Erlang distribution describes the probability of several successive random events occurring by the given time according to the Poisson process, which allows an estimate for the number of critical driver events. Methods Here we employ a computational grid search method to find global parameter optima for five probability distributions on the CDC WONDER dataset of the age distribution of childhood and young adulthood cancer incidence. Results We show that the Erlang distribution is the only classical probability distribution we found that can adequately model the age distribution of incidence for all studied childhood and young adulthood cancers, in addition to cancers of old age. Conclusions This suggests that the Poisson process governs driver accumulation at any age and that the Erlang distribution can be used to determine the number of driver events for any cancer type. The Poisson process implies the fundamentally random timing of driver events and their constant average rate. As waiting times for the occurrence of the required number of driver events are counted in decades, and most cells do not live this long, it suggests that driver mutations accumulate silently in the longest-living dividing cells in the body—the stem cells.

scholarly journals Anthropogenic risk factors as the major cause of cancer driver events

2018 ◽  
Author(s):  
Aleksey V. Belikov
Keyword(s):  
Risk Factors ◽  
Probability Distribution ◽  
Cancer Incidence ◽  
Risk Estimation ◽  
Age Distribution ◽  
Erlang Distribution ◽  
Modifiable Risk Factors ◽  
Cancer Driver ◽  
Replication Errors ◽  
Rate Limiting

AbstractBackgroundI have recently shown that the number of rate-limiting driver events per tumor can be estimated from the age distribution of cancer incidence using the gamma/Erlang probability distribution. It is important to understand how these predictions relate to established risk factors.MethodsThe number of rate-limiting driver events per tumor was estimated using the gamma/Erlang distribution and correlated to the percentage of cancer cases attributable to modifiable risk factors.ResultsThe predicted number of rate-limiting driver events per tumor strongly correlates with the proportion of cancer cases attributable to modifiable risk factors for all cancers except those induced by infection or ultraviolet radiation. The correlation was confirmed for three countries, three corresponding incidence databases and risk estimation studies, as well as for both sexes: USA, males [r=0.80, P=0.002], females [r=0.81, P=0.0003]; England, males [r=0.90, P<0.0001], females [r=0.67, P=0.002]; Australia, males [r=0.90, P=0.0004], females [r=0.68, P=0.01].ConclusionsIt is thus confirmed that predictions based on interpreting the age distribution of cancer incidence as the gamma/Erlang probability distribution have biological meaning, validating the underlying Poisson process as the law governing the development of the majority of cancer types, especially those driven by chemical mutagens. Importantly, this study suggests that the majority of driver events (60-80% in males, 50-70% in females) are induced by anthropogenic carcinogens, and not by cell replication errors or other internal processes.

scholarly journals MicroRNAs and Stem-like Properties: The Complex Regulation Underlying Stemness Maintenance and Cancer Development

Biomolecules ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1074
Author(s):  
Giuseppina Divisato ◽  
Silvia Piscitelli ◽  
Mariantonietta Elia ◽  
Emanuela Cascone ◽  
Silvia Parisi
Keyword(s):  
Stem Cells ◽  
Molecular Mechanisms ◽  
Epithelial Mesenchymal Transition ◽  
Embryonic Stem ◽  
Cell Types ◽  
Cancer Development ◽  
Special Focus ◽  
Self Renewal ◽  
Mesenchymal Transition ◽  
Different Cell Types

Embryonic stem cells (ESCs) have the extraordinary properties to indefinitely proliferate and self-renew in culture to produce different cell progeny through differentiation. This latter process recapitulates embryonic development and requires rounds of the epithelial–mesenchymal transition (EMT). EMT is characterized by the loss of the epithelial features and the acquisition of the typical phenotype of the mesenchymal cells. In pathological conditions, EMT can confer stemness or stem-like phenotypes, playing a role in the tumorigenic process. Cancer stem cells (CSCs) represent a subpopulation, found in the tumor tissues, with stem-like properties such as uncontrolled proliferation, self-renewal, and ability to differentiate into different cell types. ESCs and CSCs share numerous features (pluripotency, self-renewal, expression of stemness genes, and acquisition of epithelial–mesenchymal features), and most of them are under the control of microRNAs (miRNAs). These small molecules have relevant roles during both embryogenesis and cancer development. The aim of this review was to recapitulate molecular mechanisms shared by ESCs and CSCs, with a special focus on the recently identified classes of microRNAs (noncanonical miRNAs, mirtrons, isomiRs, and competitive endogenous miRNAs) and their complex functions during embryogenesis and cancer development.

scholarly journals On the equivalence of various definitions of mixed poisson processes

2019 ◽  
Vol 69 (2) ◽  
pp. 453-468
Author(s):  
Demetrios P. Lyberopoulos ◽  
Nikolaos D. Macheras ◽  
Spyridon M. Tzaninis
Keyword(s):  
Probability Distribution ◽  
Poisson Process ◽  
Random Variable ◽  
Poisson Processes ◽  
Counting Processes ◽  
Mixing Parameter ◽  
Mixed Poisson Process ◽  
Probability Spaces ◽  
The One

Abstract Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing probability distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a characterization of each one of the above mixed Poisson processes in terms of disintegrations is provided. Moreover, some examples of “canonical” probability spaces admitting counting processes satisfying the equivalence of all above statements are given. Finally, it is shown that our assumptions for the characterization of mixed Poisson processes in terms of disintegrations cannot be omitted.

scholarly journals NQO1 is Required for β-Lapachone-Mediated Downregulation of Breast-Cancer Stem-Cell Activity

2018 ◽  
Vol 19 (12) ◽  
pp. 3813 ◽  
Author(s):  
Dong Kim ◽  
Je-Yoel Cho
Keyword(s):  
Breast Cancer ◽  
Stem Cells ◽  
Cell Proliferation ◽  
Stem Cell ◽  
Cancer Stem Cells ◽  
Cancer Stem Cell ◽  
Breast Cancer Stem Cell ◽  
Cancer Development ◽  
Dependent Manner ◽  
Mammosphere Formation

Cancer stem cells (CSCs) exhibit self-renewal activity and give rise to other cell types in tumors. Due to the infinite proliferative potential of CSCs, drugs targeting these cells are necessary to completely inhibit cancer development. The β-lapachone (bL) compound is widely used to treat cancer development; however, its effect on cancer stem cells remain elusive. Thus, we investigated the effect of bL on mammosphere formation using breast-cancer stem-cell (BCSC) marker-positive cells, MDA-MB-231. MDA-MB-231 cells, which are negative for reduced nicotinamide adenine dinucleotide phosphate (NAD(P)H):quinone oxidoreductase (NQO1) expression, were constructed to stably express NQO1 (NQO1 stable cells). The effect of bL on these cells was evaluated by wound healing and Transwell cell-culture chambers, ALDEFLUOR assay, and mammosphere formation assay. Here, we show that bL inhibited the proliferative ability of mammospheres derived from BCSC marker-positive cells, MDA-MB-231, in an NQO1-dependent manner. The bL treatment efficiently downregulated the expression level of BCSC markers cluster of differentiation 44 (CD44), aldehyde dehydrogenase 1 family member A1 (ALDH1A1), and discs large (DLG)-associated protein 5 (DLGAP5) that was recently identified as a stem-cell proliferation marker in both cultured cells and mammosphered cells. Moreover, bL efficiently downregulated cell proliferation and migration activities. These results strongly suggest that bL could be a therapeutic agent for targeting breast-cancer stem-cells with proper NQO1 expression.

scholarly journals Modeling Stochastic Variability in the Numbers of Surviving Salmonella enterica, Enterohemorrhagic Escherichia coli, and Listeria monocytogenes Cells at the Single-Cell Level in a Desiccated Environment

2016 ◽  
Vol 83 (4) ◽  
Author(s):  
Kento Koyama ◽  
Hidekazu Hokunan ◽  
Mayumi Hasegawa ◽  
Shuso Kawamura ◽  
Shigenobu Koseki
Keyword(s):  
Escherichia Coli ◽  
Listeria Monocytogenes ◽  
Probability Distribution ◽  
Poisson Process ◽  
Poisson Distribution ◽  
Salmonella Enterica ◽  
Bacterial Cells ◽  
Content Type ◽  
Cell Numbers ◽  
Inactivation Process

ABSTRACT Despite effective inactivation procedures, small numbers of bacterial cells may still remain in food samples. The risk that bacteria will survive these procedures has not been estimated precisely because deterministic models cannot be used to describe the uncertain behavior of bacterial populations. We used the Poisson distribution as a representative probability distribution to estimate the variability in bacterial numbers during the inactivation process. Strains of four serotypes of Salmonella enterica, three serotypes of enterohemorrhagic Escherichia coli, and one serotype of Listeria monocytogenes were evaluated for survival. We prepared bacterial cell numbers following a Poisson distribution (indicated by the parameter λ, which was equal to 2) and plated the cells in 96-well microplates, which were stored in a desiccated environment at 10% to 20% relative humidity and at 5, 15, and 25°C. The survival or death of the bacterial cells in each well was confirmed by adding tryptic soy broth as an enrichment culture. Changes in the Poisson distribution parameter during the inactivation process, which represent the variability in the numbers of surviving bacteria, were described by nonlinear regression with an exponential function based on a Weibull distribution. We also examined random changes in the number of surviving bacteria using a random number generator and computer simulations to determine whether the number of surviving bacteria followed a Poisson distribution during the bacterial death process by use of the Poisson process. For small initial cell numbers, more than 80% of the simulated distributions (λ = 2 or 10) followed a Poisson distribution. The results demonstrate that variability in the number of surviving bacteria can be described as a Poisson distribution by use of the model developed by use of the Poisson process. IMPORTANCE We developed a model to enable the quantitative assessment of bacterial survivors of inactivation procedures because the presence of even one bacterium can cause foodborne disease. The results demonstrate that the variability in the numbers of surviving bacteria was described as a Poisson distribution by use of the model developed by use of the Poisson process. Description of the number of surviving bacteria as a probability distribution rather than as the point estimates used in a deterministic approach can provide a more realistic estimation of risk. The probability model should be useful for estimating the quantitative risk of bacterial survival during inactivation.

scholarly journals Population age structure only partially explains the large number of COVID-19 deaths at the oldest ages

2020 ◽  
Author(s):  
Anthony Medford ◽  
Sergi Trias-Llimós
Keyword(s):  
Old Age ◽  
Age Structure ◽  
Age Distribution ◽  
Case Fatality ◽  
European Countries ◽  
Population Age Structure ◽  
Country Comparison ◽  
Cross Country ◽  
Age Structures

AbstractTo date any attention paid to the age shape of COVID-19 deaths has been mostly in relation to attempts to understand the differences in case fatality rates between countries. The aim of this paper is to explore differences in age distribution of deaths from COVID-19 among European countries which have old age structures. We do this by way of a cross-country comparison and put forward some reasons for potential differences.

scholarly journals A simple and direct method to define clonal selection in somatic mosaicism

2021 ◽  
Author(s):  
Verena Koerber ◽  
Naser Ansari-Pour ◽  
Niels Asger Jakobsen ◽  
Rachel Moore ◽  
Nina Claudino ◽  
...  
Keyword(s):  
Stem Cells ◽  
Clonal Selection ◽  
Direct Method ◽  
Somatic Mosaicism ◽  
Fold Increase ◽  
Somatic Tissue ◽  
Driver Mutations ◽  
Neutral Drift ◽  
Stem Cell Division

Dividing somatic stem cells acquire DNA changes marking different clones. With time, clones can become large, either stochastically through neutral drift, or increased fitness and consequent selection. We present a simple, direct, and general approach that distinguishes between these two processes in normal somatic tissue in individuals. The method relies on single time point whole genome sequencing to study somatic mosaicism as tissues age. Using this method, we show that in human clonal hemopoiesis (CH), clones with CH driver mutations, that comprise a median of 24% of hematopoiesis originate decades before they are detected. They expand, through selection by a median of 26% per year. Overall, there is a 3-fold increased rate of stem cell division and an 8.6-fold increase in active long-term stem cells.

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