scholarly journals Consecutive seeding and transfer of genetic diversity in metastasis

2019 ◽  
Vol 116 (28) ◽  
pp. 14129-14137 ◽  
Author(s):  
Alexander Heyde ◽  
Johannes G. Reiter ◽  
Kamila Naxerova ◽  
Martin A. Nowak
Keyword(s):  
Genetic Diversity ◽  
Single Cell ◽  
Primary Tumor ◽  
Branching Process ◽  
Growth Conditions ◽  
Seeding Rate ◽  
Multitype Branching Process ◽  
Clinical Detection ◽  
Metastasis Growth ◽  
Multiple Cells

During metastasis, only a fraction of genetic diversity in a primary tumor is passed on to metastases. We calculate this fraction of transferred diversity as a function of the seeding rate between tumors. At one extreme, if a metastasis is seeded by a single cell, then it inherits only the somatic mutations present in the founding cell, so that none of the diversity in the primary tumor is transmitted to the metastasis. In contrast, if a metastasis is seeded by multiple cells, then some genetic diversity in the primary tumor can be transmitted. We study a multitype branching process of metastasis growth that originates from a single cell but over time receives additional cells. We derive a surprisingly simple formula that relates the expected diversity of a metastasis to the diversity in the pool of seeding cells. We calculate the probability that a metastasis is polyclonal. We apply our framework to published datasets for which polyclonality has been previously reported, analyzing 68 ovarian cancer samples, 31 breast cancer samples, and 8 colorectal cancer samples from 15 patients. For these clonally diverse metastases, under typical metastasis growth conditions, we find that 10 to 150 cells seeded each metastasis and left surviving lineages between initial formation and clinical detection.

scholarly journals Demographic Dynamics in Multitype Populations with Migrations

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 246
Author(s):  
Manuel Molina-Fernández ◽  
Manuel Mota-Medina
Keyword(s):  
Mathematical Modeling ◽  
Population Dynamics ◽  
Branching Process ◽  
Probability Model ◽  
Biological Systems ◽  
Research Work ◽  
General Setting ◽  
Process Theory ◽  
Multitype Branching Process ◽  
Demographic Dynamics

This research work deals with mathematical modeling in complex biological systems in which several types of individuals coexist in various populations. Migratory phenomena among the populations are allowed. We propose a class of mathematical models to describe the demographic dynamics of these type of complex systems. The probability model is defined through a sequence of random matrices in which rows and columns represent the various populations and the several types of individuals, respectively. We prove that this stochastic sequence can be studied under the general setting provided by the multitype branching process theory. Probabilistic properties and limiting results are then established. As application, we present an illustrative example about the population dynamics of biological systems formed by long-lived raptor colonies.

Branching processes and functional differential equations determining steady-size distributions in cell populations

1995 ◽  
Vol 32 (01) ◽  
pp. 1-10
Author(s):  
Ziad Taib
Keyword(s):  
Differential Equation ◽  
Branching Process ◽  
Branching Processes ◽  
Functional Differential Equations ◽  
Cell Populations ◽  
Size Distributions ◽  
Multitype Branching Process ◽  
Functional Differential ◽  
Intuitive Interpretation ◽  
Infinite Sum

The functional differential equation y′(x) = ay(λx) + by(x) arises in many different situations. The purpose of this note is to show how it arises in some multitype branching process cell population models. We also show how its solution can be given an intuitive interpretation as the probability density function of an infinite sum of independent but not identically distributed random variables.

scholarly journals Galton–Watson and branching process representations of the normalized Perron–Frobenius eigenvector

2019 ◽  
Vol 23 ◽  
pp. 797-802
Author(s):  
Raphaël Cerf ◽  
Joseba Dalmau
Keyword(s):  
Markov Chain ◽  
Probability Measure ◽  
Branching Process ◽  
Invariant Probability Measure ◽  
Classical Formula ◽  
Multitype Branching Process ◽  
Primitive Matrix ◽  
Watson Process

Let A be a primitive matrix and let λ be its Perron–Frobenius eigenvalue. We give formulas expressing the associated normalized Perron–Frobenius eigenvector as a simple functional of a multitype Galton–Watson process whose mean matrix is A, as well as of a multitype branching process with mean matrix e(A−I)t. These formulas are generalizations of the classical formula for the invariant probability measure of a Markov chain.

scholarly journals Genetic Diversity and Structure of Latvian Tilia cordata Populations

2021 ◽  
Vol 75 (4) ◽  
pp. 261-267
Author(s):  
Dainis Edgars Ruņģis ◽  
Baiba Krivmane
Keyword(s):  
Genetic Diversity ◽  
Microsatellite Markers ◽  
Vegetative Reproduction ◽  
Growth Conditions ◽  
Climatic Conditions ◽  
Tilia Cordata ◽  
High Genetic Diversity ◽  
Genetic Diversity And Structure ◽  
Broadleaf Tree ◽  
Broadleaf Species

Abstract Changing climatic conditions are transforming the ecological and silvicultural roles of broadleaf tree species in northern Europe. Small-leaved lime (Tilia cordata Mill.) is distributed throughout most of Europe, and is a common broadleaf species in Latvia. This species can tolerate a broad range of environmental and ecological conditions, including temperature, water availability, and soil types. The aim of this study was to assess the genetic diversity and differentiation of Latvian T. cordata populations using nuclear microsatellite markers developed for Tilia platyphyllos. After testing of 15 microsatellite markers, Latvian T. cordata samples were genotyped at 14 micro-satellite loci. Latvian T. cordata populations had high genetic diversity, and were not overly isolated from each other, with moderate gene flow between populations. No highly differentiated populations were identified. Vegetative reproduction was identified in most analysed populations, and almost one-third of analysed individuals are of clonal origin. T. cordata has high timber production potential under the current climatic and growth conditions in Latvia, and therefore this species has potential for use in forestry, as well as playing a significant role in maintaining biodiversity and other ecosystem services.

Formation of the egg-laying system inPristionchus pacificusrequires complex interactions between gonadal, mesodermal and epidermal tissues and does not rely on single cell inductions

Development ◽  
2001 ◽  
Vol 128 (18) ◽  
pp. 3395-3404
Author(s):  
Benno Jungblut ◽  
André Pires-daSilva ◽  
Ralf J. Sommer
Keyword(s):  
Single Cell ◽  
Lateral Inhibition ◽  
Cell Lineage ◽  
Egg Laying ◽  
C Elegans ◽  
Complex Interactions ◽  
Organ Systems ◽  
Vulval Precursor Cells ◽  
Sex Myoblasts ◽  
Multiple Cells

The invariant cell lineage of nematodes allows the formation of organ systems, like the egg-laying system, to be studied at a single cell level. The Caenorhabditis elegans egg-laying system is made up of the vulva, the mesodermal gonad and muscles and several neurons. The gonad plays a central role in patterning the underlying ectoderm to form the vulva and guiding the migration of the sex myoblasts to their final position. In Pristionchus pacificus, the egg-laying system is homologous to C. elegans, but comparative studies revealed several differences at the cellular and molecular levels during vulval formation. For example, the mesoblast M participates in lateral inhibition, a process that influences the fate of two vulval precursor cells. Here, we describe the M lineage in Pristionchus and show that both the dorsal and ventral M sublineages are involved in lateral inhibition. Mutations in the homeotic gene Ppa-mab-5 cause severe misspecification of the M lineage, resembling more the C. elegans Twist than the mab-5 phenotype. Ectopic differentiation of P8.p in Ppa-mab-5 results from at least two separate interactions between M and P8.p. Thus, interactions among the Pristionchus egg-laying system are complex, involving multiple cells of different tissues occurring over a distance.

scholarly journals Single-cell mass spectrometry reveals the importance of genetic diversity and plasticity for phenotypic variation in nitrogen-limited Chlamydomonas

2016 ◽  
Vol 11 (4) ◽  
pp. 988-998 ◽  
Author(s):  
Jasmin Krismer ◽  
Manu Tamminen ◽  
Simone Fontana ◽  
Renato Zenobi ◽  
Anita Narwani
Keyword(s):  
Mass Spectrometry ◽  
Genetic Diversity ◽  
Single Cell ◽  
Phenotypic Variation ◽  
Cell Mass ◽  
Cell Mass Spectrometry

scholarly journals Noise-driven growth rate gain in clonal cellular populations

2016 ◽  
Vol 113 (12) ◽  
pp. 3251-3256 ◽  
Author(s):  
Mikihiro Hashimoto ◽  
Takashi Nozoe ◽  
Hidenori Nakaoka ◽  
Reiko Okura ◽  
Sayo Akiyoshi ◽  
...  
Keyword(s):  
Growth Rate ◽  
Population Growth ◽  
Single Cell ◽  
Single Cells ◽  
Population Level ◽  
Growth Conditions ◽  
Cell Dynamics ◽  
Generation Times ◽  
Complex Population ◽  
The Mean

Cellular populations in both nature and the laboratory are composed of phenotypically heterogeneous individuals that compete with each other resulting in complex population dynamics. Predicting population growth characteristics based on knowledge of heterogeneous single-cell dynamics remains challenging. By observing groups of cells for hundreds of generations at single-cell resolution, we reveal that growth noise causes clonal populations of Escherichia coli to double faster than the mean doubling time of their constituent single cells across a broad set of balanced-growth conditions. We show that the population-level growth rate gain as well as age structures of populations and of cell lineages in competition are predictable. Furthermore, we theoretically reveal that the growth rate gain can be linked with the relative entropy of lineage generation time distributions. Unexpectedly, we find an empirical linear relation between the means and the variances of generation times across conditions, which provides a general constraint on maximal growth rates. Together, these results demonstrate a fundamental benefit of noise for population growth, and identify a growth law that sets a “speed limit” for proliferation.

scholarly journals The extinction time of a subcritical branching process related to the SIR epidemic on a random graph

2015 ◽  
Vol 52 (04) ◽  
pp. 1195-1201 ◽  
Author(s):  
Peter Windridge
Keyword(s):  
Random Graph ◽  
Epidemic Model ◽  
Branching Process ◽  
Large Population ◽  
Extinction Time ◽  
Exponential Tail ◽  
Sir Epidemic Model ◽  
Multitype Branching Process ◽  
Type Distribution ◽  
Sir Epidemic

We give an exponential tail approximation for the extinction time of a subcritical multitype branching process arising from the SIR epidemic model on a random graph with given degrees, where the type corresponds to the vertex degree. As a corollary we obtain a Gumbel limit law for the extinction time, when beginning with a large population. Our contribution is to allow countably many types (this corresponds to unbounded degrees in the random graph epidemic model, as the number of vertices tends to∞). We only require a second moment for the offspring-type distribution featuring in our model.

scholarly journals Molecular characterization and genetic diversity of four undescribed novel oleaginous Mortierella alpina strains from Libya

F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 895
Author(s):  
Fuzia Elfituri Muftah Eltariki ◽  
Kartikeya Tiwari ◽  
Mohammed Abdelfatah Alhoot
Keyword(s):  
Genetic Diversity ◽  
Single Cell ◽  
Dna Sequences ◽  
Research Study ◽  
Soil Samples ◽  
Mortierella Alpina ◽  
Morphological Identification ◽  
Single Cell Oil ◽  
North East ◽  
Fungal Isolates

Background: A large number of undiscovered fungal species still exist on earth, which can be useful for bioprospecting, particularly for single cell oil (SCO) production. Mortierella is one of the significant genera in this field and contains about hundred species. Moreover, M. alpina is the main single cell oil producer at commercial scale under this genus. Methods: Soil samples from four unique locations of North-East Libya were collected for the isolation of oleaginous Mortierella alpina strains by a serial dilution method. Morphological identification was carried out using light microscopy (Olympus, Japan) and genetic diversity of the isolated Mortierella alpina strains was assessed using conserved internal transcribed spacer (ITS) gene sequences available on the NCBI GenBank database for the confirmation of novelty. The nucleotide sequences reported in this study have been deposited at GenBank (accession no. MZ298831:MZ298835). The MultAlin program was used to align the sequences of closely related strains. The DNA sequences were analyzed for phylogenetic relationships by molecular evolutionary genetic analysis using MEGA X software consisting of Clustal_X v.2.1 for multiple sequence alignment. The neighbour-joining tree was constructed using the Kimura 2-parameter substitution model. Results: The present research study confirms four oleaginous fungal isolates from Libyan soil. These isolates (barcoded as MSU-101, MSU-201, MSU-401 and MSU-501) were discovered and reported for the first time from diverse soil samples of district Aljabal Al-Akhdar in North-East Libya and fall in the class: Zygomycetes; order: Mortierellales. Conclusions: Four oleaginous fungal isolates barcoded as MSU-101, MSU-201, MSU-401 and MSU-501 were identified and confirmed by morphological and molecular analysis. These fungal isolates showed highest similarity with Mortierella alpina species and can be potentialistic single cell oil producers. Thus, the present research study provides insight to the unseen fungal diversity and contributes to more comprehensive Mortierella alpina reference collections worldwide.

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