scholarly journals Unimodality of steady size distributions of growing cell populations

2001 ◽  
Vol 1 (4) ◽  
pp. 405-409 ◽  
Author(s):  
F. P. da Costa ◽  
M. Grinfeld ◽  
J. B. McLeod
Keyword(s):  
Cell Populations ◽  
Size Distributions ◽  
Growing Cell

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.

Synchronized oscillations in growing cell populations are explained by demographic noise

2021 ◽  
Vol 120 (8) ◽  
pp. 1314-1322
Author(s):  
Enrico Gavagnin ◽  
Sean T. Vittadello ◽  
Gency Gunasingh ◽  
Nikolas K. Haass ◽  
Matthew J. Simpson ◽  
...  
Keyword(s):  
Cell Populations ◽  
Growing Cell ◽  
Demographic Noise

scholarly journals Spectral Distribution of Transport Operator Arising in Growing Cell Populations

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hongxing Wu ◽  
Shenghua Wang ◽  
Dengbin Yuan
Keyword(s):  
Remainder Term ◽  
Smooth Boundary ◽  
Linear Operators ◽  
Cell Populations ◽  
Resolvent Operators ◽  
Transport Operator ◽  
Growing Cell ◽  
Isolated Eigenvalues ◽  
Algebraic Multiplicities ◽  
Partly Smooth

Transport equation with partly smooth boundary conditions arising in growing cell populations is studied inLp  (1<p<+∞)space. It is to prove that the transport operatorAHgenerates aC0semigroup and the ninth-order remainder termR9(t)of the Dyson-Phillips expansion of the semigroup is compact, and the spectrum of transport operatorAHconsists of only finite isolated eigenvalues with finite algebraic multiplicities in a tripΓω. The main methods rely on theory of linear operators, comparison operators, and resolvent operators approach.

Detection of Cell Cycle Stages in situ in Growing Cell Populations

Cell Biology ◽  
2006 ◽  
pp. 291-299 ◽  
Author(s):  
I SOLOVEI ◽  
L SCHERMELLEH ◽  
H ALBIEZ ◽  
T CREMER
Keyword(s):  
Cell Cycle ◽  
Cell Populations ◽  
Growing Cell

scholarly journals Streaming Instability in Growing Cell Populations

2010 ◽  
Vol 104 (20) ◽  
Author(s):  
William Mather ◽  
Octavio Mondragón-Palomino ◽  
Tal Danino ◽  
Jeff Hasty ◽  
Lev S. Tsimring
Keyword(s):  
Cell Populations ◽  
Streaming Instability ◽  
Growing Cell

scholarly journals Quantitative single cell heterogeneity profiling of patient derived tumor initiating gliomaspheres reveals unique signatures of drug response and malignancy

2020 ◽  
Author(s):  
Michael Masterman-Smith ◽  
Nicholas A. Graham ◽  
Ed Panosyan ◽  
Jack Mottahedeh ◽  
Eric E. Samuels ◽  
...  
Keyword(s):  
Single Cell ◽  
Signal Propagation ◽  
Cell Populations ◽  
High Signal ◽  
Cell Heterogeneity ◽  
Cell Array ◽  
Minimal Cell ◽  
Egfr Signaling Pathway ◽  
Egfr Expression ◽  
Growing Cell

AbstractBackgroundGlioblastoma is a deadly brain tumor with median patient survival of 14.6 months. At the core of this malignancy are rare, highly heterogenous malignant stem-like tumor initiating cells. Aberrant signaling across the EGFR-PTEN-AKT-mTOR signal transduction pathways are common oncogenic drivers in these cells. Though gene-level clustering has determined the importance of the EGFR signaling pathway as a treatment indicator, multiparameter protein-level analyses are necessary to discern functional attributes of signal propagation. Multiparameter single cell analyses is emerging as particularly useful in identifying such attributes.MethodsSingle cell targeted proteomic analysis of EGFR-PTEN-AKT-mTOR proteins profiled heterogeneity in a panel of fifteen patient derived gliomaspheres. A microfluidic cell array ‘chip’ tool served as a low cost methodology to derive high quality quantitative single cell analytical outputs. Chip design specifications produced extremely high signal-to-noise ratios and brought experimental efficiencies of cell control and minimal cell use to accommodate experimentation with these rare and often slow-growing cell populations. Quantitative imaging software generated datasets to observe similarities and differences within and between cells and patients. Bioinformatic self-organizing maps (SOMs) and hierarchical clustering stratified patients into malignancy and responder groups which were validated by phenotypic and statistical analyses.ResultsFifteen patient dissociated gliomaspheres produced 59,464 data points from 14,866 cells. Forty-nine molecularly defined signaling phenotypes were identified across samples. Bioinformatics resolved two clusters diverging on EGFR expression (p = 0.0003) and AKT/TORC1 activation (p = 0.08 and p = 0.09 respectively). TCGA status of a subset showed genetic heterogeneity with proneural, classical and mesenchymal subtypes represented in both clusters. Phenotypic validation measures indicated drug responsive phenotypes to EGFR blocking were found in the EGFR expressing cluster. EGFR expression in the subset of drug-treated lines was statistically significant (p<.05). The EGFR expressing cluster was of lower tumor initiating potential in comparison to the AKT/TORC1 activated cluster. Though not statistically significant, EGFR expression trended with improved patient prognosis while AKT/TORC1 activated samples trended with poorer outcomes.ConclusionsQuantitative single cell heterogeneity profiling resolves signaling diversity into meaningful non-obvious phenotypic groups suggesting EGFR is decoupled from AKT/TORC1 signalling while identifying potentially valuable targets for personalized therapeutic approaches for deadly tumor-initiating cell populations.

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