scholarly journals Mathematical Model of a Cell Size Checkpoint

2010 ◽  
Vol 6 (12) ◽  
pp. e1001036 ◽  
Author(s):  
Marco Vilela ◽  
Jeffrey J. Morgan ◽  
Paul A. Lindahl
Keyword(s):  
Mathematical Model ◽  
Cell Size ◽  
A Cell

Spindle scaling mechanisms

2020 ◽  
Vol 64 (2) ◽  
pp. 383-396
Author(s):  
Lara K. Krüger ◽  
Phong T. Tran
Keyword(s):  
Cell Size ◽  
Spindle Assembly ◽  
Dependent Manner ◽  
Post Translational Modification ◽  
Size Dependent ◽  
A Cell ◽  
Chromosome Separation ◽  
Spindle Elongation ◽  
Protein Gradients ◽  
Spindle Structure

Abstract The mitotic spindle robustly scales with cell size in a plethora of different organisms. During development and throughout evolution, the spindle adjusts to cell size in metazoans and yeast in order to ensure faithful chromosome separation. Spindle adjustment to cell size occurs by the scaling of spindle length, spindle shape and the velocity of spindle assembly and elongation. Different mechanisms, depending on spindle structure and organism, account for these scaling relationships. The limited availability of critical spindle components, protein gradients, sequestration of spindle components, or post-translational modification and differential expression levels have been implicated in the regulation of spindle length and the spindle assembly/elongation velocity in a cell size-dependent manner. In this review, we will discuss the phenomenon and mechanisms of spindle length, spindle shape and spindle elongation velocity scaling with cell size.

Emulsion flow which preparation excludes a presence of mechanical impurities

2012 ◽  
Vol 9 (2) ◽  
pp. 118-122
Author(s):  
A.A. Rakhimov
Keyword(s):  
Cell Size ◽  
First Case ◽  
A Cell ◽  
Emulsion Flow ◽  
Blocking Mechanism

Experiments were carried out with waterhydrocarbon emulsions with various emulsifiers in capillaries with a length of 2 cm, diameters of 40 and 100 µm. To eliminate the influence of mechanical impurities comparable in size with the diameter of the capillary in first case emulsion components were filtered through fine-meshed filters. In second case obtained that way emulsion was additionally filtered through a system consisting of 3 filters with a cell size of 30-40 microns. In a capillary of 100 µm such emulsion came in a blocked state. Additional filtration of the emulsion through the mesh filters have led to an increase in viscosity but in 100 µm capillaries the time until the blocking 2-3 times more than the original. Rheology of used emulsions is well described by the model of Ostwald-de Waale. It was determined that emulsion blocking mechanism is due to the presence of inclusions not emulsion viscosity.

scholarly journals SETI, Evolution and Human History Merged into a Mathematical Model

2013 ◽  
Vol 12 (3) ◽  
pp. 218-245 ◽  
Author(s):  
Claudio Maccone
Keyword(s):  
Mathematical Model ◽  
Exponential Growth ◽  
Numerical Estimate ◽  
Mean Value ◽  
Darwinian Evolution ◽  
Human History ◽  
The Galaxy ◽  
Positive Time ◽  
A Cell ◽  
Geometric Locus

AbstractIn this paper we propose a new mathematical model capable of merging Darwinian Evolution, Human History and SETI into a single mathematical scheme:(1) Darwinian Evolution over the last 3.5 billion years is defined as one particular realization of a certain stochastic process called Geometric Brownian Motion (GBM). This GBM yields the fluctuations in time of the number of species living on Earth. Its mean value curve is an increasing exponential curve, i.e. the exponential growth of Evolution.(2) In 2008 this author provided the statistical generalization of the Drake equation yielding the number N of communicating ET civilizations in the Galaxy. N was shown to follow the lognormal probability distribution.(3) We call “b-lognormals” those lognormals starting at any positive time b (“birth”) larger than zero. Then the exponential growth curve becomes the geometric locus of the peaks of a one-parameter family of b-lognormals: this is our way to re-define Cladistics.(4) b-lognormals may be also be interpreted as the lifespan of any living being (a cell, or an animal, a plant, a human, or even the historic lifetime of any civilization). Applying this new mathematical apparatus to Human History, leads to the discovery of the exponential progress between Ancient Greece and the current USA as the envelope of all b-lognormals of Western Civilizations over a period of 2500 years.(5) We then invoke Shannon's Information Theory. The b-lognormals' entropy turns out to be the index of “development level” reached by each historic civilization. We thus get a numerical estimate of the entropy difference between any two civilizations, like the Aztec-Spaniard difference in 1519.(6) In conclusion, we have derived a mathematical scheme capable of estimating how much more advanced than Humans an Alien Civilization will be when the SETI scientists will detect the first hints about ETs.

Theoretical Analysis of CFD-DEM Mathematical Model Solution Change With Varying Computational Cell Size

2018 ◽  
Author(s):  
Annette Volk ◽  
Urmila Ghia
Keyword(s):  
Mathematical Model ◽  
Standard Deviation ◽  
Cell Size ◽  
Volume Fraction ◽  
Particle Diameter ◽  
Independent Solution ◽  
Model Verification ◽  
Computational Cell ◽  
Drag Laws ◽  
Fraction Method

Successful verification and validation is crucial to build confidence in the application of coupled Computational Fluid Dynamics - Discrete Element Method (CFD-DEM). Model verification includes ensuring a mesh-independent solution, which poses a major difficulty in CFD-DEM due to the complicated solution relationship with computational cell size. In this paper, we investigate the theoretical relationship between the solution and computational cell size by tracing the effects of a change in cell size through the mathematical model. The porosity profile for simulations of fixed-particle beds is determined to be Gaussian, and the average and standard deviation of the representative distribution are reported against cell size. We find the standard deviation of bed porosity increases exponentially as the cell size is reduced, and the drag calculations are very sensitive to changes in the porosity standard deviation, resulting in an exponential change in expected drag when the cell size is small relative to the particle diameter. The divided volume fraction method of porosity calculation is shown to be superior to the centred volume fraction method, as it reduces the porosity standard deviation. The sensitivity of five popular drag laws to changes in the porosity profile is presented, and the Ergun and Beetstra drag laws are shown to be the least sensitive to changes in the cell size.

Growth in cell length in the fission yeast Schizosaccharomyces pombe

1985 ◽  
Vol 75 (1) ◽  
pp. 357-376 ◽  
Author(s):  
J.M. Mitchison ◽  
P. Nurse
Keyword(s):  
Schizosaccharomyces Pombe ◽  
Cell Size ◽  
Single Cells ◽  
Temperature Shift ◽  
Time Lapse ◽  
Cell Length ◽  
Wild Type ◽  
Cycle Growth ◽  
A Cell ◽  
Mutant Cells

The cylindrical cells of Schizosaccharomyces pombe grow in length by extension at the ends and not the middle. At the beginning of the cell cycle, growth is restricted to the ‘old end’, which existed in the previous cycle. Later on, the ‘new end’, formed from the septum, starts to grow at a point in the cycle that we have called NETO (‘new end take-off’). Fluorescence microscopy on cells stained with Calcofluor has been used to study NETO in size mutants, in blocked cdc mutants and with different growth temperatures and media. In wild-type cells (strain 972) NETO happens at 0.34 of the cycle with a cell length of 9.5 microns. With size mutants that are smaller at division, NETO takes place at the same size (9.0-9.5 microns) but this is not achieved until later in the cycle. Another control operates in larger size mutants since NETO occurs at the same stage of the cycle (about 0.32) as in wild type but at a larger cell size. This control is probably a requirement to have completed an event in early G2, since most cdc mutant cells blocked before this point in the cycle do not show NETO whereas most of those blocked in late G2 do show it. We conclude that NETO only happens if: (1) the cell length is greater than a critical value of 9.0-9.5 microns; and (2) the cell has traversed the first 0.3-0.35 of the cycle and passed early G2. NETO is delayed in poor media, in which cell size is also reduced. Temperature has little effect on NETO under steady-state conditions, but there is a transient delay for some hours after a temperature shift. NETO is later in another wild-type strain, 132. Time-lapse photomicrography was used to follow the rates of length growth in single cells. Wild-type cells showed two linear segments during the first 75% of the cycle. There was a rate-change point (RCP), coincident with NETO, where the rate of total length extension increased by 35%. This increase was not due simply to the start of new-end growth, since old-end growth slowed down in some cells at the RCP. cdc 11.123 is a mutant in which septation and division is blocked at 35 degrees C but nuclear division continues.(ABSTRACT TRUNCATED AT 400 WORDS)

The chemistry, reflectance, and cell size of the erlichmanite (OsS2)-laurite (RuS2) series

1983 ◽  
Vol 47 (345) ◽  
pp. 465-471 ◽  
Author(s):  
J. F. W. Bowles ◽  
D. Atkin ◽  
J. L. M. Lambert ◽  
T. Deans ◽  
R. Phillips
Keyword(s):  
Solid Solution ◽  
Cell Size ◽  
Sierra Leone ◽  
Crystal Chemistry ◽  
First Report ◽  
Complete Solid Solution ◽  
A Cell ◽  
Platinum Group

AbstractMicroprobe analyses of members of the erlichmanite-laurite series from Guma Water and Senduma, Sierra Leone and Tanah Laut, Borneo, indicate that complete solid solution is possible between OsS2 and RuS2 with considerable substitution of Os and Ru by Ir, Rh, and Pt. The cell size of the erlichmanite from Guma Water is a = 5.6183±0.0003 Å at a composition (Os0.61Ru0.30Ir0.06Rh0.03)Σ0.93S2 whilst the laurite from Senduma has a composition of (Ru0.88Os0.05Ir0.04 Rh0.03)Σ0.93S2 and a cell size of a = 5.6089±0.0005 Å. Substitution of Os for Ru provides the predominant cause of the variation of cell size. Substitution by other elements of the platinum group appears to produce little effect on cell size and is presumably controlled by genesis rather than considerations of crystal chemistry or structure. The recorded analyses for these elements indicate a pre-dominance of Ir over Rh for members of the series containing more than about 15% of the laurite molecule. For the remainder of the series Rh is more important than Ir. The reflectance in air and oil of the members of the series from Sierra Leone and Borneo are presented and the microhardness of the erlichmanite from Guma Water shown to be 1854 kg/mm2. This is the first report of laurite from Senduma, Sierra Leone.

The expected population size in a cell-size-dependent branching process

1981 ◽  
Vol 18 (01) ◽  
pp. 65-75 ◽  
Author(s):  
Aidan Sudbury
Keyword(s):  
Cell Size ◽  
Exponential Growth ◽  
Branching Process ◽  
Expected Number ◽  
Size Dependent ◽  
Daughter Cells ◽  
Rate Of Increase ◽  
A Cell ◽  
Dependent Growth ◽  
Number Of Cells

In cell-size-dependent growth the probabilistic rate of division of a cell into daughter-cells and the rate of increase of its size depend on its size. In this paper the expected number of cells in the population at time t is calculated for a variety of models, and it is shown that population growths slower and faster than exponential are both possible. When the cell sizes are bounded conditions are given for exponential growth.

scholarly journals A Cell Size Theory of Aging

2018 ◽  
Vol 45 (6) ◽  
pp. 665-666
Author(s):  
Krushna C. Patra ◽  
Nabeel Bardeesy
Keyword(s):  
Cell Size ◽  
Theory Of Aging ◽  
A Cell
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