A model of bacterial growth based on Monod kinetics is used. Two forms of inhibition are included to improve the agreement with the experimental data. The model successfully describes many features found in the
Of the large number of experiments recorded by Penfold (1914) in connexion with the question of lag in bacterial growth, a certain proportion have been carried out in such detail as to render them eminently suitable for mathematical analysis. In all work of this kind, which is intended to th...
Finally we will set j equal to the number of generations, or the number of times the cell population doubles during the time interval. Then we have, Ni=N0×2jNi=N0×2j This equation is an expression of growth by binary fission. In our example, N0 = 4, the number of generations, j...
Whatever its type, the mathematical expression of a model has several component parts, which are described and named inFigure 1. Sign in to download full-size image Figure 1.An example of a mathematical model showing the nomenclature of the component terms. The values of the independent variable...
factor. Simultaneously, the mRNA is degraded with a fixed half-life40,41,42,43. The cytokines in the plasma also have a fixed half-life44,45,46,47. IL-10 is an anti-inflammatory cytokine and will inhibit the expression of TNF, IL-1β, and IL-6 mRNA48,49,50. To prevent IL-10 ...
Expression of the persistent phenotype, a phenomenon known as "bacte- rial persistence" [1, 2], is the primary challenge in the fight against Mycobacterium tuber- culosis as persistent cells escape elimination by the immune system [3] and can remain dormant for years before starting replication...
et al. Mathematical modeling of planar cell polarity to understand domineering nonautonomy. Science 307, 423–426 (2005). Article CAS Google Scholar Huang, S. Gene expression profiling, genetic networks, and cellular states: an integrating concept for tumorigenesis and drug discovery. J. Mol. ...
(2.45) then the above expression is of order \((1+\vert x\vert )/(1+t)^{3/2}\).Regarding the nonlinear part, we first consider the case \(t-s \le 1\). For the back of the wave, we use the exponential Decay (2.42) and Estimate (2.30) of Theorem 2.4: ...
The bacterial isolateC. butyricumNE95 was cultivated in a CAB broth medium. A UV-9200 VIS spectrophotometer was used to track optical density changes of the bacterial suspension overtime at 600 nm [24]. The experiment was performed in triplicate. Growth kinetics data was represented by the Mono...
etc.) with the objective of maintaining their intracellular and extracellular medium within a narrow range of physiological properties (homeostasis)6. As cells receive chemical and/or physical external stimuli, they modify their shape, location, internal structure and genomic expression, as well as the...