User:Jaroslaw Karcz/Sandbox: Difference between revisions
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<math> \mu_{obs} = \mu_{max}\frac{[S]^n}{K_s^n + [S]^n} </math> <br> | <math> \mu_{obs} = \mu_{max}\frac{[S]^n}{K_s^n + [S]^n} \cdots (1)</math> <br> | ||
where | where | ||
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*<math>\mu_{max}</math> = maximal growth rate coefficient | *<math>\mu_{max}</math> = maximal growth rate coefficient | ||
*K_s = half-saturation coefficient | *K_s = half-saturation coefficient | ||
*n = positive co-operativity coefficient | *n = positive co-operativity coefficient<br><br> | ||
For Infector Detector, let <math>S \rightarrow E</math> such that (1) becomes<br><br> | |||
<math> \mu_{obs} = \mu_{max}\frac{[E]^n}{K_s^n + [E]^n} \cdots (2)</math> <br><br> | |||
where E = "energy" in the system | |||
Revision as of 05:55, 20 September 2007
20 September 2007
It was suggested that the levelling-off of the fluorescence-time curve for construct 1 (T9002) [1] could more realistically be attributed to the extinction of "energy" in the system. The model for Infector Dectector needed to be amended, to include this phenomenon.
Microbial growth rate as function of single rate-limiting substrate
Although a study of microbial growth rate is undertaken here, this could be altered to feature the system survival/lifetime, as we are dealing with S30 cell extract. The lifetime of the system would be reflected by the rate of change of system energy ([math]\displaystyle{ {d[nutrient]}/dt }[/math]), which here is decreasing, as there is no source of replenishment of nutrient.
A review of literature suggests that multiple models have been developed to describe this feature of the system. The most widely used models are the Monod, Grau, Teisser, Moser and Contois equations.
These equations describe the functional relationship between the microbial growth rate and essential substrate (nutrient) concentration.
It was proposed, and noted from experimental data, that the behaviour of the system is described by some sigmoidal function, the nature of which is encapsulated by the Hill function.
[math]\displaystyle{ \mu_{obs} = \mu_{max}\frac{[S]^n}{K_s^n + [S]^n} \cdots (1) }[/math]
where
- S = limiting nutrient/substrate ("energy in system")
- [math]\displaystyle{ \mu_{obs} }[/math] = instantaneous (observed) growth rate coefficient
- [math]\displaystyle{ \mu_{max} }[/math] = maximal growth rate coefficient
- K_s = half-saturation coefficient
- n = positive co-operativity coefficient
For Infector Detector, let [math]\displaystyle{ S \rightarrow E }[/math] such that (1) becomes
[math]\displaystyle{ \mu_{obs} = \mu_{max}\frac{[E]^n}{K_s^n + [E]^n} \cdots (2) }[/math]
where E = "energy" in the system
