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We propose a new mathematical model for cell cultivation in a chemostat. Our model is based on the structuring of the biomass into two main groups: dividing and nondividing cells. The model is applicable both to existing static characteristics such as the Monod model and to the deviations from it.

We determined the range of chemostat stability at the specified flow rate D and concentration of the input limiting substrate S0. We also proposed the methods for determining parameters of the chemostat structured model.

The value of the derivative of dividing cells to nondividing cells of zero age is constant for a given flow rate. That value is no less important than the equality of specific growth rate and nutrient flow rate, which determines the equilibrium of the chemostat.

We showed that the corresponding specific rate constants of limiting substrate use by dividing and nondividing cells determine the system equilibrium. We also demonstrated that the new proposed structured model of the chemostat is more general than any other existing model. In each specific case, the model provides comparable equations to the well-known models of Monod, Pirt, Moser, Andrews and Ierusalimsky.
Dear colleagues,
This model is the a special case of the common model

I invite you to take part in the discussions in Linkedin at:
Hello Sergey,

Do you mind explaining in more details what is mathematical model for cell cultivation? I opened the link you posted but I get lost in equations. I'm biologist (not that familiar with the math), but your method seams interesting and I would like to find out something more.

(10-31-2012, 06:04 PM)BojanaL Wrote: [ -> ]Hello Sergey,

Do you mind explaining in more details what is mathematical model for cell cultivation? I opened the link you posted but I get lost in equations. I'm biologist (not that familiar with the math), but your method seams interesting and I would like to find out something more.

Hi Bojana,
Pls, see
Also,I advise you to re-read the beginning, which is given above:
Monod equation and other equations is known. However, these "other" equations arose due to the Monod equation " nonuniversality ". Our model has opened the cause of this Monod equation"nonuniversality " for continuous processes.
In general, the model provides for periodic processes in the journal "Biofabrication":
Also, a universal law was given here that observed in any system:
equations (17-18) and (45).

Warm regards,

Dear Sergey ,
First of all, lot of thanks for providing valuable information on "New Mathematical Modeling -on population growth under specified conditions".
This model seems promising. Also it is innovative way by which biotechnological parameters can be predicted and can help a lot in various fermention industries. This model had shown a good conformity between the calculated and experimental data on biomass yield.
I am anxious to know, can this be further innovated or can as such be applied for stem cell cultivation or in similar applications like optimisation of important media, viral/vaccine cultivation, etc ! This model is developed using base of Pirt- Marr's equation, which is really impressive !
Keep updating on the developments of this new,worthy bio-mathematical model of cell cultivation.
- ExpertScie.
Dear expert ,thank You.
Of course, we have no reason to believe that this study is limited. The equations are common.
In any case, we need to check the specific objects of study.
This study is a continuation of a general theory:
Continuous process are a special case of periodic processes. Periodic processes may be decribed by S-shaped curves.
This has a lot of interesting results.
In the other group we discuss common properties of S- shaped curves:
Please, about vaccines see:
Modeling the bacterial vaccine strains growth for the cells survival control in suspensions to improve the product at the freeze-drying and at the storage.

Our studies on the effect of Salmonella culture growth rate on cell survival under adverse external influences [1] showed that during GIP(growth inhibition phase), if there is a lack of dissolved oxygen, the accumulation of stable cells occurs at a constant specific rate equal to that of the growth delay (A = m/a). The share of stable cells within the population is obviously equal to that of nonproliferating cells, which consume energy only for viability maintenance. Methods for the definition of parameters of the structured model describing substrate consumption and metabolite biosynthesis on the basis of preliminary calculated parameters of the unstructured model were designed. Thus, the proposed structured model assumes that within a growing population there are two groups of cells essentially differing in their physiology. Group I represents newly generated (young) cells and group II contains cells being in a state of active proliferation. Although the cells of group I are often called ‘resting’ cells [2], in our opinion these are the cells of ‘zero age’ [3], i.e. the cells being in phase G1
or in phase V as designated for eukaryotes and prokaryotes, respectively. Group I cells exhibit minimal physiological functions, and for each cell these functions are constant. A
characteristic feature of the cells is that they consume energy substrates only for their viability maintenance. In [1] these cells are called ‘stable’.
All this is important to consider when considering your question.
[1] Klykov S P, Paderin J P, Sadikov M M, Chuprunov V P,
Derbyshev V V and Gusev V V 1996 Effect of culture
growth rate on Salmonella survival Biotechnology 1 35–9
[2] Pirt S J 1975 Principles of Microbe and Cell Cultivation
(Oxford: Blackwell)
[3] Bailey J E and Ollis D F 1986 Biochemical Engineering
Fundamentals 2nd edn (New York: McGraw-Hill)

Best regards,
Dear Sergey,

Thanks a lot. Thats really great !

(11-04-2012, 03:25 AM)ExpertScie Wrote: [ -> ]Dear Sergey,

Thanks a lot. Thats really great !

Dear colleagues! Many thanks!
Honestly, I used to have almost no feedback from the readers of my articles. People whom hit my article, at best, limited to general estimates and remark: good or bad Smile I was not very clear. Not that I felt as if everyone has read, written by me, should applaud and do what I suggest. But the desire to compete and even to swear, as I thought, at least for those who reacted favorably to the reading, be sure there had to be.
Hi All !
I wonder why such a low level of activity?
Dear colleagues! We should hurry.
Most of the problems you are discussing here can be solved with the proposed methodology.
In the global network of professionals LinkedIn I have to answer a lot of questions.
"Hi Sergey,

Recently, LinkedIn reached a new milestone: 200 million members. But this isn't just our achievement to celebrate — it's also yours.

I want to personally thank you for being part of our community. Your journey is part of our journey, and we're delighted and humbled when we hear stories of how our members are using LinkedIn to connect, learn, and find opportunity.

All of us come to work each day focused on our shared mission of connecting the world's professionals to make them more productive and successful. We're excited to show you what's next.
With sincere thanks,
Deep Nishar
Senior Vice President, Products & User Experience"

Hurray! I have one of the top 1% most viewed @LinkedIn profiles for 2012.
I would like that always in our professional community there is a real debates similar as among physicists. High level. Or like mathematicians. Sharing information...
Mathematics will prevail sooner or later .If someone don't be ready for this, he stays out. Soon.

See also:
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