Hello dear colleagues,
There is a question to all fermentation specialists and for specialists in microbial growth modeling in fermenters.
In my article "S-shaped growth curves in fermentations and golden ratio", https://www.worldscientific.com/doi/abs/10.1142/S1793524520500199 , it was shown "at the tip of the pen" that the ratio Xp/XLim=Φ^2= 2.6180339887… for conditions of growth of microorganisms with oxygen limitation, where Xp is theoretical asymptotic maximum biomass concentration, [biomass units/volume units]; XLim is exponential growth phase end and beginning of GIP, [biomass units/volume units]. At the same time, it is necessary to have a clear understanding that the value of Хр differs from the value ХFinal, final biomass concentration, when total biomass, X, contains only non-dividing cells, Xst, and XFinal < Xp , [biomass units/volume units]; Xst is concentration of the biomass of zero age (stable) cells, [biomass units/volume units]; Xdiv = X − Xst is concentration of proliferating biomass, [biomass units/volume units]. Please see the Figure 1 from this article, see the link above.
Used for about 200 years in biochemistry and biometrics, the logistic curve postulates strictly mathematically the ratio Xp/XLim=2- again, please do not confuse it with the XFinal value, which is the beginning of the stationary growth phase or the phase of cell death, because Хfinal is a specific value from your experiments, but Хр is an asymptote.
Probably many of you know, that representatives of the professional community of astronomers and / or cosmologists are writing joint articles via the Internet with the number of authors up to 1000 or more. Therefore, I invite the professional community that deals with fermentation and mathematical modeling of fermentation to try to figure out the question what is the correct ratio of Xp/XLim - is it 2 or is it Φ^2? Do I have a mistake in my calculations? My practical experience of over 30 years in our field shows the answer is Φ^2. What could you personally say about your experience?
When you start preparing the answer to this question, I ask you not to forget about the "pitfalls" that may occur.
First of all, you must be sure on a basis of strong experimental data, when you analyze any of your fermentation, that you are dealing ONLY with oxygen limitation and other restrictions on the growth of bacteria / microorganisms / cells are completely absent. This is the first thing. Second, you need to be sure that the volume of the fermentation liquid in the reactor has not changed significantly in the reactor/fermenter during the fermentation from the start to finish and at OTR=const. Third, we are now discussing ONLY biomass growth without the limitations that will inevitably be available if your biomass produces large quantities of some useful product. For example, recombinant cells will not be the case that is useful for this my question. It is better to look at other possible restrictions right in my article.
I have absolutely no idea yet how I will process the data if my question gets a lot of responses. It is possible for me to do this easily when there are dozens, at most, hundreds of answers. But, if there are more, I have absolutely no idea what I will do with it. Perhaps the professional community will spontaneously do some structuring? On the other hand, the current dominant economic model in the world severely limits the number of responses due to data confidentiality. And only scientific academic divisions are more free for this kind of discussion. One of my reviewers for this article gave me a good word that this issue can be of great importance for industrial production. I want to add that this question is also of great scientific importance. First of all, for the reason that there is a need for additional verification of the logistic curve. It is known that this curve has no physical meaning, as well as the previously discussed J. Monod model . If together we can prove this also statistically, then together we will make a significant step forward in terms of the economic efficiency of microbiological production.
Considering the above, I ask you to put your "Likes" and to "Share" to maximize the spread of this post. Also, I ask you to give in your comments some of your ideas regarding my question on its essence and on how to get data from the interviewed colleagues and how best to be doing the processing of this data.
Regards,
Sergey P.Klykov,PhD,
February, 4,20201
Indeed, it is a very good question. There is a good correlation for bacterial growth under oxygen restriction. Bacteria that require oxygen to grow are called obligate aerobic bacteria. In most cases, these bacteria require oxygen to grow because their methods of energy production and respiration depend on the transfer of electrons to oxygen, which is the final electron acceptor in the electron transport reaction.
Cheers, one more time!
I really thank you for your reaction. But, if you had read my text, then I would like to draw your attention to the fact that I am asking to promote this text to the masses of biotechnologists. Therefore, I would be very grateful to receive some full comments from you, or I would like to ask you to put your "Like" and press the "Share" button, or all of the above together.
It won't take long, but I would like to have a full discussion. I am the one who sees that you have full agreement, that the question that I have raised is of fundamental importance. Therefore, I am asking for minimal assistance in the above. I don't ask A LOT :)
If you have a desire to treat this as a project, then that would also be very pleasant for me. I still have no idea how to move this issue to the masses, except for the actions I have listed. If you have any opinion, I will welcome that too.
Sincerely,
Sergey Klykov
Concerning aerobes, anaerobes and photosynthetic microorganisms.
Yes, Dr. M. D.H. Prodhan is right writing here about obligate aerobes.
However, energy consumption is also necessary for two other groups of microorganisms - anaerobes and photosynthetic microorganisms.
I left my question here with the general case of energy limiting in mind.
Of course, for anaerobes and photosynthetic microorganisms, in order to technically organize the limitation of the energy entering the reactor, other methods will be required to manage of fermentation.
But, the question will be the same as for obligate aerobes. Are we going to have a ratio of 2 or Phi^2?
Dear Sergey P. Klykov,
Thank you so much for your nice contribution and clarification.
Very interesting question.
I think this paper will give valuable input
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6812798/
Kindly check https://www.britannica.com/science/bacteria/Physical-requirements
Also check https://www.frontiersin.org/articles/10.3389/fmicb.2019.01992/full
Dear Sergey Petrovich! I cannot provide experimental data, but I will try to carry out a theoretical analysis to answer your question. So what is the (XR / XLim) ratio? The concentration of microbial cells in the XR asymptote is determined by the formula: XR = QR / m (QR is the maximum rate of oxygen mass transfer in the apparatus during this fermentation period, m is the specific rate of oxygen consumption to maintain vital activity (oxygen gram per gram of biomass per unit time). The cell concentration of XLim microorganisms at the end of the exponential growth stage (and at the same time this is the beginning of the slow growth stage) is determined by the equation: XLim = QLim / (m + aµmax) . Here, a is the stoichiometric coefficient of oxygen consumption for the formation of biomass of microorganisms, µmax is the maximum specific growth rate of microorganisms in the exponential growth phase, and QLim is the maximum rate of oxygen mass transfer at the end of exponential growth. Therefore, the ratio (XR / XLim) is determined by the formula: (XR / XLim) = (QR / QLim) [1 + (aµmax / m)]. If the maximum oxygen mass transfer rate at both points is the same (which is true for bacterial fermentations), then the ratio (XR / XLim) is determined by the ratio (aµmax / m). Thus value (XR / XLim) will be equal to 2 only if (aµmax / m) = 1. But this looks implausible, since the stoichiometric oxygen consumption for biomass growth is obviously much higher than the cost of life support. Therefore, I agree with your assumption that (XR / XLim) is greater than 2. How much - is a question. Apparently, this number will be different for different microbial cultures. And it is unlikely that it corresponds to the "golden ratio". A more complex situation arises when (QR / QLim) is not equal to 1. This can occur in mycelial fermentations. Due to an increase in the viscosity of the culture liquid with an increase in the concentration of biomass, the coefficient of mass transfer of oxygen KLa and, consequently, QR - decreases. Due to this, the ratio (QR / QLim) becomes less than 1 with all the ensuing consequences. I apologize for the lengthy comment. @
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