Dear Rasoul Shafiei

I think, this published book "Biochemical Engineering & Biotechnology" 2nd Edition Elsevier 2015 (ISBN: 9780444633576) can help you.

You can find the content list of this book from attached file here.

Good luck

As a rule log phase is when you have highest growth. So if you are observing high growth it cannot be stationary phase by definition.

How beginnig of stationary phase was measured?

OD reading can be sometimes misleading. did you make dilutions when reading high OD samples?

Try direct counting CFU what will show you real growth.

in fact, the question is about the lag phase, not the stationary phase.

I agree with you that the specific growth rate is the highest in mid-Log . However, I found that just after the Lag phase it is higher than the mid-Log.

Yes, the bacterial suspension was diluted to reach 0.2-0.6

Rasoul,

it make sense that just after the lag phase you have maximal growth. Cells have plenty of space, nutrients and desired conditions for growth.

Later, nutrient concentration will be lower, inhibiting/toxic compounds might accumulate and oxygen transfer decrease, so you MIGHT suffer decrease in your ug

Yes, it makes sense, but what about the definitions? they say that during mid-log, ug is the higher.

Well, when I'm teaching umax is found just after the lag-phase and couls last for few hours during the mid-log phase if the right conditions are present. Otherwise ug decrease

The Monod model (and others Tessier, Moser, Contois) describing cell growth also determines higher ug at early log.

My personal experience at the lab and pilot scale corroborates this fact

I agree to you that specific growth rate goes exponentially with rapid increase until maximum where it is called as maximum specific growth rate(Umax) just after when it overcome the Lag phase. If the result for O.D. is tedious, then try direct counting of cells.

To interpret the specific growth rate and maximum specific growth rate appropriate, the points of log phase should be considered, not the lag phase. In lag phase, cells do not divide and hence it is inappropriate to calculate the growth rate there. Maximum specific growth rate can be further calculated by applying monod eqaution.

Hello. Thanks for you advice.

A file has been attached.

About the your suggested method, the plot should be according to the number of bacteria?

Is it possible to use biomass instead of number of bacteria?

Dear Rasoul,

I worked a lot with growth curves and I agree with Armando in that: to see the log-phase on the growth curve you should transform your OD results into the logarithmic scale. Then compare the normal OD/time dependence curve with logOD/time-curve and you will see that in fact the log-phase (!!!! the phase described with log-equation !!!!) corresponds to the stage just after lag-phase of the normal OD/time-curve. There is no mistake in your results it's just a necessity to transform your data into log-scale and to present them in log-scale coordinates if you’d like to indicate the log-phase and, for example, differences between speeds of growth of several strains.

Best,

Sergei

Dear Rasoul

As suggested before the Gompertz model could be helpful. I personally use it quite a lot. But there are plenty of growth model (Logistic, Richards, Schnute, Stannard,...). First I would invest some time in finding which is the best model in your case and then apply it. I personally use R for fitting a given model. The grofit package by Kahm and colleagues is quite helpful. Also as also said before you might want to gather a bit more data.

The following references might be helpful.

- Kahm, M., Hasenbrink, G., Lichtenberg-Fraté, H., Ludwig, J., & Kschischo, M. (2010). grofit: Fitting biological growth curves with R. Journal of Statistical Software, 33(7), 1-21.

-Zwietering, M. H., Jongenburger, I., Rombouts, F. M., & Van't Riet, K. (1990). Modeling of the bacterial growth curve. Applied and environmental microbiology, 56(6), 1875-1881.

- Buchanan, R. L., Whiting, R. C., & Damert, W. C. (1997). When is simple good enough: a comparison of the Gompertz, Baranyi, and three-phase linear models for fitting bacterial growth curves. Food Microbiology, 14(4), 313-326.

- Many papers by Baranyi might also be helpful.

Best

Olivier

Dear Rasoul,

I can suggest an excellent book:

Quantitative Problems in Biochemistry by Edwin A Daws ISBN 0-582-4440-2

What you are observing is normal. As you get production of acetic acid (even if neutralised by the addition of alkali) the acid becomes toxic and can decrease the µ. What you should make sure of is that you obtain an exponential (used a semi-log graph of ln OD against time) and that you measure the µ over the exponential range. You may then find out that you have several exponential phases and then your µmax wil be measured over the first exponential phase where the toxic effects of acetate are not present yet.

Be careful with OD. Firstly the Beer-Lambert law applies only to absorbance and to use it for turbidity is an approximation. Secondly you should measure your zero point before inoculation and this must be very small. Thirdly, The relationship between biomass and OD can change with the growth conditions. Fourthly your organism must not contain anything that absorbs at the same wavelength that you are using for measuring essentialy the turbidity of the culture. If you have access to a Coulter Counter, use it to count the bacterial cell concentration.

Dear Rasoul

You will get very good and simple method on measurement specific growth rate under various cultivation condition in the book entitled, "Principles of Fermentation Technology" by Stanbury, Whitekar and Hall.

Good Luck

Shashi

Hello Rasoul,

Cell count would be best for the calculations but your method must be robust.

Hello Behnam,

Thanks a lot for your advice.

I would like to know if you have the electronic version of the suggested book?

Hi Rasoul

There's a great tool in Excel called DMFIt available from Josef Baranyi's lab at IFR, Norwich UK. It uses the logistic D-model and allows you to fit a sigmoidal curve to growth data and calculate growth rate and estimate lag phase. Note the version of Excel may be an issue but give it a try. Also be careful with lag phase estimates they are notoriously variable and your inoculum must be prepared in a very controlled manner to get consistency,

Website:

http://www.ifr.ac.uk/safety/dmfit/

Good luck with your work,

regards

John

Hello

OD is dependent on many factors. So it is better not to use OD for calculation of Specific growth rate.

Yes, we can do what Serge said. But I have Observed that even for one strain, during exponential phase the morphology is different specially in batch fermentation. Therefore we can not really rely just on OD to judge about Log phase. Beside OD, it is necessary to count the cells. 

Dear  Rasul,

Biomass, OD and CFU have to be cocalbrated for a particular system(strain, morphology,, culture conditions) for following growth in  each phase of culture. If you are able  to separate bacterial mass of your culture its DNA content might be a helpful parameter, especially in relation with the parameters mentioned above.

Well my dear friend: Specific growth rate depends on many factors, like: substrate concentration, competition, pH, end product concentration etc. It changes as the growth proceeds. This is because in Batch fermentation, the environment changes as a function of time, substrate concentration, end product concentration. In case of Acetobacter fermentation, (except sorbitol) acetic acid is the primary metabolite which will show a different specific growth rate as compared to glucose.

After lag phage is log phage, so your result is ok. if you give me specific informations (number), I will help you to interpret your result.

Hello Uyen Bui

which kind of information do you need to interpret the results?

can you show me you datas which you collected (exp: original cell density, cell density at different time points (after 2 hours, 6 hours, 10 hours,...)

Hi, im looking for the equation to determine specific growth rate of yeast in glucose medium......can anybody help me out plz?

Dear Rasoul Shafiei

I think, this published book "Biochemical Engineering & Biotechnology" 2nd Edition Elsevier 2015 (ISBN: 9780444633576) can help you.

You can find the content list of this book from attached file here.

Good luck

DEAR rasoul shafiei by reading your question I came to one conclusion that you doesnot have minimum basics in fermentation and wonder how you can hold such a great responsible job,. In INDIA people who join as traines knows how to calculate basics of kinetics just I pity on YOU.

 IN PRACTICAL GROWTH PHASE WILL BE HIGHEST ONLY IN LOG PHASE AND NOT IN LAG PHASE . PLEASE GO TO SCHOOL AND LEARN BASICS . WHAT IS THIS YAAR HOW DO YOU TRAIN PEOPLE UNDER YOU.i JUST CANT IMAGINE THEIR FUTURE.

((LN(OD2)-LN(OD1))/ (T2-T1 ):  THIS IS THE FINAL DERIVED FORMULA FOR CALCULATION OF SPECIFIC GROWTH OF MICROBES . PLEASE NOTE THIS AND GO AHEAD .

Theoretically µ is always high in lag phase. As µ=µmax S/Ks+S

divide numerator and denominator by S

µ= µmax/(Ks/S)+1;

when S>>Ks; µ=µmax;

and at t=0; S is always high in initial stage.;

when S decreases µ

I am trying to calculate the specific growth rate of Vibrio parahaemolyticus causing AHPND in shrimp, under different conditions of pH, temperature and salinity. Somebody can help me with data of other vibrios?

Dear Rasoul

Once you have identified an optimal media for the specific organism, in batch culture you shall start to inoculate the sterilized media; then determine the growth curve. Base on obtained growth data with respect to incubation time you lag phase can be defined by observation of growth curve. 

Your 2nd point on specific growth; you should follow a growth model based on double reciprocal or Lineweaver-Burk plot  you can define where the plot cross the y-axis that is inverse of maximum specific growth rate.

Your information please see chapter 5, my "Biochemical Engineering & Biotechnology" book published by Elsevier in 2015.

Thank you Rasoul!!! 

Thank you Najafpour!!!

Dear Sonia

I am also thankful to you for you questions and comments. If I can be any assistant to you; please feel free to contact me. 

Regards

Prof. Ghasem Najafpour

Thank you Najafpour, do you have any data of vibrios growth incubate under different tempearture, salinity or pH?

Very nice answers of Dr.Najafpour. However, I would like to add one very important thing and that is the value of specific growth rate will vary not only on factors like media composition (that too NaCl concentration), incubation temperature and time etc. but also on the growth phase which in turn will be affected by a very important factor called STRESS. 

Thank Dr. Ghosh

I am also agree with your valued comment. That is implication of stress on microbial culture.

Regards

Now, how can I compare the specific growth rate and lag phase of vibrios incubated in different culture conditions as temperature, salinity and pH?

Check for the growth patterns varying one of the parameters at a time keeping the rest constant.

Dear Sonia,

To compare conditions you can use a software called MINITAB that allows you to plant, perform and analyses your experiments in a statistically valid manner.  The lag phase cannot be calculated but measured.  For µ, use a semi-log graph to find the "apparently" linear part of the graph and fit the exponential equation.  Again, Mintiab can do this but Excel is easier.  Be careful to take lots of measurements at the beginning and to calcuate the "fastest" µ at the very start, immediately after the lag phase.  Sometimes, you get what appears to be more thatn one "exponential" phase.  

I think the book Mohammad has asked you to refer will solve your problem.

Three major phases of sigmoid growth curve can be identified by ontogenetic growth force

Ontogenetic growth process is defined as the development of an animal from birth mass to mature mass. Thus, the catabolism (maintenance) and the anabolism (new biomass) provide a general view of mass increasing as a function of time. However, time passing, more and more energy goes to sustain the organism. Therefore, the gain is the net result of metabolic forces. In order to better understanding about the mechanistic aspects of body increase, the freely available Practical Program for Modeling -PPM (https://goo.gl/5je0GV) is an appropriate instrument for interpreting the trajectory of ontogenetic metabolic force and, in addition, propound three particular timescale for growth in the sigmoidal curves function (Logistic, Gompertz, Richards and Weibull). All of these stages fall along the growth curve, and they are the key to the relationship between mechanistic viewpoints to the analysis of growth process (metabolic forces) (Shimojo et al., 2006/http://catalog.lib.kyushu-u.ac.jp/handle/2324/9243/p285.pdf), thereby allowing new aspects to production analysis and providing a fundamental concept for study of animal growth (or any biological system). The PPM program also shows that is possible to identify the energy required for gain and maintenance. Then, the value offering to ontogenetic growth force for rise will be approaching zero, close to mature body size. Likewise, the PPM demonstrates four critic points where in the growth curve the driving energy allocation to length of the: 1-exponential growth phase, 2-quasilinear phase, 3-exponential decay phase. Finally, in the saturation of the growth, the energy requirements for maintenance the asymptotic maximus body size makes impossible the synthesis the new cell mass, reflecting cessation of animal growth. Thereby, the PPM can be predicts the wave-shape the metabolic forces trajectory based on energy allocation to maintenance and to produce a new tissue. Thus, the modeling improvement that can be carried out with respect to metabolic processes, mechanistically based derivatives of well-known growth function, relating to metabolic forces and ontogenetic growth with flexibility, accuracy and meaningful analytical properties.

Thank you Manoel, I´ll chek the program. Later I tell you some questions

very useful tool

https://ocw.ehu.eus/pluginfile.php/4718/mod_resource/content/1/Temas/4._DETERMINATION_OF_THE_PARAMETERS_DEFINING_THE_BACTERIAL_GROWTH_2.pdf

Very useful tool

https://booksite.elsevier.com/samplechapters/9780123705198/Sample_Chapters/04~Chapter_3.pdf

Actually if it is an aerobe, then the rate of utilization of dissolved oxygen s a very useful tool. In case of an anaerobe, one has to determine the critical substrate and its rate of remediation will give you the actual result.

The Practical Program for Forces Modeling (PPFM) is a spreadsheet for adjusting growth curves with subsequent evaluation and analysis of acting forces. https://sites.google.com/view/ppfm-spreadsheet/ The spreadsheet is use-friendly, with point-and-click tools, being in the public domain.

Tutorial

https://drive.google.com/file/d/1yi9OZeP9q75Uan_BSJhLNgAObhokncLG/view?usp=download

Thank you Manoel Garcia Neto is very interesting, I´ll try it

Dear young research scientists

Kinetic studies for design and projection and comparative analysis would be very interesting. There are many models such as Logistics' for nice growth curve projections. Please see chapters 2, 3 & 5 my book "Biochemical Engineering & Biotechnology" 2nd Edition Elsevier 2015 (ISBN: 9780444633576). If any serious question involved I would be delighted to discuss.

Regards

More details:

Growth curve: an intelligent life history described by a mathematical model!

https://drive.google.com/u/0/uc?id=1DyYPsbKZguZq2tkszgU_StjQrt5b5XFT&export=download

Please check my research paper as follows:

Kinetic modeling and techno-economic feasibility of ethanol production from carob extract based medium in biofilm reactor

Please share with me if your wanted with your problems its. Thanks so much.

Hi Rasoul,

I completely agree with Behnam. Optical density is not the best choice for growth studies. It is fluctuating in the course of growth study since it has been affected by the parameters apart from cell numbers. Maybe cell counting and cell dry weight would be helpful. To project the model behaviour, Prof. Najafpour's book is very proficient.

Bests