I am working on consortia of Aspergillus fungi species. ~ i.e. Consortia of Aspergillus niger, oryzae and flavus
With neither respect to a specific culture, in your have a time series B(j) of biomass recorded in j-th time moment (it would be nice, if the time step is permanent), then the difference B(j)-B(j-1) yields you an (instant) growth rate. Note, it may depend on j; in other words, thei instant growth rate may vary in time.
Alternatively, you might want to plot the value \beta(j) = \frac{B(j)}{B(j-1)}; it yields you a relative growth rate. Steady state is equvalent to \beta{j}=1 \forall j; otherwise instant growth rate is equal to 0, in steady state.
Previous equation is valid for so called logarithmic (while it is exponential... :) ) growth stage, no more. More generally, dX/dt = \mu(X)\cdot X. Foir each time moment, you can determine an instant growth rate; and again, it depends on X, in general case. There is no way to solve this equation with ARBITRARY function \mu(X). What we definitely know, the function is bounded. Nonetheless, if you have a time series of discrete data, you for sure can determine the instand growth rage, at any time moment.
In general, the specific growth rate is defined as μ = (dX / dt) / X, at a given time. If you are interested in obtaining the kinetic constant "maximum specific growth rate, μmax", you can adjust your growth curve to one of the models already reported (Gompertz, Logistico, among others); but first, you have to plot Ln (N / N0) vs time.
Where, N, is the number of cells (or biomass concentration) at a time "t" and N0, is the number of initial cells (or initial concentration)
I recommend the following article: "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"
Regards
Hi guys, several comments to this very simple problem.
1 (in response to Prithu comment). Specific growth rate (SGR) calculation is uniform for ALL organisms, from viruses to human. One technical problem for fungi (to Glen) is the aggregation of mycelium, difficult to take subsamples from culture vessel accurately. Therefore instead of biomass recording, biotech people normally use other metrics, say, oxygen consumption rate, base titration rate, CO2 production rate ... as a time series.
2 (to Jan). Generally speaking SGR is not a constant apart from short period of exponential growth phase in homogeneous culture. So your advise lacks generality, probably Michael stated the same (the problem, Michael, with your post is that you probably have copied/pasted equations from LaTex; it makes simple expressions unclear)
3 All of you are talking about the apparent SGR which is the difference 'true growth - elimination'. The term 'elimination' stands for washout, grazing, lysis and any other processes of biomass removal. Just imagine to have biomass time series in chemostat running at D=0.2 h-1. All your calculations will give SGR=0 while the actual SGR is 0.2 h-1. So, Glen make sure that your system does not have sink/elimination terms.
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