# Growth Kinetics

This section is under construction (July 2010)

Various parameters need to be directly measured in order to be able to make any meaningful calculations from your chemostat:

### Substrate Concentration in the Medium Feed

Neverassume that, if you've made medium containing 25mM sucrose that the finished, autoclaved medium contains 25mM sucrose because it probably doesn't! Dilutions are never that accurate and some water always escapes in the autoclave, so you must measure the concentration in the feed. For some substrates (e.g. methanol, ethanol, benzene) this is easily done by gas chromatography, for others, (e.g.acetate, succinate, thiosulate) you can use HPLC, colorimetric methods or enzyme-based kits. Whatever you use, make calibration standards in your basal salts medium, not in water, just to be safe. The concentration should of course be in M, not in gL-1. Substrate concentration in the medium feed is termed S0 in some texts but I use [Substrate]0.

### Substrate Concentration in the Growth Vessel at Steady-State

Once the culture is at equilibrium, determine the substrate concentration in the growth vessel several times over the course of a few hours. This parameter is sometimes termed S but I use [Substrate]f. Try to avoid removing more than 1% of the culture-volume when determining [Substrate]fso as to avoid purturbing the steady-state. In most cases, [Substrate]f = 0.

### Medium Flow Rate

This is NOT the rate of flow of the medium entering the vessel - it is the rate of flow of the medium leaving the vessel. It must take into account the volume of acid/base added to the medium too. If your bioreactor can measure the amount of acid/base pumped in per hour, then this is easy enough. If not, keep the acid/base in graduated cylinders and note the volumes at intervals during steady-state. The rate of acid/base addition in an equilibrated culture can be different from one that is still reaching equilibrium. Add the rate of acid/base addition (mLh-1) to the rate of flow of medium entering the vessel to get the flow rate F, which is measured in mLh-1.

### Culture Volume

Culture volume is, of course, determined before the chemostat is started (it is described in other sections) and is termed V and measured in mL.

### Amount of Dry Biomass

The amount of biomass (X, in g) can be measured directly by taking an aliquot of culture and drying to constant mass or can be derived from optical density (OD). Never use generalised relationships like "an ODof 1.0 = 300mgL-1 dry biomass". The best way to measure biomass using ODis to first of all construct a calibration curve using your organism grown on the substrate that you will be using in the chemostat on the same basal salts medium. Dilute the culture to various different ODs at 440nm, 540nm and 600nm (some organisms give more linear OD/dry weight calibration curves at different wavelengths to other organisms, so always calibrate with several wavelengths then choose the best one) then dry to constant weight (remember to make a medium-blank to allow for the mass of salts etc!). Plot the calibration curves and find the wavelength that gives you a linear relationship. Take replicate samples from your chemostat at steady-state, measure the appropriate OD and determine the amount of dry biomass, in g, based on V.

Now you have a series of parameters directly determined, it is time to start converting them into something meaningful:

### Dilution Rate

Dilution rate (D) is, at steady-state, equal to the specific growth rate (µ) and is measured in reciprocal hours (h-1).

$D = \frac{F}{V}$

In order to do anything useful, you will need to run chemostats at about 10 different D to steady-state.

### Molar Growth Yield

Molar growth yield (Y) is the amount of dry biomass produced per mole of substrate consumed and is measured in gmol-1.

$Y = \frac{X}{[Substrate]_{0}-[Substrate]_{f}}$

### Specific Rate of Substrate Uptake

The specific rate of substrate uptake (Q) can be...

### Maximum Molar Growth Yield and Maintenance Coefficient

By determining Y for various steady-states, it is possible to calculate the maximum molar growth yield (YMAX) and the maintenance coefficient with respect to growth substrate (mS) using various graphical methods.

Double-reciprocal plot of 1/Y against 1/D.

In the above spreadsheet, a double-reciprocal plot has been constructed for 10 steady-states. YMAX can be determined from the Y-intercept (1/YMAX). Whilst mS can also be determined from this type of plot (the gradient = mS), it is not advisable as the gradient is prone to error due to the nature of the plot. mS is better determined from a plot of Q versus D.

## Rich Boden

Rich dot Boden at warwick dot ac dot uk

D14 School of Life Sciences
University of Warwick
Coventry
CV4 7AL
Lab: (024) 7652 2557