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There are multiple ways yeast cells can be grown in liquid cultures.

  • Batch cultures are easy to prepare but cell density, medium composition and physiology change over time
  • Chemostats allow to maintain cells in physiological steady-state, but growth rate is limited by nutrient availability
  • With a turbidostat, cell density is kept constant and cells can grow at their maximal rate, with excess of nutrients, but medium composition changes over time
  • Cells in a microfluidics chamber can attain maximal growth rate with constant conditions, but with extremely low numbers.

I cannot think of a way to get (a) maximal growth rate, (b) constant medium composition, (c) constant cell density and (d) a decent culture volume (>50 mL). Am I missing something?

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  • $\begingroup$ Unless I'm missing something, at steady state the cell density in a chemostat is constant and the specific growth rate is equal to the dilution rate. So you can keep density and specific growth rate at desired values. $\endgroup$ – Cell Dec 21 '18 at 17:56
  • $\begingroup$ Yes, you can keep them fixed, but what I am looking for is the maximal growth rate. In a chemostat there is at least one limiting nutrient that slows down cell division rate. $\endgroup$ – Mattia Rovetta Dec 21 '18 at 18:08
  • $\begingroup$ Im not sure I understand. Why not use media with excess nutrients? The specific growth will be equal to the dilution rate i.e. you can make the specific growth as high as you want (approaching the maximum growth rate) independent of nutrient levels. $\endgroup$ – Cell Dec 21 '18 at 18:38
  • $\begingroup$ Maybe I can approach maximal growth rate (for which I think I need a feedback mechanism to control the flow rate in order not to flush away the culture). However, I think I would not get constant medium composition anyway because each molecule in the chemostat is depleted/produced by the cells at a different rate. For example, if glucose is not limiting, it will be added to the culture faster that is consumed and thus will increase indefinitely. Multiple sources say that with chemostat you can get steady-state cultures, but to me it seems false. Where am I wrong? $\endgroup$ – Mattia Rovetta Dec 22 '18 at 9:35
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A chemostat should satisfy your criteria. The cell mass balance around a chemostat is the following (assuming no biomass in the feed): $$F-FX+V_RX\mu_g-V_Rk_dX=V_R\frac{dX}{dt}$$

At steady state there is no change in parameters with respect to time so we set the derivative equal to zero. If we also assume that the death rate ($k_d$) is negligible (for example cells in exponential/log phase) and let: $$D=\frac{F}{V_R}$$

Where $D$ represents the dilution rate (how quickly the volume in the tank is being replenished). Then rearranging the above equation you get: $$D=\mu_g$$

This says that the growth rate will be equal to the dilution rate. In other words you can set how fast the cells grow by modifying the flow rate and/or volume of the tank. But there is a limit. Cells grow as fast as they can use the limiting nutrient ($S$) and this relationship is often modeled as: $$\mu_g=\frac{\mu_mS}{K_s+S}$$ Where $\mu_m$ and $K_s$ are unique parameters for every cell type. $S$ is the concentration of the limiting substrate in the tank (which is also equal to the concentration of the substrate in the outlet stream). The maximum growth rate is $\mu_m$ and if the dilution rate is higher then this value, the cells get washed out of the chemostat. This can be troublesome if you need a flow rate higher than $\mu_m$. In this case a recycle is useful.

To answer your question in the comments regarding medium composition. You probably want to operate at steady-state. Steady state means that there is no change of parameters with respect to time. So if you write the substrate mass balance:

$$FS_0-FS-V_RX\mu_g\frac{1}{Y_{\frac{X}{S}}}--V_RXq_p\frac{1}{Y_{\frac{P}{S}}}=V_R\frac{dS}{dt}$$

And set the derivative to 0. Then you will find the outlet substrate concentration is a function of other constants (biomass, volume, product yield, etc.). You're right in that some substrates get used more than others, but when steady state is reached. They stop changing and the medium composition stays constant in the vessel.

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  • $\begingroup$ Thanks for your help! Without stating what variables and constants are, the equations are a bit obscure though. And I still don't get why in a chemostat the medium composition would stay constant. In fact, a cell uses different compounds at different rates. However, the composition of the input medium is constant and is not adjusted to correct for these differences. Therefore, all input nutrients (except the limiting one) will increase their concentration in the vessel with time. But maybe I'd better open a new question to address this $\endgroup$ – Mattia Rovetta Dec 24 '18 at 16:37
  • $\begingroup$ I think you are confusing "constant" with "the same". If you feed 20 g/L glucose and 20 g/L uracil to the vessel then hypothetically you could have 1 g/L glucose leaving and 19 g/L uracil leaving, because they are used at different rates. But these rates would be "constant" in the sense that the levels stay at 1 g/L glucose and 19 g/L uracil because the system is at steady state. In other words the nutrients don't keep dropping to 0 because you are constantly add more nutrients in the feed. $\endgroup$ – Cell Dec 24 '18 at 17:43
  • $\begingroup$ I will try to update my answer but I was having issues logging on my computer and apparantly I made a new account so I can't edit at the moment. $\endgroup$ – Cell Dec 24 '18 at 17:45
  • $\begingroup$ Finally there is no "increase over time" for unused nutrients. Whatever isn't used leaves the vessel. $\endgroup$ – Cell Dec 24 '18 at 17:47

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