Temperature dependence of growth rate standard deviation

[mpatterson]

I have noticed a temperature dependence on the standard deviation of growth rate. We are performing selection experiments at low temperature (18 ˚C) with the turbidostat in an incubator set to 15 ˚C. Before we received the incubator, David from LabMaker was helping me troubleshoot how to make the pump seals better because we require very precise measurements of growth rate. We got a fix that worked great (increase the diameter of the little wheels on the pump’s impeller to 14.8 – 15 mm with Scotch tape), at least at 25 ˚C- I was getting doubling time standard deviations that were ± 10 min. However, when we purchased the incubator and started running at low temperatures, we noticed that as the temperature decreases, the standard deviation increases by quite. a bit. Is there a way to prevent this issue? The only thing we have tried so far is to increase the dithering rate from ± 0.05 to ± 0.1 from the setpoint, but that does not help.

For reference, at 25 ˚C standard deviations range from 10-30 minutes. At 20 ˚C, from ~ 40-100 minutes, and at 18 ˚C >> 100 minutes. Sorry, I can’t figure out how to upload attachments on here (I only see an option to put in a url link) otherwise I would include one of the OD and the growth rate of the chamber.

[harrison]

Hello,
I assume that at low temperatures cells are growing more slowly – what, then, does the coefficient of variation look like in growth rate? I.e. the standard deviation divided by the mean?
One might assume that if you are measuring long doubling times you would get larger standard deviations, since any systematic noise is compounded over a longer time.
What do you think the IDEAL system standard deviation would be – accounting for biological replicates always having differences due to randomness of biology, small changes in media temperature/consistency over time, and so on?

If you are looking for other things to help improve it I’d suggest trying to reduce the gains in the temperature control algorithm so hopefully it sits closer to the set point (since you are at low temps), and also try putting your fresh media bottle on top of a magnetic stirrer (since otherwise we often find some ingredient/s settle out slightly meaning what is pumped into the reactor is varying over time).

[mpatterson]

The coefficient of variation at 25 ˚C ranges from 0.1-0.5, but at both 20 ˚C and 18 ˚C it can get as high as 7 or 8. At 18 ˚C the coefficient is always larger than 1.

You are right that the cells grow very slowly- doubling times are on the order of hours. Ideally, standard deviation wouldn’t be greater than 20-30 minutes. We’re planning to do some experiments in the future where we track changes in growth rate over time, so the standard deviation just needs to be low enough for us to track that process in a statistically significant way.

And thanks for those suggestions! We could try putting a stirrer in the incubator with the media as well, but it would be a little tight. How would one alter the temperature control algorithm? In this copied/pasted section of app.py (“Gain = 2.5” in the Thermostat function), or are there additional things I would need to change?

def Thermostat(M,item):
#Function that implements thermostat temperature control using MPC algorithm.
global sysData
global sysItems
global sysDevices
ON=sysData[M][item][‘ON’]
sysDevices[M][item][‘threadCount’]=(sysDevices[M][item][‘threadCount’]+1)%100
currentThread=sysDevices[M][item][‘threadCount’]

if (ON==0):
SetOutputOn(M,’Heat’,0)
return

MeasureTemp(M,’IR’) #Measures temperature – note that this may be happening DURING stirring.

CurrentTemp=sysData[M][‘ThermometerIR’][‘current’]
TargetTemp=sysData[M][‘Thermostat’][‘target’]
LastTemp=sysData[M][‘Thermostat’][‘last’]

#MPC Controller Component
MediaTemp=sysData[M][‘ThermometerExternal’][‘current’]
MPC=0
if (MediaTemp>0.0):
Tdiff=CurrentTemp-MediaTemp
Pumping=sysData[M][‘Pump1’][‘target’]*float(sysData[M][‘Pump1’][‘ON’])*float(sysData[M][‘OD’][‘ON’])
Gain=2.5
MPC=Gain*Tdiff*Pumping

[harrison]

Hello,
For the controller, i’d adjust “Gain=2.5” parameter to be about half. Then, adjust the line a few down from where you pasted. For example:
I=I+0.0005*dt*e
Change the 0.0005 to 0.00025 or such. This would mean it has a slower integration step and hopefully will sit more stably around the set point.

Back to your challenge at hand, I’d say decreasing both the size of the OD dither, and also the absolute value of OD you are dithering around, might be beneficial. At low temps they may enter stationary phase at quite low ODs, and hence if you are sitting them at or near the point of transition (or where it begins) you might get lots of variability since this you are pushing then back and forth across that phenotypic “switch” in behaviour.

I’d also look at the data – is it obvious where the variation might be coming from? I assume that by doing some time-averaging of the OD measurements you get a pretty smooth signal, so at that point the variations in estimated growth rate are likely down to differences in conditions experienced by the cells (e.g. inconsistent feeding/temperature), rather than measurement drift over time (which should be minimal).

[mpatterson]

Thanks! I will adjust that during our next experiment.

Halving the dither during our last experiment does seem to help a bit. We are using an OD of 0.5 as the setpoint, and in shake flasks they have grown above 1 at 18 ˚C, but we have not tried collecting a full growth curve to see where they begin to enter stationary phase.

As for the time averaging, while this isn’t exactly what you suggested, creating a moving average of doubling times does produce a smoother line at 25 ˚C and 20 ˚C. However, there is so much variation at 18 ˚C that even the moving average line jumps around quite a bit. The problem seems to be more pronounced (by that I mean I observe large spikes in growth rate) when the OD is increasing.

[harrison]

Could you link to one of the .csv files so that I could see what the OD trace looks like?
I think that if they saturate around 1, then 0.5 is WAY too high and will be firmly within “weird behaviour” territory. my impression has always been that things start to change significantly well before you reach the point at which it is obvious that exponential growth is ending. For example at 37 degrees I have found best regularity at OD~0.1 and below – which is far less than one might “traditionally” claim as the cut off for exponential growth.

[mpatterson]

So sorry for the late reply! I would be happy to send you some data, would it be okay if I shared the file via email?

[harrison]

Yeah sure, try that!

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