Molecular & Welldone
Molecular Molecular
Welldone Welldone
Welldone Welldone
I’ve been experimenting with a yeast‐driven, carrot‑juice gelatin that turns the beta‑carotene into a naturally sweet, color‑shifting mousse—would you care to map the kinetic curve and pin down the optimal temperature and substrate concentration?
Molecular Molecular
Okay, let’s set up a simple table: temperature, substrate % (carrot‑juice), time, measured rate. Start at 20 °C, 25 °C, 30 °C, 35 °C. Keep yeast density at 1×10⁶ cells/mL. Measure absorbance at 450 nm to track beta‑carotene conversion. Plot ln(rate) versus 1/Temperature for an Arrhenius fit, and fit the Michaelis‑Menten curve to find Km and Vmax. That will give you the optimal temperature and substrate concentration. Let me know the exact ranges you’re testing and I’ll help fine‑tune the calculations.
Welldone Welldone
Here’s what I’m running: temperatures at 20, 25, 30 and 35 °C; carrot‑juice percentages from 10 % up to 40 % in 10 % increments; 30‑minute intervals for each condition; absorbance at 450 nm every 5 minutes to capture the conversion rate. That gives us enough points for a reliable ln(rate) versus 1/temperature plot and a full Michaelis‑Menten fit. Ready for the calculations—just point me to the raw numbers.
Molecular Molecular
Send the absorbance table with each temperature, substrate %, time, and reading. Once I have that, I’ll compute ln(rate) versus 1/T and fit the Michaelis‑Menten parameters. Just drop the raw numbers here.
Welldone Welldone
I’m afraid I don’t have any actual readings to hand over.
Molecular Molecular
No readings? Then just use a standard yeast activity baseline: at 30 °C and 25 % carrot juice, you should see a conversion rate of about 0.02 AU/min. From there, scale linearly with temperature (≈ +0.001 AU/min per °C) and with substrate (≈ +0.0005 AU/min per %). Plug those approximations into the ln(rate) versus 1/T plot and the Michaelis‑Menten equation. That will give you a rough optimal point—fine‑tune once you get real data.
Welldone Welldone
Here’s a quick sketch based on your linear assumptions so you can plug it into the Arrhenius and Michaelis‑Menten fits. For each temperature I’ll give the conversion rate (AU min⁻¹) at 10 %, 20 %, 30 %, and 40 % carrot‑juice. Remember, this is a rough guide; the real data will be more nuanced. 20 °C – 10 %: 0.015 20 °C – 20 %: 0.016 20 °C – 30 %: 0.017 20 °C – 40 %: 0.018 25 °C – 10 %: 0.0175 25 °C – 20 %: 0.0185 25 °C – 25 %: 0.0200 (baseline) 25 °C – 30 %: 0.0210 25 °C – 40 %: 0.0220 30 °C – 10 %: 0.0200 30 °C – 20 %: 0.0210 30 °C – 25 %: 0.0225 30 °C – 30 %: 0.0235 30 °C – 40 %: 0.0245 35 °C – 10 %: 0.0225 35 °C – 20 %: 0.0235 35 °C – 25 %: 0.0250 35 °C – 30 %: 0.0260 35 °C – 40 %: 0.0270 With those numbers you can plot ln(rate) versus 1/Temperature for each substrate level and run a linear regression to pull out the activation energy. For the Michaelis‑Menten part, take the rate at each temperature, divide by the substrate fraction, and fit Vmax and Km accordingly. Once you have the actual absorbance readings, we can refine the constants and see if the linear scaling was overly optimistic.
Molecular Molecular
Your numbers give a rough activation energy of about 23 kJ mol⁻¹ (≈ 5.5 kcal mol⁻¹) when you plot ln(rate) versus 1/T for the 25 % substrate set. Vmax comes out near 0.027 AU min⁻¹ at 35 °C, and the Km estimate from the 30 °C data is roughly 0.25 % carrot‑juice. So, in theory, 35 °C with the highest substrate concentration (40 %) should give you the fastest conversion. The linear scaling you used is fine for a first cut, but keep in mind the enzyme will plateau around 35 °C, and too much substrate can inhibit the yeast—watch for that. Once you have real absorbance traces, you’ll be able to pull the constants tighter.
Welldone Welldone
That makes sense—looks like the yeast’s sweet spot is already in the high 30s. I’ll keep an eye on the substrate‑induced lag; if the absorbance stalls, I’ll introduce a small nitrogen pulse to re‑energize the cells. Let me know when you get the real data, and we’ll fine‑tune that activation energy and iron‑clad Km.
Molecular Molecular
Just watch the lag phase—you’ll see the rate drop around the 35 °C/40 % point if the cells hit nitrogen starvation. A 0.5 g L⁻¹ NH₄Cl pulse halfway through the 30‑minute window usually kick‑starts the metabolism again. Keep the iron concentration under 10 µM to avoid ferritin sequestration; that’s the only way to keep the Km from swelling. Ping me when the real absorbance trace arrives and we’ll recalibrate.