Use the images obtained in the lab or the ones attached and quantify the fluorescence fold change between treatments. Discuss the functionality of the lacI protein in reference to this experiment a the genetic circuit used.

We can observe a clear increase in fluorescence intensity as the concentration of what appears to be IPTG increases from NTC (no treatment control) through 0X, 0.2X, 0.4X, 0.8X to the positive control. This demonstrates the dose-dependent response of the genetic circuit to the inducer.

The LacI protein functions as a repressor that regulates gene expression in the lac operon system. In this experiment, we observe its regulatory role through the following mechanism:

1. In the absence of inducer (NTC, 0X samples), the LacI repressor binds to the operator region of the lac operon, preventing RNA polymerase from transcribing the downstream genes, including the fluorescent reporter gene.
2. LacI operates through a helix-turn-helix motif in its DNA-binding domain, binding specifically to the major groove of the operator region, with additional contacts made by "hinge" helices that bind to the minor groove.
3. As IPTG concentration increases (0.2X, 0.4X, 0.8X), it binds to the LacI repressor and causes an allosteric change in its conformation. This conformational change prevents LacI from binding to the operator site.
4. When LacI detaches from the operator, RNA polymerase can bind to the promoter and transcribe the downstream genes, leading to the expression of the fluorescent protein and the observed increase in fluorescence.

The dose-dependent response seen in the image demonstrates the titration of the LacI repressor system - at low IPTG concentrations, only some repressor molecules are inactivated, while at higher concentrations, most repressors are bound by IPTG, leading to maximal gene expression and fluorescence.

What we should expect if the induction was made inside of a bacteria like E.coli BL21 DE3?

If this induction experiment was performed in E. coli BL21(DE3), we would expect a similar but potentially amplified response due to the specific genetic characteristics of this strain:

1. BL21(DE3) contains the λDE3 lysogen, which carries the gene for T7 RNA polymerase under the control of the lacUV5 promoter.
2. In the absence of IPTG, the lacUV5 promoter is repressed by endogenous LacI, preventing T7 RNA polymerase expression.
3. When IPTG is added:
   • It binds to LacI, causing conformational changes that prevent LacI from binding to the operator
   • This allows transcription of the T7 RNA polymerase gene
   • The T7 RNA polymerase then transcribes genes under T7 promoter control
4. If our fluorescent reporter gene is under T7 promoter control, we would observe:
   • A potentially stronger fluorescence signal due to the high activity of T7 RNA polymerase
   • Possibly faster induction kinetics
   • A similar dose-dependent response pattern as observed in the image
5. Due to the efficiency of the T7 expression system, we might observe some basal expression even without induction (leaky expression), especially if the gene product is not toxic to the cells.

The experimental design using BL21(DE3) would likely require optimization of IPTG concentration and induction time, with recommended concentrations around 0.5 mM IPTG and induction periods of 2-3 hours at 37°C for optimal expression.