Team:Aberdeen Scotland/parameters/invest 2

Dissociation Constants Continued
Upon further investigation we have concluded that the vast majority of Kd values found in papers were inaccurately low for the following reasons:

1.	Most Kd values are measured in vitro, which gives a falsely low measurement since the conditions in the reaction (most notable being salt concentration and pressure) are completely different than in an e. coli cell. The salt concentration affects the reaction significantly since it lowers the electrostatic affinity of the protein to the operon. We know from thermodynamics that pressure and temperature will change reaction kinetics and hence the in vitro experiments will different reaction rates and hence different Kd values than the true behaviour in the cell.

2.	We have found measurements of Kd values which have been done in conditions which try to replicate in vivo conditions. These Kd values are better, but also far too low, since they do not take into account non-specific DNA binding and cell pressure.

3.	In our model, we are working in molecules per cell, instead of molarity. Upon converting the Kd values from molarity to molecules per cell we found that a great deal the Kd values we found were less than 1 molecule per cell. This implies that less than one protein (lacI, tetR etc) is needed to half the production. This is physically infeasible, the probability that one protein molecule will collide with a single operon in the cell at the correct angle is close to zero.

We consulted with Prof. Peter McGlynn of the Institute of Medical Sciences in Aberdeen, who agreed with our analysis of the Kd values and introduced the idea of non-specific DNA binding. He showed us a PhD thesis from one of his students Bryony Payne from 2006. In this thesis a far more direct and accurate measurement of the lacO repression was made. It stated that 340 tetremers of LacI was required to fully repress the lacO operon. From this value, we estimated the Kd value for the lacO operon to be 700 molecules per cell.

Our new estimations for Kd
Starting our estimation from Prof. Mcglynn’s PhD student Bryony Payne; 2006, we are given that 340 LacI tetramers completely repress a promoter. Hence roughly 120 tetramers will give half repression. Assuming the tetramers are stable this gives a value of KLacI, Kd for LacI to LacO, of 4×170 or KLacI ~ 700.

For the LacI IPTG complex formation, we estimated KIPTG ~1200 using [7] and our value of KLacI above. TetR to TetO seems to have a lower affinity to each other than LacI to LacO. However, the in vitro values suggest that TetR binds still with a strong affinity to TetR. Thus the KTetR value was roughly estimated to be up to 10 times KLacI. The in vitro values for cI to its operon seem to suggest that the in vivo KcI value is in the same order of magnitude, but possibily smaller, than KTetR.

So we now have:

KLacI = 700 molecules per cell

KcI = 7000 molecules per cell

KTetR = 7000 molecules per cell