The cDNA was subjected to RT PCR amplification using gene specific primers and 2 Brilliant II Sybr Green QPCR Mastermix
Applying these derived conditions on the initial values, we can also show that the steady states are stable. selleckbio A steady state useful handbook is stable, if, for small perturbations, necessary the sys tem returns to this steady state. CIE and CDE are not clearly defined in this case, but according to the condi tions on the initial values we derived, we know that R0 CDE0 CIE0. This means that in steady state, at least one of the two adaptor variables must be greater than zero, i. e. 0 R CDE CIE. If we apply a sufficiently small per turbation to the system, and set the obtained value as the new start vector, this last inequality will still hold due to the continuity of the functions. According to the condi tions on initial values we derived in the previous para graph, the system will tend back to R 0 and R EGF 0. Hence we showed stability of steady state class I. An analogous argument can be used to show stability of steady state class II. In it was reported that for high ligand concentrations the activated receptor is equally partitioned between CDE and CIE. Assuming similar initial abundance levels of adaptors, our simulations show that this is the case for ini tial receptor levels higher than the sum of both initial adaptor values. We thus hypothesize that in cells, where the steady state levels of internalized receptors via CIE and CDE are similar, the amount of. Ultrasensitivity has also been shown to arise in modification cycles if the enzymes operate near saturation, which makes the mechanism very sensitive to small parameter changes, if the abun dance levels of unmodified substrate and enzyme are suf ficiently high or if the enzyme is inhibited. To characterize the steepness of the here discussed mech anism, we compared its response to a Hill type reaction. Figure 5 shows the reaction velocity V of the Hill formula, compared to R i cie production in our model as a function of EGF stimulation.
To generate the stimulus response curve, we chose the same parameter set as for Fig. 3C as a reference. From this curve we extracted the Hill coefficienth, Vmax and Km to compute the corresponding Hill curve, which will be used as a reference curve later on. The Hill coef fcient is a measure of how much the input has to be increased in order to raise the response from 10% to 90% of its maximal value. Stimulus response curves with Hill coefficients of 5 or higher are generally considered ultrasensitive. The Hill coefficient obtained for the stimulus response curve shown in Figure 5 is 7. 5. receptors exceeds the capacity of both pathways. In this case, treatment of the cells with low vs high EGF stimula tions, corresponds to a transition of the system between steady state classes I and II.