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. Wortmannin mTOR A steady state http://www.selleckchem.com/products/ink128.html is stable, if, for small perturbations, selleck ACY-1215 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. 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. 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. Steepness of switch effect An ultrasensitive response of a signaling system is charac terized by a low, or damped response up to a certain threshold of stimulus, followed by an abrupt increase towards maximal response when this threshold is exceeded. It has been derived to result from positive feedback or multisite modification Approximability of switch effect by Hill curve Robustness of solution It has been argued that biologically functional modules or pathways need to be robust against variations of reaction parameters and protein concentrations in order to ensure proper functioning. The concept of robustness refers to the purpose of a certain module or pathway it is expected that intracellular network structures have under gone an evolution that guarantees their proper function ing independently of precise parameter values. To transfer this concept to the question of receptor sorting into alternative pathways, we asked to what extent the functioning of the here described module depends on exact parameter or initial values. As functioning we defined the clear cut sorting of the receptor into distinct routes, namely CDE at low, respectively CDE and CIE at high ligand concentrations. The key parameter and initial concentrations that affect the strength of the switch effect are the initial concentra k cie Obviously, the ultrasensitive response will be steeper the higher the difference in binding kinetics for the respective pathways is, i. e. the greater rk. We systematically varied rk and from each thus obtained stimulus response curve of R i cie values extracted the Hill coefficient h as a measure of steepness.
The Hill coefficients varied from 2. 8 to 7. 7 as shown in Figure 6. We also computed the mean deviation between the obtained stimulus response curves and the reference Hill curve, showing that for considerable variations of rk the stimulus response curve remains approximable by a Hill curve. In Figure 8A we plotted the steady state values of Ri cde and Ri cie as a function of initial adaptor values CDE0 and CIE0. Here, R0 and EGF0 were chosen 1. 5. Consider the curve for R i cie.