The mitogen-activated protein kinase, or MAPK, pathway is a chain of proteins in the cell that relays an extracellular signal from the Ras protein to the DNA in the nucleus of the cell. This pathway consists of multiple phosphorylations as MAPKKK phosphorylates and activates MAPKK which then phosphorylates and activates MAPK. At the end of this cascade, MAPK phosphorylates various effector proteins (Alberts, 557). This signaling pathway plays an important role in cells as it results in complex changes in cell decisions and behaviors such as proliferation, differentiation, apoptosis, and quiescence from the numerous signals being taken into the cell at all times such as nutrients, growth factors, pathogens, and pressure (Mitchell, 3).
In …show more content…
To mathematically model the intracellular signaling, we created differential equations to map out the rates of each reaction in the cascades to input into the computer system (Figure 1).
We set the initial concentration of each parameter to be constant with phosphorylations (K1, K2, K3, K4, and K5) having a concentration of 0.1 and dephosphorylations (d1, d2, d3, d4, and d5) having a concentration of 0.05. We set the growth signal (S) to 1 along with the initial concentrations of variables: MAPK, MAPKK, and MAPKKK in the dual-site phosphorylation and variables: KK as and K in the single-site phosphorylation. All other variables’ initial concentrations were set at 0.
We ran MAPK activation over time in dual-site phosphorylation versus single-site phosphorylation to show the difference between the two pathways. We also ran a batch run, changing the concentration of the k-value, or the phosphorylation parameter, to compare the MAPKP to MAPKPP activation in each system at 300 seconds, when they were in their …show more content…
The single-site phosphorylation had a steep and abrupt activation without a low steady-state. This response curve achieved its steady-state after approximately 75 seconds with a final concentration of activated MAPK being over .5 (Figure 2). The dual-site phosphorylation on the other hand had a much lower slope and acted as a switch with both low and high steady-states. In this response, this pathway remained in a steady-state until approximately 25 seconds when it then increased with a smaller slope than that of the single-site phosphorylation and reached its steady state with a MAPK activation of approximately .28 at close to 250 seconds (Figure
In …show more content…
To mathematically model the intracellular signaling, we created differential equations to map out the rates of each reaction in the cascades to input into the computer system (Figure 1).
We set the initial concentration of each parameter to be constant with phosphorylations (K1, K2, K3, K4, and K5) having a concentration of 0.1 and dephosphorylations (d1, d2, d3, d4, and d5) having a concentration of 0.05. We set the growth signal (S) to 1 along with the initial concentrations of variables: MAPK, MAPKK, and MAPKKK in the dual-site phosphorylation and variables: KK as and K in the single-site phosphorylation. All other variables’ initial concentrations were set at 0.
We ran MAPK activation over time in dual-site phosphorylation versus single-site phosphorylation to show the difference between the two pathways. We also ran a batch run, changing the concentration of the k-value, or the phosphorylation parameter, to compare the MAPKP to MAPKPP activation in each system at 300 seconds, when they were in their …show more content…
The single-site phosphorylation had a steep and abrupt activation without a low steady-state. This response curve achieved its steady-state after approximately 75 seconds with a final concentration of activated MAPK being over .5 (Figure 2). The dual-site phosphorylation on the other hand had a much lower slope and acted as a switch with both low and high steady-states. In this response, this pathway remained in a steady-state until approximately 25 seconds when it then increased with a smaller slope than that of the single-site phosphorylation and reached its steady state with a MAPK activation of approximately .28 at close to 250 seconds (Figure