For a receptor-mediated signal transduction pathway to be sensitive to changes i

Question

For a receptor-mediated signal transduction pathway to be sensitive to changes in signal concentration, it is important that the magnitude of the cellular response to the signal be proportional to the extracellular concentration of signal present. In other words, an increase in the concentration of signal should stimulate a proportional increase in the cellular response. An important factor in the sensitivity of a receptor to its signal (or ligand) is the dissociation constant (Kd). For a population of receptors on a cell’s surface to respond proportionally to increases in signal concentration, the resting concentration of signal must be below the Kd of the receptor for the ligand.
Please use the following information to answer questions A through E (show your work):
Receptor A in the plasma membrane binds to ligand B with a Kd of 2.5 X 10-7 M. The resting concentration of ligand B in the extracellular space is 4.0 X 10-9 M.
Receptor X in the plasma membrane binds to ligand Y with a Kd of 3.0 X 10-8 M. The resting concentration of ligand Y in the extracellular space is the same as the Kd, 3.0 X 10-8.
A. What fraction of receptor A is bound to ligand B ([RL]/[RT]) in the resting state?
B. What fraction of receptor A is bound if the concentration of ligand B in the extracellular space increases 5-fold?
C. What fraction of receptor X is bound to ligand Y in the resting state?
D. What fraction of receptor X is bound if the concentration of ligand Y in the extracellular space increases 5-fold?
E. Please write a paragraph that uses the results of your calculations to illustrate that surface receptors will respond proportionally to increases in signal concentration only when the resting concentration of signal is below the Kd of the receptor. For a receptor-mediated signal transduction pathway to be sensitive to changes in signal concentration, it is important that the magnitude of the cellular response to the signal be proportional to the extracellular concentration of signal present. In other words, an increase in the concentration of signal should stimulate a proportional increase in the cellular response. An important factor in the sensitivity of a receptor to its signal (or ligand) is the dissociation constant (Kd). For a population of receptors on a cell’s surface to respond proportionally to increases in signal concentration, the resting concentration of signal must be below the Kd of the receptor for the ligand.
Please use the following information to answer questions A through E (show your work):
Receptor A in the plasma membrane binds to ligand B with a Kd of 2.5 X 10-7 M. The resting concentration of ligand B in the extracellular space is 4.0 X 10-9 M.
Receptor X in the plasma membrane binds to ligand Y with a Kd of 3.0 X 10-8 M. The resting concentration of ligand Y in the extracellular space is the same as the Kd, 3.0 X 10-8.
A. What fraction of receptor A is bound to ligand B ([RL]/[RT]) in the resting state?
B. What fraction of receptor A is bound if the concentration of ligand B in the extracellular space increases 5-fold?
C. What fraction of receptor X is bound to ligand Y in the resting state?
D. What fraction of receptor X is bound if the concentration of ligand Y in the extracellular space increases 5-fold?
E. Please write a paragraph that uses the results of your calculations to illustrate that surface receptors will respond proportionally to increases in signal concentration only when the resting concentration of signal is below the Kd of the receptor. For a receptor-mediated signal transduction pathway to be sensitive to changes in signal concentration, it is important that the magnitude of the cellular response to the signal be proportional to the extracellular concentration of signal present. In other words, an increase in the concentration of signal should stimulate a proportional increase in the cellular response. An important factor in the sensitivity of a receptor to its signal (or ligand) is the dissociation constant (Kd). For a population of receptors on a cell’s surface to respond proportionally to increases in signal concentration, the resting concentration of signal must be below the Kd of the receptor for the ligand.
Please use the following information to answer questions A through E (show your work):
Receptor A in the plasma membrane binds to ligand B with a Kd of 2.5 X 10-7 M. The resting concentration of ligand B in the extracellular space is 4.0 X 10-9 M.
Receptor X in the plasma membrane binds to ligand Y with a Kd of 3.0 X 10-8 M. The resting concentration of ligand Y in the extracellular space is the same as the Kd, 3.0 X 10-8.
A. What fraction of receptor A is bound to ligand B ([RL]/[RT]) in the resting state?
B. What fraction of receptor A is bound if the concentration of ligand B in the extracellular space increases 5-fold?
C. What fraction of receptor X is bound to ligand Y in the resting state?
D. What fraction of receptor X is bound if the concentration of ligand Y in the extracellular space increases 5-fold?
E. Please write a paragraph that uses the results of your calculations to illustrate that surface receptors will respond proportionally to increases in signal concentration only when the resting concentration of signal is below the Kd of the receptor. For a receptor-mediated signal transduction pathway to be sensitive to changes in signal concentration, it is important that the magnitude of the cellular response to the signal be proportional to the extracellular concentration of signal present. In other words, an increase in the concentration of signal should stimulate a proportional increase in the cellular response. An important factor in the sensitivity of a receptor to its signal (or ligand) is the dissociation constant (Kd). For a population of receptors on a cell’s surface to respond proportionally to increases in signal concentration, the resting concentration of signal must be below the Kd of the receptor for the ligand.
Please use the following information to answer questions A through E (show your work):
Receptor A in the plasma membrane binds to ligand B with a Kd of 2.5 X 10-7 M. The resting concentration of ligand B in the extracellular space is 4.0 X 10-9 M.
Receptor X in the plasma membrane binds to ligand Y with a Kd of 3.0 X 10-8 M. The resting concentration of ligand Y in the extracellular space is the same as the Kd, 3.0 X 10-8.
A. What fraction of receptor A is bound to ligand B ([RL]/[RT]) in the resting state?
B. What fraction of receptor A is bound if the concentration of ligand B in the extracellular space increases 5-fold?
C. What fraction of receptor X is bound to ligand Y in the resting state?
D. What fraction of receptor X is bound if the concentration of ligand Y in the extracellular space increases 5-fold?
E. Please write a paragraph that uses the results of your calculations to illustrate that surface receptors will respond proportionally to increases in signal concentration only when the resting concentration of signal is below the Kd of the receptor.

Explanation / Answer

According to receptor–ligand kinetics, a single ligand L binding to a single receptor R to form a single complex C

R + L ------> C

The equilibrium concentrations are related by the dissociation constant Kd

Kd = [R] [L] / [C]

Hence

A.as per question the fraction of receptor A is bound to ligand B ([RL]/[RT]) at resting stage in the resting state will be equal to

receptor bound AB / free A =[B]/ Kd = 4.0 X 10-9 M / 2.5 X 10-7 M /= 4 / 2.5 x 10-2 = 1.6 x 10-2 = 0.016

B. when 5 fold concentration of B is increased, fraction will be = receptor bound AB / free A =[B]/ Kd

= 5 x 4.0 X 10-9 M / 2.5 X 10-7 M /= 5 x 4 / 2.5 x 10-2 = 20/2.5 x 10-2 = 8 x 10-2 = 0.08

C. fraction of receptor X is bound to ligand Y at resting stage = receptor X is bound to ligand Y

XY / X = [Y] / Kd = 3.0 X 10-8 M / 3.0 X 10-8 M= 1

D. if the concentration of y is increased by five times fraction will be

XY / X = [Y] / Kd = 5 x 3.0 X 10-8 M / 3.0 X 10-8 M= 5

E. thus on the basis of above calculation it can be said that the binding of receptor increases when the concentration of ligand is increased and the receptor X {fraction = 1} is more occupied than receptor A {fraction = 0.016} by its ligand.

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