# Chemistry Help, Equilibrium

3. Insulin resistance occurs when cells no longer bind insulin in a normal manner, thus inhibiting the cells from transporting glucose inside the cell. Without intercellular glucose the cells cannot produce energy to support life.

Let’s suppose part of your project requires you to study the equilibrium reaction between the new variation of insulin you synthesized and cell receptors on the walls of cells. This is the equilibrium expression you propose.

cell receptor + free insulin  cell receptor-insulin complex

or in abbreviated terms

R + I  R-I

You devise a method of measuring the free insulin in solution. You run two experiments under the same conditions, except one experiment uses your modified insulin and the other experiment uses normal insulin. Table 1 below provides the initial conditions of your experiment and Table 2 provides the data you collected after equilibrium was established.

Initial Conditions for both experiments – all environmental conditions are kept constant (e.g. temperature at 34oC, pressure at 1 atm, pH at 7.4). A single stock nutrient and cell receptor solution was prepared with a concentration of 70 uM. 50 mL the solution was used in all experiments. The insulins were added as powders, so the volumes essentially remained unchanged.

Table 1: Initial Experimental Conditions

Experiment 1

Experiment Control

[free modified insulin] = 100.0 uM

[free normal insulin] = 100.0 uM

[cell receptor] = 70.0 uM

[cell receptor] = 70.0 uM

Table 2: Unbound Free Modified Insulin and Unbound Free Normal Insulin Levels at Equilibrium

Experiment 1

Experimental Control

[free modified insulin] = 35.0 uM

[free normal insulin] = 50.0 uM

A. Write the equilibrium expression for this reaction using [I] to represent the insulin concentration, [R] the cell receptor concentration, and [I-R] to represent the cell receptor-insulin complex concentration. (10 pts) Show all work.

B. Determine an equilibrium constant for both the modified insulin and the normal insulin reaction at 34oC based on the data above. (10 pts)

[free modified insulin]

[receptor]

[Insulin-receptor]

I

C

E

[free normal insulin]

[receptor]

[Insulin-receptor]

I

C

E

C. Which type of insulin binds more strongly to the cell receptor? Explain your answer. (10 pts)

D. Suppose the concentration of the receptor in the stock solution dropped to 50.0 uM. If you ran the experiment again with the same initial concentration of free modified insulin as above, what would you expect the free modified insulin’s equilibrium concentration to be? (10 pts)

[free modified insulin]

[receptor]

[Insulin-receptor]

I

C

E

4. The equilibrium results on your modified insulin look promising, but it seems like it took forever for the reaction to reach equilibrium. Your supervisor now wants you to study the reaction rate for the binding of your modified insulin to the cell receptor. Show all work.

1. Using the chemical equation from Question 3 write the mathematical relationship between the rate of disappearance of free insulin and the rate of appearance of the insulin-receptor complex. (10 pts)
1. As mentioned above, you devised a method for measuring the concentration of free insulin in solution. You are able to get an estimate of the initial rate of reaction by adding a known concentration of insulin, [I]o,to a known concentration of receptor, [Ro] and then taking a measurement of the free insulin, [It], 60 seconds after mixing. From the data in Table 3 calculate the initial rate for each experiment in uM/s. Show all work. (10 pts)

Table 3: Initial rate data for insulin/receptor binding. [It] measured after 60 seconds.

[Io]

[Ro]

[It]

Initial Rate (uM/s)

Experiment 1

100 uM

70.0 uM

95.0 uM

Experiment 2

100 uM

35.0 uM

95.0 uM

Experiment 3

50.0 uM

70.0 uM

47.5 uM

1. How does the initial rate of reaction change with changing insulin concentration? How does it change with changing receptor concentration? (5 pts)
1. Write the rate law for this reaction with its correct reaction orders and calculate the rate constant. Show your calculation. (10 pts)
1. If modified insulin has a higher equilibrium constant than normal insulin does that mean the modified insulin will have a higher reaction rate than normal insulin? Explain your answer. (5 pts