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Chapter 16: Problem 10

Use the equations of Chapter 9 to determine the free energy difference represented by a \(\mathrm{Ca}^{2+}\) gradient across the sarcoplasmic reticulum membrane if the luminal (inside) concentration of \(\mathrm{Ca}^{2+}\) is \(1 \mathrm{m} M\) and the concentration of \(\mathrm{Ca}^{2+}\) in the solution bathing the muscle fibers is \(1 \mu M\).

Short Answer

Expert verified
To find the free energy difference, one must convert the ion concentrations to the same unit (M), substitute into the Nernst equation and perform the mathematical calculations. The final answer will depend on the mathematical computation mentioned in step 3.

Step by step solution

01

Conversion of Concentration Units

To facilitate calculations, it is necessary to convert both concentrations to the same unit. Hence, ion concentrations should both be in M (Molar). So, the luminal concentration is \(1 mM = 1 \times 10^{-3} M\) and the concentration in the solution bathing the muscle fibers is \(1 \mu M = 1 \times 10^{-6} M\).
02

Use Nernst Equation

The Nernst equation allows one to calculate the electrochemical potential difference (which equates to the free energy difference in this case) across a membrane due to a single ion species. Here, in its simplified form, assuming temperature is at body temperature (approximately 37°C or 310 K), the equation is: \[\Delta G = R \times T \times z \times ln \left( \frac{[Ion]_{outside}}{[Ion]_{inside}} \right) \] where \(R\) is the gas constant (8.314 J/mol K), \(T\) is the absolute temperature (310 K, in this case), \(z\) is the ion charge (+2 for \(\mathrm{Ca}^{2+}\) ions), [Ion]_{outside} and [Ion]_{inside} are the outside and inside ion concentrations respectively.
03

Calculate Free Energy Difference

Substitute the known values into the equation: \[\Delta G = 8.314 J/mol K \times 310 K \times 2 \times ln \left( \frac{10^{-6} M}{10^{-3} M} \right) \] Calculate to obtain the free energy difference. Remember to keep track of units!

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Most popular questions from this chapter

When an action potential (nerve impulse) arrives at a muscle membrane (sarcolemma), in what order do the following events occur? a. Release of \(\mathrm{Ca}^{2+}\) ions from the sarcoplasmic reticulum b. Hydrolysis of ATP, with release of energy c. Detachment of myosin from actin d. Sliding of myosin along actin filament e. Opening of switch 1 and switch 2 on myosin head

ATP stores in muscle are augmented or supplemented by stores of phosphocreatine. During periods of contraction, phosphocreatine is hydrolyzed to drive the synthesis of needed ATP in the creatine kinase reaction: Phosphocreatine \(+\mathrm{ADP} \longrightarrow\) creatine \(+\mathrm{ATP}\) Muscle cells contain two different isozymes of creatine kinase, one in the mitochondria and one in the sarcoplasm. Explain.

In which of the following tissues would you expect to find smooth muscle? a. Arteries b. Stomach c. Urinary bladder d. Diaphragm e. Uterus f. The gums in your mouth

An ATP analog, \(\beta, \gamma\) -methylene-ATP, in which a \(-\mathrm{CH}_{2}-\) group replaces the oxygen atom between the \(\beta\) - and \(\gamma\) -phosphorus atoms, is a potent inhibitor of muscle contraction. At which step in the contraction cycle would you expect \(\beta, \gamma\) -methylene-ATP to block contraction?

When athletes overexert themselves on hot days, they often suffer immobility from painful muscle cramps. Which of the following is a reasonable hypothesis to explain such cramps? a. Muscle cells do not have enough ATP for normal muscle relaxation. b. Excessive sweating has affected the salt balance within the muscles. c. Prolonged contractions have temporarily interrupted blood flow to parts of the muscle. d. All of the above.
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