The factors governing energy production in muscle are important in understanding the response of the — Analytical Chemistry Chemistry Question
Creatine kinase
The factors governing energy production in muscle are important in understanding the response of the body to exercise and also in the determination of the physiological effect of cardiac and muscular diseases.
Cells use adenosine triphosphate (ATP) as the molecular energy currency; the hydrolysis of ATP to adenosine diphosphate (ADP) is often coupled with other chemical reactions.
Biochemistry textbooks often represent this reaction as:
[VISUAL]
In order to simplify free-energy calculations for biochemical reactions the standard free-energy change at pH 7.0, typically denoted ∆rG°′, is used. The equilibrium constant at pH 7.0 is denoted K′. For the ATP hydrolysis reaction the relation between ∆rG′ and the concentration of species present will therefore be:
∆rG′ = ∆rG°′ + RT ln ([ADP][P_i]/[ATP])
At 37 °C the value of K′ for the hydrolysis of ATP to ADP is 138000.
One hypothesis for exhaustion after exercise is that an increase in the concentration of ADP relative to ATP could occur, leading to an increase in the value of ∆rG′ for ATP hydrolysis below that required for normal cellular metabolism.
The in vivo concentration of ATP and Pi can be measured using 31P NMR. Unfortunately the concentration of ADP is too low to be measured using 31P NMR. Instead the concentration of ADP has to be determined indirectly from the 31P NMR measured concentration of phosphocreatine and the value of K′ for the enzyme creatine kinase. Creatine kinase catalyses the reaction:
creatine + ATP ⇌ ADP + phosphocreatine + H+
To a good approximation this reaction is at equilibrium in the cell with a K′ value of 0.006. It is also known that ( + ) is maintained at 42.5×10–3 mol dm–3 in the cell.
The 31P NMR spectrum of a forearm muscle was measured in volunteers after a period of rest and after two different intensities of exercise (squeezing a rubber ball). These spectra were used to calculate the concentration of the following phosphorus species:
| Condition | [Phosphocreatine] (mol dm–3) | [ATP] (mol dm–3) | [Pi] (mol dm–3) |
| :--- | :--- | :--- | :--- |
| At rest | 38.2×10–3 | 8.2×10–3 | 4.0×10–3 |
| Light exercise | 20.0×10–3 | 8.5×10–3 | 22×10–3 |
| Heavy exercise | 10.0×10–3 | 7.7×10–3 | 35×10–3 |
Assuming that the pH of the cell remains constant at pH 7.0 during exercise:
A solution of ATP (c = 10 mmol dm-3) is prepared in a solution buffered at pH 7.0 at 37 °C. What are the concentrations of ATP, ADP and Pi at equilibrium?
Model Answer
Let n0 be the initial number of moles of ATP and x the number of moles of ATP that have reacted at equilibrium to form ADP and Pi.
ATP ⇌ ADP + Pi
Initial: n0, 0, 0 (Total = n0)
Equilibrium: n0 – x, x, x (Total = n0 + x)
Therefore:
[VISUAL]
Which rearranges to give:
[VISUAL]
Hence:
[ADP] = [Pi] = 9.99996377×10–3 mol dm–3
[ATP] = 3.62×10–8 mol dm–3
What is the value of ∆rG°′ at 37 °C?
Model Answer
–30.503 kJ mol–1.
Calculate the concentration of ADP present under each of the three conditions.
Model Answer
In order to calculate the [ADP], the is first calculated from the measured in the 31P NMR spectrum and the total concentration of creatine and phosphocreatine in the cell ( + = 42.5×10–3 mol dm–3).
The equilibrium constant for the creatine kinase reaction (K' = 0.006) is then used in conjunction with , [ATP] and to determine [ADP]:
- At rest:
= 3.82×10–2 mol dm–3
[ATP] = 8.20×10–3 mol dm–3
= 4.30×10–3 mol dm–3
[ADP] = 5.54×10–6 mol dm–3
- Light exercise:
= 2.00×10–2 mol dm–3
[ATP] = 8.50×10–3 mol dm–3
= 2.25×10–2 mol dm–3
[ADP] = 5.74×10–5 mol dm–3
- Heavy exercise:
= 1.00×10–2 mol dm–3
[ATP] = 7.70×10–3 mol dm–3
= 3.25×10–2 mol dm–3
[ADP] = 1.50×10–4 mol dm–3
Calculate the value of ∆rG′ for the hydrolysis of ATP under each of the three conditions.
Model Answer
Using the calculated concentrations from part 29.3 and the value of ∆rG°′ = –30.503 kJ mol–1 calculated in part 29.2, ∆rG′(ATP) is determined as follows:
- At rest:
∆rG′(ATP) = –63.5 kJ mol–1
- Light exercise:
∆rG′(ATP) = –53.2 kJ mol–1
- Heavy exercise:
∆rG′(ATP) = –49.3 kJ mol–1
Comment on whether these data support the hypothesis that exhaustion after exercise arises from an increase in the value of ∆rG′ for ATP hydrolysis.
Model Answer
The data show an increase (the value becomes less negative) in the value of ∆rG′(ATP) when subjects undertake both light and heavy exercise, and the increase is greater after heavy exercise, which would appear to support the hypothesis. However, the increase in ∆rG′(ATP) is similar for both intensities of exercise, and in both cases the value of ∆rG′(ATP) remains large and negative, so it is difficult to draw a firm conclusion from this limited data set. In fact, in the cell there is a large pH change after exercise and when this is taken into account, the values of ∆rG′(ATP) are within error after both light and heavy exercise. Further experiments suggest that the rate of recovery of the concentration of metabolites such as creatine to resting levels plays an important role in exercise-induced exhaustion.