## Energy Efficiency

### Biochemical Engineering

The following reaction represents the "burning" of glucose.
```     C6H12O6 + 6 O2 ----> 6 CO2 + 6 H2O     DHo=-686 kcal/mole
```
The free-energy change of the above reaction is -686 kcal/mol glucose under standard conditions. Hydrolysis reaction of ATP to ADP
```     ATP + H2O ----> ADP + Pi             DHo=-7.3 kcal/mole
```
under standard conditions has a free-energy change of -7.3 kcal/mol. How may moles of ATP are generated per mole of glucose metabolized via glycolysis/fermentation (without oxygen)? In the presence of oxygen, cells can continue with oxidative phosphorylation to generate more ATP. With oxygen to convert glucose to carbon dioxide, how many moles of ATP are generated for each mole of glucose metabolized? Based on these numbers, calculate and compare the energy efficiencies of the glycolysis/fermentation pathway and the oxidative phosphorylation pathway. Here we define energy efficiency to be the ratio of the amount of energy recovered in ATP over that potentially achievable by burning glucose under standard conditions. Do you expect the actual energy efficiency to be higher or lower in living organisms? Why?

Solution:

Energy recovered from glucose metabolism in the absence/presence of oxygen.

```    Presence of Oxygen                        ATP   Energy Efficiency
-----------------------------------------------------------------------
Without oxygen (Glycolysis)                 2   (7.3* 2)/686= 2%
With oxygen (Glycolysis+TCA+Respiration)   36   (7.3*36)/686=38%
```
Note that you cannot jump to TCA without going through glycolysis first to generate pyruvate. Likewise, you need glycolysis and TCA to generate NADH and FADH for oxidative phosphorylation. The baseline for comparision is the amount of energy recovered from each mole of glucose. The actual efficiency in living organisms is higher because reactions proceed in non-standard conditions (e.g., less than 1M, other temprature.)

At intracellular conditions, the free energy is about -13 kcal/mole of phosphate bond. Re-working with this number gives higher energy efficiencies.

```    Presence of Oxygen                        ATP   Energy Efficiency
-----------------------------------------------------------------------
Without oxygen (Glycolysis)                 2   (13* 2)/686= 4%
With oxygen (Glycolysis+TCA+Respiration)   36   (13*36)/686=68%
```