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Biological energy comes from solar energy. The energy from the sun is stored and transported in plants and animals as chemical energy in the bonds between atoms in molecules. Some biological energy is stored in phosphate bonds in a molecule called ATP. ATP can release its energy in many useful ways in cells, but it is not very stable, so it is not be a good way to store energy for long periods of time. For transport through an organism, or for longer term storage, biological energy can be stored in chemical bonds between carbon atoms in more stable molecules called carbohydrates. The three main types of carbohydrates are starches, sugars and fats. Biological organisms use special molecules called enzymes to make and break chemical bonds to create, change and degrade carbohydrates. Both plants and animals have enzymes to change chemical bonds, but only plants (and some simple organisms) have the ability convert solar energy into chemical energy on their own.
Plants use solar energy to combine carbon dioxide and water into ATP and carbohydrates. These reactions occur in a special compartment in the plant cells, the chloroplast, which contains the necessary molecules and complex structures. Chlorophyll in the chloroplasts is what makes most leaves green, because it absorbs some of the visible wavelengths of light to convert into chemical energy, but reflects the green light, which we see. In the chloroplast light reacting with the chlorophyll creates an electrochemical gradient (like a battery) that is used to create ATP, which can then be used to keep the plant cell healthy or to make carbohydrates. The carbohydrates made by plants are starches and sugars, which can be stored or transported throughout the plant.
Animals eat plants and use enzymes to convert the plant starches and sugars into carbohydrates that it can store easily or into the sugar glucose that it can transport through the body. Animals store some energy as a more stable complex of many glucose molecules called glycogen. Animals also store some energy as fat, which has more energy for its weight than starches, and therefore is easier to carry around. Energy is broken down from its stored forms into glucose to be transported through the body. Inside individual cells the energy from glucose is converted into ATP, which is used for contracting muscles, and keeping cells alive and functioning properly. This conversion occurs in a special cell compartments called mitochondria. They use an electrochemical gradients to make ATP like chloroplasts do in plants, but they use the energy from carbohydrates instead of energy from the sun to generate the gradient.
Animals can only get the energy out of a plant by eating it if the animal can break down the plant energy into usable molecules. Different animals have different enzymes, which allow them to take advantage of different plant energy sources. For example, cows are able to get energy by eating grass, but humans can not. However, humans can make use of energy stored in plant matter in other ways as well. For example, fossil fuels, which were once biological organisms, and trees can be burned to release their energy as heat and light.