When your cells metabolize sugar to get energy, they start by using glycolysis, a pathway that breaks glucose molecules down into pyruvate. As long as oxygen is available, they follow up with cellular respiration, which oxidizes the pyruvate to carbon dioxide and water while releasing still more energy. Glycolysis and aerobic cellular respiration differ in terms of the location in the cell where they take place, the amount of energy they release, the chemistry of each pathway and the inputs and outputs of each.
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Glycolysis takes place in the cytosol, the fluid that fills the cell. Cellular respiration, by contrast, takes place in the mitochondria, small structures enclosed by membranes and floating around in the cytosol. Glucose is the main input for glycolysis; cellular respiration, by contrast, depends primarily on pyruvate from glycolysis, although acetyl-CoA from the breakdown of fatty acids is another important input. Your liver also breaks down amino acids to yield pyruvate, oxaloacetate, fumarate and other compounds that it can feed into cellular respiration or alternatively use to make glucose.
Cells in your body can always perform glycolysis, but to carry out cellular respiration they need oxygen. Oxidation of glucose through glycolysis is incomplete; most of the energy in the original glucose molecule remains untapped in the pyruvate released at the end of the process. Glycolysis by itself produces a mere net gain of two ATP (molecules the cell uses to store energy). Depending on the cell type, aerobic respiration can yield a net gain of 30 or 32 ATP.
The steps involved in these pathways and the enzymes that catalyze each reaction are, of course, quite different. Glycolysis is a ten-step pathway, while cellular respiration involves several pathways, the most prominent of which are the electron transport chain and the citric acid cycle. The electron transport chain is especially distinctive, because it uses electron transfers to pump hydrogen ions across a membrane, building a concentration gradient that another enzyme called ATP synthase can use to make ATP.
Some tissues, like your muscle cells, prefer aerobic respiration but can get by on glycolysis alone for a while if need be. Other tissues, like the liver and brain, can't do without cellular respiration and carry it out continually. Glycolysis and cellular respiration also produce outputs that play different roles in a variety of other metabolic pathways. The citric acid cycle is especially important in this regard; it acts as a kind of metabolic hub in the cell. Succinyl-CoA, for example, is a citric acid cycle intermediate that serves as a precursor for the synthesis of porphyrins, while alpha-ketoglutarate is the immediate precursor for the amino acid glutamate. Certain intermediates in glycolysis also play alternate roles in metabolism; glucose 6-phosphate, for example, can be used to make ribose 5-phosphate via the pentose phosphate pathway.