Where does the cell get its energy? 

For eukaryotes, the inner mitochondrial membrane is home to energy used in cellular processes.  Let's take a look at the mitochondria.  The organization of this organelle is as follows (from outside to inside):

    |outer membrane|          intermembrane space        |inner membrane (folds are called cristae)|           matrix

Plants have both mitochondria and chloroplasts which are similar in structure and function.  Here is a summary of chloroplast structure in a "higher plant."

|outer memb|   |inner memb|  stroma (space)/grana (stacks of thylakoids found in stroma) |thylakoid memb|  thylakoid lumen
 

Note that each comparment has its own population of proteins.  How did the proteins get there?  The answer is in the protein targeting section.

Let's delve into the processes of energy transduction by locating where they occur, studying how ATP is made from their products, and looking at the cellular context of reactions. 

The capture and utilization of energy depends on reduced organic compounds (i.e., hydrocarbons).  Burning these compounds in the presence of oxygen will convert them into carbon monoxide or carbon dioxide (more oxidized states).  An increase in the number of hydrogen atoms available means an increase in the number of protons to be stripped for oxidation and chemical energy conversion.  Oxidation of a molecule of glucose to carbon dioxide and water releases 686 kcal/mol.  The conversion of ADP to ATP requires 7.3 kcal/mol.  Therefore, glucose catabolism will aid in the production of a large number of ATPs.  The two stages of glucose catabolism for aerobic organisms are glycolysis and the tricarboxylic acid (TCA) cycle, which is also known as the Krebs citric acid cycle.  Before we start with the first of these two stages lets have an overview of phosphorylation.

The process of phosphorylation (ATP synthesis) and ATP hydrolysis both involve 7.3 kcal/mol (hydrolysis is exothermic while synthesis is endothermic).  The hydrolysis of ATP is usually coupled to energy requiring processes like active ion pumps, ABC transporters, motor proteins, and polymer synthesis.

There are three types of phosphorylation:
1) substrate level phosphorylation - direct formation of ATP from transfer of P group from a substrate (the overall reaction in
        the initial slp in glycolysis is the oxidation of an aldehyde to carboxylic acid)
2) oxidative phosphorylation - transfer of P group for ATP formation by use of energy released during electron transport
        during substrate oxidation
3) photophosphorylation - transfer of P group by use of light energy

Cells can make processes happen through subtle changes in molecule conformations, lots of simple steps, and changes in energy yield.

Breaking down glucose to obtain its free energy for the capture of ATP (catabolism) is found in 2 stages (glycolysis and the TCA cycle)

Glycolysis
1) cytosolic
2) anaerobic (slp of ADP does not requires oxygen)
3) requires ATP to start (an initial energy investment of 2 ATP are required for future profits... welcome to the glucose
        oxidation business!)
4) generates 2 molecules of ATP by substrate level phosphorylation per molecule of glyceraldehyde 3-phosphate
        oxidized to pyruvate (generates 4 molecules of ATP per glucose molecule oxidized to pyruvate since glucose molecules produces 2 molecules of glyceraldehyde 3-phosphate)  [our investment of 2 ATP brings us to a net gain of 2 ATP]
5) stores energy as "reducing power"

Pyruvate and NADH are produced...

-lack of oxygen leads to fermentation in the cytosol
-the presence of oxygen allows for its movement into the matrix.  The Krebs (TCA) citric acid cycle is introduced.  This aerobic process allows for large amounts of energy to be extracted from the products of glycolysis.  The pyruvate is decarboxylated in the matrix to form an acetyl group that is transferred to coenzyme A to produce acetyl CoA (all of this is catalyzed by pyruvate dehydrogenase).  Acetyl CoA is put into the TCA cycle, and the summary is found below.

Oxidation of pyruvate/Krebs citric acid cycle
1) matrix
2) aerobic
3) generates ATP by substrate level phosphorylation
4) generates lots of "reducting power" (5 pairs of electrons from the hydrogen atoms of 4 NADH's and a FADH₂)
5) by product: CO₂

So how does this "reducing power" lead to ATP synthesis?
    The NADH or FADH₂ electrons are transferred to NAD⁺ or FAD and then passed down the electron-transport chain in the inner mitochondrial membrane for ATP production.  The final acceptor for electrons is O₂ which is reduced to water.
    The passage of electrons creates conformational changes in electron carriers.  This moves protons outward across the inner mitochondrial membrane.  A proton gradient is established now.
    The controlled movement of protons back across the membrane through an ATP-synthesized enzyme provides the energy required to phosphorylate ADP to ATP.
   Mitochondria can extract energy from organic materials and store it in the form of electrical energy.  The ionic gradient formed across the inner mitochondrial membrane is harnessed for ATP synthesis.
    Each pair of electrons from NADH to oxygen through the electron transport chain leads to the formation of about 3 ATP molecules.  FADH₂ leads to 2 ATP molecules.  We will look at the electron transport chain a little bit more below...

Electron Transport Chain
The reducible carrier NADH throws electrons into the chain by complex I.  FADH₂ passes electrons from succinate dehydrogenase via complex II.  The free energy released as electrons are passed from successive carriers at coupling sites is conserved by translocation of protons from the matrix across the inner membrane into intermembrane space.  This translocation of protons establishes the proton gradient that drives ATP synthesis by oxidative phosphorylation.  Notice that there is now a greater hydrogen ion concentration and positive charge in the intermembrane space.  The energy of the electrochemical gradient can be viewed as a proton motive force, which is maintained by inner membrane impermeability.   Peter Mitchell (University of Edinburgh) explained that intact mitochondrial membranes are required for ATP synthesis.  The reason is that these membranes allow for charge separation.

Now let's see how the energy from the proton electrochemical gradient drives the phosphorylation of ADP.

The Machinery for ATP Formation (CLICK HERE to check out some cool animation of ATP)
The ATP-synthesizing enzyme, class F ATP synthase, a mushroom-shaped protein complex is composed of two parts: the spherical F₁ head and a basal section (F₀) that is embedded in the inner membrane.  In the inner surface of cristae membranes, are the spheres called coupling factor 1 (F₁) that behave like ATPases.  The F class ATPase's 2 major complex subunits have the following characteristics.

F₀ complex - transmembrane protein complex (proton channel for movement from intermembrane space to the matrix)
F₁ complex - soluble, for catalytic activity

After dissociation of the subunits, the remaining F₁ complex will initiate hydrolysis of ATP.  The combination of both subunits leads to synthesis of ATP.  The three beta subunits on the F₁ head are catalytic sites that bind and affect one another.  The gamma subunit goes from the outer tip of the F₁ head through the central stalk and makes contact with the F₀ basepiece.

Behold... Paul Boyer's (UCLA) 1979 "binding change mechanism" hypothesis.
1.)  Energy released by proton movement is not directly used to phosphorylate ADP.  Instead, it changes the binding affinity of the active site for the ATP product.  In other words, 7.3 kcal/mol is not needed to bind an inorganic phosphate (P_i) with ADP to make ATP when these components are enzyme-bound (they will do so spontaneously), but the energy will be needed for release of the tightly bound product from the catalytic site.
2.)  Each active site moves through 3 distinct conformations that have different affinities for ATP hydrolysis and synthesis.  The F₁ complex has a catalytic site on each of the 3 beta subunits (ADP and P_i loosely bound, tightly bound, and open).
3.)  ATP is synthesized by rotational catalysis in which one part of the ATP synthase rotates relative to another part.  Sequencial changes in conformation of each of the catalytic sites result from the relative rotation of the alpha and beta subunits of the F₁ head.  This rotational catalysis is driven by movement of protons through the membrane via the F₀ base channel.

Boyer's hypothesis was greatly supported by Masasuke Yoshida and colleagues at Tokyo Institute of Technology and Keio University in Japan when they modified the beta subunit of an ATP synthase so that it would contain 10 histidine residues.  Histidine binded with Ni-NTA (used to coat the coverslip).  The gamma subunit was modified by replacing a serine residue with a cysteine residue.  Here an fluorescently labeled actin filament was attached.  With ATP, the actin filament was observed to rotate counterclockwise less than 4 cycles per second when viewed from the membrane side.

Glucose is the source of electron flow to oxygen to make water in the substrate-level/oxidative processes of phosphorylation in glycolysis, the TCA cycle, and the electron-transfer chain.  In the reverse, photosynthesis in plants uses water for the electron flow to carbon dioxide to make glucose.  This is a light dependent reaction that involves many subunits of a chloroplast including P680 and P700, the reaction centers.  Photosystem II (P680) gets electrons from water.  After the whole electron-transport chain thing, photosystem I (P700) boosts the electrons to an energy level above NADP⁺.  The end result is reducing power in the form of a proton gradient for the thylakoid membrane (higher proton concentration in the lumen than the stroma).  The ATP and NADPH from this process are used in the Calvin cycle (in the stroma) to create RuBP as the initial acceptor of carbon dioxide.

Remember: In mitochondria, proton concentration is higher in the intermembrane space than in the matrix.
                  In chloroplasts, proton concentration is higher in the thylakoid lumen than in the stroma.