You know what's absolutely impossible? A system going from chaos to order. You know what cells do? Turn a chaotic universe into organized, channeled motion, again and again and again. How can that be?
We know a few things about all physical systems. We know that, in the aggregate, they have to move from a low entropy to high entropy; we also know they have to neither create nor destroy energy. Every process has to obey these rules. It cannot spontaneously create energy, and it cannot create order from chaos.
These are rules that work perfectly in physics, but seem to make life impossible. How can any group of atoms assemble themselves into a human being, with a human being's need for the regular, controllable creation of particular molecules, channeled in one particular way, without too much chaos to screw things up? How, for that matter, does even a single cell — a group of organelles in a wash of liquid — have tiny machines that execute the functions which keep it alive?
The energy problem is solved in biology the same way it's solved in physics — if a system looks like it's producing energy, a wider look usually shows that it is getting energy from somewhere. A hydroelectric plant may seem like it's producing energy, but calculating the energy of the river that drives it will show that it produces less than it gets, and that most of the energy extra is dissipated as inefficient heat. The problem is, how does a non-sentient system channel energy?
And what about order? How do chaotic systems create order, even with a source of energy? This hasn't been completely solved, but there are a few fascinating ways that tiny "machines" in the cell wring orderly results from random motion.
One of the most well-known of the cells little machines is a protein called kinesin. If a mitochondrion needs to be moved through the goopy cytoplasm, kinesin does the moving. If a lipid needs a ride, kinesin gives it one. If the chromosomes need to shift during mitosis, in comes kinesin. This means that kinesin needs to move, which it does along long microfiber tubules. It moves along this tiny track by walking. This means that, in a moving goop of a cell, a mindless machine needs to pick up one foot, move that foot forward, plant it, then pick up and move the other foot forward as well. It needs to do this over and over, predictably enough that it can get enough work done to keep a cell alive.
The planting of the foot is the easy part. Imagine a pitted road, where you have to step carefully to keep your foot from falling into a hole or groove. It doesn't take energy to let your foot get stuck in a groove, but it takes energy to pull your foot loose from it. Let's start by looking at kinesin that way, leading foot stuck in a groove, and trailing foot in the air, ready to make a step. What we have to figure out is why it would consistently move forwards, instead of randomly walking both forward and backward.
Along comes a molecule of Adenosine triphosphate, or ATP, which provides power for the cell. Both binding with it and breaking it apart release some energy. The ATP binds to the foot that's stuck in the ground, and that energy tips the foot forward. You'll see in the image that the two feet are bound together with a coil a little bit like a spring. When the lead foot binds to the ATP, it stretches the spring slightly, causing some tension between the molecules. The trailing foot, in the rushing goop of the cell, could fall anywhere. It could fall behind the lead foot, making the molecule take a step backwards, but the tension on the coil makes it more likely to take a step forwards, becoming the new lead foot. When it comes into contact with the microtubule, it binds with it.
Before binding with the microtubule, the trailing foot releases a molecule of adenosine diphosphate, which it had been clutching. This adenosine diphosphate, or ADP, is the spent version of ATP. It's also why the original ATP molecule didn't bind with the trailing foot instead of the lead one. The ADP was already in place, keeping the ATP out. When the foot comes down, it gives the ADP up. The new lead foot is now without any kind of energy supply molecule.
The kinesin now has both "feet" on the microtubule, and has to spend energy, and lift one foot, to move. There's only one foot it can lift — the one with ATP. The ATP gets ripped apart, turned into ADP, and its energy helps lift the former lead foot off the microtubule. We are back where we came in. The kinesin has one foot down on the tube, empty, waiting for ATP, and one foot off the tube, filled with ADP, and ready to move.
Although the structure of the molecule, the structure of the microtubule, and the wash of the cytoplasm all partially explain how kinesin walks forward, the thing that brings the energy to that system is ATP. How, then, is ATP made?
The answer to that lies in enzymes. Most of the reactions — the splitting and joining together of molecules — in a cell would happen eventually, no matter what. The reactions bring the molecules to a lower energy state than they were before. But there is a problem. To start the reaction, the molecules need an influx of energy, known as activation energy. Left to their own devices, it would take them so long to get that energy that using these reactions to sustain life would be completely impossible.
Enzymes are highly-specific proteins, each with a pocket that exactly fits the molecules involved in a certain reaction. Think of an enzyme as a compressed spring. When the right molecules fit inside it, the spring goes off. This solves the problem of activation energy. Although the molecules get pressed together (or torn apart) by the enzyme, and their energy goes up, the enzyme's energy goes way down during the reaction, like a spring's energy goes down after it's released. The overall energy of the system drops at every stage.
Enzymes help wind up the machine that creates ATP. But perhaps it would be better to say the machine recreates ATP. ATP (triphosphate) gets ripped apart into ADP (disphosphate). It's recreated when the phosphate is reattached. The cell has the material. It just needs the energy.
It gets the energy from glucose. Glucose, which we consume at every meal, gets broken down into pyruvic acid, which, in turn, is broken and reorganized into a molecule called NADH. The main attraction of NADH is its willingness to part with both its hydrogen (that's what the H stands for) and a lot of its electrons. It parts with these inside the mitochondria, the powerhouses of the cell.
A mitochondrion has two cell walls, one inside the other. The NADH starts out inside both membranes, in the heart of the mitochondrion. In there, it meets with its first enzyme, which is embedded in the inner cell wall. When the NADH enters, the enzyme rips off the hydrogen, and ejects it - so the hydrogen is outside the inner cell wall, but still kept close by the outer cell wall. When the hydrogen gets ejected, it gets ejected sans electron. The electron is still at the heart of the mitochondrion. Without its electron, the hydrogen is slightly positively charged, stuck between the inner and outer wall. A succession of enzymes push more positive hydrogen ions outside the cell wall, and leave more negative electrons inside the cell wall.
There is a word for something that keeps a lot of negative charges on one side of a barrier and a lot of positive charges on the other — a battery. The cell has used enzymes to store up electrical energy. It uses that electrical energy to reattach the phosphate to ADP, turning it back into ATP. The energetic ATP is now ready to be used in another reaction anywhere in the cell.
It's always possible to take a step back. How do enzymes store up energy? How is the microtubule that kinesin walks on formed? How is kinesin itself formed? These examples aren't exhaustive, or even final, but they do show us how the cell manages to fuel and organize its internal structures, and how biology and physics come together.