Place yourself in a bumper car at a carnival waiting to bump into your friends. Soon enough you hear the small engine of your bumper car start and you begin to move around, bumping into anyone in your way. While the motion of your car is mostly controlled by the steering wheel, random events—like fluctuations in the motor power, your car hitting small bumps on the floor, and other cars hitting you—can affect the motion as well. What if I told you that a cell and its parts function in a similar way? Just as your car is powered by electricity, molecular motors—bio-molecules that can convert chemical energy into mechanical work—power the movement of living organisms by generating forces. In order to produce these forces, molecular motors depend on an organic molecule called ATP.
Have you ever seen those wide shapes moving in the sky at dawn, made of thousands of starlings, or the swarms of fish swimming in the ocean (see Figure 1)? The ability to organize and move in groups without a leader is called collective motion and has been observed at various spatial scales in the living world, from birds to locusts, cells, and bacteria.
The difference between a bacterium and a whale are huge, and not just their size. However, there are hidden scaling laws underlying all living things. These scaling laws are found to be due to the fractal-like nutrient distribution systems. Here, we review how to derive the scaling law for metabolic rate with organism mass, illustrating its generality and ubiquity.