What life is: cells and the cell theory

Every living thing you have ever seen, from the moss on a rock to the person sitting next to you, is built from cells. A bacterium is a single cell. A human body is roughly 30 trillion of them, plus a comparable number of bacterial cells living on and inside it. Introduction to Cell Biology is about those units: what they are made of, how they are organized, how they capture and spend energy, how they talk to each other, and how they make more of themselves. It is the first course in the Biology and Biochemistry programs, and the ideas here return in genetics (BIOL-201), molecular biology (BIOL-207), cell biology in depth (BIOL-214), microbiology (BIOL-330) and metabolism (BIOC-330 and BIOC-331).

The course assumes no previous biology beyond high school, and only basic chemistry. Where we need a chemical idea, such as a hydrogen bond or a pH value, lesson 2 or 3 introduces it. Where we need arithmetic, the worked examples show each step, and short Python programs let you check the numbers and try your own. You do not need to be a programmer; the code is there to make calculations visible and repeatable, the way a lab notebook makes an experiment repeatable.

What counts as alive?

Biologists have never agreed on a one-line definition of life, but they agree on a list of properties that living things share. No single property is enough on its own: fire grows and consumes energy, crystals reproduce their structure, and a computer virus copies itself. It is the combination that marks life.

Viruses are the classic borderline case. A virus particle has genetic material and a protein coat, and it evolves, but it has no metabolism of its own and can only reproduce inside a host cell, using the host's machinery. Most biologists therefore treat viruses as non-living, or as on the edge of life, and they do not count as cells. You will meet them again in microbiology (BIOL-330) and immunology (BIOL-380).

The cell theory and how it was built

The idea that all living things are made of cells is so familiar that it is easy to forget it had to be discovered, and that the discovery depended on technology. Cells are mostly between 1 and 100 micrometers across, below what the eye can see (about 100 micrometers at best). Until lenses improved, nobody could see them.

In 1665 the English scientist Robert Hooke looked at a thin slice of cork through an early compound microscope and saw a honeycomb of small empty boxes. He called them cells, after the small rooms monks lived in. What he saw were the walls of dead plant cells. A few years later the Dutch draper Antonie van Leeuwenhoek, grinding his own small, powerful single lenses, saw living, moving single-celled organisms in pond water and scrapings from his teeth, which he called animalcules.

It took another 170 years for the observations to become a general theory. In 1838 the botanist Matthias Schleiden concluded that all plants are made of cells, and in 1839 the zoologist Theodor Schwann extended the claim to animals. In 1855 the physician Rudolf Virchow popularized the third part, often quoted in Latin as omnis cellula e cellula: every cell arises from a pre-existing cell. (Virchow drew on the work of Robert Remak, who had shown cell division in embryos but received less credit at the time.)

The modern cell theory has three classic statements, plus refinements added in the twentieth century:

The third statement settled an old debate. For centuries people believed in spontaneous generation: that maggots arose from rotting meat or microbes from broth. Experiments by Francesco Redi (1668) and, decisively, Louis Pasteur (1859–1862) showed that when broth is boiled and protected from airborne particles, nothing grows. Life comes from life. (How the very first cells arose, about 3.5 to 4 billion years ago, is a separate scientific question about chemistry on the early Earth; the cell theory describes life since then.)

Why are cells so small? Surface area and volume

Cells are small for a physical reason. A cell exchanges nutrients, oxygen and wastes through its surface, but it consumes them throughout its volume. As a cell gets bigger, its volume grows faster than its surface area, so each unit of volume is served by less membrane.

For a cube of side \(s\), the surface area is \(6s^2\) and the volume is \(s^3\), so the ratio of surface area to volume is \(6/s\). For a sphere of radius \(r\), the area is \(4\pi r^2\) and the volume is \(\frac{4}{3}\pi r^3\), giving a ratio of \(3/r\). Either way, doubling the size halves the ratio.

import math
# Surface area to volume ratio of spherical cells of different diameters
for d_um in [1, 2, 10, 20, 100]:
    r = d_um / 2
    area = 4 * math.pi * r**2            # um^2
    vol = (4/3) * math.pi * r**3          # um^3
    print(f"diameter {d_um:>3} um: area {area:9.1f} um^2, volume {vol:11.1f} um^3, SA:V {area/vol:5.2f} per um")

diameter   1 um: area       3.1 um^2, volume         0.5 um^3, SA:V  6.00 per um
diameter   2 um: area      12.6 um^2, volume         4.2 um^3, SA:V  3.00 per um
diameter  10 um: area     314.2 um^2, volume       523.6 um^3, SA:V  0.60 per um
diameter  20 um: area    1256.6 um^2, volume      4188.8 um^3, SA:V  0.30 per um
diameter 100 um: area   31415.9 um^2, volume    523598.8 um^3, SA:V  0.06 per um

A bacterium 1 micrometer across has six units of membrane for every unit of volume; a 100-micrometer cell has only 0.06. Large cells cope in several ways: they become long and thin (nerve cells, muscle fibers), fold their membranes into microvilli (cells lining the intestine), divide their interior into compartments with their own membranes (eukaryotic organelles, lesson 5), or keep a huge central vacuole so that the active cytoplasm is a thin layer near the surface (many plant cells).

Diffusion inside the cell adds a second limit. Molecules spread by random motion, and the time it takes them to travel a distance grows with the square of that distance (lesson 7 works through the numbers). A small molecule crosses a 1-micrometer bacterium in about a millisecond but would need minutes to cross a millimeter. Cells that are big, like the egg of a frog or the long axon of a nerve, rely on active transport along internal tracks (lesson 11) rather than diffusion alone.

Two kinds of cells: prokaryotes and eukaryotes

When electron microscopes revealed the inside of cells in the mid-twentieth century, biologists saw a sharp division. Some cells have their DNA in a membrane-bound nucleus and are full of internal membrane-bound compartments called organelles. These are eukaryotic cells (from Greek for true kernel). Others have no nucleus and few or no internal membranes. These are prokaryotic cells (before the kernel).

The terms describe cell organization, not family relationships. Comparing genes in the 1970s, Carl Woese found that prokaryotes fall into two very different groups, Bacteria and Archaea, which are as different from each other as either is from eukaryotes. Life is therefore usually divided into three domains: Bacteria, Archaea and Eukarya. Archaea look like bacteria under the microscope, but many of their genes and membrane lipids are distinctive, and some live in extreme habitats such as hot springs, salt flats and the guts of cattle (where they make methane).

Where did eukaryotic cells come from? Endosymbiosis

Mitochondria (which release energy from food, lesson 9) and chloroplasts (which capture light energy, lesson 10) have a curious set of features. Each has its own small circular DNA molecule, its own 70S ribosomes like a bacterium's, and two membranes. Each divides by a process that resembles bacterial binary fission. A cell cannot make a new mitochondrion from scratch; it can only grow and divide existing ones.

The endosymbiotic theory, developed and championed by Lynn Margulis from 1967, explains these features: mitochondria descend from bacteria that were engulfed by an ancestral host cell and lived inside it as partners, and chloroplasts descend from engulfed photosynthetic bacteria (cyanobacteria) in a later event in the ancestors of algae and plants. Over time most of the bacteria's genes moved to the host's nucleus. The evidence is now overwhelming: mitochondrial genes are most closely related to those of a group of bacteria called alphaproteobacteria, and chloroplast genes to cyanobacteria. The host itself appears to have been related to archaea, which is why eukaryotes share some features with each domain.

How to study this course

Cell biology has a large vocabulary, and new terms arrive quickly. The terms list at the end of each lesson is a good place to start, but memorizing words is not the goal. Try to connect each structure to a job (what problem does the Golgi apparatus solve?), each process to energy (where does the energy come from, and where does it go?), and each claim to evidence (how do we know?). The worked examples and Python programs are there to make quantities concrete: a cell that is 10 micrometers across, a membrane 7 nanometers thick, an enzyme that turns over a thousand molecules a second.

The practice questions mix recall with reasoning. If you can explain an answer to someone else in plain language, you understand it. If you can only recognize the right option, revisit the lesson.