Cell Theory: Prokaryotes and Eukaryotes

The principles of cell theory

Cell theory, one of the unifying pillars of biology, states three ideas: every living organism is made of one or more cells; the cell is the basic unit of structure and function of life; every cell arises from a pre-existing cell (no spontaneous generation).

Prokaryotes vs eukaryotes

Prokaryotic cells (bacteria, archaea) lack a membrane-bound nucleus: their DNA, usually circular, floats in a region called the nucleoid. They have no membrane-bound organelles. Eukaryotic cells (animals, plants, fungi, protists) have a true nucleus and specialized membrane-bound organelles (mitochondria, endoplasmic reticulum, Golgi apparatus...), allowing much greater functional compartmentalization.

Animal vs plant cells

Plant cells are set apart by three structures absent in animal cells: a rigid cell wall (cellulose), chloroplasts (photosynthesis), and a large central vacuole that regulates osmotic pressure and often takes up most of the cell's volume.

Why cells stay small

The surface-area-to-volume ratio decreases as a cell grows (volume scales with the cube of the radius, surface area with the square). Exchanges (nutrients, waste, gases) occur across the membrane, proportional to surface area, while metabolic needs are proportional to volume. Beyond a certain size, surface area is no longer enough to supply the volume — a fundamental physical constraint that explains why cells stay microscopic and why complex organisms are multicellular rather than made of one very large cell.

Illustration: prokaryote vs eukaryote

Calculation: surface-area-to-volume ratio of a spherical cell

Modelling a cell as a sphere of radius $r$: surface area $S = 4\pi r^2$, volume $V = \dfrac{4}{3}\pi r^3$, so $\dfrac{S}{V} = \dfrac{3}{r}$ — the surface-to-volume ratio is inversely proportional to the radius. Example: if the radius doubles (from 10 to 20 μm), the S/V ratio is halved: the cell has half as much exchange surface available per unit of volume it needs to supply — a concrete illustration of why cells don't keep growing indefinitely.

Historical milestones and resolution limits

Cell theory was built up in stages: Robert Hooke observed and named "cells" in 1665 (in cork tissue — actually empty cell walls); Schleiden (1838, plants) and Schwann (1839, animals) together formulated the first two principles of cell theory; Rudolf Virchow added the third principle in 1855, "omnis cellula e cellula" (every cell comes from a pre-existing cell), definitively ruling out spontaneous generation. On the technical side, a light microscope is limited to a resolution of about 200 nm (a physical limit set by the wavelength of visible light) — enough to see a cell or a nucleus but not the detail of an organelle; an electron microscope reaches 1–2 nm in practice, enough to resolve membranes, ribosomes and even some viruses.

Calculation: a second surface-area-to-volume example

For a spherical cell of radius $r$: $S = 4\pi r^2$, $V = \dfrac{4}{3}\pi r^3$, so $\dfrac{S}{V} = \dfrac{3}{r}$. For $r = 5\ \mu m$: ratio $= 0.6\ \mu m^{-1}$. For $r = 10\ \mu m$ (radius doubled): ratio $= 0.3\ \mu m^{-1}$ — doubling its radius halves a cell's surface-area-to-volume ratio, exactly as predicted by the $3/r$ formula.

From cells to tissues

In multicellular organisms, specialized cells associate to form tissues, each defined by its own structure and function. In humans, four major tissue types are distinguished:

• Epithelial tissue: tightly packed cells, little extracellular matrix, resting on a basal lamina. Lining functions (skin, mucous membranes) and secretory functions (glandular epithelia).
• Connective tissue: cells dispersed in an abundant extracellular matrix (collagen/elastin fibers + ground substance). Includes connective tissue proper, but also cartilage, bone, and blood (a liquid matrix, plasma).
• Muscle tissue: contractile cells rich in actin/myosin — skeletal (striated, voluntary), cardiac (striated, involuntary), and smooth (non-striated, involuntary).
• Nervous tissue: neurons (signal transmission) and glial cells (support, myelination, nourishment) — see the dedicated nervous tissue chapter for resting/action potential detail.

This cell → tissue → organ → system hierarchy underlies the organization of every human physiology chapter in this library.

Not all eukaryotic cells lack a wall

Cell walls aren't unique to plants: fungi (eukaryotes) have one too, but of a different composition — chitin (the same polysaccharide as arthropod exoskeletons) rather than cellulose. Animal cells, by contrast, have no wall at all. Bottom line: "eukaryote" implies neither the presence nor the absence of a wall — it's a kingdom-specific trait (present in plants and fungi, absent in animals), not to be confused with the peptidoglycan wall of bacteria.

• Nucleoid — the region of the bacterial cytoplasm where the DNA is found, not bounded by a membrane.
• Surface-area-to-volume ratio — the physical constraint limiting cell size.
• Compartmentalization — separating biochemical functions into distinct organelles, unique to eukaryotes.

Think of a cell as a warehouse: the surface (the walls with their doors) has to handle all the incoming/outgoing flow for the entire volume (the stock) it contains. A warehouse twice as large in every dimension has 4 times more wall but 8 times more stock to manage — beyond a certain size, the doors just aren't enough.

• "Prokaryote" doesn't mean "no DNA" — the DNA is there, it's simply not inside a membrane-bound nucleus.
• Not all eukaryotic cells have a cell wall (animal cells don't) or chloroplasts (only photosynthetic cells do).