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Biology studies living systems: how biological cells maintain themselves, how organisms develop and reproduce, and how evolution generates diversity. Its scales connect molecules, genes, biological cells, organisms and the interactions studied by ecology. These are complementary viewpoints: a protein's chemistry can explain a cellular mechanism, while evolution explains why inherited variants of that mechanism persist. See Clark, Douglas and Choi, Biology 2e: the science of biology.

Two organizing ideas make this immense subject navigable: shared cellular organization and descent with inherited modification. A neuron and a gliding bacterium differ dramatically in shape and behavior, yet both depend on a cell membrane and metabolism. Their differences become intelligible through specialization and evolution.

Keep observations separate from the mathematical models used to explain them. A measured membrane potential is evidence; an idealized two-state ion-channel gating equation proposes a mechanism. A mathematical model earns trust through predictions and comparisons with measurements. Its assumptions delimit its usefulness, and disagreement can reveal missing biology rather than a faulty measurement.

A gliding bacterium moves along a surface without swimming through the bulk fluid. In a thin-fluid-film model, its relative motion dissipates energy through Couette flow, although the actuation mechanism can involve additional dissipation.

Approximate the gap by steady Couette flow, neglecting edge effects and additional losses from membrane deformation. Its velocity gradient is $U/h$, so the shear stress is $\eta U/h$. The force on the gliding bacterium and the rate of viscous dissipation areThe same power follows by integrating $\eta (U/h{)}^2$ over gap volume $Ah$. In SI units, $A=10^{-10}{\mathrm{m}}^2$, $h=10^{-7}\mathrm{m}$, and $U=10^{-6}\mathrm{m}{\mathrm{s}}^{-1}$. ThusAn energy needs a duration or distance: $E=10^{-18}\Delta t\mathrm{J}$ for $\Delta t$ in seconds, equivalently $E=F_{d}s$ for travel distance $s$. Moving one micrometre takes one second and dissipates $10^{-18}\mathrm{J}$. This is the mechanical cost of the sheared film. A numerical biological efficiency would additionally require the motor's input power and the losses associated with its peristaltic actuation.