Escape reactions are achieved by action potential-like phenomena, and have been observed in biofilms as well as in single cells such as cable bacteria.

First, an essential concept, popularized by Osborne Reynolds, is that the relative importance of inertia and viscosity for the motion of a fluid depends on certain details of the system under consideration.

This cannot be effective for microscale swimmers like bacteria: due to the large viscous damping, the inertial coasting time of a micron-sized object is on the order of 1 μs.

Purcell concluded that only forces that are exerted in the present moment on a microscale body contribute to its propulsion, so a constant energy conversion method is essential.

As a further consequence of the continuous dissipation of energy, biological and artificial microswimmers do not obey the laws of equilibrium statistical physics, and need to be described by non-equilibrium dynamics.

[3] Mathematically, Purcell explored the implications of low Reynolds number by taking the Navier-Stokes equation and eliminating the inertial terms: where

[3] This paper continues to inspire ongoing scientific discussion; for example, recent work by the Fischer group from the Max Planck Institute for Intelligent Systems experimentally confirmed that the scallop principle is only valid for Newtonian fluids.

[5][3] Motile systems have developed in the natural world over time and length scales spanning several orders of magnitude, and have evolved anatomically and physiologically to attain optimal strategies for self-propulsion and overcome the implications of high viscosity forces and Brownian motion, as shown in the diagram on the right.

Additionally, protein appendages can be present on the surface: fimbriae and pili can have different lengths and diameters and their functions include adhesion and twitching motility.

It is composed of the central rod and several rings: in Gram-negative bacteria, these are the outer L-ring (lipopolysaccharide) and P-ring (peptidoglycan), and the inner MS-ring (membrane/supramembrane) and C-ring (cytoplasmic).

Twitching motility depends on the extension, attachment to a surface, and retraction of type IV pili which provide the energy required to push the cell forward.

For example, the marine bacterium Vibrio alginolyticus, with its single polar flagellum, swims in a cyclic, three-step (forward, reverse, and flick) pattern.

[58][54] Rhodobacter sphaeroides with its subpolar monotrichous flagellation, represents yet another motility strategy:[55][24] the flagellum only rotates in one direction, and it stops and coils against the cell body from time to time, leading to cell body reorientations,[56][59][60] In the soil bacterium Pseudomonas putida, a tuft of helical flagella is attached to its posterior pole.

[57][3] In the pushing mode, the rotating flagella (assembled in a bundle or as an open tuft of individual filaments) drive the motion from the rear end of the cell body.

In this case the trajectories are either straight or with a tendency to bend to the left, indicating that pullers swim by turning a left-handed helical bundle in CW direction.

Finally, P. putida can swim by wrapping the filament bundle around its cell body, with the posterior pole pointing in the direction of motion.

In that case, the flagellar bundle takes the form of a left-handed helix that turns in CW direction, and the trajectories are predominantly straight.

[38][68][69] The name twitching motility is derived from the characteristic jerky and irregular motions of individual cells when viewed under the microscope.

Different types of taxis can be distinguished according to the nature of the stimulus controlling the directed movement, such as chemotaxis (chemical gradients like glucose), aerotaxis (oxygen), phototaxis (light), thermotaxis (heat), and magnetotaxis (magnetic fields).

[96] The ability of marine microbes to navigate toward chemical hotspots can determine their nutrient uptake and has the potential to affect the cycling of elements in the ocean.

The link between bacterial navigation and nutrient cycling highlights the need to understand how chemotaxis functions in the context of marine microenvironments.

Chemotaxis hinges on the stochastic binding/unbinding of molecules with surface receptors, the transduction of this information through an intracellular signaling cascade, and the activation and control of flagellar motors.

The intrinsic randomness of these processes is a central challenge that cells must deal with in order to navigate, particularly under dilute conditions where noise and signal are similar in magnitude.

[99][100] However, at the length scales relevant to individual microbes, the ocean is an intricate and dynamic landscape of nutrient patches, at times too small to be mixed by turbulence.

[104][105] However, the typical chemical gradients wild marine bacteria encounter are often very weak, ephemeral in nature, and with low background concentrations.

[114][115] The downstream signalling in phototactic archaebacteria involves CheA, a histidine kinase, which phosphorylates the response regulator, CheY.

The slow steering of these cyanobacterial filaments is the only light-direction sensing behaviour prokaryotes could evolve owing to the difficulty in detecting light direction at this small scale.

[138][139][140][141][142] The second category provides a macroscopic (i.e. population-level) view via continuum-based partial differential equations that capture the dynamics of population density over space and time, without considering the intracellular characteristics directly.

[143][144][145][146][147][148][149][150][151][137] Among the present models, Schnitzer uses the Smoluchowski equation to describe the biased random walk of the bacteria during chemotaxis to search for food.

[154][155] Building on these models, Cates highlights that bacterial dynamics does not always obey detailed balance, which means it is a biased diffusion process depending on the environmental conditions.