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A chemoattractant is a substance whose spatial distribution can bias responsive biological cells to migrate towards higher concentration. A directional response to its gradient is chemotaxis; a change only in movement speed does not by itself establish a directional response.

Haptotaxis is directed cell migration along spatial variation of an immobilized adhesive or guidance cue. It differs from guidance by a soluble chemoattractant field.

Take $x=0$ at chamber A and $x=L$ at chamber B. At steady state, the diffusion equation with constant positive diffusion coefficient givesThe two Dirichlet boundary conditions give $A=c_0$ and $B=-c_0/L$. ThusThe concentration gradient is constant, $dc/dx=-c_0/L$. By Fick's first law, the diffusive flux is $J=-Ddc/dx=D{c}_0/L$, directed from A towards B. The profile is linear independently of $D$, while the flux and the time needed to approach it depend on $D$.

This result assumes no significant bulk flow, chemoattractant loss to the walls, degradation or cellular uptake. Experimentally, a uniform-concentration control with matched reservoir concentrations tests for directional cell migration caused by flow or apparatus asymmetry; reversing the reservoir concentrations tests whether the directional response follows the chemical gradient. Keeping both reservoirs well mixed and measuring the concentration profile checks the assumed boundary concentrations and whether uptake has distorted it. These controls distinguish the assumed passive diffusion field from other directional cues; the derived profile alone does not establish the mechanism of chemotaxis.

For the same concentration gradient, the front-to-back difference scales with cell length. A much smaller bacterial cell samples a correspondingly smaller spatial signal, while stochastic arrival and binding of individual chemoattractant molecules make receptor measurements noisy. For illustration, a $2\mu \mathrm{m}$ cell in the $0.5$ cm capillary would experience only $0.04\mathrm{nM}$ across its length, compared with $0.4\mathrm{nM}$ for the longer cell. This illustrates a size penalty; it does not assume that bacterial and human detection thresholds are identical.

Many swimming bacteria, including Escherichia coli, use temporal sensing in bacterial chemotaxis: they compare recent receptor stimulation with an adapted baseline as they move. Increasing attractant suppresses reorientation and prolongs runs; decreasing attractant increases tumbling. Repeated runs and reorientations therefore generate a biased random walk up the gradient, without requiring a simultaneous comparison between the front and back. Chemotaxis feedback regulation supplies the adaptation needed to remain sensitive to changes rather than responding only to absolute concentration.

A discriminating experiment changes concentration rapidly and uniformly around the bacteria: a response then occurs without a spatial difference across the cell. The classic temporal-step experiments found increased tumbling after attractant decreases and smoother swimming after increases.^[ref] In a new experiment, compare up-steps and down-steps with constant-concentration and sham-mixing controls, holding temperature and medium composition fixed. Measure run durations and tumble frequency, rather than only average swimming speed. Such a test supports temporal comparison but does not by itself identify every molecular component or show that all bacterial species use the same mechanism.

External chemical signals can guide cell migration, but the statement is too strong if “determined” means that they uniquely specify whether, how fast and in which direction a cell moves. A chemoattractant gradient biases a cell's internal polarity machinery; it does not directly supply the mechanical work of locomotion. Chemotaxis is directional bias, whereas a change in speed or persistence without directional preference is chemokinesis.

A chemical response depends on receptor abundance, signalling adaptation and the cell's existing cell polarity. The same external field can therefore yield different trajectories in different cell states. Uniform stimulation can increase motility without providing a direction, and spontaneous fluctuations of the actin system can initiate movement without a spatial chemical instruction. Persistent migration combines feedback within the cell with a cue that biases that feedback.

Mechanical and geometrical inputs also matter. Durotaxis describes a bias associated with substrate stiffness, while haptotaxis follows spatial variation in adhesive ligands. Contact guidance by fibre alignment can channel motion even when soluble signals are uniform. Narrow spaces constrain the available paths and can force a switch of protrusive mechanism. These effects are not wholly separate from chemistry: cells sense mechanical forces through molecular interactions. Nevertheless, their directional information resides in mechanics or geometry, not necessarily in an imposed soluble concentration gradient.

Contacts between cells supply another source of organization. Experiments on neural crest cells showed that collisions can cause protrusion collapse and repolarization, and that perturbing noncanonical Wnt signalling disrupts this behaviour and group directionality.^[ref] Contact inhibition of locomotion therefore helps generate collective trajectories through local interactions, rather than each cell independently reading a complete external chemical map. Cohesion and other attractive interactions can prevent such repulsion from simply dispersing the group.

A discriminating experiment independently varies soluble gradient, adhesive pattern and mechanical confinement. Measure direction, speed and persistence separately; reverse the gradient, remove it, and then block the relevant receptor while checking viability and the ability to move. If a directional bias follows the reversed chemical field, that supports chemical guidance. If speed rises under uniform stimulation, that supports chemokinesis. If trajectories remain aligned with fibres after chemical reversal, physical guidance is influential. Manipulating intracellular polarity can test whether a cue is instructive or merely permissive.

The useful conclusion is that motion emerges from an internally powered, state-dependent cell interacting with chemical, mechanical and cellular surroundings. External chemical signals are often decisive inputs, but the trajectory is a property of the coupled system.