Relative centrifugal force is the dimensionless ratio of the local centrifugal acceleration magnitude $a$ to the conventional gravitational reference $g_0=9.80665\mathrm{m}{\mathrm{s}}^{-2}$. Despite its name, it is an acceleration ratio: the actual force on a specified mass $m$ is $ma$. With angular speed $\omega$ and rotor radius $r$, $a={\omega }^{2}r$. If $n$ is the numerical rotational speed in revolutions per minute and $r_{\mathrm{cm}}$ the numerical rotor radius in centimetres, unit conversion givesThus rpm alone does not specify the centrifugal acceleration.^[ref]

For a stipulated $3000\mathrm{rpm}$, rotor radii of $5$ and $10\mathrm{cm}$ give approximately $503$ and $1006$ times $g_0$. Doubling the rotor radius doubles relative centrifugal force; doubling rpm quadruples it. Even equal relative centrifugal forces do not guarantee equal separation: travel distance, elapsed time, viscosity, sample density and particle shape still matter. These are comparisons of a mathematical model, not instructions for running an instrument.

The rotor radius $r$ is the perpendicular distance from the rotation axis to a specified sample position, not the tube's length. A filled tube spans a range $r_{\min }\le r\le r_{\max }$. Consequently, one rotational speed produces different local centrifugal accelerations along that range. A reported relative centrifugal force needs a stated reference position, such as the outermost sample radius.

Let $p$ be the perpendicular distance from the force centre to the tangent of a regular planar orbit. Conserved physical angular momentum has magnitude $|h|=mpv$, while conserved energy is $E=m{v}^2/2+V(r)$. Eliminating speed gives the displayed equation when $h\ne 0$. For a differentiable polar curve, $p=r^2/\sqrt{r^2+(dr/d\theta {)}^2}$, connecting the geometric tangent distance to the radial energy equation.

Peptidoglycan is a mesh of linked sugar chains cross-linked by short chains of amino acids in the cell walls of most bacteria. Its absence from the cell walls of archaea helps distinguish envelope chemistry without confusing either cell wall with a cell membrane. See OpenStax Microbiology, 3.3: cell walls and peptidoglycan.

A protoplast is the living contents of a biological cell bounded by its cell membrane after removal of the cell wall. Removing the cell wall need not immediately destroy the cell membrane; stability depends on the preparation and surroundings. Lysozyme acts on susceptible bacterial peptidoglycan, not on cellulose or chitin, so it is not a universal wall-removal enzyme.

Plasmolysis is withdrawal of the membrane-bounded contents from parts of a cell wall after water loss. A sufficiently concentrated external hypertonic solution, with solutes effectively excluded by the cell membrane over the observation time, can cause this. The cell wall remains; the enclosed material contracts. Plasmolysis is therefore distinct from osmotic lysis, which breaks the cellular boundary during excessive swelling. A return to a less concentrated surrounding chemical solution can reverse plasmolysis if the biological cell remains functional.^[ref]

Turgor pressure is the internal hydrostatic pressure above the external pressure in a biological cell. When water enters a walled biological cell by osmosis, expansion loads the cell wall. Rising pressure can oppose further net entry while the cell membrane retains its selective permeability. Mechanical support therefore does not require the cell wall to block water.

As an original mechanical check, idealize a small flat patch of cell wall of surface area $A$ under uniform turgor pressure $\Delta P=P_{\mathrm{in}}-P_{\mathrm{out}}$. Its outward force is $F=\Delta PA$. Doubling $A$ at fixed pressure doubles the load; equal internal and external pressures give zero net pressure load. This is a force balance, not a measured wall strength or a complete model of a curved, growing biological cell. It says nothing about which solutes cross the cell membrane.

A fungal cell wall contains structural polysaccharides including chitin and glucans. Its composition and organization vary among fungi; the diagram illustrates a composite rather than a pure chitin shell. A fungus sharing a cell wall with a plant does not imply shared wall chemistry.^[ref]

A plant cell wall provides reinforcement outside the cell membrane, with cellulose as a major structural component. It is a composite rather than a solid sheet of pure cellulose. Wall construction varies with the kind and developmental state of the biological cell.

The cell nucleolus is a region inside a cell nucleus without a surrounding membrane, where much ribosomal RNA is made and processed and ribosome subunits begin to assemble with proteins. The subunits are exported to the cytoplasm; the cell nucleolus is not itself a translating ribosome. See Clark, Douglas and Choi, Biology 2e, 4.3: nucleolus and ribosomal subunits.

The nuclear envelope is the double-membrane boundary around a cell nucleus. Regulated passage connects nuclear processes to the surrounding cytoplasm: transcription produces RNA in the cell nucleus, while exported messenger RNA can undergo biological translation on ribosomes outside it. See NHGRI: nuclear membrane.

The fluid mosaic model describes a cell membrane as a fluid lipid bilayer with embedded membrane proteins. It connects a continuous barrier to a mosaic of functional components: diffusion within the membrane can coexist with selective passage across it. S. J. Singer and G. L. Nicolson presented the fluid mosaic model in Science in 1972; see Singer and Nicolson, The fluid mosaic model of the structure of cell membranes. The useful picture does not require every protein to move freely: attachments and interactions can restrict movement, as discussed in Cooper, The Cell: structure of the plasma membrane.

Membrane transport is the passage of substances across a cell membrane. For the small solutes considered here, distinguish the available route from its driving force: a lipid bilayer, ion channel, or carrier protein determines how passage can occur, while differences in chemical potential and membrane potential determine which direction is energetically downhill. A large driving force cannot make an unavailable route conduct. See Alberts et al.: principles of membrane transport.

For an ideal dilute chemical solution at uniform temperature and pressure, with the same reference molar chemical potential on both sides, the molar electrochemical potential change for transferring a solute from compartment A to B isHere $c_{\mathrm{A}},c_{\mathrm{B}}$ are concentrations, $T$ is absolute temperature, $R$ is the molar gas constant, $z$ is signed ion charge number, $F$ is the Faraday constant, and $V_{\mathrm{B}}-V_{\mathrm{A}}$ is the electric potential difference. The natural logarithm contains a dimensionless ratio. The electrical term vanishes for an uncharged solute. More generally, use thermodynamic activities in place of the ideal concentration ratio. This combines the ideal-solution chemical potential difference with electrical energy per mole; see IUPAC Gold Book: electrochemical potential. For a biological cell, taking B inside and A outside makes the voltage term use the existing membrane potential convention.

An ion channel is a membrane protein that provides a selective pathway for ions across a cell membrane. An open pore permits passive transport down the relevant electrochemical gradient; it does not supply the free energy for uphill transport as a pump involved in active transport does. Two things are needed for a net electric current: an available pathway and an electrochemical potential difference. Opening a pore alone need not produce a net electric current. See Ion Channels and the Electrical Properties of Membranes.

The selective permeability of an ion channel depends on interactions between its pore and the passing ions, not simply on a hole's diameter. Some ion channels strongly favor potassium over sodium; others admit several kinds of positively charged ions. Thus selective does not necessarily mean exclusive to one ion species. See Purves et al., Neuroscience, 2nd edition (2001): molecular structure of ion channels and the mixed-channel example in Purves et al.: principles derived from studies of the neuromuscular junction.

Gating is the opening and closing of an ion channel's pathway. A voltage-gated ion channel responds to membrane potential; an ionotropic receptor can respond to a bound ligand. Gating changes the available electrical conductance, while the electrochemical gradient supplies the drive for passive transport. For a fixed reversal potential in the simple model below, opening more identical ion channels increases the magnitude of the electric current at a fixed nonzero drive, without choosing its sign independently of membrane potential. The two-state ion-channel gating model describes how the open fraction can change. See the Alberts reference above.

For a worked approximation, hold an open population's electrical conductance at $g=10\mathrm{nS}$ and its reversal potential at $E_{\mathrm{rev}}=-80\mathrm{mV}$. Use $V=V_{\mathrm{inside}}-V_{\mathrm{outside}}$ for membrane potential and inward-positive conventional current:At $V=-100,-80,-60\mathrm{mV}$, respectively, the electric currents are $+200,0,-200\mathrm{pA}$, since $1\mathrm{nS}\times 1\mathrm{mV}=1\mathrm{pA}$. Positive electric current means net positive electric charge entering, or net negative electric charge leaving; it does not mean that every ion moves inward. For a pore passing only positive ions, the three results mean net inward passage, no net passage, and net outward passage. These stipulated values describe an illustrative Ohmic approximation, not measured properties of a particular ion channel; see reversal potential for the current plot and limitations.

The useful connection is between a molecular gate and a controllable electric current. A ligand can change electrical conductance through an ionotropic receptor, or membrane potential can change it through a voltage-gated ion channel, connecting recognition and electrical signaling. In a historical landmark, Erwin Neher and Bert Sakmann reported currents from individual ion channels in frog muscle membranes in 1976. See Neher and Sakmann, Single-channel currents recorded from membrane of denervated frog muscle fibres, Nature 260, 799–802 (1976).

A gap junction directly connects the cytoplasm of neighbouring animal cells through paired intercellular channels. Small ions and some small molecules pass between cells, providing electrical or metabolic coupling. In cardiomyocytes, electrical coupling helps coordinate excitation across a tissue. This is different from release into extracellular space followed by receptor binding, and permeability is selective rather than unrestricted mixing of cellular contents. ^[ref]

A membrane protein is a protein associated with a biological membrane. Its association, orientation and mobility are separate properties: being embedded does not imply spanning, and spanning does not imply moving freely. Membrane proteins supply routes for membrane transport and recognition for signal transduction.^[ref]

An ion channel supplies a pathway for ions; a carrier protein changes which side can reach a bound solute; a cell-surface receptor connects an external ligand to intracellular signal transduction. These examples distinguish passage from communication: a signal can cross the boundary as a change of protein activity without the ligand itself crossing.^[ref]

The same boundary can therefore retain substances and communicate selectively with its surroundings. Membrane topology tells us which parts can meet a given ligand; lateral mobility of membrane proteins tells us whether two parts can approach each other along the boundary. A diagram of a cell membrane becomes more useful when it answers both questions.

Selective permeability means that a cell membrane permits different substances to pass at different rates under comparable conditions. Both the lipid bilayer and the available membrane proteins contribute to this selection.

Artificial boundaries can also have selective permeability. For osmosis, specify which solutes cross and over what observation interval: a boundary that retains one solute need not retain another. A semipermeable membrane is the ideal solvent-only boundary used in the osmotic pressure calculation.

A bacterial outer membrane is an additional membrane outside the peptidoglycan in typical Gram-negative bacteria. It adds a barrier while the inner cell membrane remains the boundary of the cytoplasm.

The spindle apparatus distributes chromosomes during division of a cell nucleus.

Its microtubules and associated molecular motors organize kinetochore-microtubule attachment, positioning and chromosome segregation. Some microtubules connect to kinetochores, while others interact with opposite-pole arrays or the cell cortex. Distinct force-generating interactions therefore contribute to one coordinated division machinery. ^[ref]

Cell cycle analysis assigns evidence to stages of the cell cycle. A flow cytometric DNA-content assay measures accumulated nuclear DNA, whereas DNA pulse labeling detects synthesis over an exposure window. Agreement between these readouts is useful because an amount and a synthesis event answer different questions.