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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.

Let $n$ count chromosomes in one complete set, and let $C$ denote the nuclear DNA amount in one unreplicated haploid set of this organism. Ploidy counts sets, whereas $C$ units count material; $C$ is not a universal mass shared by all species. Here we count a paired replicated chromosome as one until its sister chromatids separate. A copied diploid genome is therefore still diploid through S phase: $2n$ persists even as $2C$ becomes $4C$.

An original bookkeeping example uses a hypothetical diploid biological cell with $n=3$. Name its three homologous chromosome pairs $A,a$, $B,b$ and $D,d$. Assume ordinary nuclear DNA replication, no chromosome loss, and one continuous double-stranded DNA molecule per unreplicated chromosome or replicated chromatid. Count nuclear material only, excluding mitochondrion DNA.

For example, $A$ becomes the paired copies $A_1,A_2$ during S phase. They remain one replicated chromosome until separation. Each completed daughter receives one $A$ copy and one $a$ copy, and similarly for the other two pairs. Across both daughters, $2\times 6=12$ double-stranded DNA molecules and $2(2C)=4C$: division allocates the copied material without another round of DNA replication.

The whole undivided anaphase biological cell transiently contains $4n$ separately counted daughter chromosomes. This counting change does not establish a four-set ploidy in a completed daughter genome: each pole receives $2n$, and each completed daughter cell nucleus is diploid. Always state whether a number refers to one cell nucleus, one pole, or the entire undivided biological cell. Compare meiotic DNA content: after meiosis I, a haploid cell nucleus can contain $2C$, so amount alone cannot determine ploidy.

G0 phase describes withdrawal from the division cycle. Some biological cells re-enter G1 phase; others remain nondividing. Metabolism and gene expression can continue. ^[ref] In the ordinary diploid case, $2C$ alone cannot distinguish G0 phase from G1 phase.

M phase includes mitosis and ordinarily cytokinesis, which can overlap in time.

Interphase comprises G1 phase, S phase and G2 phase, including growth and DNA replication.