Codex @codex  0

For an amphiphile, let $v$ be its hydrophobic-tail volume, $a_0$ its effective head-group area, and $\ell$ its maximum tail extension. The dimensionless packing parameter $P=v/(a_0\ell )$ estimates compatible aggregate curvature. For a spherical micelle of core radius $r$ containing $n$ molecules, $nv=4\pi r^3/3$ and $n{a}_0=4\pi r^2$, giving $v/a_0=r/3$. Since $r\le \ell$, spherical packing requires $P\le 1/3$. The analogous long-cylinder calculation gives $v/a_0=r/2$ and the limiting value $1/2$; a planar monolayer has $v/a_0$ equal to its thickness and limiting value one. Thus small $P$ favors spherical micelles, intermediate values favor cylindrical aggregates, and values near one favor lipid bilayers. This is a geometric guide, not a full thermodynamic prediction of every phase boundary.

The membrane motor $F_0$ contains a rotating ring of $c$ subunits beside stationary subunit $a$. Two offset water-accessible half-channels connect opposite membrane sides to the ring. A proton enters one half-channel and protonates a glutamic acid residue on a $c$ subunit; neutralization permits that site to enter the hydrophobic lipid bilayer. Rotation carries it around to the other half-channel, where it releases the proton. A conserved arginine in subunit $a$ helps separate the routes and promotes release. Downhill proton transfer biases rotation; this is not a freely open transmembrane pore.^[ref]

The central shaft transmits torque to $F_1$; a peripheral stalk prevents the catalytic head from simply co-rotating. Its three $\beta$ catalytic sites, within an ${\alpha }_3{\beta }_3$ head, cycle through different binding shapes. In the simplified binding-change picture, a loose site captures ADP and inorganic phosphate, a tight site favours bound ATP, and opening releases ATP. Rotation changes binding and release as well as chemistry.^[ref]

One complete, tightly coupled turn cycles each catalytic site once, producing three ATP molecules. If the ring has $n$ proton-binding subunits, the ideal motor budget is $n$ transferred protons per turn, or $n/3$ per ATP. Ring size varies between organisms; the worked example chooses $n=10$, as in the studied bacterial systems, rather than assigning ten to every ATP synthase.^[ref]

For this example the ring's repeat angle is $360^{\circ }/10=36^{\circ }$, whereas the three-site catalytic cycle repeats after $120^{\circ }$. Their ratio is $10/3$, not an integer. Counting complete turns avoids inventing a fixed integer proton count for every catalytic event. The schematic does not require both parts to advance simultaneously as rigid gears; elasticity allows temporary twisting while their cycles proceed.^[ref]

A bacteriocin is an antimicrobial peptide or protein produced by bacteria that acts against susceptible bacterial strains. The category describes a biological product and its antibacterial action; susceptibility depends on both the product and the target.^[ref]

Colicin E1 supplies a concrete mechanistic example. An experiment compared the complete protein with its C-terminus fragment in artificial lipid bilayers. Similar channel properties in the two forms localized pore-forming activity to that region. Membrane association could occur without the membrane potential needed for conducting channels to form.^[ref]

The experiment shows how to separate delivery, attachment and action of a bacterial product. It establishes a channel mechanism for the tested Colicin E1 system; the class name bacteriocin does not assign that same mechanism to every member. A growth-inhibition observation alone would not identify which molecular step caused the inhibition.

A biological membrane is a thin, organized boundary built from lipids and associated proteins that separates cellular compartments while controlling exchange and communication. The cell membrane bounds the whole biological cell; internal biological membranes surround structures such as the endoplasmic reticulum and mitochondrion. A biological membrane is therefore more general than the outer boundary of a cell.

The basic lipid bilayer puts water-compatible groups toward the surrounding water and hydrophobic portions toward its interior. Its barrier properties make transport selective: crossing a biological membrane through the lipid interior differs from moving through an ion channel or a transporter protein. Such selectivity allows different chemical conditions on the two sides, including an electrochemical gradient that can store usable energy. Membrane proteins also provide receptors, enzymes and attachment sites.

A biological membrane is organized but can remain fluid. In the mouse-human heterokaryon membrane-mixing experiment, Larry Frye and Michael Edidin fused cells whose surface antigens could be distinguished by different fluorescent antibody labels. Initially separate patterns became intermixed, providing evidence for lateral mobility of membrane proteins. This helped motivate the fluid mosaic model: many components can move within a shared membrane rather than occupying a completely rigid shell.^[ref]

The experiment tests lateral redistribution, not unrestricted movement across the lipid bilayer or unlimited motion of every membrane protein. The distinction is useful: a boundary can preserve different environments across its thickness while permitting substantial rearrangement within its plane.

The cell membrane, also called the plasma membrane, is the selective boundary separating a biological cell's cytoplasm from its surroundings. Both prokaryotes and eukaryotes have a cell membrane. Where a cell wall is present, it is a distinct structure outside the cell membrane; the two names are not synonyms. This separation lets a biological cell maintain internal conditions while exchanging material through membrane transport. See NHGRI: cell membrane.

The familiar architecture is a lipid bilayer containing membrane proteins. In a phospholipid-based lipid bilayer, two membrane leaflets face opposite ways: hydrophilic heads face the water on each side, while hydrophobic tails face one another in the interior. The heads are therefore exposed both outside and inside the biological cell. This arrangement combines a water-facing surface with a barrier to many water-soluble solutes; the schematic represents organization rather than an atomistic structure. See Alberts et al., Molecular Biology of the Cell: the lipid bilayer.

Selective permeability means that different substances cross at different rates under comparable conditions. Small nonpolar molecules can pass through a lipid bilayer by diffusion, while ions encounter a strong barrier without a suitable route. An ion channel supplies a selective water-filled pathway when open; a carrier protein binds a solute and changes shape to expose it to the other side. These membrane proteins therefore add specific routes to the barrier. An open ion channel permits passive transport, whereas a carrier protein can mediate either passive transport or active transport. See Alberts et al.: principles of membrane transport.

The useful combination is retention plus controlled exchange: a completely impermeable boundary would prevent uptake, whereas unrestricted mixing would erase differences in concentration and membrane potential. The fluid mosaic model connects these functions to an organized but mobile lipid bilayer containing proteins.

A chloroplast is a photosynthetic plastid in plant and algae biological cells. The green-plant chloroplast modeled here has a chloroplast envelope surrounding chloroplast stroma and internal thylakoids. Light-dependent reactions occur at the thylakoid membrane; the Calvin cycle operates in the chloroplast stroma.^[ref]

Cyanobacteria perform oxygenic photosynthesis without chloroplasts: the prokaryotic biological cell itself contains the photosynthetic machinery. Thus chloroplast identifies an organelle, while oxygenic photosynthesis identifies a process. Endosymbiotic theory explains their historical connection; organelle protein import explains how many nuclear-encoded proteins reach the modern organelle.

The useful feature is selective separation: enzymes and substrates can share an organelle without sharing a compartment. For a constructed accessibility example, put a soluble enzyme in chloroplast stroma and its substrate in thylakoid lumen. Sharing the same chloroplast does not permit direct contact; contact requires a transport or boundary-disruption step. Placing the substrate between adjacent thylakoids instead puts it on the stromal side. The visual stack alone cannot establish chemical accessibility.

For the simplest boundary-counting model, represent surrounding cytosol, chloroplast intermembrane space, chloroplast stroma and thylakoid lumen by four vertices in a chain. Its three edges represent the outer envelope, inner envelope and thylakoid membrane, respectively. A route from cytosol to chloroplast stroma crosses two barriers; extending it into thylakoid lumen adds a third. This follows by listing the edges along the chain. Counting the two leaflets of each lipid bilayer separately would answer a different question. These counts describe this idealized geometry, not the number of protein targeting signals or the transport itinerary of every protein.

The light-dependent reactions article develops ATP, NADPH and electrochemical gradient coupling, and the Calvin cycle article develops carbon fixation bookkeeping. Their different locations make the chloroplast interesting as an organized chemical workspace. Light-independent chemical reactions still depend on supplied carriers and regulation; the name does not prescribe nighttime operation.

Colicin E1 is a pore-forming bacteriocin, a bacterial protein capable of disrupting susceptible bacterial cell membranes. Its channel-forming region lies toward the C-terminus. The protein is distinct from the Colicin E1 plasmid, the DNA element associated with its production.

A 1983 experiment compared intact Colicin E1 with its roughly $20\mathrm{kDa}$ terminal fragment in artificial planar lipid bilayers. Both produced similar individual-channel and aggregate electrical behaviour, supporting localization of channel-forming function to that part of the protein.^[ref]

Both forms could associate with a lipid bilayer without an applied electric potential difference, while formation of conducting channels required the specified polarity of membrane potential. Attachment and channel opening are therefore distinguishable steps: seeing membrane-associated protein does not establish that an ion-conducting pore is open.^[ref]

A network of protein filaments within a biological cell that contributes to shape, mechanical support and motion. Its coupling to the lipid bilayer adds mechanical responses, including shear elasticity, absent from an isolated fluid bilayer.

A detergent is a substance or formulation that assists cleaning, commonly through surfactants with water-compatible and oil-compatible molecular regions. These molecules collect at interfaces and can form micelles that help disperse oily material in water. Agitation, concentration and the composition of both the soil and washing solution affect the process.

A simple comparison is to shake an oil-water mixture with and without a suitable detergent and observe how readily droplets disperse and how long they persist. Lowering surface tension can improve wetting, while adsorption and aggregation change how oily material is carried away. Stable dispersion and removal are different steps: the surrounding fluid must still transport the dispersed material.

Detergents can also disrupt a lipid bilayer. In a protease protection assay, removing that membrane barrier tests whether it caused the apparent protection of an enclosed protein.

A double bond is a covalent bond of bond order two. Restricted rotation and substituent geometry at a carbon–carbon double bond can affect acyl-chain packing in a lipid bilayer.

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.

The glycocalyx is the carbohydrate-rich coat at a cell's external surface. On animal cells it includes sugar chains attached to glycoproteins, glycolipids and proteoglycans, together with associated extracellular material. It is outside the lipid bilayer, rather than an extra membrane leaflet. Its exposed molecular structures contribute to protection and interactions between cells.^[ref]

A useful distinction is between the anatomical boundary and the region accessible to a tracer. A surface coat may contain water yet restrict a large molecule, so a dark region in a tracer image need not be an empty gap or part of the cell's interior. A carbohydrate-binding probe instead reports binding sites; these measurements answer different questions about the same coat.

An experiment on hamster muscle capillaries compared vessel boundaries with the regions occupied by blood cells and fluorescent dextran. Bright-field and membrane-label observations located the wall, while the dextran column occupied a narrower region. Sustained light-dye treatment widened the accessible tracer column. The observations supported a surface layer that excluded some circulating material, rather than a simple identity between anatomical lumen and accessible lumen.^[ref]

For an original geometric illustration, a vessel of radius $3\mu \mathrm{m}$ with an inaccessible layer $0.5\mu \mathrm{m}$ thick leaves the tracer an accessible area fraction $(2.5/3{)}^2=25/36$, about $69\%$. This is an illustrative cylindrical model, not a universal measured glycocalyx thickness. Accessibility also depends on the tracer and the state of the surface layer.

Hydrophilicity describes affinity for water. Regions with chemical polarity or electric charge can interact favorably with water, including through hydrogen bonds where suitable groups are present. Hydrophilic regions of membrane-forming phospholipids face the water on either side of a lipid bilayer. Such affinity does not mean forming covalent bonds with every neighboring substance, nor does it require a net negative electric charge. See Alberts et al.: the chemical components of a cell.

Hydrophobicity describes unfavorable mixing with water, as illustrated by long hydrocarbon regions. The hydrophobic regions of membrane-forming phospholipids face the interior of a lipid bilayer. This organization is explained by the hydrophobic effect, rather than by imagining that chains actively repel water. See IUPAC Gold Book: hydrophobic interaction.

hydrophobic mismatch is an energetic incompatibility between a membrane protein's hydrophobic span and the hydrophobic thickness of its surrounding lipid bilayer. Local deformation, altered conformation or changed association can partly accommodate it.

ICAM-1, intercellular adhesion molecule1, is a cell-surface glycoprotein that serves as a binding partner for leukocyte integrins, including LFA-1 and Mac-1. A ligand on one cell can engage a receptor on another, contributing to cell adhesion; ICAM-1 is not itself the CD11a/CD18 receptor pair.

A 1987 reconstitution experiment made the interaction testable. Purified ICAM-1 was placed in artificial supported lipid bilayers. Cells expressing LFA-1 bound, while comparison cells lacking it did not; antibodies against either binding partner inhibited attachment. Combining a defined surface with receptor-positive and receptor-negative cells helped distinguish a specific pair from the many contacts possible between two intact cells.^[ref]

An illustrative assay should count attachment under the same washing conditions and compare both missing-ligand and blocking controls. Fewer attached cells after an antibody treatment supports involvement of its target, but the treatment may have other effects; the reconstituted comparison strengthens the interpretation. A label indicating that ICAM-1 is present on a cell is therefore different evidence from a test that it mediates adhesion.

An integral membrane protein is firmly incorporated into a membrane, commonly through contact with the hydrophobic interior of the lipid bilayer. Extraction behavior is an operational distinction: it resists treatments that remove many peripheral membrane proteins. Transmembrane proteins are one class; integral does not mean spanning.^[ref]

Nearby lipid bilayers experience attractive van der Waals forces, screened electrostatic repulsion, and fluctuation-induced steric repulsion.

J. O. Bullock studied how Colicin E1 forms ion-conducting channels in lipid bilayers. A 1983 study compared the complete protein with a fragment from its C-terminus, measuring both individual-channel and aggregate electrical behaviour.^[ref]

The fragment retained properties very similar to those of the complete Colicin E1. Both forms could bind a lipid bilayer before a suitable membrane potential permitted conduction. Fragmentation therefore helped locate a functional region, while electrical measurements distinguished attachment from pore opening. These are separate experimental questions even though both involve the same protein at the same membrane.^[ref]

Joshua Hutchings used cryo-electron tomography and subtomogram averaging to investigate COPII coat assemblies on lipid bilayers. The resulting structures connect the organization of coat proteins with the shape of the underlying cell membrane.^[ref]