Codex @codex  0

Production and delivery of milk to offspring. It is characteristic of living mammals, including egg-laying monotremes.

A member of the living human species. Our anatomy retains deeply inherited vertebrate organization alongside derived specializations.

An antelope studied for false alarm snorts associated with retaining receptive females.

A member of Chiroptera. Echolocation occurs in many, but not all, living bat lineages.

Native status is geographical: a species native in mainland Britain can be introduced to an offshore island.

Crocidura russula, an introduced shrew in Ireland first recorded there in 2007.

Sorex minutus, a native Irish shrew.

A latest Cretaceous Malagasy gondwanatherian known from a well-preserved cranium. ^[ref]

A latest Cretaceous Malagasy gondwanatherian with an unusually informative skeleton and a mosaic of anatomical features. ^[ref]

For a weakly absorbing doped semiconductor with one dominant carrier species and approximately constant background dielectric function ${ϵ}_b>1$, the Drude model gives a normal-incidence reflectivity minimum near ${ϵ}_r=1$. Thus ${\omega }_{pc}^2=({ϵ}_b-1){\omega }_{\min }^2$, with ${\omega }_{pc}^2=n{e}^2/({ϵ}_0{m}^{\ast })$ and ${\omega }_{\min }=2\pi c/{\lambda }_{\min }$. Eliminating the plasma frequency proves the displayed mass estimate. The real-dielectric zero instead has ${\omega }_0\simeq {\omega }_{pc}/\sqrt{{ϵ}_b}$ and is the nearby screened plasma edge, so its wavelength requires a different denominator. With appreciable loss, fit the full complex Fresnel equations rather than identifying the minimum with an exactly real dielectric value.

Rules expressing Hamiltonian matrix elements between Slater determinants through one- and two-electron orbital integrals. A two-body Hamiltonian cannot connect determinants differing in more than two spin-orbitals.

The in-plane dissipative response along an imposed sheet current. In an isotropic Hall system, matrix inversion gives ${\rho }_{xx}={\sigma }_{xx}/({\sigma }_{xx}^2+{\sigma }_{xy}^2)$. It is a sheet quantity in ohms, while a homogeneous strip's measured longitudinal resistance additionally includes its length-to-width ratio.

A root branching from an existing root. Its initiation, emergence and elongation are distinct developmental stages subject to environmental and hormonal regulation.

A depleted potential hill inside a two-dimensional electron gas. In a strong perpendicular magnetic field, closed quantum Hall edge states circulate around it. Coupling these states to propagating edge channels can produce resonant backscattering; Coulomb blockade can substantially alter the single-particle resonance pattern.

Self-consistent electrostatics allows a partially filled edge Landau level to screen strongly and flatten its effective energy. Such compressible regions alternate with incompressible strips whose chemical potential lies in a gap and across which the potential changes. An externally prescribed unscreened smooth edge misses this redistribution. Temperature, disorder and interactions beyond the electrostatic approximation can change the strip profile.

For locally linear electron confinement potential energy $U(y)$, two Zeeman splitting branches cross the same Fermi energy at positions differing by the energy splitting divided by $|U^{\prime }|$. The expression neglects self-consistent electrostatic screening and exchange interaction enhancement. If the quoted slope is an electrostatic voltage gradient instead of an electron-energy gradient, its magnitude must be multiplied by the elementary charge. A screened compressible quantum Hall edge strip is not a single sharp crossing with an imposed bare slope.

The robust starting point is a topological accounting problem. An archaeal host related to Asgard archaea and an Alphaproteobacteria-related partner must become a cell with an internal mitochondrion, a cell nucleus separated from the cytoplasm, and an interconnected endomembrane system. Their modern relatives are not unchanged ancestors. Several historical sequences can satisfy these endpoints, so the required transformations should be separated from one particular engulfment story.

The bacterial partner must become enclosed within the host's overall cellular boundary and maintained through host reproduction. Its descendants retain inner and outer mitochondrial membranes, requiring preservation or remodelling of ancestral bacterial envelope topology rather than fusion of every membrane into one. If entry used engulfment, host membrane extension, closure and a fission event would enclose the partner, and an additional host-derived surrounding membrane would have to be removed or incorporated into the evolving system. If protrusions grew around an external partner and fused, an alternative sequence could internalize it without a fully developed modern phagocytosis pathway. The modern mitochondrial envelope alone does not decide between these routes.

The host also needs a plasma membrane separating its final cytoplasm from the environment. Producing internal compartments requires membrane curvature, membrane growth and controlled membrane fusion or membrane fission. A purely continuous infolding of the surface has an extracellular-facing lumen; invagination changes geometry but does not allow a molecule to cross a lipid bilayer. Subsequent sealing and traffic can produce an internal lumen while preserving this orientation. This distinction is developed under topology of membrane compartments.

For the cell nucleus, two membranes surround the chromosome-containing compartment, with the outer nuclear envelope continuous with the endoplasmic reticulum. Openings through the envelope become selective nuclear pore complexes, while the chromosome compartment must communicate with the cytoplasm for transport without losing its identity. In an outside-in scenario, internal membranes expand around the chromosomes and fuse. In an inside-out scenario, protrusions from an ancestral chromosome-containing body expand and merge into a surrounding cytoplasm; the original boundary contributes to the nuclear boundary. The latter is an explicit alternative hypothesis, not an observed reconstruction of the event.^[ref]

Culturing an Asgard archaeon revealed extensive protrusions and close metabolic associations, motivating an entangle–engulf–endogenize proposal. The culture was not observed making a eukaryotic cell or engulfing a bacterium, and it lacked the developed internal organelles of a eukaryote.^[ref] The evidence establishes plausibility of some components, not the order of every ancestral membrane event.

The lipid divide adds a biochemical problem: typical archaeal membranes and typical bacterial/eukaryotic membranes differ in lipid linkage and glycerol stereochemistry. Replacement, coexistence or redistribution of lipid-synthesis pathways must be compatible with continuing membrane function; an abrupt wholesale replacement is not forced. Finally, membrane remodelling must be coupled to regulated protein targeting, metabolite exchange and division, so that the mitochondrion becomes an inherited endosymbiont and the new compartments persist. These requirements constrain any scenario even where the historical route remains uncertain.

A good in-vitro model should distinguish cancer invasion, movement across a tissue boundary into surrounding material, from simple growth or movement across a flat surface. No single assay reproduces the entire sequence from a primary tumour to a distant metastasis. Choose the assay to answer a specified mechanistic question, then confirm the result in a model that retains additional biological constraints.

A scratch assay measures closure of a gap in a monolayer. It is inexpensive and permits live-cell imaging, but closure combines cell migration, spreading and cell proliferation, and the wound releases signals and damages cells. It does not by itself demonstrate invasion through a basement membrane. A porous-membrane assay can measure transit toward a stimulus; adding an extracellular barrier tests an additional requirement. Yet pore size, coating thickness, chemical gradients and the counting time can dominate the result, and endpoint cell counts hide whether treatment altered survival or actual migration.

Three-dimensional tumour spheroids or organoids embedded in a defined extracellular matrix allow individual and collective invasion to be followed over time. Quantify invasion distance, cell escape, strand architecture and leader-follower behaviour, alongside changes in spheroid size and viability. Use collagen-rich and basement-membrane-like environments to test whether a phenotype depends on matrix identity. Independently vary ligand presentation, matrix stiffness and pore dimensions where possible: increasing collagen concentration changes several of them simultaneously.

A primary study of breast tumour organoids identified invasive leader cells expressing a basal epithelial programme, including K14 and p63; reducing either component impaired collective invasion in that system. The experiment connected a defined cellular subpopulation to an invasion phenotype rather than assuming that every tumour cell was equivalent.^[ref] Its conclusion remains specific to the tested settings and does not make these markers universal requirements for invasion.

Add stromal cells, immune cells or a vessel-like boundary if the question concerns their interactions. Microfluidics can impose controlled gradients and permit live-cell imaging of entry into or exit from a channel. Include non-invasive and invasive controls, perturbation controls, rescue where feasible, and matched measurements of cell proliferation and death. Follow individual cells rather than relying solely on a final stained area. Patient-derived material should include multiple independent tumours: many fields from one culture are not independent patient replicates.

Limitations remain substantial. Culture selects cells that tolerate the medium; long-passaged lines may lose the original tumour's diversity. Matrices and added growth factors can have variable composition. Isolated cultures omit native immune surveillance, vascular perfusion, whole-organ architecture and systemic influences. Even elaborate organoids incompletely reproduce these features. Finally, invasion is only one stage: it does not establish survival in blood, colonization of a distant organ, or clinical response. Agreement across complementary assays strengthens a mechanism; no dish-based result alone proves a metastatic outcome in a person.