Stem cell

A stem cell can produce both renewed stem cells and differentiated descendants. Its developmental range depends on the type and setting; self-renewal does not imply unrestricted cell fate.

For resting-cell recruitment $g(u)=bu/(1+u^n)$, a positive constant equilibrium exists precisely when $\mu b>1$, with $u_{\ast }=(\mu b-1{)}^{1/n}$. On slow time $T=ϵt$, expand the delayed value as $u(T-ϵ)=u-ϵu_T+O({ϵ}^2)$. Substitution gives $(1+g^{\prime }(u))u_T=\mu g(u)-u$ to leading order. This reduction requires smooth slow motion and $1+g^{\prime }(u)$ bounded away from zero.

On the original fast time, only the explicit order-$ϵ$ terms are dropped, leaving $u^{\prime }=g(u(t-1))-g(u(t))$. The unit delay remains order one and cannot be Taylor-expanded on that scale. For the biological two-compartment derivation, a fixed cell-cycle time $\tau$ and proliferating death hazard ${\gamma }_d$ give survival $e^{-{\gamma }_d\tau }$ and daughter-cell gain twice the surviving exit rate. Scaling gives $b={\beta }_0\tau$, $ϵ=\delta \tau$ and $1+ϵ\mu =2e^{-{\gamma }_d\tau }$. Thus small resting-cell loss over one cycle creates the slow-fast structure.

A self-renewing stem cell with capacity to give rise to multiple blood-cell lineages.

Capacity to generate the principal embryonic cell lineages under suitable conditions. Expression of one stem-cell marker alone does not establish this capacity.

A pluripotent state associated with later epiblast and readiness to respond to lineage-specifying signals. It is experimentally and molecularly distinct from naive pluripotency.

A transitional pluripotent state in which naive circuitry has been dismantled while competence for later lineage induction is being acquired. This is a state transition, not an additional germ layer.

A pluripotent state associated with the preimplantation mouse epiblast and a characteristic regulatory network. Naive cells differ from the postimplantation epiblast in signalling requirements, chromatin state and responsiveness to differentiation cues.

Maintenance of a renewing population through balanced outcomes across cells, without requiring every division to produce exactly one renewing daughter.

A model in which one functionally defined progenitor class can explain renewal through stochastic, balanced fates. Molecular uniformity and exact independence of neighbouring cells are stronger claims than the model requires.

Experimental removal of a population defined by location or marker. The result depends on efficiency, duration, surviving cells, niche injury and the ability of other cells to replace the targeted state.

Ablation of engineered receptor-expressing cells using diphtheria toxin. Receptor-negative toxin controls, time-course verification and survival of untargeted compartments are essential.

A self-renewing cell that supplies descendants to the germline. Division orientation relative to a stem-cell niche can help give daughters different developmental outcomes.

A specialized cytoplasmic structure in relevant fly germline cells associated with localization of cell-cycle regulators. Its organization must not be assumed identical in every stem-cell system.

The local cellular and extracellular environment regulating stem-cell persistence, renewal and differentiation. In culture, supplied matrix and growth factors may substitute for components normally provided by neighbouring cells.

Capacity to generate several specified differentiated cell types. It does not imply ability to generate every cell type or a whole organism.

Production of descendants that retain the originating population's developmental capacity. For a stem-cell population, self-renewal must accompany suitable differentiated output; persistence of a label alone does not establish both properties.

A stem cell contributing sustained differentiated descendants to the intestinal lining. Marker expression is suggestive; long-term lineage tracing tests renewal and lineage output.

A functional description for a cell that can restore intestinal stem-cell output after damage. It does not by itself establish a permanently distinct, uniquely marked quiescent lineage.

A cell at the crypt base, including actively cycling Lgr5-expressing stem cells interspersed with supporting cells in the mouse small intestine.

A stem cell derived from early embryonic tissue with capacity to generate many differentiated cell types under suitable conditions.