A power law for cells

Darwin observed that multiple, lowly organized, rudimentary, or exaggerated structures show increased relative variability. However, the cellular basis for these laws has never been investigated. Some animals, such as the nematode Caenorhabditis elegans, are famous for having organs that possess the same number of cells in all individuals, a property known as eutely. But for most multicellular creatures, the extent of cell number variability is unknown. Here we estimate variability in organ cell number for a variety of animals, plants, slime moulds, and volvocine algae. We find that the mean and variance in cell number obey a power law with an exponent of 2, comparable to Taylor's law in ecological processes. Relative cell number variability, as measured by the coefficient of variation, differs widely across taxa and tissues, but is generally independent of mean cell number among homologous tissues of closely related species. We show that the power law for cell number variability can be explained by stochastic branching process models based on the properties of cell lineages. We also identify taxa in which the precision of developmental control appears to have evolved. We propose that the scale independence of relative cell number variability is maintained by natural selection.

The law of mass action governs antigen-stimulated cytolytic activity of CD8+ cytotoxic T lymphocytes.

An analysis of the initial antigen-recognition step in the destruction of target cells by CD8+ cytolytic T lymphocytes (CTLs) shows that a relationship in the form of the law of mass action can be used to describe interactions between antigen-specific receptors on T cells (TCRs) and their natural ligands on target cells (peptide-major histocompatibility protein complexes, termed pepMHC complexes), even though these reactants are confined to their respective cell membranes. For a designated level of lysis and receptor affinities below about 5 X 10(6) M-1, the product of the required number of pepMHC complexes per target cell ("epitope density") and TCR affinity for pepMHC complexes is constant; therefore, over this range TCR affinities can be predicted from epitope densities (or vice versa). At higher receptor affinities ("affinity ceiling") the epitope density required for half-maximal lysis reaches a lower limit of less than 10 complexes per target cell.