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.

Intrinsic noise in gene regulatory networks

Cells are intrinsically noisy biochemical reactors: low reactant numbers can lead to significant statistical fluctuations in molecule numbers and reaction rates. Here we use an analytic model to investigate the emergent noise properties of genetic systems. We find for a single gene that noise is essentially determined at the translational level, and that the mean and variance of protein concentration can be independently controlled. The noise strength immediately following single gene induction is almost twice the final steady-state value. We find that fluctuations in the concentrations of a regulatory protein can propagate through a genetic cascade; translational noise control could explain the inefficient translation rates observed for genes encoding such regulatory proteins. For an autoregulatory protein, we demonstrate that negative feedback efficiently decreases system noise. The model can be used to predict the noise characteristics of networks of arbitrary connectivity. The general procedure is further illustrated for an autocatalytic protein and a bistable genetic switch. The analysis of intrinsic noise reveals biological roles of gene network structures and can lead to a deeper understanding of their evolutionary origin.

Single-pair fluorescence resonance energy transfer on freely diffusing molecules: Observation of Förster distance dependence and subpopulations

Photon bursts from single diffusing donor-acceptor labeled macromolecules were used to measure intramolecular distances and identify subpopulations of freely diffusing macromolecules in a heterogeneous ensemble. By using DNA as a rigid spacer, a series of constructs with varying intramolecular donor-acceptor spacings were used to measure the mean and distribution width of fluorescence resonance energy transfer (FRET) efficiencies as a function of distance. The mean single-pair FRET efficiencies qualitatively follow the distance dependence predicted by Förster theory. Possible contributions to the widths of the FRET efficiency distributions are discussed, and potential applications in the study of biopolymer conformational dynamics are suggested. The ability to measure intramolecular (and intermolecular) distances for single molecules implies the ability to distinguish and monitor subpopulations of molecules in a mixture with different distances or conformational states. This is demonstrated by monitoring substrate and product subpopulations before and after a restriction endonuclease cleavage reaction. Distance measurements at single-molecule resolution also should facilitate the study of complex reactions such as biopolymer folding. To this end, the denaturation of a DNA hairpin was examined by using single-pair FRET.