The origin of biological morphology and form is one of the deepest problems in science, underlying our understanding of development and the functioning of living systems. In 1952, Alan Turing showed that chemical morphogenesis could arise from a linear instability of a spatially uniform state, giving rise to periodic pattern formation in reaction-diffusion systems but only those with a rapidly diffusing inhibitor and a slowly diffusing activator. These conditions are disappointingly hard to achieve in nature, and the role of Turing instabilities in biological pattern formation has been called into question. Recently, the theory was extended to include noisy activator-inhibitor birth and death processes. Surprisingly, this stochastic Turing theory predicts the existence of patterns over a wide range of parameters, in particular with no severe requirement on the ratio of activator-inhibitor diffusion coefficients. To explore whether this mechanism is viable in practice, we have genetically engineered a synthetic bacterial population in which the signaling molecules form a stochastic activator-inhibitor system. The synthetic pattern-forming gene circuit destabilizes an initially homogenous lawn of genetically engineered bacteria, producing disordered patterns with tunable features on a spatial scale much larger than that of a single cell. Spatial correlations of the experimental patterns agree quantitatively with the signature predicted by theory. These results show that Turing-type pattern-forming mechanisms, if driven by stochasticity, can potentially underlie a broad range of biological patterns. These findings provide the groundwork for a unified picture of biological morphogenesis, arising from a combination of stochastic gene expression and dynamical instabilities.
We have produced loose packings of cohesionless, frictional spheres by sequential deposition of highly-spherical, monodisperse particles through a fluid. By varying the properties of the fluid and the particles, we have identified the Stokes number (St) - rather than the buoyancy of the particles in the fluid - as the parameter controlling the approach to the loose packing limit. The loose packing limit is attained at a threshold value of St at which the kinetic energy of a particle impinging on the packing is fully dissipated by the fluid. Thus, for cohesionless particles, the dynamics of the deposition process, rather than the stability of the static packing, defines the random loose packing limit. We have made direct measurements of the interparticle friction in the fluid, and present an experimental measurement of the loose packing volume fraction, \phi_{RLP}, as a function of the friction coefficient \mu_s.Comment: 6 pages, 5 figure
The excision and reintegration of transposable elements (TEs) restructure their host genomes, generating cellular diversity involved in evolution, development, and the etiology of human diseases. Our current knowledge of TE behavior primarily results from bulk techniques that generate time and cell ensemble averages, but cannot capture cell-to-cell variation or local environmental and temporal variability. We have developed an experimental system based on the bacterial TE IS608 that uses fluorescent reporters to directly observe single TE excision events in individual cells in real time. We find that TE activity depends upon the TE's orientation in the genome and the amount of transposase protein in the cell. We also find that TE activity is highly variable throughout the lifetime of the cell. Upon entering stationary phase, TE activity increases in cells hereditarily predisposed to TE activity. These direct observations demonstrate that real-time live-cell imaging of evolution at the molecular and individual event level is a powerful tool for the exploration of genome plasticity in stressed cells.transposable elements | evolution | quantitative biology A transposable element (TE) is a mobile genetic element that propagates within its host genome by self-catalyzed copying or excision followed by genomic reintegration (1). TEs exist in all domains of life, and the activity of TEs necessarily generates mutations in the host genome. Consequently, TEs are major contributors to disease (2-8), development (9, 10), and evolution (11, 12); they are also used as molecular tools in synthetic biology and bioengineering (13).Despite their ubiquity and importance, surprisingly little is known about the behavior and dynamics of TE activity in living cells. TE propagation rates can be inferred from comparative phylogenetic analyses of related organisms (14-20) or endpoint analyses of TE abundance within populations (11,(21)(22)(23). By making assumptions about the mechanisms of TE proliferation, models can be constructed to describe the distribution of TEs within genomes over evolutionary time scales, and sequenced genomes can be analyzed and fit to TE proliferation models to infer phylogeny of TE copies and estimate their rates of propagation (24). However, most sequencing techniques require bulk sampling of cells to provide genetic material, and sequencing is therefore generally an average over many cells. As a result, without extremely deep or single-cell sequencing techniques, most current methods are sufficient to detect only those TE events that have occurred in the germ line and therefore appear in every somatic cell in the body (25).TE rates can also be estimated by measuring relative abundances in populations that have been allowed to mutate over laboratory time scales. One of the first examples of this approach was that by Paquin and Williamson (23) to study the effects of temperature on the rate of integration of Ty retrotransposons in Saccharomyces cerevisiae after growth for 6-8 generations, resulting in yeast re...
We study the electrostatic contribution to the effective potential between two spherical low-dielectric particles that carry proton-titratable sites within a linearized setting. To evaluate the needed work of charging for each possible proton occupancy configuration, together with its crucial dependence on sphere separation, we numerically solve a coarse-grained linear Debye-Hückel model that incorporates nonuniform dielectric and ionic solution properties at a series of intersphere separations and for chosen titratable charge locations on each sphere. We combine the resulting work-of-charging matrix with site-specific chemical potentials of proton binding to construct the Boltzmann-weighted probabilities of each possible occupancy pattern of the titratable sites as functions of intersphere separation. With the use of these probabilities we find that a nonmonotonic average electrostatic potential can result that is repulsive at larger sphere separations but attractive at close separations. The nonmonotonic potential corresponds to particular choices of site-specific unoccupied charge values and their corresponding proton affinities, and its occurrence is dependent on pH in relation to the pKa values of the titratable groups. For the chosen titratable groups, we identify the particular change from repulsive to attractive proton occupancy patterns with decreasing intersphere separation that gives rise to the modeled nonmonotonic dependence and derive more general conditions under which such a nonmonotonic dependence can occur. Within the present model we find that stationary points of the charge-regulated average electrostatic potential, considered as a function of intersphere separation, occur when a normalized Boltzmann-averaged intersphere charge number product equals its covariance with an average free energy of charging divided by kBT. We derive more general conditions for the location and nature of critical points in the electrostatic intersphere potential, which are not dependent on the validity of the present linear model. Analysis of the present simple prototype model can be a helpful step toward developing a framework for predicting when (i) patterned charge-regulated occupancy patterns, (ii) orientation-dependent attractions due to relatively fixed heterogeneous charging patterns, and (iii) screened net protein charge could separately dominate the electrostatic portion of the interactions between model biological macromolecules and other nanoparticles.
SignificancePhylogenetic evidence suggests that a factor in the emergence of the ancestral eukaryotic cell may have been selection pressure resulting from invasion and proliferation of retroelements. Here we experimentally determine the effects of a retroelement invasion on genetically simple host organisms, and we demonstrate theoretically that the observed effects are sufficient to explain their observed rarity in bacteria. We also show that nonhomologous end-joining (NHEJ), a mechanism of DNA repair found in all extant eukaryotes, but only some bacteria, significantly enhances the efficiency of retrotransposition and the effects of retroelements on the host. We hypothesize that the interplay of NHEJ and retroelements may have played a previously unappreciated role in the evolution of advanced life.
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