Data Efficiency, Dimensionality Reduction, and the Generalized Symmetric Information Bottleneck.

The symmetric information bottleneck (SIB), an extension of the more familiar information bottleneck, is a dimensionality-reduction technique that simultaneously compresses two random variables to preserve information between their compressed versions. We introduce the generalized symmetric information bottleneck (GSIB), which explores different functional forms of the cost of such simultaneous reduction. We then explore the data set size requirements of such simultaneous compression. We do this by deriving bounds and root-mean-squared estimates of statistical fluctuations of the involved loss functions. We show that in typical situations, the simultaneous GSIB compression requires qualitatively less data to achieve the same errors compared to compressing variables one at a time. We suggest that this is an example of a more general principle that simultaneous compression is more data efficient than independent compression of each of the input variables.

Testing the retroelement invasion hypothesis for the emergence of the ancestral eukaryotic cell.

Phylogenetic evidence suggests that the invasion and proliferation of retroelements, selfish mobile genetic elements that copy and paste themselves within a host genome, was one of the early evolutionary events in the emergence of eukaryotes. Here we test the effects of this event by determining the pressures retroelements exert on simple genomes. We transferred two retroelements, human LINE-1 and the bacterial group II intron Ll.LtrB, into bacteria, and find that both are functional and detrimental to growth. We find, surprisingly, that retroelement lethality and proliferation are enhanced by the ability to perform eukaryotic-like nonhomologous end-joining (NHEJ) DNA repair. We show that the only stable evolutionary consequence in simple cells is maintenance of retroelements in low numbers, suggesting how retrotransposition rates and costs in early eukaryotes could have been constrained to allow proliferation. Our results suggest that the interplay between NHEJ and retroelements may have played a fundamental and previously unappreciated role in facilitating the proliferation of retroelements, elements of which became the ancestors of the spliceosome components in eukaryotes.

Stochastic Turing patterns in a synthetic bacterial population.

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.

Model for screened, charge-regulated electrostatics of an eye lens protein: Bovine gammaB-crystallin.

We model screened, site-specific charge regulation of the eye lens protein bovine gammaB-crystallin (γB) and study the probability distributions of its proton occupancy patterns. Using a simplified dielectric model, we solve the linearized Poisson-Boltzmann equation to calculate a 54×54 work-of-charging matrix, each entry being the modeled voltage at a given titratable site, due to an elementary charge at another site. The matrix quantifies interactions within patches of sites, including γB charge pairs. We model intrinsic pK values that would occur hypothetically in the absence of other charges, with use of experimental data on the dependence of pK values on aqueous solution conditions, the dielectric model, and literature values. We use Monte Carlo simulations to calculate a model grand-canonical partition function that incorporates both the work-of-charging and the intrinsic pK values for isolated γB molecules and we calculate the probabilities of leading proton occupancy configurations, for 4

Real-time transposable element activity in individual live cells.

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.

Model for evaluating patterned charge-regulation contributions to electrostatic interactions between low-dielectric spheres.

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 k(B)T. 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.