Intercellular communication induces glycolytic synchronization waves between individually oscillating cells.

Many organs have internal structures with spatially differentiated and sometimes temporally synchronized groups of cells. The mechanisms leading to such differentiation and coordination are not well understood. Here we design a diffusion-limited microfluidic system to mimic a multicellular organ structure with peripheral blood flow and test whether a group of individually oscillating yeast cells could form subpopulations of spatially differentiated and temporally synchronized cells. Upon substrate addition, the dynamic response at single-cell level shows glycolytic oscillations, leading to wave fronts traveling through the monolayered population and to synchronized communities at well-defined positions in the cell chamber. A detailed mechanistic model with the architectural structure of the flow chamber incorporated successfully predicts the spatial-temporal experimental data, and allows for a molecular understanding of the observed phenomena. The intricate interplay of intracellular biochemical reaction networks leading to the oscillations, combined with intercellular communication via metabolic intermediates and fluid dynamics of the reaction chamber, is responsible for the generation of the subpopulations of synchronized cells. This mechanism, as analyzed from the model simulations, is experimentally tested using different concentrations of cyanide stress solutions. The results are reproducible and stable, despite cellular heterogeneity, and the spontaneous community development is reminiscent of a zoned cell differentiation often observed in multicellular organs.

Stochastic unfolding of nanoconfined DNA: Experiments, model and Bayesian analysis.

Nanochannels provide a means for detailed experiments on the effect of confinement on biomacromolecules, such as DNA. Here we introduce a model for the complete unfolding of DNA from the circular to linear configuration. Two main ingredients are the entropic unfolding force and the friction coefficient for the unfolding process, and we describe the associated dynamics by a non-linear Langevin equation. By analyzing experimental data where DNA molecules are photo-cut and unfolded inside a nanochannel, our model allows us to extract values for the unfolding force as well as the friction coefficient for the first time. In order to extract numerical values for these physical quantities, we employ a recently introduced Bayesian inference framework. We find that the determined unfolding force is in agreement with estimates from a simple Flory-type argument. The estimated friction coefficient is in agreement with theoretical estimates for motion of a cylinder in a channel. We further validate the estimated friction constant by extracting this parameter from DNA's center-of-mass motion before and after unfolding, yielding decent agreement. We provide publically available software for performing the required image and Bayesian analysis.

Optical manipulation for studies of collisional dynamics of micron-sized droplets under gravity.

A new experimental technique for creating and imaging collisions of micron-sized droplets settling under gravity is presented. A pair of glycerol droplets is suspended in air by means of two optical traps. The droplet relative velocities are determined by the droplet sizes. The impact parameter is precisely controlled by positioning the droplets using the two optical traps. The droplets are released by turning off the trapping light using electro-optical modulators. The motion of the sedimenting droplets is then captured by two synchronized high-speed cameras, at a frame rate of up to 63 kHz. The method allows the direct imaging of the collision of droplets without the influence of the optical confinement imposed by the trapping force. The method will facilitate efficient studies of the microphysics of neutral, as well as charged, liquid droplets and their interactions with light, electric field and thermodynamic environment, such as temperature or vapor concentration.

Visualizing the Nonhomogeneous Structure of RAD51 Filaments Using Nanofluidic Channels.

RAD51 is the key component of the homologous recombination pathway in eukaryotic cells and performs its task by forming filaments on DNA. In this study we investigate the physical properties of RAD51 filaments formed on DNA using nanofluidic channels and fluorescence microscopy. Contrary to the bacterial ortholog RecA, RAD51 forms inhomogeneous filaments on long DNA in vitro, consisting of several protein patches. We demonstrate that a permanent "kink" in the filament is formed where two patches meet if the stretch of naked DNA between the patches is short. The kinks are readily seen in the present microscopy approach but would be hard to identify using conventional single DNA molecule techniques where the DNA is more stretched. We also demonstrate that protein patches separated by longer stretches of bare DNA roll up on each other and this is visualized as transiently overlapping filaments. RAD51 filaments can be formed at several different conditions, varying the cation (Mg(2+) or Ca(2+)), the DNA substrate (single-stranded or double-stranded), and the RAD51 concentration during filament nucleation, and we compare the properties of the different filaments formed. The results provide important information regarding the physical properties of RAD51 filaments but also demonstrate that nanofluidic channels are perfectly suited to study protein-DNA complexes.

Measurement of particle motion in optical tweezers embedded in a Sagnac interferometer.

We have constructed a counterpropagating optical tweezers setup embedded in a Sagnac interferometer in order to increase the sensitivity of position tracking for particles in the geometrical optics regime. Enhanced position determination using a Sagnac interferometer has previously been described theoretically by Taylor et al. [Journal of Optics 13, 044014 (2011)] for Rayleigh-regime particles trapped in an antinode of a standing wave. We have extended their theory to a case of arbitrarily-sized particles trapped with orthogonally-polarized counter-propagating beams. The working distance of the setup was sufficiently long to optically induce particle oscillations orthogonally to the axis of the tweezers with an auxiliary laser beam. Using these oscillations as a reference, we have experimentally shown that Sagnac-enhanced back focal plane interferometry is capable of providing an improvement of more than 5 times in the signal-to-background ratio, corresponding to a more than 30-fold improvement of the signal-to-noise ratio. The experimental results obtained are consistent with our theoretical predictions. In the experimental setup, we used a method of optical levitator-assisted liquid droplet delivery in air based on commercial inkjet technology, with a novel method to precisely control the size of droplets.

How nanochannel confinement affects the DNA melting transition within the Poland-Scheraga model.

When double-stranded DNA molecules are heated, or exposed to denaturing agents, the two strands are separated. The statistical physics of this process has a long history and is commonly described in terms of the Poland-Scheraga (PS) model. Crucial to this model is the configurational entropy for a melted region (compared to the entropy of an intact region of the same size), quantified by the loop factor. In this study, we investigate how confinement affects the DNA melting transition, by using the loop factor for an ideal Gaussian chain. By subsequent numerical solutions of the PS model, we demonstrate that the melting temperature depends on the persistence lengths of single-stranded and double-stranded DNA. For realistic values of the persistence lengths, the melting temperature is predicted to decrease with decreasing channel diameter. We also demonstrate that confinement broadens the melting transition. These general findings hold for the three scenarios investigated: 1. homo-DNA, i.e., identical basepairs along the DNA molecule, 2. random sequence DNA, and 3. "real" DNA, here T4 phage DNA. We show that cases 2 and 3 in general give rise to broader transitions than case 1. Case 3 exhibits a similar phase transition as case 2 provided the random sequence DNA has the same ratio of AT to GC basepairs (A - adenine, T - thymine, G - guanine, C - cytosine). A simple analytical estimate for the shift in melting temperature is provided as a function of nanochannel diameter. For homo-DNA, we also present an analytical prediction of the melting probability as a function of temperature.

The emergence of the rescue effect from explicit within- and between-patch dynamics in a metapopulation.

Immigration can rescue local populations from extinction, helping to stabilize a metapopulation. Local population dynamics is important for determining the strength of this rescue effect, but the mechanistic link between local demographic parameters and the rescue effect at the metapopulation level has received very little attention by modellers. We develop an analytical framework that allows us to describe the emergence of the rescue effect from interacting local stochastic dynamics. We show this framework to be applicable to a wide range of spatial scales, providing a powerful and convenient alternative to individual-based models for making predictions concerning the fate of metapopulations. We show that the rescue effect plays an important role in minimizing the increase in local extinction probability associated with high demographic stochasticity, but its role is more limited in the case of high local environmental stochasticity of recruitment or survival. While most models postulate the rescue effect, our framework provides an explicit mechanistic link between local dynamics and the emergence of the rescue effect, and more generally the stability of the whole metapopulation.

An accurate model for genetic hitchhiking.

We suggest a simple deterministic approximation for the growth of the favored-allele frequency during a selective sweep. Using this approximation we introduce an accurate model for genetic hitchhiking. Only when Ns<10 (N is the population size and s denotes the selection coefficient) are discrepancies between our approximation and direct numerical simulations of a Moran model notable. Our model describes the gene genealogies of a contiguous segment of neutral loci close to the selected one, and it does not assume that the selective sweep happens instantaneously. This enables us to compute SNP distributions on the neutral segment without bias.

Clines on the seashore: The genomic architecture underlying rapid divergence in the face of gene flow.

Adaptive divergence and speciation may happen despite opposition by gene flow. Identifying the genomic basis underlying divergence with gene flow is a major task in evolutionary genomics. Most approaches (e.g., outlier scans) focus on genomic regions of high differentiation. However, not all genomic architectures potentially underlying divergence are expected to show extreme differentiation. Here, we develop an approach that combines hybrid zone analysis (i.e., focuses on spatial patterns of allele frequency change) with system-specific simulations to identify loci inconsistent with neutral evolution. We apply this to a genome-wide SNP set from an ideally suited study organism, the intertidal snail Littorina saxatilis, which shows primary divergence between ecotypes associated with different shore habitats. We detect many SNPs with clinal patterns, most of which are consistent with neutrality. Among non-neutral SNPs, most are located within three large putative inversions differentiating ecotypes. Many non-neutral SNPs show relatively low levels of differentiation. We discuss potential reasons for this pattern, including loose linkage to selected variants, polygenic adaptation and a component of balancing selection within populations (which may be expected for inversions). Our work is in line with theory predicting a role for inversions in divergence, and emphasizes that genomic regions contributing to divergence may not always be accessible with methods purely based on allele frequency differences. These conclusions call for approaches that take spatial patterns of allele frequency change into account in other systems.

A universal mechanism generating clusters of differentiated loci during divergence-with-migration.

Genome-wide patterns of genetic divergence reveal mechanisms of adaptation under gene flow. Empirical data show that divergence is mostly concentrated in narrow genomic regions. This pattern may arise because differentiated loci protect nearby mutations from gene flow, but recent theory suggests this mechanism is insufficient to explain the emergence of concentrated differentiation during biologically realistic timescales. Critically, earlier theory neglects an inevitable consequence of genetic drift: stochastic loss of local genomic divergence. Here, we demonstrate that the rate of stochastic loss of weak local differentiation increases with recombination distance to a strongly diverged locus and, above a critical recombination distance, local loss is faster than local "gain" of new differentiation. Under high migration and weak selection, this critical recombination distance is much smaller than the total recombination distance of the genomic region under selection. Consequently, divergence between populations increases by net gain of new differentiation within the critical recombination distance, resulting in tightly linked clusters of divergence. The mechanism responsible is the balance between stochastic loss and gain of weak local differentiation, a mechanism acting universally throughout the genome. Our results will help to explain empirical observations and lead to novel predictions regarding changes in genomic architectures during adaptive divergence.

Entrainment of heterogeneous glycolytic oscillations in single cells.

Cell signaling, gene expression, and metabolism are affected by cell-cell heterogeneity and random changes in the environment. The effects of such fluctuations on cell signaling and gene expression have recently been studied intensively using single-cell experiments. In metabolism heterogeneity may be particularly important because it may affect synchronisation of metabolic oscillations, an important example of cell-cell communication. This synchronisation is notoriously difficult to describe theoretically as the example of glycolytic oscillations shows: neither is the mechanism of glycolytic synchronisation understood nor the role of cell-cell heterogeneity. To pin down the mechanism and to assess its robustness and universality we have experimentally investigated the entrainment of glycolytic oscillations in individual yeast cells by periodic external perturbations. We find that oscillatory cells synchronise through phase shifts and that the mechanism is insensitive to cell heterogeneity (robustness) and similar for different types of external perturbations (universality).

Finite-size corrections for confined polymers in the extended de Gennes regime.

Theoretical results for the extension of a polymer confined to a channel are usually derived in the limit of infinite contour length. But experimental studies and simulations of DNA molecules confined to nanochannels are not necessarily in this asymptotic limit. We calculate the statistics of the span and the end-to-end distance of a semiflexible polymer of finite length in the extended de Gennes regime, exploiting the fact that the problem can be mapped to a one-dimensional weakly self-avoiding random walk. The results thus obtained compare favorably with pruned-enriched Rosenbluth method (PERM) simulations of a three-dimensional discrete wormlike chain model of DNA confined in a nanochannel. We discuss the implications for experimental studies of linear λ-DNA confined to nanochannels at the high ionic strengths used in many experiments.

The effect of multiple paternity on genetic diversity of small populations during and after colonisation.

Genetic variation within and among populations is influenced by the genetic content of the founders and the migrants following establishment. This is particularly true if populations are small, migration rate low and habitats arranged in a stepping-stone fashion. Under these circumstances the level of multiple paternity is critical since multiply mated females bring more genetic variation into founder groups than single mated females. One such example is the marine snail Littorina saxatilis that during postglacial times has invaded mainland refuge areas and thereafter small islands emerging due to isostatic uplift by occasional rafting of multiply mated females. We modelled effects of varying degrees of multiple paternity on the genetic variation of island populations colonised by the founders spreading from the mainland, by quantifying the population heterozygosity during both the transient colonisation process, and after a steady state (with migration) has been reached. During colonisation, multiple mating by [Formula: see text] males increased the heterozygosity by [Formula: see text] in comparison with single paternity, while in the steady state the increase was [Formula: see text] compared with single paternity. In the steady state the increase of heterozygosity due to multiple paternity is determined by a corresponding increase in effective population size. During colonisation, by contrast, the increase in heterozygosity is larger and it cannot be explained in terms of the effective population size alone. During the steady-state phase bursts of high genetic variation spread through the system, and far from the mainland this led to short periods of high diversity separated by long periods of low diversity. The size of these fluctuations was boosted by multiple paternity. We conclude that following glacial periods of extirpation, recolonization of isolated habitats by this species has been supported by its high level of multiple paternity.

Extreme female promiscuity in a non-social invertebrate species.

BACKGROUND: While males usually benefit from as many matings as possible, females often evolve various methods of resistance to matings. The prevalent explanation for this is that the cost of additional matings exceeds the benefits of receiving sperm from a large number of males. Here we demonstrate, however, a strongly deviating pattern of polyandry. METHODOLOGY/PRINCIPAL FINDINGS: We analysed paternity in the marine snail Littorina saxatilis by genotyping large clutches (53-79) of offspring from four females sampled in their natural habitats. We found evidence of extreme promiscuity with 15-23 males having sired the offspring of each female within the same mating period. CONCLUSIONS/SIGNIFICANCE: Such a high level of promiscuity has previously only been observed in a few species of social insects. We argue that genetic bet-hedging (as has been suggested earlier) is unlikely to explain such extreme polyandry. Instead we propose that these high levels are examples of convenience polyandry: females accept high numbers of matings if costs of refusing males are higher than costs of accepting superfluous matings.

Caustic activation of rain showers.

We show quantitatively how the collision rate of droplets of visible moisture in turbulent air increases very abruptly as the intensity of the turbulence passes a threshold, due to the formation of fold caustics in their velocity field. The formation of caustics is an activated process, in which a measure of the intensity of the turbulence, termed the Stokes number St, is analogous to temperature in a chemical reaction: the rate of collision contains a factor exp(-C/St). Our results are relevant to the long-standing problem of explaining the rapid onset of rainfall from convecting clouds. Our theory does not involve spatial clustering of particles.

Clustering by mixing flows.

We calculate the Lyapunov exponents for particles suspended in a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time. In this limit Lyapunov exponents are obtained as a power series in epsilon, a dimensionless measure of the particle inertia. Although the perturbation generates an asymptotic series, we obtain accurate results from a Padé-Borel summation. Our results prove that particles suspended in an incompressible random mixing flow can show pronounced clustering when the Stokes number is large and we characterize two distinct clustering effects which occur in that limit.

Coagulation by random velocity fields as a Kramers problem.

We analyze the motion of a system of particles suspended in a fluid which has a random velocity field. There are coagulating and noncoagulating phases. We show that the phase transition is related to a Kramers problem, and we use this to determine the phase diagram in two dimensions, as a function of the dimensionless inertia of the particles, epsilon, and a measure of the relative intensities of potential and solenoidal components of the velocity field, Gamma. We find that the phase line is described by a function which is nonanalytic at epsilon=0, and which is related to escape over a barrier in the Kramers problem. We discuss the physical realizations of this phase transition.