Akos Dobay

Discontinuous movement of mRNP particles in nucleoplasmic regions devoid of chromatin

Messenger ribonucleoprotein particles (mRNPs) move randomly within nucleoplasm before they exit from the nucleus. To further understand mRNP trafficking, we have studied the intranuclear movement of a specific mRNP, the BR2 mRNP, in salivary gland cells in Chironomus tentans. Their polytene nuclei harbor giant chromosomes separated by vast regions of nucleoplasm, which allows us to study mRNP mobility without interference of chromatin. The particles were fluorescently labeled with microinjected oligonucleotides (DNA or RNA) complementary to BR2 mRNA or with the RNA-binding protein hrp36, the C. tentans homologue of hnRNP A1. Using high-speed laser microscopy, we followed the intranuclear trajectories of single mRNPs and characterized their motion within the nucleoplasm. The Balbiani ring (BR) mRNPs moved randomly, but unexpectedly, in a discontinuous manner. When mobile, they diffused with a diffusion coefficient corresponding to their size. Between mobile phases, the mRNPs were slowed down 10-to 250-fold but were never completely immobile. Earlier electron microscopy work has indicated that BR particles can attach to thin nonchromatin fibers, which are sometimes connected to discrete fibrogranular clusters. We propose that the observed discontinuous movement reflects transient interactions between freely diffusing BR particles and these submicroscopic structures.

Dissection of cell cycle–dependent dynamics of Dnmt1 by FRAP and diffusion-coupled modeling

DNA methyltransferase 1 (Dnmt1) reestablishes methylation of hemimethylated CpG sites generated during DNA replication in mammalian cells. Two subdomains, the proliferating cell nuclear antigen (PCNA)-binding domain (PBD) and the targeting sequence (TS) domain, target Dnmt1 to the replication sites in S phase. We aimed to dissect the details of the cell cycle–dependent coordinated activity of both domains. To that end, we combined super-resolution 3D-structured illumination microscopy and fluorescence recovery after photobleaching (FRAP) experiments of GFP-Dnmt1 wild type and mutant constructs in somatic mouse cells. To interpret the differences in FRAP kinetics, we refined existing data analysis and modeling approaches to (i) account for the heterogeneous and variable distribution of Dnmt1-binding sites in different cell cycle stages; (ii) allow diffusion-coupled dynamics; (iii) accommodate multiple binding classes. We find that transient PBD-dependent interaction directly at replication sites is the predominant specific interaction in early S phase (residence time Tres ≤10 s). In late S phase, this binding class is taken over by a substantially stronger (Tres ∼22 s) TS domain-dependent interaction at PCNA-enriched replication sites and at nearby pericentromeric heterochromatin subregions. We propose a two-loading-platform-model of additional PCNA-independent loading at postreplicative, heterochromatic Dnmt1 target sites to ensure faithful maintenance of densely methylated genomic regions.

The average crossing number of equilateral random polygons

In this paper, we study the average crossing number of equilateral random walks and polygons. We show that the mean average crossing number ACN of all equilateral random walks of length n is of the form . A similar result holds for equilateral random polygons. These results are confirmed by our numerical studies. Furthermore, our numerical studies indicate that when random polygons of length n are divided into individual knot types, the for each knot type can be described by a function of the form where a, b and c are constants depending on and n0 is the minimal number of segments required to form . The profiles diverge from each other, with more complex knots showing higher than less complex knots. Moreover, the profiles intersect with the ACN profile of all closed walks. These points of intersection define the equilibrium length of , i.e., the chain length at which a statistical ensemble of configurations with given knot type —upon cutting, equilibration and reclosure to a new knot type —does not show a tendency to increase or decrease . This concept of equilibrium length seems to be universal, and applies also to other length-dependent observables for random knots, such as the mean radius of gyration Rg.

Co‐evolutionary dynamics between public good producers and cheats in the bacterium Pseudomonas aeruginosa

The production of beneficial public goods is common in the microbial world, and so is cheating – the exploitation of public goods by nonproducing mutants. Here, we examine co‐evolutionary dynamics between cooperators and cheats and ask whether cooperators can evolve strategies to reduce the burden of exploitation, and whether cheats in turn can improve their exploitation abilities. We evolved cooperators of the bacterium Pseudomonas aeruginosa, producing the shareable iron‐scavenging siderophore pyoverdine, together with cheats, defective in pyoverdine production but proficient in uptake. We found that cooperators managed to co‐exist with cheats in 56% of all replicates over approximately 150 generations of experimental evolution. Growth and competition assays revealed that co‐existence was fostered by a combination of general adaptions to the media and specific adaptions to the co‐evolving opponent. Phenotypic screening and whole‐genome resequencing of evolved clones confirmed this pattern, and suggest that cooperators became less exploitable by cheats because they significantly reduced their pyoverdine investment. Cheats, meanwhile, improved exploitation efficiency through mutations blocking the costly pyoverdine‐signalling pathway. Moreover, cooperators and cheats evolved reduced motility, a pattern that likely represents adaptation to laboratory conditions, but at the same time also affects social interactions by reducing strain mixing and pyoverdine sharing. Overall, we observed parallel evolution, where co‐existence of cooperators and cheats was enabled by a combination of adaptations to the abiotic and social environment and their interactions.

Predicting Optimal Lengths of Random Knots

In a thermally fluctuating long linear polymeric chain in a solution, the ends, from time to time, approach each other. At such an instance, the chain can be regarded as closed and thus will form a knot or rather a virtual knot. Several earlier studies of random knotting demonstrated that simpler knots show a higher occurrence for shorter random walks than do more complex knots. However, up to now there have been no rules that could be used to predict the optimal length of a random walk, i.e. the length for which a given knot reaches its highest occurrence. Using numerical simulations, we show here that a power law accurately describes the relation between the optimal lengths of random walks leading to the formation of different knots and the previously characterized lengths of ideal knots of a corresponding type.

Interaction effects of cell diffusion, cell density and public goods properties on the evolution of cooperation in digital microbes

Microbial cooperation typically consists in the sharing of secreted metabolites (referred to as public goods) within the community. Although public goods generally promote population growth, they are also vulnerable to exploitation by cheating mutants, which no longer contribute, but still benefit from the public goods produced by others. Although previous studies have identified a number of key factors that prevent the spreading of cheaters, little is known about how these factors interact and jointly shape the evolution of microbial cooperation. Here, we address this issue by investigating the interaction effects of cell diffusion, cell density, public good diffusion and durability (factors known to individually influence costs and benefits of public goods production) on selection for cooperation. To be able to quantify these effects across a wide parameter space, we developed an individual‐based simulation platform, consisting of digital cooperator and cheater bacteria inhabiting a finite two‐dimensional continuous toroidal surface. Our simulations, which closely mimic microbial microcolony growth, revealed that: (i) either reduced cell diffusion (which keeps cooperators together) or reduced public good diffusion (which keeps the public goods closer to the producer) is not only essential but also sufficient for cooperation to be promoted; (ii) the sign of selection for or against cooperation can change as a function of cell density and in interaction with diffusion parameters; and (iii) increased public goods durability has opposing effects on the evolution of cooperation depending on the level of cell and public good diffusion. Our work highlights that interactions between key parameters of public goods cooperation give rise to complex fitness landscapes, a finding that calls for multifactorial approaches when studying microbial cooperation in natural systems.

How many trimers? Modeling influenza virus fusion yields a minimum aggregate size of six trimers, three of which are fusogenic.

Conflicting reports in leading journals have indicated the minimum number of influenza hemagglutinin (HA) trimers required for fusion to be between one and eight. Interestingly, the data in these reports are either almost identical, or can be transformed to be directly comparable. Different statistical or phenomenological models, however, were used to analyze these data, resulting in the varied interpretations. In an attempt to resolve this contradiction, we use PABM, a brane calculus we recently introduced, enabling an algorithmic systems biology approach that allows the problem to be modeled in a manner following a biological logic. Since a scalable PABM executor is still under development, we sufficiently simplified the fusion model and analyzed it using the model checker, PRISM. We validated the model against older HA-expressing cell-to-cell fusion data using the same parameters with the exception of three, namely HA and sialic acid (SA) surface densities and the aggregation rate, which were expected to be different as a result of the difference in the experimental setup. Results are consistent with the interpretation that a minimum aggregate size of six HA trimers, of which three undergo a conformational change to become fusogenic, is required for fusion. Of these three, two are free, while one is bound. Finally, we determined the effects of varying the SA surface density and showed that only a limited range of densities permit fusion. Our results demonstrate the potential of modeling in providing more precise interpretations of data.

Renaissance model of an epidemic with quarantine

Quarantine is one possible solution to limit the propagation of an emerging infectious disease. Typically, infected individuals are removed from the population by avoiding physical contact with healthy individuals. A key factor for the success of a quarantine strategy is the carrying capacity of the facility. This is often a known parameter, while other parameters such as those defining the population structure are more difficult to assess. Here we develop a model where we explicitly introduce the carrying capacity of the quarantine facility into a susceptible-infected-recovered (SIR) framework. We show how the model can address the propagation and control of contact and sexually transmitted infections. We illustrate this by a case study of the city of Zurich during the 16th century, when it had to face an epidemic of syphilis. After Swiss mercenaries came back from a war in Naples in 1495, the authorities of the city addressed subsequent epidemics by, among others, placing infected members of the population in quarantine. Our results suggest that a modestly sized quarantine facility can successfully prevent or reduce an epidemic. However, false detection can present a real impediment for this solution. Indiscriminate quarantine of individuals can lead to the overfilling of the facility, and prevent the intake of infected individuals. This results in the failure of the quarantine policy. Hence, improving the rate of true over false detection becomes the key factor for quarantine strategies. Moreover, in the case of sexually transmitted infections, asymmetries in the male to female ratio, and the force of infection pertaining to each sex and class of sexual encounter can alter the effectiveness of quarantine measures. For example, a heterosexually transmitted disease that mainly affects one sex is harder to control in a population with more individuals of the opposite sex. Hence an imbalance in the sex ratios as seen in situations such as mining colonies, or populations at war, can present impediments for the success of quarantine policies.

Dynamics of a Tularemia Outbreak in a Closely Monitored Free-Roaming Population of Wild House Mice

Infectious disease outbreaks can be devastating because of their sudden occurrence, as well as the complexity of monitoring and controlling them. Outbreaks in wildlife are even more challenging to observe and describe, especially when small animals or secretive species are involved. Modeling such infectious disease events is relevant to investigating their dynamics and is critical for decision makers to accomplish outbreak management. Tularemia, caused by the bacterium Francisella tularensis, is a potentially lethal zoonosis. Of the few animal outbreaks that have been reported in the literature, only those affecting zoo animals have been closely monitored. Here, we report the first estimation of the basic reproduction number R 0 of an outbreak in wildlife caused by F. tularensis using quantitative modeling based on a susceptible-infected-recovered framework. We applied that model to data collected during an extensive investigation of an outbreak of tularemia caused by F. tularensis subsp. holarctica (also designated as type B) in a closely monitored, free-roaming house mouse (Mus musculus domesticus) population in Switzerland. Based on our model and assumptions, the best estimated basic reproduction number R 0 of the current outbreak is 1.33. Our results suggest that tularemia can cause severe outbreaks in small rodents. We also concluded that the outbreak self-exhausted in approximately three months without administrating antibiotics.

The Average Inter-crossing Number of Equilateral Random Walks and Polygons

In this paper, we study the average inter-crossing number between two random walks and two random polygons in the three-dimensional space. The random walks and polygons in this paper are the so-called equilateral random walks and polygons in which each segment of the walk or polygon is of unit length. We show that the mean average inter-crossing number ICN between two equilateral random walks of the same length n is approximately linear in terms of n and we were able to determine the prefactor of the linear term, which is . In the case of two random polygons of length n, the mean average inter-crossing number ICN is also linear, but the prefactor of the linear term is different from that of the random walks. These approximations apply when the starting points of the random walks and polygons are of a distance ρ apart and ρ is small compared to n. We propose a fitting model that would capture the theoretical asymptotic behaviour of the mean average ICN for large values of ρ. Our simulation result shows that the model in fact works very well for the entire range of ρ. We also study the mean ICN between two equilateral random walks and polygons of different lengths. An interesting result is that even if one random walk (polygon) has a fixed length, the mean average ICN between the two random walks (polygons) would still approach infinity if the length of the other random walk (polygon) approached infinity. The data provided by our simulations match our theoretical predictions very well.