Extracting Transition Rates in Particle Tracking Using Analytical Diffusion Distribution Analysis

Single-particle tracking is an important technique in the life sciences to understand the kinetics of biomolecules. The analysis of apparent diffusion coefficients in vivo, for example, enables researchers to determine whether biomolecules are moving alone, as part of a larger complex, or are bound to large cellular components such as the membrane or chromosomal DNA. A remaining challenge has been to retrieve quantitative kinetic models, especially for molecules that rapidly switch between different diffusional states. Here, we present analytical diffusion distribution analysis (anaDDA), a framework that allows for extracting transition rates from distributions of apparent diffusion coefficients calculated from short trajectories that feature less than 10 localizations per track. Under the assumption that the system is Markovian and diffusion is purely Brownian, we show that theoretically predicted distributions accurately match simulated distributions and that anaDDA outperforms existing methods to retrieve kinetics, especially in the fast regime of 0.1–10 transitions per imaging frame. AnaDDA does account for the effects of confinement and tracking window boundaries. Furthermore, we added the option to perform global fitting of data acquired at different frame times to allow complex models with multiple states to be fitted confidently. Previously, we have started to develop anaDDA to investigate the target search of CRISPR-Cas complexes. In this work, we have optimized the algorithms and reanalyzed experimental data of DNA polymerase I diffusing in live Escherichia coli. We found that long-lived DNA interaction by DNA polymerase are more abundant upon DNA damage, suggesting roles in DNA repair. We further revealed and quantified fast DNA probing interactions that last shorter than 10 ms. AnaDDA pushes the boundaries of the timescale of interactions that can be probed with single-particle tracking and is a mathematically rigorous framework that can be further expanded to extract detailed information about the behavior of biomolecules in living cells.     

A mathematical view on the decoupled sites representation

The decoupled sites representation (DSR) is a theoretical instrument which allows to regard complex pH titration curves of biomolecules with several interacting proton binding sites as composition of isolated, non-interacting sites, each with a standard Henderson–Hasselbalch titration curve. In this work, we present the mathematical framework in which the DSR is embedded and give mathematical proofs for several statements in the periphery of the DSR. These proofs also identify exceptions. To apply the DSR to any molecule, it is necessary to extend the set of binding energies from ${\mathbb{R}}$ to a stripe within ${\mathbb{C}}$ . An important observation in this context is that even positive interaction energies (repulsion) between the binding sites will not guarantee real binding energies in the decoupled system, at least if the molecule has more than four proton binding sites. Moreover, we show that for a given overall titration curve it is not only possible to find a corresponding system with an interaction energy of zero but with any arbitrary fix interaction energy. This result also effects practical work as it shows that for any given titration curve, there is an infinite number of corresponding hypothetical molecules. Furthermore, this implies that—using a common definition of cooperative binding on the level of interaction energies—a meaningful measure of cooperativity between the binding sites cannot be defined solely on the basis of the overall titration. Consequently, all measures of cooperativity based on the overall binding curve do not measure the type of cooperativity commonly defined on the basis of interaction energies. Understanding the DSR mathematically provides the basis of transferring the DSR to biomolecules with different types of interacting ligands, such as protons and electrons, which play an important role within electron transport chains like in photosynthesis.     

Buchbesprechungen

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Umbreit, W. W.: Modern microbiology. San Francisco und London, W. H. Freeman and Company, 1962, 507 S., 307 Abb., Leinen, 48 s. Reviewed by H. J. Müller.

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Recombinase-mediated cassette exchange (RMCE) — A rapidly-expanding toolbox for targeted genomic modifications

Starting in 1991, the advance of Tyr-recombinases Flp and Cre enabled superior strategies for the predictable insertion of transgenes into compatible target sites of mammalian cells. Early approaches suffered from the reversibility of integration routes and the fact that co-introduction of prokaryotic vector parts triggered uncontrolled heterochromatization. Shortcomings of this kind were overcome when Flp-Recombinase Mediated Cassette Exchange entered the field in 1994. RMCE enables enhanced tag-and-exchange strategies by precisely replacing a genomic target cassette by a compatible donor construct. After “gene swapping” the donor cassette is safely locked in, but can nevertheless be re-mobilized in case other compatible donor cassettes are provided (“serial RMCE”). These features considerably expand the options for systematic, stepwise genome modifications. The first decade was dominated by the systematic generation of cell lines for biotechnological purposes. Based on the reproducible expression capacity of the resulting strains, a comprehensive toolbox emerged to serve a multitude of purposes, which constitute the first part of this review. The concept per se did not, however, provide access to high-producer strains able to outcompete industrial multiple-copy cell lines. This fact gave rise to systematic improvements, among these certain accumulative site-specific integration pathways. The exceptional value of RMCE emerged after its entry into the stem cell field, where it started to contribute to the generation of induced pluripotent stem (iPS-) cells and their subsequent differentiation yielding a variety of cell types for diagnostic and therapeutic purposes. This topic firmly relies on the strategies developed in the first decade and can be seen as the major ambition of the present article. In this context an unanticipated, potent property of serial Flp-RMCE setups concerns the potential to re-open loci that have served to establish the iPS status before the site underwent the obligatory silencing process. Other relevant options relate to the introduction of composite Flp-recognition target sites (“heterospecific FRT-doublets”), into the LTRs of lentiviral vectors. These “twin sites” enhance the safety of iPS re-programming and -differentiation as they enable the subsequent quantitative excision of a transgene, leaving behind a single “FRT-twin”. Such a strategy combines the established expression potential of the common retro- and lentiviral systems with options to terminate the process at will. The remaining genomic tag serves to identify and characterize the insertion site with the goal to identify genomic “safe harbors” (GOIs) for re-use. This is enabled by the capacity of “FRT-twins” to accommodate any incoming RMCE-donor cassette with a compatible design.     

Nitrogen dynamics following field application of biochar in a temperate North American maize-based production system

Background and aims

Biochar additions to tropical soils have been shown to reduce N leaching and increase N use efficiency. No studies exist verifying reduced N leaching in field experiments on temperate agricultural soils or identifying the mechanism for N retention.

Methods

Biochar derived from maize stover was applied to a maize cropping system in central New York State at rates of 0, 1, 3, 12, and 30 t?ha^-1 in 2007. Secondary N fertilizer was added at 100, 90, 70, and 50 % of the recommended rate (108 kg N ha^-1). Nitrogen fertilizer enriched with ¹⁵?N was applied in 2009 to the 0 and 12 t?ha^-1 of biochar at 100 and 50 % secondary N application.

Results

Maize yield and plant N uptake did not change with biochar additions (p?>?0.05; n?=?3). Less N (by 82 %; p?<?0.05) was lost after biochar application through leaching only at 100 %?N fertilization. The reason for an observed 140 % greater retention of applied ¹⁵?N in the topsoil may have been the incorporation of added ¹⁵?N into microbial biomass which increased approximately three-fold which warrants further research. The low leaching of applied fertilizer ¹⁵?N (0.42 % of applied N; p?<?0.05) and comparatively high recovery of applied ¹⁵?N in the soil (39 %) after biochar additions after one cropping season may also indicate greater overall N retention through lower gaseous or erosion N losses with biochar.

Conclusions

Addition of biochar to fertile soil in a temperate climate did not improve crop growth or N use efficiency, but increased retention of fertilizer N in the topsoil.     

Modelling root plasticity and response of narrow-leafed lupin to heterogeneous phosphorus supply

Background & Aims

Searching for root traits underpinning efficient nutrient acquisition has received increased attention in modern breeding programs aimed at improved crop productivity. Root models provide an opportunity to investigate root-soil interactions through representing the relationships between rooting traits and the non-uniform supply of soil resources. This study used simulation modelling to predict and identify phenotypic plasticity, root growth responses and phosphorus (P) use efficiency of contrasting Lupinus angustifolius genotypes to localised soil P in a glasshouse.

Methods

Two L. angustifolius genotypes with contrasting root systems were grown in cylindrical columns containing uniform soil with three P treatments (nil and 20 mg P kg^?1 either top-dressed or banded) in the glasshouse. Computer simulations were carried out with root architecture model ROOTMAP which was parameterized with root architectural data from an earlier published hydroponic phenotyping study.

Results

The experimental and simulated results showed that plants supplied with banded P had the largest root system and the greatest P-uptake efficiency. The P addition significantly stimulated root branching in the topsoil, whereas plants with nil P had relatively deeper roots. Genotype-dependent root growth plasticity in response to P supply was shown, with the greatest response to banded P.

Conclusions

Both experimental and simulation outcomes demonstrated that 1) root hairs and root proliferation increased plant P acquisition and were more beneficial in the localised P fertilisation scenario, 2) placing P deeper in the soil might be a more effective fertilisation method with greater P uptake than top dressing, and 3) the combination of P foraging strategies (including root architecture, root hairs and root growth plasticity) is important for efficient P acquisition from a localised source of fertiliser P.