Inferring kinetic rate constants from single-molecule FRET trajectories – a blind benchmark of kinetic analysis tools

Single-molecule FRET (smFRET) is a versatile technique to study the dynamics and function of biomolecules since it makes nanoscale movements detectable as fluorescence signals. The powerful ability to infer quantitative kinetic information from smFRET data is, however, complicated by experimental limitations. Diverse analysis tools have been developed to overcome these hurdles but a systematic comparison is lacking. Here, we report the results of a blind benchmark study assessing eleven analysis tools used to infer kinetic rate constants from smFRET trajectories. We tested them against simulated and experimental data containing the most prominent difficulties encountered in analyzing smFRET experiments: different noise levels, varied model complexity, non-equilibrium dynamics, and kinetic heterogeneity. Our results highlight the current strengths and limitations in inferring kinetic information from smFRET trajectories. In addition, we formulate concrete recommendations and identify key targets for future developments, aimed to advance our understanding of biomolecular dynamics through quantitative experiment-derived models.

The effects of gravitational potential on chemical reaction rates

This study aims to answer through a mathematical model and its numerical simulation the question whether the kinetic rate constants of chemical reactions are influenced by the strength of gravitational field. In order to calculate the effects of gravity on the kinetic rate constants, the model of kinetic rate constants derived from collision theory is amended by introducing the mass and length corrections provided by general relativity. Numerical simulations of the model show that the rate constant is higher where the gravitational field is more intense.

Comparison of methods for quantitative biomolecular interaction analysis

In order to perform good kinetic experiments, not only the experimental conditions have to be optimized, but the evaluation procedure as well. The focus of this work is the in-depth comparison of different approaches and algorithms to determine kinetic rate constants for biomolecular interaction analysis (BIA). The different algorithms are applied not only to flawless simulated data, but also to real-world measurements. We compare five mathematical approaches for the evaluation of binding curves following pseudo-first-order kinetics with different noise levels. In addition, reflectometric interference spectroscopy (RIfS) measurements of two antibodies are evaluated to determine their binding kinetics. The advantages and disadvantages of the individual approach will be investigated and discussed in detail. In summary, we will raise awareness on how to evaluate and judge results from BIA by using different approaches rather than having to rely on “black box” closed (commercial) software packages.

Comparative study on heterogeneous and homogeneous catalytic ozonation efficiency in micropollutants' removal

Catalytic ozonation was applied for the removal of small concentrations (4 μM) of micropollutants benzotriazole, carbamazepine, p-CBA from aqueous solutions at pH 7. These compounds present different physicochemical characteristics and different kinetic rate constants, when reacting with ozone or hydroxyl radicals in range of <0.15–3 × 105, 5.2 × 109, and 8.8 × 109 M−1s−1, respectively. Calcite was used as heterogeneous catalyst and its catalytic activity evaluated, by applying (and optimized) different experimental conditions (i.e., pH, temperature, ozone concentration), concerning the removal efficiency of p-CBA. Study of micropollutants' removal showed all examined organic compounds can be sufficiently removed by application of catalytic ozonation either by use of calcite, or by presence of Co(II) or Fe(II) (applied as homogeneous catalysts), while the optimum catalyst between them was found to be calcite. Carbamazepine with kO3 = 3 × 105 M−1s−1 can be easily removed, even by application of single ozonation, while benzotriazole and p-CBA resulted in 50% and 68.2% higher removal after application of catalytic ozonation within 3 min of oxidation reaction, due to acceleration of hydroxyl radicals' production by presence of calcite in the ozonation system. The contribution of hydroxyl radicals in removal of all three micropollutants was evaluated by extraction of Rct and f•OH parameters.

Identifiability analysis for models of the translation kinetics after mRNA transfection

Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants, usually cannot be measured directly but need to be inferred from experimental data. In this article, we study dynamical models of the translation kinetics after mRNA transfection and analyze their parameter identifiability. Previous studies have considered ordinary differential equation (ODE) models of the process, and here we formulate a stochastic differential equation (SDE) model. For both model types, we consider structural identifiability based on the model equations and practical identifiability based on simulated as well as experimental data and find that the SDE model provides better parameter identifiability than the ODE model. Moreover, our analysis shows that even for those parameters of the ODE model that are considered to be identifiable, the obtained estimates are sometimes unreliable. Overall, our study clearly demonstrates the relevance of considering different modeling approaches and that stochastic models can provide more reliable and informative results.

Parallel and sequential pathways of molecular recognition of a tandem-repeat protein and its intrinsically disordered binding partner

The Wnt signalling pathway plays an important role in cell proliferation, differentiation and fate decisions in embryonic development and in the maintenance of adult tissues, and the twelve Armadillo (ARM) repeat-containing protein β-catenin acts as the signal transducer in this pathway. Here we investigate the interaction between β-catenin and the intrinsically disordered transcription factor TCF7L2, comprising a very long nanomolar-affinity interface of approximately 4800 Å2 that spans ten of the twelve ARM repeats of β-catenin. First, a fluorescence reporter system for the interaction was engineered and used to determine the kinetic rate constants for the association and dissociation. The association kinetics of TCF7L2 and β-catenin was monophasic and rapid (7.3 ± 0.1 ×107 M-1s-1), whereas dissociation was biphasic and slow (5.7 ± 0.4 ×10−4 s-1, 15.2 ± 2.8 ×10−4 s-1). This reporter system was then combined with site-directed mutagenesis to investigate the striking variability in the conformation adopted by TCF7L2 in the three different crystal structures of the TCF7L2-β-catenin complex. We found that mutation of the N- and C-terminal subdomains of TCF7L2 that adopt relatively fixed conformations in the crystal structures has a large effect on the dissociation kinetics, whereas mutation of the labile sub-domain connecting them has negligible effect. These results point to a two-site avidity mechanism of binding with the linker region forming a “fuzzy” complex involving transient contacts that are not site-specific. Strikingly, two mutations in the N-terminal subdomain that have the largest effects on the dissociation kinetics showed two additional phases, indicating partial flux through an alternative dissociation pathway that is inaccessible to the wild type. The results presented here provide insights into the kinetics of molecular recognition of a long intrinsically disordered region with an elongated repeat-protein surface, a process found to involve parallel routes with sequential steps in each.

Ethylene Polymerization via Zirconocene Catalysts and Organoboron Activators: An Experimental and Kinetic Modeling Study

Forty years after the discovery of metallocene catalysts, there are still several aspects that remain unresolved, especially when the “conventional” alkylaluminum activators are not used. Herein, we systematically investigated the synthesis of polyethylene (PE) via three different zirconocene catalysts, with different alkyl substituents, activated via different organoboron compounds. The polymerization behavior, as well as the properties of the materials, were evaluated. The results demonstrate that the highest catalytic activity is shown by bis(cyclopentadienyl)dimethylzirconium activated by trityl tetra(pentafluorophenyl)borate. Additionally, it was found that toluene is the optimum solvent for these systems and at these reaction conditions. Moreover, to validate our experimental results, a comprehensive mathematical model was developed on the basis of thermodynamic and kinetic principles. The concentration of ethylene transferred to the solvent phase (toluene) in a liquid–vapor equilibrium (LVE) system was estimated based on Duhem’s theorem. Arrhenius expressions for the kinetic rate constants of a proposed kinetic mechanism were estimated by a kinetic model, in which the rate of polymerization was fitted by a least-square optimization procedure and the molecular weight averages by the method of moments. The simulations of the coordination polymerization suggest the presence of two types of active sites, principally at low temperatures, and the reactivation of the deactivated sites via a boron-based activator. However, the effect of the temperature on the reactivation step was not clear; a deeper understanding via designed experiments is required.