Validation of Fractal-Like Kinetic Models by Time-Resolved Binding Kinetics of Dansylamide and Carbonic Anhydrase in Crowded Media

Abstract

Kinetic studies of biochemical reactions are typically carried out in a dilute solution that rarely contains anything more than reactants, products, and buffers. In such studies, mass-action-based kinetic models are used to analyze the progress curves. However, intracellular compartments are crowded by macromolecules. Therefore, we investigated the adequacy of the proposed generalizations of the mass-action model, which are meant to describe reactions in crowded media. To validate these models, we measured time-resolved kinetics for dansylamide binding to carbonic anhydrase in solutions crowded with polyethylene glycol and Ficoll. The measured progress curves clearly show the effects of crowding. The fractal-like model proposed by Savageau was used to fit these curves. In this model, the association rate coefficient k(a) allometrically depends on concentrations of reactants. We also considered the fractal kinetic model proposed by Schnell and Turner, in which k(a) depends on time according to a Zipf-Mandelbrot distribution, and some generalizations of these models. We found that the generalization of the mass-action model, in which association and dissociation rate coefficients are concentration-dependent, represents the preferred model. Other models based on time-dependent rate coefficients were inadequate or not preferred by model selection criteria.

Monte Carlo simulations of enzymatic reactions in crowded media. Effect of the enzyme-obstacle relative size

“…They are mainly divided into deterministic approaches, particularly comprising fractal kinetic approaches [41][42] and kinetics based on fractional reaction orders [43][44][45][46], and stochastic ones [47]. However, there are mathematical connections between deterministic and stochastic models.…”

“…[44][45][46] have proven that Schnell and Turner model applied on bimolecular reactions predicted an unlikely asymptotic concentration of the product. This approach is valid for diffusion-limited reactions and we used it in our investigation assuming that the corresponding time period of our simulations does not reach the asymptotic region.…”

“…There are numerous published papers with regard to simulations of diffusion processes [4-7, 10-12, 17, 19-20] and chemical reactions in crowded media [40][41][42][43][44][45][46][47][50][51][52][53][54][55][56]. Macromolecular crowding can lead to anomalous diffusion more likely when low dimension environments are considered especially up to percolation threshold [41].…”

“…They also generalize different approximations used in the literature in order to understand which kind of formalism better describes the biochemical reactions in crowded environment, and used them in an experimental study to test different models for reaction kinetics in intracellular environments [46].…”

Model Discrimination in Dynamic Molecular Systems: Application to Parotid De-differentiation Network

“…The procedure described in Rempala et al (2007) was based on the ideas of Bayarri et al (2007) on statistical validation in computer models, and was seen to work well for simple biological networks but not necessarily for more complicated ones such as complex signaling pathways. For these more complicated settings, a more comprehensive approach seems to be required, involving both the model validation and selection (see, e.g., Neff et al, 2011;Morton et al, 2010;Steimer et al, 2010, for applications to various molecular systems). For the latter, the ability to perform a discriminant-like analysis between competing models based on available time-course data is essential.…”