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Register a new userDiffusion and steady state distributions of flexible chemotactic enzymes
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Added by
Jaime Agudo-Canalejo
Publication date
2019
fields
Physics
and research's language is
English
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Many experiments in recent years have reported that, when exposed to their corresponding substrate, catalytic enzymes undergo enhanced diffusion as well as chemotaxis (biased motion in the direction of a substrate gradient). Among other possible mechanisms, in a number of recent works we have explored several passive mechanisms for enhanced diffusion and chemotaxis, in the sense that they require only binding and unbinding of the enzyme to the substrate rather than the catalytic reaction itself. These mechanisms rely on conformational changes of the enzyme due to binding, as well as on phoresis due to non-contact interactions between enzyme and substrate. Here, after reviewing and generalizing our previous findings, we extend them in two different ways. In the case of enhanced diffusion, we show that an exact result for the long-time diffusion coefficient of the enzyme can be obtained using generalized Taylor dispersion theory, which results in much simpler and transparent analytical expressions for the diffusion enhancement. In the case of chemotaxis, we show that the competition between phoresis and binding-induced changes in diffusion results in non-trivial steady state distributions for the enzyme, which can either accumulate in or be depleted from regions with a specific substrate concentration.
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In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional settings, the behavior of the macroscopic reaction rate and its dependence on geometric parameters are not yet understood. Modeling the geometric setup by a capped cylinder with a concentric disk-like reactive region on one of the lateral surfaces, we provide an exact semi-analytical solution of the steady-state diffusion equation and compute the diffusive flux onto the reactive region. We explore the dependence of the macroscopic reaction rate on the geometric parameters and derive asymptotic results in several limits. Using the self-consistent approximation, we also obtain a simple fully explicit formula for the reaction rate that exhibits a transition from two-dimensional to three-dimensional behavior as the separation distance between lateral surfaces increases. Biological implications of these results are discussed.
Molecular agitation more rapid than thermal Brownian motion is reported for cellular environments, motor proteins, synthetic molecular motors, enzymes, and common chemical reactions, yet that chemical activity couples to molecular motion contrasts with generations of accumulated knowledge about diffusion at equilibrium. To test the limits of this idea, a critical testbed is mobility of catalytically active enzymes. Sentiment is divided about reality of enhanced enzyme diffusion with evidence for and against. Here a master curve shows that enzyme diffusion coefficient increases in proportion to the energy release rate, the product of Michaelis-Menten reaction rate and Gibbs free energy change with the highly satisfactory correlation coefficient of 0.97. For ten catalytic enzymes (urease, acetylcholinesterase, seven enzymes from the glucose cascade cycle, and another), our measurements span from roughly 40% enhanced diffusion coefficient at high turnover rate and negative Gibbs free energy to no enhancement at slow turnover rate and positive Gibbs free energy. Moreover, two independent measures of mobility show consistency, provided that one avoids undesirable fluorescence photophysics. The master curve presented here quantifies the limits of both ideas, that enzymes display enhanced diffusion and that they do not within instrumental resolution, and has possible implications for understanding enzyme mobility in cellular environments. The striking linear dependence for the exergonic enzymes (negative Gibbs free energy) together with the vanishing effect for endergonic enzyme (positive Gibbs free energy) are consistent with a physical picture where the mechanism boosting the diffusion is an active one, utilizing the available work from the chemical reaction.
The initial surface reactions of the extrinsic coagulation pathway on live cell membranes were examined under flow conditions. Generation of fXa (activated coagulation factor X) was measured on spherical monolayers of epithelial cells with a total surface area of 41-47 cm$^{2}$ expressing TF(tissue factor) at $>25$ fmol/cm$^{2}$. Concentrations of reactants and product were monitored as a function of time with radiolabeled proteins and a chromogenic substrate at resolutions of 2-8 s. At physiological concentrations of fVIIa and fX, the reaction rate was $3.05 pm 0.75$ fmol fXa/s/cm$^{2}$, independent of flux, and 10 times slower than that expected for collision-limited reactions. Rates were also independent of surface fVIIa concentrations within the range 0.6-25 fmol/cm$^{2}$. The transit time of fX activated on the reaction chamber was prolonged relative to transit times of nonreacting tracers or preformed fXa. Membrane reactions were modeled using a set of nonlinear kinetic equations and a lagged normal density curve to track the expected surface concentration of reactants for various hypothetical reaction mechanisms. The experimental results were theoretically predicted only when the models used a slow intermediate reaction step, consistent with surface diffusion. These results provide evidence that the transfer of substrate within the membrane is rate-limiting in the kinetic mechanisms leading to initiation of blood coagulation by the tissue factor pathway.
Purpose: Diffusion-weighted steady-state free precession (DW-SSFP) is shown to provide a means to probe non-Gaussian diffusion through manipulation of the flip angle. A framework is presented to define an effective b-value in DW-SSFP. Theory: The DW-SSFP signal is a summation of coherence pathways with different b-values. The relative contribution of each pathway is dictated by the flip angle. This leads to an apparent diffusion coefficient (ADC) estimate that depends on the flip angle in non-Gaussian diffusion regimes. By acquiring DW-SSFP data at multiple flip angles and modelling the variation in ADC for a given form of non-Gaussianity, the ADC can be estimated at a well-defined effective b-value. Methods: A gamma distribution is used to model non-Gaussian diffusion, embedded in the Buxton signal model for DW-SSFP. Monte-Carlo simulations of non-Gaussian diffusion in DW-SSFP and diffusion-weighted spin-echo (DW-SE) sequences are used to verify the proposed framework. Dependence of ADC on flip angle in DW-SSFP is verified with experimental measurements in a whole, human post-mortem brain. Results: Monte-Carlo simulations reveal excellent agreement between ADCs estimated with DW-SE and the proposed framework. Experimental ADC estimates vary as a function of flip angle over the corpus callosum of the postmortem brain, estimating the mean and standard deviation of the gamma distribution as $1.50cdot 10^{-4} mm^2/s$ and $2.10cdot 10^{-4} mm^2/s$. Conclusion: DW-SSFP can be used to investigate non-Gaussian diffusion by varying the flip angle. By fitting a model of non-Gaussian diffusion, the ADC in DW-SSFP can be estimated at an effective b-value, comparable to more conventional diffusion sequences.
Enhanced diffusion and anti-chemotaxis of enzymes have been reported in several experiments in the last decade, opening up entirely new avenues of research in the bio-nanosciences both at the applied and fundamental level. Here, we introduce a novel theoretical framework, rooted in non-equilibrium effects characteristic of catalytic cycles, that explains all observations made so far in this field. In addition, our theory predicts entirely novel effects, such as dissipation-induced switch between anti-chemotactic and chemotactic behavior.
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