arXiv subjects

Sergey N. Krylov

Publications and source records attributed to Sergey N. Krylov.

3 recordsLinked to original sources

arXiv2017

A Fast Stable Discretization of the Constant-Convection-Diffusion-Reaction Equations of Kinetic Capillary Electrophoresis (KCE)

A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables, which ensures the global stability of discretization. Convection-diffusion equations are notorious for their lack of stability, arising from the algebraic interaction of the convection and diffusion terms. Unexpectedly, our implemented numerical algorithm proves to be faster than computing exact solutions derived for a special case, while remaining reasonably accurate, as demonstrated in our runtime and error analysis.

physics.comp-ph↗

arXiv2017

Estimating Kinetic Rate Constants and Plug Concentration Profiles from Simulated KCE Electropherogram Signals

Kinetic rate constants fundamentally characterize the dynamics of the chemical interaction of macromolecules, and thus their study sets a major direction in experimental biochemistry. The estimation of such constants is often challenging, partly due to the noisiness of data, and partly due to the theoretical framework. Novel and qualitatively reasonable methods are presented for the estimation of the rate constants of complex formation and dissociation in Kinetic Capillary Electrophoresis (KCE). This also serves the broader effort to resolve the inverse problem of KCE, where these estimates pose as initial starting points in the non-linear optimization space, along with the asymmetric Gaussian parameters describing the injected plug concentration profiles, which is also hereby estimated. This rate constant estimation method is also compared to an earlier one.

q-bio.QM↗

arXiv2017

A Computational Resolution of the Inverse Problem of Kinetic Capillary Electrophoresis (KCE)

Determining kinetic rate constants is a highly relevant problem in biochemistry, so various methods have been designed to extract them from experimental data. Such methods have two main components: the experimental apparatus and the subsequent analysis, the latter often dependent on mathematical theory. Thus the theoretical approach taken influences the effectiveness of constant determination. A computational inverse problem approach is hereby presented, which does not merely give a single rough approximation of the sought constants, but is inherently capable of determining them from exact signals to arbitrary accuracy. This approach is thus not merely novel, but opens a whole new category of solution approaches in the field, enabled primarily by an efficient direct solver.

q-bio.QM↗