Fitting the Elementary Rate Constants of the P-gp Transporter Network in the hMDR1-MDCK Confluent Cell Monolayer Using a Particle Swarm Algorithm

P-glycoprotein, a human multidrug resistance transporter, has been extensively studied due to its importance to human health and disease. In order to understand transport kinetics via P-gp, confluent cell monolayers overexpressing P-gp are widely used. The purpose of this study is to obtain the mass action elementary rate constants for P-gp's transport and to functionally characterize members of P-gp's network, i.e., other transporters that transport P-gp substrates in hMDR1-MDCKII confluent cell monolayers and are essential to the net substrate flux. Transport of a range of concentrations of amprenavir, loperamide, quinidine and digoxin across the confluent monolayer of cells was measured in both directions, apical to basolateral and basolateral to apical. We developed a global optimization algorithm using the Particle Swarm method that can simultaneously fit all datasets to yield accurate and exhaustive fits of these elementary rate constants. The statistical sensitivity of the fitted values was determined by using 24 identical replicate fits, yielding simple averages and standard deviations for all of the kinetic parameters, including the efflux active P-gp surface density. Digoxin required additional basolateral and apical transporters, while loperamide required just a basolateral tranporter. The data were better fit by assuming bidirectional transporters, rather than active importers, suggesting that they are not MRP or active OATP transporters. The P-gp efflux rate constants for quinidine and digoxin were about 3-fold smaller than reported ATP hydrolysis rate constants from P-gp proteoliposomes. This suggests a roughly 3∶1 stoichiometry between ATP hydrolysis and P-gp transport for these two drugs. The fitted values of the elementary rate constants for these P-gp substrates support the hypotheses that the selective pressures on P-gp are to maintain a broad substrate range and to keep xenobiotics out of the cytosol, but not out of the apical membrane

The effect of stabilization in finite element methods for the optimal boundary control of the Oseen equations”, Finite Elements in Analysis and Design

We study the effect of the Galerkin/Least-Squares (GLS) stabilizationon the finite element discretization of optimal control problems governed by the linear Oseen equations. Control is applied in the form of suction or blowing on part of the boundary. Two ways of including the GLS stabilization into the discretization of the optimal control problem are discussed. In one case the optimal control problem is first discretized and the resulting finite dimensional problem is then solved. In the other case, the optimality conditions are first formulated on the differential equation level and are then discretized. Both approaches lead to different discrete adjoint equations and, depending on the choice of the stabilization parameters and grid size, may significantly affect the computed control. The effect of the order in which the discretization is applied and the choice of the stabilization parameters are illustrated using two test problems. The cause of the differences in the computed controls are explored numerically. Diagnostics are introduced that may guide the selection of sensible stabilization parameters

Shape optimization in steady blood flow : a numerical study of Non-Newtonian effects

This paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized twodimensional arterial graft geometry. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. Using a gradient-based optimization algorithm, we compare the optimal shapes obtained using both the Newtonian and generalized Newtonian constitutive equations. Depending on the shear rate prevalent in the domain, substantial differences in the flow as well as in the computed optimal shape are observed when the Newtonian constitutive equation is replaced by the modified Cross model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution