PNP model

Crystallographic analysis was based primarily on the results of difference Fourier maps in which the interactions between residues in the active site and the inhibitor could be characterized. During these studies, about 35 inhibitor complexes were evaluated by x-ray crystallographic techniques. It is noteworthy that the resolution of the PNP model extends to only 2.8 A and that all of the difference Fourier maps were calculated at 3.2 A resolution, much lower than often considered essential for drug design. Crystallographic analysis was facilitated by the large solvent content that allowed for free diffusion of inhibitors into enzymatically active crystals. 

Equations 12.39, 12.35, and 12.40 form a coupled system of equations describing the surface function S, charge concentrations Pa, and electrostatic potential. This coupled system differs from the original PNP equations through the coupling of the surface definition are to charge concentrations and electrostatics. We call this DG-based system the "Laplace-Beltrami Poisson-Nernst-Planck" (LB-PNP) model. 

As with the equilibrium solvation models introduced earlier, it is also possible to incorporate quantum mechanical effects into the non-equilibrium transport model. Our motivation is to account for non-equilibrium ion fluxes and induced response in the electronic structure of the solute or membrane protein. To this end, we combine our DG-based DFT model with our DG-based PNP model as illustrated in Fig. 12.4 to develop a free energy functional and derive the associated governing equations. 

The distribution of proton concentration Ch+ and potential in solution is governed by the Poisson-Nernst-Planck (PNP) model, widely used in the theory of ion transport in biological membranes (Coalson and Kurnikova, 2007 Keener and Sneyd, 1998). Oxygen diffusion is determined by Pick s law. Inside the pore, the continuity and transport equations for protons and oxygen are... 

A similar approach to the boundary condition for the potential at the metal-solution interface has been applied by Biesheuvel et al., in consideration of diffuse charge effects in galvanic cells, desalination by porous electrodes, and transient response of electrochemical cells (Biesheuvel and Bazant, 2010 Biesheuvel et al., 2009 van Soestbergen et al., 2010). However, their treatment neglected the explicit effect of In principle, the PNP model could be modified to incorporate size-dependent and spatially varying dielectric constants in nanopores, as well as ion saturation effects at the interface. However, in a heuristic fashion, such variations could be accounted for in the Helmholtz capacitance of the Stern double layer model. 

These basic equations form the so-called Poisson-Nemst-Planck (PNP) model for IPMCs and describe the fundamental physics wifliin the polymer membrane. A number of aufliors have developed electromechanical (actuator) and mechanoe-lectrical (sensor) models based on the PNP model as well as modified PNP models (Nemat-Nasser 2002 Nemat-Nasser and Zamani 2006 Wallmersperger et al. 2007 Zhang and Yang 2007 Porfiri 2008 Chen and Tan 2008 Aureli et al. 2009). This model will be described further in subsequent chapters of this book. 

It is assumed that the IPMC is composed of an IP film sandwiched between two perfectly conductive metal electrodes. The linearized PNP model is used to describe the dynamics of the electric potential and the concentration of the mobile counterions within the polymer. In the case of the fiat electrodes, by solving the partial differential equation based on the PNP model, the equivalent circuit, which is composed of the following lumped capacitances - the double-layer capacitance, Cj, the bulk capacitance Q, and the bulk conductance, Si (see Fig. 6a) - can be obtained (Aureli and Porfiri 2012). 

Equations 1 and 2 make up what is commonly called the Poisson-Nemst-Planck (PNP) model for IPMCs and describes the fundamental physics within the polymer membrane. 

Figure 9. Catalytic cycle for H2 production with DuBois PNP model catalyst based on gas-phase B3LYP/6-31G calculations (see text). Arrows with T indicate thermal reactions.

Now, with the validity of Dewar s model for cyclophosphazenes apparently clearly demonstrated both theoretically and experimentally, a question arose. How is it possible to explain the remarkably high stability of such rings on the basis of localized PNP islands which practically do not interact along the ring skeleton An answer was provided by quantum chemistry. Armstrong et al. (23) and ourselves (24)... 

Darlington PNP Subckt Subcircuit model for a Darlington NPN transistor... 

We determined the structure of human PNP by x-ray crystallography and used these results in combination with computer-assisted molecular modeling to design inhibitor candidates. We examined how well the shape and chemical... 

The resulting compounds were evaluated by determination of their IC50 values (the inhibitor concentration causing 50% inhibition of PNP) and by x-ray diffraction analysis using difference Fourier maps. This iterative strategy—modeling, synthesis, and structural analysis—led us to a number of highly potent compounds that tested well in whole cells and in animals. 

The structural determinations also yielded a surprise. The shape of the enzyme changes when a purine is bound. The famous lock-and-key analogy [20] has a fallacy the shape of the lock is not static, but flexible. Awareness of these conformational changes critically aided our modeling efforts, allowing prediction of which parts of PNP could change shape to interact with a proposed inhibitor. 

Initial inhibitor modeling attempts using the native PNP structure were far less successful than subsequent analyses in which coordinates for the guanine-... 

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