Convection-diffusion model, protein

Protein Adsorption and Desorption Rates and Kinetics. The TIRF flow cell was designed to investigate protein adsorption under well-defined hydrodynamic conditions. Therefore, the adsorption process in this apparatus can be described by a mathematical convection-diffusion model (17). The rate of protein adsorption is determined by both transport of protein to the surface and intrinsic kinetics of adsorption at the surface. In general, where transport and kinetics are comparable, the model must be solved numerically to yield protein adsorption kinetics. The solution can be simplified in two limiting cases 1) In the kinetic limit, the initial rate of protein adsorption is equal to the intrinsic kinetic adsorption rate. 2) In the transport limit, the initial protein adsorption rate, as predicted by Ldveque s analysis (23), is proportional to the wall shear rate raised to the 1/3 power. In the transport-limited adsorption case, intrinsic protein adsorption kinetics are unobservable. 

We have developed a model called the dispersion model (Figure 18.5) and compared it to the tanks-in-series and transit compartment models (139). The parameters of the dispersion model estimate the relative roles of diffusion, convection, and chemical reaction in signal transduction. We found that the dispersion model was capable of simultaneously fitting mRNA and protein dynamics for tyrosine aminotransferase (TAT) after methylprednisolone treatment from a published PD study quite well (140). 

FIGURE 18.5 The mechanistic basis of the dispersion element. The three dispersion element parameters are a nondimensional dispersion number that measures the rate of signal diffusion relative to convection t, the apparent mean residence time and a, the signal-to-transcript conversion parameter. For the mRNA and protein compartments in the Hargrove-Schmidt model element, kx, kM, and kp are rate constants for translation, mRNA degradation, and protein degradation, respectively. The gray line indicates that information rather than mass is transferred from the TAT mRNA to the TAT protein compartment (140). 

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