Slab model, protein

A complete description of the protein-stationary phase interaction involves many complications and a general model is extremely difficult to formulate. The slab model described above is very simple, yet it gives interesting physical insights and may be a useful starting point for more elaborate theories. Here, we shall only briefly discuss some of the challenges a more complete model meets. For more complete discussions see Refs. [1,24]. 

The geometry. It is clear that the geometry of the system is much simplified in the slab model. Another possibility is to model the protein as a sphere and the stationary phase as a planar surface. For such systems, numerical solutions of the Poisson-Boltzmann equations are required [33]. However, by using the Equation 15.67 in combination with a Derjaguin approximation, it is possible to find an approximate expression for the interaction energy at the point where it has a minimum. The following expression is obtained [31] ... 

Both the slab thickness L and the porosity e were measured. For a given macromolecule, the bulk difFusivity, D0, is measurable or obtainable from the literature. Thus, a test of the model is to cast slabs using other proteins, measure the parameters L, e, and D0, and see whether the release kinetics follow Eq. (2). This has been done for /3-lactoglobulin and lysozyme (Fig. 2). The solid lines are predictions based on Eq. (2) which show general agreement with the data (7). 

Modeling Release of Proteins from Matrices. Consider a protein-loaded matrix that is constructed as a thin slab. Release of the protein occurs essentially through the top and bottom faces of this slab since the thickness of the slab is small compared to the other dimensions. The desorption of protein from this slab can be described by Fick s second law of diffusion. Equation (9-14), in which an effective diffusion coefficient, Dgff, is used in place of Di-p. For example ... 

Figure 1 Release of ferritin (500-kDa protein) from a matrix of EVAc. (a) The cumulative fraction of mass released from matrices containing 35% ( ) or 50% ( ) ferritin by mass is plotted versus time, (b) The same cumulative mass fraction released from the 50% loaded matrices is plotted versus the square root of time. The dashed line represents the fit to the linear model of desorption from a slab, Eq. (5). Data points represent the mean cumulative fraction of mass of ferritin released from four EVAc matrices incubated in buffered saline at 37 °C. The error bars represent 1 SD of the mean. Some error bars are smaller than the symbols.

Figure 3 summarizes some representative hydrated models for simple oligomeric proteins, i.e. dimeric citrate synthase (A,B), two dimeric phosphorylases from different sources (C-F), and tetrameric lactate dehydrogenase (G,H), after applying quite different input variables and calculation approaches. An inspection of the slabs created reveals that proteins composed of several chains may exhibit water accumulations between the constituent chains, unless compact units are formed. 

Fig. 3 Hydrated models of selected oligomeric proteins. A,B Views and slabs of the hydrated crystal structure of citrate synthase (ICTS), obtained by application of SIMS and HYDCRYST (rfdot = 3.0 A , fprobe = rw = 1.50 A, Vw = 27.0 A ) using /k = 1.0 (A Nv, = 1340) and /k = 2.0 (B = 1759). C-F Views with slabs of the hydrated crystal structure (C,E) and the hydrated AA representation (D,F) of phosphorylase from E. coli (lAHP C,D) and from rabbit muscle (3GPB E,F), as obtained by application of SIMS and HYDCRYST (C,E) or HYDMODEL (D,F) using rfdot = 3.0 A 2, rprobe = fw = 1.45 A, Vw = 24.5 A and /k = 2.0 (C Aw = 3348 D Aw = 3477 E Aw = 3558 F Aw = 3721). G,H Views with slabs of the hydrated crystal structure (G) and the hydrated AA representation (H) of lactate dehydrogenase (6LDH), as obtained by application of SIMS and HYDCRYST ((G) or HYDMODEL (H), using 4lot = 3.0 A , fprobe = fw = 1-40 A, Vw = 21.95 A ), and /k = 2.0 (G Aw = 2976 H Aw = 3084). Atoms are displayed in CPK colors, AA residues in grey, and hydration waters in cyan...

Fig. 5 Hydrated models of giant protein complexes. A,B Views with slabs of the hydrated AA representation of the capsid of bacteriophage fr (IFRS), as obtained by AA-SIMS and HYDMODEL (fildot . probe 1.45 A, = 24.4 A ) using ...

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