PERMEABILITY in .NET framework

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PERMEABILITY
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and J t VA dCA t A dt 7:24
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The donor concentration becomes constant in time, represented by the solubility, S CD 0 CD t Reverse ux can still occur, but as soon as the sample reaches the donor compartment, it would be expected to precipitate Furthermore, the concentration in the acceptor compartment would not be expected to exceed the solubility limit: CA t S After equating the two ux expressions, and solving the differential equation, we have the saturated-donor permeability equation 2:303 VA CA t log10 1 Pe S A t tLAG ! 7:25
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Ordinarily it is not possible to determine the membrane retention of solute under the circumstances of a saturated solution, so no R terms appear in the special equation [Eq (725)], nor is it important to do so, since the concentration gradient across the membrane is uniquely speci ed by S and CA t The permeability coef cient is effective in this case
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753 Gradient pH Equations with Membrane Retention: Single and Double Sinks When the pH is different on the two sides of the membrane, the transport of ionizable molecules can be dramatically altered In effect, sink conditions can be created by pH gradients Assay improvements can be achieved using such gradients between the donor and acceptor compartments of the permeation cell A three-compartment diffusion differential equation can be derived that takes into account gradient pH conditions and membrane retention of the drug molecule (which clearly still exists albeit lessened in spite of the sink condition created) As before, one begins with two ux equations
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D!A A!D J t Pe CD t Pe CA t
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7:26
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and   VD dCD t J t dt A 7:27
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It is important to note that two different permeability coef cients need to be considered, one denoted by the superscript (D!A), associated with donor (eg, pHD
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DERIVATION OF MEMBRANE-RETENTION PERMEABILITY EQUATIONS
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50, 65, or 74)-to-acceptor (pHA 74) transport, and the other denoted by the superscript (A!D), corresponding to the reverse-direction transport The two equivalent ux relationships can be reduced to an ordinary differential equation in CD t , following a route similar to that in Section 7521 The gradient pH (2-Pe) model developed here implies that some back ux (A ! D) is possible As far as we know, reported literature studies generally considered back ux to be nil under gradient pH conditions That is, either Eq (710) or (711) were used to interpret the membrane transport under a pH gradient conditions If it can be assumed that CA t in Eq (726) represents a fully charged (ie, impermeable) form of the solute, then its contribution to back ux may be neglected, and an effective sink condition would prevail; that is, the concentration of the uncharged form of the solute, cA t , is used in place of CA t , where cA t % 0 Under such circumstances, the generic sink equation, Eq (722), may be used to determine an apparent permeability coef cient, Pa apparent so as to draw attention to hidden assumptions (ie, no reverse ux) However, valid use of Eq (722) is restricted to strictly maintained sink conditions and presumes the absence of membrane retention of solute This is a rather impractical constraint in high-throughput applications, where molecules with potentially diverse transport properties may be assayed at the same time A more general analysis requires the use of two effective permeability coef cients, one for each pH, each of which would be valid in the respective iso-pH conditions Since fewer limiting assumptions are made, the more general method may be more suitable for high-throughput applications We continue to derive the appropriate new model The donor acceptor membrane mass balance is molTOT VD CD 0 VA CA 1 VD CD 1 VM CM 1 7:28
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Each side of the barrier has a different membrane buffer apparent partition coef cient Kd, de ned at t 1 as Kd A and Kd D CM 1 CD 1 7:30 CM 1 CA 1 7:29
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The moles lost to the membrane are derived from Eqs (728) (730): molM CM 1 VM VM VD CD 0 VA =Kd A VD =Kd D VM 7:31
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