Solutes, membrane permeability coefficience

As described above, some solutes such as gases can enter the cell by diffusing down an electrochemical gradient across the membrane and do not require metabolic energy. The simple passive diffusion of a solute across the membrane is limited by the thermal agitation of that specific molecule, by the concentration gradient across the membrane, and by the solubility of that solute (the permeability coefficient. Figure 41—6) in the hydrophobic core of the membrane bilayer. Solubility is... 

Membrane uptake of nonionized solute is favored over that of ionized solute by the membrane/water partition coefficient (Kp). If Kp = 1 for a nonionized solute, membrane permeability should mirror the solute ionization curve (i.e., membrane permeability should be half the maximum value when mucosal pH equals solute pKa). When the Kp is high, membrane uptake of nonionized solute shifts the ionization equilibrium in the mucosal microclimate to replace nonionized solute removed by the membrane. As a result, solute membrane permeability (absorption rate) versus pH curves are shifted toward the right for weak acids and toward the left for weak bases (Fig. 7). 

Here, Q is the solute concentration in the receptor cell at time t Q is the initial solute concentration of the donor cell V is volume of each half-cell A is the effective area of permeation and P is the membrane permeability coefficient. To determine the permeability coefficient, P a plot of — (V72A) In [1 — 2(Cf/CJ] versus time, was constructed. The linear portion yields a slope of the permeability coefficient, P in cm/s. 

Figure 13.9. Membrane permeability coefficience of solutes. Solute permeabilities across typical lipid bilayers of liposomes or lipid vesicles are presented as their respective coefficients in cm/s. In the absence of other transport processes, it would require 10 s to move Na+ across 1 cm distance. When there is a concentration difference across a membrane, multiplying the concentration difference (mole/ml equivalent to mole/cm ) by the permeability coefficient (cm/s) allows estimation of flow rate (mole/s-cm ). For example, a concentration difference of 1Q- mole/cm Na (or 1 x 10" M Na ) would provide a flow of 10 mole/cm x 10" cm/s = IQ- mole/s through 1 cm or 0.006 mole/s through 1 pm of a membrane bilayer.

A cellulose acetate membrane has a water permeability coefficient Lp = 2.105 g/cm=.s.bar and a solute (NaCl) permeability coefficient B = 4.10 cm/s. This membrane is used for a desalination experiment The feed concentration is 35 g/l of NaCl and the applied pressure is 60 bar. Calculate the water flux, salt flux, rejection coefficient and the concentration of NaCl in the permeate. The density of the solution is 103gfl. 

P = membrane permeability coefficient C = oxygen concentration of the test solution b = membrane thickness. 

Membrane permeability coefficient P, m s ) by selected ions was calculated according to the equation InC/C = k-1, where and C are initial and current concentrations of a substrate in donating solution, k—velocity constant of ions transport (c ), t—transport time, respectively. So far as it was determined, the ratio of InC/C to t was linear in experiments that were carried out (r > 0.98), permeability value can be expressed in terms of relation P = (V/S)-k, where S = membrane surface area (m ), V = volume of donating solution (m ). 

The following factors affect net diffusion of a substance (1) Its concentration gradient across the membrane. Solutes move from high to low concentration. (2) The electrical potential across the membrane. Solutes move toward the solution that has the opposite charge. The inside of the cell usually has a negative charge. (3) The permeability coefficient of the substance for the membrane. (4) The hydrostatic pressure gradient across the membrane. Increased pressure will increase the rate and force of the collision between the molecules and the membrane. (5) Temperature. Increased temperature will increase particle motion and thus increase the frequency of collisions between external particles and the membrane. In addition, a multitude of channels exist in membranes that route the entry of ions into cells. 

Permeability is a kinetic property expressed by the permeability coefficient (centimeters per second), a number indicating the rate at which molecules pass from aqueous solution across a membrane to another solution on the other side. Permeability is a molecular property used to screen for more complex absorption processes (i.e. in vitro permeabihty is measured to estimate in vivo absorption). 

The solubility-diffusion theory assumes that solute partitioning from water into and diffusion through the membrane lipid region resembles that which would occur within a homogeneous bulk solvent. Thus, the permeability coefficient, P, can be expressed as... 

The equations used to calculate permeability coefficients depend on the design of the in vitro assay to measure the transport of molecules across membrane barriers. It is important to take into account factors such as pH conditions (e.g., pH gradients), buffer capacity, acceptor sink conditions (physical or chemical), any precipitate of the solute in the donor well, presence of cosolvent in the donor compartment, geometry of the compartments, stirring speeds, filter thickness, porosity, pore size, and tortuosity. 

In PAMPA measurements each well is usually a one-point-in-time (single-timepoint) sample. By contrast, in the conventional multitimepoint Caco-2 assay, the acceptor solution is frequently replaced with fresh buffer solution so that the solution in contact with the membrane contains no more than a few percent of the total sample concentration at any time. This condition can be called a physically maintained sink. Under pseudo-steady state (when a practically linear solute concentration gradient is established in the membrane phase see Chapter 2), lipophilic molecules will distribute into the cell monolayer in accordance with the effective membrane-buffer partition coefficient, even when the acceptor solution contains nearly zero sample concentration (due to the physical sink). If the physical sink is maintained indefinitely, then eventually, all of the sample will be depleted from both the donor and membrane compartments, as the flux approaches zero (Chapter 2). In conventional Caco-2 data analysis, a very simple equation [Eq. (7.10) or (7.11)] is used to calculate the permeability coefficient. But when combinatorial (i.e., lipophilic) compounds are screened, this equation is often invalid, since a considerable portion of the molecules partitions into the membrane phase during the multitimepoint measurements. 

The popular permeability equations [(7.10) and (7.11)] derived in the preceding section presume that the solute does not distribute into the membrane to any appreciable extent. This assumption may not be valid in drug discovery research, since most of the compounds synthesized by combinatorial methods are very lipophilic and can substantially accumulate in the membrane. Neglecting this leads to underestimates of permeability coefficients. This section expands the equations to include membrane retention. 

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. (7.25)], nor is it important to do so, since the concentration gradient across the membrane is uniquely specified by S and CA (t). The permeability coefficient is effective in this case. 

The term KDm/hm is often referred to as the permeability coefficient [1], The concentrations Ci and c2 are assumed to be independent of time in Eqs. (36) and (37). This may experimentally imply that the volume of the membrane is negligible compared to that of solutions on either side of the membrane. Practically, neither these concentrations nor the concentration gradient is exactly constant. In diffusion or Caco-2 cell experiments, for example, a solution of higher concentration is initially placed in the donor compartment and a solution of lower concentration is placed in the receptor compartment. Even after sufficient time, the concentration will still fall in the donor compartment and rise in the receptor... 

The coupled processes described by Eqs. (8), (14), (17), and (22) can be added in (20) as parallel solute transport pathways across the membrane. The phenomenological coefficients (Ly) describe the membrane permeability by these pathways [potential-dependent, Eq. (8) via membrane lipid partition and diffusion, Eq. (14) carrier-mediated, Eq. (17) and convectively coupled, Eq. (22)]. These pathways define parallel resistances through the intestinal barrier in series with precellular resistances to solute transport. 

Given the low permeability of the antioxidant across MDCK cell monolayers and its large membrane partition coefficient, efflux kinetic studies using drug-loaded cell monolayers cultured on plastic dishes could yield useful information when coupled with the following biophysical model. The steady-state flux of drug from the cell monolayer is equal to the appearance rate in the receiver solution ... 

The transport of both solute and solvent can be described by an alternative approach that is based on the laws of irreversible thermodynamics. The fundamental concepts and equations for biological systems were described by Kedem and Katchalsky [6] and those for artificial membranes by Ginsburg and Katchal-sky [7], In this approach the transport process is defined in terms of three phenomenological coefficients, namely, the filtration coefficient LP, the reflection coefficient o, and the solute permeability coefficient to. 

Yasuda s free volume theory [57] has been proposed to explain the mechanism of permeation of solutes through hydrated homogeneous polymer membranes. The free volume theory relates the permeability coefficients in water-swollen homogeneous membranes to the degree of hydration and molecular size of the permeant by the following mathematical expression ... 

Figure 27. Relationship between water-hexadecane partition coefficients and membrane permeabilities for a broad selection of solutes. (Data collected by Walter and Gutknecht [124]. Reproduced with permission from the American Chemical Society)...

It was postulated that the aqueous pores are available to all molecular species, both ionic and non-ionic, while the lipoidal pathway is accessible only to un-ionised species. In addition, Ho and co-workers introduced the concept of the aqueous boundary layer (ABL) [9, 10], The ABL is considered a stagnant water layer adjacent to the apical membrane surface that is created by incomplete mixing of luminal contents near the intestinal cell surface. The influence of drug structure on permeability in these domains will be different for example ABL permeability (Paq) is inversely related to solute size, whereas membrane permeability (Pm) is dependent on both size and charge. Using this model, the apparent permeability coefficient (Papp) through the biomembrane may therefore be expressed as a function of the resistance of the ABL and... 

TABLE 1. Biophysical characteristics of human fetal liver CD34 CD38 cells. Legends Vo - cell volume in isoosmotic solutions, Vb - osmotically inactive volume, Lp - permeability coefficient of membranes for water, p - permeability coefficient of membranes for DMSO cryoprotectant, a - reflection coefficient. 

It is rather difficult to rationalize a decreased membrane permeability to water (Lp) because of oxidant exposure. We suspect, therefore, that the apparent decreased water permeability results in fact from a decreased reflection coefficient leading to solute loss and hence an apparent lower water transport rate. In any case, these data clearly demonstrate the occurrence of oxidant-induced alterations in membrane properties. 

Based on the 96-well format, OCT-PAMPA was proposed and has proved its ability to determine (indirectly) log Poet [87]. PAM PA is a method, first developed for permeability measurements, where a filter supports an artificial membrane (an organic solvent or phospholipids) [88, 89]. With this method, the apparent permeability coefficient (log P ) of the neutral form of tested compounds is derived from the measurement of the diffusion between two aqueous phases separated by 1-octanol layer (immobilized on a filter). A bilinear correlation was found between log Pa and log Poct> therefore log Poet of unknown compounds can be determined from log Pa using a calibration curve. Depending on the detection method used a range oflog P within —2 to +5 (with UV detection) and within —2 to +8 (with LC-MS detection) was successfully explored. This method requires low compound amounts (300 pi of 0.04 mM test compound) and, as for the previous method, samples can be prepared in DM SO stock solutions. For these experiments, an incubation time of 4h was determined as the best compromise in term of discrimination. The limitation of the technique lies in the lower accuracy values... 

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