Biophase concentration

Equations (1), (3) and (4) should be coupled with a balance on the biophase to determine the value of X. Under conditions characterized by hindered growth, the biophase concentration may be assumed constant in both equations. In practice, this implies effective biophase containment in the reactor. 

If we make the assumptions that drug distribution to and from the site of action is first order (i.e./ no active transport is involved) and that drug actions are directly determined by the unbound/ unionized drug concentration in water at the site of actioii/ then at steady state the drug concentration in plasma water will be directly proportional to its concentration at the site of action. We can therefore use parameters estimated from biophase concentrations (such as the EC50) to predict the drug effects from unbound/ unionized plasma concentrations. 

FIGURE 19.3 Predicted changes in QT interval after administration of intravenous (dotted line) and oral (solid line) single doses of quinidine to healthy subjects (12). The delay in effect lAuth respect to plasma concentration causes hysteresis loops. The slope of the biophase concentration effect relationship is greater after oral doses due to active metabolites formed during quinidine absorption. (Reproduced with permission from Holford NHG, Coates PE, Guentert tW, Riegelman S, Sheiner LB. Br J Clin Pharmacol 1981 11 187-95.)... 

If the relationship between change in effect (AE) and biophase concentration is linear/ biophase concentrations can be related to AE by a constant ( 6) such that... 

Biophase concentrations then are related to observations made on the effect variable (E) as follows ... 

The apparently linear relationship between biophase concentration and pharmacologic response usually reflects the fact that effects have been analyzed over only a limited concentration range (14). In many caseS/ an Ej ax model is required to analyze more pronounced effects/ such as the blood pressure response of cats to norepinephrine. This was the concentration-effect relationship initially analyzed by Segre (7) when he proposed a model for the time course of biophase concentrations. For the Ej ax model/ AE in Equation 19.8 is described by... 

In some cases. Equation 19.10 will need to be modified to account for the fact that the biophase concentration-effect relationship is sigmoid rather than hyperbolic. This modification was necessary in analyzing the pharmacokinetics and effects of d-tubocurarine (9). In this case, the following equation was used to relate estimated biophase concentrations of d-tubocurarine to the degree of skeletal muscle paralysis (AE), ranging from normal function to complete paralysis (E ax = 1) caused by this drug ... 

Changes in the Relationship Between Biophase Concentration and Drug Effect... 

LS A principles have been applied in pharmacodynanics in situations where the drug concentration-effect transduction takes place at a site, commonly denoted the biophase, that is kinetically distinct from the sampling space. LSA-based PK/PD modeling is then based on the assumption that the nonmeasurable biophase concentration, Q(0, is linearly related to the drug concentration, C(t), measured in the sampling space. 

Stirred tank reactor (ST/ ). The differential mass balance referred to the azo-dye converted by bacteria (assuming unstructured model for the biophase, i.e., that it is characterized only by cell mass or concentration X) yields... 

The assessment of reaction kinetics by means of batch tests may be strongly affected by dye adsorption on the biophase and supports. The relevance of the adsorption phenomena of dyes on biophase has been addressed in studies regarding free cells [41], granular support biofilm [24], entrapped cells [11, 18], anaerobic sludge [10,24,31,34] and biological activated carbon (BAC) [42,45,47,48]. They have pointed out that the kinetics may be overestimated if the assessment of the adsorption contribution to the dye removal is not taken into account. Under batch conditions, the dye is fastly split between the liquid phase and the biophase, resulting in a sharp reduction of the dye concentration in the liquid phase until adsorption equilibrium is approached. The rate of dye adsorption must be estimated and ruled out in the kinetic assessment. 

Fig. 4 Profiles of a species diffusing from the bulk liquid towards segregated biophase, (a) Biofilm on an impervious particle, (b) Aggregated cells or entrapped cells beads (c) Biofilm on a porous particle. qP dye concentration on the solid phase...

Whatever the typology of immobilized biophase, kinetics assessment and modeling studies should not neglect the relevance of the profiles reported in Fig. 4. In agreement with Bailey and Ollis [51], the non uniform profile of the concentrations of azo-dye and of the products may be expressed in terms of the effectiveness factor of the immobilized biophase the ratio of actual reaction rate to the reaction rate without diffusion limitation. 

The equilibration of drug between plasma and biophase is determined by the parameter KeQ and the equilibration half-time In 21 Keg, and T ITEe is the length of time it takes for plasma concentration and effective concentration to reach equilibrium this time can range from a few minutes to several hours. For drugs with short half-time, the value of KCq is large and an equilibration is reached fast, and thus the plasma concentration is a good indicator of biophase levels for drugs with low Kcg (lower than the terminal elimination-rate constant), an equilibrium will never be reached. The time at which peak concentration is achieved (Te ) is expressed as... 

To understand drug-receptor interactions, it is necessary to quantify the relationship between the drug and the biological effect it produces. Since the degree of effect produced by a drug is generally a function of the amount administered, we can express this relationship in terms of a dose-response curve. Because we cannot always quantify the concentration of drug in the biophase in the intact individual, it is customary to correlate effect with dose administered. 

If the antagonism is of the equilibrium type, the antagonism increases as the concentration of the antagonist increases. Conversely, the antagonism can be overcome (surmounted) if the concentration of the agonist in the biophase (the region of the receptors) is in-... 

The interactions between transmitters and their receptors are readily reversible, and the number of transmitter-receptor complexes formed is a direct function of the amount of transmitter in the biophase. The length of time that intact molecules of acetylcholine remain in the biophase is short because acetylcholinesterase, an enzyme that rapidly hydrolyzes acetylcholine, is highly concentrated on the outer surfaces of both the prejunctional (neuronal) and postjunctional (effector cell) membranes. A rapid hydrolysis of acetylcholine by the enzyme results in a lowering of the concentration of free transmitter and a rapid dissociation of the transmitter from its receptors little or no acetylcholine escapes into the circulation. Any acetylcholine that does reach the circulation is immediately inactivated by plasma esterases. 

Like the cholinergic transmitter, the noradrenergic transmitter is released by action potentials through ex-ocytosis, the contents of entire vesicles being emptied into the biophase (synaptic or junctional region). Similarly, the formation of transmitter-receptor complexes is a direct function of the concentration of transmitter in the biophase and is readily reversible. In this instance, the receptors are adrenoceptors. 

Factors That Influence Purine Concentration in the Receptor Biophase.356... 

The coexistence of inhibitory and facilitatory adenosine- and P2-receptors in the same nerve terminal raises the question of which factors influence the concentration of endogenous agonists in the vicinity of each receptor (i.e., in the receptor biophase) and, consequently, determine the net modulatory effect. Tissue differences in receptor expression and purine release/formation or inactivation systems create a diversity of possibilities that makes the net modulatory effect by endogenous purines quite variable from tissue to tissue. 

---