Plasma Protein Binding (PPB) Measurement of High Protein-binding Drugs: Principles and Advantages of the Flux Dialysis Methods

With the rapid development of new modalities, there is an increasing number of molecules in drug chemistry design that surpass Lipinski’s rule of five principles. For instance, Proteolysis-Targeting Proteolysis-Targeting Chimeras (PROTACs) often share common characteristics such as high molecular weight, strong lipophilicity, poor solubility, and significant non-specific binding, which exhibit high plasma protein binding (PPB). As a result, accurately determining PPB becomes challenging ¹. This article introduces a method for PPB determination of high protein-binding compounds — flux dialysis (also known as dynamic dialysis) by discussing its principle and mathematical model, showing our validation study data, and interpreting detailed key mathematical formula derivations and proofs.

How to measure plasma protein binding (PPB)?

Plasma protein binding (PPB) is one of the most controversial topics in the field of drug discovery and development. It is generally not recommended to change the PPB of a drug candidate by optimizing the structure, as there is no significant correlation between PPB and in vivo drug efficacy and PPB has a marginal effect on free drug concentrations ^2-4. A compound with high PPB does not necessarily determine whether it is a good or bad compound. However, the fraction unbound (f_u) measured by PPB assays is a key parameter that needs to be accurately determined, because it could play a significant role in predicting drug-drug interaction (DDI), estimating therapeutic indexes (TI), and exploiting PK/PD relationships ⁵.

There are several methods for determining the fraction unbound (f_u) of compounds in biological matrices, including equilibrium dialysis, ultracentrifugation, and ultrafiltration, with equilibrium dialysis being the most commonly used method. The f_u obtained by equilibrium dialysis is reliable if the system is in true equilibrium, the compound is not metabolized or degraded in the biological matrix, and the concentration of the free sample in the buffer meets the requirements of analytical sensitivity.

Figure 1. Schematic diagram of the equilibrium dialysis methods ⁶. (a) At time 0, the drug is added to a biological matrix, such as plasma or brain homogenate; (b) After 4-6 hours of dialysis, the system is free of non-specific binding, and the drug reaches equilibrium on both sides of the membrane; (c) There is non-specific binding in the system, and the compounds are still able to reach equilibrium on both sides of the membrane.

For highly protein-bound compounds, reaching equilibrium takes a long time. In some cases, it is not able to be achieved, making it difficult to accurately determine f_u. Due to the difficulty of accurately determining f_u, the lower detection limit of the PPB f_u is specified in the DDI guidelines of the FDA⁷ and EMA ⁸. f_u is estimated as 0.01 when the plasma f_u is less than 0.01, which may lead to an overestimation of the DDI effect for highly protein-bound compounds. In recent years, several articles have been published for optimizing PPB determination to improve the accuracy of f_u estimation ⁹. Among them, the flux dialysis method was developed based on the principle of equilibrium dialysis.

Principles and Methods of Flux Dialysis

Flux dialysis, developed in the 1950s, can overcome some of the limitations of equilibrium dialysis to determine a low f_u.

The basic method is to dialyze a plasma sample with the added compound against a blank plasma. With the known permeability coefficient of the compound in the dialysis membrane, the f_u of the compound in the matrix can be calculated using the initial flux rate of the compound penetrating the receiving chamber.

The basic principle is that the initial flux rate of a compound through a dialysis membrane is proportional to the product of the initial concentration, f_u, and the membrane permeability coefficient. Instead of determining the equilibrium concentrations at equilibrium, f_u can be calculated from the initial slope of the receiver/donor concentration ratio-time curve. This approach bypasses the requirement for equilibrium and has great application for the PPB determination of highly protein-bound compounds.

However, due to various reasons such as the need to determine membrane permeability, multiple sampling time points, complex study procedures, and the need for higher radio-purity compounds, this method has not been widely used in practice. With the popularization of high-throughput study devices and the establishment and development of pharmacokinetic (PK) models, this method has been improved and has been used in many studies of WuXi AppTec DMPK.

Researchers from the AbbVie research team in the United States provided a detailed mathematical proof of the theoretical model of this novel flux dialysis method ¹⁰. This article briefly introduces some key aspects of their findings.

Kinetic modeling of the flux dialysis methods

The theoretical basis of the method for calculating f_u is demonstrated below. The concentration variation of compounds in the donor and receiver compartments can be described by the two-compartment model (Figure 2).

Figure 2. Kinetic model of dialysis ¹¹. X₀: the initial amount of drug added; V: volume of the compartment; P_mem: permeability coefficient of the dialysis membrane; A: surface area of the membrane; K_nsb: binding constant of non-specific binding; C: concentration; K_loss: first-order kinetic rate constant of compound degradation.

When K_nsb and K_loss are not taken into account, it can be deduced from the model that f_{u, donor} is proportional to R_slope (R = C_receiver/C_donor, R_slope is the derivative of the concentration ratio with respect to time, i.e., dR/dt, at the initial moment, t = 0) and f_{u, donor} can be calculated once the value of R_slope is obtained_.

(see the end of the article for specific derivation)

However, since it is difficult to directly obtain an accurate R_slope at t = 0 through assays, the R values at different time points are used to plot the R-t curve according to Eq. (b). Then, the initial slope of the curve can be calculated, and the R_slope value can be obtained.

(see the end of the article for specific derivation)

After fitting the complete R-t curve based on the study data at multiple time points, the Rslope can be accurately calculated even if there are missing data at earlier time points.

When K_loss cannot be ignored, it is further assumed that the rate of matrix degradation is the same on both sides and that the degradation process conforms to first-order kinetics. The theoretical formula for R-t can be found by mathematical reasoning as Eq. (c), which is independent of K_loss. Therefore, the flux method is also applicable to compounds that are unstable in the matrix.

(The specific derivation process is omitted)

Study validation results

Based on the theory of the flux dialysis method, the compound doesn't need to reach complete equilibrium in the dialysis device to determine its f_u accurately. We selected several commercial compounds for the experimental validation of the flux dialysis method — among which 18 compounds were tested in human plasma to obtain the fraction unbound in human plasma (f_up), and 9 compounds were tested in rat brain tissue homogenate to obtain the fraction unbound in brain homogenate (f_ub). The study results show a good correlation, with the coefficients of determination (R²) all greater than 0.98.

Figure 3. The fraction unbound in plasma (f_up) of 18 commercial drugs were determined by the flux dialysis method, and the results were compared with literature reports.

The x-axis represents the in-house f_up, and the y-axis represents the Literature f_up. The compounds for the validation studies include Afatinib, crizotinib, ibrutinib, osimertinib, aspirin, enalapril, imipramine, indomethacin, itraconazole, lapatinib, quinidine sertraline, amiodarone, montelukast, mifepristone, rosiglitazone, ritonavir, and nicardipine.

Figure 4. f_ub of nine commercial drugs in rat brain tissue homogenates as determined by the flux dialysis method compared to the literature reports. The x-axis represents the in-house f_ub, and the y-axis represents the Literature f_ub. The compounds for the validation studies comprise Verapamil hydrochloride, propranolol, saquinavir, nicardipine, paclitaxel, fluoxetine, carbamazepine, chlorpromazine, and sertraline hydrochloride.

Figure 5. R-t curves of several representative compounds

Advantages of the flux dialysis method

We have established and validated flux dialysis based on the current literature. Compared with the conventional study design of equilibrium dialysis, flux dialysis offers the following advantages:

1. The accurate determination of f_u requires a short theoretical dialysis time. It is hard for some compounds to reach equilibrium using the conventional equilibrium dialysis method.

2. This method is not affected by non-specific binding and the stability in the matrix.

3. The sensitivity demand for the analytical method during sample testing is not high.

This method can be used for protein binding determination of highly protein-binding compounds and to categorize and rank the binding rates of the same series of compounds by R-t curves.

Derivation process of several formulas

Derivation process of equation a:

Based on the above model, if K_nsb and K_loss are ignored, the amount of drugs in the donor and receiver compartments can be respectively calculated as Eq 1 and Eq 2:

At time 0, the drug concentration in the donor compartment is considered to be approximately equal to the initial concentration:

flux (the rate of flux of a compound penetrating the receiver end) serves as equation 3:

When the system reaches the steady state (t→∞), the concentration of free drug on both the dosing chamber and the receiver side is the same, subsequently:

Define R = C_receiver/C_donor, the R of equilibrium, i.e., R_eq is

Since C_donor can be approximated as a constant when t = 0, it can be obtained by equation (3):

Define dR/dt at t = 0 as R_slope. Subsequently

It can be seen that f_{u, donor} is proportional to R_slope. P, A, and V are constant parameters related to the experimental setup and can be obtained based on the study data of compounds with known f_u values. The R value under the initial conditions can be obtained through the assays. The slope under the initial conditions can then be fitted to calculate f_u.

Derivation process of Equation b:

The algebraic expression of the R(t) function needs to be obtained by solving the system of differential equations of equation 1 and 2. The original literature did not provide a detailed derivation process, but directly presented the result: the analytical expression of the R(t) function.

To make this process easier to understand, this article provides two approaches to solving:

(1)By using Laplace transformation, the Laplace transforms of the concentration functions with respect to time in the dosing chamber and the receiver chamber (Cdonor(t) and Creceiver(t)) are obtained as their respective Laplace domain functions F(s). After calculation, the expression of the original function can be obtained by inverse transformation (see formulas A15 and A16). Then the ratio of C_receiver(t) and C_donor(t) gives the analytic expression of the R(t) function.

(2)Arithmetic rules of differentiation:

Where dR/dt — the differentiation of the quotient of C_Receiver(t) and C_donor (t) — can adopt the above equation, while the differential equations of C_Receiver(t) and C_donor (t) are Eq. 1 and 2. The following equation can be obtained after arithmetic simplification:

Further transforming both sides of the equation via the Laplace transformation method yields:

Further solving this equation:

which is equal to equation b:

Conclusion

Improving the accuracy of PPB testing for highly protein-bound compounds is an important task in pharmacokinetics. WuXi AppTec DMPK has developed and validated a variety of orthogonal experimental design methods to ensure the accuracy of PPB measurements for these compounds and continues to empower our customers' new drug discovery programs.

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Authors: Jie Wang, Ziqian Sun, Xiangling Wang, Genfu Chen

Committed to accelerating drug discovery and development, we offer a full range of discovery screening, preclinical development, clinical drug metabolism, and pharmacokinetic (DMPK) platforms and services. With research facilities in the United States (New Jersey) and China (Shanghai, Suzhou, Nanjing, and Nantong), 1,000+ scientists, and over fifteen years of experience in Investigational New Drug (IND) application, our DMPK team at WuXi AppTec are serving 1,500+ global clients, and have successfully supported 1,200+ IND applications.