Toward a mechanical control of drug delivery. On the relationship between Lipinski’s 2nd rule and cytosolic pH changes in doxorubicin resistance levels in cancer cells: a comparison to published data

Abstract

Based on molecular and physiological resemblance, the mechanism that controls drug bioavailability and toxicity also shares strong similarities to the one that controls drug resistance. In both cases, this mechanism relies on the expression of drug transporters and the physico-chemical properties of drugs, which together alter the intracellular accumulation of chemicals in cells or tissues. However, a parameter that is central and has received great attention in the field of bioavailability, but almost none in the field of drug resistance, is the molecular weight of drugs. In the former area, it is well known that to achieve a reasonable bioavailability, drugs must have—among other properties—a molecular weight less than 500, known as Lipinski’s 2nd rule. Accordingly, it is worth questioning whether a similar rule exists in the field of drug resistance and what subsequent mechanism would control the membrane permeability to drugs as a function of their molecular weight. I demonstrate here that cytosolic pH fixes the molecular weight of drugs entering cells, by altering the cell membrane mechanical properties and that, both cytosolic pH and membrane mechanical properties are needed and sufficient to explain doxorubicin resistance levels in different cancerous cell lines. Finally, I discuss the efficiency of a drug handling activity by transporters in MDR and suggest ways to control drug delivery mechanically. In addition, and for the first time, the literal expression of a Law similar to Lipinski’s 2nd rule will be described as a function of cytosolic pH and lipid number asymmetry.

Appendices

Appendix A: numerical determination of p ^*₀ :

From $\bar{\varepsilon }(l_{\text{c}} ) = \bar{\varepsilon }_{0} /l_{\text{c}} ,$ $\bar{\varepsilon }_{0}$ can be rewritten as $\bar{\varepsilon }_{0} = k_{\text{B}} T l_{\text{B}}$ with Bjerrum’s length defined as l _B = q ²/Dk _B T ∼ 7 Å (the dielectric constant of hydrated polar head is assumed to be close to the one of water (Peitzsch et al. 1995)). Given the iso-osmotic condition, i.e. an intracellular concentration in electrolytes ~0.1 M, it follows l _c ∼ 9.6 Å (using Debye’s length as described in Nguyen et al. (2005)). With a lipid cross section area πθ² ∼ 50 Å² it follows for a classical 2D hexagonal lattice (z = 6): $p_{0}^{*} \sim \sqrt {z\pi \theta^{2} /\pi^{2} l_{\text{c}} l_{\text{B}} } \sim 0.6.$

Appendix B: determination of the hydrogen ion-free lipid probability:

Assuming that a hydrogen ion and a negatively charged lipid interact together with a resulting energy –e ₀ (e ₀ > 0 is the magnitude of the interaction). In this case, each negatively charged lipids can be in two states, occupied (i.e. interacting with hydrogen ion) or non-occupied. It follows that the partition function of a negatively charged lipid is $\zeta = 1 + {\text{e}}^{{\left( {e_{0} + {{\upmu}}} \right)/k_{\text{B}} T}}$ (μ is the chemical potential of hydrogen ion in solution). Therefore, the probability that a negatively charged lipid is free of hydrogen ion is $p = \left[ {1 + {\text{e}}^{{\left( {e_{0} + \mu } \right)/k_{\text{B}} T}} } \right]^{ - 1}$. It follows that when p ₀/p ^*₀  ∼ 1, where p ^*₀  ∼ 0.6 (Appendix A), $p_{o} = \left[ {1 + {\text{e}}^{{\left( {e_{0} + {{\upmu}}_{0} } \right)/k_{\text{B}} T}} } \right]^{ - 1}$ can be rewritten as p ^*₀  = 0.6 = [1 + 1/γ]⁻¹ with $1/\gamma = {\text{e}}^{{\left( {e_{0} + \mu_{0} } \right)/k_{\text{B}} T}}$. It follows that γ ≅ 1.5.