European Biophysics Journal

, Volume 36, Issue 2, pp 121–131 | Cite as

Multi drug resistance-dependent “vacuum cleaner” functionality potentially driven by the interactions between endocytosis, drug size and Pgp-like transporters surface density

Article

Abstract

In cells, multi drug resistance (MDR) is associated with Pgp-like transporters expression extruding drugs from cellular membranes. MDR is efficiently generated with a relatively small fraction of membrane transporters. As the insertion of drugs into cellular membranes is widespread, there are no reasons why a drug should incorporate the membrane in the vicinity of a transporter. As a result a further elusive hypothesis is usually invoked: these transporters act like “vacuum cleaners” of drugs embedded in the membrane. Nonetheless, how these transporters attract drugs remains obscure. To clarify the “vacuum cleaner” notion, we suggest that during its residency time in cellular membranes, the lateral movement of drugs from their point of insertion to transporters is governed by Brownian’s diffusion, which allows the drugs/transporters interaction. Taking into account the functionality of Pgp-like transporters, namely the extrusion of drugs from the plasma membrane inner leaflet, we characterize how the state of drug resistance is triggered involving: membrane endocytosis, drug physico-chemical properties and the surface density of Pgp-like transporters. In addition, the theory developed provides for the first time a theoretical proof of Lipinski’s second rule with regard to drugs’ size (or MW) selectivity on their permeation across cellular membranes.

List of symbols

a

drug cross section area

D

membrane diffusion coefficient

f(K)

non-recurring step number of a two dimensional random walk

ΔG

drug dehydration energy

h

membrane thickness

kc

bending modulus of the membrane

k or k0

altered or control kinetics of endocytosis

K

step number of a two dimensional random walk

NPgp

number of Pgps in the outer cellular surface

pPgp

meeting probability between a drug and a Pgp

\({ \tilde{p}_{{\rm Pgp}}}\)

drug extrusion probability by Pgp

rMDR, rnon-MDR

escape rate (i.e. probability per unit of time) into the cytoplasm of drugs in the membrane of drug resistant (“MDR”) and drug sensitive (“non-MDR”) cells

R

vesicle radius

Scell

cellular surface area

SPgp

cross section area of Pgps in the cellular surface

t0

drug residency time in the membrane

U

membrane barrier potential

ρPgp

fraction of the cellular surface covered by Pgp transporters

ρPgpc

critical surface area covered by Pgp-like transporters leading to drug resistance

σin

inner leaflet surface tension

σout

outer and inner leaflet surface tension

Δσ = σin − σout

difference of surface tension between the inner and outer leaflets

χMDR, χnon-MDR

ratio between the endocytosis kinetics and the escape rate into the cytoplasm of drugs initially in the plasma membrane of resistant (“MDR”) and sensitive (“non-MDR”) cells

Notes

Acknowledgments

The authors are grateful to Dr Emmanuel Farge and Zoe Rauch for their comments on the manuscript. This work has been supported by BBSRC (Biotechnology and Biological Sciences Research Council, UK), Grant Nos: BB/C505308/1.

Supplementary material

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Copyright information

© EBSA 2007

Authors and Affiliations

  1. 1.School of Pharmacy and Pharmaceutical Sciences, Drug Delivery GroupUniversity of ManchesterManchesterUK
  2. 2.School of Veterinary Medicine and Science, Sutton Bonington CampusUniversity of NottinghamLeicestershireUK

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