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A Mathematical Model for Prediction of Drug Molecule Diffusion Across the Blood-Brain Barrier

Published online by Cambridge University Press:  02 December 2014

Jonathan Burns ,
Donald F. Weaver ,
Jonathan Burns  and
Donald F. Weaver
Jonathan Burns
Affiliation:
From the Department of Mathematics, University of Toronto, Ontario (JB); Departments of Medicine (Neurology), Chemistry and Biomedical Engineering, Dalhousie University, Nova Scotia (DFW), Canada.
Donald F. Weaver
Affiliation:
From the Department of Mathematics, University of Toronto, Ontario (JB); Departments of Medicine (Neurology), Chemistry and Biomedical Engineering, Dalhousie University, Nova Scotia (DFW), Canada.
Jonathan Burns
Affiliation:
From the Department of Mathematics, University of Toronto, Ontario (JB); Departments of Medicine (Neurology), Chemistry and Biomedical Engineering, Dalhousie University, Nova Scotia (DFW), Canada.
Donald F. Weaver
Affiliation:
From the Department of Mathematics, University of Toronto, Ontario (JB); Departments of Medicine (Neurology), Chemistry and Biomedical Engineering, Dalhousie University, Nova Scotia (DFW), Canada.
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Abstract

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Background:

Predicting the ability of drugs to enter the brain is a longstanding problem in neuropharmacology. The first step in creating a much-needed computational algorithm for predicting whether a drug will enter brain is to devise a rigorous mathematical model.

Methods:

Employing two experimental measures of blood-brain barrier (BBB) penetrability (brain/plasma ratio and the brain-uptake index) and 14 theoretically derived biophysical predictors, a mathematical model was developed to quantitatively correlate molecular structure with ability to traverse the BBB.

Results:

This mathematical model employs Stein's hydrogen bonding number and Randic's topological descriptors to correlate structure with ability to cross the BBB. The final model accurately predicts the ability of test molecules to cross the BBB.

Conclusion:

A mathematical method to predict blood-brain barrier penetrability of drug molecules has been successfully devised. As a result of bioinformatics, chemoinformatics and other informatics-based technologies, the number of small molecules being developed as potential therapeutics is increasing exponentially. A biophysically rigorous method to predict BBB penetrability will be a much-needed tool for the evaluation of these molecules.

Type
Other
Information
Canadian Journal of Neurological Sciences , Volume 31 , Issue 4 , November 2004 , pp. 520 - 527
Copyright
Copyright © The Canadian Journal of Neurological 2004

References

1. Ryhal, BT, Fletcher, MP. The second-generation antihistamines. What makes them different? Postgrad Med 1991; 89:87–88.CrossRefGoogle ScholarPubMed
2. Rapoport, SI. Blood-Brain Barrier in Physiology and Medicine. New York: Raven Press. 1976: 43–86, 153-176.Google Scholar
3. Pardridge, WM. Peptide Drug Delivery to the Brain. New York: Raven Press. 1991: 1–11, 23-51, 63-67, 123-134.Google Scholar
4. Pardridge, WM. Recent advances in blood-brain barrier transport. Ann Rev Pharmacol Toxicol 1988; 28:25–39.CrossRefGoogle ScholarPubMed
5. Tryba, M, Kurz-Muller, K. Penetration of roxatidine into the cerebrospinal fluid. Scand J Gastroenterol 1988; 146:153–158.CrossRefGoogle ScholarPubMed
6. Judson, IR, Rutty, CJ, Abel, G, Graham, MA. Low central nervous system penetration of N2, N4, N6-trihydroxymethyl-N2, N4, N6-trimethylmelamine (Trimelamol): a cytotoxic s-triazine with reduced neurotoxicity. Br J Cancer 1986; 53:601–606.CrossRefGoogle ScholarPubMed
7. Banks, WA, Kastin, AJ. Peptide transport systems of opiates across the blood-brain barrier. Am J Physiol 1990; 259:E1–E10.Google ScholarPubMed
8. Spector, R. Fatty acid transport through the blood-brain barrier. J Neurochem 1988; 50:639–643.CrossRefGoogle ScholarPubMed
9. Pardridge, WM. Strategies for drug delivery through the blood-brain barrier. Microbiol Aging 1989; 10:636–637.Google ScholarPubMed
10. Banks, WA, Kastin, AJ. Peptides and the blood-brain barrier: lipophilicity as a predictor of permeability. Brain Res Bull 1985;15:287–292.CrossRefGoogle ScholarPubMed
11. Bezek, S, Trnovec, T, Scasnar, V, et al. Irradiation of the head by 60Co opens the blood-brain barrier for drugs in rats. Experientia 1990; 46:1017–1020.CrossRefGoogle ScholarPubMed
12. BioByte Corporation (1994) MacLogPGoogle Scholar
13. Balaban, AT, Motoc, I, Bonchev, D, Mekenyan, O. Topological indices for structure-activity correlations. In: Charton, M, Motoc, I (Eds). Steric Effects in Drug Design (Topics in Current Chemistry, Vol 114). Berlin: Springer-Verlag, 1983; 21–55.Google Scholar
14. Stein, WD. The Movement of Molecules Across Cell Membranes. New York: Academic Press. 1967; 76.Google Scholar
15. Motoc, I, Marshall, GR. Van der Waals volume fragmental constants. Chem Phys Lett 1985; 116:415–419.CrossRefGoogle Scholar
16. Oldendorf, WH. Measurement of brain uptake of radiolabeled substances using a tritiated water internal standard. Brain Res 1970; 24:372–376.CrossRefGoogle ScholarPubMed
17. Montgomery, DC, Peck, EA. Introduction to Linear Regression Analysis. 2nd ed. New York: John Wiley & Sons. 1992; 103–105, 173-177, 189-192, 265-304, 317-318 .Google Scholar
18. Nelder, JA, McCullagh, P. Generalized Linear Models. 2nd ed. London: Chapman & Hall. 1991; 323–356.Google ScholarPubMed
19. Hansch, C, Steward, A, Anderson, SM, Bentley, D. The parabolic dependence of drug action upon lipophilic character as revealed by a study of hypnotics. J Med Chem 1968; 11:1–11.CrossRefGoogle ScholarPubMed
20. Cornford, EM, Landon, KP. Blood-brain barrier transport of CI-912: single passage equilibration of erythrocyte-borne drug. Ther Drug Monit 1985; 7:247–252.CrossRefGoogle ScholarPubMed
21. Cornford, EM, Young, D, Paxton, JW, Sofia, RD. Blood-brain barrier penetration of felbamate. Epilepsia 1992; 33:944–954.CrossRefGoogle ScholarPubMed
22. Bradbury, MW, Bloom, DS, McDowell, M. An inhibitor of cerebral uptake of noradrenaline in jaundiced blood plasma. J Cerebral Blood Flow Metab 1983; 3:516–520.CrossRefGoogle ScholarPubMed
23. Oldendorf, WH. Brain uptake of radiolabeled amino acids, amines, and hexoses after arterial injection. Am J Physiol 1971; 221:1629.CrossRefGoogle ScholarPubMed
24. Dayton, PG, Pruitt, AW, McNay, JL, Steinhorst, J. Studies with triamterene, a substituted pteridine. Unusual brain to plasma ratio in mammals. Neuropharmacol 1972; 11:435–446.CrossRefGoogle ScholarPubMed
25. Tsuneizumi, T, Babb, SM, Cohen, BM. Drug distribution between blood and brain as a determinant of antipsychotic drug effects. Biol Psychiatry 1992; 32:817–826.CrossRefGoogle ScholarPubMed
26. Selig, A, Gottschlich, R, Devant, RM. A method to determine the ability of drugs to diffuse through the blood-brain barrier. Proc Natl Acad Sci USA. 1994; 91:68–72.CrossRefGoogle Scholar
27. Schroeder, DH. Metabolism and kinetics of bupropion. J Clin Psychiatry 1983; 44:79–91.Google ScholarPubMed
28. Friis, ML, Christiansen, J, Hvidberg, EF. Brain concentrations of carbamazepine and carbamazepine-10,11-epoxide in epileptic patients. Eur J Clin Pharmacol 1978; 14:47–51.CrossRefGoogle ScholarPubMed
29. Watanabe, T, Matsuhashi, K, Takayama, S. Placental and blood-brain barrier transfer following prenatal and postnatal exposures to neuroactive drugs: relationship with partition coefficient and behavioural teratogenesis. Toxicol Appl Pharmacol 1990;105:66–77.CrossRefGoogle ScholarPubMed
30. Dubey, RK, McAllister, CB, Inoue, M, Wilkinson, GR. Plasma binding and transport of diazepam across the blood-brain barrier. No evidence for in-vivo enhanced dissociation. J Clin Invest 1989; 84:1155–1159.CrossRefGoogle ScholarPubMed
31. Evans, BD, Vogel, WH. Penetration of some O-and/or N-Methylated norepinephrine derivatives through the rat blood-brain barrier. Res Comm Chem Path Pharmacol 1977; 17:61–76.Google ScholarPubMed
32. Barkai, AI, Suckow, RF, Cooper, TB. Imipramine and its metabolites: relationship to cerebral catecholamines in rats in-vivo. J Pharmacol Exp Ther 1984; 230:330–335.Google ScholarPubMed
33. Neil-Dyer, G, Bartlett, J, McAinsh, J, Cruickshank, JM. Beta-adrenoceptor blockers and BBB. Br J Clin Pharm 1981; 11:549–553.CrossRefGoogle Scholar
34. Cornford, EM, Diep, CP, Pardridge, WM. Blood-brain barrier transport of valproic acid. J Neurochem 1985; 44:1541–1550.CrossRefGoogle ScholarPubMed
35. Tocco, DJ, Clineschmidt, BV, Duncan, AEW, deLuna, FA, Bear, JE. Uptake of the beta-adrenergic blocking agents propranolol and timolol by rodent brain: relationship to central pharmacological action. J Cardiovasc Pharmacol 1980; 2:133–143.CrossRefGoogle Scholar
36. Abernethy, DR, Arendt, RM, Greenblatt, DJ. Pharmacologic properties of acebutolol: relationship of hydrophilicity to central nervous system penetration. Am Heart J 1985; 109:1120–1125.CrossRefGoogle ScholarPubMed
37. Krause, W, Kuhn, G. Pharmacokinetics of rolipram in the rhesus and cynomolgus monkeys, the rat and the rabbit. Studies on species differences. Xenobiotica 1988; 18:561–571.CrossRefGoogle ScholarPubMed
38. MacKenzie, E, McCulloch, J, Harper, AM. Cerebral circulation and norepinephrine: relevance of the blood-brain barrier. Am J Physiol 1976; 231:483–488.CrossRefGoogle ScholarPubMed
39. Oldendorf, WH. Lipid solubility and drug penetration of the blood-brain barrier. Proc Soc Exp Invest 1974; 63:1241–1248.Google Scholar
40. Zlokovic, BV, Segal, MB, Begley, DJ, Davson, H, Rakic, L. Permeability of the blood-cerebrospinal fluid and blood-brain barriers to thyrotropin releasing hormone. Brain Res 1985; 358:191–199.CrossRefGoogle ScholarPubMed
41. Shin, WW, Fong, WF, Pang, SF, Wong, PC. Limited blood-brain barrier transport of polyamines. J Neurochem 1985; 44:1056–1059.CrossRefGoogle ScholarPubMed
42. Zlokovic, BV, Begley, DJ, Chain-Eliask, DG. Blood-brain barrier penetrability to leucine-enkephalin, D-alanine-D-Leu-enkephalin and their N-terminal amino acid (tyrosine). Brain Res 1985; 336:125–132.CrossRefGoogle Scholar
43. Engstrom, FL, Woodbury, DM. Seizure susceptibility in DBA and C57 mice: the effects of various convulsants. Epilepsia 1988; 29:389–395.CrossRefGoogle ScholarPubMed
44. Cornford, EM, Bocash, WD, Braun, LD, et al. Rapid distribution of tryptophol (3-indole ethanol) to the brain and other tissues. J Clin Invest 1979; 63:1241–1248.CrossRefGoogle Scholar
45. Feldmen, J, Bousquet, P. A new procedure for studying central acting cardiovascular drugs: the permeabilization of the blood-brain barrier. Arch Inter Pharmacodynam Ther 1988; 296:7–17.Google Scholar
46. Nagahama, S, Chen, YF, Oparil, S. Mechanism of the depressor effect of bromocriptine in the spontaneously hypertensive rat. J Pharmacol Exp Ther 1984; 228:370–375.Google ScholarPubMed
47. Kerber, CW, Sovak, M, Ranganathan, RS, Heilman, CB. Totrol: a new myelographic agent: 1. Radiography, CT, CSF clearance, and brain penetration. AJNR Am J Neuroradiol 1983; 4:317–318.Google ScholarPubMed
48. Nordling, J, Meyoff, JJ, Hald, T. Sympatholytic effect on striated urethral sphincter.A peripheral or central nervous system effect? Scand J Urol Nephrol 1981; 15:173–180.CrossRefGoogle ScholarPubMed
49. Wasserman, S. Histamine and the preclinical pharmacology of cetirizine. Ann Allergy 1987; 57:1–3.Google Scholar
50. Scasnar, V, Kallay, Z, Bezek, S, Trnovec, T, Durisova, M. Pharmacokinetics of the new local anaesthetic N-[2-(2-Heptyloxyphenyl-carbamoyloxy)ethyllpiperidinium chloride in rats and mice. Arzneimittelforschung - Drug Res 1987; 37:783–787.Google ScholarPubMed
51. Pardridge, WM. Transport of protein-bound hormones into tissue in-vivo. Endocr Rev 1981; 2:103–123.CrossRefGoogle Scholar
52. Bezek, S, Faberova, V, Scasnar, V, et al. Pharmacokinetics of carbisocaine in rats and mice. Eur J Drug Metab Pharmacokinet 1988; 13:27–34.CrossRefGoogle ScholarPubMed
53. Levin, VA. Relationship of octanol/water partition coefficient and molecular weight to rat brain capillary permeability. J Med Chem 1980; 23:682–684.CrossRefGoogle ScholarPubMed
54. Cornford, EM, Braun, LD, Oldendorf, WH, Hill, MA. Comparison of lipid-mediated blood-brain barrier penetrability in neonates and adults. Am J Physiol 1982; 243:C161–C170.CrossRefGoogle ScholarPubMed