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

Abstract

520A robust numerical algorithm to computationally predict the ability of drug molecules to cross the blood-brain barrier (BBB) is of relevance to basic neuroscience and to the pharmacology of drug design. [1][2][3][4] A molecule can cross the BBB by either active transport or passive diffusion; 4 passive diffusion remains the most important method for the greatest structural diversity of drug molecules. The two most widely recognized principal physical properties that influence passive diffusion across the BBB (with subsequent entry into the brain) are molecular size and lipophilicity. [4][5][6][7] Although equations that quantitatively relate trans-BBB diffusion to these two properties have been proposed, [8][9][10] these models use only one predictor to encode each of the factors of size and lipophilicity.This study endeavours to develop a rigorous theoretical ABSTRACT: 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 brainuptake 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. Conclusions: 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.RÉSUMÉ: Un modèle mathématique pour prédire la diffusion de molécules à travers la barrière hémato-encéphalique. Introduction : En neuropharmacologie, il est difficile de prédire quels médicaments pourront pénétrer dans le cerveau. La première étape dans la création d'un algorithme pour prédire si un médicament pénétrera dans le cerveau est d'élaborer un modèle mathématique rigoureux. Méthodes : Un modèle mathématique a été développé en utilisant deux mesures expérimentales de la perméabilité de la barrière hémato-encéphalique (BHE) [le ratio cerveau/plasma (RCP) et l'indice de captation du cerveau (ICC)] et 14 prédicteurs biophysiques théoriques, afin de corréler quantitativement la structure moléculaire d'une substance et sa capacité à pénétrer la BHE. Ce modèle mathématique utilise le nombre de liaisons hydrogène de Stein et les indices topologiques de Randic pour corréler la structure de la molécul...

Cross-validation pitfalls when selecting and assessing regression and classification models

“…There are 220 MOE 2D descriptors for each compound. However, during pre-processing we removed 30 descriptors with near zero variation and 6 descriptors that were linear combinations of others, leaving 184 descriptors for model building. bbb2 contains blood–brain barrier categories (“crossing” or “not crossing”) for 80 compounds from Burns andWeaver [14]. There are 45 compounds categorised as “crossing” and 35 compounds as “not crossing”.…”

“…bbb2 contains blood–brain barrier categories (“crossing” or “not crossing”) for 80 compounds from Burns andWeaver [14]. There are 45 compounds categorised as “crossing” and 35 compounds as “not crossing”.…”

The Blood–Brain Barrier (BBB) Score

“…Molecular weight (MW), topological polar surface area (TPSA), log P , log D , pKa, hydrogen bond donor (HBD), carbon/heteroatom ratio (C:Hetero), first kappa shaped index (Kier1), second kappa shaped index (Kier2), third kappa shaped index (Kier3), atom connectivity index (chi1), carbon connectivity index (chi1_C), hydrogen bond acceptor (HBA), hydrogen bond number (HBN = HBD + HBA), number of rotational bonds (RB), square of log P ((log P ) 2 ), , MWHBN , number of aromatic rings (Aro_R), number of heavy atoms (HA), van der Waals volume (vdw_V), area of van der Waals surface (vdw_A) were analyzed descriptors. The descriptors , MWHBN were chosen based upon simple linear regression literature studies, based upon brain-uptake index (BUI). − These descriptors were calculated using Molecular Operating Environment (MOE) and ChemAxon (CA) software. The physiochemical property space for each descriptor is mapped for the CNS and non-CNS drugs data sets, and an equation (cutoffs, linear or polynomial) was fitted as a boundary for CNS and non-CNS drug space.…”

In Silico Prediction of Blood Brain Barrier Permeability: An Artificial Neural Network Model

“…Sun 42 developed the predictive models for partition coefficient, aqueous solubility, blood brain barrier permeability, and human intestinal absorption using the Partial Least Squares (PLS) approach. Burns 43 and Weaver developed a MLR based BBB permeability model using 14 theoretically derived biophysical descriptors based on topological and hydrogen bonding properties of the molecules. Yap 9 and Chen generated Quantitative Structure-Pharmacokinetic Relationships (QSPkR) for BBB permeability, human serum albumin binding, and milk-plasma distribution by using general regression neural network, multilayer feedforward neural network, and MLR.…”