# QSAR Basics > QSAR basics in Pharmacy: Hansch equation with pi, sigma and Es descriptors, Craig plots, CoMFA 3D-QSAR, q-squared cross validation and Lipinski rules. - Canonical URL: https://prepelephant.com/topics/allied/pharmacy/qsar-basics - Exam / course: Allied Health · Subject: Pharmacy - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "QSAR Basics", PrepElephant, https://prepelephant.com/topics/allied/pharmacy/qsar-basics ## Direct answer Quantitative structure-activity relationship (QSAR) methods replace trial-and-error synthesis with equations linking structural descriptors to biological activity. The classical Hansch analysis is a multiple linear regression of potency, expressed as log(1/C), on three descriptor families: hydrophobic (π, the substituent's contribution to partitioning, or log P for the whole molecule), electronic (Hammett σ) and steric (Taft Es), with molar refractivity often added — log(1/C) = a·π + b·σ + c·Es + d. Its intellectual ancestor is the Meyer-Overton correlation between anaesthetic potency and lipid solubility, the oldest linear free-energy relationship in pharmacology. Practical tools include the Craig plot (σ against π), which flags substituent sets that decorrelate the variables so regression can separate their effects; Free-Wilson analysis, which treats group contributions additively; and modern descendants — topological indices and 3D-QSAR such as CoMFA, where steric and electrostatic fields sampled around aligned molecules feed partial least squares. Statistics decide credibility: r² for fit, cross-validated q² (leave-one-out) for predictive power on held-out compounds, and an applicability domain outside which predictions are not claimed. ## What you must remember - **The Hansch equation:** log(1/C) = a·π + b·σ + c·Es + d, with C the molar concentration for a standard effect — the form exam papers ask you to expand term by term. - **Descriptor families:** hydrophobic (π, log P), electronic (Hammett σ, resonance and inductive), steric (Taft Es, molar refractivity, Verloop parameters) — the classic triad. - **Meyer-Overton origin:** anaesthetic potency tracking lipid solubility — the founding observation that potency could be predicted from a physical property. - **Craig plot:** σ versus π scatter that lets medicinal chemists pick substituent sets spanning both axes orthogonally, avoiding collinearity in the regression. - **Free-Wilson model:** purely additive contributions of each substituent position, no physical descriptor needed — the simpler sibling of Hansch. - **CoMFA and 3D-QSAR:** aligned molecules in a lattice; steric and electrostatic field values at grid points become thousands of predictors handled by partial least squares, producing contour maps for design. - **Statistical honesty:** r² measures fit, q² from leave-one-out cross-validation measures prediction; a model is judged by compounds it has never seen and by its applicability domain. - **Companion filter:** Lipinski's rule of five — molecular weight ≤ 500, log P ≤ 5, ≤ 5 hydrogen-bond donors, ≤ 10 acceptors — a peroral solubility-permeability screen, not a QSAR itself but always asked alongside. ## Reading a Hansch equation like a designer Consider, as a teaching example, substituted aromatics whose Hansch analysis returns log(1/C) = 0.8·π − 1.2·σ + 0.3·Es + constant — numbers chosen for illustration, but read them the way a chemist would. The positive π coefficient says potency climbs with lipophilicity, plausibly better passage to a hydrophobic pocket; the negative σ coefficient says electron-donating groups (negative σ) help, pointing to ring electron density as part of the binding interaction; the small Es term says size matters little at this position. The design move follows: pick strong electron donors with decent lipophilicity — methoxy and methyl, not nitro — and check the Craig plot so the chosen set decorrelates σ and π for the next regression. Contrast the failure mode every examiner loves: add a bulkier, more lipophilic analogue and potency collapses despite a "better" π — activity versus log P is usually parabolic, an optimum near 2 for many centrally acting drugs, past which solubility and desolvation costs dominate. The linear equation was honest only inside its domain, and modern practice formalises the caution: split the data into training and test sets, report q² on held-out compounds, and state the applicability domain — a QSAR is a prediction engine, not a law. ## Where students slip Sign conventions sink more answers than the mathematics: negative σ means electron donation (Hammett defined σ against benzoic acid ionisation), so a negative σ coefficient favours donors — careless readers design the opposite substituent. Second, π versus log P: π is the substituent's incremental constant, log P the whole molecule's. Third, r² worship: heavily intercorrelated descriptors can return an impressive training r² and fail every new compound, which is why q² and test-set validation exist. Fourth, CoMFA answers that skip alignment miss the method's known sensitivity to superposition. Finally, Lipinski's rule is quoted as an absolute bar — it only flags probable poor oral absorption, and many successful drugs violate it. ## Frequently asked questions ### What are the terms of the Hansch equation? log(1/C) = a·π + b·σ + c·Es + d, where π is hydrophobic, σ the Hammett electronic and Es the Taft steric substituent constant; the coefficients guide next-round synthesis. ### What is a Craig plot used for? It plots σ against π for candidate substituents so a series can be chosen spanning both axes without collinearity, letting the regression separate hydrophobic from electronic effects. ### Why is cross-validated q² preferred over r²? r² only describes fit to the training data and inflates with intercorrelated descriptors; q² from leave-one-out or test-set validation estimates true predictive power on new compounds. ### How does CoMFA differ from classical QSAR? It uses three-dimensional steric and electrostatic fields sampled at lattice points around aligned molecules, analysed by partial least squares, and outputs contour maps showing where bulk or charge helps or hurts. ### What does Lipinski's rule of five state? Molecular weight ≤ 500, log P ≤ 5, hydrogen-bond donors ≤ 5 and acceptors ≤ 10; exceeding two thresholds flags probable poor oral absorption — a guideline, not a law.