sigmoidal

Meaning: A sigmoidal curve is S-shaped: shallow at first, steep in the middle, then leveling off at a maximum. In biochemistry it signals cooperative binding. Binding of one ligand changes the conformation of the other subunits, so later ligands bind more easily (positive cooperativity). Hemoglobin binding O₂ is the standard example; allosteric enzymes often give a sigmoidal plot of rate versus substrate concentration.

Equation: Y = [L]ⁿ / (Khalfⁿ + [L]ⁿ), where Y is fractional saturation (unitless), [L] is free ligand concentration (mol/L, or partial pressure in Pa for O₂), Khalf is the ligand level at half saturation (same unit as [L]), and n is the Hill coefficient (unitless). n = 1 gives a hyperbola; n > 1 indicates positive cooperativity.

On the MCAT: Passages show binding or rate curves and ask you to infer cooperativity from the shape. Compare hemoglobin (sigmoidal) with myoglobin (hyperbolic). A steep middle region means a small change in pO₂ causes a large change in saturation, so hemoglobin loads O₂ in the lungs and unloads it in the tissues.

Common confusion: A right or left shift changes affinity, not shape. Lower pH, more CO₂, or 2,3-BPG shifts hemoglobin's curve right, but it stays sigmoidal. Enzymes that follow Michaelis-Menten kinetics give a hyperbola because they lack cooperativity.