Dynamin binds to lipids via its PH domain.
The structure has been solved in the absence of ligands by a number of groups: Downing et al. (1994) Current Biol 4: 884-91; Ferguson et al. (1994) Cell 79: 199-209; Timm et al. (1994) Nat Stuc Biol 1: 782-88
It is not hard to imagine the positively charged pocket (see movie below) engulfing negatively charged lipids. There are not many positively charged residues on the binding surface apart from the binding pocket. The key mutation in dynamin I that wipes out lipid binding is K535A (see Vallis et al 1999) and this works as a dominant negative inhibitor of endocytosis (Cos cells). Dynamin-related proteins do not have complete conservation of this domain, but at least some are shown to interact with membranes (link to review)
The affinity of an isolated dynamin I PH domain for negatively charged lipids in very weak. Indeed the affinity for inositol(1,4,5)triphosphate is in the mM range.
Affinity of isolated PH domain for inositol headgroups, measured by Isothermal Titration Calorimetry
Inositol hexaphosphate (InsP6) has a higher affinity likely due to the extra negative charges binding to the positive surface. The above measurement is the affinity of a PH domain monomer. However, as dynamin is multimeric (dimer or tetramer, see ultracentrifugation data) and on the membrane it is oligomeric, therefore the effective affinity (avidity) will be orders of magnitude greater due to the avidity of many simultaneous interactions.
Avidity is the product of individual binding constants (or the sum of the free binding energies) for a multisite binding protein. Thus pentameric IgMs have a high avidity, even if they have a low affinity. The effect of avidity on dynamin's affinity for membranes is illustrated below.
Review on PH domains: Lemmon and Ferguson, 2000, BJ, 350, 1-18.