The longer and more saturated fatty acids chains interact more strongly with each other through their longer hydrocarbon chains and thus cause higher values of transition temperature (Tm) i.e higher temperatures are required to increase the fluidity of the bilayer. Transition temperature (Tm):As the temperature increases, the hydrophobic side chains undergo a transition from the ordered state (more gel-like or crystalline phase) to a disordered one, taking on a more liquid like or fluid arrangement. The temperature at which the structure undergoes the transition from ordered to disordered (melts) is called the transition temperature (Tm). Fluidity of membranes: are highly dependant upon the lipid composition of the membrane. In a lipid bilayer; the hydrophobic chains of the fatty acids can be highly aligned or ordered to provide a rather stiff structure. Saturated fatty acid: The longer and more saturated fatty acids chains interact more strongly with each other through their longer hydrocarbon chains and thus cause higher values of transition temperature (Tm) i.e higher temperatures are required to increase the fluidity of the bilayer: On the other hand, unsaturated bond that exists in the cis configuration tend to increase the fluidity of the bilayer' by decreasing the compactness of the side chain packing without diminishing hydrophobicity. Cholesterol modifies the fluidity of membranes at temperature belove the transition temperature (Tm). It interferes with the interaction of the hydrocarbon tails of fatty acids and thus increase fluidity. At temperatures above the transition temperature (Tm), It limits disorder; thus limiting fluidity. At high cholesterol: phospholipid ratios, transition temperatures are abolished together. Ref: Harper's, Illustrated Biochemistry, 25th Edition, Page 511.