Fig. 5. Integral membrane proteins tend to increase the magnitude of fluctuations of the bilayer. (A) Inserting 144 copies of Aqp0, an aquaporin, or Kir2.2, an inward-rectifying potassium ion channel, produces a membrane that obeys Helfrich–Canham (HC) theory at low q, however, the Aqp0 proteins lead to a pronounced hump in the intensity around q ∼ 4 nm^–1. These and all other fits are derived from Fig. S6 (ESI†). (B) POPE/POPG (3 : 1) bilayers which have had the bacterial proteins BtuB or OmpF or both proteins inserted are also well described by HC theory at low q. Likewise, adding 108 copies of the truncated peripheral cell signalling protein tN-Ras to either the (C) low or (D) high cholesterol ternary lipid mixtures produces a membrane whose dynamics are well described by HC theory. (E) The calculated values of the bending rigidity, K _c, show the integral membrane proteins (Kir2.2, BtuB & OmpF) all reduce the stiffness of the bilayers, the integral membrane protein Aqp0 increases the stiffness slightly (2σ) whereas the peripheral membrane protein, tN-Ras, has no effect on the stiffness of the ternary lipid mixture. Convergence times and errors are calculated as described in the Methods and the (Fig. S4 and S5, ESI†). The power spectra of the thickness fluctuations can be found in Fig. S7 (ESI†).