Thermodynamics and Kinetics of Protein Incorporation Into Membranes

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Thermodynamics and Kinetics of Protein Incorporation Into Membranes Proc. NatL Acad. Sci. USA Vol. 80, pp. 3691-3695, June 1983 Biophysics Thermodynamics and kinetics of protein incorporation into membranes (hydrophobic effect/protein immobilization/lipid-protein interaction/hydrogen bonds/conformational entropy) FmRIZ JAHNIG Max-Planck-Institut fir Biologie, Corrensstrasse 38, 74 Tfibingen, Federal Republic of Germany Communicated by Hans Frauenfelder, February 9, 1983 ABSTRACT The free energy and enthalpy of protein incor- tein immobilization effect has not been taken into account in poration into membranes are calculated with special emphasis on previous work. This effect was studied in the context of en- the hitherto neglected effects of immobilization of protein and zyme-coenzyme binding where it was found to lead to a con- perturbation of lipid order in the membrane. The free energy siderable reduction of the binding energy available from the change is found to be determined by the hydrophobic effect as the hydrophobic effect (7, 8). The lipid perturbation effect also was driving force for incorporation and the protein immobilization ef- not considered previously, although a priori there is no reason fect which leads to a considerable reduction of the free energy for this contribution to be small because a large number of lipid gained from the hydrophobic effect. For incorporation of a hy- molecules may be affected by one protein molecule. From ca- drophobic, bilayer-spanning a-helix, the free energy change ob- lorimetric measurements it is known that enthalpies up to tained is of the order of -15 kcal/mol (1 cal = 4.184 J) in agree- hundreds of kcal/mol are involved in lipid-protein association ment with experimental results. The lipid perturbation effect yields (9-11). only a small contribution to the free energy change due to an en- of bind- ergy/entropy compensation inherent in lipid order. This effect In the present paper, the free energy and enthalpy dominates the enthalpy change, giving rise to values on the order ing of a protein to a membrane are calculated, including the of 100kcal/mol with a pronouncedtemperature dependence around hitherto neglected effects of protein immobilization and lipid the lipid phase transition as observed experimentally. The kinetics perturbation. The immobilization effect is estimated by a slight of protein incorporation are even more strongly affected by the modification of the treatment in enzyme-coenzyme binding lipid perturbation effect, leading to an abrupt decrease of the rate (8). The lipid perturbation effect is elaborated by adopting a of incorporation below the lipid phase transition. previously developed continuum model for lipid-protein in- teraction (12-14). The results for the free energy and enthalpy It is commonly accepted that the driving force for spontaneous of binding are compared with experimental data which have incorporation of proteins into membranes is the hydrophobic become available recently. The kinetics of protein incorpora- effect. However, a number of other effects may support or tion are discussed along similar lines by estimating the contri- counteract the hydrophobic effect. In general, the free energy butions of the individual effects to the activation free energy of protein incorporation includes four contributions which arise and enthalpy. from a change of (i) water structure, (ii) protein state, (iii) lipid state, and (iv) bonds between protein and water or lipid mol- Hydrophobic effect ecules. The change of water structure represents the hydrophobic The free energy gained from the hydrophobic effect upon in- effect which originates in the reduction of the mobility of water corporation of proteins into a lipid bilayer can be calculated in molecules surrounding the protein. The change of the protein two ways: (i) on the basis of the amino acid sequence and the state comprises the external translational and rotational degrees free energies of transfer of individual amino acid side chains of freedom which become immobilized upon incorporation of from water into the vapor phase (15) or into hydrocarbons (16); the protein and the internal degrees of freedom whose changes or (ii) from the change of the protein/water interfacial area and involve conformational changes and changes of internal bonds. a value for the free energy change per unit area (2). The second The change of the lipid state accounts for the reduction of the approach is used here. From studies of hydrocarbons and hy- mobility of the lipid molecules in a fluid membrane. This par- drophobic amino acids, the free energy per area was found to allels the reduction of the mobility of water molecules in the be 20-25 cal/(molFA2) (1 cal = 4.184 J) (2, 17). The interfacial hydrophobic effect and may therefore be called lipophobic ef- area is that area of a protein molecule that is accessible to water fect of proteins. The change of bonds at the protein surface molecules. It can be estimated by describing the protein as a concerns mainly polar interactions such as hydrogen bonds and sphere or cylinder and multiplying the corresponding smooth electrostatic interactions between polar amino acid residues and area by a factor of 1.7 to account for the unevenness of the pro- water molecules because the interaction energy between apolar tein surface (2). residues and water or lipid molecules is relatively small. Considering the simple case of a protein or protein segment The gain in free energy from the hydrophobic effect has been spanning the bilayer in the form of an a-helix, the helix is de- investigated thoroughly in the past (1-4). Estimates are also scribed as a cylinder of radius R.- 5 A and height h 30 A, available for the free energy arising from the formation or the thickness of the hydrophobic core of the bilayer. If the pro- breakage of hydrogen bonds and electrostatic bonds (3, 4) as tein also forms a helix in water, the change in effective inter- well as from the change of protein conformation (5, 6). The pro- facial area is 2irRoh1.7 1,600 A2. With a value of 22 cal/ (molA2) for the free energy per area, the free energy change The publication costs of this article were defrayed in part by page charge upon incorporation is AGw -35 kcal/mol of helix, as ob- payment. This article must therefore be hereby marked "advertise- tained by others (4). If the protein in water adopts an unfolded ment" in accordance with 18 U.S.C. §1734 solely to indicate this fact. conformation, the relevant area is that of a cylinder whose length 3691 Downloaded by guest on September 29, 2021 3692 Biophysics: jdhnig Proc. Natl. Acad. Sci. USA 80 (1983) is given by the number of amino acid residues, about 20, times mobilization is found to involve an energy change AGp 20 the length of one residue, 3.7 A, and whose radius is 3.2 A in kcal/mol. The concomitant enthalpy change AHp for the six order to yield the same volume as the a-helix. The change in degrees of freedom is -3RT or AHp- -2 kcal/mol. Hence, effective interfacial area then is 2,500 A2 leading to AGw = -55 the immobilization effect is also of predominantly entropic na- kcal/mol. ture like the hydrophobic effect. These values hold for com- Because the hydrophobic effect originates in the reduction plete immobilization of the protein in the membrane, which is of the mobility of water molecules, it is predominantly of en- not attained (at least not for a fluid membrane). One expects tropic nature. The enthalpy change is relatively small (1), less that only one translational and two rotational degrees of free- than a few kcal/mol, and, will be approximated by AHw 0. dom will be immobilized so that the above values for AGp and AHp are reduced by a factor of 1/2. Hydrogen bonds and conformational changes For this estimation, the immobilized degrees of freedom were treated simply as being lost. Actually, they are subject to the If hydrogen bonds between protein and water molecules are binding potential which still allows some relative motion. In a broken upon incorporation of the protein and not restored in more realistic approach one th ore may describe the im- the membrane, an energy of 5.8 kcal/mol of hydrogen bond mobilization of the translational degrees of freedom as the tran- is lost (18). To prevent this large loss of energy, protein mol- sition from a box of volume Vfree to a smaller one of volume ecules in the membrane adopt a conformation that allows the Vbound. The latter is given by the available membrane surface intramolecular formation of hydrogen bonds. This is optimal in area multiplied by a length 8z which measures the relative mo- an a-helical conformation. Hence, the hydrogen bonds are the tion between the incorporated protein and the membrane in cause for the frequently observed a-helical conformation of the direction of the membrane normal. The corresponding membrane-incorporated protein segments (4). This implies that change in free energy, assuming ideal gas behavior of the pro- hydrogen bonds do not contribute much to the free energy tein in the boxes, is AGt = NkT ln[Vfree/Vbound]. This immo- change of protein incorporation. bilization free energy is independent of the protein mass but Considering the final conformation of the protein in the depends on the lipid concentration. For a 0.1 mM lipid disc membrane as a-helical, the change in the internal degrees of persion, assuming a membrane surface area of 50 A2 per lipid freedom depends upon the protein conformation in water. If molecule and as an upper limit for the motion of the incor- the protein in water is also helical, the internal degrees of free- porated protein &z 1 A, one obtains AGt 8 kcal/mol.
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