The cooperative response of synaptotagmin I C2A. A hypothesis for a Ca2+-driven molecular hammer

In the current understanding of exocytosis at the nerve terminal, the C2 domain of synaptotagmin (C2A) is presumed to bind Ca2+ and the membrane in a stepwise fashion: cation then membrane as cation increases the affinity of protein for membrane. Fluorescence spectroscopy data were gathered over a variety of lipid and Ca2+ concentrations, enabling the rigorous application of microscopic binding models derived from partition functions to differentiate between Ca2+ and phosphatidylserine contributions to binding. The data presented here are in variance with previously published models, which were based on the Hill approximation. Rather, the data are consistent with two forms of cooperativity that modulate the responsiveness of C2A: in Ca2+ binding to a network of three cation sites and in interaction with the membrane surface. We suggest synaptotagmin I C2A is preassociated with the synaptic vesicle membrane or nerve terminal. In this state, upon Ca2+ influx the protein will bind the three Ca2+ ions immediately and with high cooperativity. Thus, membrane association creates a high-affinity Ca2+ switch that is the basis for the role of synaptotagmin I in Ca2+-regulated exocytosis. Based on this model, we discuss the implications of protein-induced phosphatidylserine demixing to the exocytotic process.     

Mechanism of the electric response of lipid bilayers to bitter substances.

In order to clarify by what mechanism the lipid bilayer membrane changes its potential under the stimulation of bitter substances, a microscopic model for the effects of the substances on the membrane is presented and studied theoretically. It is assumed that the substances are adsorbed on the membrane and change the partition coefficients of ions between the membrane and the stimulation solution, the dipole orientation in the polar head, and the diffusion constants of ions in the membrane. It is shown, based on the comparison of the calculated results with the experimental ones, that the response arises mainly from a change in the partition coefficients. Protons play an essential role in the membrane potential variation due to the change in their partition coefficients. The present model reproduces the following observed unique properties in the response of lipid bilayers to bitter substances, which cannot be accounted for by the usual channel model for the membrane potential: 1) the response of the membrane potential appears even under the condition that there is no ion gradient across the membrane, 2) the response remains even when the salt in the stimulating solution is replaced with the salt made of an impermeable cation, and 3) the direction of the polarization of the potential is not reversed, even when the ion gradient across the bilayer is reversed.     

Cerebrocrast promotes the cotransport of H+ and Cl- in rat liver mitochondria

Considering that cerebrocrast stimulates oligomycin-inhibited state 3 respiration simultaneously with mitochondrial transmembrane potential (Deltapsi) dissipation, the mechanism underlying the uncoupler activity of cerebrocrast was assessed by its ability to permeabilize the mitochondrial inner membrane to H(+) or to K(+) or to cotransport anions with H(+). The partition coefficient of cerebrocrast in mitochondrial membrane and its ability to act as a membrane-active compound disturbing membrane lipid organization were also investigated. Cerebrocrast induced no permeabilization of mitochondrial inner membrane to H(+) or K(+), but it was able to transport H(+) in association with Cl(-). Cerebrocrast showed a strong incorporation into the mitochondrial membrane, with a partition coefficient (Kp(m/w)) of 2.7(+/-0.1)x10(5). Cerebrocrast also reduced, in a concentration dependent manner, the phase transition temperature, the cooperative unit size, and the enthalpy associated with the phase transition temperature of DMPC membrane bilayers. It was concluded that the uncoupler activity of cerebrocrast is due to its ability to promote the cotransport of H(+) with Cl(-) through the rat liver mitochondrial inner membrane, and that this cerebrocrast mechanism of action may be potentiated by alterations of membrane lipid organization and membrane lateral heterogeneity.     

Phloretin-induced changes in ion transport across lipid bilayer membranes

Phloretin, the aglucone derivative of phlorizin, increases cation conductance and decreases anion conductance in lipid bilayer membranes. In this paper we present evidence that phloretin acts almost exclusively by altering the permeability of the membrane interior and not by modifying the partition of the permanent species between the membrane and the bulk aqueous phases. We base our conclusion on an analysis of the current responses to a senylborate, and the cation complex, peptide PV-K+. These results are consistent with the hypothesis that phloretin decreases the intrinsic positive internal membrane potential but does not modify to a great extent the potential energy minima at the membrane interfaces. Phloretin increases the conductance for the nonactin-K+ complex, but above 10(-5) M the steady- state nonactin-K+ voltage-current curve changes from superlinear to sublinear. These results imply that, above 10(-5) M phloretin, the nonactin-5+ transport across the membrane becomes interfacially limited.     

Cholesterol depletion-induced inhibition of stretch-activated channels is mediated via actin rearrangement

Cholesterol is a critical regulator of lipid bilayer dynamics and plasma membrane organization in eukaryotes. A variety of ion channels have been shown to be modulated by cellular cholesterol and partition into cholesterol-enriched membrane rafts. However, very little is known about functional role of membrane cholesterol in regulation of mechanically gated channels that are ubiquitously present in living cells. In our previous study, the effect of methyl-beta-cyclodextrin (MbCD), cholesterol-sequestering agent, on Ca²⁺-permeable stretch-activated cation channels (SACs) has been described. Here, cell-attached patch-clamp method was employed to search for the mechanisms of cholesterol-dependent regulation of SACs and to clarify functional contribution of lipid bilayer and submembranous cytoskeleton to channel gating. Cholesterol-depleting treatment with MbCD significantly decreased open probability of SACs whereas alpha-cyclodextrin had no effect. F-actin disassembly fully restored high level of SAC activity in cholesterol-depleted cells. Particularly, treatment with cytochalasin D or latrunculin B abrogated inhibitory effect of MbCD on stretch-activated currents. Single channel analysis and fluorescent imaging methods indicate that inhibition of SACs after cholesterol depletion is mediated via actin remodeling initiated by disruption of lipid rafts. Our data reveal a novel mechanism of channel regulation by membrane cholesterol and lipid rafts.     

The effects of long-chain alcohols on membrane lipids and the (Na+ + K+)-ATPase

The (Na⁺ + K⁺)-ATPase obtained from sheep kidney outer medulla is irreversibly denatured by long-chain aliphatic alcohols. The denaturation proceeds by causing a change in the structure of the membrane lipids rather than by binding directly to the protein. The alcohols decrease the ability of the membrane lipid bilayer to orient the spin label 3-(4′,4′-dimethyloxazolidinyl)-5α-androstan-17β-ol. For the low molecular weight alcohols the ability of the membrane to orient the label is completely lost while for alcohols with more than five carbons only partial loss of the orienting ability of the membrane occurs. The alcohol concentrations necessary to denature the enzyme correspond to the concentrations that produce the maximal change in the ability of the membrane to orient the label, and correlate well with the hydrophobicity of the alcohols as measured by their water-octanol partition coefficients.     

Action of calcium channel and beta-adrenergic blocking agents in bilayer lipid membranes

The action of beta-adrenergic blockers (propranolol, exprenolol, metoprolol, sotalol, atenolol, timolol) and calcium-channel blockers (verapamil, diltiazem) on the electrical properties and fluidity of bilayer lipid membranes (BLM and liposomes) has been investigated. When antibiotic ionophore substances were used as a probe, the electrical measurements showed that many of the drugs inhibited the cation transport across the membrane facilitated by the mobile carrier valinomycin, while having no significant effect on the cation transport through channels formed by gramicidin. The ability of the drugs to decrease the carrier-dependent membrane conductance was correlated to their partition into the lipid bilayer and the magnitude of transmembrane potential induced by them. In the TEMPO ESR spectral measurements, a number of beta-adrenergic and calcium blockers showed the fluidizing effect on liposomes composed of different lipids. The drug concentration required for a detectable change in TEMPO spectra parameter (f) was rather high (0.01 M verapamil), and the variation of pH from 6.5 to 3.0 did not affect the fluidizing effect of the drugs.     

Fluorescence probe partitioning between Lo/Ld phases in lipid membranes

Fluorescence microscopy imaging is an important technique for studying lipid membranes and is increasingly being used for examining lipid bilayer membranes, especially those showing macroscopic coexisting domains. Lipid phase coexistence is a phenomenon of potential biological significance. The identification of lipid membrane heterogeneity by fluorescence microscopy relies on membrane markers with well-defined partitioning behavior. While the partitioning of fluorophores between gel and liquid-disordered phases has been extensively characterized, the same is not true for coexisting liquid phases. We have used fluorescence microscopy imaging to examine a large variety of lipid membrane markers for their liquid phase partitioning in membranes with various lipid compositions. Most fluorescent lipid analogs are found to partition strongly into the liquid-disordered (L_d) phase. In contrast, some fluorescent polycyclic aromatic hydrocarbons with a flat ring system were found to partition equally, but others partition preferentially into liquid-ordered (L_o) phases. We have found these fluorescent markers effective for identification of coexisting macroscopic membrane phases in ternary lipid systems composed of phospholipids and cholesterol.     

Partitioning and membrane disordering effects of dopamine antagonists: influence of lipid peroxidation, temperature, and drug concentration.

The effect of four dopamine antagonists (spiperone, haloperidol, pimozide, and domperidone) on the lipid order of caudate nucleus microsomal membranes and on liposomes from membrane lipid extracts was evaluated and related to the partition coefficients (Kp) of the drugs. Lipid membrane order was determined by fluorescence polarization using 1,6-diphenyl-1,3,5-hexatriene (DPH) as a probe of the membrane core and 1-[4-(trimethylammonium)phenyl]-6-phenyl-1,3,5-hexatriene (TMA-DPH) as a probe of the membrane surface. Dopamine antagonists decrease the fluorescence polarization of both probes, indicating that they disorder the membrane lipids at different depths. Pimozide and domperidone, the drugs with higher Kp values, are more effective at decreasing the polarization of DPH, a probe of the membrane core, than that of TMA-DPH. In contrast, spiperone and haloperidol, which have lower values for Kp, induce more significant decreases in TMA-DPH depolarization, a probe of the membrane surface. These findings indicate that higher partition coefficients of the drugs are directly correlated with an increase of fluidity in the hydrophobic core of brain membranes. Ascorbate/Fe(2+)-induced membrane lipid peroxidation increases membrane order. Membrane lipid peroxidation decreases the partition coefficients of the dopamine antagonists tested. Increasing temperature (4-37 degrees C) decreases membrane order, but temperature effect is less evident after lipid peroxidation. The disordering effect of dopamine antagonists increases with increasing drug concentrations (1-15 microM), a maximum being observed at 10 microM. However, this effect is also less evident after membrane lipid peroxidation. We can conclude that dopamine antagonists and membrane lipid peroxidation affect membrane lipid order and that the action of these drugs is dependent on initial bilayer fluidity. Membrane lipid peroxidation increases membrane order while dopamine antagonists show a disordering effect of membrane phospholipids. This disordering effect can indirectly influence the activity of membrane proteins and it is one of the mechanisms through which membrane function can be altered by these drugs.     

Interactions of hexachlorocyclohexanes with the (Ca2+ + Mg2+)-ATPase from sarcoplasmic reticulum

Hexachlorocyclohexanes have been shown to inhibit the (Ca2+ + Mg2+)-ATPase of muscle sarcoplasmic reticulum reconstituted into bilayers of dioleoylphosphatidylcholine. However, for the ATPase reconstituted into bilayers of dimyristoleoylphosphatidylcholine, a pattern of activation at low concentration followed by inhibition at higher concentration is seen for hexachlorocyclohexanes and alkanes such as decane and hexadecane. The ATPase in sarcoplasmic reticulum vesicles is also inhibited by the hexachlorocyclohexanes. The effects of hexachlorocyclohexanes on activity are largely independent of concentrations of Ca2+ and ATP. Inhibition is more marked at lower temperatures. The hexachlorocyclohexanes quench the tryptophan fluorescence of the ATPase, and the quenching can be used to obtain partition coefficients into the membrane system. As for simple lipid bilayers, partition exhibits a negative temperature coefficient. Binding is related to effects on ATPase activity.     

Allosterism in membrane binding: a common motif of the annexins?

Annexins are a family of proteins generally described as Ca(2+)-dependent for phospholipid binding. Yet, annexins have a wide variety of binding behaviors and conformational states, some of which are lipid-dependent and Ca(2+)-independent. We present a model that captures the cation and phospholipid binding behavior of the highly conserved core of the annexins. Experimental data for annexins A4 and A5, which have short N-termini, were globally modeled to gain an understanding of how the lipid-binding affinity of the conserved protein core is modulated. Analysis of the binding behavior was achieved through use of the lanthanide Tb(3+) as a Ca(2+) analogue. Binding isotherms were determined experimentally from the quenching of the intrinsic fluorescence of annexins A4 and A5 by Tb(3+) in the presence or absence of membranes. In the presence of lipid, the affinity of annexin for cation increases, and the binding isotherms change from hyperbolic to weakly sigmoidal. This behavior was modeled by isotherms derived from microscopic binding partition functions. The change from hyperbolic to sigmoidal binding occurs because of an allosteric transition from the annexin solution state to its membrane-associated state. Protein binding to lipid bilayers renders cation binding by annexins cooperative. The two annexin states denote two affinities of the protein for cation, one in the absence and another in the presence of membrane. In the framework of this model, we discuss membrane binding as well as the influence of the N-terminus in modifying the annexin cation-binding affinity by changing the probability of the protein to undergo the postulated two-state transition.     

Amantadine partition and localization in phospholipid membrane: a solution NMR study

Quantification of membrane partition potential of drug compounds is of great pharmaceutical interest. Here, a novel approach combining liquid-state NMR diffusion measurements and fast-tumbling lipid/detergent bicelles is used to measure accurately the partition coefficient K(p) of amantadine in phospholipid bilayers. Amantadine is found to have a strong membrane partition potential, with K(p) of 27.6 in DMPC and 37.8 in POPC lipids. Electrostatic interaction also plays a major role in the drug's affinity towards biological membrane as introduction of negatively charged POPG dramatically increases its K(p). Saturation transfer difference experiments in small bicelles indicate that amantadine localizes near the negatively charged phosphate group and the hydrocarbon chain of bilayer lipid. The approach undertaken in this study is generally applicable for characterizing interactions between small molecules and phospholipid membranes.     

Relationship of alcohol-induced changes in Mg2+-ATPase activity of rabbit intestinal brush border membrane with changes in fluidity of its lipid bilayer

We examined the effects of seven n-alkyl alcohols (from n-butyl to n-undecyl alcohol), isoamyl alcohol and benzyl alcohol on the activity of membrane enzyme Mg²⁺-ATPase of the rabbit small intestinal brush border membrane. Their relationships with the changes in the fluidity of the membrane lipid bilayer were examined through studies on the fluorescence anisotropies of diphenylhexatriene (DPH) and its ionic derivatives. Good linear correlations were found both between the partition coefficients of the alcohols and their concentrations causing similar decreases in the activity of Mg²⁺-ATPase and between their partition coefficients and the alcohol-induced changes in fluorescence anisotropies. Within the concentration range of the alcohols tested, including isoamyl alcohol and benzyl alcohol, the decreases in activity of the membrane enzyme Mg²⁺-ATPase clearly corresponded with the decreases in fluorescence anisotropy of DPH, which is thought to be located within the hydrophobic core of the membrane. From these findings, one possible explanation is that inhibition of this enzyme by the alcohols is due to perturbation of the lipid bilayer of the brush border membrane.The authors thank M. Takano, PhD and Y. Tomita, PhD, Department of Pharmacy, University Hospital of Kyoto University, for instruction in preparation of the brush border membrane vesicles. This work was supported in part by grants from the Japanese Ministry of Education, Science and Culture (05671795 and 06304044) and Takeda Science Foundation.     

Reorganization of lipid domain distribution in giant unilamellar vesicles upon immobilization with different membrane tethers

Characterization of phase coexistence in biologically relevant lipid mixtures is often carried out through confocal microscopy of giant unilamellar lipid vesicles (GUVs), loaded with fluorescent membrane probes. This last analysis is generally limited to the vesicle hemisphere further away from the coverslip, in order to avoid artifacts induced by the interaction with the solid surface, and immobilization of vesicles is in many cases required in order to carry out intensity, lifetime or single-molecule based microscopy. This is generally achieved through the use of membrane tethers adhering to a coverslip surface. Here, we aimed to determine whether GUV immobilization through membrane tethers induces changes in lipid domain distribution within liposomes displaying coexistence of lipid lamellar phases. Confocal imaging and a F?rster resonance energy transfer (FRET) methodology showed that biotinylated phospholipids present significantly different membrane phase partition behavior upon protein binding, depending on the presence or absence of a linker between the lipid headgroup and the biotinyl moiety. Membrane phases enriched in a membrane tether displayed in some cases a dramatically increased affinity for the immobilization surface, effectively driving sorting of lipid domains to the adherent membrane area, and in some cases complete sequestering of a lipid phase to the interaction surface was observed. On the light of these results, we conclude that tethering of lipid membranes to protein surfaces has the potential to drastically reorganize the distribution of lipid domains, and this reorganization is solely dictated by the partition properties of the protein-tether complex.     

Fluorescence probe partitioning between Lo/Ld phases in lipid membranes

Fluorescence microscopy imaging is an important technique for studying lipid membranes and is increasingly being used for examining lipid bilayer membranes, especially those showing macroscopic coexisting domains. Lipid phase coexistence is a phenomenon of potential biological significance. The identification of lipid membrane heterogeneity by fluorescence microscopy relies on membrane markers with well-defined partitioning behavior. While the partitioning of fluorophores between gel and liquid-disordered phases has been extensively characterized, the same is not true for coexisting liquid phases. We have used fluorescence microscopy imaging to examine a large variety of lipid membrane markers for their liquid phase partitioning in membranes with various lipid compositions. Most fluorescent lipid analogs are found to partition strongly into the liquid-disordered (L(d)) phase. In contrast, some fluorescent polycyclic aromatic hydrocarbons with a flat ring system were found to partition equally, but others partition preferentially into liquid-ordered (L(o)) phases. We have found these fluorescent markers effective for identification of coexisting macroscopic membrane phases in ternary lipid systems composed of phospholipids and cholesterol.     

Dynamic quenchers in fluorescently labeled membranes. Theory for quenching in a three-phase system.

The theory for quenching of fluorescently labeled membranes by dynamic quenchers is described for a three-phase system: a fluorescently labeled membrane, a nonlabeled membrane, and an aqueous phase. Two different experimental protocols are possible to determine quenching parameters. Using the first protocol, partition coefficients and bimolecular quenching constants were determined for a hydrophobic quencher in carbazole-labeled membranes in the presence of an unlabeled reference membrane. These parameters determined for 1,1-dichloro-2,2-bis(p-chlorophenyl)ethylene (DDE) using this three-phase analysis were in good agreement with values determined by a two-phase analysis without the reference lipid. Hence, the theory was verified. In the second protocol, the quencher partition coefficient was determined for unlabeled membranes in the presence of a carbazole-labeled reference membrane. Partition coefficients for DDE determined by this method were the same as partition coefficients determined for carbazole-labeled membranes using the two-phase analysis. The greater ease in determining partition coefficients and bimolecular quenching constants by the three-phase analysis and, in particular, the ability to determine the partition coefficient in unlabeled membranes make the three-phase analysis especially useful. This method was used to study the effect varying the membrane lipid composition has on the partition coefficient. The data indicate that partition coefficients of DDE in fluid membranes are not dramatically dependent upon polar head group composition, fatty acid composition, or cholesterol content. However, partitioning into gel-phase lipids is at least 100-fold less than fluid-phase lipids.     

Statistical thermodynamic analysis of peptide and protein insertion into lipid membranes.

A statistical thermodynamic approach is used to analyze the various contributions to the free energy change associated with the insertion of proteins and protein fragments into lipid bilayers. The partition coefficient that determines the equilibrium distribution of proteins between the membrane and the solution is expressed as the ratio between the partition functions of the protein in the two phases. It is shown that when all of the relevant degrees of freedom (i.e., those that change their character upon insertion into the membrane) can be treated classically, the partition coefficient is fully determined by the ratio of the configurational integrals and thus does not involve any mass-dependent factors, a conclusion that is also valid for related processes such as protein adsorption on a membrane surface or substrate binding to proteins. The partition coefficient, and hence the transfer free energy, depend only on the potential energy of the protein in the membrane. Expressing this potential as a sum of a "static" term, corresponding to the equilibrium (minimal free energy) configuration of the protein in the membrane, and a "dynamical" term representing fluctuations around the equilibrium configuration, we show that the static term contains the "solvation" and "lipid perturbation" contributions to the transfer free energy. The dynamical term is responsible for the "immobilization" free energy, reflecting the loss of translational and rotational entropy of the protein upon incorporation into the membrane. Based on a recent molecular theory of lipid-protein interactions, the lipid perturbation and immobilization contributions are then expressed in terms of the elastic deformation free energy resulting from the perturbation of the lipid environment by the foreign (protein) inclusion. The model is formulated for cylindrically shaped proteins, and numerical estimates are given for the insertion of an alpha-helical peptide into a lipid bilayer. The immobilization free energy is shown to be considerably smaller than in previous estimates of this quantity, and the origin of the difference is discussed in detail.     

Interaction of Zn2+ with phospholipid membranes

To characterize the specificity of zinc binding to phospholipid membranes in terms of headgroup structure, hydration and phase behavior we studied the zwitterionic lipid 1-palmitoyl-2-oleoyl-phosphatidylcholine as a function of hydration at 30 degreesC in the presence and absence of ZnCl2. Zinc forms a 2:1-1:1 complex with the lipid, and in particular with the negatively charged phosphate groups. Zn2(+)-bridges between neighboring lipid molecules stabilize the gel phase of the lipid relative to the liquid-crystalline state. Upon Zn2+ binding the C-O-P-O-C- backbone of the lipid headgroup changes from a gauche/gauche into the trans/trans conformation and it loses roughly 50% of the hydration shell. The ability of the Zn2(+)-bound phosphate groups to take up water is distinctly reduced, meaning that the headgroups have become less hydrophilic. The energetic cost (on the scale of Gibbs free energy) for completely dehydrating the lipid headgroups is decreased by approximately 10 kJ/mole in the presence of Zn2+. The interaction of phospholipid headgroups with Zn2+ is conveniently described by a hydrated zinc-phosphate complex the key energy contribution of which is more covalent than electrostatic in nature. Dehydration of phospholipid headgroups due to complexation with zinc cations is suggested to increase fusogenic potency of lipid membranes. Zinc appears to be one of the most potent divalent cation in inducing membrane fusion.     

Effect of phosphatidylserine on unitary conductance and Ba2+ block of the BK Ca2+-activated K+ channel: re-examination of the surface charge hypothesis

Incorporation of BK Ca2+-activated K+ channels into planar bilayers composed of negatively charged phospholipids such as phosphatidylserine (PS) or phosphatidylinositol (PI) results in a large enhancement of unitary conductance (gch) in comparison to BK channels in bilayers formed from the neutral zwitterionic lipid, phospatidylethanolamine (PE). Enhancement of gch by PS or PI is inversely dependent on KCl concentration, decreasing from 70% at 10 mM KCl to 8% at 1,000 mM KCl. This effect was explained previously by a surface charge hypothesis (Moczydlowski, E., O. Alvarez, C. Vergara, and R. Latorre. 1985. J. Membr. Biol. 83:273-282), which attributed the conductance enhancement to an increase in local K+ concentration near the entryways of the channel. To test this hypothesis, we measured the kinetics of block by external and internal Ba2+, a divalent cation that is expected to respond strongly to changes in surface electrostatics. We observed little or no effect of PS on discrete blocking kinetics by external and internal Ba2+ at 100 mM KCl and only a small enhancement of discrete and fast block by external Ba2+ in PS-containing membranes at 20 mM KCl. Model calculations of effective surface potential sensed by the K+ conduction and Ba2+-blocking reactions using the Gouy-Chapman-Stern theory of lipid surface charge do not lend support to a simple electrostatic mechanism that predicts valence-dependent increase of local cation concentration. The results imply that the conduction pore of the BK channel is electrostatically insulated from the lipid surface, presumably by a lateral distance of separation (>20 A) from the lipid head groups. The lack of effect of PS on apparent association and dissociation rates of Ba2+ suggest that lipid modulation of K+ conductance is preferentially coupled through conformational changes of the selectivity filter region that determine the high K+ flux rate of this channel relative to other cations. We discuss possible mechanisms for the effect of anionic lipids in the context of specific molecular interactions of phospholipids documented for the KcsA bacterial potassium channel and general membrane physical properties proposed to regulate membrane protein conformation via energetics of bilayer stress.     

Liposomes as carriers of poorly water-soluble substrates: linear modelling of membrane systems with catalytic or binding sites of different facedness. Significance of experimental membrane partition coefficients and of kinetic and equilibrium parameters.

1. A multiphasic modelling approach to systems containing membrane-bound receptors or catalytic sites and a liposomal preparation as a substrate carrier is described. Kinetic expressions are derived for a single-substrate enzymic reaction operating at constant liposome concentration or at a fixed substrate/liposome concentration ratio. 2. The assumption that accumulation of exchangeable components into the phospholipid bilayers can be described by linear bulk-phase partition leads to simple relationships between the initial reaction rate and (a) two kinetic coefficients (V and K'm), (b) the partition coefficients of the solutes for the lipid compartments of the membrane (Pms) and liposomal preparations (P1s) and (c) the total concentrations of substrate, membrane lipid and liposomal lipid. K'm is called the effective Michaelis constant. 3. For correct estimation of the coefficients V, K', Pms and P1s extrapolation to zero lipid concentration is required. 4. The distinction is introduced between hydrophilic and hydrophobic aqueous-faced sites, lipid-faced sites and mixed sites, i.e. sites overlapping an aqueous and a lipid region. For hydrophilic aqueous-faced sites K'm is equal to the true Km and for the other types of site to Km/Ps. For lipid-faced and for mixed sites Ps corresponds to the membrane partition coefficient Pms. For binding of homologous compounds to a hydrophobic aqueous-faced binding pocket Ps is the incremental site partition coefficient Pbss, which takes into account the energetic contribution to the binding process due to the hydrophobic tail of the ligands. 5. K'm accounts for any effects due to the facedness and nature of the enzymic sites. The dependence of the systems on the size of the lipidic partition compartment(s) is expressed exclusively by a distribution function F.6. When enzyme assays are performed with a series of chemically different substrates containing the same catalytically sensitive group, independence of K'm from partition indicates a hydrophilic aqueous-faced binding site. For the low-molecular-mass members of the homologous series a linear increase in -log (K'm) with the logarithm of the partition coefficient will be observed with any of the other site types considered 7. Equilibrium relationships for binding of a ligand to a membrane-bound receptor are also derived. 8. The significance of experimental membrane partition coefficients is discussed.