Modulation of physiological and pathological activities of lysozyme by biological membranes

The molecular details of interactions between lipid membranes and lysozyme (Lz), a small polycationic protein with a wide range of biological activities, have long been the focus of numerous studies. The biological consequences of this process are considered to embrace at least two aspects: i) correlation between antimicrobial and membranotropic properties of this protein, and ii) lipid-mediated Lz amyloidogenesis. The mechanisms underlying the lipid-assisted protein fibrillogenesis and membrane disruption exerted by Lz in bacterial cells are believed to be similar. The present investigation was undertaken to gain further insight into Lz-lipid interactions and explore the routes by which Lz exerts its antimicrobial and amyloidogenic actions. Binding and Förster resonance energy transfer studies revealed that upon increasing the content of anionic lipids in lipid vesicles, Lz forms aggregates in a membrane environment. Total internal reflection fluorescence microscopy and pyrene excimerization reaction were employed to study the effect of Lz on the structural and dynamic properties of lipid bilayers. It was found that Lz induces lipid demixing and reduction of bilayer free volume, the magnitude of this effect being much more pronounced for oligomeric protein. Electronic Supplementary Material Supplementary material is available for this article at 10.2478/s11658-012-0015-6 and is accessible for authorized users.

where K a is the association constant, F is the concentration of the protein free in solution, γ is the activity coefficient of adsorbed ligand, Φ is the fraction of surface area occupied by adsorbed protein, a L nB / = Φ , B is the concentration of bound protein, n is the number of lipid molecules covered by a single protein, L a is the concentration of accessible lipids related to total lipid concentration (L) as L a = 0.5L, and ε is a shape parameter (for disc-like ligand ε =1).
The equilibrium binding constant can be represented as consisting of electrostatic (K el ) and intrinsic or non-electrostatic (K o ) terms: (K a =K el K o ). The electrostatic component of the binding constant, dependent on electrostatic surface potential, environmental conditions (pH, ionic strength), and degree of surface coverage by a protein, is given by [2]: where T is the temperature, k B is Boltzmann's constant, and el F Δ is the total gain in electrostatic free energy, being a function of the number of adsorbed protein molecules, where s el F and P el F are the electrostatic free energies of a membrane surface and a protein, respectively. The electrostatic free energy of a spherical protein molecule with effective charge +ze and uniform charge distribution can be written as [3]: where r o is the protein radius, and κ is the reciprocal Debye length where S L is the mean area per lipid molecule, , f PC and f A are the mole fractions of PC and acidic phospholipids (PG, PS or CL), S PC and S A are mean areas per PC and acidic phospholipid headgroups, respectively (taken as 0.65 nm 2 for PC, PG and PS, and 1.2 nm 2 for CL), and σ is the surface charge density given by: whereα is the degree of anionic phospholipid ionization, which in the case of one-step deprotonation can be written as: Numerical solution of the set of Eqs. S1-S10 yields theoretical isotherms that can be fitted to experimental binding curves. Two-state model for the adsorption of a large self-associating ligand. The model is based on the assumption that the adsorbed protein exists in only two states, as a monomer and z a -mer. This model can be represented by [1]: are fractions of surface area occupied by monomers and z a -mers, respectively, Φ Φ Φ = + 1 z , q = R z /R 1 , R z , and R 1 are the radii of the circles representing z a -mer and monomer, and z K 1 is the equilibrium constant for the formation of z a -mer. For the case of conserved area upon self-association Cluster model. In contrast to the two-state model, the cluster model considers highly heterogeneous populations of aggregated protein (protein clusters of arbitrary size and shape). The activity coefficients of individual adsorbate species can be derived from scaled particle theory of a mixture of hard convex particles in two dimensions [5]: where i ρ , i a , and i s are the surface number density, area, and circumference of the footprint of species i, respectively. The equilibrium constants for monomer association with the surface (K 1 ) and formation of species i (K ci ) are defined as: where m i is the degree of oligomerization of species i. The equilibrium constant K ci is considered as a function of the number of intermolecular contacts in cluster species i (N ci ). In particular, when all cluster footprints are represented by circles and m i = i for species i the following empirical relationship holds (Minton, 2000): Multimodal adsorption model. This model allows for the possibility of multiple interconvertible adsorbate conformations or protein association with heterogeneous surface, which contains binding sites differing in their size and free energy of adsorption. The activity coefficient of the protein adsorbed in a particular conformation i or associated with the site of i-th type is given by Eq. S15. More specifically, if the membrane in question contains two types of protein binding centers (i.e. there exist two populations of the adsorbed protein differing in free energy of adsorption) and adsorbed protein has a circular footprint, Eqs. S15 and S16 can be rewritten as [6]: and the adsorption isotherm can be described by the following set of equations:

FRET models
General theory of FRET in two-dimensions. In the absence of acceptors fluorescence decay of the donor is described by: In the case of randomly diffusing donor and acceptors donor fluorescence decay can be written as: Here c R ≈ [7]. To estimate s A c , the concentration of bound acceptor was calculated within the framework of the above mentioned scaled particle theory based adsorption models described in detail elsewhere.
FRET in protein oligomers. FRET data for oligomeric complex were analyzed according to the simulation procedure developed by Li et al. [8] Lz aggregates are modeled as symmetric ring-shaped structures consisting of n subunits (monomers). Each subunit (indexed by j ) is assumed to be labeled with either donor or acceptor. Protein oligomers are supposed to be in thermodynamic equilibrium with monomeric species. Denoting the fraction of monomeric donors that take part in aggregation as X , the general expression for donor fluorescence intensity decay is given by: where D k is donor decay rate in the absence of acceptor, D P and A P are the molar fraction of donor and acceptor, respectively, j k is energy transfer rate from donor to acceptor on subunit j , determined as: Here j r is the distance between donor and acceptor on subunit j :  is apparent radius of protein oligomer.
Steady-state fluorescence intensity can be written as: and corresponding transfer efficiency is given by: The extent of pyrene dimerization is determined by the probe concentration and environment polarity. Although pyrene molecules tend to aggregate in the aqueous phase, no aggregates were observed in the suspension of PC liposomes [13]. Pyrene dimerization in PC/CL liposomes seems to be hardly probable because: 1) dimer formation should manifest itself in rather strong hypochromism and monomer fluorescence decrease. However, in our experiments no significant changes in the intensity of pyrene fluorescence were observed at increasing CL content from 0 to 40 mol % (data not shown); 2) according to our estimates, the equilibrium constant of dimer formation is ca. 32 M -1 , the value being an order of magnitude higher than that derived by Blackwell [10]  2 + = , we found that in our systems c D was about 3-4% of C PL , suggesting that the contribution of static excimers to the total fluorescence is insignificant. In this regard it is also noteworthy that no ground state dimers or other type of molecular aggregates were detected with up to 4 mol % of pyrene incorporated into PC liposomes [14]. Based on these arguments, we concluded that under the experimental conditions employed here pyrene excimerization proceeds mainly via diffusion-controlled rather than a static mechanism. Since diffusion in membranes is commonly described in terms of the free volume model, decrease in E/M ratio induced by Lz oligomers was interpreted as arising from reduced free volume of the lipid bilayer.