Study of curcumin behavior in two different lipid bilayer models of liposomal curcumin using molecular dynamics simulation

Liposomal formulation of curcumin is an important therapeutic agent for the treatment of various cancers. Despite extensive studies on the biological effects of this formulation in cancer treatment, much remains unknown about curcumin–liposome interactions. Understanding how different lipid bilayers respond to curcumin molecule may help us to design more effective liposomal curcumin. Here, we used molecular dynamics simulation method to investigate the behavior of curcumin in two lipid bilayers commonly used in preparation of liposomal curcumin, namely dipalmitoylphosphatidylcholine (DPPC) and dimyristoylphosphatidylglycerol (DMPG). First, the free energy barriers for translocation of one curcumin molecule from water to the lipid bilayer were determined by using the potential of mean force (PMF). The computed free energy profile exhibits a global minimum at the solvent–headgroup interface (LH region) for both lipid membranes. We also evaluated the free energy difference between the equilibrium position of curcumin in the lipid bilayer and bulk water as the excess chemical potential. Our results show that curcumin has the higher affinity in DMPG compared to DPPC lipid bilayer (?8.39 vs. ?1.69 k_BT) and this is related to more hydrogen bond possibility for curcumin in DMPG lipid membrane. Next, using an unconstrained molecular dynamic simulation with curcumin initially positioned at the center of lipid bilayer, we studied various properties of each lipid bilayer system in the presence of curcumin molecule that was in full agreement with PMF and experimental data. The results of these simulation studies suggest that membrane composition could have a large effect on interaction of curcumin–lipid bilayer.     

Protein shape change has a major effect on the gating energy of a mechanosensitive channel

Increasing experimental evidence has shown that membrane protein functionality depends on molecular composition of cell membranes. However, the origin of this dependence is not fully understood. It is reasonable to assume that specific lipid-protein interactions are important, yet more generic effects due to mechanical properties of lipid bilayers likely play a significant role too. Previously it has been demonstrated using models for elastic properties of membranes and lateral pressure profiles of lipid bilayers that the mechanical properties of a lipid bilayer can contribute as much as ∼10 k_BT to the free energy difference associated with a change in protein conformational state. Here, we extend those previous approaches to a more realistic model for a large mechanosensitive channel (MscL). We use molecular dynamics together with the MARTINI model to simulate the open and closed states of MscL embedded in a DOPC bilayer. We introduce a procedure to calculate the mechanical energy change in the channel gating using a three-dimensional pressure distribution inside a membrane, computed from the molecular dynamics simulations. We decompose the mechanical energy to terms associated with area dilation and shape contribution. Our results highlight that the lateral pressure profile of a lipid bilayer together with the shape change in gating can induce a contribution of ∼30 k_BT on the gating energy of MscL. This contribution arises largely from the interfacial tension between hydrophobic and hydrophilic regions in a lipid bilayer.     

Calculation of free energy barriers to the fusion of small vesicles

The fusion of small vesicles, either with a planar bilayer or with one another, is studied using a microscopic model in which the bilayers are composed of hexagonal- and lamellar-forming amphiphiles. The free energy of the system is obtained within the self-consistent field approximation. We find that the free energy barrier to form the initial stalk is hardly affected by the radius of the vesicle, but that the barrier to expand the hemifusion diaphragm and form a fusion pore decreases rapidly as the radius decreases. As a consequence, once the initial barrier to stalk formation is overcome, one which we estimate at 13 k_BT for biological membranes, fusion involving small vesicles should proceed with little or no further input of energy.     

Free energy analysis of membrane pore formation process in the presence of multiple melittin peptides

Understanding the molecular mechanism underlying pore formation in lipid membranes by antimicrobial peptides is of great importance in biological sciences as well as in drug design applications. Melittin has been widely studied as a pore forming peptide, though the molecular mechanism for pore formation is still illusive. We examined the free energy barrier for the creation of a pore in lipid membranes with and without multiple melittin peptides. It was found that six melittin peptides significantly stabilized a pore, though a small barrier (a few k_BT) for the formation still existed. With five melittin peptides or fewer, the pore formation barrier was much higher, though the established pore was in a local energy minimum. Although seven melittins effectively reduced the free energy barrier, a single melittin peptide left the pore after a long time MD simulation probably because of the overcrowded environment around the bilayer pore. Thus, it is highly selective for the number of melittin peptides to stabilize the membrane pore, as was also suggested by the line tension evaluations. The free energy cost required to insert a single melittin into the membrane is too high to explain the one-by-one insertion mechanism for pore formation, which also supports the collective melittin mechanism for pore formation.     

Effect of cholesterol on bilayer location of the class A peptide Ac-18A-NH<Subscript>2</Subscript> as revealed by fluorescence resonance energy transfer

An amphipathic class A peptide, Ac-18A-NH₂, has been employed in modeling the -helical lipid-binding site of apolipoprotein A-I (apoA-I). To gain insight into the nature of protein–lipid interactions responsible for the ability of apoA-I to promote the efflux of intracellular cholesterol, the peptide disposition in model membranes composed of phosphatidylcholine (PC) and its mixture with cholesterol (Chol) has been characterized. By examining resonance energy transfer between the peptide Trp as a donor and anthrylvinyl-labeled PC as an acceptor it was found that Chol inclusion is conducive to shallower bilayer location of the Ac-18A-NH₂ -helix. The limits for the Trp distance from the membrane center were estimated to be 1.5–1.7 nm (PC) and 1.9–2.1 nm (PC:Chol), indicating that in the PC bilayer the Trp resides at the level of the glycerol backbone and carbonyl groups while the region of the phosphocholine moieties is preferable for Trp location in the PC:Chol bilayer. These findings suggest that Chol can modulate the interactions between apoA-I and membrane lipids via reducing the depth of -helix bilayer penetration.Abbreviations apoA-I apolipoprotein A-I - AV-PC anthrylvinyl-labeled phosphatidylcholine - Chol cholesterol - HDL high-density lipoproteins - LUV large unilamellar vesicles - PC phosphatidylcholine - RET fluorescence resonance energy transfer     

Conformational transitions of a dipeptide in water: Effects of imposed pathways using umbrella sampling techniques

The free energy difference between two states of a molecular system separated by an energy barrier can generally be computed using the technique of umbrella sampling along a chosen reaction coordinate or pathway. The effect of a particular choice of pathway upon the obtained free energy difference is investigated by molecular dynamics simulation of a model system consisting of a glycine dipeptide in aqueous solution. Two different reaction coordinates connecting the so-called C₅ and C₇ conformations, one involving intramolecular hydrogen bonds and the other involving the peptide ?, ψ angles, are considered. The Gibbs free energy differences ΔG(C₅ – C₇) are small in both cases, 1.5 ± 1 kJ mol^?1 and 2.2 ± 1 kJ mol ^?1, respectively. The two different reaction coordinates yield free energy differences that are identical to within their statistical error. It is found that the exchange of solute–solute, solute–water, and water–water hydrogen bonds involves free energy changes of less than k_BT, which points at the existence of a multitutde of low free energy pathways connecting the C₅ and C₇ dipeptide conformations. © 1994 John Wiley & Sons, Inc.     

Solid-state NMR study of membrane interactions of the pore-forming cytolysin, equinatoxin II

Equinatoxin II (EqtII) is a pore-forming protein from Actinia equina that lyses red blood cell and model membranes. Lysis is dependent on the presence of sphingomyelin (SM) and is greatest for vesicles composed of equimolar SM and phosphatidylcholine (PC). Since SM and cholesterol (Chol) interact strongly, forming domains or “rafts” in PC membranes, ³¹P and ²H solid-state NMR were used to investigate changes in the lipid order and bilayer morphology of multilamellar vesicles comprised of different ratios of dimyristoylphosphatidylcholine (DMPC), SM and Chol following addition of EqtII. The toxin affects the phase transition temperature of the lipid acyl chains, causes formation of small vesicle type structures with increasing temperature, and changes the T₂ relaxation time of the phospholipid headgroup, with a tendency to order the liquid disordered phases and disorder the more ordered lipid phases. The solid-state NMR results indicate that Chol stabilizes the DMPC bilayer in the presence of EqtII but leads to greater disruption when SM is in the bilayer. This supports the proposal that EqtII is more lytic when both SM and Chol are present as a consequence of the formation of domain boundaries between liquid ordered and disordered phases in lipid bilayers leading to membrane disruption.     

The Fusion of Membranes and Vesicles: Pathway and Energy Barriers from Dissipative Particle Dynamics

The fusion of lipid bilayers is studied with dissipative particle dynamics simulations. First, to achieve control over membrane properties, the effects of individual simulation parameters are studied and optimized. Then, a large number of fusion events for a vesicle and a planar bilayer are simulated using the optimized parameter set. In the observed fusion pathway, configurations of individual lipids play an important role. Fusion starts with individual lipids assuming a splayed tail configuration with one tail inserted in each membrane. To determine the corresponding energy barrier, we measure the average work for interbilayer flips of a lipid tail, i.e., the average work to displace one lipid tail from one bilayer to the other. This energy barrier is found to depend strongly on a certain dissipative particle dynamics parameter, and, thus, can be adjusted in the simulations. Overall, three subprocesses have been identified in the fusion pathway. Their energy barriers are estimated to lie in the range 8-15 k_BT. The fusion probability is found to possess a maximum at intermediate tension values. As one decreases the tension, the fusion probability seems to vanish before the tensionless membrane state is attained. This would imply that the tension has to exceed a certain threshold value to induce fusion.     

Electrical noise from lipid bilayer membranes in the presence of hydrophobic ions

Summary In the presence of the hydrophobic ion dipicrylamine, lipid bilayer membranes exhibit a characteristic type of noise spectrum which is different from other forms of noise described so far. The spectral density of current noise measured at zero voltage increases in proportion to the square of frequency at low frequencies and becomes constant at high frequencies. The observed form of the noise spectrum can be interpreted on the basis of a transport model for hydrophobic ions in which it is assumed that the ions are adsorbed in potential-energy minima at either membrane surface and are able to cross the central energy barrier by thermal activation. Accordingly, current-noise results from random fluctuations in the number of ions jumping over the barrier from right to left and from left to right. On the basis of this model the rate constantk _i for the translocation of the hydrophobic ion across the barrier, as well as the mean surface concentrationN _t of adsorbed ions may be caluculated from the observed spectral intensity of current noise. The values ofk _i obtained in this way closely agree with the results of previous relaxation experiments. A similar, although less quantitative, agreement is also found for the surface concentrationN _t .     

Protein rotation and chromophore orientation in reconstituted bacteriorhodopsin vesicles

Bacteriorhodopsin has been reconstituted into lipid vesicles with dipalmitoyl and dimyristoyls phosphatidylcholine. Circular dichroism (CD) measurements show that the proteins are in a monomeric state above the main lipid phase transition temperature (T_c), 41 and 23°C for dipalmitoyl and dimyristoyl phosphatidylcholine, respectively. Below T_c, the CD spectrum is the same as that found for the purple membrane. The latter result implies that the orientation of the chromophore at these temperatures is most likely the same as in the purple membrane ($\text{70° ± 5°}$ from the normal to the membrane plane).Transient dichroism measurements show that below T_c the proteins are immobile, while above this temperature protein rotation around an axis normal to the plane of the membrane is occurring. In addition, from the data the angle of the chromophore for the rotating proteins with respect to the rotational diffusion axis can be calculated. This angle is found to be $\text{30° ± 3°}$ and $\text{29° ± 4°}$ in dimyristoyl phosphatidylcholine and dipalmitoyl phosphatidylcholine, respectively. This is considerably smaller than the value of $\text{70° ± 5°}$ for the natural biomembrane. A reversible reorientation of the chromophore above and below the respective main T_c transition temperature could explain the change of angle observed provided that all the molecules rotate above T_c.     

Single-molecule measurements of dissociation rates and energy landscapes of binary trans snare complexes in parallel versus antiparallel orientation

Interactions between synaptobrevin 2 (Sb2) and syntaxin 1A (Sx1A) can be readily isolated and studied with the use of force spectroscopy single-molecule measurements. We studied interactions between Sx1A and Sb2 in two different orientations (parallel and antiparallel) using four different terminus configurations of these proteins. Force-loading experiments indicated that protein pairs in any configuration/orientation are zippered. We measured the extension and force for disassembly of these interactions, calculated the spontaneous dissociation lifetimes, and determined their free energies, enthalpies, and entropies. Although the free energies were very similar for all four configurations (∼28 k_BT (Eyring model) and ∼20 k_BT (Kramers model)), the enthalpy changes of binary Sx1A-Sb2 interactions varied between 24.7 k_BT and 33.1 k_BT. This variation is consistent with the conformation changes that occur during disassembly of the various protein terminus configurations, as verified by alterations in the extension. The parallel interactions appear to be energetically somewhat advantageous over antiparallel configurations/orientation, especially when the N-termini of Sx1A-Sb2 are left to interact freely.     

Deuterium magnetic resonance of selectively deuterated cholesteryl esters in dipalmitoyl phosphatidylcholine dispersions

Dispersions (50 wt% water) containing 95 mol% dipalmitoyl phosphatidylcholine/5 mol% deuterated cholesteryl palmitate (or stearate) were studied using ²H-NMR. Incorporation of ester into the phospholipid bilayer was found to be 0.5 mol% at 50°C. From the profile of ²H quadrupolar splitting vs. chain position, support for an average conformation resembling a ‘horseshoe’ within the bilayer is obtained. Quadrupolar relaxation times $\text{T}{}_{2e}$ of approx. 250 μs and approx. 850 μs are measured for cholesteryl palmitate-2,2-d₂ and cholesteryl palmitate-16,16,16-d₃, respectively, which are less than one-half those obtained for the corresponding positions in dipalmitoyl-d₆₂ phosphatidylcholine. This is ascribed to a slower rate of motion of the ester chain and/or an extra, slow motion of the molecule.     

Experimental evidence for membrane-mediated protein-protein interaction

Membrane proteins diffuse within the membrane, form oligomers and supramolecular assemblies. Using high-speed atomic force microscopy, we present direct experimental measure of an in-membrane-plane interaction potential between membrane proteins. In purple membranes, ATP-synthase c-rings formed dimers that temporarily dissociated. C-ring dimers revealed subdiffusive motion, while dissociated monomers diffused freely. C-rings center-to-center distance probability distribution allowed the calculation and modeling of an in-membrane-plane energy landscape that presented repulsion at 80 Å, most stable dimer association at 103 Å (−3.5 k_BT strength), and dissociation at 125 Å (−1 k_BT strength). This first experimental data of nonlabeled membrane protein diffusion and the corresponding in-membrane-plane interaction energy landscape characterized membrane protein interaction with an attractive range of several k_BT that reaches to a radius of ∼50 Å within the membrane plane.     

Vacancy clustering and diffusion in germanium using kinetic lattice Monte Carlo simulations

We investigated vacancy-assisted self-diffusion in germanium by means of kinetic lattice Monte Carlo (KLMC) simulations below the melting temperature, for a vacancy concentration of 1 × 10¹⁸/cm³. At higher temperatures, fewer clusters formed, but there was less variation in the number of clusters than at lower temperatures as the time increased. Equilibrium diffusivities in the clustering region were 10² lower than those of free vacancies in the initial stage of KLMC simulations. They were expressed according to three temperature regimes: 6.5 × 10^? 4 exp(–0.35/k _B T) cm²/s at temperatures above 1100 K, 5.2 × 10⁵ exp(–2.32/k _B T) cm²/s at temperatures of 900–1100 K and 6.0 × 0^–7 exp(–0.19/k _B T) cm²/s at temperatures below 900 K. The effective mean migration energy, 1.1 eV, closely coincided with that of the 1.0–1.2 eV in experiments and was very different from the migration energy of the free vacancy.     

What can we learn about the lipid vesicle structure from the small-angle neutron scattering experiment?

Small-angle neutron scattering (SANS) on the unilamellar vesicle (ULV) populations (diameter 500 and 1,000 Å) in D₂O was used to characterize lipid vesicles from dimyristoylphosphatidylcholine (DMPC) at three phases: gel L_β′, ripple P_β′ and liquid L_α. Parameters of vesicle populations and internal structure of the DMPC bilayer were characterized on the basis of the separated form factor (SFF) model. Vesicle shape changes from nearly spherical in the L_α phase to elliptical in the P_β′ and L_β′ phases. This is true for vesicles prepared via extrusion through pores with the diameter 500 Å. Parameters of the internal bilayer structure (thickness of the membrane and the hydrophobic core, hydration and the surface area of the lipid molecule) were determined on the basis of the hydrophobic–hydrophilic (HH) approximation of neutron scattering length density across the bilayer ρ(x) and of the step function (SF) approximation of ρ(x). DMPC membrane thickness in the L_α phase (T=30°C) demonstrates a dependence on the membrane curvature for extruded vesicles. Prepared via extrusion through 500 Å diameter pores, vesicle population in the L_α phase has the following characteristics: average value of minor semi-axis 266±2 Å, ellipse eccentricity 1.11±0.02, polydispersity 26%, thickness of the membrane 48.9±0.2 Å and of the hydrophobic core 19.9±0.4 Å, surface area 60.7±0.5 Ų and number of water molecules 12.8±0.3 per DMPC molecule. Vesicles prepared via extrusion through pores with the diameter 1,000 Å have polydispersity of 48% and membrane thickness of 45.5±0.6 Å in the L_α phase. SF approximation was used to describe the DMPC membrane structure in L_β′ (T=10°C) and P_β′ (T=20°C) phases. Extruded DMPC vesicles in D₂O have membrane thickness of 49.6±0.5 Å in the L_β′ phase and 48.3±0.6 Å in the P_β′ phase. The dependence of the DMPC membrane thickness on temperature was restored from the SANS experiment.     

Is the cholesterol bilayer domain a barrier to oxygen transport into the eye lens?

In the eye lens, the oxygen partial pressure is very low and the cholesterol (Chol) content in cell membranes is very high. Disturbance of these quantities results in cataract development. In human lens membranes, both bulk phospholipid-Chol domains and the pure Chol bilayer domains (CBDs) were experimentally detected. It is hypothesized that the CBD constitutes a significant barrier to oxygen transport into the lens. Transmembrane profiles of the oxygen diffusion-concentration product, obtained with electron paramagnetic resonance spin-labeling methods, allow evaluation of the oxygen permeability (P_M) of phospholipid membranes but not the CBD. Molecular dynamics simulation can independently provide components of the product across any bilayer domain, thus allowing evaluation of the P_M across the CBD. Therefore, to test the hypothesis, MD simulation was used. Three bilayers containing palmitoyl-oleoyl-phosphorylcholine (POPC) and Chol were built. The pure Chol bilayer modeled the CBD, the 1:1 POPC-Chol bilayer modeled the bulk membrane in which the CBD is embedded, and the POPC bilayer was a reference. To each model, 200 oxygen molecules were added. After equilibration, the oxygen concentration and diffusion profiles were calculated for each model and multiplied by each other. From the respective product profiles, the P_M of each bilayer was calculated. Favorable comparison with experimental data available only for the POPC and POPC-Chol bilayers validated these bilayer models and allowed the conclusion that oxygen permeation across the CBD is ~ 10 smaller than across the bulk membrane, supporting the hypothesis that the CBD is a barrier to oxygen transport into the eye lens.     

Decrease of elastic moduli of DOPC bilayers induced by a macrolide antibiotic, azithromycin

The elastic properties of membrane bilayers are key parameters that control its deformation and can be affected by pharmacological agents. Our previous atomic force microscopy studies revealed that the macrolide antibiotic, azithromycin, leads to erosion of DPPC domains in a fluid DOPC matrix [A. Berquand, M. P. Mingeot-Leclercq, Y. F. Dufrene, Real-time imaging of drug-membrane interactions by atomic force microscopy, Biochim. Biophys. Acta 1664 (2004) 198-205.]. Since this observation could be due to an effect on DOPC cohesion, we investigated the effect of azithromycin on elastic properties of DOPC giant unilamellar vesicles (GUVs). Microcinematographic and morphometric analyses revealed that azithromycin addition enhanced lipid membranes fluctuations, leading to eventual disruption of the largest GUVs. These effects were related to change of elastic moduli of DOPC, quantified by the micropipette aspiration technique. Azithromycin decreased both the bending modulus (k_c, from 23.1 ± 3.5 to 10.6 ± 4.5 k_BT) and the apparent area compressibility modulus (K_app, from 176 ± 35 to 113 ± 25 mN/m). These data suggested that insertion of azithromycin into the DOPC bilayer reduced the requirement level of both the energy for thermal fluctuations and the stress to stretch the bilayer. Computer modeling of azithromycin interaction with DOPC bilayer, based on minimal energy, independently predicted that azithromycin (i) inserts at the interface of phospholipid bilayers, (ii) decreases the energy of interaction between DOPC molecules, and (iii) increases the mean surface occupied by each phospholipid molecule. We conclude that azithromycin inserts into the DOPC lipid bilayer, so as to decrease its cohesion and to facilitate the merging of DPPC into the DOPC fluid matrix, as observed by atomic force microscopy. These investigations, based on three complementary approaches, provide the first biophysical evidence for the ability of an amphiphilic antibiotic to alter lipid elastic moduli. This may be an important determinant for drug: lipid interactions and cellular pharmacology.     

Hysteresis-based mechanism for the directed motility of the Ncd motor

Ncd is a Kinesin-14 family protein that walks to the microtubule's minus end. Although available structures show its α-helical neck in either pre- or post-stroke orientations, little is known about the transition between these two states. Using a combination of molecular dynamics simulations and structural analyses, we find that the neck sequentially makes intermediate contacts with the motor head along its mostly longitudinal path, and it develops a 24° twist in the post-stroke orientation. The forward (pre-stroke to post-stroke) motion has an ∼4.5 k_BT (where k_B is the Boltzmann constant, and T = 300 K) free-energy barrier and is a diffusion guided by the intermediate contacts. The post-stroke free-energy minimum is higher and is formed ∼10° before reaching the orientation in the post-stroke crystal structure, consistent with previous structural data. The importance of intermediate contacts correlates with the existing motility data, including those for mutant Ncds. Unlike the forward motion, the recovery stroke goes nearly downhill in free energy, powered in part by torsional relaxation of the neck. The hysteresis in the energetics of the neck motion arises from the mechanical compliance of the protein, and together with guided diffusion, it may be key to the directed motility of Ncd.     

Mechanical properties of the high cholesterol-containing membrane: An AFM study

Cholesterol (Chol) content in most cellular membranes does not exceed 50 mol%, only in the eye lens's fiber cell plasma membrane, its content surpasses 50 mol%. At this high concentration, Chol induces the formation of pure cholesterol bilayer domains (CBDs), which coexist with the surrounding phospholipid-cholesterol domain (PCD). Here, we applied atomic force microscopy to study the mechanical properties of Chol/phosphatidylcholine membranes where the Chol content was increased from 0 to 75 mol%, relevant to eye lens membranes. The surface roughness of the membrane decreases with an increase of Chol content until it reaches 60 mol%, and roughness increases with a further increment in Chol content. We propose that the increased roughness at higher Chol content results from the formation of CBDs. Force spectroscopy on the membrane with Chol content of 50 mol% or lesser exhibited single breakthrough events, whereas two distinct puncture events were observed for membranes with the Chol content greater than 50 mol%. We propose that the first puncture force corresponds to the membranes containing coexisting PCD and CBDs. In contrast, the second puncture force corresponds to the “CBD water pocket” formed due to coexisting CBDs and PCD. Membrane area compressibility modulus (K_A) increases with an increase in Chol content until it reaches 60 mol%, and with further increment in Chol content, CBDs are formed, and K_A starts to decrease. Our results report the increase in membrane roughness and decrease K_A at very high Chol content (>60 mol%) relevant to the eye lens membrane.     

Intrinsic perturbing ability of alkanols in lipid bilayers

The proportionality constant between the equipotency concentrations of a series of solutes and the fraction of a solute in the membrane phase is directly related to the solute to lipid mol ratio. Experimental measurements of partition coefficient and of several alkanol-induced effects show that the solute/lipid mol ratlos for a series of alkanols are not constant at their equipotency concentrations. The deviations in the solute/lipid ratios are similar in the various systems, and these deviations seem to depend primarily upon the chain length and branching in alkanols. It is suggested that such intrinsic differences in the perturbing ability of alcohols arise from a specificity of interaction between alkanols and lipid bilayer. We have correlated partition coefficients (in n-octanol, in egg phosphatidylcholine liposomes, and in dipalmitoyl phosphatidylcholine liposomes) for thirteen alkanols to the equipotency concentrations for their ability to modify the order-disorder thermotropic transition in dipalmitoyl phosphatidylcholine, ability to stimulate the hydrolysis of phosphatidylcholine in a bilayer by bee venom phospholipase A₂, and for the activation of the galactoside transport system in Escherichia coli. Significant correlation is found between equipotency concentrations for perturbing the order-disorder transition, the activation of phospholipase A₂-catalyzed hydrolysis and the activation of galactoside transport system.