Simple sequential model for the kinetics of conformational transitions of oligomeric helices and proteins

A simple sequential model is developed which is applicable to the kinetics of melting of some types of oligomeric helices and as an idealization to the kinetics of unfolding of some protein molecules. A procedure is presented for calculating the concentrations of all conformational species as functions of time. The time course of experimentally observable quantities which depend on these concentrations may then be computed. One of the most characteristic features of the model is the distinction between a transient and a steady-state phase. During the latter all molecular parameters change at the same rate, which depends strongly on the difficulty of nucleation and the length of the sequence. Simple approximations to the steady-state rate are discussed in terms of the exact solution. Rates of transient processes dependless strongly on the rate of nucleation and the number of steps and are a more direct reflection of the rates of the rates of the elementary process of propagation. The value of experimental observation of transient process is emphasized.     

Dipole cooperative model of ion channels of excitable biomembranes. Conductance of ion channels

An analysis of ionic channel conductance is presented in terms of dipole cooperative model. The dependence of conductance on displaced charge is found to be an S-shaped function. Basing on this function and kinetics of gating currents, the kinetic curves for the conductance are calculated. These curves are compared with Hodgkin--Huxley results on sodium channel. A good agreement may be observed for the case of positive jumps of the potential. Less accurate coincidence takes place for negative jumps of the potential.     

Folding funnels and conformational transitions via hinge-bending motions

In this article we focus on presenting a broad range of examples illustrating low-energy transitions via hinge-bending motions. The examples are divided according to the type of hinge-bending involved; namely, motions involving fragments of the protein chains, hinge-bending motions involving protein domains, and hinge-bending motions between the covalently unconnected subunits. We further make a distinction between allosterically and nonallosterically regulated proteins. These transitions are discussed within the general framework of folding and binding funnels. We propose that the conformers manifesting such swiveling motions are not the outcome of “induced fit” binding mechanism; instead, molecules exist in an ensemble of conformations that are in equilibrium in solution. These ensembles, which populate the bottoms of the funnels,a priori contain both the “open” and the “closed” conformational isomers. Furthermore, we argue that there are no fundamental differences among the physical principles behind the folding and binding funnels. Hence, there is no basic difference between funnels depicting ensembles of conformers of single molecules with fragment, or domain motions, as compared to subunits in multimeric quaternary structures, also showing such conformational transitions. The difference relates only to the size and complexity of the system. The larger the system, the more complex its corresponding fused funnel(s). In particular, funnels associated with allosterically regulated proteins are expected to be more complicated, because allostery is frequently involved with movements between subunits, and consequently is often observed in multichain and multimolecular complexes. This review centers on the critical role played by flexibility and conformational fluctuations in enzyme activity. Internal motions that extend over different time scales and with different amplitudes are known to be essential for the catalytic cycle. The conformational change observed in enzyme-substrate complexes as compared to the unbound enzyme state, and in particular the hinge-bending motions observed in enzymes with two domains, have a substantial effect on the enzymatic catalytic activity. The examples we review span the lipolytic enzymes that are particularly interesting, owing to their activation at the water-oil interface; an allosterically controlled dehydrogenase (lactate dehydrogenase); a DNA methyltransferase, with a covalently-bound intermediate; large-scale flexible loop motions in a glycolytic enzyme (TIM); domain motion in PGK, an enzyme which is essential in most cells, both for ATP generation in aerobes and for fermentation in anaerobes; adenylate kinase, showing large conformational changes, owing to their need to shield their catalytic centers from water; a calcium-binding protein (calmodulin), involved in a wide range of cellular calcium-dependent signaling; diphtheria toxin, whose large domain motion has been shown to yield “domain swapping” the hexameric glutamate dehydrogenase, which has been studied both in a thermophile and in a mesophile; an allosteric enzyme, showing subunit motion between the R and the T states (aspartate transcarbamoylase), and the historically well-studied lac represoor. Nonallosteric subunit transitions are also addressed with some examples (aspartate receptor andBamHI endonuclease). Hence, using this enzyme-catalysis-centered discussion, we address energy funnel landscapes of large-scale conformational transitions, rather than the faster, quasi-harmonic, thermal fluctuations.     

Simple model of ion transport through alamethicin channels in lipid membranes

The electrical characteristics of wide membrane channels such as those induced in lipid membranes by alamethicin have been analyzed using an electrodiffusion model. The channel is considered to be a water filled cylinder in which the potential energy barrier is a result of the difference in polarization energy of the ion environment when the ion is located inside as compared to outside of the channel. In addition, an electric field related to the channel structure is assumed. It is shown that without postulating any specific chemical ion-channel interaction one can reproduce experimental membrane potentials for NaCl, KCl, and CaCl₂ concentration gradients with a single set of channel parameters. The calculations also yield experimental J-V characteristics of discrete conduction states. In addition, a simple mechanism of interchannel coupling based on the above model is discussed. The model suggests a unifying approach to the problem of the origin of interionic selectivity of membrane channels induced by polyene antibiotics.     

Mathematical model of polar auxin transport

Polar auxin transport can be simulated by a model which achieves polarity through the preferential secretion of more auxin from the lower end than from the upper end of each cell. Solution of the model using a computer provides a possible explanation of the differences between the polarity expressed by different tissues and the differences between pieces of different lengths, on the basis of small differences in the polarity of auxin secretion from individual cells. A method of estimating the polarity of individual cells is described.     

Lipid phase transitions in model biomembranes: The effect of ions on phosphatidylcholine bilayers

Differential scanning calorimetry has been used to study the endothermic phase behaviour of some model biomembranes (i.e. phosphatidylcholine-water systems) in the presence of a wide range of alkaline, alkaline earth and heavy metal salts. Studies and comparisons were made of both cation and anion effects. Shifts occur in the temperatures of both the pre-transition and main transition endotherms. The observed shifts are smaller than those which have been reported for charged lipids, and no evidence has been found for the formation of specific complexes. Electron microscopic studies on freeze-fractured dispersions of phosphatidylcholine-water-salt systems show that with some salts the typical rippled surface observed with l-α-dimyristoyl phosphatidylcholine, when in the gel state, is replaced by a smooth surface.     

Predicting order of conformational changes during protein conformational transitions using an interpolated elastic network model

The decryption of sequence of structural events during protein conformational transitions is essential to a detailed understanding of molecular functions ofvarious biological nanomachines. Coarse‐grained models have proven useful by allowing highly efficient simulations of protein conformational dynamics. By combining two coarse‐grained elastic network models constructed based on the beginning and end conformations of a transition, we have developed an interpolated elastic network model to generate a transition pathway between the two protein conformations. For validation, we have predicted the order of local and global conformational changes during key ATP‐driven transitions in three important biological nanomachines (myosin, F₁ ATPase and chaperonin GroEL). We have found that the local conformational change associated with the closing of active site precedes the global conformational change leading to mechanical motions. Our finding is in good agreement with the distribution of intermediate experimental structures, and it supports the importance of local motions at active site to drive or gate various conformational transitions underlying the workings of a diverse range of biological nanomachines. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Monensin A acid complexes as a model of electrogenic transport of sodium cation

New Monensin A acid complexes with water molecule, sodium chloride and sodium perchlorate were obtained and studied by X-ray and (1)H, (13)C NMR and FT-IR methods as well as ab initio calculations. The crystal structure of the complexes indicates the complexation of the water molecule and Na(+) cation in the pseudo-cycle conformation of the Monensin acid molecule stabilised by intramolecular hydrogen bonds. Important for stabilisation of this structure is also the intermolecular hydrogen bonds with water molecule or the coordination bonds with Na(+) cation. It is demonstrated that the counterions forming intermolecular hydrogen bonds with OH groups influence the strength of the intramolecular hydrogen bonds, but they have no influence on the formation of pseudo-cyclic structure. Spectroscopic studies of the complexes in dichloromethane solution have shown that the pseudo-cyclic structure of the compounds is conserved. As follows from the ab initio calculations, the interactions between the Na(+) cation and the electronegative oxygen atoms of Monensin acid totally change the molecular electrostatic potential around the supramolecular Monensin acid-Na(+) cationic complex relative to that of the neutral Monensin acid molecule.     

Residue ionization and ion transport through OmpF channels

Single trimeric channels of the general bacterial porin, OmpF, were reconstituted into planar lipid membranes and their conductance, selectivity, and open-channel noise were studied over a wide range of proton concentrations. From pH 1 to pH 12, channel transport properties displayed three characteristic regimes. First, in acidic solutions, channel conductance is a strong function of pH; it increases by approximately threefold as the proton concentration decreases from pH 1 to pH 5. This rise in conductance is accompanied by a sharp increase in cation transport number and by pronounced open-channel low-frequency current noise with a peak at ~pH 2.5. Random stepwise transients with amplitudes at ~1/5 of the monomer conductance are major contributors to this noise. Second, over the middle range (pH 5 ÷ pH 9), channel conductance and selectivity stay virtually constant; open channel noise is at its minimum. Third, over the basic range (pH 9 ÷ pH 12), channel conductance and cation selectivity start to grow again with an onset of a higher frequency open-channel noise. We attribute these effects to the reversible protonation of channel residues whose pH-dependent charge influences transport by direct interactions with ions passing through the channel.     

Diffusion of beta-lactam antibiotics through oligomeric or monomeric porin channels of some gram-negative bacteria

The penetration of anionic beta-lactam antibiotics through porins was evaluated as a mechanism of drug resistance. The major proteins with porin activity were purified from the outer membranes of six bacteria. Three of the six porins were oligomeric porins. The molecular weights of their monomers were 37 kDa from Photobacterium damsela, 42 kDa from Serratia liquefaciens, and 36 kDa from E. coli B. The other three porins were heat-modifiable monomeric porins with molecular weights of 43 kDa from Porphyromonas asaccharolytica and Acinetobacter baumannii, and 37 kDa from Escherichia coli K12.Comparison of the six porin proteins revealed that, independent of their aggregation state, their amino acid content is similar but not identical. All have double the amount of negatively charged amino acids compared with positively charged amino acids. They have a similar polarity and polarity index. Two of the six tested bacteria do not produce beta-lactamase. These two bacteria were sensitive to the different beta-lactams tested. The other four bacteria were resistant to all or to several beta-lactams.A modified liposome swelling method was used for determining the rate of penetration of charged beta-lactam antibiotics. Zwitterionic beta-lactams were found to penetrate into liposomes at a rate that more or less fits their molecular weight, whether the porins are monomeric or oligomeric. The penetration rates of negatively charged beta-lactams are different for oligomeric and monomeric porins. Negatively charged beta-lactams penetrate through oligomeric porins better than estimated by their molecular weight, whereas monomeric porins are less penetrable to negatively charged beta-lactams than estimated by their molecular weight. The contribution of all types of porins to the susceptibility of bacteria to beta-lactam antibiotics (zwitterionic or negatively charged) is apparently doubtful. The porins may decrease or increase bacterial penetration rates to beta-lactams, and only the existence of a potential beta-lactamase that can destroy the penetrating drug will cause resistance.     

Lipid-induced conformational transitions of beta-lactoglobulin

Bovine beta-lactoglobulin (betaLG) provides an excellent model protein system for beta-to-alpha conformational change, but its behavior varies when the change is induced by alcohols, surfactants, or lipid vesicles. Here the interaction and orientation of betaLG in association with various artificial lipid vesicles at neutral and acidic pH have been studied by use of several complementary spectroscopic techniques. Circular dichroism (CD) and Fourier transform infrared (FTIR) spectra demonstrated that betaLG acquires a non-native alpha-helical structure upon binding with anionic lipids, while zwitterionic lipids do not have a significant effect on its conformation. The degree of induced alpha-helix depends on the lipid concentration and is strongly affected by the charge of the protein and lipids as well as the ionic strength of the solution. Near-UV CD and Trp emission spectra revealed that the tertiary structure of lipid-bound betaLG is highly expanded but not completely disrupted. Fluorescence quenching together with a Trp emission blue shift showed that the Trp residues remain largely shielded from the solvent when interacting with DMPG, which would be consistent with at least some portions of betaLG having been inserted into the lipid membrane. The orientations of the alpha-helix and beta-sheet axes in membrane-bound betaLG were found to be parallel and perpendicular, respectively, to the membrane film normal, as determined by use of polarized attenuated total reflection (ATR) FTIR spectra. Our findings reveal that the lipid-induced beta-to-alpha transition in betaLG, accompanied by a substantial disruption in tertiary structure, is mainly driven by strong electrostatic interactions. Once the tightly packed betaLG is disrupted, hydrophobic residues become exposed and available for insertion into the lipid bilayer, where hydrophobic interaction with the lipids may play a role in stabilizing the helical components.     

Combined transport of water and ions through membrane channels

The coupling of ion and water flow through membrane channels is under dispute. Among all human aquaporins only aquaporin-6 exhibits ion channel activity. Whether aquaporin-6 functions also as a water channel cannot yet be determined with confidence. Similarly, a comparison of single-channel water permeabilities from ion channels and aquaporins suggests that ion channels may play a secondary role as water channels. However, the fraction of absorbed fluid that crosses epithelial ion channels still remains to be determined.     

Formation of the hydrophobic core of ribonuclease A through sequential coordinated conformational transitions

With steady-state and time-resolved fluorescence energy-transfer measurements, we determined the distributions of intramolecular distances in nine mutants to study the conformations of wild-type ribonuclease A in the reduced state under folding conditions. Although far-UV-CD measurements show no evidence for a secondary-structure transition, temperature- and GdnHCl-induced changes in intramolecular distance distributions in the reduced state revealed evidence for long-range subdomain structures in the denatured protein. These poorly defined structures, reflected here by wide distributions corresponding to a wide range of energies, form during refolding in a complex sequence of multiple subdomain transitions. A more well-defined structure emerges only when this structural framework, which directs the successive steps in the folding process, matures and is reinforced by stronger interactions such as disulfide bonds.     

Gating mechanisms of mechanosensitive channels of large conductance, II: systematic study of conformational transitions

Part II of this study is based on the continuum mechanics-based molecular dynamics-decorated finite element method (MDeFEM) framework established in Part I. In Part II, the gating pathways of Escherichia coli-MscL channels under various basic deformation modes are simulated. Upon equibiaxial tension (which is verified to be the most effective mode for gating), the MDeFEM results agree well with both experiments and all-atom simulations in literature, as well as the analytical continuum models and elastic network models developed in Part I. Different levels of model sophistication and effects of structural motifs are explored in detail, where the importance of mechanical roles of transmembrane helices, cytoplasmic helices, and loops are discussed. The conformation transitions under complex membrane deformations are predicted, including bending, torsion, cooperativity, patch clamp, and indentation. Compared to atom-based molecular dynamics simulations and elastic network models, the MDeFEM framework is unusually well-suited for simulating complex deformations at large length scales. The versatile hierarchical framework can be further applied to simulate the gating transition of other mechanosensitive channels and other biological processes where mechanical perturbation is important.     

A kinetic model for determining the consequences of electrogenic active transport in cardiac muscle

When active transport is electrogenic in a tissue that is continuously active, such as cardiac muscle, the active transport current is as important in the generation of the action potential as are the passive currents. A thermodynamically constrained kinetic model of electrogenic active transport of sodium and potassium ions has been developed in which the influences of voltage and chemical composition are explicitly defined. This model is coupled to a system of passive permeabilities, of the minimum degree of complexity, to simulate the integrated activity of active and passive ion transport in the generation of the cardiac action potential. Results of preliminary simulations indicate that electrogenic active transport provides a mechanism for slowly changing currents both within the time scale of an action potential as well as of many action potentials. The presence of active transport also complicates the interpretation of isotopic flux measurements and the separation of currents.