The basic structure and dynamics of cell membranes: An update of the Singer–Nicolson model

The fluid mosaic model of Singer and Nicolson (1972) is a commonly used representation of the cell membrane structure and dynamics. However a number of features, the result of four decades of research, must be incorporated to obtain a valid, contemporary version of the model. Among the novel aspects to be considered are: (i) the high density of proteins in the bilayer, that makes the bilayer a molecularly “crowded” space, with important physiological consequences; (ii) the proteins that bind the membranes on a temporary basis, thus establishing a continuum between the purely soluble proteins, never in contact with membranes, and those who cannot exist unless bilayer-bound; (iii) the progress in our knowledge of lipid phases, the putative presence of non-lamellar intermediates in membranes, and the role of membrane curvature and its relation to lipid geometry, (iv) the existence of lateral heterogeneity (domain formation) in cell membranes, including the transient microdomains known as rafts, and (v) the possibility of transient and localized transbilayer (flip-flop) lipid motion. This article is part of a Special Issue entitled: Membrane Structure and Function: Relevance in the Cell's Physiology, Pathology and Therapy.     

Kinetic analysis of the heparin-enhanced plasmin–antithrombin III reaction. Apparent catalytic role of heparin

Inactivation of plasmin by a 3-4-fold molar excess of antithrombin III follows pseudo-first-order kinetics and the apparent rate constants are proportional to the concentration of the inhibitor. Heparin accelerates the inactivation reaction without changing its pseudo-first-order character, and the apparent rate constants are also proportional to the concentration of the polysaccharide. Heparin results in a minimum 20-fold rate enhancement of the reaction between plasmin and antithrombin III when the concentrations of heparin and plasmin are approx. 0.5mum and 1mum respectively. Heparin at a molar concentration well below that of plasmin still accelerates the reaction: one molecule of the polysaccharide is able to facilitate the inactivation of about 100 molecules of plasmin. Heparin must bind to plasmin to accelerate the plasmin-antithrombin III reaction, since the modification of four to five lysine residues of the enzyme inhibits the rate-enhancement effect of heparin and the dissociation of heparin-plasmin complex decreases the inactivation rate of plasmin. Increasing the concentration of antithrombin III, at a constant amount of heparin, results in increase of the inactivation rate. By contrast, the effect of increasing the amount of plasmin in the presence of constant amount of heparin and antithrombin III is such that higher plasmin-to-heparin ratios are associated with lower rates of inactivation. It seems, therefore, that to obtain ;optimal' conditions for fast enzyme inactivation, the amount of heparin should be matched to plasmin rather than to antithrombin III. Arrhenius plots of the plasmin-antithrombin III reaction are linear both in the absence and presence of heparin, at concentrations of 1 or 2mug/ml, over a range of 26K. Under these experimental conditions, heparin increases activation entropy. The findings show that heparin seems to fulfil some criteria that are characteristic for biological catalysis: binding, reaction-rate enhancement (increasing activation entropy), recycling of heparin (effectiveness of non-stoichiometric amounts of the polysaccharide) and specificity.     

Molecular dynamics analysis of the wild type and dF508 mutant structures of the human CFTR–nucleotide binding domain 1

Mutations of CFTR (Cystic Fibrosis transmembrane Conductance Regulator), a membrane protein expressed in the epithelium that forms a chloride channel, cause a chronic, developmental and hereditary disease, known as Cystic Fibrosis. The most common mutation is the deletion of F508, a residue present in the first nucleotide binding domain (NBD1). We studied the thermodynamic properties of NBD1 wild type (WT) and mutant (dF508), starting from the crystallographic structures in the Protein Data Bank using the techniques of Molecular Dynamics. The two structures were similarly stable at room temperature, showed no change enthalpy or entropy, maintaining the same dimensions and the same order of magnitude of atomic fluctuations; the only difference was the energy of interaction with the solvent, in which the mutant appears slightly disadvantaged; these differences between the two models are at microscopic level and relate to local variations (in residues at 8 Å from F508) of the surface exposed to the solvent. We also found a decrease in the mutant of about 30 times of affinity for ATP compared to WT.     

An angiosperm-wide analysis of the gynodioecy–dioecy pathway

Background and Aims

About 6 % of an estimated total of 240 000 species of angiosperms are dioecious. The main precursors of this sexual system are thought to be monoecy and gynodioecy. A previous angiosperm-wide study revealed that many dioecious species have evolved through the monoecy pathway; some case studies and a large body of theoretical research also provide evidence in support of the gynodioecy pathway. If plants have evolved through the gynodioecy pathway, gynodioecious and dioecious species should co-occur in the same genera. However, to date, no large-scale analysis has been conducted to determine the prevalence of the gynodioecy pathway in angiosperms. In this study, this gap in knowledge was addressed by performing an angiosperm-wide survey in order to test for co-occurrence as evidence of the gynodioecy pathway.

Methods

Data from different sources were compiled to obtain (to our knowledge) the largest dataset on gynodioecy available, with 275 genera that include at least one gynodioecious species. This dataset was combined with a dioecy dataset from the literature, and a study was made of how often dioecious and gynodioecious species could be found in the same genera using a contingency table framework.

Key Results

It was found that, overall, angiosperm genera with both gynodioecious and dioecious species occur more frequently than expected, in agreement with the gynodioecy pathway. Importantly, this trend holds when studying different classes separately (or sub-classes, orders and families), suggesting that the gynodioecy pathway is not restricted to a few taxa but may instead be widespread in angiosperms.

Conclusions

This work complements that previously carried out on the monoecy pathway and suggests that gynodioecy is also a common pathway in angiosperms. The results also identify angiosperm families where some (or all) dioecious species may have evolved from gynodioecious precursors. These families could be the targets of future small-scale studies on transitions to dioecy taking phylogeny explicitly into account.     

How is an NMR structure best defined? An analysis of molecular dynamics distance-based approaches

Summary Model studies on the macrocyclic immunosuppressive agent FK506 challenge traditional approaches to defining a structure from data collected during a 2D NMR experiment. A variety of joint molecular dynamics/NMR-distance refinement methodologies are characterized. From the results it is clear that the traditional presentation of an NMR structure as a single representative minimized conformation or as a fairly tight envelope of conformers best meeting the imposed restraints can be misleading; a greater emphasis is required on dynamics and on the fact that an NMR structure represents a time average.     

An introduction to the mathematical structure of the Wright–Fisher model of population genetics

In this paper, we develop the mathematical structure of the Wright–Fisher model for evolution of the relative frequencies of two alleles at a diploid locus under random genetic drift in a population of fixed size in its simplest form, that is, without mutation or selection. We establish a new concept of a global solution for the diffusion approximation (Fokker–Planck equation), prove its existence and uniqueness and then show how one can easily derive all the essential properties of this random genetic drift process from our solution. Thus, our solution turns out to be superior to the local solution constructed by Kimura.     

An in silico biomechanical analysis of the stent–esophagus interaction

Despite all technological innovations in esophageal stent design over the past 20 years, the association between the stent design’s mechanical behavior and its effect on the clinical outcome has not yet been thoroughly explored. A parametric numerical model of a commercially available esophageal bioresorbable polymeric braided wire stent is set up, accounting for stent design aspects such as braiding angle, strut material, wire thickness, degradation and friction between the wires comprising a predictive tool on the device’s mechanical behavior. Combining this tool with complex multilayered numerical models of the pathological in vivo stressed, actively contracting and buckling esophagus could provide clinicians and engineers with a patient-specific window into the mechanical aspects of stent-based esophageal intervention. This study integrates device and soft tissue mechanics in one computational framework to potentially aid in the understanding of the occurrence of specific symptoms and complications after stent placement.     

Effect of glycerol–water binary mixtures on the structure and dynamics of protein solutions

We have performed 20?ns of fully atomistic molecular dynamics simulations of Hen Egg-White Lysozyme in 0, 10, 20, 30, and 100% by weight of glycerol in water to better understand the microscopic physics behind the bioprotection offered by glycerol to naturally occuring biological systems. The solvent exposure of protein surface residues changes when glycerol is introduced. The dynamic behavior of the protein, as quantified by the incoherent intermediate scattering function, shows a nonmonotonic dependence on glycerol content. The fluctuations of the protein residues with respect to each other were found to be similar in all water-containing solvents, but different from the pure glycerol case. The increase in the number of protein–glycerol hydrogen bonds in glycerol–water binary mixtures explains the slowing down of protein dynamics as the glycerol content increases. We also explored the dynamic behavior of the hydration layer. We show that the short length scale dynamics of this layer are insensitive to glycerol concentration. However, the long length scale behavior shows a significant dependence on glycerol content. We also provide insights into the behavior of bound and mobile water molecules.     

Occurrence of dead core in catalytic particles containing immobilized enzymes: analysis for the Michaelis–Menten kinetics and assessment of numerical methods

In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis–Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis–Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis–Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion–reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.     

NMR structure of the transmembrane domain of the n-acetylcholine receptor β2 subunit

Nicotinic acetylcholine receptors (nAChRs) are involved in fast synaptic transmission in the central and peripheral nervous system. Among the many different types of subunits in nAChRs, the β2 subunit often combines with the α4 subunit to form α4β2 pentameric channels, the most abundant subtype of nAChRs in the brain. Besides computational predictions, there is limited experimental data available on the structure of the β2 subunit. Using high-resolution NMR spectroscopy, we solved the structure of the entire transmembrane domain (TM1234) of the β2 subunit. We found that TM1234 formed a four-helix bundle in the absence of the extracellular and intracellular domains. The structure exhibited many similarities to those previously determined for the Torpedo nAChR and the bacterial ion channel GLIC. We also assessed the influence of the fourth transmembrane helix (TM4) on the rest of the domain. Although secondary structures and tertiary arrangements were similar, the addition of TM4 caused dramatic changes in TM3 dynamics and subtle changes in TM1 and TM2. Taken together, this study suggests that the structures of the transmembrane domains of these proteins are largely shaped by determinants inherent in their sequence, but their dynamics may be sensitive to modulation by tertiary and quaternary contacts.     

Nuclear dynamics of topoisomerase IIβ reflects its catalytic activity that is regulated by binding of RNA to the C-terminal domain

DNA topoisomerase II (topo II) changes DNA topology by cleavage/re-ligation cycle(s) and thus contributes to various nuclear DNA transactions. It is largely unknown how the enzyme is controlled in a nuclear context. Several studies have suggested that its C-terminal domain (CTD), which is dispensable for basal relaxation activity, has some regulatory influence. In this work, we examined the impact of nuclear localization on regulation of activity in nuclei. Specifically, human cells were transfected with wild-type and mutant topo IIβ tagged with EGFP. Activity attenuation experiments and nuclear localization data reveal that the endogenous activity of topo IIβ is correlated with its subnuclear distribution. The enzyme shuttles between an active form in the nucleoplasm and a quiescent form in the nucleolus in a dynamic equilibrium. Mechanistically, the process involves a tethering event with RNA. Isolated RNA inhibits the catalytic activity of topo IIβ in vitro through the interaction with a specific 50-residue region of the CTD (termed the CRD). Taken together, these results suggest that both the subnuclear distribution and activity regulation of topo IIβ are mediated by the interplay between cellular RNA and the CRD.     

Mechanical principles of effects of botulinum toxin on muscle length–force characteristics: An assessment by finite element modeling

Recent experiments involving muscle force measurements over a range of muscle lengths show that effects of botulinum toxin (BTX) are complex e.g., force reduction varies as a function of muscle length. We hypothesized that altered conditions of sarcomeres within active parts of partially paralyzed muscle is responsible for this effect. Using finite element modeling, the aim was to test this hypothesis and to study principles of how partial activation as a consequence of BTX affects muscle mechanics. In order to model the paralyzing effect of BTX, only 50% of the fascicles (most proximal, or middle, or most distal) of the modeled muscle were activated. For all muscle lengths, a vast majority of sarcomeres of these BTX-cases were at higher lengths than identical sarcomeres of the BTX-free muscle. Due to such “longer sarcomere effect”, activated muscle parts show an enhanced potential of active force exertion (up to 14.5%). Therefore, a muscle force reduction originating exclusively from the paralyzed muscle fiber populations, is compromised by the changes of active sarcomeres leading to a smaller net force reduction. Moreover, such “compromise to force reduction” varies as a function of muscle length and is a key determinant of muscle length dependence of force reduction caused by BTX. Due to longer sarcomere effect, muscle optimum length tends to shift to a lower muscle length. Muscle fiber–extracellular matrix interactions occurring via their mutual connections along full peripheral fiber lengths (i.e., myofascial force transmission) are central to these effects. Our results may help improving our understanding of mechanisms of how the toxin secondarily affects the muscle mechanically.     

NMR structure determination of the tetramerization domain of the Mnt repressor: An asymmetric α-helical assembly in slow exchange

The structure and dynamics of the chymotryptic tetramerization domain of the Mnt repressor of Salmonella bacteriophage P22 have been studied by NMR spectroscopy. Two sets of resonances (A and B) were found, representing the asymmetry within the homotetramer. Triple-resonance techniques were used to obtain unambiguous assignments of the A and B resonances. Intra-monomeric NOEs, which were distinguished from the inter-monomeric NOEs by exploiting ¹³C/¹⁵N-filtered NOE experiments, demonstrated a continuous -helix of approximately seven turns for both the A and B monomers. The asymmetry facilitated the interpretation of inter-subunit NOEs, whereas the antiparallel alignment of the subunits allowed further discrimination of inter-monomeric NOEs. The three-dimensional structure revealed an unusual asymmetric packing of a dimer of two antiparallel right-handed intertwined coiled -helices. The A and B forms exchange on a timescale of seconds by a mechanism that probably involves a relative sliding of the two coiled coils. The amide proton solvent exchange rates demonstrate a stable tetrameric structure. The essential role of Tyr 78 in oligomerization of Mnt, found by previous mutagenesis studies, can be explained by the many hydrophobic and hydrogen bonding interactions that this residue participates in with adjacent monomers.     

Three-dimensional structure of the catalytic domain of the yeast β-(1,3)-glucan transferase Gas1: a molecular modeling investigation

The three-dimensional (3D) structure of the catalytic domain of Gas1p, a protein belonging to the only family of β-(1,3)-glucan transferases so far identified in yeasts and some pathogenic fungi (family GH-72), has been predicted by combining results derived from threading methods, multiple sequence alignments and secondary-structure predictions. The 3D model has allowed the identification of several residues that are predicted to play a crucial role in structural integrity, substrate recognition and catalysis. In particular, the model of the catalytic domain can be useful for designing site-directed mutagenesis experiments and for developing inhibitors of Gas1p enzymatic activity. Figure Three-dimensional models of the Gas1p catalytic domain as predicted using as template 7A3H (PDB code) protein Electronic Supplementary Material Supplementary material is available for this article at     

Modeling of toxin–antibody interaction and toxin transport toward the endoplasmic reticulum

A model for toxin–antibody interaction and toxin trafficking towards the endoplasmic-reticulum is presented. Antibody and toxin (ricin) initially are delivered outside the cell. The model involves: the pinocytotic (cellular drinking) and receptor-mediated toxin internalization modes from the extracellular into the intracellular domain, its exocytotic excretion from the cytosol back to the extracellular medium, the intact toxin retrograde transport to the endoplasmic reticulum, the anterograde toxin movement outward from the cell across the plasma membrane, the lysosomal toxin degradation, and the toxin clearance (removal from the system) flux. The model consists of a set of coupled PDEs. Using an averaging procedure, the model is reduced to a system of coupled ODEs. Both PDEs and ODEs systems are solved numerically. Numerical results are illustrated by figures and discussed.     

An anisotropic constitutive model for immersogeometric fluid–structure interaction analysis of bioprosthetic heart valves

This paper considers an anisotropic hyperelastic soft tissue model, originally proposed for native valve tissue and referred to herein as the Lee–Sacks model, in an isogeometric thin shell analysis framework that can be readily combined with immersogeometric fluid–structure interaction (FSI) analysis for high-fidelity simulations of bioprosthetic heart valves (BHVs) interacting with blood flow. We find that the Lee–Sacks model is well-suited to reproduce the anisotropic stress–strain behavior of the cross-linked bovine pericardial tissues that are commonly used in BHVs. An automated procedure for parameter selection leads to an instance of the Lee–Sacks model that matches biaxial stress–strain data from the literature more closely, over a wider range of strains, than other soft tissue models. The relative simplicity of the Lee–Sacks model is attractive for computationally-demanding applications such as FSI analysis and we use the model to demonstrate how the presence and direction of material anisotropy affect the FSI dynamics of BHV leaflets.     

An immunohistochemical analysis of SERT in the blood–brain barrier of the male rat brain

5-Hydroxytryptamine (5-HT) was originally discovered as a vasoconstrictor. 5-HT lowers blood pressure when administered peripherally to both normotensive and hypertensive male rats. Because the serotonin transporter (SERT) can function bidirectionally, we must consider whether 5-HT can be transported from the bloodstream to the central nervous system (CNS) in facilitating the fall in blood pressure. The blood–brain barrier (BBB) is a highly selective barrier that restricts movement of substances from the bloodstream to the CNS and vice versa, but the rat BBB has not been investigated in terms of SERT expression. This requires us to determine whether the BBB of the rat, the species in which we first observed a fall in blood pressure to infused 5-HT, expresses SERT. We hypothesized that SERT is present in the BBB of the male rat. To test this hypothesis, over 500 blood vessels were sampled from coronal slices of six male rat brains. Immunofluorescence of these coronal slices was used to determine whether SERT and RecA-1 (an endothelial cell marker) colocalized to the BBB. Blood vessels were considered to be capillaries if they were between 1.5 and 23 µm (intraluminal diameter). SERT was identified in the largest pial vessels of the BBB (mean ± SEM = 228.70 ± 18.71 µm, N = 9) and the smallest capillaries (mean ± SEM = 2.75 ± 0.12 µm, N = 369). SERT was not identified in the endothelium of blood vessels ranging from 20 to 135 µm (N = 45). The expression of SERT in the rat BBB means that 5-HT entry into the CNS must be considered a potential mechanism when investigating 5-HT-induced fall in blood pressure.     

Fluid–structure interaction analysis of the left coronary artery with variable angulation

The aim of this study is to elucidate the correlation between coronary artery branch angulation, local mechanical and haemodynamic forces at the vicinity of bifurcation. Using a coupled fluid–structure interaction (FSI) modelling approach, five idealized left coronary artery models with various angles ranging from 70° to 110° were developed to investigate the influence of branch angulations. In addition, one CT image-based model was reconstructed to further demonstrate the medical application potential of the proposed FSI coupling method. The results show that the angulation strongly alters its mechanical stress distribution, and the instantaneous wall shear stress distributions are substantially moderated by the arterial wall compliance. As high tensile stress is hypothesized to cause stenosis, the left circumflex side bifurcation shoulder is indicated to induce atherosclerotic changes with a high tendency for wide-angled models.     

Study of the influence of temperature on the dynamics of the catalytic cleft in 1,3-1,4-β-glucanase by molecular dynamics simulations

The dependence of some molecular motions in the enzyme 1,3-1,4-β-glucanase from Bacillus licheniformis on temperature changes and the role of the calcium ion in them were explored. For this purpose, two molecular dynamics simulated trajectories along 4 ns at low (300 K) and high (325 K) temperatures were generated by the GROMOS96 package. Several structural and thermodynamic parameters were calculated, including entropy values, solvation energies, and essential dynamics (ED). In addition, thermoinactivation experiments to study the influence of the calcium ion and some residues on the activity were conducted. The results showed the release of the calcium ion, which, in turn, significantly affected the movements of loops 1, 2, and 3, as shown by essential dynamics. These movements differ at low and high temperatures and affect dramatically the activity of the enzyme, as observed by thermoinactivation studies. The first two authors contributed equally to this work