A multiscale approach to the elastic moduli of biomembrane networks

We develop equilibrium fluctuation formulae for the isothermal elastic moduli of discrete biomembrane models at different scales. We account for the coupling of large stretching and bending strains of triangulated network models endowed with harmonic and dihedral angle potentials, on the basis of the discrete-continuum approach presented in Schmidt and Fraternali (J Mech Phys Solids 60:172-180, 2012). We test the proposed equilibrium fluctuation formulae with reference to a coarse-grained molecular dynamics model of the red blood cell (RBC) membrane (Marcelli et al. in Biophys J 89:2473-2480, 2005; Hale et al. in Soft Matter 5:3603-3606, 2009), employing a local maximum-entropy regularization of the fluctuating configurations (Fraternali et al. in J Comput Phys 231:528-540, 2012). We obtain information about membrane stiffening/softening due to stretching, curvature, and microscopic undulations of the RBC model. We detect local dependence of the elastic moduli over the RBC membrane, establishing comparisons between the present theory and different approaches available in the literature.     

An ultrasonic technique for the measurement of the elastic moduli of human cornea

In the hopes of reducing the unpredictability associated with refractive surgical procedures and ultimately improving surgical techniques, many investigators have attempted to determine the elastic moduli of the cornea. Techniques such as stress-strain tests of corneal strips and the measurement of mercury drop displacement in a whole eye under increasing pressure have resulted in a range of values for Young's modulus from 10⁵ to 10⁷ N m⁻². Both of these methods are limited because these mechanical tests cannot be performed in the physiological state and because of the large amount of force applied during testing. We used an ultrasonic technique to determine the elastic moduli of the human cornea. Two groups of six corneas prepared under different conditions (in saline and in dextran) were examined separately and the shear waves were generated and detected in these 12 human eye bank eyes. All the waveforms were digitized and saved in files of binary format. Fast Fourier transformation (FFT) was applied to calculate the speed and attenuation of the shear wave. Using the resulting wave speeds and attenuation coefficients, the Young's moduli of the corneal samples were calculated as (5.3±1.1)×10⁶ N m⁻² and (2.0±1.0)×10⁷ N m⁻² for cornea samples prepared in saline and in dextran at 2.25 MHz, respectively.     

Effects of age on elastic moduli of human lungs.

The model of the lung as an elastic continuum undergoing small distortions from a uniformly inflated state has been used to describe many lung deformation problems. Lung stress-strain material properties needed for this model are described by two elastic moduli: the bulk modulus, which describes a uniform inflation, and the shear modulus, which describes an isovolume deformation. In this study we measured the bulk modulus and shear modulus of human lungs obtained at autopsy at several fixed transpulmonary pressures (Ptp). The bulk modulus was obtained from small pressure-volume perturbations on different points of the deflation pressure-volume curve. The shear modulus was obtained from indentation tests on the lung surface. The results indicated that, at a constant Ptp, both bulk and shear moduli increased with age, and the increase was greater at higher Ptp values. The micromechanical basis for these changes remains to be elucidated.     

Determination of homeostatic elastic moduli in two layers of the esophagus

The function of the esophagus is mechanical. To understand the function, it is necessary to know how the stress and strain in the esophagus can be computed, and how to determine the stress-strain relationship of the wall materials. The present article is devoted to the issue of determining the incremental elastic moduli in the layers of the esophagus under homeostatic conditions. The esophagus is treated as a two-layered structure consisting of an inner collagen-rich submucosa layer and an outer muscle layer. We adopt a theory based on small perturbation experiments at homeostatic conditions for determination of incremental moduli in circumferential, axial, and cross directions in the two layers. The experiments are inflation, axial stretching, circumferential bending, and axial bending. The analysis takes advantage of knowing the esophageal zero-stress state (an open sector with an opening angle of 59.4 +/- 13.2 deg). The neutral axis was located 27% +/- 1.9%away from the mucosal surface. It is demonstrated that under homeostatic conditions, the incremental moduli are layer and direction dependent. The incremental modulus is the highest in the axial direction. Furthermore, the axial moduli for the two layers are similar, whereas in the circumferential direction, the incremental modulus is a factor of 6 higher in the mucosa-submucosa layer compared to the muscle layer. Hence, the esophagus has to be treated as a composite, anisotropic body. With this additional information, we can then look forward to a vision of truly understanding the mechanical events of the esophagus.     

Molecular modeling of the axial and circumferential elastic moduli of tubulin

Microtubules play a number of important mechanical roles in almost all cell types in nearly all major phylogenetic trees. We have used a molecular mechanics approach to perform tensile tests on individual tubulin monomers and determined values for the axial and circumferential moduli for all currently known complete sequences. The axial elastic moduli, in vacuo, were found to be 1.25 GPa and 1.34 GPa for α- and β-bovine tubulin monomers. In the circumferential direction, these moduli were 378 MPa for α- and 460 MPa for β-structures. Using bovine tubulin as a template, 269 homologous tubulin structures were also subjected to simulated tensile loads yielding an average axial elastic modulus of 1.10 ± 0.14 GPa for α-tubulin structures and 1.39 ± 0.68 GPa for β-tubulin. Circumferentially the α- and β-moduli were 936 ± 216 MPa and 658 ± 134 MPa, respectively. Our primary finding is that that the axial elastic modulus of tubulin diminishes as the length of the monomer increases. However, in the circumferential direction, no correlation exists. These predicted anisotropies and scale dependencies may assist in interpreting the macroscale behavior of microtubules during mitosis or cell growth. Additionally, an intergenomic approach to investigating the mechanical properties of proteins may provide a way to elucidate the evolutionary mechanical constraints imposed by nature upon individual subcellular components.     

Anatomical variation of orthotropic elastic moduli of the proximal human tibia

The anatomical variation of orthotropic elastic moduli of the cancellous bone from three human proximal tibiae was investigated using an ultrasonic technique. With this technique, it was possible to measure three orthogonal elastic moduli and three shear moduli from cubic specimens of cancellous bone as small as 8 mm per side. Correlation with mechanical tensile testing has shown this technique to offer a precise measure of cancellous modulus (Eten = 0.94Eult + 144.6 MPa, r2 = 0.96, n = 34). The cancellous bone of the proximal tibia was found to be very inhomogeneous, with the axial modulus ranging between 340 and 3350 MPa. A course map is presented, showing measured Young's moduli as a function of anatomical position. The anisotropy of the cancellous bone, determined by the relative differences between the three orthogonal moduli, was shown to be relatively constant over the entire range of cancellous densities tested. The relationship between the axial elastic modulus and the apparent density was found to be approximately linear, as reported by others for proximal tibial cancellous bone.     

Biaxial incremental homeostatic elastic moduli of coronary artery: two-layer model

The detailed mechanical properties of various layers of the coronary artery are important for understanding the function of the vessel. The present article is focused on the determination of the incremental modulus in different layers and directions in the neighborhood of the in vivo state. The incremental modulus can be defined for any material subjected to a large deformation if small perturbations in strain lead to small perturbations of stresses in a linear fashion. This analysis was applied to the porcine coronary artery, which was treated as a two-layered structure consisting of an inner intima-media layer and an outer adventitia layer. We adopted a theory based on small-perturbation experiments at homeostatic conditions for determination of incremental moduli in circumferential, axial, and cross directions in the two layers. The experiments were based on inflation and axial stretch. We demonstrate that under homeostatic conditions the incremental moduli are layer- and direction dependent. The incremental modulus is highest in the circumferential direction. Furthermore, in the circumferential direction, the media is stiffer than the whole wall, which is stiffer than the adventitia. In the axial direction, the adventitia is stiffer than the intact wall, which is stiffer than the media. Hence, the coronary artery must be treated as a composite, nonisotropic body. The data acquire physiological relevance in relation to coronary artery health and disease.     

Measurements of elastic moduli of silicone gel substrates with a microfluidic device

Thin layers of gels with mechanical properties mimicking animal tissues are widely used to study the rigidity sensing of adherent animal cells and to measure forces applied by cells to their substrate with traction force microscopy. The gels are usually based on polyacrylamide and their elastic modulus is measured with an atomic force microscope (AFM). Here we present a simple microfluidic device that generates high shear stresses in a laminar flow above a gel-coated substrate and apply the device to gels with elastic moduli in a range from 0.4 to 300 kPa that are all prepared by mixing two components of a transparent commercial silicone Sylgard 184. The elastic modulus is measured by tracking beads on the gel surface under a wide-field fluorescence microscope without any other specialized equipment. The measurements have small and simple to estimate errors and their results are confirmed by conventional tensile tests. A master curve is obtained relating the mixing ratios of the two components of Sylgard 184 with the resulting elastic moduli of the gels. The rigidity of the silicone gels is less susceptible to effects from drying, swelling, and aging than polyacrylamide gels and can be easily coated with fluorescent tracer particles and with molecules promoting cellular adhesion. This work can lead to broader use of silicone gels in the cell biology laboratory and to improved repeatability and accuracy of cell traction force microscopy and rigidity sensing experiments.     

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(B)T) 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.     

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.     

Determination of elastic moduli of thin layers of soft material using the atomic force microscope

We address three problems that limit the use of the atomic force microscope when measuring elastic moduli of soft materials at microscopic scales. The first concerns the use of sharp cantilever tips, which typically induce local strains that far exceed the linear material regime. We show that this problem can be alleviated by using microspheres as probes, and we establish the criteria for their use. The second relates to the common use of the Hertz contact mechanics model, which leads to significant errors when applied to thin samples. We develop novel, simple to use corrections to apply for such cases. Samples that are either bonded or not bonded to a rigid substrate are considered. The third problem concerns the difficulty in establishing when contact occurs on a soft material. We obtain error estimates for the elastic modulus resulting from such uncertainty and discuss the sensitivity of the estimation methods to error in contact point. The theoretical and experimental results are compared to macroscopic measurements on poly(vinyl-alcohol) gels.     

A probabilistic measure for alignment-free sequence comparison

MOTIVATION: Alignment-free sequence comparison methods are still in the early stages of development compared to those of alignment-based sequence analysis. In this paper, we introduce a probabilistic measure of similarity between two biological sequences without alignment. The method is based on the concept of comparing the similarity/dissimilarity between two constructed Markov models. RESULTS: The method was tested against six DNA sequences, which are the thrA, thrB and thrC genes of the threonine operons from Escherichia coli K-12 and from Shigella flexneri; and one random sequence having the same base composition as thrA from E.coli. These results were compared with those obtained from CLUSTAL W algorithm (alignment-based) and the chaos game representation (alignment-free). The method was further tested against a more complex set of 40 DNA sequences and compared with other existing sequence similarity measures (alignment-free). AVAILABILITY: All datasets and computer codes written in MATLAB are available upon request from the first author.     

A probabilistic framework for nutrient uptake length

The nutrient uptake length, the average displacement of a nutrient in a stream before being taken up by the biota, is an important quantity to characterize and compare streams and rivers, or to quantify certain aspects of their related ecosystems. This concept has been widely used for almost 30 years now, and uptake lengths have been estimated for several nutrients in many systems, but it also suffers from a number of limitations, one of them being the requirement of a spatially homogeneous stream or river. We combine recently advocated, transport-based models of stream processes with current concepts of dispersal theory into a novel framework for nutrient uptake length. The framework is based on the theory for dispersal kernels in terrestrial systems, where the entire distribution of dispersal distances is calculated and not only the average. Within this framework, we can re-derive all previous results and formulae for uptake length, and we can include spatially heterogeneous stream environments. In addition, we propose a number of new characteristic quantities that can complement nutrient uptake length when evaluating the health of a stream system or the impact of a source of nutrients. We illustrate our method with two examples of spatially non-homogeneous streams: point-source input of nutrients (e.g., wastewater treatment plant) and diffuse lateral input (e.g., agricultural run-off), and we show how to measure the relative contribution of the two sources to the uptake length and other characteristics.     

A probabilistic classifier for olfactory receptor pseudogenes

Background  

Olfactory receptors (ORs), the largest mammalian gene superfamily (900–1400 genes), has >50% pseudogenes in humans. While most of these inactive genes are identified via coding frame (nonsense) disruptions, seemingly intact genes may also be inactive due to other deleterious (missense) mutations. An ultimate assessment of the actual size of the functional human OR repertoire thus requires an accurate distinction between genes and pseudogenes.     

An inverse approach for the mechanical characterisation of vascular tissues via a generalised rule of mixtures

Mechanical factors such as stresses and strains play a major role in the growth and remodelling of soft biological tissues. The main constituents of tissue undergo different processes reacting to mechanical stimulus. Thereby, the characterisation of growth and remodelling requires an accurate estimation of the stresses and strains of their main components. Many soft tissues can be considered as composite materials and can be analysed using an appropriate rule of mixtures. Particularly, arterial tissue can be modelled as an isotropic soft matrix reinforced with preferentially oriented collagen fibres. An inverse approach to obtain the mechanical characterisation of each main component is proposed in this work. The procedure is based on a rule of mixtures raised in a finite deformation framework and generalised to include kinematics and compatibility equations for serial–parallel behaviour. This methodology allows obtaining the stress–strain relationship of the components fitting experimental data.     

A probabilistic generative model for GO enrichment analysis

The Gene Ontology (GO) is extensively used to analyze all types of high-throughput experiments. However, researchers still face several challenges when using GO and other functional annotation databases. One problem is the large number of multiple hypotheses that are being tested for each study. In addition, categories often overlap with both direct parents/descendents and other distant categories in the hierarchical structure. This makes it hard to determine if the identified significant categories represent different functional outcomes or rather a redundant view of the same biological processes. To overcome these problems we developed a generative probabilistic model which identifies a (small) subset of categories that, together, explain the selected gene set. Our model accommodates noise and errors in the selected gene set and GO. Using controlled GO data our method correctly recovered most of the selected categories, leading to dramatic improvements over current methods for GO analysis. When used with microarray expression data and ChIP-chip data from yeast and human our method was able to correctly identify both general and specific enriched categories which were overlooked by other methods.     

A frequency matrix for probabilistic identification of some bacilli

A matrix comprising frequencies for positive results for 44 Bacillus taxa for 30 characters has been constructed. The 44 taxa include most of the common species and several clusters of environmental isolates including those described as B. firmus-B. lentus intermediates. The tests, which were chosen for their high diagnostic value, included some of the traditional tests used for identification of bacilli supplemented with a range of sugar fermentations and other characterization tests. The matrix was evaluated by identifying hypothetical median organisms, cluster representatives and a panel of 23 reference strains. All reference strains achieved Willcox probabilities above 0.995. Fifty-eight environmental isolates were also subjected to the 30 tests and identification was attempted. Forty-one strains (70%) achieved a Willcox probability greater than 0.95, which was considered an acceptable identification, and were assigned to 12 taxa. If the SE of taxonomic distance was also considered in the identification score (an acceptable value being less than 7.0), the number of acceptable identifications was reduced to 34 (59%). It was encouraging that bacteria from garden soils identified to the common species such as B. subtilis, B. cereus and B. licheniformis whereas some of the bacteria from an estuarine habitat were identified as species such as B. firmus which are normally identified with that habitat.     

A probabilistic model for the evolution of RNA structure

Background  

For the purposes of finding and aligning noncoding RNA gene- and cis-regulatory elements in multiple-genome datasets, it is useful to be able to derive multi-sequence stochastic grammars (and hence multiple alignment algorithms) systematically, starting from hypotheses about the various kinds of random mutation event and their rates.     

A probabilistic model for the establishment of neuron polarity

The main aim of this paper is to present a simple probabilistic model for the early stage of neuron growth: the specification on an axon out of several initially similar neurites. The model is a Markov process with competition between the growing neurites, wherein longer objects have more chances to grow, and parameter alpha determines the intensity of the competition. For alpha > 1 the model provides results which are qualitatively similar to the experimental ones, i.e. selection of one rapidly elongating axon out of several neurites while other less successful neurites stop growing at some random time. Rigorous mathematical proofs are given.