Gating mechanism of mechanosensitive channel of large conductance: a coupled continuum mechanical-continuum solvation approach

Gating transition of the mechanosensitive channel of large conductance (MscL) represents a good example of important biological processes that are difficult to describe using atomistic simulations due to the large (submicron) length scale and long (millisecond) time scale. Here we develop a novel computational framework that tightly couples continuum mechanics with continuum solvation models to study the detailed gating behavior of E. coli-MscL. The components of protein molecules are modeled by continuum elements that properly describe their shape, material properties and physicochemical features (e.g., charge distribution). The lipid membrane is modeled as a three-layer material in which the lipid head group and tail regions are treated separately, taking into account the fact that fluidic lipid bilayers do not bear shear stress. Coupling between mechanical and chemical responses of the channel is realized by an iterative integration of continuum mechanics (CM) modeling and continuum solvation (CS) computation. Compared to previous continuum mechanics studies, the present model is capable of capturing the most essential features of the gating process in a much more realistic fashion: due mainly to the apolar solvation contribution, the membrane tension for full opening of MscL is reduced substantially to the experimental measured range. Moreover, the pore size stabilizes constantly during gating because of the intricate interactions of the multiple components of the system, implying the mechanism for sub-conducting states of MscL gating. A significant fraction (\(\sim \)2/3) of the gating membrane strain is required to reach the first sub-conducting state of our model, which is featured with a relative conductance of 0.115 to the fully opened state. These trends agree well with experimental observations. We anticipate that the coupled CM/CS modeling framework is uniquely suited for the analysis of many biomolecules and their assemblies under external mechanical stimuli.     

Gating mechanisms of mechanosensitive channels of large conductance, I: a continuum mechanics-based hierarchical framework

A hierarchical simulation framework that integrates information from molecular dynamics (MD) simulations into a continuum model is established to study the mechanical response of mechanosensitive channel of large-conductance (MscL) using the finite element method (FEM). The proposed MD-decorated FEM (MDeFEM) approach is used to explore the detailed gating mechanisms of the MscL in Escherichia coli embedded in a palmitoyloleoylphosphatidylethanolamine lipid bilayer. In Part I of this study, the framework of MDeFEM is established. The transmembrane and cytoplasmic helices are taken to be elastic rods, the loops are modeled as springs, and the lipid bilayer is approximated by a three-layer sheet. The mechanical properties of the continuum components, as well as their interactions, are derived from molecular simulations based on atomic force fields. In addition, analytical closed-form continuum model and elastic network model are established to complement the MDeFEM approach and to capture the most essential features of gating. In Part II of this study, the detailed gating mechanisms of E. coli-MscL under various types of loading are presented and compared with experiments, structural model, and all-atom simulations, as well as the analytical models established in Part I. It is envisioned that such a hierarchical multiscale framework will find great value in the study of a variety of biological processes involving complex mechanical deformations such as muscle contraction and mechanotransduction.     

Role of glucagon-like peptide-1 and its agonists on early prevention of cardiac remodeling in type 1 diabetic rat hearts

Glucagon-like peptide-1 (GLP-1) is an incretin hormone secreted from intestinal L cells upon nutrients ingestion, and is currently used for treating diabetes mellitus. It plays an important role in receptor modulation and cross talk with insulin at the coronary endothelium (CE) and cardiomyocytes (CM) in diabetic type 1 rat heart model. We studied the effects of insulin, GLP-1 analogues (exendin-4), and dipeptidyl peptidase-IV (DPP-IV) inhibitor on GLP-1 cardiac receptor modulation. The binding affinity of GLP-1 to its receptor on CE and CM was calculated using a rat heart perfusion model with [(125)I]-GLP-1(7-36). Tissue samples from the heart were used for immunostaining and Western blot analyses. GLP-1 systemic blood levels were measured using ELISA. GLP-1 binding affinity (τ) increased on the CE (0.33 ± 0.01 vs. 0.25 ± 0.01 min; p < 0.001) and decreased on the CM (0.29 ± 0.02 vs. 0.43 ± 0.02 min; p < 0.001) in the diabetic non-treated rats when compared to normal. There was normalization of τ back to baseline on the CE and CM levels with insulin and DPP-IV inhibitor treatment, respectively. Histological sections and immunofluorescence showed receptor up-regulation in diabetic rats with significant decrease and even normalization with the different treatment strategies. Systemic GLP-1 levels increased after 14 days of diabetes induction (10 ± 3.7 vs. 103 ± 58 pM; p = 0.0005). In conclusion, there is a significant GLP-1 receptor affinity modulation on the CE and CM levels in rats with diabetes type 1, and a cross talk with GLP-1 analogues in early prevention of cardiac remodeling.     

A novel growth-promoting protein in the conditioned media from the rotifer <Emphasis Type="Italic">Brachionus plicatilis</Emphasis> at an early exponential growth phase

We confirmed the existence of growth-promoting substances in the conditioned media (CM) from the rotifer Brachionus plicatilis at an early exponential growth phase and isolated a novel protein with a growth-promoting activity from the crude extract (CE) of rotifer cells. CM was prepared from the culture media where rotifers had been cultured at an early exponential growth phase and filtered through a 0.22-μm filter membrane. The growth-promoting activity was determined using rotifers in CM for 5 days. As a result, the increase of rotifers added with CM was significantly higher than that of the control in artificial seawater (P < 0.001). Moreover, the growth-promoting activity of CM was dose-dependent and inactivated by heat treatment at 80°C for 60 min. Meanwhile, CM filtered through a <10 kDa ultrafiltration membrane showed a low activity, whereas proteinase K treatment resulted in a complete inactivation. These results suggest that the rotifer secrets growth-promoting proteins into CM. CE also contained a protein with the activity and properties similar to those found in CM. Then, CE was subjected to purification of a growth-promoting protein for convenience using various types of chromatography after fractionation with 30–80% saturated ammonium sulfate. Subsequently, a protein with an approximate molecular weight of 25000 was isolated, and its N-terminal amino acid sequence was determined to be PAVVDFTAVWFGPLQMIKP. An orthologue was found in the EST database of B. plicatilis, the full sequence of which showed about 50% identity to the corresponding regions of thioredoxins from other organisms.     

Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method

The V–W exponential hyperelastic model is adopted to describe the instantaneous elastic response of the periodontal ligament (PDL). The general theoretical framework of constitutive modeling is described based on nonlinear continuum mechanics, and the elasticity tensor used to develop UMAT subroutine is formulated. Nanoindentation experiment is performed to characterize mechanical properties of an adult pig PDL specimen. Then the experiment is simulated by using the finite element (FE) analysis. Meanwhile, the optimized material parameters are identified by the inverse FE method. The good agreement between the simulated results and experimental data demonstrates that the V–W model is capable of describing the mechanical behavior of the PDL. Therefore, the model and its implementation into FE code are validated. By using the model, we simulate the tooth movement under orthodontic loading to predict the mechanical responses of the PDL. The results show that local concentrations of stress and strain in the PDL are found.     

Discrete Element Framework for Modelling Extracellular Matrix,Deformable Cells and Subcellular Components

This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an ‘agent’, meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.     

Viscoelastic nature of isolated tomato (Solanum lycopersicum) fruit cuticles: a mathematical model

Viscoelastic behaviour of isolated tomato fruit cuticle (CM) is well known and extensively described. Temperature and hydration conditions modify the mechanical properties of CM. Mechanical data from previous transient‐creep analysis developed in tomato fruit cuticle under different temperature and hydration conditions have been used to propose a rheological model that describes the viscoelastic nature of CM. As a composite material, the biomechanical behaviour of the plant cuticle will depend not only on the mechanical characteristics of the individual components by themselves but also on the sum of them. Based on this previous information, we proposed a two‐element model to describe the experimental behaviour: an elastic hookean element connected in parallel to a viscous element or Voigt element that will describe the mechanical behaviour of the isolated CM and cutin under the studied conditions. The main parameters of the model, E₁ and E₂ will reflect the elastic and viscoelastic behaviour of the cuticle. Relationship between these physical parameters and the change in CM properties were discussed in order to elucidate the rheological processes taking place in CM. This model describes both the influence of temperature and hydration and the behaviour of the isolated cutin and the inferred contribution of the cuticle fraction of polysaccharides when the whole cuticle is tested.     

Constitutive material modeling of cell: a micromechanics approach

The variations in mechanical properties of cells obtained from experimental and theoretical studies can be overcome only through the development of a sound mathematical framework correlating the derived mechanical property with the cellular structure. Such a formulation accounting for the inhomogeneity of the cytoplasm due to stress fibers and actin cortex is developed in this work. The proposed model is developed using the Mori-Tanaka method of homogenization by treating the cell as a fiber-reinforced composite medium satisfying the continuum hypothesis. The validation of the constitutive model using finite element analysis on atomic force microscopy (AFM) and magnetic twisting cytometry (MTC) has been carried out and is found to yield good correlation with reported experimental results. It is observed from the study that as the volume fraction of the stress fiber increases, the stiffness of the cell increases and it alters the force displacement behavior for the AFM and MTC experiments. Through this model, we have also been able to find the stress fiber as a likely cause of the differences in the derived mechanical property from the AFM and MTC experiments. The correlation of the mechanical behavior of the cell with the cell composition, as obtained through this study, is an important observation in cell mechanics.     

A Mechanistic Collective Cell Model for Epithelial Colony Growth and Contact Inhibition

We present a mechanistic hybrid continuum-discrete model to simulate the dynamics of epithelial cell colonies. Collective cell dynamics are modeled using continuum equations that capture plastic, viscoelastic, and elastic deformations in the clusters while providing single-cell resolution. The continuum equations can be viewed as a coarse-grained version of previously developed discrete models that treat epithelial clusters as a two-dimensional network of vertices or stochastic interacting particles and follow the framework of dynamic density functional theory appropriately modified to account for cell size and shape variability. The discrete component of the model implements cell division and thus influences cell size and shape that couple to the continuum component. The model is validated against recent in vitro studies of epithelial cell colonies using Madin-Darby canine kidney cells. In good agreement with experiments, we find that mechanical interactions and constraints on the local expansion of cell size cause inhibition of cell motion and reductive cell division. This leads to successively smaller cells and a transition from exponential to quadratic growth of the colony that is associated with a constant-thickness rim of growing cells at the cluster edge, as well as the emergence of short-range ordering and solid-like behavior. A detailed analysis of the model reveals a scale invariance of the growth and provides insight into the generation of stresses and their influence on the dynamics of the colonies. Compared to previous models, our approach has several advantages: it is independent of dimension, it can be parameterized using classical elastic properties (Poisson’s ratio and Young’s modulus), and it can easily be extended to incorporate multiple cell types and general substrate geometries.     

Rapid prototyping of anatomically shaped, tissue-engineered implants for restoring congruent articulating surfaces in small joints

Background:  Preliminary studies investigated advanced scaffold design and tissue engineering approaches towards restoring congruent articulating surfaces in small joints.
Materials and methods:  Anatomical femoral and tibial cartilage constructs, fabricated by three-dimensional fibre deposition (3DF) or compression moulding/particulate leaching (CM), were evaluated in vitro and in vivo in an autologous rabbit model. Effects of scaffold pore architecture on rabbit chondrocyte differentiation and mechanical properties were evaluated following in vitro culture and subcutaneous implantation in nude mice. After femoral and tibial osteotomy and autologous implantation of tissue-engineered constructs in rabbit knee joints, implant fixation and joint articulation were evaluated.
Results:  Rapid prototyping of 3DF architectures with 100% interconnecting pores promoted homogeneous distribution of viable cells, glycosaminoglycan (GAG) and collagen type II; significantly greater GAG content and differentiation capacity (GAG/DNA) in vitro compared to CM architectures; and higher mechanical equilibrium modulus and dynamic stiffness (at 0.1 Hz). Six weeks after implantation, femoral and tibial constructs had integrated with rabbit bone and knee flexion/extension and partial load bearing were regained. Histology demonstrated articulating surfaces between femoral and tibial constructs for CM and 3DF architectures; however, repair tissue appeared fibrocartilage-like and did not resemble implanted cartilage.
Conclusions:  Anatomically shaped, tissue-engineered constructs with designed mechanical properties and internal pore architectures may offer alternatives for reconstruction or restoration of congruent articulating surfaces in small joints.     

RecA protein acts at the initiation of stable DNA replication in rnh mutants of Escherichia coli K-12.

Escherichia coli rnh mutants lacking RNase H activity are capable of recA+-dependent DNA replication in the absence of concomitant protein synthesis (stable DNA replication). In rnh dnaA::Tn10 and rnh delta oriC double mutants in which the dnaA+-dependent initiation of DNA replication at oriC is completely blocked, the recA200 mutation encoding a thermolabile RecA protein renders both colony formation and DNA synthesis of these mutants temperature sensitive. To determine which stage of DNA replication (initiation, elongation, or termination) was blocked, we analyzed populations of these mutant cells incubated at 30 or 42 degrees C in the presence or absence of chloramphenicol (CM) by dual-parameter (DNA-light scatter) flow cytometry. Incubation at 30 degrees C in the presence of CM resulted in cells with a continuum of DNA content up to seven or more chromosome equivalents per cell. The cultures which had been incubated at 42 degrees C in the absence or presence of CM consisted of cells with integral numbers of chromosomes per cell. It is concluded that active RecA protein is required specifically for the initiation of stable DNA replication.     

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.     

Tomato (Lycopersicon esculentum Mill.) fruit growth and ripening as related to the biomechanical properties of fruit skin and isolated cuticle

The control of growth rate and the mechanical integrity of the tomato (Lycopersicon esculentum Mill.) fruit has been attributed to the exocarp. This study focused on the biomechanics of the fruit skin (FS) comprising cuticle, epidermis and a few subdermal cell layers, and the enzymatically isolated cuticular membrane (CM) during fruit growth and ripening. Morphology and mechanical properties of the FS and the CM of three cultivars were analysed separately at three distinct ripening stages by scanning electron microscopy (SEM) and one-dimensional tension testing, respectively. Both were subject to significant cultivar-specific changes. Thickness of the CM increased during ripening from 7.8-8.6 to 9.9-15.7 microm and exceeded by far that of the epidermal cell wall. The mechanical properties, such as modulus of elasticity, strength, and failure strain, were highest in the FS for all cultivars at any stage, with only one exception; however, the cuticle largely mirrored these properties throughout fruit maturation. Stiffness of both isolated CM and FS increased from immature to fully ripe fruits for all cultivars, while failure stress and failure strain displayed a tendency to decrease for two of them. Stress-strain behaviour of the CM could be described as strain softening, mostly linear elastic throughout, and strain hardening, and was subject to growth-related changes. The FS displayed strain hardening throughout. The results indicate evidence for the cuticle to become increasingly important as a structural component for the integrity of the tomato fruit in addition to the epidermis. A supplementary putative model for tomato fruit growth is proposed.     

Toward a robust model of packing and scale-up for chromatographic beds. 1. Mechanical compression

The packing of compressible biochromatographic resins at large scale suffers from a poor understanding of how column packing method, resin properties, and column geometry impact column performance. To improve understanding, we develop and evaluate a one-dimensional, continuum mechanics model of column packing by mechanical compression. We show that the model can quantitatively predict the change in bed height, applied stress, and internal axial porosity profile without adjustable parameters when the modulus and wall friction coefficients are determined independently. The model possesses theoretical relationships for wall support and resin rigidity that should enable it to describe the mechanical compression of any biochromatographic resin for any column diameter. Moreover, this framework could provide a path to analogous models for flow packing and dynamic axial compression.     

Integrin organization: linking adhesion ligand nanopatterns with altered cell responses

This paper presents a modelling framework in which the mechanochemical properties of smooth muscle cells may be studied. The activation of smooth muscles is considered in a three-dimensional continuum model which is key to realistically capture the function of hollow organs such as blood vessels. On the basis of a general thermodynamical framework the mechanical and chemical phases are specialized in order to quantify the coupled mechanochemical process. A free-energy function is proposed as the sum of a mechanical energy stored in the passive tissue, a coupling between the mechanical and chemical kinetics and an energy related purely to the chemical kinetics and the calcium ion concentration. For the chemical phase it is shown that the cross-bridge model of Hai and Murphy [1988. Am. J. Physiol. Cell Physiol. 254, C99-C106] is included in the developed evolution law as a special case. In order to show the specific features and the potential of the proposed continuum model a uniaxial extension test of a tissue strip is analysed in detail and the related kinematics and stress-stretch relations are derived. Parameter studies point to coupling phenomena; in particular the tissue response is analysed in terms of the calcium ion level. The model for smooth muscle contraction may significantly contribute to current modelling efforts of smooth muscle tissue responses.     

Mutagenic characterization of cholesterol epoxides in Chinese hamster V79 cells

The uptake, metabolism and alkylating properties of the diastereomeric cholesterol epoxides were studied using Chinese hamster lung fibroblasts (V79 cells). Specific emphasis is given to the comparative cyto- and geno-toxic effects of cholesterol 5 beta,6 beta-epoxide (beta CE) and cholesterol 5 alpha,6 alpha-epoxide (alpha CE) and data are provided for the first time indicating that beta CE can induce more 6-thioguanine-resistant cells than alpha CE. Cholesterol 5 beta,6 beta-epoxide induced colonies of cells resistant to 6-thioguanine at 2-3-fold the frequencies observed with the alpha-isomer, but neither compound produced ouabain-resistant colonies. The cytotoxicity (LD50) of alpha CE was estimated to be 45-50 microM whereas beta CE displayed an LD50 of 25-29 microM. Inhibition of DNA synthesis (IC50) was observed over the same dose ranges as the LD50 for each epoxide isomer. The epoxides were assimilated by cells to an equal extent, however, beta CE was metabolized to cholestane 3 beta,5 alpha-6 beta-triol twice as rapidly as the alpha-isomer. Both epoxides reacted with 4-(4'-nitrobenzyl)-pyridine to a similar extent, and with identical nucleophilic selectivity at pH 7.4, but their alkylating activity was estimated on this basis to be two orders of magnitude less than methyl methanesulfonate. Binding experiments with the DNA or cultured V79 cells or with calf-thymus DNA indicated that interactions were noncovalent and DNA binding did not correlate with the potency of the epoxides to induce the 6-thioguanine-resistant phenotype. Our results could be interpreted as indicating that both cholesterol epoxide isomers are weak mutagens or that they might induce some epigenetic event repressing the hypoxanthine guanine-phosphoribosyltransferase gene. The similarity of the epoxides' alkylating activity and their DNA-binding properties are inconsistent with their different potencies in inducing the 6-thioguanine-resistant phenotype, suggesting that the mechanism leading to this phenotype is not necessarily the result of DNA alkylation.     

Loss of translational entropy in molecular associations

Molecular associations in solution are opposed by the loss of entropy (DeltaS) that results from the restriction of motion of each component in the complex. Theoretical estimates of DeltaS are essential for rationalizing binding affinities, as well as for calculating entropic contribution to enzyme catalysis. Recently a statistical-mechanical framework has been proposed for estimating efficiently the translational entropy loss (DeltaS(trsl)), while taking explicitly into account the complex intermolecular interactions between the solute and the solvent. This framework relates the translational entropy of a solute in solution to its "free volume," defined as the volume accessible to the center of mass of the solute in the presence of the solvent and calculated by using an extension of the cell model (CM) for condensed phases. The translational entropy of pure water, estimated with the CM algorithm, shows good agreement with the experimental information. The free volume of various solutes in water, calculated within the CM by using molecular dynamics simulations with explicit solvent, displays a strong correlation with the solutes' polar and total surface areas. This correlation is used to propose a parameterization that can be used to calculate routinely the translational entropy of a solute in water. We also applied the CM formalism to calculate the free volume and translational entropy loss (DeltaS(trsl)) on binding of benzene to a cavity in a mutant T4-lysozyme. Our results agree with previously published estimates of the binding of benzene to this mutant T4-lysozyme. These and other considerations suggest that the cell model is a simple yet efficient theoretical framework to evaluate the translational entropy loss on molecular association in solution.     

Effect of lignocellulosic filler type and content on the behavior of polycaprolactone based eco-composites for packaging applications

This study was based on the influence of lignocellulosic fillers and content on the morphology, crystallization behavior and thermal, mechanical and barrier properties of fully biodegradable eco-composites based on polycaprolactone for packaging applications. The biodegradation in soil as a function of time was also analyzed. Composites with 5 and 15 wt% of cotton (CO); cellulose (CE) and hydrolyzed-cellulose (HCE) were prepared by melt-mixing. It was determined that, whereas lower content of CO and CE produced a decrease on the crystallinity of the matrix, HCE did not affect it. Increasing the filler content, the crystallinity degree of the matrix decreased at less extent, which was independent on the filler type. A clear reduction on the theoretical melting point, attributed to heterogeneous nucleation sites, took place for the lower content of CO and CE. Induction and half-crystallization times diminished when fillers were incorporated but the effect was less notorious at higher filler contents. All fillers enhanced the Young's modulus of the matrix but the optimal mechanical properties were not obtained with HCE, as was expected, but with CE. After analyzing the main parameters that affect the mechanical properties of the composite; such as morphology, hydrophilicity, crystallinity, mechanical properties and thermal stability of the fillers themselves, interface interaction, filler dispersion and thermal aspects of the composites, we concluded that the parameters responsible for such behavior were the larger aspect ratio, better dispersion and enhanced interface interaction of the CE filler. These parameters also affected the barrier properties and the process of biodegradation in soil of the composites.     

Calculating pH-dependent free energy of proteins by using Monte Carlo protonation probabilities of ionizable residues

Protein folding, stability, and function are usually influenced by pH. And free energy plays a fundamental role in analysis of such pH-dependent properties. Electrostatics-based theoretical framework using dielectric solvent continuum model and solving Poisson-Boltzmann equation numerically has been shown to be very successful in understanding the pH-dependent properties. However, in this approach the exact computation of pH-dependent free energy becomes impractical for proteins possessing more than several tens of ionizable sites (e.g.>30), because exact evaluation of the partition function requires a summation over a vast number of possible protonation microstates. Here we present a method which computes the free energy using the average energy and the protonation probabilities of ionizable sites obtained by the well-established Monte Carlo sampling procedure. The key feature is to calculate the entropy by using the protonation probabilities. We used this method to examine a well-studied protein (lysozyme) and produced results which agree very well with the exact calculations. Applications to the optimum pH of maximal stability of proteins and protein–DNA interactions have also resulted in good agreement with experimental data. These examples recommend our method for application to the elucidation of the pH-dependent properties of proteins.