A 3-D model of ligand transport in a deforming extracellular space

Cells communicate through shed or secreted ligands that traffic through the interstitium. Force-induced changes in interstitial geometry can initiate mechanotransduction responses through changes in local ligand concentrations. To gain insight into the temporal and spatial evolution of such mechanotransduction responses, we developed a 3-D computational model that couples geometric changes observed in the lateral intercellular space (LIS) of mechanically loaded airway epithelial cells to the diffusion-convection equations that govern ligand transport. By solving the 3-D fluid field under changing boundary geometries, and then coupling the fluid velocities to the ligand transport equations, we calculated the temporal changes in the 3-D ligand concentration field. Our results illustrate the steady-state heterogeneities in ligand distribution that arise from local variations in interstitial geometry, and demonstrate that highly localized changes in ligand concentration can be induced by mechanical loading, depending on both local deformations and ligand convection effects. The occurrence of inhomogeneities at steady state and in response to mechanical loading suggest that local variations in ligand concentration may have important effects on cell-to-cell variations in basal signaling state and localized mechanotransduction responses.     

Effect of endplate calcification and mechanical deformation on the distribution of glucose in intervertebral disc: a 3D finite element study

The intervertebral disc (IVD) is avascular, receiving nutrition from surrounding vasculature. Theoretical modelling can supplement experimental results to understand nutrition to IVD more clearly. A new, 3D finite element model of the IVD was developed to investigate effects of endplate calcification and mechanical deformation on glucose distributions in IVD. The model included anatomical disc geometry, non-linear coupling of cellular metabolism with pH and oxygen concentration and strain-dependent properties of the extracellular matrix. Calcification was simulated by reducing endplate permeability (～79%). Mechanical loading was applied based on in vivo disc deformation during the transition from supine to standing positions. Three static strain conditions were considered: supine, standing and weight-bearing standing. Minimum glucose concentrations decreased 45% with endplate calcification, whereas disc deformation led to a 4.8-63% decrease, depending on the endplate condition (i.e. normal vs. calcified). Furthermore, calcification more strongly affected glucose concentrations in the nucleus compared to the annulus fibrous region. This study provides important insight into nutrient distributions in IVD under mechanical deformation.     

A three-dimensional random network model of the cytoskeleton and its role in mechanotransduction and nucleus deformation

We have developed a three-dimensional random network model of the intracellular actin cytoskeleton and have used it to study the role of the cytoskeleton in mechanotransduction and nucleus deformation. We use the model to predict the deformation of the nucleus when mechanical stresses applied on the plasma membrane are propagated through the random cytoskeletal network to the nucleus membrane. We found that our results agree with previous experiments utilizing micropipette pulling. Therefore, we propose that stress propagation through the random cytoskeletal network can be a mechanism to effect nucleus deformation, without invoking any biochemical signaling activity. Using our model, we also predict how nucleus strain and its relative displacement within the cytosol vary with varying concentrations of actin filaments and actin-binding proteins. We find that nucleus strain varies in a sigmoidal manner with actin filament concentration, while there exists an optimal concentration of actin-binding proteins that maximize nucleus displacement. We provide a theoretical analysis for these nonlinearities in terms of the connectivity of the random cytoskeletal network. Finally, we discuss laser ablation experiments that can be performed to validate these results in order to advance our understanding of the role of the cytoskeleton in mechanotransduction.     

Elastic network normal mode dynamics reveal the GPCR activation mechanism

G‐protein‐coupled receptors (GPCR) are a family of membrane‐embedded metabotropic receptors which translate extracellular ligand binding into an intracellular response. Here, we calculate the motion of several GPCR family members such as the M2 and M3 muscarinic acetylcholine receptors, the A_2A adenosine receptor, the β₂‐adrenergic receptor, and the CXCR4 chemokine receptor using elastic network normal modes. The normal modes reveal a dilation and a contraction of the GPCR vestibule associated with ligand passage, and activation, respectively. Contraction of the vestibule on the extracellular side is correlated with cavity formation of the G‐protein binding pocket on the intracellular side, which initiates intracellular signaling. Interestingly, the normal modes of rhodopsin do not correlate well with the motion of other GPCR family members. Electrostatic potential calculation of the GPCRs reveal a negatively charged field around the ligand binding site acting as a siphon to draw‐in positively charged ligands on the membrane surface. Altogether, these results expose the GPCR activation mechanism and show how conformational changes on the cell surface side of the receptor are allosterically translated into structural changes on the inside. Proteins 2014; 82:579–586. © 2013 Wiley Periodicals, Inc.     

Synthetic matrices reveal contributions of ECM biophysical and biochemical properties to epithelial morphogenesis

Epithelial cells cultured within collagen and laminin gels proliferate to form hollow and polarized spherical structures, recapitulating the formation of a rudimentary epithelial organ. However, the contributions of extracellular matrix (ECM) biochemical and biophysical properties to morphogenesis are poorly understood because of uncontrolled presentation of multiple adhesive ligands, limited control over mechanical properties, and lot-to-lot compositional variability in these natural ECMs. We engineered synthetic ECM-mimetic hydrogels with independent control over adhesive ligand density, mechanical properties, and proteolytic degradation to study the impact of ECM properties on epithelial morphogenesis. Normal cyst growth, polarization, and lumen formation were restricted to a narrow range of ECM elasticity, whereas abnormal morphogenesis was observed at lower and higher elastic moduli. Adhesive ligand density dramatically regulated apicobasal polarity and lumenogenesis independently of cell proliferation. Finally, a threshold level of ECM protease degradability was required for apicobasal polarity and lumen formation. This synthetic ECM technology provides new insights into how cells transduce ECM properties into complex morphogenetic behaviors.     

Metalloprotease disintegrin-mediated ectodomain shedding of EGFR ligands promotes intestinal epithelial restitution

EGF receptor (EGFR) promotes intestinal epithelial restitution, an important early process in the reepithelialization of ulcers. During epithelial restitution, the mechanism of EGFR activation is not known. We evaluated the role of TNF-converting enzyme (TACE), a metalloprotease disintegrin that proteolytically processes plasma membrane-anchored EGFR ligand precursors into their mature active forms, in wound-induced EGFR activation and epithelial restitution. With the use of scrape-wounded rat intestinal epithelial-1 (RIE-1) cell monolayers to model epithelial ulceration and restitution, we observed the rapid wound-dependent release of EGFR ligands into culture medium. RIE-1 cells express TACE, and treatment with phorbol ester, an established TACE stimulus, triggered the extracellular release of an EGFR ligand, transforming growth factor-alpha. Blockade of TACE using TNF processing inhibitor (TAPI-1), a specific hydroxamate inhibitor of metalloprotease disintegrins, prevented release of EGFR ligands from wounded RIE-1 cell monolayers. The restitution of wounded RIE-1 cell monolayers was also dose-dependently inhibited by TAPI-1, establishing the role of metalloprotease disintegrins in this process. These results have established a mechanism of EGFR activation in wounded intestinal epithelium and show an important functional role for metalloprotease disintegrin-mediated ectodomain shedding during intestinal epithelial restitution. Therefore, activation of the TACE-EGFR system might promote the healing of intestinal tract ulcers in patients.     

Finite element analysis of the effects of focal adhesion mechanical properties and substrate stiffness on cell migration

The attachment of cells to the extracellular matrix (ECM) is achieved by the specific binding of cell-surface receptors to ligands present in the ECM. These interactions are important for many biological processes, including cell migration, cancer development, and wound healing. Our objective was to develop a computational model to investigate how focal adhesion mechanical properties, substrate stiffness, and intracellular stresses affect cell-matrix interactions during cell migration on a flat substrate. In our model, the cell-substrate traction was proportional to the bound receptor concentration, relative velocity between the cell and substrate, and the cell-substrate friction coefficient. Simulation results showed that even if the receptor number and ligand density were fixed, the mechanical properties of the focal adhesions still affected cell-ECM interactions. In fact, the cell-substrate traction was biphasic with respect to the friction coefficient, a parameter that can be used to quantify focal adhesion properties. In contrast, the cell speed was a monotonically decreasing function with respect to this parameter. Furthermore, tractions showed greater increases when the maximum intracellular stress was increased from 400 to 600Pa than when substrate stiffness was increased from 0.5 to 100kPa. This mathematical model is able to quantify the effects of focal adhesion mechanical properties, extracellular stiffness, and intracellular stresses on cell-ECM interactions, and should be beneficial to research in cancer development.     

Biochemical and mechanical extracellular matrix properties dictate mammary epithelial cell motility and assembly

Biochemical and mechanical cues of the extracellular matrix have been shown to play important roles in cell-matrix and cell-cell interactions. We have experimentally tested the combined influence of these cues to better understand cell motility, force generation, cell-cell interaction, and assembly in an in vitro breast cancer model. MCF-10A non-tumorigenic mammary epithelial cells were observed on surfaces with varying fibronectin ligand concentration and polyacrylamide gel rigidity. Our data show that cell velocity is biphasic in both matrix rigidity and adhesiveness. The maximum cell migration velocity occurs only at specific combination of substrate stiffness and ligand density. We found cell-cell interactions reduce migration velocity. However, the traction forces cells exert onto the substrate increase linearly with both cues, with cells in pairs exerting higher maximum tractions observed over single cells. A relationship between force and motility shows a maximum in single cell velocity not observed in cell pairs. Cell-cell adhesion becomes strongly favored on softer gels with elasticity ≤ 1250 Pascals (Pa), implying the existence of a compliance threshold that promotes cell-cell over cell-matrix adhesion. Finally on gels with stiffness similar to pre-malignant breast tissue, 400 Pa, cells undergo multicellular assembly and division into 3D spherical aggregates on a 2D surface.     

A feasibility study into adenosine triphosphate measurement in exhaled breath condensate: a potential bedside method to monitor alveolar deformation

Recent research suggested an important role for pulmonary extracellular adenosine triphosphate (ATP) in the development of ventilation-induced lung injury. This injury is induced by mechanical deformation of alveolar epithelial cells, which in turn release ATP to the extracellular space. Measuring extracellular ATP in exhaled breath condensate (EBC) may be a non-invasive biomarker for alveolar deformation. Here, we study the feasibility of bedside ATP measurement in EBC. We measured ATP levels in EBC in ten subjects before and after an exercise test, which increases respiratory parameters and alveolar deformation. EBC lactate concentrations were measured as a dilution marker. We found a significant increase in ATP levels in EBC (before 73 RLU [IQR 50–209] versus after 112 RLU [IQR 86–203]; p value 0.047), and the EBC ATP-to-EBC lactate ratio increased as well (p value 0.037). We present evidence that bedside measurement of ATP in EBC is feasible and that ATP levels in EBC increase after exercise. Future research should measure ATP levels in EBC during mechanical ventilation as a potential biomarker for alveolar deformation.     

A Fast Flexible Docking Method using an Incremental Construction Algorithm

We present an automatic method for docking organic ligands into protein binding sites. The method can be used in the design process of specific protein ligands. It combines an appropriate model of the physico-chemical properties of the docked molecules with efficient methods for sampling the conformational space of the ligand. If the ligand is flexible, it can adopt a large variety of different conformations. Each such minimum in conformational space presents a potential candidate for the conformation of the ligand in the complexed state. Our docking method samples the conformation space of the ligand on the basis of a discrete model and uses a tree-search technique for placing the ligand incrementally into the active site. For placing the first fragment of the ligand into the protein, we use hashing techniques adapted from computer vision. The incremental construction algorithm is based on a greedy strategy combined with efficient methods for overlap detection and for the search of new interactions. We present results on 19 complexes of which the binding geometry has been crystallographically determined. All considered ligands are docked in at most three minutes on a current workstation. The experimentally observed binding mode of the ligand is reproduced with 0.5 to 1.2 Å rms deviation. It is almost always found among the highest-ranking conformations computed.     

A response calculus for immobilized T cell receptor ligands

To address the molecular mechanism of T cell receptor (TCR) signaling, we have formulated a model for T cell activation, termed the 2D-affinity model, in which the density of TCR on the T cell surface, the density of ligand on the presenting surface, and their corresponding two-dimensional affinity determine the level of T cell activation. When fitted to T cell responses against purified ligands immobilized on plastic surfaces, the 2D-affinity model adequately simulated changes in cellular activation as a result of varying ligand affinity and ligand density. These observations further demonstrated the importance of receptor cross-linking density in determining TCR signaling. Moreover, it was found that the functional two-dimensional affinity of TCR ligands was affected by the chemical composition of the ligand-presenting surface. This makes it possible that cell-bound TCR ligands, despite their low affinity in solution, are of optimal two-dimensional affinity thereby allowing effective TCR binding under physiological conditions, i.e. at low ligand densities in cellular interfaces.     

Regulation of CFTR chloride channel macroscopic conductance by extracellular bicarbonate

The CFTR contributes to Cl? and HCO?? transport across epithelial cell apical membranes. The extracellular face of CFTR is exposed to varying concentrations of Cl? and HCO?? in epithelial tissues, and there is evidence that CFTR is sensitive to changes in extracellular anion concentrations. Here we present functional evidence that extracellular Cl? and HCO?? regulate anion conduction in open CFTR channels. Using cell-attached and inside-out patch-clamp recordings from constitutively active mutant E1371Q-CFTR channels, we show that voltage-dependent inhibition of CFTR currents in intact cells is significantly stronger when the extracellular solution contains HCO?? than when it contains Cl?. This difference appears to reflect differences in the ability of extracellular HCO?? and Cl? to interact with and repel intracellular blocking anions from the pore. Strong block by endogenous cytosolic anions leading to reduced CFTR channel currents in intact cells occurs at physiologically relevant HCO?? concentrations and membrane potentials and can result in up to ～50% inhibition of current amplitude. We propose that channel block by cytosolic anions is a previously unrecognized, physiologically relevant mechanism of channel regulation that confers on CFTR channels sensitivity to different anions in the extracellular fluid. We further suggest that this anion sensitivity represents a feedback mechanism by which CFTR-dependent anion secretion could be regulated by the composition of the secretions themselves. Implications for the mechanism and regulation of CFTR-dependent secretion in epithelial tissues are discussed.     

Study of protein structural deformations under external mechanical perturbations by a coarse-grained simulation method

The mechanical properties of biomolecules play pivotal roles in regulating cellular functions. For instance, extracellular mechanical stimuli are converted to intracellular biochemical activities by membrane receptors and their downstream adaptor proteins during mechanotransduction. In general, proteins favor the conformation with the lowest free energy. External forces modify the energy landscape of proteins and drive them to unfolded or deformed conformations that are of functional relevance. Therefore, the study of the physical properties of proteins under external forces is of fundamental importance to understand their functions in cellular mechanics. Here, a coarse-grained computational model was developed to simulate the unfolding or deformation of proteins under mechanical perturbation. By applying this method to unfolding of previously studied proteins or protein fragments with external forces, we demonstrated that our results are quantitatively comparable to previous experimental or all-atom computational studies. The model was further extended to the problem of elastic deformation of large protein complexes formed between membrane receptors and their ligands. Our studies of binding between T cell receptor (TCR) and major histocompatibility complex (MHC) illustrated that stretching of MHC ligand initially lowers its binding energy with TCR, supporting the recent experimental report that TCR/MHC complex is formed through the catch-bond mechanism. Finally, the method was, for the first time, applied to pulling of an eight-cadherin cluster that was formed by their trans and cis binding interfaces. Our simulation results show that mechanical properties of adherens junctions are functionally important to cell adhesion.     

Effect of membrane potential on the mechanical equilibrium of biological membranes

The mechanical equilibrium of a membranous sac, whose wall is sandwiched by two oppositely charged fluid layers, is investigated as a mathematical model of a living cell. In so doing, it is assumed that the space charge density in the inner and the outer charged fluid layer is constant. It is also assumed that the fluid inside and outside of the charged fluid layer is a perfect conductor. By solving Maxwell's equation, the electric field and the thickness of the inner and the outer charged fluid layer is determined as a function of the geometry of the sac. Then, the fluid pressure in the charged fluid layer is derived by considering the body force created by the electrostatic field. The condition of mechanical equilibrium of the sac membrane yields an equation which reveals the inter-relation between the geometry, the sac fluid pressure and the membrane potential. According to this equation, the change of membrane potential causes a deformation of the sac. If the wall of the membranous sac is permeable, increase (decrease) of the absolute value of the membrane potential results in swelling (shrinking) of the sac. On the other hand, the mechanical change of the sac volume results in the change of the membrane potential. This analysis provides also an explanation of how the red blood cell maintains the biconcave shape, when the red blood cell is assumed to be a fluid filled membranous sac with non-zero membrane potential.     

Transmission of Mechanical Information by Purinergic Signaling

The skeleton constantly interacts and adapts to the physical world. We have previously reported that physiologically relevant mechanical forces lead to small repairable membrane injuries in bone-forming osteoblasts, resulting in release of ATP and stimulation of purinergic (P2) calcium responses in neighboring cells. The goal of this study was to develop a theoretical model describing injury-related ATP and ADP release, their extracellular diffusion and degradation, and purinergic responses in neighboring cells. After validation using experimental data for intracellular free calcium elevations, ATP, and vesicular release after mechanical stimulation of a single osteoblast, the model was scaled to a tissue-level injury to investigate how purinergic signaling communicates information about injuries with varying geometries. We found that total ATP released, peak extracellular ATP concentration, and the ADP-mediated signaling component contributed complementary information regarding the mechanical stimulation event. The total amount of ATP released governed spatial factors, such as the maximal distance from the injury at which purinergic responses were stimulated. The peak ATP concentration reflected the severity of an individual cell injury, allowing to discriminate between minor and severe injuries that released similar amounts of ATP because of differences in injury repair, and determined temporal aspects of the response, such as signal propagation velocity. ADP-mediated signaling became relevant only in larger tissue-level injuries, conveying information about the distance to the injury site and its geometry. Thus, we identified specific features of extracellular ATP and ADP spatiotemporal signals that depend on tissue mechanoresilience and encode the severity, scope, and proximity of the mechanical stimulus.     

How are hydrogen bonds modified by metal binding?

We have used density functional theory calculations to investigate how the hydrogen-bond strength is modified when a ligand is bound to a metal using over 60 model systems involving six metals and eight ligands frequently encountered in metalloproteins. We study how the hydrogen-bond geometry and energy vary with the nature of metal, the oxidation state, the coordination number, the ligand involved in the hydrogen bond, other first-sphere ligands, and different hydrogen-bond probe molecules. The results show that, in general, the hydrogen-bond strength is increased for neutral ligands and decreased for negatively charged ligands. The size of the effect is mainly determined by the net charge of the metal complex, and all effects are typically decreased when the model is solvated. In water solution, the hydrogen-bond strength can increase by up to 37 kJ/mol for neutral ligands, and that of negatively charged ligands can increase (for complexes with a negative net charge) or decrease (for positively charged complexes). If the net charge of the complex does not change, there is normally little difference between different metals or different types of complexes. The only exception is observed for sulphur-containing ligands (Met and Cys) and if the ligand is redox-active (e.g. high-valence Fe–O complexes).     

Ligand-assisted aggregation of proteins. Dimerization of serum amyloid P component by bivalent ligands

A comprehensive series of solution and crystallographic studies reveal how simple, achiral, bivalent ligands of the cyclic pyruvate of glycerol promote face-to-face complex formation of the pentraxin, serum amyloid P component (SAP) into decamers. SAP, a protein of the human innate immune system, is universally present in amyloids, including cerebral amyloid deposits found in the brain of Alzheimer disease patients. Removal of SAP through a specific aggregation mechanism mediated by multivalent ligands appears to provide therapeutic benefit in the progression of this disease. Crystallographic studies reveal that in our novel series of ligands only the methyl and carboxylate moieties of the pyruvate ketal directly interact with the protein, but the geometric constraints imposed by the tether dictate which of two chair conformations are adopted by the pyruvate dioxane ring. Solution studies, as interpreted through a simple thermodynamic model, account for the distribution of pentameric and decameric bound states at different ligand concentrations and indicate that differences in the flexibility of the tether determine the geometry and stability of the specific aggregates formed between SAP and two different bivalent ligands. The factors affecting the design of ligands promoting face-to-face protein dimerization as well as potential biological implications are discussed.