On the Significance of Microtubule Flexural Behavior in Cytoskeletal Mechanics

Quantitative description of cell mechanics has challenged biological scientists for the past two decades. Various structural models have been attempted to analyze the structure of the cytoskeleton. One important aspect that has been largely ignored in all these modeling approaches is related to the flexural and buckling behavior of microtubular filaments. The objective of this paper is to explore the influence of this flexural and buckling behavior in cytoskeletal mechanics

A hybrid solution approach for a multi-objective closed-loop logistics network under uncertainty

The design of closed-loop logistics (forward and reverse logistics) has attracted growing attention with the stringent pressures of customer expectations, environmental concerns and economic factors. This paper considers a multi-product, multi-period and multi-objective closed-loop logistics network model with regard to facility expansion as a facility location-allocation problem, which more closely approximates real-world conditions. A multiobjective mixed integer nonlinear programming formulation is linearized by defining new variables and adding new constraints to the model. By considering the aforementioned model under uncertainty, this paper develops a hybrid solution approach by combining an interactive fuzzy goal programming approach and robust counterpart optimization based on three well-known robust counterpart optimization formulations. Finally, this paper compares the results of the three formulations using different test scenarios and parameter-sensitive analysis in terms of the quality of the final solution, CPU time, the level of conservatism, the degree of closeness to the ideal solution, the degree of balance involved in developing a compromise solution, and satisfaction degree

Molecular Dynamics Models of Integrin Clustering and Activation Mechanisms

Integrins are Alpha-Beta transmembrane receptors that mediate cell-­matrix and cell-­cell adhesion, comprised of multi-­domain, massive ectodomains, single-­pass, transmembrane domains, and short, floppy cytoplasmic domains. They link the extracellular matrix or counter-­receptors on other cells with the contractile cytoskeleton, mediating the transduction of mechanochemical signals across the plasma membrane and playing critical roles in a host of cellular functions, such as migration, cell traction, motility, platelet aggregation, and leukocyte transmigration.Functionally, integrins are switch-­like proteins that can take on at least three different functional states: inactive, active, and ligand-bound. Integrin function is dependent upon allosteric conformational changes in its structure. Integrins are by default in an inactive (low affinity) state and can be activated via interacting with cytoplasmic proteins (e.g. talin) and/or engaging with extracellular ligands (e.g. fibrinogen). Integrin activation triggered by a cytoplasmic signal is called inside-­out signaling, while outside-­in signaling is defined as ligand-­integrin binding followed by conformational changes in the transmembrane and cytoplasmic domains. Association of the integrin with the ligand induces quaternary changes in the integrin, leading to cell signaling and dynamic cell adhesion. However, atomistic details of these conformational changes as well as mechanisms of integrin clustering are not fully understood.This study employs molecular dynamics techniques to provide detailed, mechanistic answers for a few key questions on integrin (Alpha)IIb(Beta)3 function, a ­platelet-specific integrin member that plays a critical role in thrombosis. It is highly debated whether integrin transmembrane domains form homo-­oligomers, leading to focal adhesion growth. This study suggests that homo-­ oligomerization of the Beta subunit potentially regulates integrin clustering, as opposed to the Alpha subunit, which appears to be a poor regulator for the clustering process. Two distinct hypotheses are proposed to explain the atomic mechanism of integrin activation and how conformational changes triggered by cytoplasmic/extracellular proteins are propagated across the integrin structure: The switch-blade and the deadbolt model. To reconcile these apparently-contradictory models for integrin activation, this work investigated the mechanism of integrin (Alpha)IIb(Beta)3 inside-­out activation triggered by interactions with the cytoplasmic protein talin, and its outside-­in activation as a result of exposure to the soluble RGD ligand. Finally, it was shown that the integrin Alpha subunit head domain regulates integrin-­ligand binding affinity indirectly via inducing conformational changes in a key metal ion binding site (named LIMBS) in the Beta subunit head domain. Hence, it was concluded that different ligand binding affinities of integrin (Alpha)IIb(Beta)3 and (Alpha)V(Beta)3 is attributed to the larger attraction between the (Alpha)V subunit head domain and the metal ion binding site LIMBS

Localized lipid packing of transmembrane domains impedes integrin clustering.

Integrin clustering plays a pivotal role in a host of cell functions. Hetero-dimeric integrin adhesion receptors regulate cell migration, survival, and differentiation by communicating signals bidirectionally across the plasma membrane. Thus far, crystallographic structures of integrin components are solved only separately, and for some integrin types. Also, the sequence of interactions that leads to signal transduction remains ambiguous. Particularly, it remains controversial whether the homo-dimerization of integrin transmembrane domains occurs following the integrin activation (i.e. when integrin ectodomain is stretched out) or if it regulates integrin clustering. This study employs molecular dynamics modeling approaches to address these questions in molecular details and sheds light on the crucial effect of the plasma membrane. Conducting a normal mode analysis of the intact αllbβ3 integrin, it is demonstrated that the ectodomain and transmembrane-cytoplasmic domains are connected via a membrane-proximal hinge region, thus merely transmembrane-cytoplasmic domains are modeled. By measuring the free energy change and force required to form integrin homo-oligomers, this study suggests that the β-subunit homo-oligomerization potentially regulates integrin clustering, as opposed to α-subunit, which appears to be a poor regulator for the clustering process. If α-subunits are to regulate the clustering they should overcome a high-energy barrier formed by a stable lipid pack around them. Finally, an outside-in activation-clustering scenario is speculated, explaining how further loading the already-active integrin affects its homo-oligomerization so that focal adhesions grow in size

On the significance of microtubule flexural behavior in cytoskeletal mechanics.

Quantitative description of cell mechanics has challenged biological scientists for the past two decades. Various structural models have been attempted to analyze the structure of the cytoskeleton. One important aspect that has been largely ignored in all these modeling approaches is related to the flexural and buckling behavior of microtubular filaments. The objective of this paper is to explore the influence of this flexural and buckling behavior in cytoskeletal mechanics.In vitro the microtubules are observed to buckle in the first mode, reminiscent of a free, simply-supported beam. In vivo images of microtubules, however, indicate that the buckling mostly occurs in higher modes. This buckling mode switch takes place mostly because of the lateral support of microtubules via their connections to actin and intermediate filaments. These lateral loads are exerted throughout the microtubule length and yield a considerable bending behavior that, unless properly accounted for, would produce erroneous results in the modeling and analysis of the cytoskeletal mechanics.One of the promising attempts towards mechanical modeling of the cytoskeleton is the tensegrity model, which simplifies the complex network of cytoskeletal filaments into a combination merely of tension-bearing actin filaments and compression-bearing microtubules. Interestingly, this discrete model can qualitatively explain many experimental observations in cell mechanics. However, evidence suggests that the simplicity of this model may undermine the accuracy of its predictions, given the model's underlying assumption that "every single member bears solely either tensile or compressive behavior," i.e. neglecting the flexural behavior of the microtubule filaments. We invoke an anisotropic continuum model for microtubules and compare the bending energy stored in a single microtubule with its axial strain energy at the verge of buckling. Our results suggest that the bending energy can exceed the axial energy of microtubules by 40 folds. A modification to tensegrity model is, therefore, proved necessary in order to take into account the flexural response of microtubules. The concept of "bendo-tensegrity" is proposed as a modification to contemporary cytoskeletal tensegrity models