Biological cells embedded in fibrous matrices have been observed to form intercellular bands of dense and aligned fibers through which they mechanically interact over long distances. Such matrix-mediated cellular interactions have been shown to regulate various biological processes. This study aimed to explore the effects of elastic nonlinearity of the fibers contained in the extracellular matrix (ECM) on the transmission of mechanical loads between contracting cells. Based on our biological experiments, we developed a finite-element model of two contracting cells embedded within a fibrous network. The individual fibers were modeled as showing linear elasticity, compression microbuckling, tension stiffening, or both of the latter two. Fiber compression buckling resulted in smaller loads in the ECM, which were primarily directed toward the neighboring cell. These loads decreased with increasing cell-to-cell distance; when cells were >9 cell diameters apart, no such intercellular interaction was observed. Tension stiffening further contributed to directing the loads toward the neighboring cell, though to a smaller extent. The contraction of two neighboring cells resulted in mutual attraction forces, which were considerably increased by tension stiffening and decayed with increasing cell-to-cell distances. Nonlinear elasticity contributed also to the onset of force polarity on the cell boundaries, manifested by larger contractile forces pointing toward the neighboring cell. The density and alignment of the fibers within the intercellular band were greater when fibers buckled under compression, with tension stiffening further contributing to this structural remodeling. Although previous studies have established the role of the ECM nonlinear mechanical behavior in increasing the range of force transmission, our model demonstrates the contribution of nonlinear elasticity of biological gels to directional and efficient mechanical signal transfer between distant cells, and rehighlights the importance of using fibrous gels in experimental settings for facilitating intercellular communication. VIDEO ABSTRACT.

Restricted motions in proteins (e.g., N–H bonds dynamics) are studied effectively with NMR. By analogy with restricted motions in liquid crystals (LC), the local ordering has in the past been primarily represented by potentials comprising the L = 2, |K| = 0, 2 spherical harmonics. However, probes dissolved in LC’s experience non-polar ordering, often referred to as alignment, while protein-anchored probes experience polar ordering, often referred to as orientation. In this study we investigate the role of local (site) symmetry in the context of the polarity of the local ordering. We find that potentials comprising the L = 1, |K| = 0, 1 spherical harmonics represent adequately polar ordering. It is useful to characterize potential symmetry in terms of the irreducible representations of D2h point group, which is already implicit in the definition of the rotational diffusion tensor. Thus, the relevant rhombic L = 1 potentials have B1u and B3u symmetry whereas the relevant rhombic L = 2 potentials have Ag symmetry. A comprehensive scheme where local potentials and corresponding probability density functions (PDFs) are represented in Cartesian and spherical coordinates clarifies how they are affected by polar and non-polar ordering. The Cartesian coordinates are chosen so that the principal axis of polar axial PDF is pointing along the z-axis, whereas the principal axis of the non-polar axial PDF is pointing along ±z. Two-term axial potentials with 1 ≤ L ≤ 3 exhibit substantial diversity; they are expected to be useful in NMR-relaxation-data-fitting. It is shown how potential coefficients are reflected in the experimental order parameters. The comprehensive scheme representing local potentials and PDFs is exemplified for the L = 2 case using experimental data from 15N-labeled plexin-B1 and thioredoxin, 2H-, and 13C-labeled benzenehexa-n-alkanoates, and nitroxide-labeled T4 lysozyme. Future prospects for improved ordering analysis based on combined atomistic and mesoscopic approaches are delineated.

Force chains (FCs) are a key determinant of the micromechanical properties and behaviour of heterogeneous materials, such as granular systems. However, less is known about FCs in fibrous materials, such as the networks composing the extracellular matrix (ECM) of biological systems. Using a finite-element computational model, we simulated the contraction of a single cell and two nearby cells embedded in two-dimensional fibrous elastic networks and analysed the tensile FCs that developed in the ECM. The role of ECM nonlinear elasticity on FC formation was evaluated by considering linear and nonlinear, i.e. exhibiting ‘buckling’ and/or ‘strain-stiffening’, stress–strain curves. The effect of the degree of cell contraction and network coordination value was assessed. We found that nonlinear elasticity of the ECM fibres influenced the structure of the FCs, facilitating the transition towards more distinct chains that were less branched and more radially oriented than the chains formed in linear elastic networks. When two neighbouring cells contract, a larger number of FCs bridged between the cells in nonlinear networks, and these chains had a larger effective rigidity than the chains that did not reach a neighbouring cell. These results suggest that FCs function as a route for mechanical communication between distant cells and highlight the contribution of ECM fibre nonlinear elasticity to the formation of FCs.

We report on progress toward improving NMR relaxation analysis in proteins in terms of the slowly relaxing local structure (SRLS) approach by developing a method that combines SRLS with molecular dynamics (MD) simulations. 15 N−H bonds from the Rho GTPase binding domain of plexin-B1 are used as test case. We focus on the locally restricting/ordering potential of mean force (POMF), u(θ,φ), at the N−H site (θ and φ specify the orientation of the N−H bond in the protein). In SRLS, u(θ,φ) is expanded in the basis set of the real linear combinations of the Wigner rotation matrix elements with M = 0, D L,|K| (θ,φ). Because of limited data sensitivity, only the lowest (L = 2) terms are preserved; this potential function is denoted by u (SRLS) . In MD, the force-fieldparametrized POMF is the potential, u (MD) , defined in terms of the probability distribution, P eq (MD) ∝ exp(−u (MD) ). P eq (MD), and subsequently u (MD) , can be derived from the MD trajectory as histograms. One might contemplate utilizing u (MD) instead of u (SRLS) ; however, histograms cannot be used in SRLS analyses. Here, we approximate u(θ,φ) in terms of linear combinations of the D L,|K| functions with L = 1−4 and appropriate symmetry, denoted by u (DLK) , and optimize the latter (via P eq ) against u (MD) . This yields for every N−H bond an analytical ordering potential, u (DLK-BEST) , which exceeds u (SRLS) considerably in accuracy. u (DLK-BEST) can be used fixed in SRLS data fitting, thereby enabling the determination of additional parameters. This yields a substantially improved picture of structural dynamics, which is a significant benefit. The primary achievement of this work is to have employed for the first time MD data to derive a suitable (in terms of composition and symmetry) approximation to the SRLS POMF.

Motor proteins such as myosin and kinesin are responsible for actively directed movement in vivo. The physicochemical mechanism underlying their function is still obscure. A novel and unifying model concerning the motors driving mechanism is suggested here. This model resides within the framework of the well-studied "swinging lever-arm" hypothesis, stating that cis/trans peptide bond isomerization (CTI) is a key stage in the chemo-mechanical coupling within actomyosin--the complex of the motor (myosin) and its specific track (actin). CTI is suggested to propel myosin's lever-arm swing. The model addresses on the submolecular level a broad spectrum of actomyosin's functional characteristics, such as kinetics, energetics, force exertion, stepping, and directionality. The model may be tested first with relative ease in kinesin--a smaller motor that could be specifically modified with unnatural amino acids using bacterial expression. Suggested modifications may be used for labeling and functional decoupling.